{"nl": {"description": "Have you ever played Hanabi? If not, then you've got to try it out! This problem deals with a simplified version of the game.Overall, the game has 25 types of cards (5 distinct colors and 5 distinct values). Borya is holding n cards. The game is somewhat complicated by the fact that everybody sees Borya's cards except for Borya himself. Borya knows which cards he has but he knows nothing about the order they lie in. Note that Borya can have multiple identical cards (and for each of the 25 types of cards he knows exactly how many cards of this type he has).The aim of the other players is to achieve the state when Borya knows the color and number value of each of his cards. For that, other players can give him hints. The hints can be of two types: color hints and value hints. A color hint goes like that: a player names some color and points at all the cards of this color. Similarly goes the value hint. A player names some value and points at all the cards that contain the value.Determine what minimum number of hints the other players should make for Borya to be certain about each card's color and value.", "input_spec": "The first line contains integer n (1 ≤ n ≤ 100) — the number of Borya's cards. The next line contains the descriptions of n cards. The description of each card consists of exactly two characters. The first character shows the color (overall this position can contain five distinct letters — R, G, B, Y, W). The second character shows the card's value (a digit from 1 to 5). Borya doesn't know exact order of the cards they lie in.", "output_spec": "Print a single integer — the minimum number of hints that the other players should make.", "sample_inputs": ["2\nG3 G3", "4\nG4 R4 R3 B3", "5\nB1 Y1 W1 G1 R1"], "sample_outputs": ["0", "2", "4"], "notes": "NoteIn the first sample Borya already knows for each card that it is a green three.In the second sample we can show all fours and all red cards.In the third sample you need to make hints about any four colors."}, "src_uid": "3b12863997b377b47bae43566ec1a63b"}
{"nl": {"description": "As you know, Vova has recently become a new shaman in the city of Ultima Thule. So, he has received the shaman knowledge about the correct bracket sequences. The shamans of Ultima Thule have been using lots of different types of brackets since prehistoric times. A bracket type is a positive integer. The shamans define a correct bracket sequence as follows:  An empty sequence is a correct bracket sequence.  If {a1, a2, ..., al} and {b1, b2, ..., bk} are correct bracket sequences, then sequence {a1, a2, ..., al, b1, b2, ..., bk} (their concatenation) also is a correct bracket sequence.  If {a1, a2, ..., al} — is a correct bracket sequence, then sequence  also is a correct bracket sequence, where v (v > 0) is an integer. For example, sequences {1, 1,  - 1, 2,  - 2,  - 1} and {3,  - 3} are correct bracket sequences, and {2,  - 3} is not.Moreover, after Vova became a shaman, he learned the most important correct bracket sequence {x1, x2, ..., xn}, consisting of n integers. As sequence x is the most important, Vova decided to encrypt it just in case.Encrypting consists of two sequences. The first sequence {p1, p2, ..., pn} contains types of brackets, that is, pi = |xi| (1 ≤ i ≤ n). The second sequence {q1, q2, ..., qt} contains t integers — some positions (possibly, not all of them), which had negative numbers in sequence {x1, x2, ..., xn}.Unfortunately, Vova forgot the main sequence. But he was lucky enough to keep the encryption: sequences {p1, p2, ..., pn} and {q1, q2, ..., qt}. Help Vova restore sequence x by the encryption. If there are multiple sequences that correspond to the encryption, restore any of them. If there are no such sequences, you should tell so.", "input_spec": "The first line of the input contains integer n (1 ≤ n ≤ 106). The second line contains n integers: p1, p2, ..., pn (1 ≤ pi ≤ 109). The third line contains integer t (0 ≤ t ≤ n), followed by t distinct integers q1, q2, ..., qt (1 ≤ qi ≤ n). The numbers in each line are separated by spaces.", "output_spec": "Print a single string \"NO\" (without the quotes) if Vova is mistaken and a suitable sequence {x1, x2, ..., xn} doesn't exist. Otherwise, in the first line print \"YES\" (without the quotes) and in the second line print n integers x1, x2, ..., xn (|xi| = pi; xqj < 0). If there are multiple sequences that correspond to the encrypting, you are allowed to print any of them.", "sample_inputs": ["2\n1 1\n0", "4\n1 1 1 1\n1 3", "3\n1 1 1\n0", "4\n1 2 2 1\n2 3 4"], "sample_outputs": ["YES\n1 -1", "YES\n1 1 -1 -1", "NO", "YES\n1 2 -2 -1"], "notes": null}, "src_uid": "be82b8f209217875221ebe5de8675971"}
{"nl": {"description": "Petya loves lucky numbers. Everybody knows that lucky numbers are positive integers whose decimal representation contains only the lucky digits 4 and 7. For example, numbers 47, 744, 4 are lucky and 5, 17, 467 are not.One day Petya was delivered a string s, containing only digits. He needs to find a string that represents a lucky number without leading zeroes, is not empty, is contained in s as a substring the maximum number of times.Among all the strings for which the three conditions given above are fulfilled, Petya only needs the lexicographically minimum one. Find this string for Petya.", "input_spec": "The single line contains a non-empty string s whose length can range from 1 to 50, inclusive. The string only contains digits. The string can contain leading zeroes.", "output_spec": "In the only line print the answer to Petya's problem. If the sought string does not exist, print \"-1\" (without quotes).", "sample_inputs": ["047", "16", "472747"], "sample_outputs": ["4", "-1", "7"], "notes": "NoteThe lexicographical comparison of strings is performed by the < operator in the modern programming languages. String x is lexicographically less than string y either if x is a prefix of y, or exists such i (1 ≤ i ≤ min(|x|, |y|)), that xi < yi and for any j (1 ≤ j < i) xj = yj. Here |a| denotes the length of string a.In the first sample three conditions are fulfilled for strings \"4\", \"7\" and \"47\". The lexicographically minimum one is \"4\".In the second sample s has no substrings which are lucky numbers.In the third sample the three conditions are only fulfilled for string \"7\"."}, "src_uid": "639b8b8d0dc42df46b139f0aeb3a7a0a"}
{"nl": {"description": "Let's consider a table consisting of n rows and n columns. The cell located at the intersection of i-th row and j-th column contains number i × j. The rows and columns are numbered starting from 1.You are given a positive integer x. Your task is to count the number of cells in a table that contain number x.", "input_spec": "The single line contains numbers n and x (1 ≤ n ≤ 105, 1 ≤ x ≤ 109) — the size of the table and the number that we are looking for in the table.", "output_spec": "Print a single number: the number of times x occurs in the table.", "sample_inputs": ["10 5", "6 12", "5 13"], "sample_outputs": ["2", "4", "0"], "notes": "NoteA table for the second sample test is given below. The occurrences of number 12 are marked bold.   "}, "src_uid": "c4b139eadca94201596f1305b2f76496"}
{"nl": {"description": "The HR manager was disappointed again. The last applicant failed the interview the same way as 24 previous ones. \"Do I give such a hard task?\" — the HR manager thought. \"Just raise number 5 to the power of n and get last two digits of the number. Yes, of course, n can be rather big, and one cannot find the power using a calculator, but we need people who are able to think, not just follow the instructions.\"Could you pass the interview in the machine vision company in IT City?", "input_spec": "The only line of the input contains a single integer n (2 ≤ n ≤ 2·1018) — the power in which you need to raise number 5.", "output_spec": "Output the last two digits of 5n without spaces between them.", "sample_inputs": ["2"], "sample_outputs": ["25"], "notes": null}, "src_uid": "dcaff75492eafaf61d598779d6202c9d"}
{"nl": {"description": "Let's assume that we have a pair of numbers (a, b). We can get a new pair (a + b, b) or (a, a + b) from the given pair in a single step.Let the initial pair of numbers be (1,1). Your task is to find number k, that is, the least number of steps needed to transform (1,1) into the pair where at least one number equals n.", "input_spec": "The input contains the only integer n (1 ≤ n ≤ 106).", "output_spec": "Print the only integer k.", "sample_inputs": ["5", "1"], "sample_outputs": ["3", "0"], "notes": "NoteThe pair (1,1) can be transformed into a pair containing 5 in three moves: (1,1)  →  (1,2)  →  (3,2)  →  (5,2)."}, "src_uid": "75739f77378b21c331b46b1427226fa1"}
{"nl": {"description": "Petya loves lucky numbers. We all know that lucky numbers are the positive integers whose decimal representations contain only the lucky digits 4 and 7. For example, numbers 47, 744, 4 are lucky and 5, 17, 467 are not.Unfortunately, not all numbers are lucky. Petya calls a number nearly lucky if the number of lucky digits in it is a lucky number. He wonders whether number n is a nearly lucky number.", "input_spec": "The only line contains an integer n (1 ≤ n ≤ 1018). Please do not use the %lld specificator to read or write 64-bit numbers in С++. It is preferred to use the cin, cout streams or the %I64d specificator.", "output_spec": "Print on the single line \"YES\" if n is a nearly lucky number. Otherwise, print \"NO\" (without the quotes).", "sample_inputs": ["40047", "7747774", "1000000000000000000"], "sample_outputs": ["NO", "YES", "NO"], "notes": "NoteIn the first sample there are 3 lucky digits (first one and last two), so the answer is \"NO\".In the second sample there are 7 lucky digits, 7 is lucky number, so the answer is \"YES\".In the third sample there are no lucky digits, so the answer is \"NO\"."}, "src_uid": "33b73fd9e7f19894ea08e98b790d07f1"}
{"nl": {"description": "You have two integers $$$l$$$ and $$$r$$$. Find an integer $$$x$$$ which satisfies the conditions below:  $$$l \\le x \\le r$$$.  All digits of $$$x$$$ are different. If there are multiple answers, print any of them.", "input_spec": "The first line contains two integers $$$l$$$ and $$$r$$$ ($$$1 \\le l \\le r \\le 10^{5}$$$).", "output_spec": "If an answer exists, print any of them. Otherwise, print $$$-1$$$.", "sample_inputs": ["121 130", "98766 100000"], "sample_outputs": ["123", "-1"], "notes": "NoteIn the first example, $$$123$$$ is one of the possible answers. However, $$$121$$$ can't be the answer, because there are multiple $$$1$$$s on different digits.In the second example, there is no valid answer."}, "src_uid": "3041b1240e59341ad9ec9ac823e57dd7"}
{"nl": {"description": "Jzzhu has a big rectangular chocolate bar that consists of n × m unit squares. He wants to cut this bar exactly k times. Each cut must meet the following requirements:  each cut should be straight (horizontal or vertical);  each cut should go along edges of unit squares (it is prohibited to divide any unit chocolate square with cut);  each cut should go inside the whole chocolate bar, and all cuts must be distinct. The picture below shows a possible way to cut a 5 × 6 chocolate for 5 times.  Imagine Jzzhu have made k cuts and the big chocolate is splitted into several pieces. Consider the smallest (by area) piece of the chocolate, Jzzhu wants this piece to be as large as possible. What is the maximum possible area of smallest piece he can get with exactly k cuts? The area of a chocolate piece is the number of unit squares in it.", "input_spec": "A single line contains three integers n, m, k (1 ≤ n, m ≤ 109; 1 ≤ k ≤ 2·109).", "output_spec": "Output a single integer representing the answer. If it is impossible to cut the big chocolate k times, print -1.", "sample_inputs": ["3 4 1", "6 4 2", "2 3 4"], "sample_outputs": ["6", "8", "-1"], "notes": "NoteIn the first sample, Jzzhu can cut the chocolate following the picture below:  In the second sample the optimal division looks like this:  In the third sample, it's impossible to cut a 2 × 3 chocolate 4 times."}, "src_uid": "bb453bbe60769bcaea6a824c72120f73"}
{"nl": {"description": "n children are standing in a circle and playing a game. Children's numbers in clockwise order form a permutation a1, a2, ..., an of length n. It is an integer sequence such that each integer from 1 to n appears exactly once in it.The game consists of m steps. On each step the current leader with index i counts out ai people in clockwise order, starting from the next person. The last one to be pointed at by the leader becomes the new leader.You are given numbers l1, l2, ..., lm — indices of leaders in the beginning of each step. Child with number l1 is the first leader in the game. Write a program which will restore a possible permutation a1, a2, ..., an. If there are multiple solutions then print any of them. If there is no solution then print -1.", "input_spec": "The first line contains two integer numbers n, m (1 ≤ n, m ≤ 100). The second line contains m integer numbers l1, l2, ..., lm (1 ≤ li ≤ n) — indices of leaders in the beginning of each step.", "output_spec": "Print such permutation of n numbers a1, a2, ..., an that leaders in the game will be exactly l1, l2, ..., lm if all the rules are followed. If there are multiple solutions print any of them.  If there is no permutation which satisfies all described conditions print -1.", "sample_inputs": ["4 5\n2 3 1 4 4", "3 3\n3 1 2"], "sample_outputs": ["3 1 2 4", "-1"], "notes": "NoteLet's follow leadership in the first example:   Child 2 starts.  Leadership goes from 2 to 2 + a2 = 3.  Leadership goes from 3 to 3 + a3 = 5. As it's greater than 4, it's going in a circle to 1.  Leadership goes from 1 to 1 + a1 = 4.  Leadership goes from 4 to 4 + a4 = 8. Thus in circle it still remains at 4. "}, "src_uid": "4a7c959ca279d0a9bd9bbf0ce88cf72b"}
{"nl": {"description": "Kolya is very absent-minded. Today his math teacher asked him to solve a simple problem with the equation $$$a + 1 = b$$$ with positive integers $$$a$$$ and $$$b$$$, but Kolya forgot the numbers $$$a$$$ and $$$b$$$. He does, however, remember that the first (leftmost) digit of $$$a$$$ was $$$d_a$$$, and the first (leftmost) digit of $$$b$$$ was $$$d_b$$$.Can you reconstruct any equation $$$a + 1 = b$$$ that satisfies this property? It may be possible that Kolya misremembers the digits, and there is no suitable equation, in which case report so.", "input_spec": "The only line contains two space-separated digits $$$d_a$$$ and $$$d_b$$$ ($$$1 \\leq d_a, d_b \\leq 9$$$).", "output_spec": "If there is no equation $$$a + 1 = b$$$ with positive integers $$$a$$$ and $$$b$$$ such that the first digit of $$$a$$$ is $$$d_a$$$, and the first digit of $$$b$$$ is $$$d_b$$$, print a single number $$$-1$$$. Otherwise, print any suitable $$$a$$$ and $$$b$$$ that both are positive and do not exceed $$$10^9$$$. It is guaranteed that if a solution exists, there also exists a solution with both numbers not exceeding $$$10^9$$$.", "sample_inputs": ["1 2", "4 4", "5 7", "6 2"], "sample_outputs": ["199 200", "412 413", "-1", "-1"], "notes": null}, "src_uid": "3eff6f044c028146bea5f0dfd2870d23"}
{"nl": {"description": "Let us call a pair of integer numbers m-perfect, if at least one number in the pair is greater than or equal to m. Thus, the pairs (3, 3) and (0, 2) are 2-perfect while the pair (-1, 1) is not.Two integers x, y are written on the blackboard. It is allowed to erase one of them and replace it with the sum of the numbers, (x + y).What is the minimum number of such operations one has to perform in order to make the given pair of integers m-perfect?", "input_spec": "Single line of the input contains three integers x, y and m ( - 1018 ≤ x, y, m ≤ 1018). Please, do not use the %lld specifier to read or write 64-bit integers in C++. It is preffered to use the cin, cout streams or the %I64d specifier.", "output_spec": "Print the minimum number of operations or \"-1\" (without quotes), if it is impossible to transform the given pair to the m-perfect one.", "sample_inputs": ["1 2 5", "-1 4 15", "0 -1 5"], "sample_outputs": ["2", "4", "-1"], "notes": "NoteIn the first sample the following sequence of operations is suitable: (1, 2)  (3, 2)  (5, 2).In the second sample: (-1, 4)  (3, 4)  (7, 4)  (11, 4)  (15, 4).Finally, in the third sample x, y cannot be made positive, hence there is no proper sequence of operations."}, "src_uid": "82026a3c3d9a6bda2e2ac6e14979d821"}
{"nl": {"description": "There is a white sheet of paper lying on a rectangle table. The sheet is a rectangle with its sides parallel to the sides of the table. If you will take a look from above and assume that the bottom left corner of the table has coordinates $$$(0, 0)$$$, and coordinate axes are left and bottom sides of the table, then the bottom left corner of the white sheet has coordinates $$$(x_1, y_1)$$$, and the top right — $$$(x_2, y_2)$$$.After that two black sheets of paper are placed on the table. Sides of both black sheets are also parallel to the sides of the table. Coordinates of the bottom left corner of the first black sheet are $$$(x_3, y_3)$$$, and the top right — $$$(x_4, y_4)$$$. Coordinates of the bottom left corner of the second black sheet are $$$(x_5, y_5)$$$, and the top right — $$$(x_6, y_6)$$$.     Example of three rectangles. Determine if some part of the white sheet can be seen from the above after the two black sheets are placed. The part of the white sheet can be seen if there is at least one point lying not strictly inside the white sheet and strictly outside of both black sheets.", "input_spec": "The first line of the input contains four integers $$$x_1, y_1, x_2, y_2$$$ $$$(0 \\le x_1 < x_2 \\le 10^{6}, 0 \\le y_1 < y_2 \\le 10^{6})$$$ — coordinates of the bottom left and the top right corners of the white sheet. The second line of the input contains four integers $$$x_3, y_3, x_4, y_4$$$ $$$(0 \\le x_3 < x_4 \\le 10^{6}, 0 \\le y_3 < y_4 \\le 10^{6})$$$ — coordinates of the bottom left and the top right corners of the first black sheet. The third line of the input contains four integers $$$x_5, y_5, x_6, y_6$$$ $$$(0 \\le x_5 < x_6 \\le 10^{6}, 0 \\le y_5 < y_6 \\le 10^{6})$$$ — coordinates of the bottom left and the top right corners of the second black sheet. The sides of each sheet of paper are parallel (perpendicular) to the coordinate axes.", "output_spec": "If some part of the white sheet can be seen from the above after the two black sheets are placed, print \"YES\" (without quotes). Otherwise print \"NO\".", "sample_inputs": ["2 2 4 4\n1 1 3 5\n3 1 5 5", "3 3 7 5\n0 0 4 6\n0 0 7 4", "5 2 10 5\n3 1 7 6\n8 1 11 7", "0 0 1000000 1000000\n0 0 499999 1000000\n500000 0 1000000 1000000"], "sample_outputs": ["NO", "YES", "YES", "YES"], "notes": "NoteIn the first example the white sheet is fully covered by black sheets.In the second example the part of the white sheet can be seen after two black sheets are placed. For example, the point $$$(6.5, 4.5)$$$ lies not strictly inside the white sheet and lies strictly outside of both black sheets."}, "src_uid": "05c90c1d75d76a522241af6bb6af7781"}
{"nl": {"description": "Pupils decided to go to amusement park. Some of them were with parents. In total, n people came to the park and they all want to get to the most extreme attraction and roll on it exactly once.Tickets for group of x people are sold on the attraction, there should be at least one adult in each group (it is possible that the group consists of one adult). The ticket price for such group is c1 + c2·(x - 1)2 (in particular, if the group consists of one person, then the price is c1). All pupils who came to the park and their parents decided to split into groups in such a way that each visitor join exactly one group, and the total price of visiting the most extreme attraction is as low as possible. You are to determine this minimum possible total price. There should be at least one adult in each group. ", "input_spec": "The first line contains three integers n, c1 and c2 (1 ≤ n ≤ 200 000, 1 ≤ c1, c2 ≤ 107) — the number of visitors and parameters for determining the ticket prices for a group. The second line contains the string of length n, which consists of zeros and ones. If the i-th symbol of the string is zero, then the i-th visitor is a pupil, otherwise the i-th person is an adult. It is guaranteed that there is at least one adult. It is possible that there are no pupils.", "output_spec": "Print the minimum price of visiting the most extreme attraction for all pupils and their parents. Each of them should roll on the attraction exactly once.", "sample_inputs": ["3 4 1\n011", "4 7 2\n1101"], "sample_outputs": ["8", "18"], "notes": "NoteIn the first test one group of three people should go to the attraction. Then they have to pay 4 + 1 * (3 - 1)2 = 8.In the second test it is better to go to the attraction in two groups. The first group should consist of two adults (for example, the first and the second person), the second should consist of one pupil and one adult (the third and the fourth person). Then each group will have a size of two and for each the price of ticket is 7 + 2 * (2 - 1)2 = 9. Thus, the total price for two groups is 18."}, "src_uid": "78d013b01497053b8e321fe7b6ce3760"}
{"nl": {"description": "You've got a rectangular parallelepiped with integer edge lengths. You know the areas of its three faces that have a common vertex. Your task is to find the sum of lengths of all 12 edges of this parallelepiped.", "input_spec": "The first and the single line contains three space-separated integers — the areas of the parallelepiped's faces. The area's values are positive ( > 0) and do not exceed 104. It is guaranteed that there exists at least one parallelepiped that satisfies the problem statement.", "output_spec": "Print a single number — the sum of all edges of the parallelepiped.", "sample_inputs": ["1 1 1", "4 6 6"], "sample_outputs": ["12", "28"], "notes": "NoteIn the first sample the parallelepiped has sizes 1 × 1 × 1, in the second one — 2 × 2 × 3."}, "src_uid": "c0a3290be3b87f3a232ec19d4639fefc"}
{"nl": {"description": "Once upon a time in the thicket of the mushroom forest lived mushroom gnomes. They were famous among their neighbors for their magic mushrooms. Their magic nature made it possible that between every two neighboring mushrooms every minute grew another mushroom with the weight equal to the sum of weights of two neighboring ones. The mushroom gnomes loved it when everything was in order, that's why they always planted the mushrooms in one line in the order of their weights' increasing. Well... The gnomes planted the mushrooms and went to eat. After x minutes they returned and saw that new mushrooms had grown up, so that the increasing order had been violated. The gnomes replanted all the mushrooms in the correct order, that is, they sorted the mushrooms in the order of the weights' increasing. And went to eat again (those gnomes were quite big eaters). What total weights modulo p will the mushrooms have in another y minutes?", "input_spec": "The first line contains four integers n, x, y, p (1 ≤ n ≤ 106, 0 ≤ x, y ≤ 1018, x + y > 0, 2 ≤ p ≤ 109) which represent the number of mushrooms, the number of minutes after the first replanting, the number of minutes after the second replanting and the module. The next line contains n integers ai which represent the mushrooms' weight in the non-decreasing order (0 ≤ ai ≤ 109). Please, do not use %lld specificator to read or write 64-bit integers in C++. It is preffered to use cin (also you may use %I64d).", "output_spec": "The answer should contain a single number which is the total weights of the mushrooms modulo p in the end after x + y minutes.", "sample_inputs": ["2 1 0 657276545\n1 2", "2 1 1 888450282\n1 2", "4 5 0 10000\n1 2 3 4"], "sample_outputs": ["6", "14", "1825"], "notes": null}, "src_uid": "b5dd2b94570973b3e312ae4b7a43284f"}
{"nl": {"description": "IT City company developing computer games invented a new way to reward its employees. After a new game release users start buying it actively, and the company tracks the number of sales with precision to each transaction. Every time when the next number of sales is divisible by all numbers from 2 to 10 every developer of this game gets a small bonus.A game designer Petya knows that the company is just about to release a new game that was partly developed by him. On the basis of his experience he predicts that n people will buy the game during the first month. Now Petya wants to determine how many times he will get the bonus. Help him to know it.", "input_spec": "The only line of the input contains one integer n (1 ≤ n ≤ 1018) — the prediction on the number of people who will buy the game.", "output_spec": "Output one integer showing how many numbers from 1 to n are divisible by all numbers from 2 to 10.", "sample_inputs": ["3000"], "sample_outputs": ["1"], "notes": null}, "src_uid": "8551308e5ff435e0fc507b89a912408a"}
{"nl": {"description": "n hobbits are planning to spend the night at Frodo's house. Frodo has n beds standing in a row and m pillows (n ≤ m). Each hobbit needs a bed and at least one pillow to sleep, however, everyone wants as many pillows as possible. Of course, it's not always possible to share pillows equally, but any hobbit gets hurt if he has at least two pillows less than some of his neighbors have. Frodo will sleep on the k-th bed in the row. What is the maximum number of pillows he can have so that every hobbit has at least one pillow, every pillow is given to some hobbit and no one is hurt?", "input_spec": "The only line contain three integers n, m and k (1 ≤ n ≤ m ≤ 109, 1 ≤ k ≤ n) — the number of hobbits, the number of pillows and the number of Frodo's bed.", "output_spec": "Print single integer — the maximum number of pillows Frodo can have so that no one is hurt.", "sample_inputs": ["4 6 2", "3 10 3", "3 6 1"], "sample_outputs": ["2", "4", "3"], "notes": "NoteIn the first example Frodo can have at most two pillows. In this case, he can give two pillows to the hobbit on the first bed, and one pillow to each of the hobbits on the third and the fourth beds.In the second example Frodo can take at most four pillows, giving three pillows to each of the others.In the third example Frodo can take three pillows, giving two pillows to the hobbit in the middle and one pillow to the hobbit on the third bed."}, "src_uid": "da9ddd00f46021e8ee9db4a8deed017c"}
{"nl": {"description": "Capitalization is writing a word with its first letter as a capital letter. Your task is to capitalize the given word.Note, that during capitalization all the letters except the first one remains unchanged.", "input_spec": "A single line contains a non-empty word. This word consists of lowercase and uppercase English letters. The length of the word will not exceed 103.", "output_spec": "Output the given word after capitalization.", "sample_inputs": ["ApPLe", "konjac"], "sample_outputs": ["ApPLe", "Konjac"], "notes": null}, "src_uid": "29e0fc0c5c0e136ac8e58011c91397e4"}
{"nl": {"description": "Two little greedy bears have found two pieces of cheese in the forest of weight a and b grams, correspondingly. The bears are so greedy that they are ready to fight for the larger piece. That's where the fox comes in and starts the dialog: \"Little bears, wait a little, I want to make your pieces equal\" \"Come off it fox, how are you going to do that?\", the curious bears asked. \"It's easy\", said the fox. \"If the mass of a certain piece is divisible by two, then I can eat exactly a half of the piece. If the mass of a certain piece is divisible by three, then I can eat exactly two-thirds, and if the mass is divisible by five, then I can eat four-fifths. I'll eat a little here and there and make the pieces equal\". The little bears realize that the fox's proposal contains a catch. But at the same time they realize that they can not make the two pieces equal themselves. So they agreed to her proposal, but on one condition: the fox should make the pieces equal as quickly as possible. Find the minimum number of operations the fox needs to make pieces equal.", "input_spec": "The first line contains two space-separated integers a and b (1 ≤ a, b ≤ 109). ", "output_spec": "If the fox is lying to the little bears and it is impossible to make the pieces equal, print -1. Otherwise, print the required minimum number of operations. If the pieces of the cheese are initially equal, the required number is 0.", "sample_inputs": ["15 20", "14 8", "6 6"], "sample_outputs": ["3", "-1", "0"], "notes": null}, "src_uid": "75a97f4d85d50ea0e1af0d46f7565b49"}
{"nl": {"description": "In the year of 3000 travelling around parallel realities became a routine thing. However one has to take into consideration that travelling like that is highly dangerous as you never know beforehand where you're gonna get...Little Vasya, for instance, found himself in a gaming reality and now he has to successfully complete all levels of a very weird game to get back. The gaming reality is a three-dimensional space where n points are given. The game has m levels and at the beginning of the i-th level the player is positioned at some plane Qi that passes through the origin. On each level Vasya has to use special robots to construct and activate n powerful energy spheres of the equal radius with centers at the given points. The player chooses the radius of the spheres himself. The player has to spend R units of money to construct spheres whose radius equals R (consequently, one can construct spheres whose radius equals zero for free). Besides, once for each level a player can choose any point in space and release a laser ray from there, perpendicular to plane Qi (this action costs nothing). The ray can either be directed towards the plane or from the plane. The spheres that share at least one point with the ray will be immediately activated. The level is considered completed if the player has managed to activate all spheres. Note that the centers of the spheres are the same for all m levels but the spheres do not remain: the player should construct them anew on each new level.Help Vasya find out what minimum sum of money will be enough to complete each level.", "input_spec": "The first line contains two integers n and m (1 ≤ n ≤ 900, 1 ≤ m ≤ 100) — the number of energetic spheres and the number of levels in the game correspondingly.  Each of the following n lines contains three integers xi, yi, zi (0 ≤ xi, yi, zi ≤ 104) — the coordinates of the center of the i-th sphere. Assume that these points do not change their positions throughout the game. Then follow m lines, each containing three integers ai, bi, ci (0 ≤ ai, bi, ci ≤ 100, ai2 + bi2 + ci2 > 0). These numbers are the coefficients in the equation of plane Qi (aix + biy + ciz = 0), where the player is positioned at the beginning of the i-th level.", "output_spec": "Print m numbers, one per line: the i-th line should contain the minimum sum of money needed to complete the i-th level. The absolute or relative error should not exceed 10 - 6.", "sample_inputs": ["4 1\n0 0 0\n0 1 0\n1 0 0\n1 1 0\n0 0 1", "5 3\n0 1 0\n1 0 1\n1 2 1\n2 0 1\n1 3 0\n1 1 1\n1 2 3\n3 0 3", "2 1\n0 20 0\n0 0 0\n0 10 0"], "sample_outputs": ["0.7071067812", "1.6329931619\n1.6366341768\n1.5411035007", "0.0000000000"], "notes": null}, "src_uid": "25b2a84f0c3f574cdffd59a902b2326e"}
{"nl": {"description": "Permutation p is an ordered set of integers p1,  p2,  ...,  pn, consisting of n distinct positive integers, each of them doesn't exceed n. We'll denote the i-th element of permutation p as pi. We'll call number n the size or the length of permutation p1,  p2,  ...,  pn.Petya decided to introduce the sum operation on the set of permutations of length n. Let's assume that we are given two permutations of length n: a1, a2, ..., an and b1, b2, ..., bn. Petya calls the sum of permutations a and b such permutation c of length n, where ci = ((ai - 1 + bi - 1) mod n) + 1 (1 ≤ i ≤ n).Operation  means taking the remainder after dividing number x by number y.Obviously, not for all permutations a and b exists permutation c that is sum of a and b. That's why Petya got sad and asked you to do the following: given n, count the number of such pairs of permutations a and b of length n, that exists permutation c that is sum of a and b. The pair of permutations x, y (x ≠ y) and the pair of permutations y, x are considered distinct pairs.As the answer can be rather large, print the remainder after dividing it by 1000000007 (109 + 7).", "input_spec": "The single line contains integer n (1 ≤ n ≤ 16).", "output_spec": "In the single line print a single non-negative integer — the number of such pairs of permutations a and b, that exists permutation c that is sum of a and b, modulo 1000000007 (109 + 7).", "sample_inputs": ["3", "5"], "sample_outputs": ["18", "1800"], "notes": null}, "src_uid": "a6a804ce23bc48ec825c17d64ac0bb69"}
{"nl": {"description": "You are given a string q. A sequence of k strings s1, s2, ..., sk is called beautiful, if the concatenation of these strings is string q (formally, s1 + s2 + ... + sk = q) and the first characters of these strings are distinct.Find any beautiful sequence of strings or determine that the beautiful sequence doesn't exist.", "input_spec": "The first line contains a positive integer k (1 ≤ k ≤ 26) — the number of strings that should be in a beautiful sequence.  The second line contains string q, consisting of lowercase Latin letters. The length of the string is within range from 1 to 100, inclusive.", "output_spec": "If such sequence doesn't exist, then print in a single line \"NO\" (without the quotes). Otherwise, print in the first line \"YES\" (without the quotes) and in the next k lines print the beautiful sequence of strings s1, s2, ..., sk. If there are multiple possible answers, print any of them.", "sample_inputs": ["1\nabca", "2\naaacas", "4\nabc"], "sample_outputs": ["YES\nabca", "YES\naaa\ncas", "NO"], "notes": "NoteIn the second sample there are two possible answers: {\"aaaca\", \"s\"} and {\"aaa\", \"cas\"}."}, "src_uid": "c1b071f09ef375f19031ce99d10e90ab"}
{"nl": {"description": "Shaass thinks a kitchen with all white floor tiles is so boring. His kitchen floor is made of n·m square tiles forming a n × m rectangle. Therefore he's decided to color some of the tiles in black so that the floor looks like a checkerboard, which is no two side-adjacent tiles should have the same color.Shaass wants to use a painter robot to color the tiles. In the beginning the robot is standing in a border tile (xs, ys) facing a diagonal direction (i.e. upper-left, upper-right, down-left or down-right). As the robot walks in the kitchen he paints every tile he passes even if it's painted before. Painting each tile consumes one unit of black paint. If at any moment the robot hits a wall of the kitchen he changes his direction according the reflection rules. Note that a tile gets painted when the robot enters the tile from another tile, in other words changing direction in the same tile doesn't lead to any painting. The first tile the robot is standing on, is also painted.The robot stops painting the first moment the floor is checkered. Given the dimensions of the kitchen and the position of the robot, find out the amount of paint the robot consumes before it stops painting the floor.Let's consider an examples depicted below.  If the robot starts at tile number 1 (the tile (1, 1)) of the left grid heading to down-right it'll pass tiles 1354236 and consumes 7 units of black paint on his way until he stops at tile number 6. But if it starts at tile number 1 in the right grid heading to down-right it will get stuck in a loop painting tiles 1, 2, and 3.", "input_spec": "The first line of the input contains two integers n and m, (2 ≤ n, m ≤ 105). The second line contains two integers xs and ys (1 ≤ xs ≤ n, 1 ≤ ys ≤ m) and the direction robot is facing initially. Direction is one of the strings: \"UL\" (upper-left direction), \"UR\" (upper-right), \"DL\" (down-left) or \"DR\" (down-right). Note, that record (xs, ys) denotes the tile that is located at the xs-th row from the top and at the ys-th column from the left of the kitchen. It's guaranteed that the starting position will be a border tile (a tile with less than four side-adjacent tiles).", "output_spec": "Print the amount of paint the robot consumes to obtain a checkered kitchen floor. Or print -1 if it never happens. Please do not use the %lld specificator to read or write 64-bit integers in С++. It is preferred to use the cin, cout streams or the %I64d specificator.", "sample_inputs": ["3 4\n1 1 DR", "3 4\n3 3 DR", "3 3\n1 1 DR", "3 3\n1 2 DL"], "sample_outputs": ["7", "11", "-1", "4"], "notes": null}, "src_uid": "8a59247013a9b1f34700f4bfc7d1831d"}
{"nl": {"description": "Alice and Bob have decided to play the game \"Rock, Paper, Scissors\". The game consists of several rounds, each round is independent of each other. In each round, both players show one of the following things at the same time: rock, paper or scissors. If both players showed the same things then the round outcome is a draw. Otherwise, the following rules applied:  if one player showed rock and the other one showed scissors, then the player who showed rock is considered the winner and the other one is considered the loser;  if one player showed scissors and the other one showed paper, then the player who showed scissors is considered the winner and the other one is considered the loser;  if one player showed paper and the other one showed rock, then the player who showed paper is considered the winner and the other one is considered the loser. Alice and Bob decided to play exactly $$$n$$$ rounds of the game described above. Alice decided to show rock $$$a_1$$$ times, show scissors $$$a_2$$$ times and show paper $$$a_3$$$ times. Bob decided to show rock $$$b_1$$$ times, show scissors $$$b_2$$$ times and show paper $$$b_3$$$ times. Though, both Alice and Bob did not choose the sequence in which they show things. It is guaranteed that $$$a_1 + a_2 + a_3 = n$$$ and $$$b_1 + b_2 + b_3 = n$$$.Your task is to find two numbers:  the minimum number of round Alice can win;  the maximum number of rounds Alice can win. ", "input_spec": "The first line of the input contains one integer $$$n$$$ ($$$1 \\le n \\le 10^{9}$$$) — the number of rounds. The second line of the input contains three integers $$$a_1, a_2, a_3$$$ ($$$0 \\le a_i \\le n$$$) — the number of times Alice will show rock, scissors and paper, respectively. It is guaranteed that $$$a_1 + a_2 + a_3 = n$$$. The third line of the input contains three integers $$$b_1, b_2, b_3$$$ ($$$0 \\le b_j \\le n$$$) — the number of times Bob will show rock, scissors and paper, respectively. It is guaranteed that $$$b_1 + b_2 + b_3 = n$$$.", "output_spec": "Print two integers: the minimum and the maximum number of rounds Alice can win.", "sample_inputs": ["2\n0 1 1\n1 1 0", "15\n5 5 5\n5 5 5", "3\n0 0 3\n3 0 0", "686\n479 178 29\n11 145 530", "319\n10 53 256\n182 103 34"], "sample_outputs": ["0 1", "0 15", "3 3", "22 334", "119 226"], "notes": "NoteIn the first example, Alice will not win any rounds if she shows scissors and then paper and Bob shows rock and then scissors. In the best outcome, Alice will win one round if she shows paper and then scissors, and Bob shows rock and then scissors.In the second example, Alice will not win any rounds if Bob shows the same things as Alice each round.In the third example, Alice always shows paper and Bob always shows rock so Alice will win all three rounds anyway."}, "src_uid": "e6dc3bc64fc66b6127e2b32cacc06402"}
{"nl": {"description": "Anya loves to fold and stick. Today she decided to do just that.Anya has n cubes lying in a line and numbered from 1 to n from left to right, with natural numbers written on them. She also has k stickers with exclamation marks. We know that the number of stickers does not exceed the number of cubes.Anya can stick an exclamation mark on the cube and get the factorial of the number written on the cube. For example, if a cube reads 5, then after the sticking it reads 5!, which equals 120.You need to help Anya count how many ways there are to choose some of the cubes and stick on some of the chosen cubes at most k exclamation marks so that the sum of the numbers written on the chosen cubes after the sticking becomes equal to S. Anya can stick at most one exclamation mark on each cube. Can you do it?Two ways are considered the same if they have the same set of chosen cubes and the same set of cubes with exclamation marks.", "input_spec": "The first line of the input contains three space-separated integers n, k and S (1 ≤ n ≤ 25, 0 ≤ k ≤ n, 1 ≤ S ≤ 1016) — the number of cubes and the number of stickers that Anya has, and the sum that she needs to get.  The second line contains n positive integers ai (1 ≤ ai ≤ 109) — the numbers, written on the cubes. The cubes in the input are described in the order from left to right, starting from the first one.  Multiple cubes can contain the same numbers.", "output_spec": "Output the number of ways to choose some number of cubes and stick exclamation marks on some of them so that the sum of the numbers became equal to the given number S.", "sample_inputs": ["2 2 30\n4 3", "2 2 7\n4 3", "3 1 1\n1 1 1"], "sample_outputs": ["1", "1", "6"], "notes": "NoteIn the first sample the only way is to choose both cubes and stick an exclamation mark on each of them.In the second sample the only way is to choose both cubes but don't stick an exclamation mark on any of them.In the third sample it is possible to choose any of the cubes in three ways, and also we may choose to stick or not to stick the exclamation mark on it. So, the total number of ways is six."}, "src_uid": "2821a11066dffc7e8f6a60a8751cea37"}
{"nl": {"description": "Anton and Dasha like to play different games during breaks on checkered paper. By the 11th grade they managed to play all the games of this type and asked Vova the programmer to come up with a new game. Vova suggested to them to play a game under the code name \"dot\" with the following rules:  On the checkered paper a coordinate system is drawn. A dot is initially put in the position (x, y).  A move is shifting a dot to one of the pre-selected vectors. Also each player can once per game symmetrically reflect a dot relatively to the line y = x.  Anton and Dasha take turns. Anton goes first.  The player after whose move the distance from the dot to the coordinates' origin exceeds d, loses. Help them to determine the winner.", "input_spec": "The first line of the input file contains 4 integers x, y, n, d ( - 200 ≤ x, y ≤ 200, 1 ≤ d ≤ 200, 1 ≤ n ≤ 20) — the initial coordinates of the dot, the distance d and the number of vectors. It is guaranteed that the initial dot is at the distance less than d from the origin of the coordinates. The following n lines each contain two non-negative numbers xi and yi (0 ≤ xi, yi ≤ 200) — the coordinates of the i-th vector. It is guaranteed that all the vectors are nonzero and different.", "output_spec": "You should print \"Anton\", if the winner is Anton in case of both players play the game optimally, and \"Dasha\" otherwise.", "sample_inputs": ["0 0 2 3\n1 1\n1 2", "0 0 2 4\n1 1\n1 2"], "sample_outputs": ["Anton", "Dasha"], "notes": "NoteIn the first test, Anton goes to the vector (1;2), and Dasha loses. In the second test Dasha with her first move shifts the dot so that its coordinates are (2;3), and Anton loses, as he has the only possible move — to reflect relatively to the line y = x. Dasha will respond to it with the same move and return the dot in position (2;3)."}, "src_uid": "645a6ca9a8dda6946c2cc055a4beb08f"}
{"nl": {"description": "Every summer Vitya comes to visit his grandmother in the countryside. This summer, he got a huge wart. Every grandma knows that one should treat warts when the moon goes down. Thus, Vitya has to catch the moment when the moon is down.Moon cycle lasts 30 days. The size of the visible part of the moon (in Vitya's units) for each day is 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, and then cycle repeats, thus after the second 1 again goes 0.As there is no internet in the countryside, Vitya has been watching the moon for n consecutive days and for each of these days he wrote down the size of the visible part of the moon. Help him find out whether the moon will be up or down next day, or this cannot be determined by the data he has.", "input_spec": "The first line of the input contains a single integer n (1 ≤ n ≤ 92) — the number of consecutive days Vitya was watching the size of the visible part of the moon.  The second line contains n integers ai (0 ≤ ai ≤ 15) — Vitya's records. It's guaranteed that the input data is consistent.", "output_spec": "If Vitya can be sure that the size of visible part of the moon on day n + 1 will be less than the size of the visible part on day n, then print \"DOWN\" at the only line of the output. If he might be sure that the size of the visible part will increase, then print \"UP\". If it's impossible to determine what exactly will happen with the moon, print -1.", "sample_inputs": ["5\n3 4 5 6 7", "7\n12 13 14 15 14 13 12", "1\n8"], "sample_outputs": ["UP", "DOWN", "-1"], "notes": "NoteIn the first sample, the size of the moon on the next day will be equal to 8, thus the answer is \"UP\".In the second sample, the size of the moon on the next day will be 11, thus the answer is \"DOWN\".In the third sample, there is no way to determine whether the size of the moon on the next day will be 7 or 9, thus the answer is -1."}, "src_uid": "8330d9fea8d50a79741507b878da0a75"}
{"nl": {"description": "You are given three integers k, pa and pb.You will construct a sequence with the following algorithm: Initially, start with the empty sequence. Each second, you do the following. With probability pa / (pa + pb), add 'a' to the end of the sequence. Otherwise (with probability pb / (pa + pb)), add 'b' to the end of the sequence.You stop once there are at least k subsequences that form 'ab'. Determine the expected number of times 'ab' is a subsequence in the resulting sequence. It can be shown that this can be represented by P / Q, where P and Q are coprime integers, and . Print the value of .", "input_spec": "The first line will contain three integers integer k, pa, pb (1 ≤ k ≤ 1 000, 1 ≤ pa, pb ≤ 1 000 000).", "output_spec": "Print a single integer, the answer to the problem.", "sample_inputs": ["1 1 1", "3 1 4"], "sample_outputs": ["2", "370000006"], "notes": "NoteThe first sample, we will keep appending to our sequence until we get the subsequence 'ab' at least once. For instance, we get the sequence 'ab' with probability 1/4, 'bbab' with probability 1/16, and 'aab' with probability 1/8. Note, it's impossible for us to end with a sequence like 'aabab', since we would have stopped our algorithm once we had the prefix 'aab'. The expected amount of times that 'ab' will occur across all valid sequences is 2. For the second sample, the answer is equal to ."}, "src_uid": "0dc9f5d75143a2bc744480de859188b4"}
{"nl": {"description": "Chris the Rabbit has been interested in arrays ever since he was a child. At the moment he is researching arrays with the length of n, containing only integers from 1 to n. He is not good at math, that's why some simple things drive him crazy. For example, yesterday he grew keen on counting how many different beautiful arrays there are. Chris thinks that an array is beautiful if it meets one of the two conditions:   each elements, starting from the second one, is no more than the preceding one  each element, starting from the second one, is no less than the preceding one Having got absolutely mad at himself and at math, Chris came to Stewie and Brian to ask them for help. However, they only laughed at him and said that the answer is too simple and not interesting. Help Chris the Rabbit to find the answer at last.", "input_spec": "The single line contains an integer n which is the size of the array (1 ≤ n ≤ 105).", "output_spec": "You must print the answer on a single line. As it can be rather long, you should print it modulo 1000000007.", "sample_inputs": ["2", "3"], "sample_outputs": ["4", "17"], "notes": null}, "src_uid": "13a9ffe5acaa79d97df88a069fc520b9"}
{"nl": {"description": "Bear Limak wants to become the largest of bears, or at least to become larger than his brother Bob.Right now, Limak and Bob weigh a and b respectively. It's guaranteed that Limak's weight is smaller than or equal to his brother's weight.Limak eats a lot and his weight is tripled after every year, while Bob's weight is doubled after every year.After how many full years will Limak become strictly larger (strictly heavier) than Bob?", "input_spec": "The only line of the input contains two integers a and b (1 ≤ a ≤ b ≤ 10) — the weight of Limak and the weight of Bob respectively.", "output_spec": "Print one integer, denoting the integer number of years after which Limak will become strictly larger than Bob.", "sample_inputs": ["4 7", "4 9", "1 1"], "sample_outputs": ["2", "3", "1"], "notes": "NoteIn the first sample, Limak weighs 4 and Bob weighs 7 initially. After one year their weights are 4·3 = 12 and 7·2 = 14 respectively (one weight is tripled while the other one is doubled). Limak isn't larger than Bob yet. After the second year weights are 36 and 28, so the first weight is greater than the second one. Limak became larger than Bob after two years so you should print 2.In the second sample, Limak's and Bob's weights in next years are: 12 and 18, then 36 and 36, and finally 108 and 72 (after three years). The answer is 3. Remember that Limak wants to be larger than Bob and he won't be satisfied with equal weights.In the third sample, Limak becomes larger than Bob after the first year. Their weights will be 3 and 2 then."}, "src_uid": "a1583b07a9d093e887f73cc5c29e444a"}
{"nl": {"description": "Luba thinks about watering her garden. The garden can be represented as a segment of length k. Luba has got n buckets, the i-th bucket allows her to water some continuous subsegment of garden of length exactly ai each hour. Luba can't water any parts of the garden that were already watered, also she can't water the ground outside the garden.Luba has to choose one of the buckets in order to water the garden as fast as possible (as mentioned above, each hour she will water some continuous subsegment of length ai if she chooses the i-th bucket). Help her to determine the minimum number of hours she has to spend watering the garden. It is guaranteed that Luba can always choose a bucket so it is possible water the garden.See the examples for better understanding.", "input_spec": "The first line of input contains two integer numbers n and k (1 ≤ n, k ≤ 100) — the number of buckets and the length of the garden, respectively. The second line of input contains n integer numbers ai (1 ≤ ai ≤ 100) — the length of the segment that can be watered by the i-th bucket in one hour. It is guaranteed that there is at least one bucket such that it is possible to water the garden in integer number of hours using only this bucket.", "output_spec": "Print one integer number — the minimum number of hours required to water the garden.", "sample_inputs": ["3 6\n2 3 5", "6 7\n1 2 3 4 5 6"], "sample_outputs": ["2", "7"], "notes": "NoteIn the first test the best option is to choose the bucket that allows to water the segment of length 3. We can't choose the bucket that allows to water the segment of length 5 because then we can't water the whole garden.In the second test we can choose only the bucket that allows us to water the segment of length 1."}, "src_uid": "80520be9916045aca3a7de7bc925af1f"}
{"nl": {"description": "Fox Ciel has n boxes in her room. They have the same size and weight, but they might have different strength. The i-th box can hold at most xi boxes on its top (we'll call xi the strength of the box). Since all the boxes have the same size, Ciel cannot put more than one box directly on the top of some box. For example, imagine Ciel has three boxes: the first has strength 2, the second has strength 1 and the third has strength 1. She cannot put the second and the third box simultaneously directly on the top of the first one. But she can put the second box directly on the top of the first one, and then the third box directly on the top of the second one. We will call such a construction of boxes a pile.Fox Ciel wants to construct piles from all the boxes. Each pile will contain some boxes from top to bottom, and there cannot be more than xi boxes on the top of i-th box. What is the minimal number of piles she needs to construct?", "input_spec": "The first line contains an integer n (1 ≤ n ≤ 100). The next line contains n integers x1, x2, ..., xn (0 ≤ xi ≤ 100).", "output_spec": "Output a single integer — the minimal possible number of piles.", "sample_inputs": ["3\n0 0 10", "5\n0 1 2 3 4", "4\n0 0 0 0", "9\n0 1 0 2 0 1 1 2 10"], "sample_outputs": ["2", "1", "4", "3"], "notes": "NoteIn example 1, one optimal way is to build 2 piles: the first pile contains boxes 1 and 3 (from top to bottom), the second pile contains only box 2.In example 2, we can build only 1 pile that contains boxes 1, 2, 3, 4, 5 (from top to bottom)."}, "src_uid": "7c710ae68f27f140e7e03564492f7214"}
{"nl": {"description": "Petya and Vasya decided to play a game. They have n cards (n is an even number). A single integer is written on each card.Before the game Petya will choose an integer and after that Vasya will choose another integer (different from the number that Petya chose). During the game each player takes all the cards with number he chose. For example, if Petya chose number 5 before the game he will take all cards on which 5 is written and if Vasya chose number 10 before the game he will take all cards on which 10 is written.The game is considered fair if Petya and Vasya can take all n cards, and the number of cards each player gets is the same.Determine whether Petya and Vasya can choose integer numbers before the game so that the game is fair. ", "input_spec": "The first line contains a single integer n (2 ≤ n ≤ 100) — number of cards. It is guaranteed that n is an even number. The following n lines contain a sequence of integers a1, a2, ..., an (one integer per line, 1 ≤ ai ≤ 100) — numbers written on the n cards.", "output_spec": "If it is impossible for Petya and Vasya to choose numbers in such a way that the game will be fair, print \"NO\" (without quotes) in the first line. In this case you should not print anything more. In the other case print \"YES\" (without quotes) in the first line. In the second line print two distinct integers — number that Petya should choose and the number that Vasya should choose to make the game fair. If there are several solutions, print any of them.", "sample_inputs": ["4\n11\n27\n27\n11", "2\n6\n6", "6\n10\n20\n30\n20\n10\n20", "6\n1\n1\n2\n2\n3\n3"], "sample_outputs": ["YES\n11 27", "NO", "NO", "NO"], "notes": "NoteIn the first example the game will be fair if, for example, Petya chooses number 11, and Vasya chooses number 27. Then the will take all cards — Petya will take cards 1 and 4, and Vasya will take cards 2 and 3. Thus, each of them will take exactly two cards.In the second example fair game is impossible because the numbers written on the cards are equal, but the numbers that Petya and Vasya should choose should be distinct.In the third example it is impossible to take all cards. Petya and Vasya can take at most five cards — for example, Petya can choose number 10 and Vasya can choose number 20. But for the game to be fair it is necessary to take 6 cards."}, "src_uid": "2860b4fb22402ea9574c2f9e403d63d8"}
{"nl": {"description": "Prof. Vasechkin wants to represent positive integer n as a sum of addends, where each addends is an integer number containing only 1s. For example, he can represent 121 as 121=111+11+–1. Help him to find the least number of digits 1 in such sum.", "input_spec": "The first line of the input contains integer n (1 ≤ n < 1015).", "output_spec": "Print expected minimal number of digits 1.", "sample_inputs": ["121"], "sample_outputs": ["6"], "notes": null}, "src_uid": "1b17a7b3b41077843ee1d6e0607720d6"}
{"nl": {"description": "You've got a rectangular table with length a and width b and the infinite number of plates of radius r. Two players play the following game: they take turns to put the plates on the table so that the plates don't lie on each other (but they can touch each other), and so that any point on any plate is located within the table's border. During the game one cannot move the plates that already lie on the table. The player who cannot make another move loses. Determine which player wins, the one who moves first or the one who moves second, provided that both players play optimally well.", "input_spec": "A single line contains three space-separated integers a, b, r (1 ≤ a, b, r ≤ 100) — the table sides and the plates' radius, correspondingly.", "output_spec": "If wins the player who moves first, print \"First\" (without the quotes). Otherwise print \"Second\" (without the quotes).", "sample_inputs": ["5 5 2", "6 7 4"], "sample_outputs": ["First", "Second"], "notes": "NoteIn the first sample the table has place for only one plate. The first player puts a plate on the table, the second player can't do that and loses.  In the second sample the table is so small that it doesn't have enough place even for one plate. So the first player loses without making a single move.  "}, "src_uid": "90b9ef939a13cf29715bc5bce26c9896"}
{"nl": {"description": "A monster is chasing after Rick and Morty on another planet. They're so frightened that sometimes they scream. More accurately, Rick screams at times b, b + a, b + 2a, b + 3a, ... and Morty screams at times d, d + c, d + 2c, d + 3c, ....   The Monster will catch them if at any point they scream at the same time, so it wants to know when it will catch them (the first time they scream at the same time) or that they will never scream at the same time.", "input_spec": "The first line of input contains two integers a and b (1 ≤ a, b ≤ 100).  The second line contains two integers c and d (1 ≤ c, d ≤ 100).", "output_spec": "Print the first time Rick and Morty will scream at the same time, or  - 1 if they will never scream at the same time.", "sample_inputs": ["20 2\n9 19", "2 1\n16 12"], "sample_outputs": ["82", "-1"], "notes": "NoteIn the first sample testcase, Rick's 5th scream and Morty's 8th time are at time 82. In the second sample testcase, all Rick's screams will be at odd times and Morty's will be at even times, so they will never scream at the same time."}, "src_uid": "158cb12d45f4ee3368b94b2b622693e7"}
{"nl": {"description": "Furik loves painting stars. A star is a shape that results if we take a regular pentagon and paint all diagonals in it.   Recently he decided to teach Rubik to paint stars. After many years of training Rubik could paint stars easily. But now Furik decided to test Rubik and complicated the task. Rubik must paint n stars, observing the following rules:  all stars must be painted in a single move (i.e. it is forbidden to take the pen away from the paper);  it is forbidden to paint the same segment of non-zero length more than once;  the stars can intersect only in their vertexes;  the length of a side of the regular pentagon, in which Rubik paints each star, must equal 10. Help Rubik to cope with this hard task.", "input_spec": "A single line contains an integer (1 ≤ n ≤ 100) — the number of stars to paint.", "output_spec": "On the first line print an integer m (1 ≤ m ≤ 5·n). On the next m lines print coordinates of m distinct points with accuracy of at least 9 and at most 100 digits after decimal point. All coordinates should not exceed 5000 in their absolute value. On each of the next n lines print 5 integers — the indexes of the points that form the given star in the clockwise or counterclockwise order. On the next line print 5·n + 1 integers — the numbers of points in the order, in which Rubik paints stars. That is, if number with index i is ai, and number with index i + 1 is ai + 1, then points with indexes ai and ai + 1 will have a segment painted between them.  You can consider all m printed points indexed from 1 to m in the order, in which they occur in the output. Separate the numbers on the lines with whitespaces. Note that the answer has an imprecise validation. Try to obtain as accurate a solution as possible. The validator performs all calculations considering that the absolute error of a participant's answer is not more than 10 - 8.", "sample_inputs": ["1"], "sample_outputs": ["5\n3.830127018922193 3.366025403784439\n-3.601321235851749 10.057331467373021\n0.466045194906253 19.192786043799030\n10.411264148588986 18.147501411122495\n12.490381056766580 8.366025403784439\n1 2 3 4 5\n1 3 5 2 4 1"], "notes": "NoteThe initial position of points in the sample is:  The order in which Rubik can paint segments is:  "}, "src_uid": "db263b866e93e3a97731e11102923902"}
{"nl": {"description": "Johnny has a younger sister Anne, who is very clever and smart. As she came home from the kindergarten, she told his brother about the task that her kindergartener asked her to solve. The task was just to construct a triangle out of four sticks of different colours. Naturally, one of the sticks is extra. It is not allowed to break the sticks or use their partial length. Anne has perfectly solved this task, now she is asking Johnny to do the same.The boy answered that he would cope with it without any difficulty. However, after a while he found out that different tricky things can occur. It can happen that it is impossible to construct a triangle of a positive area, but it is possible to construct a degenerate triangle. It can be so, that it is impossible to construct a degenerate triangle even. As Johnny is very lazy, he does not want to consider such a big amount of cases, he asks you to help him.", "input_spec": "The first line of the input contains four space-separated positive integer numbers not exceeding 100 — lengthes of the sticks.", "output_spec": "Output TRIANGLE if it is possible to construct a non-degenerate triangle. Output SEGMENT if the first case cannot take place and it is possible to construct a degenerate triangle. Output IMPOSSIBLE if it is impossible to construct any triangle. Remember that you are to use three sticks. It is not allowed to break the sticks or use their partial length.", "sample_inputs": ["4 2 1 3", "7 2 2 4", "3 5 9 1"], "sample_outputs": ["TRIANGLE", "SEGMENT", "IMPOSSIBLE"], "notes": null}, "src_uid": "8f5df9a41e6e100aa65b9fc1d26e447a"}
{"nl": {"description": "A very tense moment: n cowboys stand in a circle and each one points his colt at a neighbor. Each cowboy can point the colt to the person who follows or precedes him in clockwise direction. Human life is worthless, just like in any real western.The picture changes each second! Every second the cowboys analyse the situation and, if a pair of cowboys realize that they aim at each other, they turn around. In a second all such pairs of neighboring cowboys aiming at each other turn around. All actions happen instantaneously and simultaneously in a second.We'll use character \"A\" to denote a cowboy who aims at his neighbour in the clockwise direction, and character \"B\" for a cowboy who aims at his neighbour in the counter clockwise direction. Then a string of letters \"A\" and \"B\" will denote the circle of cowboys, the record is made from the first of them in a clockwise direction.For example, a circle that looks like \"ABBBABBBA\" after a second transforms into \"BABBBABBA\" and a circle that looks like \"BABBA\" transforms into \"ABABB\".     This picture illustrates how the circle \"BABBA\" transforms into \"ABABB\"  A second passed and now the cowboys' position is described by string s. Your task is to determine the number of possible states that lead to s in a second. Two states are considered distinct if there is a cowboy who aims at his clockwise neighbor in one state and at his counter clockwise neighbor in the other state.", "input_spec": "The input data consists of a single string s. Its length is from 3 to 100 characters, inclusive. Line s consists of letters \"A\" and \"B\".", "output_spec": "Print the sought number of states.", "sample_inputs": ["BABBBABBA", "ABABB", "ABABAB"], "sample_outputs": ["2", "2", "4"], "notes": "NoteIn the first sample the possible initial states are \"ABBBABBAB\" and \"ABBBABBBA\".In the second sample the possible initial states are \"AABBB\" and \"BABBA\"."}, "src_uid": "ad27d991516054ea473b384bb2563b38"}
{"nl": {"description": "The \"Bulls and Cows\" game needs two people to play. The thinker thinks of a number and the guesser tries to guess it.The thinker thinks of a four-digit number in the decimal system. All the digits in the number are different and the number may have a leading zero. It can't have more than one leading zero, because all it's digits should be different. The guesser tries to guess the number. He makes a series of guesses, trying experimental numbers and receives answers from the first person in the format \"x bulls y cows\". x represents the number of digits in the experimental number that occupy the same positions as in the sought number. y represents the number of digits of the experimental number that present in the sought number, but occupy different positions. Naturally, the experimental numbers, as well as the sought number, are represented by four-digit numbers where all digits are different and a leading zero can be present.For example, let's suppose that the thinker thought of the number 0123. Then the guessers' experimental number 1263 will receive a reply \"1 bull 2 cows\" (3 occupies the same positions in both numbers and 1 and 2 are present in both numbers but they occupy different positions). Also, the answer to number 8103 will be \"2 bulls 1 cow\" (analogically, 1 and 3 occupy the same positions and 0 occupies a different one). When the guesser is answered \"4 bulls 0 cows\", the game is over.Now the guesser has already made several guesses and wants to know whether his next guess can possibly be the last one.", "input_spec": "The first input line contains an integer n (1 ≤ n ≤ 10) which represents the number of already made guesses. Then follow n lines in the form of \"ai bi ci\", where ai is the i-th experimental number, bi is the number of bulls, ci is the number of cows (1 ≤ i ≤ n, 0 ≤ bi, ci, bi + ci ≤ 4). The experimental numbers are correct, i.e., each of them contains exactly four digits, in each of them all the four digits are different, and there can be a leading zero. All the experimental numbers are different. As the guesser hasn't guessed the number yet, the answer \"4 bulls 0 cows\" is not present.", "output_spec": "If the input data is enough to determine the sought number, print the number with four digits on a single line. If it has less than four digits, add leading zero. If the data is not enough, print \"Need more data\" without the quotes. If the thinker happens to have made a mistake in his replies, print \"Incorrect data\" without the quotes.", "sample_inputs": ["2\n1263 1 2\n8103 2 1", "2\n1234 2 2\n1256 0 2", "2\n0123 1 1\n4567 1 2"], "sample_outputs": ["Need more data", "2134", "Incorrect data"], "notes": null}, "src_uid": "142e5f2f08724e53c234fc2379216b4c"}
{"nl": {"description": "One day Vasya was going home when he saw a box lying on the road. The box can be represented as a rectangular parallelepiped. Vasya needed no time to realize that the box is special, as all its edges are parallel to the coordinate axes, one of its vertices is at point (0, 0, 0), and the opposite one is at point (x1, y1, z1). The six faces of the box contain some numbers a1, a2, ..., a6, exactly one number right in the center of each face.  The numbers are located on the box like that:   number a1 is written on the face that lies on the ZOX plane;  a2 is written on the face, parallel to the plane from the previous point;  a3 is written on the face that lies on the XOY plane;  a4 is written on the face, parallel to the plane from the previous point;  a5 is written on the face that lies on the YOZ plane;  a6 is written on the face, parallel to the plane from the previous point. At the moment Vasya is looking at the box from point (x, y, z). Find the sum of numbers that Vasya sees. Note that all faces of the box are not transparent and Vasya can't see the numbers through the box. The picture contains transparent faces just to make it easier to perceive. You can consider that if Vasya is looking from point, lying on the plane of some face, than he can not see the number that is written on this face. It is enough to see the center of a face to see the corresponding number for Vasya. Also note that Vasya always reads correctly the ai numbers that he sees, independently of their rotation, angle and other factors (that is, for example, if Vasya sees some ai = 6, then he can't mistake this number for 9 and so on). ", "input_spec": "The fist input line contains three space-separated integers x, y and z (|x|, |y|, |z| ≤ 106) — the coordinates of Vasya's position in space. The second line contains three space-separated integers x1, y1, z1 (1 ≤ x1, y1, z1 ≤ 106) — the coordinates of the box's vertex that is opposite to the vertex at point (0, 0, 0). The third line contains six space-separated integers a1, a2, ..., a6 (1 ≤ ai ≤ 106) — the numbers that are written on the box faces.  It is guaranteed that point (x, y, z) is located strictly outside the box.", "output_spec": "Print a single integer — the sum of all numbers on the box faces that Vasya sees.", "sample_inputs": ["2 2 2\n1 1 1\n1 2 3 4 5 6", "0 0 10\n3 2 3\n1 2 3 4 5 6"], "sample_outputs": ["12", "4"], "notes": "NoteThe first sample corresponds to perspective, depicted on the picture. Vasya sees numbers a2 (on the top face that is the darkest), a6 (on the right face that is the lightest) and a4 (on the left visible face).In the second sample Vasya can only see number a4."}, "src_uid": "c7889a8f64c57cf7be4df870f68f749e"}
{"nl": {"description": "As behooves any intelligent schoolboy, Kevin Sun is studying psycowlogy, cowculus, and cryptcowgraphy at the Bovinia State University (BGU) under Farmer Ivan. During his Mathematics of Olympiads (MoO) class, Kevin was confronted with a weird functional equation and needs your help. For two fixed integers k and p, where p is an odd prime number, the functional equation states that  for some function . (This equation should hold for any integer x in the range 0 to p - 1, inclusive.)It turns out that f can actually be many different functions. Instead of finding a solution, Kevin wants you to count the number of distinct functions f that satisfy this equation. Since the answer may be very large, you should print your result modulo 109 + 7.", "input_spec": "The input consists of two space-separated integers p and k (3 ≤ p ≤ 1 000 000, 0 ≤ k ≤ p - 1) on a single line. It is guaranteed that p is an odd prime number.", "output_spec": "Print a single integer, the number of distinct functions f modulo 109 + 7.", "sample_inputs": ["3 2", "5 4"], "sample_outputs": ["3", "25"], "notes": "NoteIn the first sample, p = 3 and k = 2. The following functions work:   f(0) = 0, f(1) = 1, f(2) = 2.  f(0) = 0, f(1) = 2, f(2) = 1.  f(0) = f(1) = f(2) = 0. "}, "src_uid": "580bf65af24fb7f08250ddbc4ca67e0e"}
{"nl": {"description": "Recently Ivan the Fool decided to become smarter and study the probability theory. He thinks that he understands the subject fairly well, and so he began to behave like he already got PhD in that area.To prove his skills, Ivan decided to demonstrate his friends a concept of random picture. A picture is a field of $$$n$$$ rows and $$$m$$$ columns, where each cell is either black or white. Ivan calls the picture random if for every cell it has at most one adjacent cell of the same color. Two cells are considered adjacent if they share a side.Ivan's brothers spent some time trying to explain that it's not how the randomness usually works. Trying to convince Ivan, they want to count the number of different random (according to Ivan) pictures. Two pictures are considered different if at least one cell on those two picture is colored differently. Since the number of such pictures may be quite large, print it modulo $$$10^9 + 7$$$.", "input_spec": "The only line contains two integers $$$n$$$ and $$$m$$$ ($$$1 \\le n, m \\le 100\\,000$$$), the number of rows and the number of columns of the field.", "output_spec": "Print one integer, the number of random pictures modulo $$$10^9 + 7$$$.", "sample_inputs": ["2 3"], "sample_outputs": ["8"], "notes": "NoteThe picture below shows all possible random pictures of size $$$2$$$ by $$$3$$$.   "}, "src_uid": "0f1ab296cbe0952faa904f2bebe0567b"}
{"nl": {"description": "Gerald got a very curious hexagon for his birthday. The boy found out that all the angles of the hexagon are equal to . Then he measured the length of its sides, and found that each of them is equal to an integer number of centimeters. There the properties of the hexagon ended and Gerald decided to draw on it.He painted a few lines, parallel to the sides of the hexagon. The lines split the hexagon into regular triangles with sides of 1 centimeter. Now Gerald wonders how many triangles he has got. But there were so many of them that Gerald lost the track of his counting. Help the boy count the triangles.", "input_spec": "The first and the single line of the input contains 6 space-separated integers a1, a2, a3, a4, a5 and a6 (1 ≤ ai ≤ 1000) — the lengths of the sides of the hexagons in centimeters in the clockwise order. It is guaranteed that the hexagon with the indicated properties and the exactly such sides exists.", "output_spec": "Print a single integer — the number of triangles with the sides of one 1 centimeter, into which the hexagon is split.", "sample_inputs": ["1 1 1 1 1 1", "1 2 1 2 1 2"], "sample_outputs": ["6", "13"], "notes": "NoteThis is what Gerald's hexagon looks like in the first sample:And that's what it looks like in the second sample:"}, "src_uid": "382475475427f0e76c6b4ac6e7a02e21"}
{"nl": {"description": "Like any unknown mathematician, Yuri has favourite numbers: $$$A$$$, $$$B$$$, $$$C$$$, and $$$D$$$, where $$$A \\leq B \\leq C \\leq D$$$. Yuri also likes triangles and once he thought: how many non-degenerate triangles with integer sides $$$x$$$, $$$y$$$, and $$$z$$$ exist, such that $$$A \\leq x \\leq B \\leq y \\leq C \\leq z \\leq D$$$ holds?Yuri is preparing problems for a new contest now, so he is very busy. That's why he asked you to calculate the number of triangles with described property.The triangle is called non-degenerate if and only if its vertices are not collinear.", "input_spec": "The first line contains four integers: $$$A$$$, $$$B$$$, $$$C$$$ and $$$D$$$ ($$$1 \\leq A \\leq B \\leq C \\leq D \\leq 5 \\cdot 10^5$$$) — Yuri's favourite numbers.", "output_spec": "Print the number of non-degenerate triangles with integer sides $$$x$$$, $$$y$$$, and $$$z$$$ such that the inequality $$$A \\leq x \\leq B \\leq y \\leq C \\leq z \\leq D$$$ holds.", "sample_inputs": ["1 2 3 4", "1 2 2 5", "500000 500000 500000 500000"], "sample_outputs": ["4", "3", "1"], "notes": "NoteIn the first example Yuri can make up triangles with sides $$$(1, 3, 3)$$$, $$$(2, 2, 3)$$$, $$$(2, 3, 3)$$$ and $$$(2, 3, 4)$$$.In the second example Yuri can make up triangles with sides $$$(1, 2, 2)$$$, $$$(2, 2, 2)$$$ and $$$(2, 2, 3)$$$.In the third example Yuri can make up only one equilateral triangle with sides equal to $$$5 \\cdot 10^5$$$."}, "src_uid": "4f92791b9ec658829f667fcea1faee01"}
{"nl": {"description": "Let's consider equation:x2 + s(x)·x - n = 0,  where x, n are positive integers, s(x) is the function, equal to the sum of digits of number x in the decimal number system.You are given an integer n, find the smallest positive integer root of equation x, or else determine that there are no such roots.", "input_spec": "A single line contains integer n (1 ≤ n ≤ 1018) — the equation parameter. Please, do not use the %lld specifier to read or write 64-bit integers in С++. It is preferred to use cin, cout streams or the %I64d specifier. ", "output_spec": "Print -1, if the equation doesn't have integer positive roots. Otherwise print such smallest integer x (x > 0), that the equation given in the statement holds.", "sample_inputs": ["2", "110", "4"], "sample_outputs": ["1", "10", "-1"], "notes": "NoteIn the first test case x = 1 is the minimum root. As s(1) = 1 and 12 + 1·1 - 2 = 0.In the second test case x = 10 is the minimum root. As s(10) = 1 + 0 = 1 and 102 + 1·10 - 110 = 0.In the third test case the equation has no roots."}, "src_uid": "e1070ad4383f27399d31b8d0e87def59"}
{"nl": {"description": "Finished her homework, Nastya decided to play computer games. Passing levels one by one, Nastya eventually faced a problem. Her mission is to leave a room, where a lot of monsters live, as quickly as possible.There are $$$n$$$ manholes in the room which are situated on one line, but, unfortunately, all the manholes are closed, and there is one stone on every manhole. There is exactly one coin under every manhole, and to win the game Nastya should pick all the coins. Initially Nastya stands near the $$$k$$$-th manhole from the left. She is thinking what to do.In one turn, Nastya can do one of the following:   if there is at least one stone on the manhole Nastya stands near, throw exactly one stone from it onto any other manhole (yes, Nastya is strong).  go to a neighboring manhole;  if there are no stones on the manhole Nastya stays near, she can open it and pick the coin from it. After it she must close the manhole immediately (it doesn't require additional moves).     The figure shows the intermediate state of the game. At the current position Nastya can throw the stone to any other manhole or move left or right to the neighboring manholes. If she were near the leftmost manhole, she could open it (since there are no stones on it). Nastya can leave the room when she picks all the coins. Monsters are everywhere, so you need to compute the minimum number of moves Nastya has to make to pick all the coins.Note one time more that Nastya can open a manhole only when there are no stones onto it.", "input_spec": "The first and only line contains two integers $$$n$$$ and $$$k$$$, separated by space ($$$2 \\leq n \\leq 5000$$$, $$$1 \\leq k \\leq n$$$) — the number of manholes and the index of manhole from the left, near which Nastya stays initially. Initially there is exactly one stone near each of the $$$n$$$ manholes. ", "output_spec": "Print a single integer — minimum number of moves which lead Nastya to pick all the coins.", "sample_inputs": ["2 2", "4 2", "5 1"], "sample_outputs": ["6", "13", "15"], "notes": "NoteLet's consider the example where $$$n = 2$$$, $$$k = 2$$$. Nastya should play as follows:  At first she throws the stone from the second manhole to the first. Now there are two stones on the first manhole.  Then she opens the second manhole and pick the coin from it.  Then she goes to the first manhole, throws two stones by two moves to the second manhole and then opens the manhole and picks the coin from it. So, $$$6$$$ moves are required to win."}, "src_uid": "24b02afe8d86314ec5f75a00c72af514"}
{"nl": {"description": "Recently Vasya found a golden ticket — a sequence which consists of $$$n$$$ digits $$$a_1a_2\\dots a_n$$$. Vasya considers a ticket to be lucky if it can be divided into two or more non-intersecting segments with equal sums. For example, ticket $$$350178$$$ is lucky since it can be divided into three segments $$$350$$$, $$$17$$$ and $$$8$$$: $$$3+5+0=1+7=8$$$. Note that each digit of sequence should belong to exactly one segment.Help Vasya! Tell him if the golden ticket he found is lucky or not.", "input_spec": "The first line contains one integer $$$n$$$ ($$$2 \\le n \\le 100$$$) — the number of digits in the ticket. The second line contains $$$n$$$ digits $$$a_1 a_2 \\dots a_n$$$ ($$$0 \\le a_i \\le 9$$$) — the golden ticket. Digits are printed without spaces.", "output_spec": "If the golden ticket is lucky then print \"YES\", otherwise print \"NO\" (both case insensitive).", "sample_inputs": ["5\n73452", "4\n1248"], "sample_outputs": ["YES", "NO"], "notes": "NoteIn the first example the ticket can be divided into $$$7$$$, $$$34$$$ and $$$52$$$: $$$7=3+4=5+2$$$.In the second example it is impossible to divide ticket into segments with equal sum."}, "src_uid": "410296a01b97a0a39b6683569c84d56c"}
{"nl": {"description": "Mike has a frog and a flower. His frog is named Xaniar and his flower is named Abol. Initially(at time 0), height of Xaniar is h1 and height of Abol is h2. Each second, Mike waters Abol and Xaniar.  So, if height of Xaniar is h1 and height of Abol is h2, after one second height of Xaniar will become  and height of Abol will become  where x1, y1, x2 and y2 are some integer numbers and  denotes the remainder of a modulo b.Mike is a competitive programmer fan. He wants to know the minimum time it takes until height of Xania is a1 and height of Abol is a2.Mike has asked you for your help. Calculate the minimum time or say it will never happen.", "input_spec": "The first line of input contains integer m (2 ≤ m ≤ 106). The second line of input contains integers h1 and a1 (0 ≤ h1, a1 < m). The third line of input contains integers x1 and y1 (0 ≤ x1, y1 < m). The fourth line of input contains integers h2 and a2 (0 ≤ h2, a2 < m). The fifth line of input contains integers x2 and y2 (0 ≤ x2, y2 < m). It is guaranteed that h1 ≠ a1 and h2 ≠ a2.", "output_spec": "Print the minimum number of seconds until Xaniar reaches height a1 and Abol reaches height a2 or print -1 otherwise.", "sample_inputs": ["5\n4 2\n1 1\n0 1\n2 3", "1023\n1 2\n1 0\n1 2\n1 1"], "sample_outputs": ["3", "-1"], "notes": "NoteIn the first sample, heights sequences are following:Xaniar: Abol: "}, "src_uid": "7225266f663699ff7e16b726cadfe9ee"}
{"nl": {"description": "Bear Limak likes watching sports on TV. He is going to watch a game today. The game lasts 90 minutes and there are no breaks.Each minute can be either interesting or boring. If 15 consecutive minutes are boring then Limak immediately turns TV off.You know that there will be n interesting minutes t1, t2, ..., tn. Your task is to calculate for how many minutes Limak will watch the game.", "input_spec": "The first line of the input contains one integer n (1 ≤ n ≤ 90) — the number of interesting minutes. The second line contains n integers t1, t2, ..., tn (1 ≤ t1 < t2 < ... tn ≤ 90), given in the increasing order.", "output_spec": "Print the number of minutes Limak will watch the game.", "sample_inputs": ["3\n7 20 88", "9\n16 20 30 40 50 60 70 80 90", "9\n15 20 30 40 50 60 70 80 90"], "sample_outputs": ["35", "15", "90"], "notes": "NoteIn the first sample, minutes 21, 22, ..., 35 are all boring and thus Limak will turn TV off immediately after the 35-th minute. So, he would watch the game for 35 minutes.In the second sample, the first 15 minutes are boring.In the third sample, there are no consecutive 15 boring minutes. So, Limak will watch the whole game."}, "src_uid": "5031b15e220f0ff6cc1dd3731ecdbf27"}
{"nl": {"description": " — Thanks a lot for today.— I experienced so many great things.— You gave me memories like dreams... But I have to leave now...— One last request, can you...— Help me solve a Codeforces problem?— ......— What?Chtholly has been thinking about a problem for days:If a number is palindrome and length of its decimal representation without leading zeros is even, we call it a zcy number. A number is palindrome means when written in decimal representation, it contains no leading zeros and reads the same forwards and backwards. For example 12321 and 1221 are palindromes and 123 and 12451 are not. Moreover, 1221 is zcy number and 12321 is not.Given integers k and p, calculate the sum of the k smallest zcy numbers and output this sum modulo p.Unfortunately, Willem isn't good at solving this kind of problems, so he asks you for help!", "input_spec": "The first line contains two integers k and p (1 ≤ k ≤ 105, 1 ≤ p ≤ 109).", "output_spec": "Output single integer — answer to the problem.", "sample_inputs": ["2 100", "5 30"], "sample_outputs": ["33", "15"], "notes": "NoteIn the first example, the smallest zcy number is 11, and the second smallest zcy number is 22.In the second example, ."}, "src_uid": "00e90909a77ce9e22bb7cbf1285b0609"}
{"nl": {"description": "Kirill plays a new computer game. He came to the potion store where he can buy any potion. Each potion is characterized by two integers — amount of experience and cost. The efficiency of a potion is the ratio of the amount of experience to the cost. Efficiency may be a non-integer number.For each two integer numbers a and b such that l ≤ a ≤ r and x ≤ b ≤ y there is a potion with experience a and cost b in the store (that is, there are (r - l + 1)·(y - x + 1) potions).Kirill wants to buy a potion which has efficiency k. Will he be able to do this?", "input_spec": "First string contains five integer numbers l, r, x, y, k (1 ≤ l ≤ r ≤ 107, 1 ≤ x ≤ y ≤ 107, 1 ≤ k ≤ 107).", "output_spec": "Print \"YES\" without quotes if a potion with efficiency exactly k can be bought in the store and \"NO\" without quotes otherwise. You can output each of the letters in any register.", "sample_inputs": ["1 10 1 10 1", "1 5 6 10 1"], "sample_outputs": ["YES", "NO"], "notes": null}, "src_uid": "1110d3671e9f77fd8d66dca6e74d2048"}
{"nl": {"description": "There are $$$n$$$ candy boxes in front of Tania. The boxes are arranged in a row from left to right, numbered from $$$1$$$ to $$$n$$$. The $$$i$$$-th box contains $$$r_i$$$ candies, candies have the color $$$c_i$$$ (the color can take one of three values ​​— red, green, or blue). All candies inside a single box have the same color (and it is equal to $$$c_i$$$).Initially, Tanya is next to the box number $$$s$$$. Tanya can move to the neighbor box (that is, with a number that differs by one) or eat candies in the current box. Tanya eats candies instantly, but the movement takes one second.If Tanya eats candies from the box, then the box itself remains in place, but there is no more candies in it. In other words, Tanya always eats all the candies from the box and candies in the boxes are not refilled.It is known that Tanya cannot eat candies of the same color one after another (that is, the colors of candies in two consecutive boxes from which she eats candies are always different). In addition, Tanya's appetite is constantly growing, so in each next box from which she eats candies, there should be strictly more candies than in the previous one.Note that for the first box from which Tanya will eat candies, there are no restrictions on the color and number of candies.Tanya wants to eat at least $$$k$$$ candies. What is the minimum number of seconds she will need? Remember that she eats candies instantly, and time is spent only on movements.", "input_spec": "The first line contains three integers $$$n$$$, $$$s$$$ and $$$k$$$ ($$$1 \\le n \\le 50$$$, $$$1 \\le s \\le n$$$, $$$1 \\le k \\le 2000$$$) — number of the boxes, initial position of Tanya and lower bound on number of candies to eat. The following line contains $$$n$$$ integers $$$r_i$$$ ($$$1 \\le r_i \\le 50$$$) — numbers of candies in the boxes. The third line contains sequence of $$$n$$$ letters 'R', 'G' and 'B', meaning the colors of candies in the correspondent boxes ('R' for red, 'G' for green, 'B' for blue). Recall that each box contains candies of only one color. The third line contains no spaces.", "output_spec": "Print minimal number of seconds to eat at least $$$k$$$ candies. If solution doesn't exist, print \"-1\".", "sample_inputs": ["5 3 10\n1 2 3 4 5\nRGBRR", "2 1 15\n5 6\nRG"], "sample_outputs": ["4", "-1"], "notes": "NoteThe sequence of actions of Tanya for the first example:  move from the box $$$3$$$ to the box $$$2$$$;  eat candies from the box $$$2$$$;  move from the box $$$2$$$ to the box $$$3$$$;  eat candy from the box $$$3$$$;  move from the box $$$3$$$ to the box $$$4$$$;  move from the box $$$4$$$ to the box $$$5$$$;  eat candies from the box $$$5$$$. Since Tanya eats candy instantly, the required time is four seconds."}, "src_uid": "a95e54a7e38cc0d61b39e4a01a6f8d3f"}
{"nl": {"description": "At the beginning of the school year Berland State University starts two city school programming groups, for beginners and for intermediate coders. The children were tested in order to sort them into groups. According to the results, each student got some score from 1 to m points. We know that c1 schoolchildren got 1 point, c2 children got 2 points, ..., cm children got m points. Now you need to set the passing rate k (integer from 1 to m): all schoolchildren who got less than k points go to the beginner group and those who get at strictly least k points go to the intermediate group. We know that if the size of a group is more than y, then the university won't find a room for them. We also know that if a group has less than x schoolchildren, then it is too small and there's no point in having classes with it. So, you need to split all schoolchildren into two groups so that the size of each group was from x to y, inclusive. Help the university pick the passing rate in a way that meets these requirements.", "input_spec": "The first line contains integer m (2 ≤ m ≤ 100). The second line contains m integers c1, c2, ..., cm, separated by single spaces (0 ≤ ci ≤ 100). The third line contains two space-separated integers x and y (1 ≤ x ≤ y ≤ 10000). At least one ci is greater than 0.", "output_spec": "If it is impossible to pick a passing rate in a way that makes the size of each resulting groups at least x and at most y, print 0. Otherwise, print an integer from 1 to m — the passing rate you'd like to suggest. If there are multiple possible answers, print any of them.", "sample_inputs": ["5\n3 4 3 2 1\n6 8", "5\n0 3 3 4 2\n3 10", "2\n2 5\n3 6"], "sample_outputs": ["3", "4", "0"], "notes": "NoteIn the first sample the beginner group has 7 students, the intermediate group has 6 of them. In the second sample another correct answer is 3."}, "src_uid": "e595a1d0c0e4bbcc99454d3148b4557b"}
{"nl": {"description": "Little Johnny has recently learned about set theory. Now he is studying binary relations. You've probably heard the term \"equivalence relation\". These relations are very important in many areas of mathematics. For example, the equality of the two numbers is an equivalence relation.A set ρ of pairs (a, b) of elements of some set A is called a binary relation on set A. For two elements a and b of the set A we say that they are in relation ρ, if pair , in this case we use a notation .Binary relation is equivalence relation, if: It is reflexive (for any a it is true that ); It is symmetric (for any a, b it is true that if , then ); It is transitive (if  and , than ).Little Johnny is not completely a fool and he noticed that the first condition is not necessary! Here is his \"proof\":Take any two elements, a and b. If , then  (according to property (2)), which means  (according to property (3)).It's very simple, isn't it? However, you noticed that Johnny's \"proof\" is wrong, and decided to show him a lot of examples that prove him wrong.Here's your task: count the number of binary relations over a set of size n such that they are symmetric, transitive, but not an equivalence relations (i.e. they are not reflexive).Since their number may be very large (not 0, according to Little Johnny), print the remainder of integer division of this number by 109 + 7.", "input_spec": "A single line contains a single integer n (1 ≤ n ≤ 4000).", "output_spec": "In a single line print the answer to the problem modulo 109 + 7.", "sample_inputs": ["1", "2", "3"], "sample_outputs": ["1", "3", "10"], "notes": "NoteIf n = 1 there is only one such relation — an empty one, i.e. . In other words, for a single element x of set A the following is hold: .If n = 2 there are three such relations. Let's assume that set A consists of two elements, x and y. Then the valid relations are , ρ = {(x, x)}, ρ = {(y, y)}. It is easy to see that the three listed binary relations are symmetric and transitive relations, but they are not equivalence relations."}, "src_uid": "aa2c3e94a44053a0d86f61da06681023"}
{"nl": {"description": "Alex enjoys performing magic tricks. He has a trick that requires a deck of n cards. He has m identical decks of n different cards each, which have been mixed together. When Alex wishes to perform the trick, he grabs n cards at random and performs the trick with those. The resulting deck looks like a normal deck, but may have duplicates of some cards.The trick itself is performed as follows: first Alex allows you to choose a random card from the deck. You memorize the card and put it back in the deck. Then Alex shuffles the deck, and pulls out a card. If the card matches the one you memorized, the trick is successful.You don't think Alex is a very good magician, and that he just pulls a card randomly from the deck. Determine the probability of the trick being successful if this is the case.", "input_spec": "First line of the input consists of two integers n and m (1 ≤ n, m ≤ 1000), separated by space — number of cards in each deck, and number of decks.", "output_spec": "On the only line of the output print one floating point number – probability of Alex successfully performing the trick. Relative or absolute error of your answer should not be higher than 10 - 6.", "sample_inputs": ["2 2", "4 4", "1 2"], "sample_outputs": ["0.6666666666666666", "0.4000000000000000", "1.0000000000000000"], "notes": "NoteIn the first sample, with probability  Alex will perform the trick with two cards with the same value from two different decks. In this case the trick is guaranteed to succeed.With the remaining  probability he took two different cards, and the probability of pulling off the trick is .The resulting probability is "}, "src_uid": "0b9ce20c36e53d4702869660cbb53317"}
{"nl": {"description": "The only difference between easy and hard versions is the number of elements in the array.You are given an array $$$a$$$ consisting of $$$n$$$ integers. In one move you can choose any $$$a_i$$$ and divide it by $$$2$$$ rounding down (in other words, in one move you can set $$$a_i := \\lfloor\\frac{a_i}{2}\\rfloor$$$).You can perform such an operation any (possibly, zero) number of times with any $$$a_i$$$.Your task is to calculate the minimum possible number of operations required to obtain at least $$$k$$$ equal numbers in the array.Don't forget that it is possible to have $$$a_i = 0$$$ after some operations, thus the answer always exists.", "input_spec": "The first line of the input contains two integers $$$n$$$ and $$$k$$$ ($$$1 \\le k \\le n \\le 50$$$) — the number of elements in the array and the number of equal numbers required. The second line of the input contains $$$n$$$ integers $$$a_1, a_2, \\dots, a_n$$$ ($$$1 \\le a_i \\le 2 \\cdot 10^5$$$), where $$$a_i$$$ is the $$$i$$$-th element of $$$a$$$.", "output_spec": "Print one integer — the minimum possible number of operations required to obtain at least $$$k$$$ equal numbers in the array.", "sample_inputs": ["5 3\n1 2 2 4 5", "5 3\n1 2 3 4 5", "5 3\n1 2 3 3 3"], "sample_outputs": ["1", "2", "0"], "notes": null}, "src_uid": "ed1a2ae733121af6486568e528fe2d84"}
{"nl": {"description": "Ivan has number $$$b$$$. He is sorting through the numbers $$$a$$$ from $$$1$$$ to $$$10^{18}$$$, and for every $$$a$$$ writes $$$\\frac{[a, \\,\\, b]}{a}$$$ on blackboard. Here $$$[a, \\,\\, b]$$$ stands for least common multiple of $$$a$$$ and $$$b$$$. Ivan is very lazy, that's why this task bored him soon. But he is interested in how many different numbers he would write on the board if he would finish the task. Help him to find the quantity of different numbers he would write on the board.", "input_spec": "The only line contains one integer — $$$b$$$ $$$(1 \\le b \\le 10^{10})$$$.", "output_spec": "Print one number — answer for the problem.", "sample_inputs": ["1", "2"], "sample_outputs": ["1", "2"], "notes": "NoteIn the first example $$$[a, \\,\\, 1] = a$$$, therefore $$$\\frac{[a, \\,\\, b]}{a}$$$ is always equal to $$$1$$$.In the second example $$$[a, \\,\\, 2]$$$ can be equal to $$$a$$$ or $$$2 \\cdot a$$$ depending on parity of $$$a$$$. $$$\\frac{[a, \\,\\, b]}{a}$$$ can be equal to $$$1$$$ and $$$2$$$."}, "src_uid": "7fc9e7d7e25ab97d8ebc10ed8ae38fd1"}
{"nl": {"description": "You are given two bracket sequences (not necessarily regular) $$$s$$$ and $$$t$$$ consisting only of characters '(' and ')'. You want to construct the shortest regular bracket sequence that contains both given bracket sequences as subsequences (not necessarily contiguous).Recall what is the regular bracket sequence:  () is the regular bracket sequence;  if $$$S$$$ is the regular bracket sequence, then ($$$S$$$) is a regular bracket sequence;  if $$$S$$$ and $$$T$$$ regular bracket sequences, then $$$ST$$$ (concatenation of $$$S$$$ and $$$T$$$) is a regular bracket sequence. Recall that the subsequence of the string $$$s$$$ is such string $$$t$$$ that can be obtained from $$$s$$$ by removing some (possibly, zero) amount of characters. For example, \"coder\", \"force\", \"cf\" and \"cores\" are subsequences of \"codeforces\", but \"fed\" and \"z\" are not.", "input_spec": "The first line of the input contains one bracket sequence $$$s$$$ consisting of no more than $$$200$$$ characters '(' and ')'. The second line of the input contains one bracket sequence $$$t$$$ consisting of no more than $$$200$$$ characters '(' and ')'.", "output_spec": "Print one line — the shortest regular bracket sequence that contains both given bracket sequences as subsequences (not necessarily contiguous). If there are several answers, you can print any.", "sample_inputs": ["(())(()\n()))()", ")\n((", ")\n)))", "())\n(()(()(()("], "sample_outputs": ["(())()()", "(())", "((()))", "(()()()(()()))"], "notes": null}, "src_uid": "cc222aab45b3ad3d0e71227592c883f1"}
{"nl": {"description": "Vitaly is a very weird man. He's got two favorite digits a and b. Vitaly calls a positive integer good, if the decimal representation of this integer only contains digits a and b. Vitaly calls a good number excellent, if the sum of its digits is a good number.For example, let's say that Vitaly's favourite digits are 1 and 3, then number 12 isn't good and numbers 13 or 311 are. Also, number 111 is excellent and number 11 isn't. Now Vitaly is wondering, how many excellent numbers of length exactly n are there. As this number can be rather large, he asks you to count the remainder after dividing it by 1000000007 (109 + 7).A number's length is the number of digits in its decimal representation without leading zeroes.", "input_spec": "The first line contains three integers: a, b, n (1 ≤ a < b ≤ 9, 1 ≤ n ≤ 106).", "output_spec": "Print a single integer — the answer to the problem modulo 1000000007 (109 + 7).", "sample_inputs": ["1 3 3", "2 3 10"], "sample_outputs": ["1", "165"], "notes": null}, "src_uid": "d3e3da5b6ba37c8ac5f22b18c140ce81"}
{"nl": {"description": "After Fox Ciel won an onsite round of a programming contest, she took a bus to return to her castle. The fee of the bus was 220 yen. She met Rabbit Hanako in the bus. They decided to play the following game because they got bored in the bus.  Initially, there is a pile that contains x 100-yen coins and y 10-yen coins.  They take turns alternatively. Ciel takes the first turn.  In each turn, they must take exactly 220 yen from the pile. In Ciel's turn, if there are multiple ways to take 220 yen, she will choose the way that contains the maximal number of 100-yen coins. In Hanako's turn, if there are multiple ways to take 220 yen, she will choose the way that contains the maximal number of 10-yen coins.  If Ciel or Hanako can't take exactly 220 yen from the pile, she loses.  Determine the winner of the game.", "input_spec": "The first line contains two integers x (0 ≤ x ≤ 106) and y (0 ≤ y ≤ 106), separated by a single space.", "output_spec": "If Ciel wins, print \"Ciel\". Otherwise, print \"Hanako\".", "sample_inputs": ["2 2", "3 22"], "sample_outputs": ["Ciel", "Hanako"], "notes": "NoteIn the first turn (Ciel's turn), she will choose 2 100-yen coins and 2 10-yen coins. In the second turn (Hanako's turn), she will choose 1 100-yen coin and 12 10-yen coins. In the third turn (Ciel's turn), she can't pay exactly 220 yen, so Ciel will lose."}, "src_uid": "8ffee18bbc4bb281027f91193002b7f5"}
{"nl": {"description": "Petya likes horse racing very much. Horses numbered from l to r take part in the races. Petya wants to evaluate the probability of victory; for some reason, to do that he needs to know the amount of nearly lucky horses' numbers. A nearly lucky number is an integer number that has at least two lucky digits the distance between which does not exceed k. Petya learned from some of his mates from Lviv that lucky digits are digits 4 and 7. The distance between the digits is the absolute difference between their positions in the number of a horse. For example, if k = 2, then numbers 412395497, 404, 4070400000070004007 are nearly lucky and numbers 4, 4123954997, 4007000040070004007 are not.Petya prepared t intervals [li, ri] and invented number k, common for all of them. Your task is to find how many nearly happy numbers there are in each of these segments. Since the answers can be quite large, output them modulo 1000000007 (109 + 7).", "input_spec": "The first line contains two integers t and k (1 ≤ t, k ≤ 1000) — the number of segments and the distance between the numbers correspondingly. Next t lines contain pairs of integers li and ri (1 ≤ l ≤ r ≤ 101000). All numbers are given without the leading zeroes. Numbers in each line are separated by exactly one space character.", "output_spec": "Output t lines. In each line print one integer — the answer for the corresponding segment modulo 1000000007 (109 + 7).", "sample_inputs": ["1 2\n1 100", "1 2\n70 77", "2 1\n1 20\n80 100"], "sample_outputs": ["4", "2", "0\n0"], "notes": "NoteIn the first sample, the four nearly lucky numbers are 44, 47, 74, 77.In the second sample, only 74 and 77 are in the given segment."}, "src_uid": "5517efa2fc9362fdf342d32adac889f4"}
{"nl": {"description": "Buses run between the cities A and B, the first one is at 05:00 AM and the last one departs not later than at 11:59 PM. A bus from the city A departs every a minutes and arrives to the city B in a ta minutes, and a bus from the city B departs every b minutes and arrives to the city A in a tb minutes.The driver Simion wants to make his job diverse, so he counts the buses going towards him. Simion doesn't count the buses he meet at the start and finish.You know the time when Simion departed from the city A to the city B. Calculate the number of buses Simion will meet to be sure in his counting.", "input_spec": "The first line contains two integers a, ta (1 ≤ a, ta ≤ 120) — the frequency of the buses from the city A to the city B and the travel time. Both values are given in minutes. The second line contains two integers b, tb (1 ≤ b, tb ≤ 120) — the frequency of the buses from the city B to the city A and the travel time. Both values are given in minutes. The last line contains the departure time of Simion from the city A in the format hh:mm. It is guaranteed that there are a bus from the city A at that time. Note that the hours and the minutes are given with exactly two digits.", "output_spec": "Print the only integer z — the number of buses Simion will meet on the way. Note that you should not count the encounters in cities A and B.", "sample_inputs": ["10 30\n10 35\n05:20", "60 120\n24 100\n13:00"], "sample_outputs": ["5", "9"], "notes": "NoteIn the first example Simion departs form the city A at 05:20 AM and arrives to the city B at 05:50 AM. He will meet the first 5 buses from the city B that departed in the period [05:00 AM - 05:40 AM]. Also Simion will meet a bus in the city B at 05:50 AM, but he will not count it.Also note that the first encounter will be between 05:26 AM and 05:27 AM (if we suggest that the buses are go with the sustained speed)."}, "src_uid": "1c4cf1c3cb464a483511a8a61f8685a7"}
{"nl": {"description": "Two boys decided to compete in text typing on the site \"Key races\". During the competition, they have to type a text consisting of s characters. The first participant types one character in v1 milliseconds and has ping t1 milliseconds. The second participant types one character in v2 milliseconds and has ping t2 milliseconds.If connection ping (delay) is t milliseconds, the competition passes for a participant as follows:   Exactly after t milliseconds after the start of the competition the participant receives the text to be entered.  Right after that he starts to type it.  Exactly t milliseconds after he ends typing all the text, the site receives information about it. The winner is the participant whose information on the success comes earlier. If the information comes from both participants at the same time, it is considered that there is a draw.Given the length of the text and the information about participants, determine the result of the game.", "input_spec": "The first line contains five integers s, v1, v2, t1, t2 (1 ≤ s, v1, v2, t1, t2 ≤ 1000) — the number of characters in the text, the time of typing one character for the first participant, the time of typing one character for the the second participant, the ping of the first participant and the ping of the second participant.", "output_spec": "If the first participant wins, print \"First\". If the second participant wins, print \"Second\". In case of a draw print \"Friendship\".", "sample_inputs": ["5 1 2 1 2", "3 3 1 1 1", "4 5 3 1 5"], "sample_outputs": ["First", "Second", "Friendship"], "notes": "NoteIn the first example, information on the success of the first participant comes in 7 milliseconds, of the second participant — in 14 milliseconds. So, the first wins.In the second example, information on the success of the first participant comes in 11 milliseconds, of the second participant — in 5 milliseconds. So, the second wins.In the third example, information on the success of the first participant comes in 22 milliseconds, of the second participant — in 22 milliseconds. So, it is be a draw."}, "src_uid": "10226b8efe9e3c473239d747b911a1ef"}
{"nl": {"description": "Each of you probably has your personal experience of riding public transportation and buying tickets. After a person buys a ticket (which traditionally has an even number of digits), he usually checks whether the ticket is lucky. Let us remind you that a ticket is lucky if the sum of digits in its first half matches the sum of digits in its second half.But of course, not every ticket can be lucky. Far from it! Moreover, sometimes one look at a ticket can be enough to say right away that the ticket is not lucky. So, let's consider the following unluckiness criterion that can definitely determine an unlucky ticket. We'll say that a ticket is definitely unlucky if each digit from the first half corresponds to some digit from the second half so that each digit from the first half is strictly less than the corresponding digit from the second one or each digit from the first half is strictly more than the corresponding digit from the second one. Each digit should be used exactly once in the comparisons. In other words, there is such bijective correspondence between the digits of the first and the second half of the ticket, that either each digit of the first half turns out strictly less than the corresponding digit of the second half or each digit of the first half turns out strictly more than the corresponding digit from the second half.For example, ticket 2421 meets the following unluckiness criterion and will not be considered lucky (the sought correspondence is 2 > 1 and 4 > 2), ticket 0135 also meets the criterion (the sought correspondence is 0 < 3 and 1 < 5), and ticket 3754 does not meet the criterion. You have a ticket in your hands, it contains 2n digits. Your task is to check whether it meets the unluckiness criterion.", "input_spec": "The first line contains an integer n (1 ≤ n ≤ 100). The second line contains a string that consists of 2n digits and defines your ticket.", "output_spec": "In the first line print \"YES\" if the ticket meets the unluckiness criterion. Otherwise, print \"NO\" (without the quotes).", "sample_inputs": ["2\n2421", "2\n0135", "2\n3754"], "sample_outputs": ["YES", "YES", "NO"], "notes": null}, "src_uid": "e4419bca9d605dbd63f7884377e28769"}
{"nl": {"description": "\"Contestant who earns a score equal to or greater than the k-th place finisher's score will advance to the next round, as long as the contestant earns a positive score...\" — an excerpt from contest rules.A total of n participants took part in the contest (n ≥ k), and you already know their scores. Calculate how many participants will advance to the next round.", "input_spec": "The first line of the input contains two integers n and k (1 ≤ k ≤ n ≤ 50) separated by a single space. The second line contains n space-separated integers a1, a2, ..., an (0 ≤ ai ≤ 100), where ai is the score earned by the participant who got the i-th place. The given sequence is non-increasing (that is, for all i from 1 to n - 1 the following condition is fulfilled: ai ≥ ai + 1).", "output_spec": "Output the number of participants who advance to the next round.", "sample_inputs": ["8 5\n10 9 8 7 7 7 5 5", "4 2\n0 0 0 0"], "sample_outputs": ["6", "0"], "notes": "NoteIn the first example the participant on the 5th place earned 7 points. As the participant on the 6th place also earned 7 points, there are 6 advancers.In the second example nobody got a positive score."}, "src_uid": "193ec1226ffe07522caf63e84a7d007f"}
{"nl": {"description": "Not so long ago company R2 bought company R1 and consequently, all its developments in the field of multicore processors. Now the R2 laboratory is testing one of the R1 processors.The testing goes in n steps, at each step the processor gets some instructions, and then its temperature is measured. The head engineer in R2 is keeping a report record on the work of the processor: he writes down the minimum and the maximum measured temperature in his notebook. His assistant had to write down all temperatures into his notebook, but (for unknown reasons) he recorded only m.The next day, the engineer's assistant filed in a report with all the m temperatures. However, the chief engineer doubts that the assistant wrote down everything correctly (naturally, the chief engineer doesn't doubt his notes). So he asked you to help him. Given numbers n, m, min, max and the list of m temperatures determine whether you can upgrade the set of m temperatures to the set of n temperatures (that is add n - m temperatures), so that the minimum temperature was min and the maximum one was max.", "input_spec": "The first line contains four integers n, m, min, max (1 ≤ m < n ≤ 100; 1 ≤ min < max ≤ 100). The second line contains m space-separated integers ti (1 ≤ ti ≤ 100) — the temperatures reported by the assistant. Note, that the reported temperatures, and the temperatures you want to add can contain equal temperatures.", "output_spec": "If the data is consistent, print 'Correct' (without the quotes). Otherwise, print 'Incorrect' (without the quotes).", "sample_inputs": ["2 1 1 2\n1", "3 1 1 3\n2", "2 1 1 3\n2"], "sample_outputs": ["Correct", "Correct", "Incorrect"], "notes": "NoteIn the first test sample one of the possible initial configurations of temperatures is [1, 2].In the second test sample one of the possible initial configurations of temperatures is [2, 1, 3].In the third test sample it is impossible to add one temperature to obtain the minimum equal to 1 and the maximum equal to 3."}, "src_uid": "99f9cdc85010bd89434f39b78f15b65e"}
{"nl": {"description": "A large banner with word CODEFORCES was ordered for the 1000-th onsite round of Codeforcesω that takes place on the Miami beach. Unfortunately, the company that made the banner mixed up two orders and delivered somebody else's banner that contains someone else's word. The word on the banner consists only of upper-case English letters.There is very little time to correct the mistake. All that we can manage to do is to cut out some substring from the banner, i.e. several consecutive letters. After that all the resulting parts of the banner will be glued into a single piece (if the beginning or the end of the original banner was cut out, only one part remains); it is not allowed change the relative order of parts of the banner (i.e. after a substring is cut, several first and last letters are left, it is allowed only to glue the last letters to the right of the first letters). Thus, for example, for example, you can cut a substring out from string 'TEMPLATE' and get string 'TEMPLE' (if you cut out string AT), 'PLATE' (if you cut out TEM), 'T' (if you cut out EMPLATE), etc.Help the organizers of the round determine whether it is possible to cut out of the banner some substring in such a way that the remaining parts formed word CODEFORCES.", "input_spec": "The single line of the input contains the word written on the banner. The word only consists of upper-case English letters. The word is non-empty and its length doesn't exceed 100 characters. It is guaranteed that the word isn't word CODEFORCES.", "output_spec": "Print 'YES', if there exists a way to cut out the substring, and 'NO' otherwise (without the quotes).", "sample_inputs": ["CODEWAITFORITFORCES", "BOTTOMCODER", "DECODEFORCES", "DOGEFORCES"], "sample_outputs": ["YES", "NO", "YES", "NO"], "notes": null}, "src_uid": "bda4b15827c94b526643dfefc4bc36e7"}
{"nl": {"description": "Overlooking the captivating blend of myriads of vernal hues, Arkady the painter lays out a long, long canvas.Arkady has a sufficiently large amount of paint of three colours: cyan, magenta, and yellow. On the one-dimensional canvas split into n consecutive segments, each segment needs to be painted in one of the colours.Arkady has already painted some (possibly none or all) segments and passes the paintbrush to you. You are to determine whether there are at least two ways of colouring all the unpainted segments so that no two adjacent segments are of the same colour. Two ways are considered different if and only if a segment is painted in different colours in them.", "input_spec": "The first line contains a single positive integer n (1 ≤ n ≤ 100) — the length of the canvas. The second line contains a string s of n characters, the i-th of which is either 'C' (denoting a segment painted in cyan), 'M' (denoting one painted in magenta), 'Y' (one painted in yellow), or '?' (an unpainted one).", "output_spec": "If there are at least two different ways of painting, output \"Yes\"; otherwise output \"No\" (both without quotes). You can print each character in any case (upper or lower).", "sample_inputs": ["5\nCY??Y", "5\nC?C?Y", "5\n?CYC?", "5\nC??MM", "3\nMMY"], "sample_outputs": ["Yes", "Yes", "Yes", "No", "No"], "notes": "NoteFor the first example, there are exactly two different ways of colouring: CYCMY and CYMCY.For the second example, there are also exactly two different ways of colouring: CMCMY and CYCMY.For the third example, there are four ways of colouring: MCYCM, MCYCY, YCYCM, and YCYCY.For the fourth example, no matter how the unpainted segments are coloured, the existing magenta segments will prevent the painting from satisfying the requirements. The similar is true for the fifth example."}, "src_uid": "f8adfa0dde7ac1363f269dbdf00212c3"}
{"nl": {"description": "Dwarfs have planted a very interesting plant, which is a triangle directed \"upwards\". This plant has an amusing feature. After one year a triangle plant directed \"upwards\" divides into four triangle plants: three of them will point \"upwards\" and one will point \"downwards\". After another year, each triangle plant divides into four triangle plants: three of them will be directed in the same direction as the parent plant, and one of them will be directed in the opposite direction. Then each year the process repeats. The figure below illustrates this process.  Help the dwarfs find out how many triangle plants that point \"upwards\" will be in n years.", "input_spec": "The first line contains a single integer n (0 ≤ n ≤ 1018) — the number of full years when the plant grew. Please do not use the %lld specifier to read or write 64-bit integers in С++. It is preferred to use cin, cout streams or the %I64d specifier.", "output_spec": "Print a single integer — the remainder of dividing the number of plants that will point \"upwards\" in n years by 1000000007 (109 + 7).", "sample_inputs": ["1", "2"], "sample_outputs": ["3", "10"], "notes": "NoteThe first test sample corresponds to the second triangle on the figure in the statement. The second test sample corresponds to the third one."}, "src_uid": "782b819eb0bfc86d6f96f15ac09d5085"}
{"nl": {"description": "Vasya likes everything infinite. Now he is studying the properties of a sequence s, such that its first element is equal to a (s1 = a), and the difference between any two neighbouring elements is equal to c (si - si - 1 = c). In particular, Vasya wonders if his favourite integer b appears in this sequence, that is, there exists a positive integer i, such that si = b. Of course, you are the person he asks for a help.", "input_spec": "The first line of the input contain three integers a, b and c ( - 109 ≤ a, b, c ≤ 109) — the first element of the sequence, Vasya's favorite number and the difference between any two neighbouring elements of the sequence, respectively.", "output_spec": "If b appears in the sequence s print \"YES\" (without quotes), otherwise print \"NO\" (without quotes).", "sample_inputs": ["1 7 3", "10 10 0", "1 -4 5", "0 60 50"], "sample_outputs": ["YES", "YES", "NO", "NO"], "notes": "NoteIn the first sample, the sequence starts from integers 1, 4, 7, so 7 is its element.In the second sample, the favorite integer of Vasya is equal to the first element of the sequence.In the third sample all elements of the sequence are greater than Vasya's favorite integer.In the fourth sample, the sequence starts from 0, 50, 100, and all the following elements are greater than Vasya's favorite integer."}, "src_uid": "9edf42c20ddf22a251b84553d7305a7d"}
{"nl": {"description": "You are given a non-negative integer n, its decimal representation consists of at most 100 digits and doesn't contain leading zeroes.Your task is to determine if it is possible in this case to remove some of the digits (possibly not remove any digit at all) so that the result contains at least one digit, forms a non-negative integer, doesn't have leading zeroes and is divisible by 8. After the removing, it is forbidden to rearrange the digits.If a solution exists, you should print it.", "input_spec": "The single line of the input contains a non-negative integer n. The representation of number n doesn't contain any leading zeroes and its length doesn't exceed 100 digits. ", "output_spec": "Print \"NO\" (without quotes), if there is no such way to remove some digits from number n.  Otherwise, print \"YES\" in the first line and the resulting number after removing digits from number n in the second line. The printed number must be divisible by 8. If there are multiple possible answers, you may print any of them.", "sample_inputs": ["3454", "10", "111111"], "sample_outputs": ["YES\n344", "YES\n0", "NO"], "notes": null}, "src_uid": "0a2a5927d24c70aca24fc17aa686499e"}
{"nl": {"description": "Consider the following equation:  where sign [a] represents the integer part of number a.Let's find all integer z (z > 0), for which this equation is unsolvable in positive integers. The phrase \"unsolvable in positive integers\" means that there are no such positive integers x and y (x, y > 0), for which the given above equation holds.Let's write out all such z in the increasing order: z1, z2, z3, and so on (zi < zi + 1). Your task is: given the number n, find the number zn.", "input_spec": "The first line contains a single integer n (1 ≤ n ≤ 40).", "output_spec": "Print a single integer — the number zn modulo 1000000007 (109 + 7). It is guaranteed that the answer exists.", "sample_inputs": ["1", "2", "3"], "sample_outputs": ["1", "3", "15"], "notes": null}, "src_uid": "c2cbc35012c6ff7ab0d6899e6015e4e7"}
{"nl": {"description": "This version of the problem differs from the next one only in the constraint on $$$n$$$.Note that the memory limit in this problem is lower than in others.You have a vertical strip with $$$n$$$ cells, numbered consecutively from $$$1$$$ to $$$n$$$ from top to bottom.You also have a token that is initially placed in cell $$$n$$$. You will move the token up until it arrives at cell $$$1$$$.Let the token be in cell $$$x > 1$$$ at some moment. One shift of the token can have either of the following kinds:   Subtraction: you choose an integer $$$y$$$ between $$$1$$$ and $$$x-1$$$, inclusive, and move the token from cell $$$x$$$ to cell $$$x - y$$$.  Floored division: you choose an integer $$$z$$$ between $$$2$$$ and $$$x$$$, inclusive, and move the token from cell $$$x$$$ to cell $$$\\lfloor \\frac{x}{z} \\rfloor$$$ ($$$x$$$ divided by $$$z$$$ rounded down). Find the number of ways to move the token from cell $$$n$$$ to cell $$$1$$$ using one or more shifts, and print it modulo $$$m$$$. Note that if there are several ways to move the token from one cell to another in one shift, all these ways are considered distinct (check example explanation for a better understanding).", "input_spec": "The only line contains two integers $$$n$$$ and $$$m$$$ ($$$2 \\le n \\le 2 \\cdot 10^5$$$; $$$10^8 < m < 10^9$$$; $$$m$$$ is a prime number) — the length of the strip and the modulo.", "output_spec": "Print the number of ways to move the token from cell $$$n$$$ to cell $$$1$$$, modulo $$$m$$$.", "sample_inputs": ["3 998244353", "5 998244353", "42 998244353"], "sample_outputs": ["5", "25", "793019428"], "notes": "NoteIn the first test, there are three ways to move the token from cell $$$3$$$ to cell $$$1$$$ in one shift: using subtraction of $$$y = 2$$$, or using division by $$$z = 2$$$ or $$$z = 3$$$.There are also two ways to move the token from cell $$$3$$$ to cell $$$1$$$ via cell $$$2$$$: first subtract $$$y = 1$$$, and then either subtract $$$y = 1$$$ again or divide by $$$z = 2$$$.Therefore, there are five ways in total."}, "src_uid": "a524aa54e83fd0223489a19531bf0e79"}
{"nl": {"description": "Limak is a little polar bear. He has n balls, the i-th ball has size ti.Limak wants to give one ball to each of his three friends. Giving gifts isn't easy — there are two rules Limak must obey to make friends happy:  No two friends can get balls of the same size.  No two friends can get balls of sizes that differ by more than 2. For example, Limak can choose balls with sizes 4, 5 and 3, or balls with sizes 90, 91 and 92. But he can't choose balls with sizes 5, 5 and 6 (two friends would get balls of the same size), and he can't choose balls with sizes 30, 31 and 33 (because sizes 30 and 33 differ by more than 2).Your task is to check whether Limak can choose three balls that satisfy conditions above.", "input_spec": "The first line of the input contains one integer n (3 ≤ n ≤ 50) — the number of balls Limak has. The second line contains n integers t1, t2, ..., tn (1 ≤ ti ≤ 1000) where ti denotes the size of the i-th ball.", "output_spec": "Print \"YES\" (without quotes) if Limak can choose three balls of distinct sizes, such that any two of them differ by no more than 2. Otherwise, print \"NO\" (without quotes).", "sample_inputs": ["4\n18 55 16 17", "6\n40 41 43 44 44 44", "8\n5 972 3 4 1 4 970 971"], "sample_outputs": ["YES", "NO", "YES"], "notes": "NoteIn the first sample, there are 4 balls and Limak is able to choose three of them to satisfy the rules. He must must choose balls with sizes 18, 16 and 17.In the second sample, there is no way to give gifts to three friends without breaking the rules.In the third sample, there is even more than one way to choose balls:  Choose balls with sizes 3, 4 and 5.  Choose balls with sizes 972, 970, 971. "}, "src_uid": "d6c876a84c7b92141710be5d76536eab"}
{"nl": {"description": "Vadim loves decorating the Christmas tree, so he got a beautiful garland as a present. It consists of $$$n$$$ light bulbs in a single row. Each bulb has a number from $$$1$$$ to $$$n$$$ (in arbitrary order), such that all the numbers are distinct. While Vadim was solving problems, his home Carp removed some light bulbs from the garland. Now Vadim wants to put them back on.Vadim wants to put all bulb back on the garland. Vadim defines complexity of a garland to be the number of pairs of adjacent bulbs with numbers with different parity (remainder of the division by $$$2$$$). For example, the complexity of 1 4 2 3 5 is $$$2$$$ and the complexity of 1 3 5 7 6 4 2 is $$$1$$$.No one likes complexity, so Vadim wants to minimize the number of such pairs. Find the way to put all bulbs back on the garland, such that the complexity is as small as possible.", "input_spec": "The first line contains a single integer $$$n$$$ ($$$1 \\le n \\le 100$$$) — the number of light bulbs on the garland. The second line contains $$$n$$$ integers $$$p_1,\\ p_2,\\ \\ldots,\\ p_n$$$ ($$$0 \\le p_i \\le n$$$) — the number on the $$$i$$$-th bulb, or $$$0$$$ if it was removed.", "output_spec": "Output a single number — the minimum complexity of the garland.", "sample_inputs": ["5\n0 5 0 2 3", "7\n1 0 0 5 0 0 2"], "sample_outputs": ["2", "1"], "notes": "NoteIn the first example, one should place light bulbs as 1 5 4 2 3. In that case, the complexity would be equal to 2, because only $$$(5, 4)$$$ and $$$(2, 3)$$$ are the pairs of adjacent bulbs that have different parity.In the second case, one of the correct answers is 1 7 3 5 6 4 2. "}, "src_uid": "90db6b6548512acfc3da162144169dba"}
{"nl": {"description": "Polycarpus has postcards and photos hung in a row on the wall. He decided to put them away to the closet and hang on the wall a famous painter's picture. Polycarpus does it like that: he goes from the left to the right and removes the objects consecutively. As Polycarpus doesn't want any mix-ups to happen, he will not carry in his hands objects of two different types. In other words, Polycarpus can't carry both postcards and photos simultaneously. Sometimes he goes to the closet and puts the objects there, thus leaving his hands free. Polycarpus must put all the postcards and photos to the closet. He cannot skip objects. What minimum number of times he should visit the closet if he cannot carry more than 5 items?", "input_spec": "The only line of the input data contains a non-empty string consisting of letters \"С\" and \"P\" whose length does not exceed 100 characters. If the i-th character in the string is the letter \"С\", that means that the i-th object (the numbering goes from the left to the right) on Polycarpus' wall is a postcard. And if the i-th character is the letter \"P\", than the i-th object on the wall is a photo.", "output_spec": "Print the only number — the minimum number of times Polycarpus has to visit the closet.", "sample_inputs": ["CPCPCPC", "CCCCCCPPPPPP", "CCCCCCPPCPPPPPPPPPP", "CCCCCCCCCC"], "sample_outputs": ["7", "4", "6", "2"], "notes": "NoteIn the first sample Polycarpus needs to take one item to the closet 7 times.In the second sample Polycarpus can first take 3 postcards to the closet; then 3 more. He can take the 6 photos that are left in the similar way, going to the closet twice.In the third sample Polycarpus can visit the closet twice, both times carrying 3 postcards. Then he can take there 2 photos at once, then one postcard and finally, he can carry the last 10 photos if he visits the closet twice.In the fourth sample Polycarpus can visit the closet twice and take there all 10 postcards (5 items during each go)."}, "src_uid": "5257f6b50f5a610a17c35a47b3a0da11"}
{"nl": {"description": "Vus the Cossack holds a programming competition, in which $$$n$$$ people participate. He decided to award them all with pens and notebooks. It is known that Vus has exactly $$$m$$$ pens and $$$k$$$ notebooks.Determine whether the Cossack can reward all participants, giving each of them at least one pen and at least one notebook.", "input_spec": "The first line contains three integers $$$n$$$, $$$m$$$, and $$$k$$$ ($$$1 \\leq n, m, k \\leq 100$$$) — the number of participants, the number of pens, and the number of notebooks respectively.", "output_spec": "Print \"Yes\" if it possible to reward all the participants. Otherwise, print \"No\". You can print each letter in any case (upper or lower).", "sample_inputs": ["5 8 6", "3 9 3", "8 5 20"], "sample_outputs": ["Yes", "Yes", "No"], "notes": "NoteIn the first example, there are $$$5$$$ participants. The Cossack has $$$8$$$ pens and $$$6$$$ notebooks. Therefore, he has enough pens and notebooks.In the second example, there are $$$3$$$ participants. The Cossack has $$$9$$$ pens and $$$3$$$ notebooks. He has more than enough pens but only the minimum needed number of notebooks.In the third example, there are $$$8$$$ participants but only $$$5$$$ pens. Since the Cossack does not have enough pens, the answer is \"No\"."}, "src_uid": "6cd07298b23cc6ce994bb1811b9629c4"}
{"nl": {"description": "At a geometry lesson Bob learnt that a triangle is called right-angled if it is nondegenerate and one of its angles is right. Bob decided to draw such a triangle immediately: on a sheet of paper he drew three points with integer coordinates, and joined them with segments of straight lines, then he showed the triangle to Peter. Peter said that Bob's triangle is not right-angled, but is almost right-angled: the triangle itself is not right-angled, but it is possible to move one of the points exactly by distance 1 so, that all the coordinates remain integer, and the triangle become right-angled. Bob asks you to help him and find out if Peter tricks him. By the given coordinates of the triangle you should find out if it is right-angled, almost right-angled, or neither of these.", "input_spec": "The first input line contains 6 space-separated integers x1, y1, x2, y2, x3, y3 — coordinates of the triangle's vertices. All the coordinates are integer and don't exceed 100 in absolute value. It's guaranteed that the triangle is nondegenerate, i.e. its total area is not zero.", "output_spec": "If the given triangle is right-angled, output RIGHT, if it is almost right-angled, output ALMOST, and if it is neither of these, output NEITHER.", "sample_inputs": ["0 0 2 0 0 1", "2 3 4 5 6 6", "-1 0 2 0 0 1"], "sample_outputs": ["RIGHT", "NEITHER", "ALMOST"], "notes": null}, "src_uid": "8324fa542297c21bda1a4aed0bd45a2d"}
{"nl": {"description": "Smart Beaver is careful about his appearance and pays special attention to shoes so he has a huge number of pairs of shoes from the most famous brands of the forest. He's trying to handle his shoes carefully so that each pair stood side by side. But by the end of the week because of his very active lifestyle in his dressing room becomes a mess.Smart Beaver from ABBYY is not only the brightest beaver in the area, but he also is the most domestically oriented. For example, on Mondays the Smart Beaver cleans everything in his home.It's Monday morning. Smart Beaver does not want to spend the whole day cleaning, besides, there is much in to do and it’s the gym day, so he wants to clean up as soon as possible. Now the floors are washed, the dust is wiped off — it’s time to clean up in the dressing room. But as soon as the Smart Beaver entered the dressing room, all plans for the day were suddenly destroyed: chaos reigned there and it seemed impossible to handle, even in a week. Give our hero some hope: tell him what is the minimum number of shoes need to change the position to make the dressing room neat.The dressing room is rectangular and is divided into n × m equal squares, each square contains exactly one shoe. Each pair of shoes has a unique number that is integer from 1 to , more formally, a square with coordinates (i, j) contains an integer number of the pair which is lying on it. The Smart Beaver believes that the dressing room is neat only when each pair of sneakers lies together. We assume that the pair of sneakers in squares (i1, j1) and (i2, j2) lies together if |i1 - i2| + |j1 - j2| = 1.", "input_spec": "The first line contains two space-separated integers n and m. They correspond to the dressing room size. Next n lines contain m space-separated integers each. Those numbers describe the dressing room. Each number corresponds to a snicker.  It is guaranteed that:    n·m is even.  All numbers, corresponding to the numbers of pairs of shoes in the dressing room, will lie between 1 and .  Each number from 1 to  will occur exactly twice.  The input limits for scoring 30 points are (subproblem C1):    2 ≤ n, m ≤ 8.  The input limits for scoring 100 points are (subproblems C1+C2):    2 ≤ n, m ≤ 80. ", "output_spec": "Print exactly one integer — the minimum number of the sneakers that need to change their location.", "sample_inputs": ["2 3\n1 1 2\n2 3 3", "3 4\n1 3 2 6\n2 1 5 6\n4 4 5 3"], "sample_outputs": ["2", "4"], "notes": "Note   The second sample.  "}, "src_uid": "1f0e8bbd5bf4fcdea927fbb505a8949b"}
{"nl": {"description": "Dawid has four bags of candies. The $$$i$$$-th of them contains $$$a_i$$$ candies. Also, Dawid has two friends. He wants to give each bag to one of his two friends. Is it possible to distribute the bags in such a way that each friend receives the same amount of candies in total?Note, that you can't keep bags for yourself or throw them away, each bag should be given to one of the friends.", "input_spec": "The only line contains four integers $$$a_1$$$, $$$a_2$$$, $$$a_3$$$ and $$$a_4$$$ ($$$1 \\leq a_i \\leq 100$$$) — the numbers of candies in each bag.", "output_spec": "Output YES if it's possible to give the bags to Dawid's friends so that both friends receive the same amount of candies, or NO otherwise. Each character can be printed in any case (either uppercase or lowercase).", "sample_inputs": ["1 7 11 5", "7 3 2 5"], "sample_outputs": ["YES", "NO"], "notes": "NoteIn the first sample test, Dawid can give the first and the third bag to the first friend, and the second and the fourth bag to the second friend. This way, each friend will receive $$$12$$$ candies.In the second sample test, it's impossible to distribute the bags."}, "src_uid": "5a623c49cf7effacfb58bc82f8eaff37"}
{"nl": {"description": " When the curtains are opened, a canvas unfolds outside. Kanno marvels at all the blonde colours along the riverside — not tangerines, but blossoms instead.\"What a pity it's already late spring,\" sighs Mino with regret, \"one more drizzling night and they'd be gone.\"\"But these blends are at their best, aren't they?\" Absorbed in the landscape, Kanno remains optimistic. The landscape can be expressed as a row of consecutive cells, each of which either contains a flower of colour amber or buff or canary yellow, or is empty.When a flower withers, it disappears from the cell that it originally belonged to, and it spreads petals of its colour in its two neighbouring cells (or outside the field if the cell is on the side of the landscape). In case petals fall outside the given cells, they simply become invisible.You are to help Kanno determine whether it's possible that after some (possibly none or all) flowers shed their petals, at least one of the cells contains all three colours, considering both petals and flowers. Note that flowers can wither in arbitrary order.", "input_spec": "The first and only line of input contains a non-empty string $$$s$$$ consisting of uppercase English letters 'A', 'B', 'C' and characters '.' (dots) only ($$$\\lvert s \\rvert \\leq 100$$$) — denoting cells containing an amber flower, a buff one, a canary yellow one, and no flowers, respectively.", "output_spec": "Output \"Yes\" if it's possible that all three colours appear in some cell, and \"No\" otherwise. You can print each letter in any case (upper or lower).", "sample_inputs": [".BAC.", "AA..CB"], "sample_outputs": ["Yes", "No"], "notes": "NoteIn the first example, the buff and canary yellow flowers can leave their petals in the central cell, blending all three colours in it.In the second example, it's impossible to satisfy the requirement because there is no way that amber and buff meet in any cell."}, "src_uid": "ba6ff507384570152118e2ab322dd11f"}
{"nl": {"description": "One beautiful July morning a terrible thing happened in Mainframe: a mean virus Megabyte somehow got access to the memory of his not less mean sister Hexadecimal. He loaded there a huge amount of n different natural numbers from 1 to n to obtain total control over her energy.But his plan failed. The reason for this was very simple: Hexadecimal didn't perceive any information, apart from numbers written in binary format. This means that if a number in a decimal representation contained characters apart from 0 and 1, it was not stored in the memory. Now Megabyte wants to know, how many numbers were loaded successfully.", "input_spec": "Input data contains the only number n (1 ≤ n ≤ 109).", "output_spec": "Output the only number — answer to the problem.", "sample_inputs": ["10"], "sample_outputs": ["2"], "notes": "NoteFor n = 10 the answer includes numbers 1 and 10."}, "src_uid": "64a842f9a41f85a83b7d65bfbe21b6cb"}
{"nl": {"description": "Ilya is a very clever lion, he lives in an unusual city ZooVille. In this city all the animals have their rights and obligations. Moreover, they even have their own bank accounts. The state of a bank account is an integer. The state of a bank account can be a negative number. This means that the owner of the account owes the bank money.Ilya the Lion has recently had a birthday, so he got a lot of gifts. One of them (the gift of the main ZooVille bank) is the opportunity to delete the last digit or the digit before last from the state of his bank account no more than once. For example, if the state of Ilya's bank account is -123, then Ilya can delete the last digit and get his account balance equal to -12, also he can remove its digit before last and get the account balance equal to -13. Of course, Ilya is permitted not to use the opportunity to delete a digit from the balance.Ilya is not very good at math, and that's why he asks you to help him maximize his bank account. Find the maximum state of the bank account that can be obtained using the bank's gift.", "input_spec": "The single line contains integer n (10 ≤ |n| ≤ 109) — the state of Ilya's bank account.", "output_spec": "In a single line print an integer — the maximum state of the bank account that Ilya can get. ", "sample_inputs": ["2230", "-10", "-100003"], "sample_outputs": ["2230", "0", "-10000"], "notes": "NoteIn the first test sample Ilya doesn't profit from using the present.In the second test sample you can delete digit 1 and get the state of the account equal to 0."}, "src_uid": "4b0a8798a6d53351226d4f06e3356b1e"}
{"nl": {"description": "You are given an array a with n distinct integers. Construct an array b by permuting a such that for every non-empty subset of indices S = {x1, x2, ..., xk} (1 ≤ xi ≤ n, 0 < k < n) the sums of elements on that positions in a and b are different, i. e. ", "input_spec": "The first line contains one integer n (1 ≤ n ≤ 22) — the size of the array. The second line contains n space-separated distinct integers a1, a2, ..., an (0 ≤ ai ≤ 109) — the elements of the array.", "output_spec": "If there is no such array b, print -1. Otherwise in the only line print n space-separated integers b1, b2, ..., bn. Note that b must be a permutation of a. If there are multiple answers, print any of them.", "sample_inputs": ["2\n1 2", "4\n1000 100 10 1"], "sample_outputs": ["2 1", "100 1 1000 10"], "notes": "NoteAn array x is a permutation of y, if we can shuffle elements of y such that it will coincide with x.Note that the empty subset and the subset containing all indices are not counted."}, "src_uid": "e314642ca1f82be8f223e2eba00b5531"}
{"nl": {"description": "Alexander is learning how to convert numbers from the decimal system to any other, however, he doesn't know English letters, so he writes any number only as a decimal number, it means that instead of the letter A he will write the number 10. Thus, by converting the number 475 from decimal to hexadecimal system, he gets 11311 (475 = 1·162 + 13·161 + 11·160). Alexander lived calmly until he tried to convert the number back to the decimal number system.Alexander remembers that he worked with little numbers so he asks to find the minimum decimal number so that by converting it to the system with the base n he will get the number k.", "input_spec": "The first line contains the integer n (2 ≤ n ≤ 109). The second line contains the integer k (0 ≤ k < 1060), it is guaranteed that the number k contains no more than 60 symbols. All digits in the second line are strictly less than n. Alexander guarantees that the answer exists and does not exceed 1018. The number k doesn't contain leading zeros.", "output_spec": "Print the number x (0 ≤ x ≤ 1018) — the answer to the problem.", "sample_inputs": ["13\n12", "16\n11311", "20\n999", "17\n2016"], "sample_outputs": ["12", "475", "3789", "594"], "notes": "NoteIn the first example 12 could be obtained by converting two numbers to the system with base 13: 12 = 12·130 or 15 = 1·131 + 2·130."}, "src_uid": "be66399c558c96566a6bb0a63d2503e5"}
{"nl": {"description": "You have a grid with n rows and n columns. Each cell is either empty (denoted by '.') or blocked (denoted by 'X').Two empty cells are directly connected if they share a side. Two cells (r1, c1) (located in the row r1 and column c1) and (r2, c2) are connected if there exists a sequence of empty cells that starts with (r1, c1), finishes with (r2, c2), and any two consecutive cells in this sequence are directly connected. A connected component is a set of empty cells such that any two cells in the component are connected, and there is no cell in this set that is connected to some cell not in this set.Your friend Limak is a big grizzly bear. He is able to destroy any obstacles in some range. More precisely, you can choose a square of size k × k in the grid and Limak will transform all blocked cells there to empty ones. However, you can ask Limak to help only once.The chosen square must be completely inside the grid. It's possible that Limak won't change anything because all cells are empty anyway.You like big connected components. After Limak helps you, what is the maximum possible size of the biggest connected component in the grid?", "input_spec": "The first line of the input contains two integers n and k (1 ≤ k ≤ n ≤ 500) — the size of the grid and Limak's range, respectively. Each of the next n lines contains a string with n characters, denoting the i-th row of the grid. Each character is '.' or 'X', denoting an empty cell or a blocked one, respectively.", "output_spec": "Print the maximum possible size (the number of cells) of the biggest connected component, after using Limak's help.", "sample_inputs": ["5 2\n..XXX\nXX.XX\nX.XXX\nX...X\nXXXX.", "5 3\n.....\n.XXX.\n.XXX.\n.XXX.\n....."], "sample_outputs": ["10", "25"], "notes": "NoteIn the first sample, you can choose a square of size 2 × 2. It's optimal to choose a square in the red frame on the left drawing below. Then, you will get a connected component with 10 cells, marked blue in the right drawing.  "}, "src_uid": "d575f9bbdf625202807db59490c5c327"}
{"nl": {"description": "Yaroslav calls an array of r integers a1, a2, ..., ar good, if it meets the following conditions: |a1 - a2| = 1, |a2 - a3| = 1, ..., |ar - 1 - ar| = 1, |ar - a1| = 1, at that . An array of integers b1, b2, ..., br is called great, if it meets the following conditions:  The elements in it do not decrease (bi ≤ bi + 1).  If the inequalities 1 ≤ r ≤ n and 1 ≤ bi ≤ m hold.  If we can rearrange its elements and get at least one and at most k distinct good arrays. Yaroslav has three integers n, m, k. He needs to count the number of distinct great arrays. Help Yaroslav! As the answer may be rather large, print the remainder after dividing it by 1000000007 (109 + 7).Two arrays are considered distinct if there is a position in which they have distinct numbers.", "input_spec": "The single line contains three integers n, m, k (1 ≤ n, m, k ≤ 100).", "output_spec": "In a single line print the remainder after dividing the answer to the problem by number 1000000007 (109 + 7).", "sample_inputs": ["1 1 1", "3 3 3"], "sample_outputs": ["0", "2"], "notes": null}, "src_uid": "c6d275b1e1d5c9e39e2cf990a635fa6b"}
{"nl": {"description": "Jeff loves regular bracket sequences.Today Jeff is going to take a piece of paper and write out the regular bracket sequence, consisting of nm brackets. Let's number all brackets of this sequence from 0 to nm - 1 from left to right. Jeff knows that he is going to spend ai mod n liters of ink on the i-th bracket of the sequence if he paints it opened and bi mod n liters if he paints it closed.You've got sequences a, b and numbers n, m. What minimum amount of ink will Jeff need to paint a regular bracket sequence of length nm?Operation x mod y means taking the remainder after dividing number x by number y.", "input_spec": "The first line contains two integers n and m (1 ≤ n ≤ 20; 1 ≤ m ≤ 107; m is even). The next line contains n integers: a0, a1, ..., an - 1 (1 ≤ ai ≤ 10). The next line contains n integers: b0, b1, ..., bn - 1 (1 ≤ bi ≤ 10). The numbers are separated by spaces.", "output_spec": "In a single line print the answer to the problem — the minimum required amount of ink in liters.", "sample_inputs": ["2 6\n1 2\n2 1", "1 10000000\n2\n3"], "sample_outputs": ["12", "25000000"], "notes": "NoteIn the first test the optimal sequence is: ()()()()()(), the required number of ink liters is 12."}, "src_uid": "f40900973f4ebeb6fdafd75ebe4e9601"}
{"nl": {"description": "You know that Japan is the country with almost the largest 'electronic devices per person' ratio. So you might be quite surprised to find out that the primary school in Japan teaches to count using a Soroban — an abacus developed in Japan. This phenomenon has its reasons, of course, but we are not going to speak about them. Let's have a look at the Soroban's construction.  Soroban consists of some number of rods, each rod contains five beads. We will assume that the rods are horizontal lines. One bead on each rod (the leftmost one) is divided from the others by a bar (the reckoning bar). This single bead is called go-dama and four others are ichi-damas. Each rod is responsible for representing a single digit from 0 to 9. We can obtain the value of a digit by following simple algorithm:  Set the value of a digit equal to 0.  If the go-dama is shifted to the right, add 5.  Add the number of ichi-damas shifted to the left. Thus, the upper rod on the picture shows digit 0, the middle one shows digit 2 and the lower one shows 7. We will consider the top rod to represent the last decimal digit of a number, so the picture shows number 720.Write the program that prints the way Soroban shows the given number n.", "input_spec": "The first line contains a single integer n (0 ≤ n < 109).", "output_spec": "Print the description of the decimal digits of number n from the last one to the first one (as mentioned on the picture in the statement), one per line. Print the beads as large English letters 'O', rod pieces as character '-' and the reckoning bar as '|'. Print as many rods, as many digits are in the decimal representation of number n without leading zeroes. We can assume that number 0 has no leading zeroes.", "sample_inputs": ["2", "13", "720"], "sample_outputs": ["O-|OO-OO", "O-|OOO-O\nO-|O-OOO", "O-|-OOOO\nO-|OO-OO\n-O|OO-OO"], "notes": null}, "src_uid": "c2e3aced0bc76b6484360563355d23a7"}
{"nl": {"description": "JATC and his friend Giraffe are currently in their room, solving some problems. Giraffe has written on the board an array $$$a_1$$$, $$$a_2$$$, ..., $$$a_n$$$ of integers, such that $$$1 \\le a_1 < a_2 < \\ldots < a_n \\le 10^3$$$, and then went to the bathroom.JATC decided to prank his friend by erasing some consecutive elements in the array. Since he doesn't want for the prank to go too far, he will only erase in a way, such that Giraffe can still restore the array using the information from the remaining elements. Because Giraffe has created the array, he's also aware that it's an increasing array and all the elements are integers in the range $$$[1, 10^3]$$$.JATC wonders what is the greatest number of elements he can erase?", "input_spec": "The first line of the input contains a single integer $$$n$$$ ($$$1 \\le n \\le 100$$$) — the number of elements in the array. The second line of the input contains $$$n$$$ integers $$$a_i$$$ ($$$1 \\le a_1<a_2<\\dots<a_n \\le 10^3$$$) — the array written by Giraffe.", "output_spec": "Print a single integer — the maximum number of consecutive elements in the array that JATC can erase. If it is impossible to erase even a single element, print $$$0$$$.", "sample_inputs": ["6\n1 3 4 5 6 9", "3\n998 999 1000", "5\n1 2 3 4 5"], "sample_outputs": ["2", "2", "4"], "notes": "NoteIn the first example, JATC can erase the third and fourth elements, leaving the array $$$[1, 3, \\_, \\_, 6, 9]$$$. As you can see, there is only one way to fill in the blanks.In the second example, JATC can erase the second and the third elements. The array will become $$$[998, \\_, \\_]$$$. Because all the elements are less than or equal to $$$1000$$$, the array is still can be restored. Note, that he can't erase the first $$$2$$$ elements.In the third example, JATC can erase the first $$$4$$$ elements. Since all the elements are greater than or equal to $$$1$$$, Giraffe can still restore the array. Note, that he can't erase the last $$$4$$$ elements."}, "src_uid": "858b5e75e21c4cba6d08f3f66be0c198"}
{"nl": {"description": "n participants of the competition were split into m teams in some manner so that each team has at least one participant. After the competition each pair of participants from the same team became friends.Your task is to write a program that will find the minimum and the maximum number of pairs of friends that could have formed by the end of the competition.", "input_spec": "The only line of input contains two integers n and m, separated by a single space (1 ≤ m ≤ n ≤ 109) — the number of participants and the number of teams respectively. ", "output_spec": "The only line of the output should contain two integers kmin and kmax — the minimum possible number of pairs of friends and the maximum possible number of pairs of friends respectively.", "sample_inputs": ["5 1", "3 2", "6 3"], "sample_outputs": ["10 10", "1 1", "3 6"], "notes": "NoteIn the first sample all the participants get into one team, so there will be exactly ten pairs of friends.In the second sample at any possible arrangement one team will always have two participants and the other team will always have one participant. Thus, the number of pairs of friends will always be equal to one.In the third sample minimum number of newly formed friendships can be achieved if participants were split on teams consisting of 2 people, maximum number can be achieved if participants were split on teams of 1, 1 and 4 people."}, "src_uid": "a081d400a5ce22899b91df38ba98eecc"}
{"nl": {"description": "Petya has equal wooden bars of length n. He wants to make a frame for two equal doors. Each frame has two vertical (left and right) sides of length a and one top side of length b. A solid (i.e. continuous without breaks) piece of bar is needed for each side.Determine a minimal number of wooden bars which are needed to make the frames for two doors. Petya can cut the wooden bars into any parts, but each side of each door should be a solid piece of a wooden bar (or a whole wooden bar).", "input_spec": "The first line contains a single integer n (1 ≤ n ≤ 1 000) — the length of each wooden bar. The second line contains a single integer a (1 ≤ a ≤ n) — the length of the vertical (left and right) sides of a door frame. The third line contains a single integer b (1 ≤ b ≤ n) — the length of the upper side of a door frame.", "output_spec": "Print the minimal number of wooden bars with length n which are needed to make the frames for two doors.", "sample_inputs": ["8\n1\n2", "5\n3\n4", "6\n4\n2", "20\n5\n6"], "sample_outputs": ["1", "6", "4", "2"], "notes": "NoteIn the first example one wooden bar is enough, since the total length of all six sides of the frames for two doors is 8.In the second example 6 wooden bars is enough, because for each side of the frames the new wooden bar is needed."}, "src_uid": "1a50fe39e18f86adac790093e195979a"}
{"nl": {"description": "Nick is interested in prime numbers. Once he read about Goldbach problem. It states that every even integer greater than 2 can be expressed as the sum of two primes. That got Nick's attention and he decided to invent a problem of his own and call it Noldbach problem. Since Nick is interested only in prime numbers, Noldbach problem states that at least k prime numbers from 2 to n inclusively can be expressed as the sum of three integer numbers: two neighboring prime numbers and 1. For example, 19 = 7 + 11 + 1, or 13 = 5 + 7 + 1.Two prime numbers are called neighboring if there are no other prime numbers between them.You are to help Nick, and find out if he is right or wrong.", "input_spec": "The first line of the input contains two integers n (2 ≤ n ≤ 1000) and k (0 ≤ k ≤ 1000).", "output_spec": "Output YES if at least k prime numbers from 2 to n inclusively can be expressed as it was described above. Otherwise output NO.", "sample_inputs": ["27 2", "45 7"], "sample_outputs": ["YES", "NO"], "notes": "NoteIn the first sample the answer is YES since at least two numbers can be expressed as it was described (for example, 13 and 19). In the second sample the answer is NO since it is impossible to express 7 prime numbers from 2 to 45 in the desired form."}, "src_uid": "afd2b818ed3e2a931da9d682f6ad660d"}
{"nl": {"description": "They've screwed something up yet again... In one nuclear reactor of a research station an uncontrolled reaction is in progress and explosion which will destroy the whole station will happen soon.The station is represented by a square n × n divided into 1 × 1 blocks. Each block is either a reactor or a laboratory. There can be several reactors and exactly one of them will explode soon. The reactors can be considered impassable blocks, but one can move through laboratories. Between any two laboratories, which are in adjacent blocks, there is a corridor. Blocks are considered adjacent if they have a common edge.In each laboratory there is some number of scientists and some number of rescue capsules. Once the scientist climbs into a capsule, he is considered to be saved. Each capsule has room for not more than one scientist.The reactor, which is about to explode, is damaged and a toxic coolant trickles from it into the neighboring blocks. The block, which contains the reactor, is considered infected. Every minute the coolant spreads over the laboratories through corridors. If at some moment one of the blocks is infected, then the next minute all the neighboring laboratories also become infected. Once a lab is infected, all the scientists there that are not in rescue capsules die. The coolant does not spread through reactor blocks.There are exactly t minutes to the explosion. Any scientist in a minute can move down the corridor to the next lab, if it is not infected. On any corridor an unlimited number of scientists can simultaneously move in both directions. It is believed that the scientists inside a lab moves without consuming time. Moreover, any scientist could get into the rescue capsule instantly. It is also believed that any scientist at any given moment always has the time to perform their actions (move from the given laboratory into the next one, or climb into the rescue capsule) before the laboratory will be infected.Find the maximum number of scientists who will be able to escape.", "input_spec": "The first line contains two integers n and t (2 ≤ n ≤ 10, 1 ≤ t ≤ 60). Each of the next n lines contains n characters. These lines describe the scientists' locations. Then exactly one empty line follows. Each of the next n more lines contains n characters. These lines describe the rescue capsules' locations. In the description of the scientists' and the rescue capsules' locations the character \"Y\" stands for a properly functioning reactor, \"Z\" stands for the malfunctioning reactor. The reactors' positions in both descriptions coincide. There is exactly one malfunctioning reactor on the station. The digits \"0\" - \"9\" stand for the laboratories. In the description of the scientists' locations those numbers stand for the number of scientists in the corresponding laboratories. In the rescue capsules' descriptions they stand for the number of such capsules in each laboratory.", "output_spec": "Print a single number — the maximum number of scientists who will manage to save themselves.", "sample_inputs": ["3 3\n1YZ\n1YY\n100\n\n0YZ\n0YY\n003", "4 4\nY110\n1Y1Z\n1Y0Y\n0100\n\nY001\n0Y0Z\n0Y0Y\n0005"], "sample_outputs": ["2", "3"], "notes": "NoteIn the second sample the events could take place as follows:   "}, "src_uid": "544de9c3729a35eb08c143b1cb9ee085"}
{"nl": {"description": "It's New Year's Eve soon, so Ivan decided it's high time he started setting the table. Ivan has bought two cakes and cut them into pieces: the first cake has been cut into a pieces, and the second one — into b pieces.Ivan knows that there will be n people at the celebration (including himself), so Ivan has set n plates for the cakes. Now he is thinking about how to distribute the cakes between the plates. Ivan wants to do it in such a way that all following conditions are met:  Each piece of each cake is put on some plate;  Each plate contains at least one piece of cake;  No plate contains pieces of both cakes. To make his guests happy, Ivan wants to distribute the cakes in such a way that the minimum number of pieces on the plate is maximized. Formally, Ivan wants to know the maximum possible number x such that he can distribute the cakes according to the aforementioned conditions, and each plate will contain at least x pieces of cake.Help Ivan to calculate this number x!", "input_spec": "The first line contains three integers n, a and b (1 ≤ a, b ≤ 100, 2 ≤ n ≤ a + b) — the number of plates, the number of pieces of the first cake, and the number of pieces of the second cake, respectively.", "output_spec": "Print the maximum possible number x such that Ivan can distribute the cake in such a way that each plate will contain at least x pieces of cake.", "sample_inputs": ["5 2 3", "4 7 10"], "sample_outputs": ["1", "3"], "notes": "NoteIn the first example there is only one way to distribute cakes to plates, all of them will have 1 cake on it.In the second example you can have two plates with 3 and 4 pieces of the first cake and two plates both with 5 pieces of the second cake. Minimal number of pieces is 3."}, "src_uid": "a254b1e3451c507cf7ce3e2496b3d69e"}
{"nl": {"description": "Numbers k-bonacci (k is integer, k > 1) are a generalization of Fibonacci numbers and are determined as follows:  F(k, n) = 0, for integer n, 1 ≤ n < k;  F(k, k) = 1;  F(k, n) = F(k, n - 1) + F(k, n - 2) + ... + F(k, n - k), for integer n, n > k. Note that we determine the k-bonacci numbers, F(k, n), only for integer values of n and k.You've got a number s, represent it as a sum of several (at least two) distinct k-bonacci numbers. ", "input_spec": "The first line contains two integers s and k (1 ≤ s, k ≤ 109; k > 1).", "output_spec": "In the first line print an integer m (m ≥ 2) that shows how many numbers are in the found representation. In the second line print m distinct integers a1, a2, ..., am. Each printed integer should be a k-bonacci number. The sum of printed integers must equal s. It is guaranteed that the answer exists. If there are several possible answers, print any of them.", "sample_inputs": ["5 2", "21 5"], "sample_outputs": ["3\n0 2 3", "3\n4 1 16"], "notes": null}, "src_uid": "da793333b977ed179fdba900aa604b52"}
{"nl": {"description": "Our bear's forest has a checkered field. The checkered field is an n × n table, the rows are numbered from 1 to n from top to bottom, the columns are numbered from 1 to n from left to right. Let's denote a cell of the field on the intersection of row x and column y by record (x, y). Each cell of the field contains growing raspberry, at that, the cell (x, y) of the field contains x + y raspberry bushes.The bear came out to walk across the field. At the beginning of the walk his speed is (dx, dy). Then the bear spends exactly t seconds on the field. Each second the following takes place:  Let's suppose that at the current moment the bear is in cell (x, y).  First the bear eats the raspberry from all the bushes he has in the current cell. After the bear eats the raspberry from k bushes, he increases each component of his speed by k. In other words, if before eating the k bushes of raspberry his speed was (dx, dy), then after eating the berry his speed equals (dx + k, dy + k).  Let's denote the current speed of the bear (dx, dy) (it was increased after the previous step). Then the bear moves from cell (x, y) to cell (((x + dx - 1) mod n) + 1, ((y + dy - 1) mod n) + 1).  Then one additional raspberry bush grows in each cell of the field. You task is to predict the bear's actions. Find the cell he ends up in if he starts from cell (sx, sy). Assume that each bush has infinitely much raspberry and the bear will never eat all of it.", "input_spec": "The first line of the input contains six space-separated integers: n, sx, sy, dx, dy, t (1 ≤ n ≤ 109; 1 ≤ sx, sy ≤ n;  - 100 ≤ dx, dy ≤ 100; 0 ≤ t ≤ 1018).", "output_spec": "Print two integers — the coordinates of the cell the bear will end up in after t seconds.", "sample_inputs": ["5 1 2 0 1 2", "1 1 1 -1 -1 2"], "sample_outputs": ["3 1", "1 1"], "notes": "NoteOperation a mod b means taking the remainder after dividing a by b. Note that the result of the operation is always non-negative. For example, ( - 1) mod 3 = 2.In the first sample before the first move the speed vector will equal (3,4) and the bear will get to cell (4,1). Before the second move the speed vector will equal (9,10) and he bear will get to cell (3,1). Don't forget that at the second move, the number of berry bushes increased by 1.In the second sample before the first move the speed vector will equal (1,1) and the bear will get to cell (1,1). Before the second move, the speed vector will equal (4,4) and the bear will get to cell (1,1). Don't forget that at the second move, the number of berry bushes increased by 1."}, "src_uid": "ee9fa8be2ae05a4e831a4f608c0cc785"}
{"nl": {"description": "You are given a string s consisting of n lowercase Latin letters. You have to type this string using your keyboard.Initially, you have an empty string. Until you type the whole string, you may perform the following operation:  add a character to the end of the string. Besides, at most once you may perform one additional operation: copy the string and append it to itself.For example, if you have to type string abcabca, you can type it in 7 operations if you type all the characters one by one. However, you can type it in 5 operations if you type the string abc first and then copy it and type the last character.If you have to type string aaaaaaaaa, the best option is to type 4 characters one by one, then copy the string, and then type the remaining character.Print the minimum number of operations you need to type the given string.", "input_spec": "The first line of the input containing only one integer number n (1 ≤ n ≤ 100) — the length of the string you have to type. The second line containing the string s consisting of n lowercase Latin letters.", "output_spec": "Print one integer number — the minimum number of operations you need to type the given string.", "sample_inputs": ["7\nabcabca", "8\nabcdefgh"], "sample_outputs": ["5", "8"], "notes": "NoteThe first test described in the problem statement.In the second test you can only type all the characters one by one."}, "src_uid": "ed8725e4717c82fa7cfa56178057bca3"}
{"nl": {"description": "Dima and Seryozha live in an ordinary dormitory room for two. One day Dima had a date with his girl and he asked Seryozha to leave the room. As a compensation, Seryozha made Dima do his homework.The teacher gave Seryozha the coordinates of n distinct points on the abscissa axis and asked to consecutively connect them by semi-circus in a certain order: first connect the first point with the second one, then connect the second point with the third one, then the third one with the fourth one and so on to the n-th point. Two points with coordinates (x1, 0) and (x2, 0) should be connected by a semi-circle that passes above the abscissa axis with the diameter that coincides with the segment between points. Seryozha needs to find out if the line on the picture intersects itself. For clarifications, see the picture Seryozha showed to Dima (the left picture has self-intersections, the right picture doesn't have any).  Seryozha is not a small boy, so the coordinates of the points can be rather large. Help Dima cope with the problem.", "input_spec": "The first line contains a single integer n (1 ≤ n ≤ 103). The second line contains n distinct integers x1, x2, ..., xn ( - 106 ≤ xi ≤ 106) — the i-th point has coordinates (xi, 0). The points are not necessarily sorted by their x coordinate.", "output_spec": "In the single line print \"yes\" (without the quotes), if the line has self-intersections. Otherwise, print \"no\" (without the quotes).", "sample_inputs": ["4\n0 10 5 15", "4\n0 15 5 10"], "sample_outputs": ["yes", "no"], "notes": "NoteThe first test from the statement is on the picture to the left, the second test is on the picture to the right."}, "src_uid": "f1b6b81ebd49f31428fe57913dfc604d"}
{"nl": {"description": "Nikolay has a lemons, b apples and c pears. He decided to cook a compote. According to the recipe the fruits should be in the ratio 1: 2: 4. It means that for each lemon in the compote should be exactly 2 apples and exactly 4 pears. You can't crumble up, break up or cut these fruits into pieces. These fruits — lemons, apples and pears — should be put in the compote as whole fruits.Your task is to determine the maximum total number of lemons, apples and pears from which Nikolay can cook the compote. It is possible that Nikolay can't use any fruits, in this case print 0. ", "input_spec": "The first line contains the positive integer a (1 ≤ a ≤ 1000) — the number of lemons Nikolay has.  The second line contains the positive integer b (1 ≤ b ≤ 1000) — the number of apples Nikolay has.  The third line contains the positive integer c (1 ≤ c ≤ 1000) — the number of pears Nikolay has.", "output_spec": "Print the maximum total number of lemons, apples and pears from which Nikolay can cook the compote.", "sample_inputs": ["2\n5\n7", "4\n7\n13", "2\n3\n2"], "sample_outputs": ["7", "21", "0"], "notes": "NoteIn the first example Nikolay can use 1 lemon, 2 apples and 4 pears, so the answer is 1 + 2 + 4 = 7.In the second example Nikolay can use 3 lemons, 6 apples and 12 pears, so the answer is 3 + 6 + 12 = 21.In the third example Nikolay don't have enough pears to cook any compote, so the answer is 0. "}, "src_uid": "82a4a60eac90765fb62f2a77d2305c01"}
{"nl": {"description": "One day the Codeforces round author sat exams. He had n exams and he needed to get an integer from 2 to 5 for each exam. He will have to re-sit each failed exam, i.e. the exam that gets mark 2. The author would need to spend too much time and effort to make the sum of his marks strictly more than k. That could have spoilt the Codeforces round. On the other hand, if the sum of his marks is strictly less than k, the author's mum won't be pleased at all. The Codeforces authors are very smart and they always get the mark they choose themselves. Also, the Codeforces authors just hate re-sitting exams. Help the author and find the minimum number of exams he will have to re-sit if he passes the exams in the way that makes the sum of marks for all n exams equal exactly k.", "input_spec": "The single input line contains space-separated integers n and k (1 ≤ n ≤ 50, 1 ≤ k ≤ 250) — the number of exams and the required sum of marks. It is guaranteed that there exists a way to pass n exams in the way that makes the sum of marks equal exactly k.", "output_spec": "Print the single number — the minimum number of exams that the author will get a 2 for, considering that the sum of marks for all exams must equal k.", "sample_inputs": ["4 8", "4 10", "1 3"], "sample_outputs": ["4", "2", "0"], "notes": "NoteIn the first sample the author has to get a 2 for all his exams.In the second sample he should get a 3 for two exams and a 2 for two more.In the third sample he should get a 3 for one exam."}, "src_uid": "5a5e46042c3f18529a03cb5c868df7e8"}
{"nl": {"description": "Manao is trying to open a rather challenging lock. The lock has n buttons on it and to open it, you should press the buttons in a certain order to open the lock. When you push some button, it either stays pressed into the lock (that means that you've guessed correctly and pushed the button that goes next in the sequence), or all pressed buttons return to the initial position. When all buttons are pressed into the lock at once, the lock opens.Consider an example with three buttons. Let's say that the opening sequence is: {2, 3, 1}. If you first press buttons 1 or 3, the buttons unpress immediately. If you first press button 2, it stays pressed. If you press 1 after 2, all buttons unpress. If you press 3 after 2, buttons 3 and 2 stay pressed. As soon as you've got two pressed buttons, you only need to press button 1 to open the lock.Manao doesn't know the opening sequence. But he is really smart and he is going to act in the optimal way. Calculate the number of times he's got to push a button in order to open the lock in the worst-case scenario.", "input_spec": "A single line contains integer n (1 ≤ n ≤ 2000) — the number of buttons the lock has.", "output_spec": "In a single line print the number of times Manao has to push a button in the worst-case scenario.", "sample_inputs": ["2", "3"], "sample_outputs": ["3", "7"], "notes": "NoteConsider the first test sample. Manao can fail his first push and push the wrong button. In this case he will already be able to guess the right one with his second push. And his third push will push the second right button. Thus, in the worst-case scenario he will only need 3 pushes."}, "src_uid": "6df251ac8bf27427a24bc23d64cb9884"}
{"nl": {"description": "In some country live wizards. They love playing with numbers. The blackboard has two numbers written on it — a and b. The order of the numbers is not important. Let's consider a ≤ b for the sake of definiteness. The players can cast one of the two spells in turns:  Replace b with b - ak. Number k can be chosen by the player, considering the limitations that k > 0 and b - ak ≥ 0. Number k is chosen independently each time an active player casts a spell.  Replace b with b mod a. If a > b, similar moves are possible.If at least one of the numbers equals zero, a player can't make a move, because taking a remainder modulo zero is considered somewhat uncivilized, and it is far too boring to subtract a zero. The player who cannot make a move, loses.To perform well in the magic totalizator, you need to learn to quickly determine which player wins, if both wizards play optimally: the one that moves first or the one that moves second.", "input_spec": "The first line contains a single integer t — the number of input data sets (1 ≤ t ≤ 104). Each of the next t lines contains two integers a, b (0 ≤ a, b ≤ 1018). The numbers are separated by a space. Please do not use the %lld specificator to read or write 64-bit integers in С++. It is preferred to use the cin, cout streams or the %I64d specificator.", "output_spec": "For any of the t input sets print \"First\" (without the quotes) if the player who moves first wins. Print \"Second\" (without the quotes) if the player who moves second wins. Print the answers to different data sets on different lines in the order in which they are given in the input. ", "sample_inputs": ["4\n10 21\n31 10\n0 1\n10 30"], "sample_outputs": ["First\nSecond\nSecond\nFirst"], "notes": "NoteIn the first sample, the first player should go to (11,10). Then, after a single move of the second player to (1,10), he will take 10 modulo 1 and win.In the second sample the first player has two moves to (1,10) and (21,10). After both moves the second player can win.In the third sample, the first player has no moves.In the fourth sample, the first player wins in one move, taking 30 modulo 10."}, "src_uid": "5f5b320c7f314bd06c0d2a9eb311de6c"}
{"nl": {"description": "Little C loves number «3» very much. He loves all things about it.Now he is playing a game on a chessboard of size $$$n \\times m$$$. The cell in the $$$x$$$-th row and in the $$$y$$$-th column is called $$$(x,y)$$$. Initially, The chessboard is empty. Each time, he places two chessmen on two different empty cells, the Manhattan distance between which is exactly $$$3$$$. The Manhattan distance between two cells $$$(x_i,y_i)$$$ and $$$(x_j,y_j)$$$ is defined as $$$|x_i-x_j|+|y_i-y_j|$$$.He want to place as many chessmen as possible on the chessboard. Please help him find the maximum number of chessmen he can place.", "input_spec": "A single line contains two integers $$$n$$$ and $$$m$$$ ($$$1 \\leq n,m \\leq 10^9$$$) — the number of rows and the number of columns of the chessboard.", "output_spec": "Print one integer — the maximum number of chessmen Little C can place.", "sample_inputs": ["2 2", "3 3"], "sample_outputs": ["0", "8"], "notes": "NoteIn the first example, the Manhattan distance between any two cells is smaller than $$$3$$$, so the answer is $$$0$$$.In the second example, a possible solution is $$$(1,1)(3,2)$$$, $$$(1,2)(3,3)$$$, $$$(2,1)(1,3)$$$, $$$(3,1)(2,3)$$$."}, "src_uid": "02ce135a4b276d1e9ba6a4ce37f2fe70"}
{"nl": {"description": "Yaroslav, Andrey and Roman love playing cubes. Sometimes they get together and play cubes for hours and hours! Today they got together again and they are playing cubes. Yaroslav took unit cubes and composed them into an a × a × a cube, Andrey made a b × b × b cube and Roman made a c × c × c cube. After that the game was finished and the guys left. But later, Vitaly entered the room. He saw the cubes and wanted to make a cube as well. But what size should the cube be? Of course it should be a large cube with the side of length a + b + c. Besides, Vitaly decided to decompose the cubes built by Yaroslav, Andrey and Roman and compose his own large cube out of them. However, it turned out that the unit cubes he got from destroying the three cubes just weren't enough to make a large cube. We know that Vitaly was short of exactly n cubes. Vitaly got upset, demolished everything and left. As he was leaving, he met Petya and told him that there had been three cubes in the room and that he needed another n unit cubes to make his own large cube.Petya entered the room and saw the messily scattered cubes. He wanted to make it neat and orderly again. But he only knows that there had been three cubes, made of small unit cubes and that Vitaly needed n more unit cubes to make a large one! Help Petya understand, how many ways of sizes a, b, c are there to restore Yaroslav's, Andrey's and Roman's cubes.", "input_spec": "The single line of the input contains integer n (1 ≤ n ≤ 1014). We know that all numbers a, b, c are positive integers. Please, do not use the %lld specifier to read or write 64-bit integers in С++. It is preferred to use the cin, cout streams or the %I64d specifier.", "output_spec": "In the single line print the required number of ways. If it turns out that there isn't a single way of suitable sizes of a, b, c, print 0. ", "sample_inputs": ["24", "648", "5", "93163582512000"], "sample_outputs": ["1", "7", "0", "39090"], "notes": null}, "src_uid": "07e58a46f2d562a44b7c771edad361b4"}
{"nl": {"description": "Alice and Bob begin their day with a quick game. They first choose a starting number X0 ≥ 3 and try to reach one million by the process described below. Alice goes first and then they take alternating turns. In the i-th turn, the player whose turn it is selects a prime number smaller than the current number, and announces the smallest multiple of this prime number that is not smaller than the current number.Formally, he or she selects a prime p < Xi - 1 and then finds the minimum Xi ≥ Xi - 1 such that p divides Xi. Note that if the selected prime p already divides Xi - 1, then the number does not change.Eve has witnessed the state of the game after two turns. Given X2, help her determine what is the smallest possible starting number X0. Note that the players don't necessarily play optimally. You should consider all possible game evolutions.", "input_spec": "The input contains a single integer X2 (4 ≤ X2 ≤ 106). It is guaranteed that the integer X2 is composite, that is, is not prime.", "output_spec": "Output a single integer — the minimum possible X0.", "sample_inputs": ["14", "20", "8192"], "sample_outputs": ["6", "15", "8191"], "notes": "NoteIn the first test, the smallest possible starting number is X0 = 6. One possible course of the game is as follows:   Alice picks prime 5 and announces X1 = 10  Bob picks prime 7 and announces X2 = 14. In the second case, let X0 = 15.   Alice picks prime 2 and announces X1 = 16  Bob picks prime 5 and announces X2 = 20. "}, "src_uid": "43ff6a223c68551eff793ba170110438"}
{"nl": {"description": "You have a plate and you want to add some gilding to it. The plate is a rectangle that we split into $$$w\\times h$$$ cells. There should be $$$k$$$ gilded rings, the first one should go along the edge of the plate, the second one — $$$2$$$ cells away from the edge and so on. Each ring has a width of $$$1$$$ cell. Formally, the $$$i$$$-th of these rings should consist of all bordering cells on the inner rectangle of size $$$(w - 4(i - 1))\\times(h - 4(i - 1))$$$.  The picture corresponds to the third example. Your task is to compute the number of cells to be gilded.", "input_spec": "The only line contains three integers $$$w$$$, $$$h$$$ and $$$k$$$ ($$$3 \\le w, h \\le 100$$$, $$$1 \\le k \\le \\left\\lfloor \\frac{min(n, m) + 1}{4}\\right\\rfloor$$$, where $$$\\lfloor x \\rfloor$$$ denotes the number $$$x$$$ rounded down) — the number of rows, columns and the number of rings, respectively.", "output_spec": "Print a single positive integer — the number of cells to be gilded.", "sample_inputs": ["3 3 1", "7 9 1", "7 9 2"], "sample_outputs": ["8", "28", "40"], "notes": "NoteThe first example is shown on the picture below.  The second example is shown on the picture below.  The third example is shown in the problem description."}, "src_uid": "2c98d59917337cb321d76f72a1b3c057"}
{"nl": {"description": "Iahub and his friend Floyd have started painting a wall. Iahub is painting the wall red and Floyd is painting it pink. You can consider the wall being made of a very large number of bricks, numbered 1, 2, 3 and so on. Iahub has the following scheme of painting: he skips x - 1 consecutive bricks, then he paints the x-th one. That is, he'll paint bricks x, 2·x, 3·x and so on red. Similarly, Floyd skips y - 1 consecutive bricks, then he paints the y-th one. Hence he'll paint bricks y, 2·y, 3·y and so on pink.After painting the wall all day, the boys observed that some bricks are painted both red and pink. Iahub has a lucky number a and Floyd has a lucky number b. Boys wonder how many bricks numbered no less than a and no greater than b are painted both red and pink. This is exactly your task: compute and print the answer to the question. ", "input_spec": "The input will have a single line containing four integers in this order: x, y, a, b. (1 ≤ x, y ≤ 1000, 1 ≤ a, b ≤ 2·109, a ≤ b).", "output_spec": "Output a single integer — the number of bricks numbered no less than a and no greater than b that are painted both red and pink.", "sample_inputs": ["2 3 6 18"], "sample_outputs": ["3"], "notes": "NoteLet's look at the bricks from a to b (a = 6, b = 18). The bricks colored in red are numbered 6, 8, 10, 12, 14, 16, 18. The bricks colored in pink are numbered 6, 9, 12, 15, 18. The bricks colored in both red and pink are numbered with 6, 12 and 18. "}, "src_uid": "c7aa8a95d5f8832015853cffa1374c48"}
{"nl": {"description": "Gerald is setting the New Year table. The table has the form of a circle; its radius equals R. Gerald invited many guests and is concerned whether the table has enough space for plates for all those guests. Consider all plates to be round and have the same radii that equal r. Each plate must be completely inside the table and must touch the edge of the table. Of course, the plates must not intersect, but they can touch each other. Help Gerald determine whether the table is large enough for n plates.", "input_spec": "The first line contains three integers n, R and r (1 ≤ n ≤ 100, 1 ≤ r, R ≤ 1000) — the number of plates, the radius of the table and the plates' radius.", "output_spec": "Print \"YES\" (without the quotes) if it is possible to place n plates on the table by the rules given above. If it is impossible, print \"NO\". Remember, that each plate must touch the edge of the table. ", "sample_inputs": ["4 10 4", "5 10 4", "1 10 10"], "sample_outputs": ["YES", "NO", "YES"], "notes": "NoteThe possible arrangement of the plates for the first sample is:   "}, "src_uid": "2fedbfccd893cde8f2fab2b5bf6fb6f6"}
{"nl": {"description": "Hongcow is learning to spell! One day, his teacher gives him a word that he needs to learn to spell. Being a dutiful student, he immediately learns how to spell the word.Hongcow has decided to try to make new words from this one. He starts by taking the word he just learned how to spell, and moves the last character of the word to the beginning of the word. He calls this a cyclic shift. He can apply cyclic shift many times. For example, consecutively applying cyclic shift operation to the word \"abracadabra\" Hongcow will get words \"aabracadabr\", \"raabracadab\" and so on.Hongcow is now wondering how many distinct words he can generate by doing the cyclic shift arbitrarily many times. The initial string is also counted.", "input_spec": "The first line of input will be a single string s (1 ≤ |s| ≤ 50), the word Hongcow initially learns how to spell. The string s consists only of lowercase English letters ('a'–'z').", "output_spec": "Output a single integer equal to the number of distinct strings that Hongcow can obtain by applying the cyclic shift arbitrarily many times to the given string.", "sample_inputs": ["abcd", "bbb", "yzyz"], "sample_outputs": ["4", "1", "2"], "notes": "NoteFor the first sample, the strings Hongcow can generate are \"abcd\", \"dabc\", \"cdab\", and \"bcda\".For the second sample, no matter how many times Hongcow does the cyclic shift, Hongcow can only generate \"bbb\".For the third sample, the two strings Hongcow can generate are \"yzyz\" and \"zyzy\"."}, "src_uid": "8909ac99ed4ab2ee4d681ec864c7831e"}
{"nl": {"description": "Nearly each project of the F company has a whole team of developers working on it. They often are in different rooms of the office in different cities and even countries. To keep in touch and track the results of the project, the F company conducts shared online meetings in a Spyke chat.One day the director of the F company got hold of the records of a part of an online meeting of one successful team. The director watched the record and wanted to talk to the team leader. But how can he tell who the leader is? The director logically supposed that the leader is the person who is present at any conversation during a chat meeting. In other words, if at some moment of time at least one person is present on the meeting, then the leader is present on the meeting.You are the assistant director. Given the 'user logged on'/'user logged off' messages of the meeting in the chronological order, help the director determine who can be the leader. Note that the director has the record of only a continuous part of the meeting (probably, it's not the whole meeting).", "input_spec": "The first line contains integers n and m (1 ≤ n, m ≤ 105) — the number of team participants and the number of messages. Each of the next m lines contains a message in the format:   '+ id': the record means that the person with number id (1 ≤ id ≤ n) has logged on to the meeting.  '- id': the record means that the person with number id (1 ≤ id ≤ n) has logged off from the meeting.  Assume that all the people of the team are numbered from 1 to n and the messages are given in the chronological order. It is guaranteed that the given sequence is the correct record of a continuous part of the meeting. It is guaranteed that no two log on/log off events occurred simultaneously.", "output_spec": "In the first line print integer k (0 ≤ k ≤ n) — how many people can be leaders. In the next line, print k integers in the increasing order — the numbers of the people who can be leaders. If the data is such that no member of the team can be a leader, print a single number 0.", "sample_inputs": ["5 4\n+ 1\n+ 2\n- 2\n- 1", "3 2\n+ 1\n- 2", "2 4\n+ 1\n- 1\n+ 2\n- 2", "5 6\n+ 1\n- 1\n- 3\n+ 3\n+ 4\n- 4", "2 4\n+ 1\n- 2\n+ 2\n- 1"], "sample_outputs": ["4\n1 3 4 5", "1\n3", "0", "3\n2 3 5", "0"], "notes": null}, "src_uid": "a3a337c7b919e7dfd7ff45ebf59681b5"}
{"nl": {"description": "Many students live in a dormitory. A dormitory is a whole new world of funny amusements and possibilities but it does have its drawbacks. There is only one shower and there are multiple students who wish to have a shower in the morning. That's why every morning there is a line of five people in front of the dormitory shower door. As soon as the shower opens, the first person from the line enters the shower. After a while the first person leaves the shower and the next person enters the shower. The process continues until everybody in the line has a shower.Having a shower takes some time, so the students in the line talk as they wait. At each moment of time the students talk in pairs: the (2i - 1)-th man in the line (for the current moment) talks with the (2i)-th one. Let's look at this process in more detail. Let's number the people from 1 to 5. Let's assume that the line initially looks as 23154 (person number 2 stands at the beginning of the line). Then, before the shower opens, 2 talks with 3, 1 talks with 5, 4 doesn't talk with anyone. Then 2 enters the shower. While 2 has a shower, 3 and 1 talk, 5 and 4 talk too. Then, 3 enters the shower. While 3 has a shower, 1 and 5 talk, 4 doesn't talk to anyone. Then 1 enters the shower and while he is there, 5 and 4 talk. Then 5 enters the shower, and then 4 enters the shower.We know that if students i and j talk, then the i-th student's happiness increases by gij and the j-th student's happiness increases by gji. Your task is to find such initial order of students in the line that the total happiness of all students will be maximum in the end. Please note that some pair of students may have a talk several times. In the example above students 1 and 5 talk while they wait for the shower to open and while 3 has a shower.", "input_spec": "The input consists of five lines, each line contains five space-separated integers: the j-th number in the i-th line shows gij (0 ≤ gij ≤ 105). It is guaranteed that gii = 0 for all i. Assume that the students are numbered from 1 to 5.", "output_spec": "Print a single integer — the maximum possible total happiness of the students.", "sample_inputs": ["0 0 0 0 9\n0 0 0 0 0\n0 0 0 0 0\n0 0 0 0 0\n7 0 0 0 0", "0 43 21 18 2\n3 0 21 11 65\n5 2 0 1 4\n54 62 12 0 99\n87 64 81 33 0"], "sample_outputs": ["32", "620"], "notes": "NoteIn the first sample, the optimal arrangement of the line is 23154. In this case, the total happiness equals:(g23 + g32 + g15 + g51) + (g13 + g31 + g54 + g45) + (g15 + g51) + (g54 + g45) = 32."}, "src_uid": "be6d4df20e9a48d183dd8f34531df246"}
{"nl": {"description": "An expedition group flew from planet ACM-1 to Earth in order to study the bipedal species (its representatives don't even have antennas on their heads!).The flying saucer, on which the brave pioneers set off, consists of three sections. These sections are connected by a chain: the 1-st section is adjacent only to the 2-nd one, the 2-nd one — to the 1-st and the 3-rd ones, the 3-rd one — only to the 2-nd one. The transitions are possible only between the adjacent sections.The spacecraft team consists of n aliens. Each of them is given a rank — an integer from 1 to n. The ranks of all astronauts are distinct. The rules established on the Saucer, state that an alien may move from section a to section b only if it is senior in rank to all aliens who are in the segments a and b (besides, the segments a and b are of course required to be adjacent). Any alien requires exactly 1 minute to make a move. Besides, safety regulations require that no more than one alien moved at the same minute along the ship.Alien A is senior in rank to alien B, if the number indicating rank A, is more than the corresponding number for B.At the moment the whole saucer team is in the 3-rd segment. They all need to move to the 1-st segment. One member of the crew, the alien with the identification number CFR-140, decided to calculate the minimum time (in minutes) they will need to perform this task.Help CFR-140, figure out the minimum time (in minutes) that all the astronauts will need to move from the 3-rd segment to the 1-st one. Since this number can be rather large, count it modulo m.", "input_spec": "The first line contains two space-separated integers: n and m (1 ≤ n, m ≤ 109) — the number of aliens on the saucer and the number, modulo which you should print the answer, correspondingly.", "output_spec": "Print a single number — the answer to the problem modulo m.", "sample_inputs": ["1 10", "3 8"], "sample_outputs": ["2", "2"], "notes": "NoteIn the first sample the only crew member moves from segment 3 to segment 2, and then from segment 2 to segment 1 without any problems. Thus, the whole moving will take two minutes.To briefly describe the movements in the second sample we will use value , which would correspond to an alien with rank i moving from the segment in which it is at the moment, to the segment number j. Using these values, we will describe the movements between the segments in the second sample: , , , , , , , , , , , , , , , , , , , , , , , , , ; In total: the aliens need 26 moves. The remainder after dividing 26 by 8 equals 2, so the answer to this test is 2."}, "src_uid": "c62ad7c7d1ea7aec058d99223c57d33c"}
{"nl": {"description": "You have two positive integers w and h. Your task is to count the number of rhombi which have the following properties:   Have positive area.  With vertices at integer points.  All vertices of the rhombi are located inside or on the border of the rectangle with vertices at points (0, 0), (w, 0), (w, h), (0, h). In other words, for all vertices (xi, yi) of the rhombus the following conditions should fulfill: 0 ≤ xi ≤ w and 0 ≤ yi ≤ h.  Its diagonals are parallel to the axis.  Count the number of such rhombi.Let us remind you that a rhombus is a quadrilateral whose four sides all have the same length.", "input_spec": "The first line contains two integers w and h (1 ≤ w, h ≤ 4000) — the rectangle's sizes.", "output_spec": "Print a single number — the number of sought rhombi. Please do not use the %lld specifier to read or write 64-bit integers in С++. It is preferred to use cin, cout streams or the %I64d specifier.", "sample_inputs": ["2 2", "1 2"], "sample_outputs": ["1", "0"], "notes": "NoteIn the first example there exists only one such rhombus. Its vertices are located at points (1, 0), (2, 1), (1, 2), (0, 1)."}, "src_uid": "42454dcf7d073bf12030367eb094eb8c"}
{"nl": {"description": "One day, the Grasshopper was jumping on the lawn and found a piece of paper with a string. Grasshopper became interested what is the minimum jump ability he should have in order to be able to reach the far end of the string, jumping only on vowels of the English alphabet. Jump ability is the maximum possible length of his jump. Formally, consider that at the begginning the Grasshopper is located directly in front of the leftmost character of the string. His goal is to reach the position right after the rightmost character of the string. In one jump the Grasshopper could jump to the right any distance from 1 to the value of his jump ability.    The picture corresponds to the first example. The following letters are vowels: 'A', 'E', 'I', 'O', 'U' and 'Y'.", "input_spec": "The first line contains non-empty string consisting of capital English letters. It is guaranteed that the length of the string does not exceed 100. ", "output_spec": "Print single integer a — the minimum jump ability of the Grasshopper (in the number of symbols) that is needed to overcome the given string, jumping only on vowels.", "sample_inputs": ["ABABBBACFEYUKOTT", "AAA"], "sample_outputs": ["4", "1"], "notes": null}, "src_uid": "1fc7e939cdeb015fe31f3cf1c0982fee"}
{"nl": {"description": "Luba is surfing the Internet. She currently has n opened tabs in her browser, indexed from 1 to n from left to right. The mouse cursor is currently located at the pos-th tab. Luba needs to use the tabs with indices from l to r (inclusive) for her studies, and she wants to close all the tabs that don't belong to this segment as fast as possible.Each second Luba can either try moving the cursor to the left or to the right (if the cursor is currently at the tab i, then she can move it to the tab max(i - 1, a) or to the tab min(i + 1, b)) or try closing all the tabs to the left or to the right of the cursor (if the cursor is currently at the tab i, she can close all the tabs with indices from segment [a, i - 1] or from segment [i + 1, b]). In the aforementioned expressions a and b denote the minimum and maximum index of an unclosed tab, respectively. For example, if there were 7 tabs initially and tabs 1, 2 and 7 are closed, then a = 3, b = 6.What is the minimum number of seconds Luba has to spend in order to leave only the tabs with initial indices from l to r inclusive opened?", "input_spec": "The only line of input contains four integer numbers n, pos, l, r (1 ≤ n ≤ 100, 1 ≤ pos ≤ n, 1 ≤ l ≤ r ≤ n) — the number of the tabs, the cursor position and the segment which Luba needs to leave opened.", "output_spec": "Print one integer equal to the minimum number of seconds required to close all the tabs outside the segment [l, r].", "sample_inputs": ["6 3 2 4", "6 3 1 3", "5 2 1 5"], "sample_outputs": ["5", "1", "0"], "notes": "NoteIn the first test Luba can do the following operations: shift the mouse cursor to the tab 2, close all the tabs to the left of it, shift the mouse cursor to the tab 3, then to the tab 4, and then close all the tabs to the right of it.In the second test she only needs to close all the tabs to the right of the current position of the cursor.In the third test Luba doesn't need to do anything."}, "src_uid": "5deaac7bd3afedee9b10e61997940f78"}
{"nl": {"description": "Polycarpus has got n candies and m friends (n ≥ m). He wants to make a New Year present with candies to each friend. Polycarpus is planning to present all candies and he wants to do this in the fairest (that is, most equal) manner. He wants to choose such ai, where ai is the number of candies in the i-th friend's present, that the maximum ai differs from the least ai as little as possible.For example, if n is divisible by m, then he is going to present the same number of candies to all his friends, that is, the maximum ai won't differ from the minimum one.", "input_spec": "The single line of the input contains a pair of space-separated positive integers n, m (1 ≤ n, m ≤ 100;n ≥ m) — the number of candies and the number of Polycarpus's friends.", "output_spec": "Print the required sequence a1, a2, ..., am, where ai is the number of candies in the i-th friend's present. All numbers ai must be positive integers, total up to n, the maximum one should differ from the minimum one by the smallest possible value.", "sample_inputs": ["12 3", "15 4", "18 7"], "sample_outputs": ["4 4 4", "3 4 4 4", "2 2 2 3 3 3 3"], "notes": "NotePrint ai in any order, separate the numbers by spaces."}, "src_uid": "0b2c1650979a9931e00ffe32a70e3c23"}
{"nl": {"description": "You are given set of n points in 5-dimensional space. The points are labeled from 1 to n. No two points coincide.We will call point a bad if there are different points b and c, not equal to a, from the given set such that angle between vectors  and  is acute (i.e. strictly less than ). Otherwise, the point is called good.The angle between vectors  and  in 5-dimensional space is defined as , where  is the scalar product and  is length of .Given the list of points, print the indices of the good points in ascending order.", "input_spec": "The first line of input contains a single integer n (1 ≤ n ≤ 103) — the number of points. The next n lines of input contain five integers ai, bi, ci, di, ei (|ai|, |bi|, |ci|, |di|, |ei| ≤ 103)  — the coordinates of the i-th point. All points are distinct.", "output_spec": "First, print a single integer k — the number of good points. Then, print k integers, each on their own line — the indices of the good points in ascending order.", "sample_inputs": ["6\n0 0 0 0 0\n1 0 0 0 0\n0 1 0 0 0\n0 0 1 0 0\n0 0 0 1 0\n0 0 0 0 1", "3\n0 0 1 2 0\n0 0 9 2 0\n0 0 5 9 0"], "sample_outputs": ["1\n1", "0"], "notes": "NoteIn the first sample, the first point forms exactly a  angle with all other pairs of points, so it is good.In the second sample, along the cd plane, we can see the points look as follows:We can see that all angles here are acute, so no points are good."}, "src_uid": "c1cfe1f67217afd4c3c30a6327e0add9"}
{"nl": {"description": "Consider the infinite sequence of integers: 1, 1, 2, 1, 2, 3, 1, 2, 3, 4, 1, 2, 3, 4, 5.... The sequence is built in the following way: at first the number 1 is written out, then the numbers from 1 to 2, then the numbers from 1 to 3, then the numbers from 1 to 4 and so on. Note that the sequence contains numbers, not digits. For example number 10 first appears in the sequence in position 55 (the elements are numerated from one).Find the number on the n-th position of the sequence.", "input_spec": "The only line contains integer n (1 ≤ n ≤ 1014) — the position of the number to find. Note that the given number is too large, so you should use 64-bit integer type to store it. In C++ you can use the long long integer type and in Java you can use long integer type.", "output_spec": "Print the element in the n-th position of the sequence (the elements are numerated from one).", "sample_inputs": ["3", "5", "10", "55", "56"], "sample_outputs": ["2", "2", "4", "10", "1"], "notes": null}, "src_uid": "1db5631847085815461c617854b08ee5"}
{"nl": {"description": "Xenia the beginner mathematician is a third year student at elementary school. She is now learning the addition operation.The teacher has written down the sum of multiple numbers. Pupils should calculate the sum. To make the calculation easier, the sum only contains numbers 1, 2 and 3. Still, that isn't enough for Xenia. She is only beginning to count, so she can calculate a sum only if the summands follow in non-decreasing order. For example, she can't calculate sum 1+3+2+1 but she can calculate sums 1+1+2 and 3+3.You've got the sum that was written on the board. Rearrange the summans and print the sum in such a way that Xenia can calculate the sum.", "input_spec": "The first line contains a non-empty string s — the sum Xenia needs to count. String s contains no spaces. It only contains digits and characters \"+\". Besides, string s is a correct sum of numbers 1, 2 and 3. String s is at most 100 characters long.", "output_spec": "Print the new sum that Xenia can count.", "sample_inputs": ["3+2+1", "1+1+3+1+3", "2"], "sample_outputs": ["1+2+3", "1+1+1+3+3", "2"], "notes": null}, "src_uid": "76c7312733ef9d8278521cf09d3ccbc8"}
{"nl": {"description": "Recently Luba learned about a special kind of numbers that she calls beautiful numbers. The number is called beautiful iff its binary representation consists of k + 1 consecutive ones, and then k consecutive zeroes.Some examples of beautiful numbers:   12 (110);  1102 (610);  11110002 (12010);  1111100002 (49610). More formally, the number is beautiful iff there exists some positive integer k such that the number is equal to (2k - 1) * (2k - 1).Luba has got an integer number n, and she wants to find its greatest beautiful divisor. Help her to find it!", "input_spec": "The only line of input contains one number n (1 ≤ n ≤ 105) — the number Luba has got.", "output_spec": "Output one number — the greatest beautiful divisor of Luba's number. It is obvious that the answer always exists.", "sample_inputs": ["3", "992"], "sample_outputs": ["1", "496"], "notes": null}, "src_uid": "339246a1be81aefe19290de0d1aead84"}
{"nl": {"description": "Let's consider an n × n square matrix, consisting of digits one and zero.We'll consider a matrix good, if it meets the following condition: in each row of the matrix all ones go in one group. That is, each row of the matrix looks like that 00...0011...1100...00 (or simply consists of zeroes if it has no ones).You are given matrix a of size n × n, consisting of zeroes and ones. Your task is to determine whether you can get a good matrix b from it by rearranging the columns or not.", "input_spec": "The first line contains integer n (1 ≤ n ≤ 500) — the size of matrix a. Each of n following lines contains n characters \"0\" and \"1\" — matrix a. Note that the characters are written without separators.", "output_spec": "Print \"YES\" in the first line, if you can rearrange the matrix columns so as to get a good matrix b. In the next n lines print the good matrix b. If there are multiple answers, you are allowed to print any of them. If it is impossible to get a good matrix, print \"NO\".", "sample_inputs": ["6\n100010\n110110\n011001\n010010\n000100\n011001", "3\n110\n101\n011"], "sample_outputs": ["YES\n011000\n111100\n000111\n001100\n100000\n000111", "NO"], "notes": null}, "src_uid": "af8d46722e1bd8f7392e5596eaf4def8"}
{"nl": {"description": "There are literally dozens of snooker competitions held each year, and team Jinotega tries to attend them all (for some reason they prefer name \"snookah\")! When a competition takes place somewhere far from their hometown, Ivan, Artsem and Konstantin take a flight to the contest and back.Jinotega's best friends, team Base have found a list of their itinerary receipts with information about departure and arrival airports. Now they wonder, where is Jinotega now: at home or at some competition far away? They know that:   this list contains all Jinotega's flights in this year (in arbitrary order),  Jinotega has only flown from his hometown to a snooker contest and back,  after each competition Jinotega flies back home (though they may attend a competition in one place several times),  and finally, at the beginning of the year Jinotega was at home. Please help them to determine Jinotega's location!", "input_spec": "In the first line of input there is a single integer n: the number of Jinotega's flights (1 ≤ n ≤ 100). In the second line there is a string of 3 capital Latin letters: the name of Jinotega's home airport. In the next n lines there is flight information, one flight per line, in form \"XXX->YYY\", where \"XXX\" is the name of departure airport \"YYY\" is the name of arrival airport. Exactly one of these airports is Jinotega's home airport. It is guaranteed that flights information is consistent with the knowledge of Jinotega's friends, which is described in the main part of the statement.", "output_spec": "If Jinotega is now at home, print \"home\" (without quotes), otherwise print \"contest\".", "sample_inputs": ["4\nSVO\nSVO->CDG\nLHR->SVO\nSVO->LHR\nCDG->SVO", "3\nSVO\nSVO->HKT\nHKT->SVO\nSVO->RAP"], "sample_outputs": ["home", "contest"], "notes": "NoteIn the first sample Jinotega might first fly from SVO to CDG and back, and then from SVO to LHR and back, so now they should be at home. In the second sample Jinotega must now be at RAP because a flight from RAP back to SVO is not on the list."}, "src_uid": "51d1c79a52d3d4f80c98052b6ec77222"}
{"nl": {"description": "Три брата договорились о встрече. Пронумеруем братьев следующим образом: пусть старший брат имеет номер 1, средний брат имеет номер 2, а младший брат — номер 3. Когда пришло время встречи, один из братьев опоздал. По заданным номерам двух братьев, которые пришли вовремя, вам предстоит определить номер опоздавшего брата.", "input_spec": "В первой строке входных данных следуют два различных целых числа a и b (1 ≤ a, b ≤ 3, a ≠ b) — номера братьев, которые пришли на встречу вовремя. Номера даны в произвольном порядке.", "output_spec": "Выведите единственное целое число — номер брата, который опоздал на встречу.", "sample_inputs": ["3 1"], "sample_outputs": ["2"], "notes": null}, "src_uid": "e167dc35a0d3b98c0414c66099e35920"}
{"nl": {"description": "Two friends are on the coordinate axis Ox in points with integer coordinates. One of them is in the point x1 = a, another one is in the point x2 = b. Each of the friends can move by one along the line in any direction unlimited number of times. When a friend moves, the tiredness of a friend changes according to the following rules: the first move increases the tiredness by 1, the second move increases the tiredness by 2, the third — by 3 and so on. For example, if a friend moves first to the left, then to the right (returning to the same point), and then again to the left his tiredness becomes equal to 1 + 2 + 3 = 6.The friends want to meet in a integer point. Determine the minimum total tiredness they should gain, if they meet in the same point.", "input_spec": "The first line contains a single integer a (1 ≤ a ≤ 1000) — the initial position of the first friend.  The second line contains a single integer b (1 ≤ b ≤ 1000) — the initial position of the second friend. It is guaranteed that a ≠ b.", "output_spec": "Print the minimum possible total tiredness if the friends meet in the same point.", "sample_inputs": ["3\n4", "101\n99", "5\n10"], "sample_outputs": ["1", "2", "9"], "notes": "NoteIn the first example the first friend should move by one to the right (then the meeting happens at point 4), or the second friend should move by one to the left (then the meeting happens at point 3). In both cases, the total tiredness becomes 1.In the second example the first friend should move by one to the left, and the second friend should move by one to the right. Then they meet in the point 100, and the total tiredness becomes 1 + 1 = 2.In the third example one of the optimal ways is the following. The first friend should move three times to the right, and the second friend — two times to the left. Thus the friends meet in the point 8, and the total tiredness becomes 1 + 2 + 3 + 1 + 2 = 9."}, "src_uid": "d3f2c6886ed104d7baba8dd7b70058da"}
{"nl": {"description": "When Igor K. was a freshman, his professor strictly urged him, as well as all other freshmen, to solve programming Olympiads. One day a problem called \"Flags\" from a website called Timmy's Online Judge caught his attention. In the problem one had to find the number of three-colored flags that would satisfy the condition... actually, it doesn't matter. Igor K. quickly found the formula and got the so passionately desired Accepted.However, the professor wasn't very much impressed. He decided that the problem represented on Timmy's Online Judge was very dull and simple: it only had three possible colors of flag stripes and only two limitations. He suggested a complicated task to Igor K. and the fellow failed to solve it. Of course, we won't tell anybody that the professor couldn't solve it as well.And how about you? Can you solve the problem?The flags consist of one or several parallel stripes of similar width. The stripes can be one of the following colors: white, black, red or yellow. You should find the number of different flags with the number of stripes from L to R, if:  a flag cannot have adjacent stripes of one color;  a flag cannot have adjacent white and yellow stripes;  a flag cannot have adjacent red and black stripes;  a flag cannot have the combination of black, white and red stripes following one after another in this or reverse order;  symmetrical flags (as, for example, a WB and a BW flag, where W and B stand for the white and black colors) are considered the same. ", "input_spec": "The only line contains two integers L and R (1 ≤ L ≤ R ≤ 109). They are the lower and upper borders of the number of stripes on the flag.", "output_spec": "Print a single number — the number of different flags that would satisfy the condition of the problem and would have from L to R stripes, modulo 1000000007.", "sample_inputs": ["3 4", "5 6"], "sample_outputs": ["23", "64"], "notes": "NoteIn the first test the following flags exist (they are listed in the lexicographical order, the letters B, R, W, Y stand for Black, Red, White and Yellow correspondingly):3 stripes: BWB, BYB, BYR, RWR, RYR, WBW, WBY, WRW, WRY, YBY, YRY (overall 11 flags).4 stripes: BWBW, BWBY, BYBW, BYBY, BYRW, BYRY, RWRW, RWRY, RYBW, RYBY, RYRW, RYRY (12 flags).That's why the answer to test 1 is equal to 11 + 12 = 23."}, "src_uid": "e04b6957d9c1659e9d2460410cb57f10"}
{"nl": {"description": "Petya started to attend programming lessons. On the first lesson his task was to write a simple program. The program was supposed to do the following: in the given string, consisting if uppercase and lowercase Latin letters, it:   deletes all the vowels,  inserts a character \".\" before each consonant,  replaces all uppercase consonants with corresponding lowercase ones. Vowels are letters \"A\", \"O\", \"Y\", \"E\", \"U\", \"I\", and the rest are consonants. The program's input is exactly one string, it should return the output as a single string, resulting after the program's processing the initial string.Help Petya cope with this easy task.", "input_spec": "The first line represents input string of Petya's program. This string only consists of uppercase and lowercase Latin letters and its length is from 1 to 100, inclusive.", "output_spec": "Print the resulting string. It is guaranteed that this string is not empty.", "sample_inputs": ["tour", "Codeforces", "aBAcAba"], "sample_outputs": [".t.r", ".c.d.f.r.c.s", ".b.c.b"], "notes": null}, "src_uid": "db9520e85b3e9186dd3a09ff8d1e8c1b"}
{"nl": {"description": "There are five people playing a game called \"Generosity\". Each person gives some non-zero number of coins b as an initial bet. After all players make their bets of b coins, the following operation is repeated for several times: a coin is passed from one player to some other player.Your task is to write a program that can, given the number of coins each player has at the end of the game, determine the size b of the initial bet or find out that such outcome of the game cannot be obtained for any positive number of coins b in the initial bet.", "input_spec": "The input consists of a single line containing five integers c1, c2, c3, c4 and c5 — the number of coins that the first, second, third, fourth and fifth players respectively have at the end of the game (0 ≤ c1, c2, c3, c4, c5 ≤ 100).", "output_spec": "Print the only line containing a single positive integer b — the number of coins in the initial bet of each player. If there is no such value of b, then print the only value \"-1\" (quotes for clarity).", "sample_inputs": ["2 5 4 0 4", "4 5 9 2 1"], "sample_outputs": ["3", "-1"], "notes": "NoteIn the first sample the following sequence of operations is possible:  One coin is passed from the fourth player to the second player;  One coin is passed from the fourth player to the fifth player;  One coin is passed from the first player to the third player;  One coin is passed from the fourth player to the second player. "}, "src_uid": "af1ec6a6fc1f2360506fc8a34e3dcd20"}
{"nl": {"description": "Mashmokh works in a factory. At the end of each day he must turn off all of the lights. The lights on the factory are indexed from 1 to n. There are n buttons in Mashmokh's room indexed from 1 to n as well. If Mashmokh pushes button with index i, then each light with index not less than i that is still turned on turns off.Mashmokh is not very clever. So instead of pushing the first button he pushes some of the buttons randomly each night. He pushed m distinct buttons b1, b2, ..., bm (the buttons were pushed consecutively in the given order) this night. Now he wants to know for each light the index of the button that turned this light off. Please note that the index of button bi is actually bi, not i.Please, help Mashmokh, print these indices.", "input_spec": "The first line of the input contains two space-separated integers n and m (1 ≤ n, m ≤ 100), the number of the factory lights and the pushed buttons respectively. The next line contains m distinct space-separated integers b1, b2, ..., bm (1 ≤ bi ≤ n). It is guaranteed that all lights will be turned off after pushing all buttons.", "output_spec": "Output n space-separated integers where the i-th number is index of the button that turns the i-th light off.", "sample_inputs": ["5 4\n4 3 1 2", "5 5\n5 4 3 2 1"], "sample_outputs": ["1 1 3 4 4", "1 2 3 4 5"], "notes": "NoteIn the first sample, after pressing button number 4, lights 4 and 5 are turned off and lights 1, 2 and 3 are still on. Then after pressing button number 3, light number 3 is turned off as well. Pressing button number 1 turns off lights number 1 and 2 as well so pressing button number 2 in the end has no effect. Thus button number 4 turned lights 4 and 5 off, button number 3 turned light 3 off and button number 1 turned light 1 and 2 off."}, "src_uid": "2e44c8aabab7ef7b06bbab8719a8d863"}
{"nl": {"description": "Galois is one of the strongest chess players of Byteforces. He has even invented a new variant of chess, which he named «PawnChess».This new game is played on a board consisting of 8 rows and 8 columns. At the beginning of every game some black and white pawns are placed on the board. The number of black pawns placed is not necessarily equal to the number of white pawns placed.   Lets enumerate rows and columns with integers from 1 to 8. Rows are numbered from top to bottom, while columns are numbered from left to right. Now we denote as (r, c) the cell located at the row r and at the column c.There are always two players A and B playing the game. Player A plays with white pawns, while player B plays with black ones. The goal of player A is to put any of his pawns to the row 1, while player B tries to put any of his pawns to the row 8. As soon as any of the players completes his goal the game finishes immediately and the succeeded player is declared a winner.Player A moves first and then they alternate turns. On his move player A must choose exactly one white pawn and move it one step upward and player B (at his turn) must choose exactly one black pawn and move it one step down. Any move is possible only if the targeted cell is empty. It's guaranteed that for any scenario of the game there will always be at least one move available for any of the players.Moving upward means that the pawn located in (r, c) will go to the cell (r - 1, c), while moving down means the pawn located in (r, c) will go to the cell (r + 1, c). Again, the corresponding cell must be empty, i.e. not occupied by any other pawn of any color.Given the initial disposition of the board, determine who wins the game if both players play optimally. Note that there will always be a winner due to the restriction that for any game scenario both players will have some moves available.", "input_spec": "The input consists of the board description given in eight lines, each line contains eight characters. Character 'B' is used to denote a black pawn, and character 'W' represents a white pawn. Empty cell is marked with '.'.  It's guaranteed that there will not be white pawns on the first row neither black pawns on the last row.", "output_spec": "Print 'A' if player A wins the game on the given board, and 'B' if player B will claim the victory. Again, it's guaranteed that there will always be a winner on the given board.", "sample_inputs": ["........\n........\n.B....B.\n....W...\n........\n..W.....\n........\n........", "..B.....\n..W.....\n......B.\n........\n.....W..\n......B.\n........\n........"], "sample_outputs": ["A", "B"], "notes": "NoteIn the first sample player A is able to complete his goal in 3 steps by always moving a pawn initially located at (4, 5). Player B needs at least 5 steps for any of his pawns to reach the row 8. Hence, player A will be the winner."}, "src_uid": "0ddc839e17dee20e1a954c1289de7fbd"}
{"nl": {"description": "The only difference between this problem and D2 is that you don't have to provide the way to construct the answer in this problem, but you have to do it in D2.There's a table of $$$n \\times m$$$ cells ($$$n$$$ rows and $$$m$$$ columns). The value of $$$n \\cdot m$$$ is even.A domino is a figure that consists of two cells having a common side. It may be horizontal (one of the cells is to the right of the other) or vertical (one of the cells is above the other).You need to find out whether it is possible to place $$$\\frac{nm}{2}$$$ dominoes on the table so that exactly $$$k$$$ of them are horizontal and all the other dominoes are vertical. The dominoes cannot overlap and must fill the whole table.", "input_spec": "The first line contains one integer $$$t$$$ ($$$1 \\le t \\le 10$$$) — the number of test cases. Then $$$t$$$ test cases follow. Each test case consists of a single line. The line contains three integers $$$n$$$, $$$m$$$, $$$k$$$ ($$$1 \\le n,m \\le 100$$$, $$$0 \\le k \\le \\frac{nm}{2}$$$, $$$n \\cdot m$$$ is even) — the number of rows, columns and horizontal dominoes, respectively.", "output_spec": "For each test case output \"YES\", if it is possible to place dominoes in the desired way, or \"NO\" otherwise. You may print each letter in any case (YES, yes, Yes will all be recognized as positive answer, NO, no and nO will all be recognized as negative answer).", "sample_inputs": ["8\n4 4 2\n2 3 0\n3 2 3\n1 2 0\n2 4 2\n5 2 2\n2 17 16\n2 1 1"], "sample_outputs": ["YES\nYES\nYES\nNO\nYES\nNO\nYES\nNO"], "notes": null}, "src_uid": "4d0c0cc8faca62eb6384f8135b30feb8"}
{"nl": {"description": "There is a very secret base in Potatoland where potato mash is made according to a special recipe. The neighbours from Porridgia decided to seize this recipe and to sell it to Pilauland. For this mission they have been preparing special agent Pearlo for many years. When, finally, Pearlo learned all secrets of espionage, he penetrated into the Potatoland territory and reached the secret base.Now he is standing at the entrance, but to get inside he need to pass combination lock. Minute ago one of the workers entered the password on the terminal and opened the door. The terminal is a square digital keyboard 3 × 3 with digits from 1 to 9.Pearlo knows that the password consists from distinct digits and is probably symmetric with respect to the central button of the terminal. He has heat sensor which allowed him to detect the digits which the worker pressed. Now he wants to check whether the password entered by the worker is symmetric with respect to the central button of the terminal. This fact can Help Pearlo to reduce the number of different possible password combinations.", "input_spec": "Input contains the matrix of three rows of three symbols each. Symbol «X» means that the corresponding button was pressed, and «.» means that is was not pressed. The matrix may contain no «X», also it may contain no «.».", "output_spec": "Print YES if the password is symmetric with respect to the central button of the terminal and NO otherwise.", "sample_inputs": ["XX.\n...\n.XX", "X.X\nX..\n..."], "sample_outputs": ["YES", "NO"], "notes": "NoteIf you are not familiar with the term «central symmetry», you may look into http://en.wikipedia.org/wiki/Central_symmetry"}, "src_uid": "6a5fe5fac8a4e3993dc3423180cdd6a9"}
{"nl": {"description": "A permutation of length $$$n$$$ is an array consisting of $$$n$$$ distinct integers from $$$1$$$ to $$$n$$$ in arbitrary order. For example, $$$[2,3,1,5,4]$$$ is a permutation, but $$$[1,2,2]$$$ is not a permutation ($$$2$$$ appears twice in the array) and $$$[1,3,4]$$$ is also not a permutation ($$$n=3$$$ but there is $$$4$$$ in the array).Consider a permutation $$$p$$$ of length $$$n$$$, we build a graph of size $$$n$$$ using it as follows:   For every $$$1 \\leq i \\leq n$$$, find the largest $$$j$$$ such that $$$1 \\leq j < i$$$ and $$$p_j > p_i$$$, and add an undirected edge between node $$$i$$$ and node $$$j$$$  For every $$$1 \\leq i \\leq n$$$, find the smallest $$$j$$$ such that $$$i < j \\leq n$$$ and $$$p_j > p_i$$$, and add an undirected edge between node $$$i$$$ and node $$$j$$$ In cases where no such $$$j$$$ exists, we make no edges. Also, note that we make edges between the corresponding indices, not the values at those indices.For clarity, consider as an example $$$n = 4$$$, and $$$p = [3,1,4,2]$$$; here, the edges of the graph are $$$(1,3),(2,1),(2,3),(4,3)$$$.A permutation $$$p$$$ is cyclic if the graph built using $$$p$$$ has at least one simple cycle. Given $$$n$$$, find the number of cyclic permutations of length $$$n$$$. Since the number may be very large, output it modulo $$$10^9+7$$$.Please refer to the Notes section for the formal definition of a simple cycle", "input_spec": "The first and only line contains a single integer $$$n$$$ ($$$3 \\le n \\le 10^6$$$).", "output_spec": "Output a single integer $$$0 \\leq x < 10^9+7$$$, the number of cyclic permutations of length $$$n$$$ modulo $$$10^9+7$$$.", "sample_inputs": ["4", "583291"], "sample_outputs": ["16", "135712853"], "notes": "NoteThere are $$$16$$$ cyclic permutations for $$$n = 4$$$. $$$[4,2,1,3]$$$ is one such permutation, having a cycle of length four: $$$4 \\rightarrow 3 \\rightarrow 2 \\rightarrow 1 \\rightarrow 4$$$.Nodes $$$v_1$$$, $$$v_2$$$, $$$\\ldots$$$, $$$v_k$$$ form a simple cycle if the following conditions hold:   $$$k \\geq 3$$$.  $$$v_i \\neq v_j$$$ for any pair of indices $$$i$$$ and $$$j$$$. ($$$1 \\leq i < j \\leq k$$$)  $$$v_i$$$ and $$$v_{i+1}$$$ share an edge for all $$$i$$$ ($$$1 \\leq i < k$$$), and $$$v_1$$$ and $$$v_k$$$ share an edge. "}, "src_uid": "3dc1ee09016a25421ae371fa8005fce1"}
{"nl": {"description": "wHAT DO WE NEED cAPS LOCK FOR?Caps lock is a computer keyboard key. Pressing it sets an input mode in which typed letters are capital by default. If it is pressed by accident, it leads to accidents like the one we had in the first passage. Let's consider that a word has been typed with the Caps lock key accidentally switched on, if:   either it only contains uppercase letters;  or all letters except for the first one are uppercase. In this case we should automatically change the case of all letters. For example, the case of the letters that form words \"hELLO\", \"HTTP\", \"z\" should be changed.Write a program that applies the rule mentioned above. If the rule cannot be applied, the program should leave the word unchanged.", "input_spec": "The first line of the input data contains a word consisting of uppercase and lowercase Latin letters. The word's length is from 1 to 100 characters, inclusive.", "output_spec": "Print the result of the given word's processing.", "sample_inputs": ["cAPS", "Lock"], "sample_outputs": ["Caps", "Lock"], "notes": null}, "src_uid": "db0eb44d8cd8f293da407ba3adee10cf"}
{"nl": {"description": "Mr. Kitayuta has kindly given you a string s consisting of lowercase English letters. You are asked to insert exactly one lowercase English letter into s to make it a palindrome. A palindrome is a string that reads the same forward and backward. For example, \"noon\", \"testset\" and \"a\" are all palindromes, while \"test\" and \"kitayuta\" are not.You can choose any lowercase English letter, and insert it to any position of s, possibly to the beginning or the end of s. You have to insert a letter even if the given string is already a palindrome.If it is possible to insert one lowercase English letter into s so that the resulting string will be a palindrome, print the string after the insertion. Otherwise, print \"NA\" (without quotes, case-sensitive). In case there is more than one palindrome that can be obtained, you are allowed to print any of them.", "input_spec": "The only line of the input contains a string s (1 ≤ |s| ≤ 10). Each character in s is a lowercase English letter.", "output_spec": "If it is possible to turn s into a palindrome by inserting one lowercase English letter, print the resulting string in a single line. Otherwise, print \"NA\" (without quotes, case-sensitive). In case there is more than one solution, any of them will be accepted. ", "sample_inputs": ["revive", "ee", "kitayuta"], "sample_outputs": ["reviver", "eye", "NA"], "notes": "NoteFor the first sample, insert 'r' to the end of \"revive\" to obtain a palindrome \"reviver\".For the second sample, there is more than one solution. For example, \"eve\" will also be accepted.For the third sample, it is not possible to turn \"kitayuta\" into a palindrome by just inserting one letter."}, "src_uid": "24e8aaa7e3e1776adf342ffa1baad06b"}
{"nl": {"description": "A few years ago, Hitagi encountered a giant crab, who stole the whole of her body weight. Ever since, she tried to avoid contact with others, for fear that this secret might be noticed.To get rid of the oddity and recover her weight, a special integer sequence is needed. Hitagi's sequence has been broken for a long time, but now Kaiki provides an opportunity.Hitagi's sequence a has a length of n. Lost elements in it are denoted by zeros. Kaiki provides another sequence b, whose length k equals the number of lost elements in a (i.e. the number of zeros). Hitagi is to replace each zero in a with an element from b so that each element in b should be used exactly once. Hitagi knows, however, that, apart from 0, no integer occurs in a and b more than once in total.If the resulting sequence is not an increasing sequence, then it has the power to recover Hitagi from the oddity. You are to determine whether this is possible, or Kaiki's sequence is just another fake. In other words, you should detect whether it is possible to replace each zero in a with an integer from b so that each integer from b is used exactly once, and the resulting sequence is not increasing.", "input_spec": "The first line of input contains two space-separated positive integers n (2 ≤ n ≤ 100) and k (1 ≤ k ≤ n) — the lengths of sequence a and b respectively. The second line contains n space-separated integers a1, a2, ..., an (0 ≤ ai ≤ 200) — Hitagi's broken sequence with exactly k zero elements. The third line contains k space-separated integers b1, b2, ..., bk (1 ≤ bi ≤ 200) — the elements to fill into Hitagi's sequence. Input guarantees that apart from 0, no integer occurs in a and b more than once in total.", "output_spec": "Output \"Yes\" if it's possible to replace zeros in a with elements in b and make the resulting sequence not increasing, and \"No\" otherwise.", "sample_inputs": ["4 2\n11 0 0 14\n5 4", "6 1\n2 3 0 8 9 10\n5", "4 1\n8 94 0 4\n89", "7 7\n0 0 0 0 0 0 0\n1 2 3 4 5 6 7"], "sample_outputs": ["Yes", "No", "Yes", "Yes"], "notes": "NoteIn the first sample:   Sequence a is 11, 0, 0, 14.  Two of the elements are lost, and the candidates in b are 5 and 4.  There are two possible resulting sequences: 11, 5, 4, 14 and 11, 4, 5, 14, both of which fulfill the requirements. Thus the answer is \"Yes\". In the second sample, the only possible resulting sequence is 2, 3, 5, 8, 9, 10, which is an increasing sequence and therefore invalid."}, "src_uid": "40264e84c041fcfb4f8c0af784df102a"}
{"nl": {"description": "Vasilisa the Wise from a far away kingdom got a present from her friend Helga the Wise from a farther away kingdom. The present is a surprise box, yet Vasilisa the Wise doesn't know yet what the surprise actually is because she cannot open the box. She hopes that you can help her in that.The box's lock is constructed like that. The box itself is represented by an absolutely perfect black cube with the identical deepening on each face (those are some foreign nanotechnologies that the far away kingdom scientists haven't dreamt of). The box is accompanied by six gems whose form matches the deepenings in the box's faces. The box can only be opened after it is correctly decorated by the gems, that is, when each deepening contains exactly one gem. Two ways of decorating the box are considered the same if they can be obtained one from the other one by arbitrarily rotating the box (note that the box is represented by a perfect nanotechnological cube)Now Vasilisa the Wise wants to know by the given set of colors the following: in how many ways would she decorate the box in the worst case to open it? To answer this question it is useful to know that two gems of one color are indistinguishable from each other. Help Vasilisa to solve this challenging problem.", "input_spec": "The first line contains exactly 6 characters without spaces from the set {R, O, Y, G, B, V} — they are the colors of gems with which the box should be decorated.", "output_spec": "Print the required number of different ways to decorate the box.", "sample_inputs": ["YYYYYY", "BOOOOB", "ROYGBV"], "sample_outputs": ["1", "2", "30"], "notes": null}, "src_uid": "8176c709c774fa87ca0e45a5a502a409"}
{"nl": {"description": "Arkady and his friends love playing checkers on an $$$n \\times n$$$ field. The rows and the columns of the field are enumerated from $$$1$$$ to $$$n$$$.The friends have recently won a championship, so Arkady wants to please them with some candies. Remembering an old parable (but not its moral), Arkady wants to give to his friends one set of candies per each cell of the field: the set of candies for cell $$$(i, j)$$$ will have exactly $$$(i^2 + j^2)$$$ candies of unique type.There are $$$m$$$ friends who deserve the present. How many of these $$$n \\times n$$$ sets of candies can be split equally into $$$m$$$ parts without cutting a candy into pieces? Note that each set has to be split independently since the types of candies in different sets are different.", "input_spec": "The only line contains two integers $$$n$$$ and $$$m$$$ ($$$1 \\le n \\le 10^9$$$, $$$1 \\le m \\le 1000$$$) — the size of the field and the number of parts to split the sets into.", "output_spec": "Print a single integer — the number of sets that can be split equally.", "sample_inputs": ["3 3", "6 5", "1000000000 1"], "sample_outputs": ["1", "13", "1000000000000000000"], "notes": "NoteIn the first example, only the set for cell $$$(3, 3)$$$ can be split equally ($$$3^2 + 3^2 = 18$$$, which is divisible by $$$m=3$$$).In the second example, the sets for the following cells can be divided equally:   $$$(1, 2)$$$ and $$$(2, 1)$$$, since $$$1^2 + 2^2 = 5$$$, which is divisible by $$$5$$$;  $$$(1, 3)$$$ and $$$(3, 1)$$$;  $$$(2, 4)$$$ and $$$(4, 2)$$$;  $$$(2, 6)$$$ and $$$(6, 2)$$$;  $$$(3, 4)$$$ and $$$(4, 3)$$$;  $$$(3, 6)$$$ and $$$(6, 3)$$$;  $$$(5, 5)$$$. In the third example, sets in all cells can be divided equally, since $$$m = 1$$$."}, "src_uid": "2ec9e7cddc634d7830575e14363a4657"}
{"nl": {"description": "Polycarp loves ciphers. He has invented his own cipher called repeating.Repeating cipher is used for strings. To encrypt the string $$$s=s_{1}s_{2} \\dots s_{m}$$$ ($$$1 \\le m \\le 10$$$), Polycarp uses the following algorithm:  he writes down $$$s_1$$$ ones,  he writes down $$$s_2$$$ twice,  he writes down $$$s_3$$$ three times,  ...  he writes down $$$s_m$$$ $$$m$$$ times. For example, if $$$s$$$=\"bab\" the process is: \"b\" $$$\\to$$$ \"baa\" $$$\\to$$$ \"baabbb\". So the encrypted $$$s$$$=\"bab\" is \"baabbb\".Given string $$$t$$$ — the result of encryption of some string $$$s$$$. Your task is to decrypt it, i. e. find the string $$$s$$$.", "input_spec": "The first line contains integer $$$n$$$ ($$$1 \\le n \\le 55$$$) — the length of the encrypted string. The second line of the input contains $$$t$$$ — the result of encryption of some string $$$s$$$. It contains only lowercase Latin letters. The length of $$$t$$$ is exactly $$$n$$$. It is guaranteed that the answer to the test exists.", "output_spec": "Print such string $$$s$$$ that after encryption it equals $$$t$$$.", "sample_inputs": ["6\nbaabbb", "10\nooopppssss", "1\nz"], "sample_outputs": ["bab", "oops", "z"], "notes": null}, "src_uid": "08e8c0c37b223f6aae01d5609facdeaf"}
{"nl": {"description": "The main street of Berland is a straight line with n houses built along it (n is an even number). The houses are located at both sides of the street. The houses with odd numbers are at one side of the street and are numbered from 1 to n - 1 in the order from the beginning of the street to the end (in the picture: from left to right). The houses with even numbers are at the other side of the street and are numbered from 2 to n in the order from the end of the street to its beginning (in the picture: from right to left). The corresponding houses with even and odd numbers are strictly opposite each other, that is, house 1 is opposite house n, house 3 is opposite house n - 2, house 5 is opposite house n - 4 and so on.  Vasya needs to get to house number a as quickly as possible. He starts driving from the beginning of the street and drives his car to house a. To get from the beginning of the street to houses number 1 and n, he spends exactly 1 second. He also spends exactly one second to drive the distance between two neighbouring houses. Vasya can park at any side of the road, so the distance between the beginning of the street at the houses that stand opposite one another should be considered the same.Your task is: find the minimum time Vasya needs to reach house a.", "input_spec": "The first line of the input contains two integers, n and a (1 ≤ a ≤ n ≤ 100 000) — the number of houses on the street and the number of the house that Vasya needs to reach, correspondingly. It is guaranteed that number n is even.", "output_spec": "Print a single integer — the minimum time Vasya needs to get from the beginning of the street to house a.", "sample_inputs": ["4 2", "8 5"], "sample_outputs": ["2", "3"], "notes": "NoteIn the first sample there are only four houses on the street, two houses at each side. House 2 will be the last at Vasya's right.The second sample corresponds to picture with n = 8. House 5 is the one before last at Vasya's left."}, "src_uid": "aa62dcdc47d0abbba7956284c1561de8"}
{"nl": {"description": "Cucumber boy is fan of Kyubeat, a famous music game.Kyubeat has 16 panels for playing arranged in 4 × 4 table. When a panel lights up, he has to press that panel.Each panel has a timing to press (the preffered time when a player should press it), and Cucumber boy is able to press at most k panels in a time with his one hand. Cucumber boy is trying to press all panels in perfect timing, that is he wants to press each panel exactly in its preffered time. If he cannot press the panels with his two hands in perfect timing, his challenge to press all the panels in perfect timing will fail.You are given one scene of Kyubeat's panel from the music Cucumber boy is trying. Tell him is he able to press all the panels in perfect timing.", "input_spec": "The first line contains a single integer k (1 ≤ k ≤ 5) — the number of panels Cucumber boy can press with his one hand. Next 4 lines contain 4 characters each (digits from 1 to 9, or period) — table of panels. If a digit i was written on the panel, it means the boy has to press that panel in time i. If period was written on the panel, he doesn't have to press that panel.", "output_spec": "Output \"YES\" (without quotes), if he is able to press all the panels in perfect timing. If not, output \"NO\" (without quotes).", "sample_inputs": ["1\n.135\n1247\n3468\n5789", "5\n..1.\n1111\n..1.\n..1.", "1\n....\n12.1\n.2..\n.2.."], "sample_outputs": ["YES", "YES", "NO"], "notes": "NoteIn the third sample boy cannot press all panels in perfect timing. He can press all the panels in timing in time 1, but he cannot press the panels in time 2 in timing with his two hands."}, "src_uid": "5fdaf8ee7763cb5815f49c0c38398f16"}
{"nl": {"description": "Imp is in a magic forest, where xorangles grow (wut?)  A xorangle of order n is such a non-degenerate triangle, that lengths of its sides are integers not exceeding n, and the xor-sum of the lengths is equal to zero. Imp has to count the number of distinct xorangles of order n to get out of the forest. Formally, for a given integer n you have to find the number of such triples (a, b, c), that:  1 ≤ a ≤ b ≤ c ≤ n;  , where  denotes the bitwise xor of integers x and y.  (a, b, c) form a non-degenerate (with strictly positive area) triangle. ", "input_spec": "The only line contains a single integer n (1 ≤ n ≤ 2500).", "output_spec": "Print the number of xorangles of order n.", "sample_inputs": ["6", "10"], "sample_outputs": ["1", "2"], "notes": "NoteThe only xorangle in the first sample is (3, 5, 6)."}, "src_uid": "838f2e75fdff0f13f002c0dfff0b2e8d"}
{"nl": {"description": "You have probably registered on Internet sites many times. And each time you should enter your invented password. Usually the registration form automatically checks the password's crypt resistance. If the user's password isn't complex enough, a message is displayed. Today your task is to implement such an automatic check.Web-developers of the company Q assume that a password is complex enough, if it meets all of the following conditions:  the password length is at least 5 characters;  the password contains at least one large English letter;  the password contains at least one small English letter;  the password contains at least one digit. You are given a password. Please implement the automatic check of its complexity for company Q.", "input_spec": "The first line contains a non-empty sequence of characters (at most 100 characters). Each character is either a large English letter, or a small English letter, or a digit, or one of characters: \"!\", \"?\", \".\", \",\", \"_\".", "output_spec": "If the password is complex enough, print message \"Correct\" (without the quotes), otherwise print message \"Too weak\" (without the quotes).", "sample_inputs": ["abacaba", "X12345", "CONTEST_is_STARTED!!11"], "sample_outputs": ["Too weak", "Too weak", "Correct"], "notes": null}, "src_uid": "42a964b01e269491975965860ec92be7"}
{"nl": {"description": "Petya loves lucky numbers. We all know that lucky numbers are the positive integers whose decimal representations contain only the lucky digits 4 and 7. For example, numbers 47, 744, 4 are lucky and 5, 17, 467 are not.Petya and his friend Vasya play an interesting game. Petya randomly chooses an integer p from the interval [pl, pr] and Vasya chooses an integer v from the interval [vl, vr] (also randomly). Both players choose their integers equiprobably. Find the probability that the interval [min(v, p), max(v, p)] contains exactly k lucky numbers.", "input_spec": "The single line contains five integers pl, pr, vl, vr and k (1 ≤ pl ≤ pr ≤ 109, 1 ≤ vl ≤ vr ≤ 109, 1 ≤ k ≤ 1000).", "output_spec": "On the single line print the result with an absolute error of no more than 10 - 9.", "sample_inputs": ["1 10 1 10 2", "5 6 8 10 1"], "sample_outputs": ["0.320000000000", "1.000000000000"], "notes": "NoteConsider that [a, b] denotes an interval of integers; this interval includes the boundaries. That is, In first case there are 32 suitable pairs: (1, 7), (1, 8), (1, 9), (1, 10), (2, 7), (2, 8), (2, 9), (2, 10), (3, 7), (3, 8), (3, 9), (3, 10), (4, 7), (4, 8), (4, 9), (4, 10), (7, 1), (7, 2), (7, 3), (7, 4), (8, 1), (8, 2), (8, 3), (8, 4), (9, 1), (9, 2), (9, 3), (9, 4), (10, 1), (10, 2), (10, 3), (10, 4). Total number of possible pairs is 10·10 = 100, so answer is 32 / 100.In second case Petya always get number less than Vasya and the only lucky 7 is between this numbers, so there will be always 1 lucky number."}, "src_uid": "5d76ec741a9d873ce9d7c3ef55eb984c"}
{"nl": {"description": "A few years ago Sajjad left his school and register to another one due to security reasons. Now he wishes to find Amir, one of his schoolmates and good friends.There are n schools numerated from 1 to n. One can travel between each pair of them, to do so, he needs to buy a ticket. The ticker between schools i and j costs  and can be used multiple times. Help Sajjad to find the minimum cost he needs to pay for tickets to visit all schools. He can start and finish in any school.", "input_spec": "The first line contains a single integer n (1 ≤ n ≤ 105) — the number of schools.", "output_spec": "Print single integer: the minimum cost of tickets needed to visit all schools.", "sample_inputs": ["2", "10"], "sample_outputs": ["0", "4"], "notes": "NoteIn the first example we can buy a ticket between the schools that costs ."}, "src_uid": "dfe9446431325c73e88b58ba204d0e47"}
{"nl": {"description": "You are given a binary string s (each character of this string is either 0 or 1).Let's denote the cost of string t as the number of occurences of s in t. For example, if s is 11 and t is 111011, then the cost of t is 3.Let's also denote the Fibonacci strings sequence as follows: F(0) is 0; F(1) is 1; F(i) = F(i - 1) + F(i - 2) if i > 1, where  +  means the concatenation of two strings.Your task is to calculate the sum of costs of all subsequences of the string F(x). Since answer may be large, calculate it modulo 109 + 7.", "input_spec": "The first line contains two integers n and x (1 ≤ n ≤ 100, 0 ≤ x ≤ 100) — the length of s and the index of a Fibonacci string you are interested in, respectively. The second line contains s — a string consisting of n characters. Each of these characters is either 0 or 1.", "output_spec": "Print the only integer — the sum of costs of all subsequences of the string F(x), taken modulo 109 + 7. ", "sample_inputs": ["2 4\n11", "10 100\n1010101010"], "sample_outputs": ["14", "553403224"], "notes": null}, "src_uid": "52c6aa73ff4460799402c646c6263630"}
{"nl": {"description": "When Valera was playing football on a stadium, it suddenly began to rain. Valera hid in the corridor under the grandstand not to get wet. However, the desire to play was so great that he decided to train his hitting the ball right in this corridor. Valera went back far enough, put the ball and hit it. The ball bounced off the walls, the ceiling and the floor corridor and finally hit the exit door. As the ball was wet, it left a spot on the door. Now Valera wants to know the coordinates for this spot.Let's describe the event more formally. The ball will be considered a point in space. The door of the corridor will be considered a rectangle located on plane xOz, such that the lower left corner of the door is located at point (0, 0, 0), and the upper right corner is located at point (a, 0, b) . The corridor will be considered as a rectangular parallelepiped, infinite in the direction of increasing coordinates of y. In this corridor the floor will be considered as plane xOy, and the ceiling as plane, parallel to xOy and passing through point (a, 0, b). We will also assume that one of the walls is plane yOz, and the other wall is plane, parallel to yOz and passing through point (a, 0, b).We'll say that the ball hit the door when its coordinate y was equal to 0. Thus the coordinates of the spot are point (x0, 0, z0), where 0 ≤ x0 ≤ a, 0 ≤ z0 ≤ b. To hit the ball, Valera steps away from the door at distance m and puts the ball in the center of the corridor at point . After the hit the ball flies at speed (vx, vy, vz). This means that if the ball has coordinates (x, y, z), then after one second it will have coordinates (x + vx, y + vy, z + vz).See image in notes for clarification.When the ball collides with the ceiling, the floor or a wall of the corridor, it bounces off in accordance with the laws of reflection (the angle of incidence equals the angle of reflection). In the problem we consider the ideal physical model, so we can assume that there is no air resistance, friction force, or any loss of energy.", "input_spec": "The first line contains three space-separated integers a, b, m (1 ≤ a, b, m ≤ 100). The first two integers specify point (a, 0, b), through which the ceiling and one of the corridor walls pass. The third integer is the distance at which Valera went away from the door. The second line has three space-separated integers vx, vy, vz (|vx|, |vy|, |vz| ≤ 100, vy < 0, vz ≥ 0) — the speed of the ball after the hit. It is guaranteed that the ball hits the door.", "output_spec": "Print two real numbers x0, z0 — the x and z coordinates of point (x0, 0, z0), at which the ball hits the exit door. The answer will be considered correct, if its absolute or relative error does not exceed 10  - 6.", "sample_inputs": ["7 2 11\n3 -11 2", "7 2 11\n4 -3 3"], "sample_outputs": ["6.5000000000 2.0000000000", "4.1666666667 1.0000000000"], "notes": "Note"}, "src_uid": "84848b8bd92fd2834db1ee9cb0899cff"}
{"nl": {"description": "Petr has just bought a new car. He's just arrived at the most known Petersburg's petrol station to refuel it when he suddenly discovered that the petrol tank is secured with a combination lock! The lock has a scale of $$$360$$$ degrees and a pointer which initially points at zero:  Petr called his car dealer, who instructed him to rotate the lock's wheel exactly $$$n$$$ times. The $$$i$$$-th rotation should be $$$a_i$$$ degrees, either clockwise or counterclockwise, and after all $$$n$$$ rotations the pointer should again point at zero.This confused Petr a little bit as he isn't sure which rotations should be done clockwise and which should be done counterclockwise. As there are many possible ways of rotating the lock, help him and find out whether there exists at least one, such that after all $$$n$$$ rotations the pointer will point at zero again.", "input_spec": "The first line contains one integer $$$n$$$ ($$$1 \\leq n \\leq 15$$$) — the number of rotations. Each of the following $$$n$$$ lines contains one integer $$$a_i$$$ ($$$1 \\leq a_i \\leq 180$$$) — the angle of the $$$i$$$-th rotation in degrees.", "output_spec": "If it is possible to do all the rotations so that the pointer will point at zero after all of them are performed, print a single word \"YES\". Otherwise, print \"NO\". Petr will probably buy a new car in this case. You can print each letter in any case (upper or lower).", "sample_inputs": ["3\n10\n20\n30", "3\n10\n10\n10", "3\n120\n120\n120"], "sample_outputs": ["YES", "NO", "YES"], "notes": "NoteIn the first example, we can achieve our goal by applying the first and the second rotation clockwise, and performing the third rotation counterclockwise.In the second example, it's impossible to perform the rotations in order to make the pointer point at zero in the end.In the third example, Petr can do all three rotations clockwise. In this case, the whole wheel will be rotated by $$$360$$$ degrees clockwise and the pointer will point at zero again."}, "src_uid": "01b50fcba4185ceb1eb8e4ba04a0cc10"}
{"nl": {"description": "There is an infinite board of square tiles. Initially all tiles are white.Vova has a red marker and a blue marker. Red marker can color $$$a$$$ tiles. Blue marker can color $$$b$$$ tiles. If some tile isn't white then you can't use marker of any color on it. Each marker must be drained completely, so at the end there should be exactly $$$a$$$ red tiles and exactly $$$b$$$ blue tiles across the board.Vova wants to color such a set of tiles that:  they would form a rectangle, consisting of exactly $$$a+b$$$ colored tiles;  all tiles of at least one color would also form a rectangle. Here are some examples of correct colorings:  Here are some examples of incorrect colorings:  Among all correct colorings Vova wants to choose the one with the minimal perimeter. What is the minimal perimeter Vova can obtain?It is guaranteed that there exists at least one correct coloring.", "input_spec": "A single line contains two integers $$$a$$$ and $$$b$$$ ($$$1 \\le a, b \\le 10^{14}$$$) — the number of tiles red marker should color and the number of tiles blue marker should color, respectively.", "output_spec": "Print a single integer — the minimal perimeter of a colored rectangle Vova can obtain by coloring exactly $$$a$$$ tiles red and exactly $$$b$$$ tiles blue. It is guaranteed that there exists at least one correct coloring.", "sample_inputs": ["4 4", "3 9", "9 3", "3 6", "506 2708"], "sample_outputs": ["12", "14", "14", "12", "3218"], "notes": "NoteThe first four examples correspond to the first picture of the statement.Note that for there exist multiple correct colorings for all of the examples.In the first example you can also make a rectangle with sides $$$1$$$ and $$$8$$$, though its perimeter will be $$$18$$$ which is greater than $$$8$$$.In the second example you can make the same resulting rectangle with sides $$$3$$$ and $$$4$$$, but red tiles will form the rectangle with sides $$$1$$$ and $$$3$$$ and blue tiles will form the rectangle with sides $$$3$$$ and $$$3$$$."}, "src_uid": "7d0c5f77bca792b6ab4fd4088fe18ff1"}
{"nl": {"description": "Long time ago Alex created an interesting problem about parallelogram. The input data for this problem contained four integer points on the Cartesian plane, that defined the set of vertices of some non-degenerate (positive area) parallelogram. Points not necessary were given in the order of clockwise or counterclockwise traversal.Alex had very nice test for this problem, but is somehow happened that the last line of the input was lost and now he has only three out of four points of the original parallelogram. He remembers that test was so good that he asks you to restore it given only these three points.", "input_spec": "The input consists of three lines, each containing a pair of integer coordinates xi and yi ( - 1000 ≤ xi, yi ≤ 1000). It's guaranteed that these three points do not lie on the same line and no two of them coincide.", "output_spec": "First print integer k — the number of ways to add one new integer point such that the obtained set defines some parallelogram of positive area. There is no requirement for the points to be arranged in any special order (like traversal), they just define the set of vertices. Then print k lines, each containing a pair of integer — possible coordinates of the fourth point.", "sample_inputs": ["0 0\n1 0\n0 1"], "sample_outputs": ["3\n1 -1\n-1 1\n1 1"], "notes": "NoteIf you need clarification of what parallelogram is, please check Wikipedia page:https://en.wikipedia.org/wiki/Parallelogram"}, "src_uid": "7725f9906a1b87bf4e866df03112f1e0"}
{"nl": {"description": "A boy named Vasya wants to play an old Russian solitaire called \"Accordion\". In this solitaire, the player must observe the following rules:  A deck of n cards is carefully shuffled, then all n cards are put on the table in a line from left to right;  Before each move the table has several piles of cards lying in a line (initially there are n piles, each pile has one card). Let's number the piles from left to right, from 1 to x. During one move, a player can take the whole pile with the maximum number x (that is the rightmost of remaining) and put it on the top of pile x - 1 (if it exists) or on the top of pile x - 3 (if it exists). The player can put one pile on top of another one only if the piles' top cards have the same suits or values. Please note that if pile x goes on top of pile y, then the top card of pile x becomes the top card of the resulting pile. Also note that each move decreases the total number of piles by 1;  The solitaire is considered completed if all cards are in the same pile. Vasya has already shuffled the cards and put them on the table, help him understand whether completing this solitaire is possible or not. ", "input_spec": "The first input line contains a single integer n (1 ≤ n ≤ 52) — the number of cards in Vasya's deck. The next line contains n space-separated strings c1, c2, ..., cn, where string ci describes the i-th card on the table. Each string ci consists of exactly two characters, the first one represents the card's value, the second one represents its suit. Cards on the table are numbered from left to right.  A card's value is specified by one of these characters: \"2\", \"3\", \"4\", \"5\", \"6\", \"7\", \"8\", \"9\", \"T\", \"J\", \"Q\", \"K\", \"A\". A card's suit is specified by one of these characters: \"S\", \"D\", \"H\", \"C\". It is not guaranteed that the deck has all possible cards. Also, the cards in Vasya's deck can repeat.", "output_spec": "On a single line print the answer to the problem: string \"YES\" (without the quotes) if completing the solitaire is possible, string \"NO\" (without the quotes) otherwise.", "sample_inputs": ["4\n2S 2S 2C 2C", "2\n3S 2C"], "sample_outputs": ["YES", "NO"], "notes": "NoteIn the first sample you can act like that:   put the 4-th pile on the 1-st one;  put the 3-rd pile on the 2-nd one;  put the 2-nd pile on the 1-st one. In the second sample there is no way to complete the solitaire."}, "src_uid": "1805771e194d323edacf2526a1eb6768"}
{"nl": {"description": "Manao is taking part in a quiz. The quiz consists of n consecutive questions. A correct answer gives one point to the player. The game also has a counter of consecutive correct answers. When the player answers a question correctly, the number on this counter increases by 1. If the player answers a question incorrectly, the counter is reset, that is, the number on it reduces to 0. If after an answer the counter reaches the number k, then it is reset, and the player's score is doubled. Note that in this case, first 1 point is added to the player's score, and then the total score is doubled. At the beginning of the game, both the player's score and the counter of consecutive correct answers are set to zero.Manao remembers that he has answered exactly m questions correctly. But he does not remember the order in which the questions came. He's trying to figure out what his minimum score may be. Help him and compute the remainder of the corresponding number after division by 1000000009 (109 + 9).", "input_spec": "The single line contains three space-separated integers n, m and k (2 ≤ k ≤ n ≤ 109; 0 ≤ m ≤ n).", "output_spec": "Print a single integer — the remainder from division of Manao's minimum possible score in the quiz by 1000000009 (109 + 9).", "sample_inputs": ["5 3 2", "5 4 2"], "sample_outputs": ["3", "6"], "notes": "NoteSample 1. Manao answered 3 questions out of 5, and his score would double for each two consecutive correct answers. If Manao had answered the first, third and fifth questions, he would have scored as much as 3 points.Sample 2. Now Manao answered 4 questions. The minimum possible score is obtained when the only wrong answer is to the question 4.Also note that you are asked to minimize the score and not the remainder of the score modulo 1000000009. For example, if Manao could obtain either 2000000000 or 2000000020 points, the answer is 2000000000 mod 1000000009, even though 2000000020 mod 1000000009 is a smaller number."}, "src_uid": "9cc1aecd70ed54400821c290e2c8018e"}
{"nl": {"description": "Professor GukiZ makes a new robot. The robot are in the point with coordinates (x1, y1) and should go to the point (x2, y2). In a single step the robot can change any of its coordinates (maybe both of them) by one (decrease or increase). So the robot can move in one of the 8 directions. Find the minimal number of steps the robot should make to get the finish position.", "input_spec": "The first line contains two integers x1, y1 ( - 109 ≤ x1, y1 ≤ 109) — the start position of the robot. The second line contains two integers x2, y2 ( - 109 ≤ x2, y2 ≤ 109) — the finish position of the robot.", "output_spec": "Print the only integer d — the minimal number of steps to get the finish position.", "sample_inputs": ["0 0\n4 5", "3 4\n6 1"], "sample_outputs": ["5", "3"], "notes": "NoteIn the first example robot should increase both of its coordinates by one four times, so it will be in position (4, 4). After that robot should simply increase its y coordinate and get the finish position.In the second example robot should simultaneously increase x coordinate and decrease y coordinate by one three times."}, "src_uid": "a6e9405bc3d4847fe962446bc1c457b4"}
{"nl": {"description": "You are given a regular polygon with $$$n$$$ vertices labeled from $$$1$$$ to $$$n$$$ in counter-clockwise order. The triangulation of a given polygon is a set of triangles such that each vertex of each triangle is a vertex of the initial polygon, there is no pair of triangles such that their intersection has non-zero area, and the total area of all triangles is equal to the area of the given polygon. The weight of a triangulation is the sum of weigths of triangles it consists of, where the weight of a triagle is denoted as the product of labels of its vertices.Calculate the minimum weight among all triangulations of the polygon.", "input_spec": "The first line contains single integer $$$n$$$ ($$$3 \\le n \\le 500$$$) — the number of vertices in the regular polygon.", "output_spec": "Print one integer — the minimum weight among all triangulations of the given polygon.", "sample_inputs": ["3", "4"], "sample_outputs": ["6", "18"], "notes": "NoteAccording to Wiki: polygon triangulation is the decomposition of a polygonal area (simple polygon) $$$P$$$ into a set of triangles, i. e., finding a set of triangles with pairwise non-intersecting interiors whose union is $$$P$$$.In the first example the polygon is a triangle, so we don't need to cut it further, so the answer is $$$1 \\cdot 2 \\cdot 3 = 6$$$.In the second example the polygon is a rectangle, so it should be divided into two triangles. It's optimal to cut it using diagonal $$$1-3$$$ so answer is $$$1 \\cdot 2 \\cdot 3 + 1 \\cdot 3 \\cdot 4 = 6 + 12 = 18$$$."}, "src_uid": "1bd29d7a8793c22e81a1f6fd3991307a"}
{"nl": {"description": "In one of the games Arkady is fond of the game process happens on a rectangular field. In the game process Arkady can buy extensions for his field, each extension enlarges one of the field sizes in a particular number of times. Formally, there are n extensions, the i-th of them multiplies the width or the length (by Arkady's choice) by ai. Each extension can't be used more than once, the extensions can be used in any order.Now Arkady's field has size h × w. He wants to enlarge it so that it is possible to place a rectangle of size a × b on it (along the width or along the length, with sides parallel to the field sides). Find the minimum number of extensions needed to reach Arkady's goal.", "input_spec": "The first line contains five integers a, b, h, w and n (1 ≤ a, b, h, w, n ≤ 100 000) — the sizes of the rectangle needed to be placed, the initial sizes of the field and the number of available extensions. The second line contains n integers a1, a2, ..., an (2 ≤ ai ≤ 100 000), where ai equals the integer a side multiplies by when the i-th extension is applied.", "output_spec": "Print the minimum number of extensions needed to reach Arkady's goal. If it is not possible to place the rectangle on the field with all extensions, print -1. If the rectangle can be placed on the initial field, print 0.", "sample_inputs": ["3 3 2 4 4\n2 5 4 10", "3 3 3 3 5\n2 3 5 4 2", "5 5 1 2 3\n2 2 3", "3 4 1 1 3\n2 3 2"], "sample_outputs": ["1", "0", "-1", "3"], "notes": "NoteIn the first example it is enough to use any of the extensions available. For example, we can enlarge h in 5 times using the second extension. Then h becomes equal 10 and it is now possible to place the rectangle on the field."}, "src_uid": "18cb436618b2b85c3f5dc348c80882d5"}
{"nl": {"description": "I have an undirected graph consisting of n nodes, numbered 1 through n. Each node has at most two incident edges. For each pair of nodes, there is at most an edge connecting them. No edge connects a node to itself.I would like to create a new graph in such a way that:   The new graph consists of the same number of nodes and edges as the old graph.  The properties in the first paragraph still hold.  For each two nodes u and v, if there is an edge connecting them in the old graph, there is no edge connecting them in the new graph. Help me construct the new graph, or tell me if it is impossible.", "input_spec": "The first line consists of two space-separated integers: n and m (1 ≤ m ≤ n ≤ 105), denoting the number of nodes and edges, respectively. Then m lines follow. Each of the m lines consists of two space-separated integers u and v (1 ≤ u, v ≤ n; u ≠ v), denoting an edge between nodes u and v.", "output_spec": "If it is not possible to construct a new graph with the mentioned properties, output a single line consisting of -1. Otherwise, output exactly m lines. Each line should contain a description of edge in the same way as used in the input format.", "sample_inputs": ["8 7\n1 2\n2 3\n4 5\n5 6\n6 8\n8 7\n7 4", "3 2\n1 2\n2 3", "5 4\n1 2\n2 3\n3 4\n4 1"], "sample_outputs": ["1 4\n4 6\n1 6\n2 7\n7 5\n8 5\n2 8", "-1", "1 3\n3 5\n5 2\n2 4"], "notes": "NoteThe old graph of the first example:A possible new graph for the first example:In the second example, we cannot create any new graph.The old graph of the third example:A possible new graph for the third example:"}, "src_uid": "c4c85cde8a5bb5fefa4eb68fc68657d5"}
{"nl": {"description": "Luba has a ticket consisting of 6 digits. In one move she can choose digit in any position and replace it with arbitrary digit. She wants to know the minimum number of digits she needs to replace in order to make the ticket lucky.The ticket is considered lucky if the sum of first three digits equals to the sum of last three digits.", "input_spec": "You are given a string consisting of 6 characters (all characters are digits from 0 to 9) — this string denotes Luba's ticket. The ticket can start with the digit 0.", "output_spec": "Print one number — the minimum possible number of digits Luba needs to replace to make the ticket lucky.", "sample_inputs": ["000000", "123456", "111000"], "sample_outputs": ["0", "2", "1"], "notes": "NoteIn the first example the ticket is already lucky, so the answer is 0.In the second example Luba can replace 4 and 5 with zeroes, and the ticket will become lucky. It's easy to see that at least two replacements are required.In the third example Luba can replace any zero with 3. It's easy to see that at least one replacement is required."}, "src_uid": "09601fd1742ffdc9f822950f1d3e8494"}
{"nl": {"description": "Shapur was an extremely gifted student. He was great at everything including Combinatorics, Algebra, Number Theory, Geometry, Calculus, etc. He was not only smart but extraordinarily fast! He could manage to sum 1018 numbers in a single second.One day in 230 AD Shapur was trying to find out if any one can possibly do calculations faster than him. As a result he made a very great contest and asked every one to come and take part.In his contest he gave the contestants many different pairs of numbers. Each number is made from digits 0 or 1. The contestants should write a new number corresponding to the given pair of numbers. The rule is simple: The i-th digit of the answer is 1 if and only if the i-th digit of the two given numbers differ. In the other case the i-th digit of the answer is 0.Shapur made many numbers and first tried his own speed. He saw that he can perform these operations on numbers of length ∞ (length of a number is number of digits in it) in a glance! He always gives correct answers so he expects the contestants to give correct answers, too. He is a good fellow so he won't give anyone very big numbers and he always gives one person numbers of same length.Now you are going to take part in Shapur's contest. See if you are faster and more accurate.", "input_spec": "There are two lines in each input. Each of them contains a single number. It is guaranteed that the numbers are made from 0 and 1 only and that their length is same. The numbers may start with 0. The length of each number doesn't exceed 100.", "output_spec": "Write one line — the corresponding answer. Do not omit the leading 0s.", "sample_inputs": ["1010100\n0100101", "000\n111", "1110\n1010", "01110\n01100"], "sample_outputs": ["1110001", "111", "0100", "00010"], "notes": null}, "src_uid": "3714b7596a6b48ca5b7a346f60d90549"}
{"nl": {"description": "One day student Vasya was sitting on a lecture and mentioned a string s1s2... sn, consisting of letters \"a\", \"b\" and \"c\" that was written on his desk. As the lecture was boring, Vasya decided to complete the picture by composing a graph G with the following properties:   G has exactly n vertices, numbered from 1 to n.  For all pairs of vertices i and j, where i ≠ j, there is an edge connecting them if and only if characters si and sj are either equal or neighbouring in the alphabet. That is, letters in pairs \"a\"-\"b\" and \"b\"-\"c\" are neighbouring, while letters \"a\"-\"c\" are not. Vasya painted the resulting graph near the string and then erased the string. Next day Vasya's friend Petya came to a lecture and found some graph at his desk. He had heard of Vasya's adventure and now he wants to find out whether it could be the original graph G, painted by Vasya. In order to verify this, Petya needs to know whether there exists a string s, such that if Vasya used this s he would produce the given graph G.", "input_spec": "The first line of the input contains two integers n and m  — the number of vertices and edges in the graph found by Petya, respectively. Each of the next m lines contains two integers ui and vi (1 ≤ ui, vi ≤ n, ui ≠ vi) — the edges of the graph G. It is guaranteed, that there are no multiple edges, that is any pair of vertexes appear in this list no more than once.", "output_spec": "In the first line print \"Yes\" (without the quotes), if the string s Petya is interested in really exists and \"No\" (without the quotes) otherwise. If the string s exists, then print it on the second line of the output. The length of s must be exactly n, it must consist of only letters \"a\", \"b\" and \"c\" only, and the graph built using this string must coincide with G. If there are multiple possible answers, you may print any of them.", "sample_inputs": ["2 1\n1 2", "4 3\n1 2\n1 3\n1 4"], "sample_outputs": ["Yes\naa", "No"], "notes": "NoteIn the first sample you are given a graph made of two vertices with an edge between them. So, these vertices can correspond to both the same and adjacent letters. Any of the following strings \"aa\", \"ab\", \"ba\", \"bb\", \"bc\", \"cb\", \"cc\" meets the graph's conditions. In the second sample the first vertex is connected to all three other vertices, but these three vertices are not connected with each other. That means that they must correspond to distinct letters that are not adjacent, but that is impossible as there are only two such letters: a and c."}, "src_uid": "e71640f715f353e49745eac5f72e682a"}
{"nl": {"description": "There are a lot of things which could be cut — trees, paper, \"the rope\". In this problem you are going to cut a sequence of integers.There is a sequence of integers, which contains the equal number of even and odd numbers. Given a limited budget, you need to make maximum possible number of cuts such that each resulting segment will have the same number of odd and even integers.Cuts separate a sequence to continuous (contiguous) segments. You may think about each cut as a break between two adjacent elements in a sequence. So after cutting each element belongs to exactly one segment. Say, $$$[4, 1, 2, 3, 4, 5, 4, 4, 5, 5]$$$ $$$\\to$$$ two cuts $$$\\to$$$ $$$[4, 1 | 2, 3, 4, 5 | 4, 4, 5, 5]$$$. On each segment the number of even elements should be equal to the number of odd elements.The cost of the cut between $$$x$$$ and $$$y$$$ numbers is $$$|x - y|$$$ bitcoins. Find the maximum possible number of cuts that can be made while spending no more than $$$B$$$ bitcoins.", "input_spec": "First line of the input contains an integer $$$n$$$ ($$$2 \\le n \\le 100$$$) and an integer $$$B$$$ ($$$1 \\le B \\le 100$$$) — the number of elements in the sequence and the number of bitcoins you have. Second line contains $$$n$$$ integers: $$$a_1$$$, $$$a_2$$$, ..., $$$a_n$$$ ($$$1 \\le a_i \\le 100$$$) — elements of the sequence, which contains the equal number of even and odd numbers", "output_spec": "Print the maximum possible number of cuts which can be made while spending no more than $$$B$$$ bitcoins.", "sample_inputs": ["6 4\n1 2 5 10 15 20", "4 10\n1 3 2 4", "6 100\n1 2 3 4 5 6"], "sample_outputs": ["1", "0", "2"], "notes": "NoteIn the first sample the optimal answer is to split sequence between $$$2$$$ and $$$5$$$. Price of this cut is equal to $$$3$$$ bitcoins.In the second sample it is not possible to make even one cut even with unlimited number of bitcoins.In the third sample the sequence should be cut between $$$2$$$ and $$$3$$$, and between $$$4$$$ and $$$5$$$. The total price of the cuts is $$$1 + 1 = 2$$$ bitcoins."}, "src_uid": "b3f8e769ee7719ea5c9f458428b16a4e"}
{"nl": {"description": "Lavrenty, a baker, is going to make several buns with stuffings and sell them.Lavrenty has n grams of dough as well as m different stuffing types. The stuffing types are numerated from 1 to m. Lavrenty knows that he has ai grams left of the i-th stuffing. It takes exactly bi grams of stuffing i and ci grams of dough to cook a bun with the i-th stuffing. Such bun can be sold for di tugriks.Also he can make buns without stuffings. Each of such buns requires c0 grams of dough and it can be sold for d0 tugriks. So Lavrenty can cook any number of buns with different stuffings or without it unless he runs out of dough and the stuffings. Lavrenty throws away all excess material left after baking.Find the maximum number of tugriks Lavrenty can earn.", "input_spec": "The first line contains 4 integers n, m, c0 and d0 (1 ≤ n ≤ 1000, 1 ≤ m ≤ 10, 1 ≤ c0, d0 ≤ 100). Each of the following m lines contains 4 integers. The i-th line contains numbers ai, bi, ci and di (1 ≤ ai, bi, ci, di ≤ 100).", "output_spec": "Print the only number — the maximum number of tugriks Lavrenty can earn.", "sample_inputs": ["10 2 2 1\n7 3 2 100\n12 3 1 10", "100 1 25 50\n15 5 20 10"], "sample_outputs": ["241", "200"], "notes": "NoteTo get the maximum number of tugriks in the first sample, you need to cook 2 buns with stuffing 1, 4 buns with stuffing 2 and a bun without any stuffing.In the second sample Lavrenty should cook 4 buns without stuffings."}, "src_uid": "4e166b8b44427b1227e0f811161d3a6f"}
{"nl": {"description": "Imagine a city with n horizontal streets crossing m vertical streets, forming an (n - 1) × (m - 1) grid. In order to increase the traffic flow, mayor of the city has decided to make each street one way. This means in each horizontal street, the traffic moves only from west to east or only from east to west. Also, traffic moves only from north to south or only from south to north in each vertical street. It is possible to enter a horizontal street from a vertical street, or vice versa, at their intersection.  The mayor has received some street direction patterns. Your task is to check whether it is possible to reach any junction from any other junction in the proposed street direction pattern.", "input_spec": "The first line of input contains two integers n and m, (2 ≤ n, m ≤ 20), denoting the number of horizontal streets and the number of vertical streets. The second line contains a string of length n, made of characters '<' and '>', denoting direction of each horizontal street. If the i-th character is equal to '<', the street is directed from east to west otherwise, the street is directed from west to east. Streets are listed in order from north to south. The third line contains a string of length m, made of characters '^' and 'v', denoting direction of each vertical street. If the i-th character is equal to '^', the street is directed from south to north, otherwise the street is directed from north to south. Streets are listed in order from west to east.", "output_spec": "If the given pattern meets the mayor's criteria, print a single line containing \"YES\", otherwise print a single line containing \"NO\".", "sample_inputs": ["3 3\n><>\nv^v", "4 6\n<><>\nv^v^v^"], "sample_outputs": ["NO", "YES"], "notes": "NoteThe figure above shows street directions in the second sample test case."}, "src_uid": "eab5c84c9658eb32f5614cd2497541cf"}
{"nl": {"description": "One day, $$$n$$$ people ($$$n$$$ is an even number) met on a plaza and made two round dances, each round dance consists of exactly $$$\\frac{n}{2}$$$ people. Your task is to find the number of ways $$$n$$$ people can make two round dances if each round dance consists of exactly $$$\\frac{n}{2}$$$ people. Each person should belong to exactly one of these two round dances.Round dance is a dance circle consisting of $$$1$$$ or more people. Two round dances are indistinguishable (equal) if one can be transformed to another by choosing the first participant. For example, round dances $$$[1, 3, 4, 2]$$$, $$$[4, 2, 1, 3]$$$ and $$$[2, 1, 3, 4]$$$ are indistinguishable.For example, if $$$n=2$$$ then the number of ways is $$$1$$$: one round dance consists of the first person and the second one of the second person.For example, if $$$n=4$$$ then the number of ways is $$$3$$$. Possible options:  one round dance — $$$[1,2]$$$, another — $$$[3,4]$$$;  one round dance — $$$[2,4]$$$, another — $$$[3,1]$$$;  one round dance — $$$[4,1]$$$, another — $$$[3,2]$$$. Your task is to find the number of ways $$$n$$$ people can make two round dances if each round dance consists of exactly $$$\\frac{n}{2}$$$ people.", "input_spec": "The input contains one integer $$$n$$$ ($$$2 \\le n \\le 20$$$), $$$n$$$ is an even number.", "output_spec": "Print one integer — the number of ways to make two round dances. It is guaranteed that the answer fits in the $$$64$$$-bit integer data type.", "sample_inputs": ["2", "4", "8", "20"], "sample_outputs": ["1", "3", "1260", "12164510040883200"], "notes": null}, "src_uid": "ad0985c56a207f76afa2ecd642f56728"}
{"nl": {"description": "On her way to programming school tiger Dasha faced her first test — a huge staircase!  The steps were numbered from one to infinity. As we know, tigers are very fond of all striped things, it is possible that it has something to do with their color. So on some interval of her way she calculated two values — the number of steps with even and odd numbers. You need to check whether there is an interval of steps from the l-th to the r-th (1 ≤ l ≤ r), for which values that Dasha has found are correct.", "input_spec": "In the only line you are given two integers a, b (0 ≤ a, b ≤ 100) — the number of even and odd steps, accordingly.", "output_spec": "In the only line print \"YES\", if the interval of steps described above exists, and \"NO\" otherwise.", "sample_inputs": ["2 3", "3 1"], "sample_outputs": ["YES", "NO"], "notes": "NoteIn the first example one of suitable intervals is from 1 to 5. The interval contains two even steps — 2 and 4, and three odd: 1, 3 and 5."}, "src_uid": "ec5e3b3f5ee6a13eaf01b9a9a66ff037"}
{"nl": {"description": "The Professor has lost his home robot yet again. After some thinking Professor understood that he had left the robot in the basement.The basement in Professor's house is represented by a rectangle n × m, split into 1 × 1 squares. Some squares are walls which are impassable; other squares are passable. You can get from any passable square to any other passable square moving through edge-adjacent passable squares. One passable square is the exit from the basement. The robot is placed exactly in one passable square. Also the robot may be placed in the exit square.Professor is scared of going to the dark basement looking for the robot at night. However, he has a basement plan and the robot's remote control. Using the remote, Professor can send signals to the robot to shift one square left, right, up or down. When the robot receives a signal, it moves in the required direction if the robot's neighboring square in the given direction is passable. Otherwise, the robot stays idle.Professor wrote a sequence of k commands on a piece of paper. He thinks that the sequence can lead the robot out of the basement, wherever it's initial position might be. Professor programmed another robot to press the required buttons on the remote according to the notes on the piece of paper. Professor was just about to run the program and go to bed, when he had an epiphany.Executing each command takes some energy and Professor doesn't want to get huge electricity bill at the end of the month. That's why he wants to find in the sequence he has written out the minimal possible prefix that would guarantee to lead the robot out to the exit after the prefix is fulfilled. And that's the problem Professor challenges you with at this late hour.", "input_spec": "The first line contains three integers n, m and k (3 ≤ n, m ≤ 150, 1 ≤ k ≤ 105). Next n lines contain m characters each — that is the Professor's basement's description: \"#\" stands for a wall, \".\" stands for a passable square and \"E\" stands for the exit from the basement (this square also is passable). It is possible to get from each passable square to the exit, all squares located by the n × m rectangle's perimeter are the walls. Exactly one square is the exit from the basement. The last line contains k characters, the description of the sequence of commands that Professor has written out on a piece of paper. \"L\", \"R\", \"U\", \"D\" stand for commands left, right, up and down correspondingly.", "output_spec": "Print in the output file the length of the smallest possible prefix that will lead the robot to the exit square. In other words, wherever the robot had been positioned initially, it should be positioned in the exit square after all the commands from the prefix are fulfilled (during doing commands the robot can come and leave the exit square, but only the last position of the robot is interesting for us). If Professor is mistaken and no prefix (including the whole sequence) can bring the robot to the exit, print \"-1\" (without the quotes). If there is the only passable square and it is the exit, print \"0\" (without the quotes).", "sample_inputs": ["5 5 7\n#####\n#...#\n#...#\n#E..#\n#####\nUULLDDR", "5 5 7\n#####\n#.#.#\n#...#\n#E..#\n#####\nUULLDDR", "5 3 2\n###\n#.#\n#.#\n#E#\n###\nDD"], "sample_outputs": ["6", "-1", "2"], "notes": null}, "src_uid": "70ab617d9b8813ddf3039c6fb137d817"}
{"nl": {"description": "Vasya has recently learned to type and log on to the Internet. He immediately entered a chat room and decided to say hello to everybody. Vasya typed the word s. It is considered that Vasya managed to say hello if several letters can be deleted from the typed word so that it resulted in the word \"hello\". For example, if Vasya types the word \"ahhellllloou\", it will be considered that he said hello, and if he types \"hlelo\", it will be considered that Vasya got misunderstood and he didn't manage to say hello. Determine whether Vasya managed to say hello by the given word s.", "input_spec": "The first and only line contains the word s, which Vasya typed. This word consisits of small Latin letters, its length is no less that 1 and no more than 100 letters.", "output_spec": "If Vasya managed to say hello, print \"YES\", otherwise print \"NO\".", "sample_inputs": ["ahhellllloou", "hlelo"], "sample_outputs": ["YES", "NO"], "notes": null}, "src_uid": "c5d19dc8f2478ee8d9cba8cc2e4cd838"}
{"nl": {"description": "Mad scientist Mike is building a time machine in his spare time. To finish the work, he needs a resistor with a certain resistance value.However, all Mike has is lots of identical resistors with unit resistance R0 = 1. Elements with other resistance can be constructed from these resistors. In this problem, we will consider the following as elements:   one resistor;  an element and one resistor plugged in sequence;  an element and one resistor plugged in parallel.   With the consecutive connection the resistance of the new element equals R = Re + R0. With the parallel connection the resistance of the new element equals . In this case Re equals the resistance of the element being connected.Mike needs to assemble an element with a resistance equal to the fraction . Determine the smallest possible number of resistors he needs to make such an element.", "input_spec": "The single input line contains two space-separated integers a and b (1 ≤ a, b ≤ 1018). It is guaranteed that the fraction  is irreducible. It is guaranteed that a solution always exists.", "output_spec": "Print a single number — the answer to the problem. Please do not use the %lld specifier to read or write 64-bit integers in С++. It is recommended to use the cin, cout streams or the %I64d specifier.", "sample_inputs": ["1 1", "3 2", "199 200"], "sample_outputs": ["1", "3", "200"], "notes": "NoteIn the first sample, one resistor is enough.In the second sample one can connect the resistors in parallel, take the resulting element and connect it to a third resistor consecutively. Then, we get an element with resistance . We cannot make this element using two resistors."}, "src_uid": "792efb147f3668a84c866048361970f8"}
{"nl": {"description": "Petya loves lucky numbers. Everybody knows that positive integers are lucky if their decimal representation doesn't contain digits other than 4 and 7. For example, numbers 47, 744, 4 are lucky and 5, 17, 467 are not.Lucky number is super lucky if it's decimal representation contains equal amount of digits 4 and 7. For example, numbers 47, 7744, 474477 are super lucky and 4, 744, 467 are not.One day Petya came across a positive integer n. Help him to find the least super lucky number which is not less than n.", "input_spec": "The only line contains a positive integer n (1 ≤ n ≤ 10100000). This number doesn't have leading zeroes.", "output_spec": "Output the least super lucky number that is more than or equal to n.", "sample_inputs": ["4500", "47"], "sample_outputs": ["4747", "47"], "notes": null}, "src_uid": "77b5f83cdadf4b0743618a46b646a849"}
{"nl": {"description": "For a positive integer n let's define a function f:f(n) =  - 1 + 2 - 3 + .. + ( - 1)nn Your task is to calculate f(n) for a given integer n.", "input_spec": "The single line contains the positive integer n (1 ≤ n ≤ 1015).", "output_spec": "Print f(n) in a single line.", "sample_inputs": ["4", "5"], "sample_outputs": ["2", "-3"], "notes": "Notef(4) =  - 1 + 2 - 3 + 4 = 2f(5) =  - 1 + 2 - 3 + 4 - 5 =  - 3"}, "src_uid": "689e7876048ee4eb7479e838c981f068"}
{"nl": {"description": "Rock... Paper!After Karen have found the deterministic winning (losing?) strategy for rock-paper-scissors, her brother, Koyomi, comes up with a new game as a substitute. The game works as follows.A positive integer n is decided first. Both Koyomi and Karen independently choose n distinct positive integers, denoted by x1, x2, ..., xn and y1, y2, ..., yn respectively. They reveal their sequences, and repeat until all of 2n integers become distinct, which is the only final state to be kept and considered.Then they count the number of ordered pairs (i, j) (1 ≤ i, j ≤ n) such that the value xi xor yj equals to one of the 2n integers. Here xor means the bitwise exclusive or operation on two integers, and is denoted by operators ^ and/or xor in most programming languages.Karen claims a win if the number of such pairs is even, and Koyomi does otherwise. And you're here to help determine the winner of their latest game.", "input_spec": "The first line of input contains a positive integer n (1 ≤ n ≤ 2 000) — the length of both sequences. The second line contains n space-separated integers x1, x2, ..., xn (1 ≤ xi ≤ 2·106) — the integers finally chosen by Koyomi. The third line contains n space-separated integers y1, y2, ..., yn (1 ≤ yi ≤ 2·106) — the integers finally chosen by Karen. Input guarantees that the given 2n integers are pairwise distinct, that is, no pair (i, j) (1 ≤ i, j ≤ n) exists such that one of the following holds: xi = yj; i ≠ j and xi = xj; i ≠ j and yi = yj.", "output_spec": "Output one line — the name of the winner, that is, \"Koyomi\" or \"Karen\" (without quotes). Please be aware of the capitalization.", "sample_inputs": ["3\n1 2 3\n4 5 6", "5\n2 4 6 8 10\n9 7 5 3 1"], "sample_outputs": ["Karen", "Karen"], "notes": "NoteIn the first example, there are 6 pairs satisfying the constraint: (1, 1), (1, 2), (2, 1), (2, 3), (3, 2) and (3, 3). Thus, Karen wins since 6 is an even number.In the second example, there are 16 such pairs, and Karen wins again."}, "src_uid": "1649d2592eadaa8f8d076eae2866cffc"}
{"nl": {"description": "Mike has a string s consisting of only lowercase English letters. He wants to change exactly one character from the string so that the resulting one is a palindrome. A palindrome is a string that reads the same backward as forward, for example strings \"z\", \"aaa\", \"aba\", \"abccba\" are palindromes, but strings \"codeforces\", \"reality\", \"ab\" are not.", "input_spec": "The first and single line contains string s (1 ≤ |s| ≤ 15).", "output_spec": "Print \"YES\" (without quotes) if Mike can change exactly one character so that the resulting string is palindrome or \"NO\" (without quotes) otherwise. ", "sample_inputs": ["abccaa", "abbcca", "abcda"], "sample_outputs": ["YES", "NO", "YES"], "notes": null}, "src_uid": "fe74313abcf381f6c5b7b2057adaaa52"}
{"nl": {"description": "В Берляндском государственном университете локальная сеть между серверами не всегда работает без ошибок. При передаче двух одинаковых сообщений подряд возможна ошибка, в результате которой эти два сообщения сливаются в одно. При таком слиянии конец первого сообщения совмещается с началом второго. Конечно, совмещение может происходить только по одинаковым символам. Длина совмещения должна быть положительным числом, меньшим длины текста сообщения. Например, при передаче двух сообщений «abrakadabra» подряд возможно, что оно будет передано с ошибкой описанного вида, и тогда будет получено сообщение вида «abrakadabrabrakadabra» или «abrakadabrakadabra» (в первом случае совмещение произошло по одному символу, а во втором — по четырем).По полученному сообщению t определите, возможно ли, что это результат ошибки описанного вида работы локальной сети, и если возможно, определите возможное значение s. Не следует считать ошибкой ситуацию полного наложения друга на друга двух сообщений. К примеру, если получено сообщение «abcd», следует считать, что в нём ошибки нет. Аналогично, простое дописывание одного сообщения вслед за другим не является признаком ошибки. Например, если получено сообщение «abcabc», следует считать, что в нём ошибки нет.", "input_spec": "В единственной строке выходных данных следует непустая строка t, состоящая из строчных букв латинского алфавита. Длина строки t не превосходит 100 символов.", "output_spec": "Если сообщение t не может содержать ошибки, выведите «NO» (без кавычек) в единственную строку выходных данных. В противном случае в первой строке выведите «YES» (без кавычек), а в следующей строке выведите строку s — возможное сообщение, которое могло привести к ошибке. Если возможных ответов несколько, разрешается вывести любой из них.", "sample_inputs": ["abrakadabrabrakadabra", "acacacaca", "abcabc", "abababab", "tatbt"], "sample_outputs": ["YES\nabrakadabra", "YES\nacaca", "NO", "YES\nababab", "NO"], "notes": "ПримечаниеВо втором примере подходящим ответом также является строка acacaca. "}, "src_uid": "bfa78f72af4875f670f7adc5ed127033"}
{"nl": {"description": "Petya loves lucky numbers. Everybody knows that lucky numbers are positive integers whose decimal representation contains only the lucky digits 4 and 7. For example, numbers 47, 744, 4 are lucky and 5, 17, 467 are not.Let next(x) be the minimum lucky number which is larger than or equals x. Petya is interested what is the value of the expression next(l) + next(l + 1) + ... + next(r - 1) + next(r). Help him solve this problem.", "input_spec": "The single line contains two integers l and r (1 ≤ l ≤ r ≤ 109) — the left and right interval limits.", "output_spec": "In the single line print the only number — the sum next(l) + next(l + 1) + ... + next(r - 1) + next(r). Please do not use the %lld specificator to read or write 64-bit integers in C++. It is preferred to use the cin, cout streams or the %I64d specificator.", "sample_inputs": ["2 7", "7 7"], "sample_outputs": ["33", "7"], "notes": "NoteIn the first sample: next(2) + next(3) + next(4) + next(5) + next(6) + next(7) = 4 + 4 + 4 + 7 + 7 + 7 = 33In the second sample: next(7) = 7"}, "src_uid": "8a45fe8956d3ac9d501f4a13b55638dd"}
{"nl": {"description": "Victor tries to write his own text editor, with word correction included. However, the rules of word correction are really strange.Victor thinks that if a word contains two consecutive vowels, then it's kinda weird and it needs to be replaced. So the word corrector works in such a way: as long as there are two consecutive vowels in the word, it deletes the first vowel in a word such that there is another vowel right before it. If there are no two consecutive vowels in the word, it is considered to be correct.You are given a word s. Can you predict what will it become after correction?In this problem letters a, e, i, o, u and y are considered to be vowels.", "input_spec": "The first line contains one integer n (1 ≤ n ≤ 100) — the number of letters in word s before the correction. The second line contains a string s consisting of exactly n lowercase Latin letters — the word before the correction.", "output_spec": "Output the word s after the correction.", "sample_inputs": ["5\nweird", "4\nword", "5\naaeaa"], "sample_outputs": ["werd", "word", "a"], "notes": "NoteExplanations of the examples:  There is only one replace: weird  werd; No replace needed since there are no two consecutive vowels; aaeaa  aeaa  aaa  aa  a. "}, "src_uid": "63a4a5795d94f698b0912bb8d4cdf690"}
{"nl": {"description": "There is an old tradition of keeping 4 boxes of candies in the house in Cyberland. The numbers of candies are special if their arithmetic mean, their median and their range are all equal. By definition, for a set {x1, x2, x3, x4} (x1 ≤ x2 ≤ x3 ≤ x4) arithmetic mean is , median is  and range is x4 - x1. The arithmetic mean and median are not necessary integer. It is well-known that if those three numbers are same, boxes will create a \"debugging field\" and codes in the field will have no bugs.For example, 1, 1, 3, 3 is the example of 4 numbers meeting the condition because their mean, median and range are all equal to 2.Jeff has 4 special boxes of candies. However, something bad has happened! Some of the boxes could have been lost and now there are only n (0 ≤ n ≤ 4) boxes remaining. The i-th remaining box contains ai candies.Now Jeff wants to know: is there a possible way to find the number of candies of the 4 - n missing boxes, meeting the condition above (the mean, median and range are equal)?", "input_spec": "The first line of input contains an only integer n (0 ≤ n ≤ 4). The next n lines contain integers ai, denoting the number of candies in the i-th box (1 ≤ ai ≤ 500).", "output_spec": "In the first output line, print \"YES\" if a solution exists, or print \"NO\" if there is no solution. If a solution exists, you should output 4 - n more lines, each line containing an integer b, denoting the number of candies in a missing box. All your numbers b must satisfy inequality 1 ≤ b ≤ 106. It is guaranteed that if there exists a positive integer solution, you can always find such b's meeting the condition. If there are multiple answers, you are allowed to print any of them. Given numbers ai may follow in any order in the input, not necessary in non-decreasing. ai may have stood at any positions in the original set, not necessary on lowest n first positions.", "sample_inputs": ["2\n1\n1", "3\n1\n1\n1", "4\n1\n2\n2\n3"], "sample_outputs": ["YES\n3\n3", "NO", "YES"], "notes": "NoteFor the first sample, the numbers of candies in 4 boxes can be 1, 1, 3, 3. The arithmetic mean, the median and the range of them are all 2.For the second sample, it's impossible to find the missing number of candies.In the third example no box has been lost and numbers satisfy the condition.You may output b in any order."}, "src_uid": "230e613abf0f6a768829cbc1f1a09219"}
{"nl": {"description": "There is a developed network of flights between Berland and Beerland. All of them belong to the Berland state company BerAvia. Each flight connects some Berland city with some Beerland city. For each flight airplanes fly in both directions.Changes are coming to Berland — the state decided to privatize BerAvia, namely, to sell out all flights to t private companies. Each of these companies wants to get the maximal number of flights, so if the Berland flights are sold unevenly, Berland can be accused of partiality. Berland Government decided to sell the flights as evenly as possible between the t companies.The unevenness of the distribution of flights between companies is calculated as follows. For each city i (both Berland and Beerland) we'll calculate the value of  where aij is the number of flights from city i, which belong to company j. The sum of wi for all cities in both countries is called the unevenness of the distribution. The distribution with the minimal unevenness is the most even one.Help the Berland government come up with the most even distribution plan of selling flights.", "input_spec": "The first input line contains four integers n, m, k and t (1 ≤ n, m, t ≤ 200;1 ≤ k ≤ 5000), where n, m are the numbers of cities in Berland and Beerland, correspondingly, k is the number of flights between them, and t is the number of private companies. Next k lines describe the flights, one per line, as pairs of positive integers xi, yi (1 ≤ xi ≤ n;1 ≤ yi ≤ m), where xi and yi are the indexes of cities in Berland and Beerland, correspondingly, connected by the i-th flight. There is at most one flight between any pair of cities, each flight connects cities of different countries. The cities in Berland are indexed from 1 to n, and in Beerland — from 1 to m.", "output_spec": "Print the unevenness of the sought plan on the first line. On the second line print a sequence of k integers c1, c2, ..., ck (1 ≤ ci ≤ t), where ci is the index of the company that should buy the i-th flight. Assume that the flights are indexed from 1 to k in the order they appear in the input. If there are multiple solutions, print any of them.", "sample_inputs": ["3 5 8 2\n1 4\n1 3\n3 3\n1 2\n1 1\n2 1\n1 5\n2 2"], "sample_outputs": ["4\n2 1 2 1 2 1 2 2"], "notes": null}, "src_uid": "99b97aabec566e5f966777947271ad3c"}
{"nl": {"description": "You are given a tree with n vertexes and n points on a plane, no three points lie on one straight line.Your task is to paint the given tree on a plane, using the given points as vertexes. That is, you should correspond each vertex of the tree to exactly one point and each point should correspond to a vertex. If two vertexes of the tree are connected by an edge, then the corresponding points should have a segment painted between them. The segments that correspond to non-adjacent edges, should not have common points. The segments that correspond to adjacent edges should have exactly one common point.", "input_spec": "The first line contains an integer n (1 ≤ n ≤ 1500) — the number of vertexes on a tree (as well as the number of chosen points on the plane). Each of the next n - 1 lines contains two space-separated integers ui and vi (1 ≤ ui, vi ≤ n, ui ≠ vi) — the numbers of tree vertexes connected by the i-th edge. Each of the next n lines contain two space-separated integers xi and yi ( - 109 ≤ xi, yi ≤ 109) — the coordinates of the i-th point on the plane. No three points lie on one straight line. It is guaranteed that under given constraints problem has a solution.", "output_spec": "Print n distinct space-separated integers from 1 to n: the i-th number must equal the number of the vertex to place at the i-th point (the points are numbered in the order, in which they are listed in the input). If there are several solutions, print any of them.", "sample_inputs": ["3\n1 3\n2 3\n0 0\n1 1\n2 0", "4\n1 2\n2 3\n1 4\n-1 -2\n3 5\n-3 3\n2 0"], "sample_outputs": ["1 3 2", "4 2 1 3"], "notes": "NoteThe possible solutions for the sample are given below.   "}, "src_uid": "d65e91dc274c6659cfdb50bc8b8020ba"}
{"nl": {"description": "Vector Willman and Array Bolt are the two most famous athletes of Byteforces. They are going to compete in a race with a distance of L meters today.  Willman and Bolt have exactly the same speed, so when they compete the result is always a tie. That is a problem for the organizers because they want a winner. While watching previous races the organizers have noticed that Willman can perform only steps of length equal to w meters, and Bolt can perform only steps of length equal to b meters. Organizers decided to slightly change the rules of the race. Now, at the end of the racetrack there will be an abyss, and the winner will be declared the athlete, who manages to run farther from the starting point of the the racetrack (which is not the subject to change by any of the athletes). Note that none of the athletes can run infinitely far, as they both will at some moment of time face the point, such that only one step further will cause them to fall in the abyss. In other words, the athlete will not fall into the abyss if the total length of all his steps will be less or equal to the chosen distance L.Since the organizers are very fair, the are going to set the length of the racetrack as an integer chosen randomly and uniformly in range from 1 to t (both are included). What is the probability that Willman and Bolt tie again today?", "input_spec": "The first line of the input contains three integers t, w and b (1 ≤ t, w, b ≤ 5·1018) — the maximum possible length of the racetrack, the length of Willman's steps and the length of Bolt's steps respectively.", "output_spec": "Print the answer to the problem as an irreducible fraction . Follow the format of the samples output. The fraction  (p and q are integers, and both p ≥ 0 and q > 0 holds) is called irreducible, if there is no such integer d > 1, that both p and q are divisible by d.", "sample_inputs": ["10 3 2", "7 1 2"], "sample_outputs": ["3/10", "3/7"], "notes": "NoteIn the first sample Willman and Bolt will tie in case 1, 6 or 7 are chosen as the length of the racetrack."}, "src_uid": "7a1d8ca25bce0073c4eb5297b94501b5"}
{"nl": {"description": "Vasya the programmer lives in the middle of the Programming subway branch. He has two girlfriends: Dasha and Masha, who live at the different ends of the branch, each one is unaware of the other one's existence.When Vasya has some free time, he goes to one of his girlfriends. He descends into the subway at some time, waits the first train to come and rides on it to the end of the branch to the corresponding girl. However, the trains run with different frequencies: a train goes to Dasha's direction every a minutes, but a train goes to Masha's direction every b minutes. If two trains approach at the same time, Vasya goes toward the direction with the lower frequency of going trains, that is, to the girl, to whose directions the trains go less frequently (see the note to the third sample).We know that the trains begin to go simultaneously before Vasya appears. That is the train schedule is such that there exists a moment of time when the two trains arrive simultaneously.Help Vasya count to which girlfriend he will go more often.", "input_spec": "The first line contains two integers a and b (a ≠ b, 1 ≤ a, b ≤ 106).", "output_spec": "Print \"Dasha\" if Vasya will go to Dasha more frequently, \"Masha\" if he will go to Masha more frequently, or \"Equal\" if he will go to both girlfriends with the same frequency.", "sample_inputs": ["3 7", "5 3", "2 3"], "sample_outputs": ["Dasha", "Masha", "Equal"], "notes": "NoteLet's take a look at the third sample. Let the trains start to go at the zero moment of time. It is clear that the moments of the trains' arrival will be periodic with period 6. That's why it is enough to show that if Vasya descends to the subway at a moment of time inside the interval (0, 6], he will go to both girls equally often. If he descends to the subway at a moment of time from 0 to 2, he leaves for Dasha on the train that arrives by the second minute.If he descends to the subway at a moment of time from 2 to 3, he leaves for Masha on the train that arrives by the third minute.If he descends to the subway at a moment of time from 3 to 4, he leaves for Dasha on the train that arrives by the fourth minute.If he descends to the subway at a moment of time from 4 to 6, he waits for both trains to arrive by the sixth minute and goes to Masha as trains go less often in Masha's direction.In sum Masha and Dasha get equal time — three minutes for each one, thus, Vasya will go to both girlfriends equally often."}, "src_uid": "06eb66df61ff5d61d678bbb3bb6553cc"}
{"nl": {"description": "Kurt reaches nirvana when he finds the product of all the digits of some positive integer. Greater value of the product makes the nirvana deeper.Help Kurt find the maximum possible product of digits among all integers from $$$1$$$ to $$$n$$$.", "input_spec": "The only input line contains the integer $$$n$$$ ($$$1 \\le n \\le 2\\cdot10^9$$$).", "output_spec": "Print the maximum product of digits among all integers from $$$1$$$ to $$$n$$$.", "sample_inputs": ["390", "7", "1000000000"], "sample_outputs": ["216", "7", "387420489"], "notes": "NoteIn the first example the maximum product is achieved for $$$389$$$ (the product of digits is $$$3\\cdot8\\cdot9=216$$$).In the second example the maximum product is achieved for $$$7$$$ (the product of digits is $$$7$$$).In the third example the maximum product is achieved for $$$999999999$$$ (the product of digits is $$$9^9=387420489$$$)."}, "src_uid": "38690bd32e7d0b314f701f138ce19dfb"}
{"nl": {"description": "Vanya got an important task — he should enumerate books in the library and label each book with its number. Each of the n books should be assigned with a number from 1 to n. Naturally, distinct books should be assigned distinct numbers.Vanya wants to know how many digits he will have to write down as he labels the books.", "input_spec": "The first line contains integer n (1 ≤ n ≤ 109) — the number of books in the library.", "output_spec": "Print the number of digits needed to number all the books.", "sample_inputs": ["13", "4"], "sample_outputs": ["17", "4"], "notes": "NoteNote to the first test. The books get numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, which totals to 17 digits.Note to the second sample. The books get numbers 1, 2, 3, 4, which totals to 4 digits."}, "src_uid": "4e652ccb40632bf4b9dd95b9f8ae1ec9"}
{"nl": {"description": "Wet Shark asked Rat Kwesh to generate three positive real numbers x, y and z, from 0.1 to 200.0, inclusive. Wet Krash wants to impress Wet Shark, so all generated numbers will have exactly one digit after the decimal point.Wet Shark knows Rat Kwesh will want a lot of cheese. So he will give the Rat an opportunity to earn a lot of cheese. He will hand the three numbers x, y and z to Rat Kwesh, and Rat Kwesh will pick one of the these twelve options:  a1 = xyz;  a2 = xzy;  a3 = (xy)z;  a4 = (xz)y;  a5 = yxz;  a6 = yzx;  a7 = (yx)z;  a8 = (yz)x;  a9 = zxy;  a10 = zyx;  a11 = (zx)y;  a12 = (zy)x. Let m be the maximum of all the ai, and c be the smallest index (from 1 to 12) such that ac = m. Rat's goal is to find that c, and he asks you to help him. Rat Kwesh wants to see how much cheese he gets, so he you will have to print the expression corresponding to that ac. ", "input_spec": "The only line of the input contains three space-separated real numbers x, y and z (0.1 ≤ x, y, z ≤ 200.0). Each of x, y and z is given with exactly one digit after the decimal point.", "output_spec": "Find the maximum value of expression among xyz, xzy, (xy)z, (xz)y, yxz, yzx, (yx)z, (yz)x, zxy, zyx, (zx)y, (zy)x and print the corresponding expression. If there are many maximums, print the one that comes first in the list.  xyz should be outputted as x^y^z (without brackets), and (xy)z should be outputted as (x^y)^z (quotes for clarity). ", "sample_inputs": ["1.1 3.4 2.5", "2.0 2.0 2.0", "1.9 1.8 1.7"], "sample_outputs": ["z^y^x", "x^y^z", "(x^y)^z"], "notes": null}, "src_uid": "a71cb5cda754ad2bf479bc3b0164fc4c"}
{"nl": {"description": "A string a of length m is called antipalindromic iff m is even, and for each i (1 ≤ i ≤ m) ai ≠ am - i + 1.Ivan has a string s consisting of n lowercase Latin letters; n is even. He wants to form some string t that will be an antipalindromic permutation of s. Also Ivan has denoted the beauty of index i as bi, and the beauty of t as the sum of bi among all indices i such that si = ti.Help Ivan to determine maximum possible beauty of t he can get.", "input_spec": "The first line contains one integer n (2 ≤ n ≤ 100, n is even) — the number of characters in s. The second line contains the string s itself. It consists of only lowercase Latin letters, and it is guaranteed that its letters can be reordered to form an antipalindromic string. The third line contains n integer numbers b1, b2, ..., bn (1 ≤ bi ≤ 100), where bi is the beauty of index i.", "output_spec": "Print one number — the maximum possible beauty of t.", "sample_inputs": ["8\nabacabac\n1 1 1 1 1 1 1 1", "8\nabaccaba\n1 2 3 4 5 6 7 8", "8\nabacabca\n1 2 3 4 4 3 2 1"], "sample_outputs": ["8", "26", "17"], "notes": null}, "src_uid": "896555ddb6e1c268cd7b3b6b063fce50"}
{"nl": {"description": "Berland traffic is very different from traffic in other countries. The capital of Berland consists of n junctions and m roads. Each road connects a pair of junctions. There can be multiple roads between a pair of junctions. For each road we know its capacity: value ci is the maximum number of cars that can drive along a road in any direction per a unit of time. For each road, the cars can drive along it in one of two direction. That it, the cars can't simultaneously move in both directions. A road's traffic is the number of cars that goes along it per a unit of time. For road (ai, bi) this value is negative, if the traffic moves from bi to ai. A road's traffic can be a non-integer number.The capital has two special junctions — the entrance to the city (junction 1) and the exit from the city (junction n). For all other junctions it is true that the traffic is not lost there. That is, for all junctions except for 1 and n the incoming traffic sum equals the outgoing traffic sum.Traffic has an unusual peculiarity in the capital of Berland — for any pair of junctions (x, y) the sum of traffics along any path from x to y doesn't change depending on the choice of the path. Such sum includes traffic along all roads on the path (possible with the \"minus\" sign, if the traffic along the road is directed against the direction of the road on the path from x to y).Your task is to find the largest traffic that can pass trough the city per one unit of time as well as the corresponding traffic for each road. ", "input_spec": "The first line contains a positive integer n — the number of junctions (2 ≤ n ≤ 100). The second line contains integer m (1 ≤ m ≤ 5000) — the number of roads. Next m lines contain the roads' descriptions. Each road contains a group of three numbers ai, bi, ci, where ai, bi are the numbers of junctions, connected by the given road, and ci (1 ≤ ai, bi ≤ n; ai ≠ bi; 0 ≤ ci ≤ 10000) is the largest permissible traffic along this road.", "output_spec": "In the first line print the required largest traffic across the city. Then print m lines, on each line print the speed, at which the traffic moves along the corresponding road. If the direction doesn't match the order of the junctions, given in the input, then print the traffic with the minus sign. Print the numbers with accuracy of at least five digits after the decimal point. If there are many optimal solutions, print any of them.", "sample_inputs": ["2\n3\n1 2 2\n1 2 4\n2 1 1000", "7\n11\n1 2 7\n1 2 7\n1 3 7\n1 4 7\n2 3 7\n2 5 7\n3 6 7\n4 7 7\n5 4 7\n5 6 7\n6 7 7"], "sample_outputs": ["6.00000\n2.00000\n2.00000\n-2.00000", "13.00000\n2.00000\n2.00000\n3.00000\n6.00000\n1.00000\n3.00000\n4.00000\n7.00000\n1.00000\n2.00000\n6.00000"], "notes": null}, "src_uid": "93fa614f174816d241c0fa302c6476e2"}
{"nl": {"description": "After making bad dives into swimming pools, Wilbur wants to build a swimming pool in the shape of a rectangle in his backyard. He has set up coordinate axes, and he wants the sides of the rectangle to be parallel to them. Of course, the area of the rectangle must be positive. Wilbur had all four vertices of the planned pool written on a paper, until his friend came along and erased some of the vertices.Now Wilbur is wondering, if the remaining n vertices of the initial rectangle give enough information to restore the area of the planned swimming pool.", "input_spec": "The first line of the input contains a single integer n (1 ≤ n ≤ 4) — the number of vertices that were not erased by Wilbur's friend. Each of the following n lines contains two integers xi and yi ( - 1000 ≤ xi, yi ≤ 1000) —the coordinates of the i-th vertex that remains. Vertices are given in an arbitrary order. It's guaranteed that these points are distinct vertices of some rectangle, that has positive area and which sides are parallel to the coordinate axes.", "output_spec": "Print the area of the initial rectangle if it could be uniquely determined by the points remaining. Otherwise, print  - 1. ", "sample_inputs": ["2\n0 0\n1 1", "1\n1 1"], "sample_outputs": ["1", "-1"], "notes": "NoteIn the first sample, two opposite corners of the initial rectangle are given, and that gives enough information to say that the rectangle is actually a unit square.In the second sample there is only one vertex left and this is definitely not enough to uniquely define the area."}, "src_uid": "ba49b6c001bb472635f14ec62233210e"}
{"nl": {"description": "Heidi the Cow is aghast: cracks in the northern Wall? Zombies gathering outside, forming groups, preparing their assault? This must not happen! Quickly, she fetches her HC2 (Handbook of Crazy Constructions) and looks for the right chapter:How to build a wall:  Take a set of bricks.  Select one of the possible wall designs. Computing the number of possible designs is left as an exercise to the reader.  Place bricks on top of each other, according to the chosen design. This seems easy enough. But Heidi is a Coding Cow, not a Constructing Cow. Her mind keeps coming back to point 2b. Despite the imminent danger of a zombie onslaught, she wonders just how many possible walls she could build with up to n bricks.A wall is a set of wall segments as defined in the easy version. How many different walls can be constructed such that the wall consists of at least 1 and at most n bricks? Two walls are different if there exist a column c and a row r such that one wall has a brick in this spot, and the other does not.Along with n, you will be given C, the width of the wall (as defined in the easy version). Return the number of different walls modulo 106 + 3.", "input_spec": "The first line contains two space-separated integers n and C, 1 ≤ n ≤ 500000, 1 ≤ C ≤ 200000.", "output_spec": "Print the number of different walls that Heidi could build, modulo 106 + 3.", "sample_inputs": ["5 1", "2 2", "3 2", "11 5", "37 63"], "sample_outputs": ["5", "5", "9", "4367", "230574"], "notes": "NoteThe number 106 + 3 is prime.In the second sample case, the five walls are:             B        BB., .B, BB, B., and .BIn the third sample case, the nine walls are the five as in the second sample case and in addition the following four: B    BB    B  B        BB., .B, BB, and BB"}, "src_uid": "e63c70a9c96a94bce99618f2e695f83a"}
{"nl": {"description": "The Bytelandian Institute for Biological Research (BIBR) is investigating the properties of two species of bacteria, named simply 0 and 1. Even under a microscope, bacteria of those two species are very difficult to distinguish. In fact, the only thing the scientists possess that is able to differentiate between them is a plant called Formurosa.If the scientists place a sample of colonies of bacteria on each on Formurosa's leaves, it will activate a complicated nutrition process. During that process color of Formurosa changes to reflect the result of a — possibly very complicated — logical formula on the species of bacteria, involving constants and the operators | (OR), & (AND) and ^ (XOR). If it is 0, the plant will turn red, otherwise — it will turn blue.For example, if the nutrition process of Formurosa is described by the formula: (((?^?)|?)&(1^?)); then Formurosa has four leaves (the \"?\" signs denote the leaves). If we place 0, 1, 0, 0 on the respective leaves, the result of the nutrition process will be (((0^1)|0)&(1^0)) = 1, therefore the plant will turn blue.The scientists have n colonies of bacteria. They do not know their types; the only thing they know for sure is that not all colonies are of the same type. They want to attempt to determine the bacteria's species by repeated evaluations with Formurosa. During each evaluation they must place exactly one sample on every leaf of the plant. However, they may use multiple samples of one colony during a single evaluation; they can even cover the whole plant with bacteria from one colony!Is it possible for them to always determine the species of each colony, no matter what they are (assuming they are not all the same)?", "input_spec": "The first line of input contains a single integer n (2 ≤ n ≤ 106) — the number of colonies of bacteria. The second line contains the formula describing the nutrition process of Formurosa. This line contains only characters «0», «1», «?», «|», «&», «^», «(», «)» and complies with the following grammar: s → 0|1|?|(s|s)|(s&s)|(s^s) The formula consists of no more than 106 characters.", "output_spec": "If it is always possible to determine the species of each colony, output \"YES\" (without quotes). Otherwise, output \"NO\" (without quotes).", "sample_inputs": ["2\n(?^?)", "10\n?", "2\n((?^?)&?)"], "sample_outputs": ["NO", "YES", "YES"], "notes": null}, "src_uid": "e060d26dc3b9ffb628f2380781d1cbe9"}
{"nl": {"description": "There exists an island called Arpa’s land, some beautiful girls live there, as ugly ones do.Mehrdad wants to become minister of Arpa’s land. Arpa has prepared an exam. Exam has only one question, given n, print the last digit of 1378n.   Mehrdad has become quite confused and wants you to help him. Please help, although it's a naive cheat.", "input_spec": "The single line of input contains one integer n (0  ≤  n  ≤  109).", "output_spec": "Print single integer — the last digit of 1378n.", "sample_inputs": ["1", "2"], "sample_outputs": ["8", "4"], "notes": "NoteIn the first example, last digit of 13781 = 1378 is 8.In the second example, last digit of 13782 = 1378·1378 = 1898884 is 4."}, "src_uid": "4b51b99d1dea367bf37dc5ead08ca48f"}
{"nl": {"description": "You are given an array of $$$n$$$ integers: $$$a_1, a_2, \\ldots, a_n$$$. Your task is to find some non-zero integer $$$d$$$ ($$$-10^3 \\leq d \\leq 10^3$$$) such that, after each number in the array is divided by $$$d$$$, the number of positive numbers that are presented in the array is greater than or equal to half of the array size (i.e., at least $$$\\lceil\\frac{n}{2}\\rceil$$$). Note that those positive numbers do not need to be an integer (e.g., a $$$2.5$$$ counts as a positive number). If there are multiple values of $$$d$$$ that satisfy the condition, you may print any of them. In case that there is no such $$$d$$$, print a single integer $$$0$$$.Recall that $$$\\lceil x \\rceil$$$ represents the smallest integer that is not less than $$$x$$$ and that zero ($$$0$$$) is neither positive nor negative.", "input_spec": "The first line contains one integer $$$n$$$ ($$$1 \\le n \\le 100$$$) — the number of elements in the array. The second line contains $$$n$$$ space-separated integers $$$a_1, a_2, \\ldots, a_n$$$ ($$$-10^3 \\le a_i \\le 10^3$$$).", "output_spec": "Print one integer $$$d$$$ ($$$-10^3 \\leq d \\leq 10^3$$$ and $$$d \\neq 0$$$) that satisfies the given condition. If there are multiple values of $$$d$$$ that satisfy the condition, you may print any of them. In case that there is no such $$$d$$$, print a single integer $$$0$$$.", "sample_inputs": ["5\n10 0 -7 2 6", "7\n0 0 1 -1 0 0 2"], "sample_outputs": ["4", "0"], "notes": "NoteIn the first sample, $$$n = 5$$$, so we need at least $$$\\lceil\\frac{5}{2}\\rceil = 3$$$ positive numbers after division. If $$$d = 4$$$, the array after division is $$$[2.5, 0, -1.75, 0.5, 1.5]$$$, in which there are $$$3$$$ positive numbers (namely: $$$2.5$$$, $$$0.5$$$, and $$$1.5$$$).In the second sample, there is no valid $$$d$$$, so $$$0$$$ should be printed."}, "src_uid": "a13cb35197f896cd34614c6c0b369a49"}
{"nl": {"description": "On a chessboard with a width of $$$n$$$ and a height of $$$n$$$, rows are numbered from bottom to top from $$$1$$$ to $$$n$$$, columns are numbered from left to right from $$$1$$$ to $$$n$$$. Therefore, for each cell of the chessboard, you can assign the coordinates $$$(r,c)$$$, where $$$r$$$ is the number of the row, and $$$c$$$ is the number of the column.The white king has been sitting in a cell with $$$(1,1)$$$ coordinates for a thousand years, while the black king has been sitting in a cell with $$$(n,n)$$$ coordinates. They would have sat like that further, but suddenly a beautiful coin fell on the cell with coordinates $$$(x,y)$$$...Each of the monarchs wanted to get it, so they decided to arrange a race according to slightly changed chess rules:As in chess, the white king makes the first move, the black king makes the second one, the white king makes the third one, and so on. However, in this problem, kings can stand in adjacent cells or even in the same cell at the same time.The player who reaches the coin first will win, that is to say, the player who reaches the cell with the coordinates $$$(x,y)$$$ first will win.Let's recall that the king is such a chess piece that can move one cell in all directions, that is, if the king is in the $$$(a,b)$$$ cell, then in one move he can move from $$$(a,b)$$$ to the cells $$$(a + 1,b)$$$, $$$(a - 1,b)$$$, $$$(a,b + 1)$$$, $$$(a,b - 1)$$$, $$$(a + 1,b - 1)$$$, $$$(a + 1,b + 1)$$$, $$$(a - 1,b - 1)$$$, or $$$(a - 1,b + 1)$$$. Going outside of the field is prohibited.Determine the color of the king, who will reach the cell with the coordinates $$$(x,y)$$$ first, if the white king moves first.", "input_spec": "The first line contains a single integer $$$n$$$ ($$$2 \\le n \\le 10^{18}$$$) — the length of the side of the chess field. The second line contains two integers $$$x$$$ and $$$y$$$ ($$$1 \\le x,y \\le n$$$) — coordinates of the cell, where the coin fell.", "output_spec": "In a single line print the answer \"White\" (without quotes), if the white king will win, or \"Black\" (without quotes), if the black king will win. You can print each letter in any case (upper or lower).", "sample_inputs": ["4\n2 3", "5\n3 5", "2\n2 2"], "sample_outputs": ["White", "Black", "Black"], "notes": "NoteAn example of the race from the first sample where both the white king and the black king move optimally: The white king moves from the cell $$$(1,1)$$$ into the cell $$$(2,2)$$$. The black king moves form the cell $$$(4,4)$$$ into the cell $$$(3,3)$$$. The white king moves from the cell $$$(2,2)$$$ into the cell $$$(2,3)$$$. This is cell containing the coin, so the white king wins.  An example of the race from the second sample where both the white king and the black king move optimally: The white king moves from the cell $$$(1,1)$$$ into the cell $$$(2,2)$$$. The black king moves form the cell $$$(5,5)$$$ into the cell $$$(4,4)$$$. The white king moves from the cell $$$(2,2)$$$ into the cell $$$(3,3)$$$. The black king moves from the cell $$$(4,4)$$$ into the cell $$$(3,5)$$$. This is the cell, where the coin fell, so the black king wins.  In the third example, the coin fell in the starting cell of the black king, so the black king immediately wins.  "}, "src_uid": "b8ece086b35a36ca873e2edecc674557"}
{"nl": {"description": "Once again Tavas started eating coffee mix without water! Keione told him that it smells awful, but he didn't stop doing that. That's why Keione told his smart friend, SaDDas to punish him! SaDDas took Tavas' headphones and told him: \"If you solve the following problem, I'll return it to you.\"  The problem is: You are given a lucky number n. Lucky numbers are the positive integers whose decimal representations contain only the lucky digits 4 and 7. For example, numbers 47, 744, 4 are lucky and 5, 17, 467 are not.If we sort all lucky numbers in increasing order, what's the 1-based index of n? Tavas is not as smart as SaDDas, so he asked you to do him a favor and solve this problem so he can have his headphones back.", "input_spec": "The first and only line of input contains a lucky number n (1 ≤ n ≤ 109).", "output_spec": "Print the index of n among all lucky numbers.", "sample_inputs": ["4", "7", "77"], "sample_outputs": ["1", "2", "6"], "notes": null}, "src_uid": "6a10bfe8b3da9c11167e136b3c6fb2a3"}
{"nl": {"description": "Greg is a beginner bodybuilder. Today the gym coach gave him the training plan. All it had was n integers a1, a2, ..., an. These numbers mean that Greg needs to do exactly n exercises today. Besides, Greg should repeat the i-th in order exercise ai times.Greg now only does three types of exercises: \"chest\" exercises, \"biceps\" exercises and \"back\" exercises. Besides, his training is cyclic, that is, the first exercise he does is a \"chest\" one, the second one is \"biceps\", the third one is \"back\", the fourth one is \"chest\", the fifth one is \"biceps\", and so on to the n-th exercise.Now Greg wonders, which muscle will get the most exercise during his training. We know that the exercise Greg repeats the maximum number of times, trains the corresponding muscle the most. Help Greg, determine which muscle will get the most training.", "input_spec": "The first line contains integer n (1 ≤ n ≤ 20). The second line contains n integers a1, a2, ..., an (1 ≤ ai ≤ 25) — the number of times Greg repeats the exercises.", "output_spec": "Print word \"chest\" (without the quotes), if the chest gets the most exercise, \"biceps\" (without the quotes), if the biceps gets the most exercise and print \"back\" (without the quotes) if the back gets the most exercise. It is guaranteed that the input is such that the answer to the problem is unambiguous.", "sample_inputs": ["2\n2 8", "3\n5 1 10", "7\n3 3 2 7 9 6 8"], "sample_outputs": ["biceps", "back", "chest"], "notes": "NoteIn the first sample Greg does 2 chest, 8 biceps and zero back exercises, so the biceps gets the most exercises.In the second sample Greg does 5 chest, 1 biceps and 10 back exercises, so the back gets the most exercises.In the third sample Greg does 18 chest, 12 biceps and 8 back exercises, so the chest gets the most exercise."}, "src_uid": "579021de624c072f5e0393aae762117e"}
{"nl": {"description": "Jack is working on his jumping skills recently. Currently he's located at point zero of the number line. He would like to get to the point x. In order to train, he has decided that he'll first jump by only one unit, and each subsequent jump will be exactly one longer than the previous one. He can go either left or right with each jump. He wonders how many jumps he needs to reach x.", "input_spec": "The input data consists of only one integer x ( - 109 ≤ x ≤ 109).", "output_spec": "Output the minimal number of jumps that Jack requires to reach x.", "sample_inputs": ["2", "6", "0"], "sample_outputs": ["3", "3", "0"], "notes": null}, "src_uid": "18644c9df41b9960594fdca27f1d2fec"}
{"nl": {"description": "«One dragon. Two dragon. Three dragon», — the princess was counting. She had trouble falling asleep, and she got bored of counting lambs when she was nine.However, just counting dragons was boring as well, so she entertained herself at best she could. Tonight she imagined that all dragons were here to steal her, and she was fighting them off. Every k-th dragon got punched in the face with a frying pan. Every l-th dragon got his tail shut into the balcony door. Every m-th dragon got his paws trampled with sharp heels. Finally, she threatened every n-th dragon to call her mom, and he withdrew in panic.How many imaginary dragons suffered moral or physical damage tonight, if the princess counted a total of d dragons?", "input_spec": "Input data contains integer numbers k, l, m, n and d, each number in a separate line (1 ≤ k, l, m, n ≤ 10, 1 ≤ d ≤ 105).", "output_spec": "Output the number of damaged dragons.", "sample_inputs": ["1\n2\n3\n4\n12", "2\n3\n4\n5\n24"], "sample_outputs": ["12", "17"], "notes": "NoteIn the first case every first dragon got punched with a frying pan. Some of the dragons suffered from other reasons as well, but the pan alone would be enough.In the second case dragons 1, 7, 11, 13, 17, 19 and 23 escaped unharmed."}, "src_uid": "46bfdec9bfc1e91bd2f5022f3d3c8ce7"}
{"nl": {"description": "After winning gold and silver in IOI 2014, Akshat and Malvika want to have some fun. Now they are playing a game on a grid made of n horizontal and m vertical sticks.An intersection point is any point on the grid which is formed by the intersection of one horizontal stick and one vertical stick.In the grid shown below, n = 3 and m = 3. There are n + m = 6 sticks in total (horizontal sticks are shown in red and vertical sticks are shown in green). There are n·m = 9 intersection points, numbered from 1 to 9.  The rules of the game are very simple. The players move in turns. Akshat won gold, so he makes the first move. During his/her move, a player must choose any remaining intersection point and remove from the grid all sticks which pass through this point. A player will lose the game if he/she cannot make a move (i.e. there are no intersection points remaining on the grid at his/her move).Assume that both players play optimally. Who will win the game?", "input_spec": "The first line of input contains two space-separated integers, n and m (1 ≤ n, m ≤ 100).", "output_spec": "Print a single line containing \"Akshat\" or \"Malvika\" (without the quotes), depending on the winner of the game.", "sample_inputs": ["2 2", "2 3", "3 3"], "sample_outputs": ["Malvika", "Malvika", "Akshat"], "notes": "NoteExplanation of the first sample:The grid has four intersection points, numbered from 1 to 4.  If Akshat chooses intersection point 1, then he will remove two sticks (1 - 2 and 1 - 3). The resulting grid will look like this.  Now there is only one remaining intersection point (i.e. 4). Malvika must choose it and remove both remaining sticks. After her move the grid will be empty.In the empty grid, Akshat cannot make any move, hence he will lose.Since all 4 intersection points of the grid are equivalent, Akshat will lose no matter which one he picks."}, "src_uid": "a4b9ce9c9f170a729a97af13e81b5fe4"}
{"nl": {"description": "Berland Football Cup starts really soon! Commentators from all over the world come to the event.Organizers have already built $$$n$$$ commentary boxes. $$$m$$$ regional delegations will come to the Cup. Every delegation should get the same number of the commentary boxes. If any box is left unoccupied then the delegations will be upset. So each box should be occupied by exactly one delegation.If $$$n$$$ is not divisible by $$$m$$$, it is impossible to distribute the boxes to the delegations at the moment.Organizers can build a new commentary box paying $$$a$$$ burles and demolish a commentary box paying $$$b$$$ burles. They can both build and demolish boxes arbitrary number of times (each time paying a corresponding fee). It is allowed to demolish all the existing boxes.What is the minimal amount of burles organizers should pay to satisfy all the delegations (i.e. to make the number of the boxes be divisible by $$$m$$$)?", "input_spec": "The only line contains four integer numbers $$$n$$$, $$$m$$$, $$$a$$$ and $$$b$$$ ($$$1 \\le n, m \\le 10^{12}$$$, $$$1 \\le a, b \\le 100$$$), where $$$n$$$ is the initial number of the commentary boxes, $$$m$$$ is the number of delegations to come, $$$a$$$ is the fee to build a box and $$$b$$$ is the fee to demolish a box.", "output_spec": "Output the minimal amount of burles organizers should pay to satisfy all the delegations (i.e. to make the number of the boxes be divisible by $$$m$$$). It is allowed that the final number of the boxes is equal to $$$0$$$.", "sample_inputs": ["9 7 3 8", "2 7 3 7", "30 6 17 19"], "sample_outputs": ["15", "14", "0"], "notes": "NoteIn the first example organizers can build $$$5$$$ boxes to make the total of $$$14$$$ paying $$$3$$$ burles for the each of them.In the second example organizers can demolish $$$2$$$ boxes to make the total of $$$0$$$ paying $$$7$$$ burles for the each of them.In the third example organizers are already able to distribute all the boxes equally among the delegations, each one get $$$5$$$ boxes."}, "src_uid": "c05d753b35545176ad468b99ff13aa39"}
{"nl": {"description": "Limak is going to participate in a contest on the last day of the 2016. The contest will start at 20:00 and will last four hours, exactly until midnight. There will be n problems, sorted by difficulty, i.e. problem 1 is the easiest and problem n is the hardest. Limak knows it will take him 5·i minutes to solve the i-th problem.Limak's friends organize a New Year's Eve party and Limak wants to be there at midnight or earlier. He needs k minutes to get there from his house, where he will participate in the contest first.How many problems can Limak solve if he wants to make it to the party?", "input_spec": "The only line of the input contains two integers n and k (1 ≤ n ≤ 10, 1 ≤ k ≤ 240) — the number of the problems in the contest and the number of minutes Limak needs to get to the party from his house.", "output_spec": "Print one integer, denoting the maximum possible number of problems Limak can solve so that he could get to the party at midnight or earlier.", "sample_inputs": ["3 222", "4 190", "7 1"], "sample_outputs": ["2", "4", "7"], "notes": "NoteIn the first sample, there are 3 problems and Limak needs 222 minutes to get to the party. The three problems require 5, 10 and 15 minutes respectively. Limak can spend 5 + 10 = 15 minutes to solve first two problems. Then, at 20:15 he can leave his house to get to the party at 23:57 (after 222 minutes). In this scenario Limak would solve 2 problems. He doesn't have enough time to solve 3 problems so the answer is 2.In the second sample, Limak can solve all 4 problems in 5 + 10 + 15 + 20 = 50 minutes. At 20:50 he will leave the house and go to the party. He will get there exactly at midnight.In the third sample, Limak needs only 1 minute to get to the party. He has enough time to solve all 7 problems."}, "src_uid": "41e554bc323857be7b8483ee358a35e2"}
{"nl": {"description": "Polycarp loves lowercase letters and dislikes uppercase ones. Once he got a string s consisting only of lowercase and uppercase Latin letters.Let A be a set of positions in the string. Let's call it pretty if following conditions are met:  letters on positions from A in the string are all distinct and lowercase;  there are no uppercase letters in the string which are situated between positions from A (i.e. there is no such j that s[j] is an uppercase letter, and a1 < j < a2 for some a1 and a2 from A). Write a program that will determine the maximum number of elements in a pretty set of positions.", "input_spec": "The first line contains a single integer n (1 ≤ n ≤ 200) — length of string s. The second line contains a string s consisting of lowercase and uppercase Latin letters.", "output_spec": "Print maximum number of elements in pretty set of positions for string s.", "sample_inputs": ["11\naaaaBaabAbA", "12\nzACaAbbaazzC", "3\nABC"], "sample_outputs": ["2", "3", "0"], "notes": "NoteIn the first example the desired positions might be 6 and 8 or 7 and 8. Positions 6 and 7 contain letters 'a', position 8 contains letter 'b'. The pair of positions 1 and 8 is not suitable because there is an uppercase letter 'B' between these position.In the second example desired positions can be 7, 8 and 11. There are other ways to choose pretty set consisting of three elements.In the third example the given string s does not contain any lowercase letters, so the answer is 0."}, "src_uid": "567ce65f87d2fb922b0f7e0957fbada3"}
{"nl": {"description": "Way to go! Heidi now knows how many brains there must be for her to get one. But throwing herself in the midst of a clutch of hungry zombies is quite a risky endeavor. Hence Heidi wonders: what is the smallest number of brains that must be in the chest for her to get out at all (possibly empty-handed, but alive)?The brain dinner night will evolve just as in the previous subtask: the same crowd is present, the N - 1 zombies have the exact same mindset as before and Heidi is to make the first proposal, which must be accepted by at least half of the attendees for her to survive.", "input_spec": "The only line of input contains one integer: N, the number of attendees (1 ≤ N ≤ 109).", "output_spec": "Output one integer: the smallest number of brains in the chest which allows Heidi to merely survive.", "sample_inputs": ["1", "3", "99"], "sample_outputs": ["0", "1", "49"], "notes": null}, "src_uid": "422abdf2f705c069e540d4f5c09a4948"}
{"nl": {"description": "To celebrate the second ABBYY Cup tournament, the Smart Beaver decided to throw a party. The Beaver has a lot of acquaintances, some of them are friends with each other, and some of them dislike each other. To make party successful, the Smart Beaver wants to invite only those of his friends who are connected by friendship relations, and not to invite those who dislike each other. Both friendship and dislike are mutual feelings.More formally, for each invited person the following conditions should be fulfilled:   all his friends should also be invited to the party;  the party shouldn't have any people he dislikes;  all people who are invited to the party should be connected with him by friendship either directly or through a chain of common friends of arbitrary length. We'll say that people a1 and ap are connected through a chain of common friends if there exists a sequence of people a2, a3, ..., ap - 1 such that all pairs of people ai and ai + 1 (1 ≤ i < p) are friends. Help the Beaver find the maximum number of acquaintances he can invite.", "input_spec": "The first line of input contains an integer n — the number of the Beaver's acquaintances.  The second line contains an integer k  — the number of pairs of friends. Next k lines contain space-separated pairs of integers ui, vi  — indices of people who form the i-th pair of friends. The next line contains an integer m  — the number of pairs of people who dislike each other. Next m lines describe pairs of people who dislike each other in the same format as the pairs of friends were described. Each pair of people is mentioned in the input at most once . In particular, two persons cannot be friends and dislike each other at the same time. The input limitations for getting 30 points are:    2 ≤ n ≤ 14  The input limitations for getting 100 points are:    2 ≤ n ≤ 2000 ", "output_spec": "Output a single number — the maximum number of people that can be invited to the party. If a group of people that meets all the requirements is impossible to select, output 0.", "sample_inputs": ["9\n8\n1 2\n1 3\n2 3\n4 5\n6 7\n7 8\n8 9\n9 6\n2\n1 6\n7 9"], "sample_outputs": ["3"], "notes": "NoteLet's have a look at the example.   Two groups of people can be invited: {1, 2, 3} and {4, 5}, thus the answer will be the size of the largest of these groups. Group {6, 7, 8, 9} doesn't fit, since it includes people 7 and 9 who dislike each other. Group {1, 2, 3, 4, 5} also doesn't fit, because not all of its members are connected by a chain of common friends (for example, people 2 and 5 aren't connected)."}, "src_uid": "e1ebaf64b129edb8089f9e2f89a0e1e1"}
{"nl": {"description": "One day Greg and his friends were walking in the forest. Overall there were n people walking, including Greg. Soon he found himself in front of a river. The guys immediately decided to get across the river. Luckily, there was a boat by the river bank, just where the guys were standing. We know that the boat can hold people with the total weight of at most k kilograms.Greg immediately took a piece of paper and listed there the weights of all people in his group (including himself). It turned out that each person weights either 50 or 100 kilograms. Now Greg wants to know what minimum number of times the boat needs to cross the river to transport the whole group to the other bank. The boat needs at least one person to navigate it from one bank to the other. As the boat crosses the river, it can have any non-zero number of passengers as long as their total weight doesn't exceed k.Also Greg is wondering, how many ways there are to transport everybody to the other side in the minimum number of boat rides. Two ways are considered distinct if during some ride they have distinct sets of people on the boat.Help Greg with this problem. ", "input_spec": "The first line contains two integers n, k (1 ≤ n ≤ 50, 1 ≤ k ≤ 5000) — the number of people, including Greg, and the boat's weight limit. The next line contains n integers — the people's weights. A person's weight is either 50 kilos or 100 kilos. You can consider Greg and his friends indexed in some way.", "output_spec": "In the first line print an integer — the minimum number of rides. If transporting everyone to the other bank is impossible, print an integer -1. In the second line print the remainder after dividing the number of ways to transport the people in the minimum number of rides by number 1000000007 (109 + 7). If transporting everyone to the other bank is impossible, print integer 0.", "sample_inputs": ["1 50\n50", "3 100\n50 50 100", "2 50\n50 50"], "sample_outputs": ["1\n1", "5\n2", "-1\n0"], "notes": "NoteIn the first test Greg walks alone and consequently, he needs only one ride across the river.In the second test you should follow the plan:  transport two 50 kg. people;  transport one 50 kg. person back;  transport one 100 kg. person;  transport one 50 kg. person back;  transport two 50 kg. people. That totals to 5 rides. Depending on which person to choose at step 2, we can get two distinct ways."}, "src_uid": "ebb0323a854e19794c79ab559792a1f7"}
{"nl": {"description": "Little Sofia is in fourth grade. Today in the geometry lesson she learned about segments and squares. On the way home, she decided to draw $$$n$$$ squares in the snow with a side length of $$$1$$$. For simplicity, we assume that Sofia lives on a plane and can draw only segments of length $$$1$$$, parallel to the coordinate axes, with vertices at integer points.In order to draw a segment, Sofia proceeds as follows. If she wants to draw a vertical segment with the coordinates of the ends $$$(x, y)$$$ and $$$(x, y+1)$$$. Then Sofia looks if there is already a drawn segment with the coordinates of the ends $$$(x', y)$$$ and $$$(x', y+1)$$$ for some $$$x'$$$. If such a segment exists, then Sofia quickly draws a new segment, using the old one as a guideline. If there is no such segment, then Sofia has to take a ruler and measure a new segment for a long time. Same thing happens when Sofia wants to draw a horizontal segment, but only now she checks for the existence of a segment with the same coordinates $$$x$$$, $$$x+1$$$ and the differing coordinate $$$y$$$.For example, if Sofia needs to draw one square, she will have to draw two segments using a ruler:   After that, she can draw the remaining two segments, using the first two as a guide:   If Sofia needs to draw two squares, she will have to draw three segments using a ruler:   After that, she can draw the remaining four segments, using the first three as a guide:   Sofia is in a hurry, so she wants to minimize the number of segments that she will have to draw with a ruler without a guide. Help her find this minimum number.", "input_spec": "The only line of input contains a single integer $$$n$$$ ($$$1 \\le n \\le 10^{9}$$$), the number of squares that Sofia wants to draw.", "output_spec": "Print single integer, the minimum number of segments that Sofia will have to draw with a ruler without a guide in order to draw $$$n$$$ squares in the manner described above.", "sample_inputs": ["1", "2", "4"], "sample_outputs": ["2", "3", "4"], "notes": null}, "src_uid": "eb8212aec951f8f69b084446da73eaf7"}
{"nl": {"description": "Quite recently a creative student Lesha had a lecture on trees. After the lecture Lesha was inspired and came up with the tree of his own which he called a k-tree.A k-tree is an infinite rooted tree where:  each vertex has exactly k children;  each edge has some weight;  if we look at the edges that goes from some vertex to its children (exactly k edges), then their weights will equal 1, 2, 3, ..., k. The picture below shows a part of a 3-tree.      As soon as Dima, a good friend of Lesha, found out about the tree, he immediately wondered: \"How many paths of total weight n (the sum of all weights of the edges in the path) are there, starting from the root of a k-tree and also containing at least one edge of weight at least d?\".Help Dima find an answer to his question. As the number of ways can be rather large, print it modulo 1000000007 (109 + 7). ", "input_spec": "A single line contains three space-separated integers: n, k and d (1 ≤ n, k ≤ 100; 1 ≤ d ≤ k).", "output_spec": "Print a single integer — the answer to the problem modulo 1000000007 (109 + 7). ", "sample_inputs": ["3 3 2", "3 3 3", "4 3 2", "4 5 2"], "sample_outputs": ["3", "1", "6", "7"], "notes": null}, "src_uid": "894a58c9bba5eba11b843c5c5ca0025d"}
{"nl": {"description": "Bob and Alice are often participating in various programming competitions. Like many competitive programmers, Alice and Bob have good and bad days. They noticed, that their lucky and unlucky days are repeating with some period. For example, for Alice days $$$[l_a; r_a]$$$ are lucky, then there are some unlucky days: $$$[r_a + 1; l_a + t_a - 1]$$$, and then there are lucky days again: $$$[l_a + t_a; r_a + t_a]$$$ and so on. In other words, the day is lucky for Alice if it lies in the segment $$$[l_a + k t_a; r_a + k t_a]$$$ for some non-negative integer $$$k$$$.The Bob's lucky day have similar structure, however the parameters of his sequence are different: $$$l_b$$$, $$$r_b$$$, $$$t_b$$$. So a day is a lucky for Bob if it lies in a segment $$$[l_b + k t_b; r_b + k t_b]$$$, for some non-negative integer $$$k$$$.Alice and Bob want to participate in team competitions together and so they want to find out what is the largest possible number of consecutive days, which are lucky for both Alice and Bob.", "input_spec": "The first line contains three integers $$$l_a$$$, $$$r_a$$$, $$$t_a$$$ ($$$0 \\le l_a \\le r_a \\le t_a - 1, 2 \\le t_a \\le 10^9$$$) and describes Alice's lucky days. The second line contains three integers $$$l_b$$$, $$$r_b$$$, $$$t_b$$$ ($$$0 \\le l_b \\le r_b \\le t_b - 1, 2 \\le t_b \\le 10^9$$$) and describes Bob's lucky days. It is guaranteed that both Alice and Bob have some unlucky days.", "output_spec": "Print one integer: the maximum number of days in the row that are lucky for both Alice and Bob.", "sample_inputs": ["0 2 5\n1 3 5", "0 1 3\n2 3 6"], "sample_outputs": ["2", "1"], "notes": "NoteThe graphs below correspond to the two sample tests and show the lucky and unlucky days of Alice and Bob as well as the possible solutions for these tests."}, "src_uid": "faa75751c05c3ff919ddd148c6784910"}
{"nl": {"description": "Not so long ago the Codecraft-17 contest was held on Codeforces. The top 25 participants, and additionally random 25 participants out of those who got into top 500, will receive a Codeforces T-shirt.Unfortunately, you didn't manage to get into top 25, but you got into top 500, taking place p.Now the elimination round of 8VC Venture Cup 2017 is being held. It has been announced that the Codecraft-17 T-shirt winners will be chosen as follows. Let s be the number of points of the winner of the elimination round of 8VC Venture Cup 2017. Then the following pseudocode will be executed: i := (s div 50) mod 475repeat 25 times:    i := (i * 96 + 42) mod 475    print (26 + i)Here \"div\" is the integer division operator, \"mod\" is the modulo (the remainder of division) operator.As the result of pseudocode execution, 25 integers between 26 and 500, inclusive, will be printed. These will be the numbers of places of the participants who get the Codecraft-17 T-shirts. It is guaranteed that the 25 printed integers will be pairwise distinct for any value of s.You're in the lead of the elimination round of 8VC Venture Cup 2017, having x points. You believe that having at least y points in the current round will be enough for victory.To change your final score, you can make any number of successful and unsuccessful hacks. A successful hack brings you 100 points, an unsuccessful one takes 50 points from you. It's difficult to do successful hacks, though.You want to win the current round and, at the same time, ensure getting a Codecraft-17 T-shirt. What is the smallest number of successful hacks you have to do to achieve that?", "input_spec": "The only line contains three integers p, x and y (26 ≤ p ≤ 500; 1 ≤ y ≤ x ≤ 20000) — your place in Codecraft-17, your current score in the elimination round of 8VC Venture Cup 2017, and the smallest number of points you consider sufficient for winning the current round.", "output_spec": "Output a single integer — the smallest number of successful hacks you have to do in order to both win the elimination round of 8VC Venture Cup 2017 and ensure getting a Codecraft-17 T-shirt. It's guaranteed that your goal is achievable for any valid input data.", "sample_inputs": ["239 10880 9889", "26 7258 6123", "493 8000 8000", "101 6800 6500", "329 19913 19900"], "sample_outputs": ["0", "2", "24", "0", "8"], "notes": "NoteIn the first example, there is no need to do any hacks since 10880 points already bring the T-shirt to the 239-th place of Codecraft-17 (that is, you). In this case, according to the pseudocode, the T-shirts will be given to the participants at the following places: 475 422 84 411 453 210 157 294 146 188 420 367 29 356 398 155 102 239 91 133 365 312 449 301 343In the second example, you have to do two successful and one unsuccessful hack to make your score equal to 7408.In the third example, you need to do as many as 24 successful hacks to make your score equal to 10400.In the fourth example, it's sufficient to do 6 unsuccessful hacks (and no successful ones) to make your score equal to 6500, which is just enough for winning the current round and also getting the T-shirt."}, "src_uid": "c9c22e03c70a94a745b451fc79e112fd"}
{"nl": {"description": "Let quasi-palindromic number be such number that adding some leading zeros (possible none) to it produces a palindromic string. String t is called a palindrome, if it reads the same from left to right and from right to left.For example, numbers 131 and 2010200 are quasi-palindromic, they can be transformed to strings \"131\" and \"002010200\", respectively, which are palindromes.You are given some integer number x. Check if it's a quasi-palindromic number.", "input_spec": "The first line contains one integer number x (1 ≤ x ≤ 109). This number is given without any leading zeroes.", "output_spec": "Print \"YES\" if number x is quasi-palindromic. Otherwise, print \"NO\" (without quotes).", "sample_inputs": ["131", "320", "2010200"], "sample_outputs": ["YES", "NO", "YES"], "notes": null}, "src_uid": "d82278932881e3aa997086c909f29051"}
{"nl": {"description": "Karlsson has visited Lillebror again. They found a box of chocolates and a big whipped cream cake at Lillebror's place. Karlsson immediately suggested to divide the sweets fairly between Lillebror and himself. Specifically, to play together a game he has just invented with the chocolates. The winner will get the cake as a reward.The box of chocolates has the form of a hexagon. It contains 19 cells for the chocolates, some of which contain a chocolate. The players move in turns. During one move it is allowed to eat one or several chocolates that lay in the neighboring cells on one line, parallel to one of the box's sides. The picture below shows the examples of allowed moves and of an unacceptable one. The player who cannot make a move loses.  Karlsson makes the first move as he is Lillebror's guest and not vice versa. The players play optimally. Determine who will get the cake.", "input_spec": "The input data contains 5 lines, containing 19 words consisting of one symbol. The word \"O\" means that the cell contains a chocolate and a \".\" stands for an empty cell. It is guaranteed that the box contains at least one chocolate. See the examples for better understanding.", "output_spec": "If Karlsson gets the cake, print \"Karlsson\" (without the quotes), otherwise print \"Lillebror\" (yet again without the quotes).", "sample_inputs": [". . .\n . . O .\n. . O O .\n . . . .\n  . . .", ". . .\n . . . O\n. . . O .\n O . O .\n  . O ."], "sample_outputs": ["Lillebror", "Karlsson"], "notes": null}, "src_uid": "eaa022cc7846c983a826900dc6dd919f"}
{"nl": {"description": "The only difference between easy and hard versions is constraints.The BerTV channel every day broadcasts one episode of one of the $$$k$$$ TV shows. You know the schedule for the next $$$n$$$ days: a sequence of integers $$$a_1, a_2, \\dots, a_n$$$ ($$$1 \\le a_i \\le k$$$), where $$$a_i$$$ is the show, the episode of which will be shown in $$$i$$$-th day.The subscription to the show is bought for the entire show (i.e. for all its episodes), for each show the subscription is bought separately.How many minimum subscriptions do you need to buy in order to have the opportunity to watch episodes of purchased shows $$$d$$$ ($$$1 \\le d \\le n$$$) days in a row? In other words, you want to buy the minimum number of TV shows so that there is some segment of $$$d$$$ consecutive days in which all episodes belong to the purchased shows.", "input_spec": "The first line contains an integer $$$t$$$ ($$$1 \\le t \\le 100$$$) — the number of test cases in the input. Then $$$t$$$ test case descriptions follow. The first line of each test case contains three integers $$$n, k$$$ and $$$d$$$ ($$$1 \\le n \\le 100$$$, $$$1 \\le k \\le 100$$$, $$$1 \\le d \\le n$$$). The second line contains $$$n$$$ integers $$$a_1, a_2, \\dots, a_n$$$ ($$$1 \\le a_i \\le k$$$), where $$$a_i$$$ is the show that is broadcasted on the $$$i$$$-th day. It is guaranteed that the sum of the values ​​of $$$n$$$ for all test cases in the input does not exceed $$$100$$$.", "output_spec": "Print $$$t$$$ integers — the answers to the test cases in the input in the order they follow. The answer to a test case is the minimum number of TV shows for which you need to purchase a subscription so that you can watch episodes of the purchased TV shows on BerTV for $$$d$$$ consecutive days. Please note that it is permissible that you will be able to watch more than $$$d$$$ days in a row.", "sample_inputs": ["4\n5 2 2\n1 2 1 2 1\n9 3 3\n3 3 3 2 2 2 1 1 1\n4 10 4\n10 8 6 4\n16 9 8\n3 1 4 1 5 9 2 6 5 3 5 8 9 7 9 3"], "sample_outputs": ["2\n1\n4\n5"], "notes": "NoteIn the first test case to have an opportunity to watch shows for two consecutive days, you need to buy a subscription on show $$$1$$$ and on show $$$2$$$. So the answer is two.In the second test case, you can buy a subscription to any show because for each show you can find a segment of three consecutive days, consisting only of episodes of this show.In the third test case in the unique segment of four days, you have four different shows, so you need to buy a subscription to all these four shows.In the fourth test case, you can buy subscriptions to shows $$$3,5,7,8,9$$$, and you will be able to watch shows for the last eight days."}, "src_uid": "56da4ec7cd849c4330d188d8c9bd6094"}
{"nl": {"description": "Little Petya has recently started attending a programming club. Naturally he is facing the problem of choosing a programming language. After long considerations he realized that Java is the best choice. The main argument in favor of choosing Java was that it has a very large integer data type, called BigInteger.But having attended several classes of the club, Petya realized that not all tasks require using the BigInteger type. It turned out that in some tasks it is much easier to use small data types. That's why a question arises: \"Which integer type to use if one wants to store a positive integer n?\"Petya knows only 5 integer types:1) byte occupies 1 byte and allows you to store numbers from  - 128 to 1272) short occupies 2 bytes and allows you to store numbers from  - 32768 to 327673) int occupies 4 bytes and allows you to store numbers from  - 2147483648 to 21474836474) long occupies 8 bytes and allows you to store numbers from  - 9223372036854775808 to 92233720368547758075) BigInteger can store any integer number, but at that it is not a primitive type, and operations with it are much slower.For all the types given above the boundary values are included in the value range.From this list, Petya wants to choose the smallest type that can store a positive integer n. Since BigInteger works much slower, Peter regards it last. Help him.", "input_spec": "The first line contains a positive number n. It consists of no more than 100 digits and doesn't contain any leading zeros. The number n can't be represented as an empty string. Please, do not use %lld specificator to read or write 64-bit integers in C++. It is preffered to use cout (also you may use %I64d).", "output_spec": "Print the first type from the list \"byte, short, int, long, BigInteger\", that can store the natural number n, in accordance with the data given above.", "sample_inputs": ["127", "130", "123456789101112131415161718192021222324"], "sample_outputs": ["byte", "short", "BigInteger"], "notes": null}, "src_uid": "33041f1832fa7f641e37c4c638ab08a1"}
{"nl": {"description": "You're given a string of lower-case Latin letters. Your task is to find the length of its longest substring that can be met in the string at least twice. These occurrences can overlap (see sample test 2).", "input_spec": "The first input line contains the string. It's guaranteed, that the string is non-empty, consists of lower-case Latin letters, and its length doesn't exceed 100.", "output_spec": "Output one number — length of the longest substring that can be met in the string at least twice.", "sample_inputs": ["abcd", "ababa", "zzz"], "sample_outputs": ["0", "3", "2"], "notes": null}, "src_uid": "13b5cf94f2fabd053375a5ccf3fd44c7"}
{"nl": {"description": "The bear decided to store some raspberry for the winter. He cunningly found out the price for a barrel of honey in kilos of raspberry for each of the following n days. According to the bear's data, on the i-th (1 ≤ i ≤ n) day, the price for one barrel of honey is going to is xi kilos of raspberry.Unfortunately, the bear has neither a honey barrel, nor the raspberry. At the same time, the bear's got a friend who is ready to lend him a barrel of honey for exactly one day for c kilograms of raspberry. That's why the bear came up with a smart plan. He wants to choose some day d (1 ≤ d < n), lent a barrel of honey and immediately (on day d) sell it according to a daily exchange rate. The next day (d + 1) the bear wants to buy a new barrel of honey according to a daily exchange rate (as he's got some raspberry left from selling the previous barrel) and immediately (on day d + 1) give his friend the borrowed barrel of honey as well as c kilograms of raspberry for renting the barrel.The bear wants to execute his plan at most once and then hibernate. What maximum number of kilograms of raspberry can he earn? Note that if at some point of the plan the bear runs out of the raspberry, then he won't execute such a plan.", "input_spec": "The first line contains two space-separated integers, n and c (2 ≤ n ≤ 100, 0 ≤ c ≤ 100), — the number of days and the number of kilos of raspberry that the bear should give for borrowing the barrel. The second line contains n space-separated integers x1, x2, ..., xn (0 ≤ xi ≤ 100), the price of a honey barrel on day i.", "output_spec": "Print a single integer — the answer to the problem.", "sample_inputs": ["5 1\n5 10 7 3 20", "6 2\n100 1 10 40 10 40", "3 0\n1 2 3"], "sample_outputs": ["3", "97", "0"], "notes": "NoteIn the first sample the bear will lend a honey barrel at day 3 and then sell it for 7. Then the bear will buy a barrel for 3 and return it to the friend. So, the profit is (7 - 3 - 1) = 3.In the second sample bear will lend a honey barrel at day 1 and then sell it for 100. Then the bear buy the barrel for 1 at the day 2. So, the profit is (100 - 1 - 2) = 97."}, "src_uid": "411539a86f2e94eb6386bb65c9eb9557"}
{"nl": {"description": " The number \"zero\" is called \"love\" (or \"l'oeuf\" to be precise, literally means \"egg\" in French), for example when denoting the zero score in a game of tennis. Aki is fond of numbers, especially those with trailing zeros. For example, the number $$$9200$$$ has two trailing zeros. Aki thinks the more trailing zero digits a number has, the prettier it is.However, Aki believes, that the number of trailing zeros of a number is not static, but depends on the base (radix) it is represented in. Thus, he considers a few scenarios with some numbers and bases. And now, since the numbers he used become quite bizarre, he asks you to help him to calculate the beauty of these numbers.Given two integers $$$n$$$ and $$$b$$$ (in decimal notation), your task is to calculate the number of trailing zero digits in the $$$b$$$-ary (in the base/radix of $$$b$$$) representation of $$$n\\,!$$$ (factorial of $$$n$$$). ", "input_spec": "The only line of the input contains two integers $$$n$$$ and $$$b$$$ ($$$1 \\le n \\le 10^{18}$$$, $$$2 \\le b \\le 10^{12}$$$).", "output_spec": "Print an only integer — the number of trailing zero digits in the $$$b$$$-ary representation of $$$n!$$$", "sample_inputs": ["6 9", "38 11", "5 2", "5 10"], "sample_outputs": ["1", "3", "3", "1"], "notes": "NoteIn the first example, $$$6!_{(10)} = 720_{(10)} = 880_{(9)}$$$.In the third and fourth example, $$$5!_{(10)} = 120_{(10)} = 1111000_{(2)}$$$.The representation of the number $$$x$$$ in the $$$b$$$-ary base is $$$d_1, d_2, \\ldots, d_k$$$ if $$$x = d_1 b^{k - 1} + d_2 b^{k - 2} + \\ldots + d_k b^0$$$, where $$$d_i$$$ are integers and $$$0 \\le d_i \\le b - 1$$$. For example, the number $$$720$$$ from the first example is represented as $$$880_{(9)}$$$ since $$$720 = 8 \\cdot 9^2 + 8 \\cdot 9 + 0 \\cdot 1$$$.You can read more about bases here."}, "src_uid": "491748694c1a53771be69c212a5e0e25"}
{"nl": {"description": "After seeing the \"ALL YOUR BASE ARE BELONG TO US\" meme for the first time, numbers X and Y realised that they have different bases, which complicated their relations.You're given a number X represented in base bx and a number Y represented in base by. Compare those two numbers.", "input_spec": "The first line of the input contains two space-separated integers n and bx (1 ≤ n ≤ 10, 2 ≤ bx ≤ 40), where n is the number of digits in the bx-based representation of X.  The second line contains n space-separated integers x1, x2, ..., xn (0 ≤ xi < bx) — the digits of X. They are given in the order from the most significant digit to the least significant one. The following two lines describe Y in the same way: the third line contains two space-separated integers m and by (1 ≤ m ≤ 10, 2 ≤ by ≤ 40, bx ≠ by), where m is the number of digits in the by-based representation of Y, and the fourth line contains m space-separated integers y1, y2, ..., ym (0 ≤ yi < by) — the digits of Y. There will be no leading zeroes. Both X and Y will be positive. All digits of both numbers are given in the standard decimal numeral system.", "output_spec": "Output a single character (quotes for clarity):    '<' if X < Y  '>' if X > Y  '=' if X = Y ", "sample_inputs": ["6 2\n1 0 1 1 1 1\n2 10\n4 7", "3 3\n1 0 2\n2 5\n2 4", "7 16\n15 15 4 0 0 7 10\n7 9\n4 8 0 3 1 5 0"], "sample_outputs": ["=", "<", ">"], "notes": "NoteIn the first sample, X = 1011112 = 4710 = Y.In the second sample, X = 1023 = 215 and Y = 245 = 1123, thus X < Y.In the third sample,  and Y = 48031509. We may notice that X starts with much larger digits and bx is much larger than by, so X is clearly larger than Y."}, "src_uid": "d6ab5f75a7bee28f0af2bf168a0b2e67"}
{"nl": {"description": "Today on Informatics class Nastya learned about GCD and LCM (see links below). Nastya is very intelligent, so she solved all the tasks momentarily and now suggests you to solve one of them as well.We define a pair of integers (a, b) good, if GCD(a, b) = x and LCM(a, b) = y, where GCD(a, b) denotes the greatest common divisor of a and b, and LCM(a, b) denotes the least common multiple of a and b.You are given two integers x and y. You are to find the number of good pairs of integers (a, b) such that l ≤ a, b ≤ r. Note that pairs (a, b) and (b, a) are considered different if a ≠ b.", "input_spec": "The only line contains four integers l, r, x, y (1 ≤ l ≤ r ≤ 109, 1 ≤ x ≤ y ≤ 109).", "output_spec": "In the only line print the only integer — the answer for the problem.", "sample_inputs": ["1 2 1 2", "1 12 1 12", "50 100 3 30"], "sample_outputs": ["2", "4", "0"], "notes": "NoteIn the first example there are two suitable good pairs of integers (a, b): (1, 2) and (2, 1).In the second example there are four suitable good pairs of integers (a, b): (1, 12), (12, 1), (3, 4) and (4, 3).In the third example there are good pairs of integers, for example, (3, 30), but none of them fits the condition l ≤ a, b ≤ r."}, "src_uid": "d37dde5841116352c9b37538631d0b15"}
{"nl": {"description": "The end of the school year is near and Ms. Manana, the teacher, will soon have to say goodbye to a yet another class. She decided to prepare a goodbye present for her n students and give each of them a jigsaw puzzle (which, as wikipedia states, is a tiling puzzle that requires the assembly of numerous small, often oddly shaped, interlocking and tessellating pieces).The shop assistant told the teacher that there are m puzzles in the shop, but they might differ in difficulty and size. Specifically, the first jigsaw puzzle consists of f1 pieces, the second one consists of f2 pieces and so on.Ms. Manana doesn't want to upset the children, so she decided that the difference between the numbers of pieces in her presents must be as small as possible. Let A be the number of pieces in the largest puzzle that the teacher buys and B be the number of pieces in the smallest such puzzle. She wants to choose such n puzzles that A - B is minimum possible. Help the teacher and find the least possible value of A - B.", "input_spec": "The first line contains space-separated integers n and m (2 ≤ n ≤ m ≤ 50). The second line contains m space-separated integers f1, f2, ..., fm (4 ≤ fi ≤ 1000) — the quantities of pieces in the puzzles sold in the shop.", "output_spec": "Print a single integer — the least possible difference the teacher can obtain.", "sample_inputs": ["4 6\n10 12 10 7 5 22"], "sample_outputs": ["5"], "notes": "NoteSample 1. The class has 4 students. The shop sells 6 puzzles. If Ms. Manana buys the first four puzzles consisting of 10, 12, 10 and 7 pieces correspondingly, then the difference between the sizes of the largest and the smallest puzzle will be equal to 5. It is impossible to obtain a smaller difference. Note that the teacher can also buy puzzles 1, 3, 4 and 5 to obtain the difference 5."}, "src_uid": "7830aabb0663e645d54004063746e47f"}
{"nl": {"description": "Not long ago Billy came across such a problem, where there were given three natural numbers A, B and C from the range [1, N], and it was asked to check whether the equation AB = C is correct. Recently Billy studied the concept of a digital root of a number. We should remind you that a digital root d(x) of the number x is the sum s(x) of all the digits of this number, if s(x) ≤ 9, otherwise it is d(s(x)). For example, a digital root of the number 6543 is calculated as follows: d(6543) = d(6 + 5 + 4 + 3) = d(18) = 9. Billy has counted that the digital root of a product of numbers is equal to the digital root of the product of the factors' digital roots, i.e. d(xy) = d(d(x)d(y)). And the following solution to the problem came to his mind: to calculate the digital roots and check if this condition is met. However, Billy has doubts that this condition is sufficient. That's why he asks you to find out the amount of test examples for the given problem such that the algorithm proposed by Billy makes mistakes.", "input_spec": "The first line contains the only number N (1 ≤ N ≤ 106).", "output_spec": "Output one number — the amount of required A, B and C from the range [1, N].", "sample_inputs": ["4", "5"], "sample_outputs": ["2", "6"], "notes": "NoteFor the first sample the required triples are (3, 4, 3) and (4, 3, 3)."}, "src_uid": "fc133fe6353089a0ebee08dec919f608"}
{"nl": {"description": "What are you doing at the end of the world? Are you busy? Will you save us?Nephren is playing a game with little leprechauns.She gives them an infinite array of strings, f0... ∞.f0 is \"What are you doing at the end of the world? Are you busy? Will you save us?\".She wants to let more people know about it, so she defines fi =  \"What are you doing while sending \"fi - 1\"? Are you busy? Will you send \"fi - 1\"?\" for all i ≥ 1.For example, f1 is\"What are you doing while sending \"What are you doing at the end of the world? Are you busy? Will you save us?\"? Are you busy? Will you send \"What are you doing at the end of the world? Are you busy? Will you save us?\"?\". Note that the quotes in the very beginning and in the very end are for clarity and are not a part of f1.It can be seen that the characters in fi are letters, question marks, (possibly) quotation marks and spaces.Nephren will ask the little leprechauns q times. Each time she will let them find the k-th character of fn. The characters are indexed starting from 1. If fn consists of less than k characters, output '.' (without quotes).Can you answer her queries?", "input_spec": "The first line contains one integer q (1 ≤ q ≤ 10) — the number of Nephren's questions. Each of the next q lines describes Nephren's question and contains two integers n and k (0 ≤ n ≤ 105, 1 ≤ k ≤ 1018).", "output_spec": "One line containing q characters. The i-th character in it should be the answer for the i-th query.", "sample_inputs": ["3\n1 1\n1 2\n1 111111111111", "5\n0 69\n1 194\n1 139\n0 47\n1 66", "10\n4 1825\n3 75\n3 530\n4 1829\n4 1651\n3 187\n4 584\n4 255\n4 774\n2 474"], "sample_outputs": ["Wh.", "abdef", "Areyoubusy"], "notes": "NoteFor the first two examples, refer to f0 and f1 given in the legend."}, "src_uid": "da09a893a33f2bf8fd00e321e16ab149"}
{"nl": {"description": "Polycarp urgently needs a shovel! He comes to the shop and chooses an appropriate one. The shovel that Policarp chooses is sold for k burles. Assume that there is an unlimited number of such shovels in the shop.In his pocket Polycarp has an unlimited number of \"10-burle coins\" and exactly one coin of r burles (1 ≤ r ≤ 9).What is the minimum number of shovels Polycarp has to buy so that he can pay for the purchase without any change? It is obvious that he can pay for 10 shovels without any change (by paying the requied amount of 10-burle coins and not using the coin of r burles). But perhaps he can buy fewer shovels and pay without any change. Note that Polycarp should buy at least one shovel.", "input_spec": "The single line of input contains two integers k and r (1 ≤ k ≤ 1000, 1 ≤ r ≤ 9) — the price of one shovel and the denomination of the coin in Polycarp's pocket that is different from \"10-burle coins\".  Remember that he has an unlimited number of coins in the denomination of 10, that is, Polycarp has enough money to buy any number of shovels.", "output_spec": "Print the required minimum number of shovels Polycarp has to buy so that he can pay for them without any change. ", "sample_inputs": ["117 3", "237 7", "15 2"], "sample_outputs": ["9", "1", "2"], "notes": "NoteIn the first example Polycarp can buy 9 shovels and pay 9·117 = 1053 burles. Indeed, he can pay this sum by using 10-burle coins and one 3-burle coin. He can't buy fewer shovels without any change.In the second example it is enough for Polycarp to buy one shovel.In the third example Polycarp should buy two shovels and pay 2·15 = 30 burles. It is obvious that he can pay this sum without any change. "}, "src_uid": "18cd1cd809df4744bb7bcd7cad94e2d3"}
{"nl": {"description": "Alena has successfully passed the entrance exams to the university and is now looking forward to start studying.One two-hour lesson at the Russian university is traditionally called a pair, it lasts for two academic hours (an academic hour is equal to 45 minutes).The University works in such a way that every day it holds exactly n lessons. Depending on the schedule of a particular group of students, on a given day, some pairs may actually contain classes, but some may be empty (such pairs are called breaks).The official website of the university has already published the schedule for tomorrow for Alena's group. Thus, for each of the n pairs she knows if there will be a class at that time or not.Alena's House is far from the university, so if there are breaks, she doesn't always go home. Alena has time to go home only if the break consists of at least two free pairs in a row, otherwise she waits for the next pair at the university.Of course, Alena does not want to be sleepy during pairs, so she will sleep as long as possible, and will only come to the first pair that is presented in her schedule. Similarly, if there are no more pairs, then Alena immediately goes home.Alena appreciates the time spent at home, so she always goes home when it is possible, and returns to the university only at the beginning of the next pair. Help Alena determine for how many pairs she will stay at the university. Note that during some pairs Alena may be at the university waiting for the upcoming pair.", "input_spec": "The first line of the input contains a positive integer n (1 ≤ n ≤ 100) — the number of lessons at the university.  The second line contains n numbers ai (0 ≤ ai ≤ 1). Number ai equals 0, if Alena doesn't have the i-th pairs, otherwise it is equal to 1. Numbers a1, a2, ..., an are separated by spaces.", "output_spec": "Print a single number — the number of pairs during which Alena stays at the university.", "sample_inputs": ["5\n0 1 0 1 1", "7\n1 0 1 0 0 1 0", "1\n0"], "sample_outputs": ["4", "4", "0"], "notes": "NoteIn the first sample Alena stays at the university from the second to the fifth pair, inclusive, during the third pair she will be it the university waiting for the next pair. In the last sample Alena doesn't have a single pair, so she spends all the time at home."}, "src_uid": "2896aadda9e7a317d33315f91d1ca64d"}
{"nl": {"description": "One day Petya was solving a very interesting problem. But although he used many optimization techniques, his solution still got Time limit exceeded verdict. Petya conducted a thorough analysis of his program and found out that his function for finding maximum element in an array of n positive integers was too slow. Desperate, Petya decided to use a somewhat unexpected optimization using parameter k, so now his function contains the following code:int fast_max(int n, int a[]) {     int ans = 0;    int offset = 0;    for (int i = 0; i < n; ++i)        if (ans < a[i]) {            ans = a[i];            offset = 0;        } else {            offset = offset + 1;            if (offset == k)                return ans;        }    return ans;}That way the function iteratively checks array elements, storing the intermediate maximum, and if after k consecutive iterations that maximum has not changed, it is returned as the answer.Now Petya is interested in fault rate of his function. He asked you to find the number of permutations of integers from 1 to n such that the return value of his function on those permutations is not equal to n. Since this number could be very big, output the answer modulo 109 + 7.", "input_spec": "The only line contains two integers n and k (1 ≤ n, k ≤ 106), separated by a space — the length of the permutations and the parameter k.", "output_spec": "Output the answer to the problem modulo 109 + 7.", "sample_inputs": ["5 2", "5 3", "6 3"], "sample_outputs": ["22", "6", "84"], "notes": "NotePermutations from second example: [4, 1, 2, 3, 5], [4, 1, 3, 2, 5], [4, 2, 1, 3, 5], [4, 2, 3, 1, 5], [4, 3, 1, 2, 5], [4, 3, 2, 1, 5]."}, "src_uid": "0644605611a2cd10ab3a9f12f18d7ae4"}
{"nl": {"description": "Sometimes Mister B has free evenings when he doesn't know what to do. Fortunately, Mister B found a new game, where the player can play against aliens.All characters in this game are lowercase English letters. There are two players: Mister B and his competitor.Initially the players have a string s consisting of the first a English letters in alphabetical order (for example, if a = 5, then s equals to \"abcde\").The players take turns appending letters to string s. Mister B moves first.Mister B must append exactly b letters on each his move. He can arbitrary choose these letters. His opponent adds exactly a letters on each move.Mister B quickly understood that his opponent was just a computer that used a simple algorithm. The computer on each turn considers the suffix of string s of length a and generates a string t of length a such that all letters in the string t are distinct and don't appear in the considered suffix. From multiple variants of t lexicographically minimal is chosen (if a = 4 and the suffix is \"bfdd\", the computer chooses string t equal to \"aceg\"). After that the chosen string t is appended to the end of s.Mister B soon found the game boring and came up with the following question: what can be the minimum possible number of different letters in string s on the segment between positions l and r, inclusive. Letters of string s are numerated starting from 1.", "input_spec": "First and only line contains four space-separated integers: a, b, l and r (1 ≤ a, b ≤ 12, 1 ≤ l ≤ r ≤ 109) — the numbers of letters each player appends and the bounds of the segment.", "output_spec": "Print one integer — the minimum possible number of different letters in the segment from position l to position r, inclusive, in string s.", "sample_inputs": ["1 1 1 8", "4 2 2 6", "3 7 4 6"], "sample_outputs": ["2", "3", "1"], "notes": "NoteIn the first sample test one of optimal strategies generate string s = \"abababab...\", that's why answer is 2.In the second sample test string s = \"abcdbcaefg...\" can be obtained, chosen segment will look like \"bcdbc\", that's why answer is 3.In the third sample test string s = \"abczzzacad...\" can be obtained, chosen, segment will look like \"zzz\", that's why answer is 1."}, "src_uid": "d055b2a594ae7788ecafb3ef80f246ec"}
{"nl": {"description": "You are given a positive integer $$$n$$$, written without leading zeroes (for example, the number 04 is incorrect). In one operation you can delete any digit of the given integer so that the result remains a positive integer without leading zeros.Determine the minimum number of operations that you need to consistently apply to the given integer $$$n$$$ to make from it the square of some positive integer or report that it is impossible.An integer $$$x$$$ is the square of some positive integer if and only if $$$x=y^2$$$ for some positive integer $$$y$$$.", "input_spec": "The first line contains a single integer $$$n$$$ ($$$1 \\le n \\le 2 \\cdot 10^{9}$$$). The number is given without leading zeroes.", "output_spec": "If it is impossible to make the square of some positive integer from $$$n$$$, print -1. In the other case, print the minimal number of operations required to do it.", "sample_inputs": ["8314", "625", "333"], "sample_outputs": ["2", "0", "-1"], "notes": "NoteIn the first example we should delete from $$$8314$$$ the digits $$$3$$$ and $$$4$$$. After that $$$8314$$$ become equals to $$$81$$$, which is the square of the integer $$$9$$$.In the second example the given $$$625$$$ is the square of the integer $$$25$$$, so you should not delete anything. In the third example it is impossible to make the square from $$$333$$$, so the answer is -1."}, "src_uid": "fa4b1de79708329bb85437e1413e13df"}
{"nl": {"description": "You can find anything whatsoever in our Galaxy! A cubical planet goes round an icosahedral star. Let us introduce a system of axes so that the edges of the cubical planet are parallel to the coordinate axes and two opposite vertices lay in the points (0, 0, 0) and (1, 1, 1). Two flies live on the planet. At the moment they are sitting on two different vertices of the cubical planet. Your task is to determine whether they see each other or not. The flies see each other when the vertices they occupy lie on the same face of the cube.", "input_spec": "The first line contains three space-separated integers (0 or 1) — the coordinates of the first fly, the second line analogously contains the coordinates of the second fly.", "output_spec": "Output \"YES\" (without quotes) if the flies see each other. Otherwise, output \"NO\".", "sample_inputs": ["0 0 0\n0 1 0", "1 1 0\n0 1 0", "0 0 0\n1 1 1"], "sample_outputs": ["YES", "YES", "NO"], "notes": null}, "src_uid": "91c9dbbceb467d5fd420e92c2919ecb6"}
{"nl": {"description": "Lengths are measures in Baden in inches and feet. To a length from centimeters it is enough to know that an inch equals three centimeters in Baden and one foot contains 12 inches.You are given a length equal to n centimeters. Your task is to convert it to feet and inches so that the number of feet was maximum. The result should be an integer rounded to the closest value containing an integral number of inches.Note that when you round up, 1 cm rounds up to 0 inches and 2 cm round up to 1 inch.", "input_spec": "The only line contains an integer n (1 ≤ n ≤ 10000).", "output_spec": "Print two non-negative space-separated integers a and b, where a is the numbers of feet and b is the number of inches.", "sample_inputs": ["42", "5"], "sample_outputs": ["1 2", "0 2"], "notes": null}, "src_uid": "5d4f38ffd1849862623325fdbe06cd00"}
{"nl": {"description": "There is a beautiful garden of stones in Innopolis.Its most beautiful place is the $$$n$$$ piles with stones numbered from $$$1$$$ to $$$n$$$.EJOI participants have visited this place twice. When they first visited it, the number of stones in piles was $$$x_1, x_2, \\ldots, x_n$$$, correspondingly. One of the participants wrote down this sequence in a notebook. They visited it again the following day, and the number of stones in piles was equal to $$$y_1, y_2, \\ldots, y_n$$$. One of the participants also wrote it down in a notebook.It is well known that every member of the EJOI jury during the night either sits in the room $$$108$$$ or comes to the place with stones. Each jury member who comes there either takes one stone for himself or moves one stone from one pile to another. We can assume that there is an unlimited number of jury members. No one except the jury goes to the place with stones at night.Participants want to know whether their notes can be correct or they are sure to have made a mistake.", "input_spec": "The first line of the input file contains a single integer $$$n$$$, the number of piles with stones in the garden ($$$1 \\leq n \\leq 50$$$). The second line contains $$$n$$$ integers separated by spaces $$$x_1, x_2, \\ldots, x_n$$$, the number of stones in piles recorded in the notebook when the participants came to the place with stones for the first time ($$$0 \\leq x_i \\leq 1000$$$). The third line contains $$$n$$$ integers separated by spaces $$$y_1, y_2, \\ldots, y_n$$$, the number of stones in piles recorded in the notebook when the participants came to the place with stones for the second time ($$$0 \\leq y_i \\leq 1000$$$).", "output_spec": "If the records can be consistent output \"Yes\", otherwise output \"No\" (quotes for clarity).", "sample_inputs": ["5\n1 2 3 4 5\n2 1 4 3 5", "5\n1 1 1 1 1\n1 0 1 0 1", "3\n2 3 9\n1 7 9"], "sample_outputs": ["Yes", "Yes", "No"], "notes": "NoteIn the first example, the following could have happened during the night: one of the jury members moved one stone from the second pile to the first pile, and the other jury member moved one stone from the fourth pile to the third pile.In the second example, the jury took stones from the second and fourth piles.It can be proved that it is impossible for the jury members to move and took stones to convert the first array into the second array."}, "src_uid": "e0ddac5c6d3671070860dda10d50c28a"}
{"nl": {"description": "Luba has to do n chores today. i-th chore takes ai units of time to complete. It is guaranteed that for every  the condition ai ≥ ai - 1 is met, so the sequence is sorted.Also Luba can work really hard on some chores. She can choose not more than k any chores and do each of them in x units of time instead of ai ().Luba is very responsible, so she has to do all n chores, and now she wants to know the minimum time she needs to do everything. Luba cannot do two chores simultaneously.", "input_spec": "The first line contains three integers n, k, x (1 ≤ k ≤ n ≤ 100, 1 ≤ x ≤ 99) — the number of chores Luba has to do, the number of chores she can do in x units of time, and the number x itself. The second line contains n integer numbers ai (2 ≤ ai ≤ 100) — the time Luba has to spend to do i-th chore. It is guaranteed that , and for each  ai ≥ ai - 1.", "output_spec": "Print one number — minimum time Luba needs to do all n chores.", "sample_inputs": ["4 2 2\n3 6 7 10", "5 2 1\n100 100 100 100 100"], "sample_outputs": ["13", "302"], "notes": "NoteIn the first example the best option would be to do the third and the fourth chore, spending x = 2 time on each instead of a3 and a4, respectively. Then the answer is 3 + 6 + 2 + 2 = 13.In the second example Luba can choose any two chores to spend x time on them instead of ai. So the answer is 100·3 + 2·1 = 302."}, "src_uid": "92a233f8d9c73d9f33e4e6116b7d0a96"}
{"nl": {"description": "Little boy Valera studies an algorithm of sorting an integer array. After studying the theory, he went on to the practical tasks. As a result, he wrote a program that sorts an array of n integers a1, a2, ..., an in the non-decreasing order. The pseudocode of the program, written by Valera, is given below. The input of the program gets number n and array a.loop integer variable i from 1 to n - 1    loop integer variable j from i to n - 1        if (aj > aj + 1), then swap the values of elements aj and aj + 1But Valera could have made a mistake, because he hasn't yet fully learned the sorting algorithm. If Valera made a mistake in his program, you need to give a counter-example that makes his program work improperly (that is, the example that makes the program sort the array not in the non-decreasing order). If such example for the given value of n doesn't exist, print -1.", "input_spec": "You've got a single integer n (1 ≤ n ≤ 50) — the size of the sorted array.", "output_spec": "Print n space-separated integers a1, a2, ..., an (1 ≤ ai ≤ 100) — the counter-example, for which Valera's algorithm won't work correctly. If the counter-example that meets the described conditions is impossible to give, print -1. If there are several counter-examples, consisting of n numbers, you are allowed to print any of them.", "sample_inputs": ["1"], "sample_outputs": ["-1"], "notes": null}, "src_uid": "fe8a0332119bd182a0a5b7758716317e"}
{"nl": {"description": "Ivan likes to learn different things about numbers, but he is especially interested in really big numbers. Ivan thinks that a positive integer number x is really big if the difference between x and the sum of its digits (in decimal representation) is not less than s. To prove that these numbers may have different special properties, he wants to know how rare (or not rare) they are — in fact, he needs to calculate the quantity of really big numbers that are not greater than n.Ivan tried to do the calculations himself, but soon realized that it's too difficult for him. So he asked you to help him in calculations.", "input_spec": "The first (and the only) line contains two integers n and s (1 ≤ n, s ≤ 1018).", "output_spec": "Print one integer — the quantity of really big numbers that are not greater than n.", "sample_inputs": ["12 1", "25 20", "10 9"], "sample_outputs": ["3", "0", "1"], "notes": "NoteIn the first example numbers 10, 11 and 12 are really big.In the second example there are no really big numbers that are not greater than 25 (in fact, the first really big number is 30: 30 - 3 ≥ 20).In the third example 10 is the only really big number (10 - 1 ≥ 9)."}, "src_uid": "9704e2ac6a158d5ced8fd1dc1edb356b"}
{"nl": {"description": "Manao works on a sports TV. He's spent much time watching the football games of some country. After a while he began to notice different patterns. For example, each team has two sets of uniforms: home uniform and guest uniform. When a team plays a game at home, the players put on the home uniform. When a team plays as a guest on somebody else's stadium, the players put on the guest uniform. The only exception to that rule is: when the home uniform color of the host team matches the guests' uniform, the host team puts on its guest uniform as well. For each team the color of the home and guest uniform is different.There are n teams taking part in the national championship. The championship consists of n·(n - 1) games: each team invites each other team to its stadium. At this point Manao wondered: how many times during the championship is a host team going to put on the guest uniform? Note that the order of the games does not affect this number.You know the colors of the home and guest uniform for each team. For simplicity, the colors are numbered by integers in such a way that no two distinct colors have the same number. Help Manao find the answer to his question.", "input_spec": "The first line contains an integer n (2 ≤ n ≤ 30). Each of the following n lines contains a pair of distinct space-separated integers hi, ai (1 ≤ hi, ai ≤ 100) — the colors of the i-th team's home and guest uniforms, respectively.", "output_spec": "In a single line print the number of games where the host team is going to play in the guest uniform.", "sample_inputs": ["3\n1 2\n2 4\n3 4", "4\n100 42\n42 100\n5 42\n100 5", "2\n1 2\n1 2"], "sample_outputs": ["1", "5", "0"], "notes": "NoteIn the first test case the championship consists of 6 games. The only game with the event in question is the game between teams 2 and 1 on the stadium of team 2.In the second test sample the host team will have to wear guest uniform in the games between teams: 1 and 2, 2 and 1, 2 and 3, 3 and 4, 4 and 2 (the host team is written first)."}, "src_uid": "745f81dcb4f23254bf6602f9f389771b"}
{"nl": {"description": "One hot summer day Pete and his friend Billy decided to buy a watermelon. They chose the biggest and the ripest one, in their opinion. After that the watermelon was weighed, and the scales showed w kilos. They rushed home, dying of thirst, and decided to divide the berry, however they faced a hard problem.Pete and Billy are great fans of even numbers, that's why they want to divide the watermelon in such a way that each of the two parts weighs even number of kilos, at the same time it is not obligatory that the parts are equal. The boys are extremely tired and want to start their meal as soon as possible, that's why you should help them and find out, if they can divide the watermelon in the way they want. For sure, each of them should get a part of positive weight.", "input_spec": "The first (and the only) input line contains integer number w (1 ≤ w ≤ 100) — the weight of the watermelon bought by the boys.", "output_spec": "Print YES, if the boys can divide the watermelon into two parts, each of them weighing even number of kilos; and NO in the opposite case.", "sample_inputs": ["8"], "sample_outputs": ["YES"], "notes": "NoteFor example, the boys can divide the watermelon into two parts of 2 and 6 kilos respectively (another variant — two parts of 4 and 4 kilos)."}, "src_uid": "230a3c4d7090401e5fa3c6b9d994cdf2"}
{"nl": {"description": "As you may know, MemSQL has American offices in both San Francisco and Seattle. Being a manager in the company, you travel a lot between the two cities, always by plane.You prefer flying from Seattle to San Francisco than in the other direction, because it's warmer in San Francisco. You are so busy that you don't remember the number of flights you have made in either direction. However, for each of the last n days you know whether you were in San Francisco office or in Seattle office. You always fly at nights, so you never were at both offices on the same day. Given this information, determine if you flew more times from Seattle to San Francisco during the last n days, or not.", "input_spec": "The first line of input contains single integer n (2 ≤ n ≤ 100) — the number of days. The second line contains a string of length n consisting of only capital 'S' and 'F' letters. If the i-th letter is 'S', then you were in Seattle office on that day. Otherwise you were in San Francisco. The days are given in chronological order, i.e. today is the last day in this sequence.", "output_spec": "Print \"YES\" if you flew more times from Seattle to San Francisco, and \"NO\" otherwise. You can print each letter in any case (upper or lower).", "sample_inputs": ["4\nFSSF", "2\nSF", "10\nFFFFFFFFFF", "10\nSSFFSFFSFF"], "sample_outputs": ["NO", "YES", "NO", "YES"], "notes": "NoteIn the first example you were initially at San Francisco, then flew to Seattle, were there for two days and returned to San Francisco. You made one flight in each direction, so the answer is \"NO\".In the second example you just flew from Seattle to San Francisco, so the answer is \"YES\".In the third example you stayed the whole period in San Francisco, so the answer is \"NO\".In the fourth example if you replace 'S' with ones, and 'F' with zeros, you'll get the first few digits of π in binary representation. Not very useful information though."}, "src_uid": "ab8a2070ea758d118b3c09ee165d9517"}
{"nl": {"description": "Dima and his friends have been playing hide and seek at Dima's place all night. As a result, Dima's place got messy. In the morning they decided that they need to clean the place.To decide who exactly would clean the apartment, the friends want to play a counting-out game. First, all the guys stand in a circle, and then each of them shows some number of fingers on one hand (one to five), and then the boys count in a circle, starting from Dima, the number of people, respective to the total number of fingers shown. The person on who the countdown stops will clean the apartment.For example, if Dima and one of his friends played hide and seek, and 7 fingers were shown during the counting-out, then Dima would clean the place. If there were 2 or say, 8 fingers shown, then his friend would clean the place.Dima knows how many fingers each of his friends will show during the counting-out. Now he is interested in the number of ways to show some number of fingers on one hand (one to five), so that he did not have to clean the place. Help Dima.", "input_spec": "The first line contains integer n (1 ≤ n ≤ 100) — the number of Dima's friends. Dima himself isn't considered to be his own friend. The second line contains n positive integers, not exceeding 5, representing, how many fingers the Dima's friends will show.  The numbers in the lines are separated by a single space.", "output_spec": "In a single line print the answer to the problem.", "sample_inputs": ["1\n1", "1\n2", "2\n3 5"], "sample_outputs": ["3", "2", "3"], "notes": "NoteIn the first sample Dima can show 1, 3 or 5 fingers. If Dima shows 3 fingers, then the counting-out will go like that: Dima, his friend, Dima, his friend.In the second sample Dima can show 2 or 4 fingers."}, "src_uid": "ff6b3fd358c758324c19a26283ab96a4"}
{"nl": {"description": "Tokitsukaze is playing a game derivated from Japanese mahjong. In this game, she has three tiles in her hand. Each tile she owns is a suited tile, which means it has a suit (manzu, pinzu or souzu) and a number (a digit ranged from $$$1$$$ to $$$9$$$). In this problem, we use one digit and one lowercase letter, which is the first character of the suit, to represent a suited tile. All possible suited tiles are represented as 1m, 2m, $$$\\ldots$$$, 9m, 1p, 2p, $$$\\ldots$$$, 9p, 1s, 2s, $$$\\ldots$$$, 9s.In order to win the game, she must have at least one mentsu (described below) in her hand, so sometimes she should draw extra suited tiles. After drawing a tile, the number of her tiles increases by one. She can draw any tiles she wants, including those already in her hand.Do you know the minimum number of extra suited tiles she needs to draw so that she can win?Here are some useful definitions in this game:  A mentsu, also known as meld, is formed by a koutsu or a shuntsu;  A koutsu, also known as triplet, is made of three identical tiles, such as [1m, 1m, 1m], however, [1m, 1p, 1s] or [1m, 4m, 7m] is NOT a koutsu;  A shuntsu, also known as sequence, is made of three sequential numbered tiles in the same suit, such as [1m, 2m, 3m] and [5s, 7s, 6s], however, [9m, 1m, 2m] or [1m, 2p, 3s] is NOT a shuntsu. Some examples:   [2m, 3p, 2s, 4m, 1s, 2s, 4s] — it contains no koutsu or shuntsu, so it includes no mentsu;  [4s, 3m, 3p, 4s, 5p, 4s, 5p] — it contains a koutsu, [4s, 4s, 4s], but no shuntsu, so it includes a mentsu;  [5p, 5s, 9m, 4p, 1s, 7p, 7m, 6p] — it contains no koutsu but a shuntsu, [5p, 4p, 6p] or [5p, 7p, 6p], so it includes a mentsu. Note that the order of tiles is unnecessary and you can assume the number of each type of suited tiles she can draw is infinite.", "input_spec": "The only line contains three strings — the tiles in Tokitsukaze's hand. For each string, the first character is a digit ranged from $$$1$$$ to $$$9$$$ and the second character is m, p or s.", "output_spec": "Print a single integer — the minimum number of extra suited tiles she needs to draw.", "sample_inputs": ["1s 2s 3s", "9m 9m 9m", "3p 9m 2p"], "sample_outputs": ["0", "0", "1"], "notes": "NoteIn the first example, Tokitsukaze already has a shuntsu.In the second example, Tokitsukaze already has a koutsu.In the third example, Tokitsukaze can get a shuntsu by drawing one suited tile — 1p or 4p. The resulting tiles will be [3p, 9m, 2p, 1p] or [3p, 9m, 2p, 4p]."}, "src_uid": "7e42cebc670e76ace967e01021f752d3"}
{"nl": {"description": "You are given three integers $$$a$$$, $$$b$$$ and $$$x$$$. Your task is to construct a binary string $$$s$$$ of length $$$n = a + b$$$ such that there are exactly $$$a$$$ zeroes, exactly $$$b$$$ ones and exactly $$$x$$$ indices $$$i$$$ (where $$$1 \\le i < n$$$) such that $$$s_i \\ne s_{i + 1}$$$. It is guaranteed that the answer always exists.For example, for the string \"01010\" there are four indices $$$i$$$ such that $$$1 \\le i < n$$$ and $$$s_i \\ne s_{i + 1}$$$ ($$$i = 1, 2, 3, 4$$$). For the string \"111001\" there are two such indices $$$i$$$ ($$$i = 3, 5$$$).Recall that binary string is a non-empty sequence of characters where each character is either 0 or 1.", "input_spec": "The first line of the input contains three integers $$$a$$$, $$$b$$$ and $$$x$$$ ($$$1 \\le a, b \\le 100, 1 \\le x < a + b)$$$.", "output_spec": "Print only one string $$$s$$$, where $$$s$$$ is any binary string satisfying conditions described above. It is guaranteed that the answer always exists.", "sample_inputs": ["2 2 1", "3 3 3", "5 3 6"], "sample_outputs": ["1100", "101100", "01010100"], "notes": "NoteAll possible answers for the first example:   1100;  0011. All possible answers for the second example:   110100;  101100;  110010;  100110;  011001;  001101;  010011;  001011. "}, "src_uid": "ef4123b8f3f3b511fde8b79ea9a6b20c"}
{"nl": {"description": "Your friend has n cards.You know that each card has a lowercase English letter on one side and a digit on the other.Currently, your friend has laid out the cards on a table so only one side of each card is visible.You would like to know if the following statement is true for cards that your friend owns: \"If a card has a vowel on one side, then it has an even digit on the other side.\" More specifically, a vowel is one of 'a', 'e', 'i', 'o' or 'u', and even digit is one of '0', '2', '4', '6' or '8'.For example, if a card has 'a' on one side, and '6' on the other side, then this statement is true for it. Also, the statement is true, for example, for a card with 'b' and '4', and for a card with 'b' and '3' (since the letter is not a vowel). The statement is false, for example, for card with 'e' and '5'. You are interested if the statement is true for all cards. In particular, if no card has a vowel, the statement is true.To determine this, you can flip over some cards to reveal the other side. You would like to know what is the minimum number of cards you need to flip in the worst case in order to verify that the statement is true.", "input_spec": "The first and only line of input will contain a string s (1 ≤ |s| ≤ 50), denoting the sides of the cards that you can see on the table currently. Each character of s is either a lowercase English letter or a digit.", "output_spec": "Print a single integer, the minimum number of cards you must turn over to verify your claim.", "sample_inputs": ["ee", "z", "0ay1"], "sample_outputs": ["2", "0", "2"], "notes": "NoteIn the first sample, we must turn over both cards. Note that even though both cards have the same letter, they could possibly have different numbers on the other side.In the second sample, we don't need to turn over any cards. The statement is vacuously true, since you know your friend has no cards with a vowel on them.In the third sample, we need to flip the second and fourth cards."}, "src_uid": "b4af2b8a7e9844bf58ad3410c2cb5223"}
{"nl": {"description": "It's one more school day now. Sasha doesn't like classes and is always bored at them. So, each day he invents some game and plays in it alone or with friends.Today he invented one simple game to play with Lena, with whom he shares a desk. The rules are simple. Sasha draws n sticks in a row. After that the players take turns crossing out exactly k sticks from left or right in each turn. Sasha moves first, because he is the inventor of the game. If there are less than k sticks on the paper before some turn, the game ends. Sasha wins if he makes strictly more moves than Lena. Sasha wants to know the result of the game before playing, you are to help him.", "input_spec": "The first line contains two integers n and k (1 ≤ n, k ≤ 1018, k ≤ n) — the number of sticks drawn by Sasha and the number k — the number of sticks to be crossed out on each turn.", "output_spec": "If Sasha wins, print \"YES\" (without quotes), otherwise print \"NO\" (without quotes). You can print each letter in arbitrary case (upper of lower).", "sample_inputs": ["1 1", "10 4"], "sample_outputs": ["YES", "NO"], "notes": "NoteIn the first example Sasha crosses out 1 stick, and then there are no sticks. So Lena can't make a move, and Sasha wins.In the second example Sasha crosses out 4 sticks, then Lena crosses out 4 sticks, and after that there are only 2 sticks left. Sasha can't make a move. The players make equal number of moves, so Sasha doesn't win."}, "src_uid": "05fd61dd0b1f50f154eec85d8cfaad50"}
{"nl": {"description": "Well, the series which Stepan watched for a very long time, ended. In total, the series had n episodes. For each of them, Stepan remembers either that he definitely has watched it, or that he definitely hasn't watched it, or he is unsure, has he watched this episode or not. Stepan's dissatisfaction is the maximum number of consecutive series that Stepan did not watch.Your task is to determine according to Stepan's memories if his dissatisfaction could be exactly equal to k.", "input_spec": "The first line contains two integers n and k (1 ≤ n ≤ 100, 0 ≤ k ≤ n) — the number of episodes in the series and the dissatisfaction which should be checked.  The second line contains the sequence which consists of n symbols \"Y\", \"N\" and \"?\". If the i-th symbol equals \"Y\", Stepan remembers that he has watched the episode number i. If the i-th symbol equals \"N\", Stepan remembers that he hasn't watched the epizode number i. If the i-th symbol equals \"?\", Stepan doesn't exactly remember if he has watched the episode number i or not.", "output_spec": "If Stepan's dissatisfaction can be exactly equal to k, then print \"YES\" (without qoutes). Otherwise print \"NO\" (without qoutes).", "sample_inputs": ["5 2\nNYNNY", "6 1\n????NN"], "sample_outputs": ["YES", "NO"], "notes": "NoteIn the first test Stepan remembers about all the episodes whether he has watched them or not. His dissatisfaction is 2, because he hasn't watch two episodes in a row — the episode number 3 and the episode number 4. The answer is \"YES\", because k = 2.In the second test k = 1, Stepan's dissatisfaction is greater than or equal to 2 (because he remembers that he hasn't watch at least two episodes in a row — number 5 and number 6), even if he has watched the episodes from the first to the fourth, inclusive."}, "src_uid": "5bd578d3da5837c259b222336a194d12"}
{"nl": {"description": "During the breaks between competitions, top-model Izabella tries to develop herself and not to be bored. For example, now she tries to solve Rubik's cube 2x2x2.It's too hard to learn to solve Rubik's cube instantly, so she learns to understand if it's possible to solve the cube in some state using 90-degrees rotation of one face of the cube in any direction.To check her answers she wants to use a program which will for some state of cube tell if it's possible to solve it using one rotation, described above.Cube is called solved if for each face of cube all squares on it has the same color.https://en.wikipedia.org/wiki/Rubik's_Cube", "input_spec": "In first line given a sequence of 24 integers ai (1 ≤ ai ≤ 6), where ai denotes color of i-th square. There are exactly 4 occurrences of all colors in this sequence.", "output_spec": "Print «YES» (without quotes) if it's possible to solve cube using one rotation and «NO» (without quotes) otherwise.", "sample_inputs": ["2 5 4 6 1 3 6 2 5 5 1 2 3 5 3 1 1 2 4 6 6 4 3 4", "5 3 5 3 2 5 2 5 6 2 6 2 4 4 4 4 1 1 1 1 6 3 6 3"], "sample_outputs": ["NO", "YES"], "notes": "NoteIn first test case cube looks like this:  In second test case cube looks like this:   It's possible to solve cube by rotating face with squares with numbers 13, 14, 15, 16."}, "src_uid": "881a820aa8184d9553278a0002a3b7c4"}
{"nl": {"description": "There are n cities in Bearland, numbered 1 through n. Cities are arranged in one long row. The distance between cities i and j is equal to |i - j|.Limak is a police officer. He lives in a city a. His job is to catch criminals. It's hard because he doesn't know in which cities criminals are. Though, he knows that there is at most one criminal in each city.Limak is going to use a BCD (Bear Criminal Detector). The BCD will tell Limak how many criminals there are for every distance from a city a. After that, Limak can catch a criminal in each city for which he is sure that there must be a criminal.You know in which cities criminals are. Count the number of criminals Limak will catch, after he uses the BCD.", "input_spec": "The first line of the input contains two integers n and a (1 ≤ a ≤ n ≤ 100) — the number of cities and the index of city where Limak lives. The second line contains n integers t1, t2, ..., tn (0 ≤ ti ≤ 1). There are ti criminals in the i-th city.", "output_spec": "Print the number of criminals Limak will catch.", "sample_inputs": ["6 3\n1 1 1 0 1 0", "5 2\n0 0 0 1 0"], "sample_outputs": ["3", "1"], "notes": "NoteIn the first sample, there are six cities and Limak lives in the third one (blue arrow below). Criminals are in cities marked red.  Using the BCD gives Limak the following information:  There is one criminal at distance 0 from the third city — Limak is sure that this criminal is exactly in the third city.  There is one criminal at distance 1 from the third city — Limak doesn't know if a criminal is in the second or fourth city.  There are two criminals at distance 2 from the third city — Limak is sure that there is one criminal in the first city and one in the fifth city.  There are zero criminals for every greater distance. So, Limak will catch criminals in cities 1, 3 and 5, that is 3 criminals in total.In the second sample (drawing below), the BCD gives Limak the information that there is one criminal at distance 2 from Limak's city. There is only one city at distance 2 so Limak is sure where a criminal is.  "}, "src_uid": "4840d571d4ce6e1096bb678b6c100ae5"}
{"nl": {"description": "Ralph has a magic field which is divided into n × m blocks. That is to say, there are n rows and m columns on the field. Ralph can put an integer in each block. However, the magic field doesn't always work properly. It works only if the product of integers in each row and each column equals to k, where k is either 1 or -1.Now Ralph wants you to figure out the number of ways to put numbers in each block in such a way that the magic field works properly. Two ways are considered different if and only if there exists at least one block where the numbers in the first way and in the second way are different. You are asked to output the answer modulo 1000000007 = 109 + 7.Note that there is no range of the numbers to put in the blocks, but we can prove that the answer is not infinity.", "input_spec": "The only line contains three integers n, m and k (1 ≤ n, m ≤ 1018, k is either 1 or -1).", "output_spec": "Print a single number denoting the answer modulo 1000000007.", "sample_inputs": ["1 1 -1", "1 3 1", "3 3 -1"], "sample_outputs": ["1", "1", "16"], "notes": "NoteIn the first example the only way is to put -1 into the only block.In the second example the only way is to put 1 into every block."}, "src_uid": "6b9eff690fae14725885cbc891ff7243"}
{"nl": {"description": "Polycarp is preparing the first programming contest for robots. There are $$$n$$$ problems in it, and a lot of robots are going to participate in it. Each robot solving the problem $$$i$$$ gets $$$p_i$$$ points, and the score of each robot in the competition is calculated as the sum of $$$p_i$$$ over all problems $$$i$$$ solved by it. For each problem, $$$p_i$$$ is an integer not less than $$$1$$$.Two corporations specializing in problem-solving robot manufacturing, \"Robo-Coder Inc.\" and \"BionicSolver Industries\", are going to register two robots (one for each corporation) for participation as well. Polycarp knows the advantages and flaws of robots produced by these companies, so, for each problem, he knows precisely whether each robot will solve it during the competition. Knowing this, he can try predicting the results — or manipulating them. For some reason (which absolutely cannot involve bribing), Polycarp wants the \"Robo-Coder Inc.\" robot to outperform the \"BionicSolver Industries\" robot in the competition. Polycarp wants to set the values of $$$p_i$$$ in such a way that the \"Robo-Coder Inc.\" robot gets strictly more points than the \"BionicSolver Industries\" robot. However, if the values of $$$p_i$$$ will be large, it may look very suspicious — so Polycarp wants to minimize the maximum value of $$$p_i$$$ over all problems. Can you help Polycarp to determine the minimum possible upper bound on the number of points given for solving the problems?", "input_spec": "The first line contains one integer $$$n$$$ ($$$1 \\le n \\le 100$$$) — the number of problems. The second line contains $$$n$$$ integers $$$r_1$$$, $$$r_2$$$, ..., $$$r_n$$$ ($$$0 \\le r_i \\le 1$$$). $$$r_i = 1$$$ means that the \"Robo-Coder Inc.\" robot will solve the $$$i$$$-th problem, $$$r_i = 0$$$ means that it won't solve the $$$i$$$-th problem. The third line contains $$$n$$$ integers $$$b_1$$$, $$$b_2$$$, ..., $$$b_n$$$ ($$$0 \\le b_i \\le 1$$$). $$$b_i = 1$$$ means that the \"BionicSolver Industries\" robot will solve the $$$i$$$-th problem, $$$b_i = 0$$$ means that it won't solve the $$$i$$$-th problem.", "output_spec": "If \"Robo-Coder Inc.\" robot cannot outperform the \"BionicSolver Industries\" robot by any means, print one integer $$$-1$$$. Otherwise, print the minimum possible value of $$$\\max \\limits_{i = 1}^{n} p_i$$$, if all values of $$$p_i$$$ are set in such a way that the \"Robo-Coder Inc.\" robot gets strictly more points than the \"BionicSolver Industries\" robot.", "sample_inputs": ["5\n1 1 1 0 0\n0 1 1 1 1", "3\n0 0 0\n0 0 0", "4\n1 1 1 1\n1 1 1 1", "8\n1 0 0 0 0 0 0 0\n0 1 1 0 1 1 1 1"], "sample_outputs": ["3", "-1", "-1", "7"], "notes": "NoteIn the first example, one of the valid score assignments is $$$p = [3, 1, 3, 1, 1]$$$. Then the \"Robo-Coder\" gets $$$7$$$ points, the \"BionicSolver\" — $$$6$$$ points.In the second example, both robots get $$$0$$$ points, and the score distribution does not matter.In the third example, both robots solve all problems, so their points are equal."}, "src_uid": "b62338bff0cbb4df4e5e27e1a3ffaa07"}
{"nl": {"description": "You are given an array of positive integers a1, a2, ..., an × T of length n × T. We know that for any i > n it is true that ai = ai - n. Find the length of the longest non-decreasing sequence of the given array.", "input_spec": "The first line contains two space-separated integers: n, T (1 ≤ n ≤ 100, 1 ≤ T ≤ 107). The second line contains n space-separated integers a1, a2, ..., an (1 ≤ ai ≤ 300).", "output_spec": "Print a single number — the length of a sought sequence.", "sample_inputs": ["4 3\n3 1 4 2"], "sample_outputs": ["5"], "notes": "NoteThe array given in the sample looks like that: 3, 1, 4, 2, 3, 1, 4, 2, 3, 1, 4, 2. The elements in bold form the largest non-decreasing subsequence. "}, "src_uid": "26cf484fa4cb3dc2ab09adce7a3fc9b2"}
{"nl": {"description": "Find the minimum number with the given sum of digits $$$s$$$ such that all digits in it are distinct (i.e. all digits are unique).For example, if $$$s=20$$$, then the answer is $$$389$$$. This is the minimum number in which all digits are different and the sum of the digits is $$$20$$$ ($$$3+8+9=20$$$).For the given $$$s$$$ print the required number.", "input_spec": "The first line contains an integer $$$t$$$ ($$$1 \\le t \\le 45$$$) — the number of test cases. Each test case is specified by a line that contains the only integer $$$s$$$ ($$$1 \\le s \\le 45$$$).", "output_spec": "Print $$$t$$$ integers — the answers to the given test cases.", "sample_inputs": ["4\n\n20\n\n8\n\n45\n\n10"], "sample_outputs": ["389\n8\n123456789\n19"], "notes": null}, "src_uid": "fe126aaa93acaca8c8559bc9e7e27b9f"}
{"nl": {"description": "Let's introduce the designation , where x is a string, n is a positive integer and operation \" + \" is the string concatenation operation. For example, [abc, 2] = abcabc.We'll say that string s can be obtained from string t, if we can remove some characters from string t and obtain string s. For example, strings ab and aсba can be obtained from string xacbac, and strings bx and aaa cannot be obtained from it.Sereja has two strings, w = [a, b] and q = [c, d]. He wants to find such maximum integer p (p > 0), that [q, p] can be obtained from string w.", "input_spec": "The first line contains two integers b, d (1 ≤ b, d ≤ 107). The second line contains string a. The third line contains string c. The given strings are not empty and consist of lowercase English letters. Their lengths do not exceed 100.", "output_spec": "In a single line print an integer — the largest number p. If the required value of p doesn't exist, print 0.", "sample_inputs": ["10 3\nabab\nbab"], "sample_outputs": ["3"], "notes": null}, "src_uid": "5ea0351ac9f949dedae1928bfb7ebffa"}
{"nl": {"description": "Sasha is a very happy guy, that's why he is always on the move. There are $$$n$$$ cities in the country where Sasha lives. They are all located on one straight line, and for convenience, they are numbered from $$$1$$$ to $$$n$$$ in increasing order. The distance between any two adjacent cities is equal to $$$1$$$ kilometer. Since all roads in the country are directed, it's possible to reach the city $$$y$$$ from the city $$$x$$$ only if $$$x < y$$$. Once Sasha decided to go on a trip around the country and to visit all $$$n$$$ cities. He will move with the help of his car, Cheetah-2677. The tank capacity of this model is $$$v$$$ liters, and it spends exactly $$$1$$$ liter of fuel for $$$1$$$ kilometer of the way. At the beginning of the journey, the tank is empty. Sasha is located in the city with the number $$$1$$$ and wants to get to the city with the number $$$n$$$. There is a gas station in each city. In the $$$i$$$-th city, the price of $$$1$$$ liter of fuel is $$$i$$$ dollars. It is obvious that at any moment of time, the tank can contain at most $$$v$$$ liters of fuel.Sasha doesn't like to waste money, that's why he wants to know what is the minimum amount of money is needed to finish the trip if he can buy fuel in any city he wants. Help him to figure it out!", "input_spec": "The first line contains two integers $$$n$$$ and $$$v$$$ ($$$2 \\le n \\le 100$$$, $$$1 \\le v \\le 100$$$)  — the number of cities in the country and the capacity of the tank.", "output_spec": "Print one integer — the minimum amount of money that is needed to finish the trip.", "sample_inputs": ["4 2", "7 6"], "sample_outputs": ["4", "6"], "notes": "NoteIn the first example, Sasha can buy $$$2$$$ liters for $$$2$$$ dollars ($$$1$$$ dollar per liter) in the first city, drive to the second city, spend $$$1$$$ liter of fuel on it, then buy $$$1$$$ liter for $$$2$$$ dollars in the second city and then drive to the $$$4$$$-th city. Therefore, the answer is $$$1+1+2=4$$$.In the second example, the capacity of the tank allows to fill the tank completely in the first city, and drive to the last city without stops in other cities."}, "src_uid": "f8eb96deeb82d9f011f13d7dac1e1ab7"}
{"nl": {"description": "This task will exclusively concentrate only on the arrays where all elements equal 1 and/or 2.Array a is k-period if its length is divisible by k and there is such array b of length k, that a is represented by array b written exactly  times consecutively. In other words, array a is k-periodic, if it has period of length k.For example, any array is n-periodic, where n is the array length. Array [2, 1, 2, 1, 2, 1] is at the same time 2-periodic and 6-periodic and array [1, 2, 1, 1, 2, 1, 1, 2, 1] is at the same time 3-periodic and 9-periodic.For the given array a, consisting only of numbers one and two, find the minimum number of elements to change to make the array k-periodic. If the array already is k-periodic, then the required value equals 0.", "input_spec": "The first line of the input contains a pair of integers n, k (1 ≤ k ≤ n ≤ 100), where n is the length of the array and the value n is divisible by k. The second line contains the sequence of elements of the given array a1, a2, ..., an (1 ≤ ai ≤ 2), ai is the i-th element of the array.", "output_spec": "Print the minimum number of array elements we need to change to make the array k-periodic. If the array already is k-periodic, then print 0.", "sample_inputs": ["6 2\n2 1 2 2 2 1", "8 4\n1 1 2 1 1 1 2 1", "9 3\n2 1 1 1 2 1 1 1 2"], "sample_outputs": ["1", "0", "3"], "notes": "NoteIn the first sample it is enough to change the fourth element from 2 to 1, then the array changes to [2, 1, 2, 1, 2, 1].In the second sample, the given array already is 4-periodic.In the third sample it is enough to replace each occurrence of number two by number one. In this case the array will look as [1, 1, 1, 1, 1, 1, 1, 1, 1] — this array is simultaneously 1-, 3- and 9-periodic."}, "src_uid": "5f94c2ecf1cf8fdbb6117cab801ed281"}
{"nl": {"description": "Today an outstanding event is going to happen in the forest — hedgehog Filya will come to his old fried Sonya!Sonya is an owl and she sleeps during the day and stay awake from minute l1 to minute r1 inclusive. Also, during the minute k she prinks and is unavailable for Filya.Filya works a lot and he plans to visit Sonya from minute l2 to minute r2 inclusive.Calculate the number of minutes they will be able to spend together.", "input_spec": "The only line of the input contains integers l1, r1, l2, r2 and k (1 ≤ l1, r1, l2, r2, k ≤ 1018, l1 ≤ r1, l2 ≤ r2), providing the segments of time for Sonya and Filya and the moment of time when Sonya prinks.", "output_spec": "Print one integer — the number of minutes Sonya and Filya will be able to spend together.", "sample_inputs": ["1 10 9 20 1", "1 100 50 200 75"], "sample_outputs": ["2", "50"], "notes": "NoteIn the first sample, they will be together during minutes 9 and 10.In the second sample, they will be together from minute 50 to minute 74 and from minute 76 to minute 100."}, "src_uid": "9a74b3b0e9f3a351f2136842e9565a82"}
{"nl": {"description": "Furik loves math lessons very much, so he doesn't attend them, unlike Rubik. But now Furik wants to get a good mark for math. For that Ms. Ivanova, his math teacher, gave him a new task. Furik solved the task immediately. Can you?You are given a system of equations:   You should count, how many there are pairs of integers (a, b) (0 ≤ a, b) which satisfy the system.", "input_spec": "A single line contains two integers n, m (1 ≤ n, m ≤ 1000) — the parameters of the system. The numbers on the line are separated by a space.", "output_spec": "On a single line print the answer to the problem.", "sample_inputs": ["9 3", "14 28", "4 20"], "sample_outputs": ["1", "1", "0"], "notes": "NoteIn the first sample the suitable pair is integers (3, 0). In the second sample the suitable pair is integers (3, 5). In the third sample there is no suitable pair."}, "src_uid": "03caf4ddf07c1783e42e9f9085cc6efd"}
{"nl": {"description": "Little girl Alyona is in a shop to buy some copybooks for school. She study four subjects so she wants to have equal number of copybooks for each of the subjects. There are three types of copybook's packs in the shop: it is possible to buy one copybook for a rubles, a pack of two copybooks for b rubles, and a pack of three copybooks for c rubles. Alyona already has n copybooks.What is the minimum amount of rubles she should pay to buy such number of copybooks k that n + k is divisible by 4? There are infinitely many packs of any type in the shop. Alyona can buy packs of different type in the same purchase.", "input_spec": "The only line contains 4 integers n, a, b, c (1 ≤ n, a, b, c ≤ 109).", "output_spec": "Print the minimum amount of rubles she should pay to buy such number of copybooks k that n + k is divisible by 4.", "sample_inputs": ["1 1 3 4", "6 2 1 1", "4 4 4 4", "999999999 1000000000 1000000000 1000000000"], "sample_outputs": ["3", "1", "0", "1000000000"], "notes": "NoteIn the first example Alyona can buy 3 packs of 1 copybook for 3a = 3 rubles in total. After that she will have 4 copybooks which she can split between the subjects equally. In the second example Alyuna can buy a pack of 2 copybooks for b = 1 ruble. She will have 8 copybooks in total.In the third example Alyona can split the copybooks she already has between the 4 subject equally, so she doesn't need to buy anything.In the fourth example Alyona should buy one pack of one copybook."}, "src_uid": "c74537b7e2032c1d928717dfe15ccfb8"}
{"nl": {"description": "Baby Ehab was toying around with arrays. He has an array $$$a$$$ of length $$$n$$$. He defines an array to be good if there's no way to partition it into $$$2$$$ subsequences such that the sum of the elements in the first is equal to the sum of the elements in the second. Now he wants to remove the minimum number of elements in $$$a$$$ so that it becomes a good array. Can you help him?A sequence $$$b$$$ is a subsequence of an array $$$a$$$ if $$$b$$$ can be obtained from $$$a$$$ by deleting some (possibly zero or all) elements. A partitioning of an array is a way to divide it into $$$2$$$ subsequences such that every element belongs to exactly one subsequence, so you must use all the elements, and you can't share any elements.", "input_spec": "The first line contains an integer $$$n$$$ ($$$2 \\le n \\le 100$$$) — the length of the array $$$a$$$. The second line contains $$$n$$$ integers $$$a_1$$$, $$$a_2$$$, $$$\\ldots$$$, $$$a_{n}$$$ ($$$1 \\le a_i \\le 2000$$$) — the elements of the array $$$a$$$.", "output_spec": "The first line should contain the minimum number of elements you need to remove. The second line should contain the indices of the elements you're removing, separated by spaces. We can show that an answer always exists. If there are multiple solutions, you can print any.", "sample_inputs": ["4\n6 3 9 12", "2\n1 2"], "sample_outputs": ["1\n2", "0"], "notes": "NoteIn the first example, you can partition the array into $$$[6,9]$$$ and $$$[3,12]$$$, so you must remove at least $$$1$$$ element. Removing $$$3$$$ is sufficient.In the second example, the array is already good, so you don't need to remove any elements."}, "src_uid": "29063ad54712b4911c6bf871969ee147"}
{"nl": {"description": "Sasha and Ira are two best friends. But they aren’t just friends, they are software engineers and experts in artificial intelligence. They are developing an algorithm for two bots playing a two-player game. The game is cooperative and turn based. In each turn, one of the players makes a move (it doesn’t matter which player, it's possible that players turns do not alternate). Algorithm for bots that Sasha and Ira are developing works by keeping track of the state the game is in. Each time either bot makes a move, the state changes. And, since the game is very dynamic, it will never go back to the state it was already in at any point in the past.Sasha and Ira are perfectionists and want their algorithm to have an optimal winning strategy. They have noticed that in the optimal winning strategy, both bots make exactly N moves each. But, in order to find the optimal strategy, their algorithm needs to analyze all possible states of the game (they haven’t learned about alpha-beta pruning yet) and pick the best sequence of moves.They are worried about the efficiency of their algorithm and are wondering what is the total number of states of the game that need to be analyzed? ", "input_spec": "The first and only line contains integer N.   1 ≤ N ≤ 106 ", "output_spec": "Output should contain a single integer – number of possible states modulo 109 + 7.", "sample_inputs": ["2"], "sample_outputs": ["19"], "notes": "NoteStart: Game is in state A.   Turn 1: Either bot can make a move (first bot is red and second bot is blue), so there are two possible states after the first turn – B and C.  Turn 2: In both states B and C, either bot can again make a turn, so the list of possible states is expanded to include D, E, F and G.  Turn 3: Red bot already did N=2 moves when in state D, so it cannot make any more moves there. It can make moves when in state E, F and G, so states I, K and M are added to the list. Similarly, blue bot cannot make a move when in state G, but can when in D, E and F, so states H, J and L are added.  Turn 4: Red bot already did N=2 moves when in states H, I and K, so it can only make moves when in J, L and M, so states P, R and S are added. Blue bot cannot make a move when in states J, L and M, but only when in H, I and K, so states N, O and Q are added. Overall, there are 19 possible states of the game their algorithm needs to analyze."}, "src_uid": "a18833c987fd7743e8021196b5dcdd1b"}
{"nl": {"description": "Comrade Dujikov is busy choosing artists for Timofey's birthday and is recieving calls from Taymyr from Ilia-alpinist.Ilia-alpinist calls every n minutes, i.e. in minutes n, 2n, 3n and so on. Artists come to the comrade every m minutes, i.e. in minutes m, 2m, 3m and so on. The day is z minutes long, i.e. the day consists of minutes 1, 2, ..., z. How many artists should be killed so that there are no artists in the room when Ilia calls? Consider that a call and a talk with an artist take exactly one minute.", "input_spec": "The only string contains three integers — n, m and z (1 ≤ n, m, z ≤ 104).", "output_spec": "Print single integer — the minimum number of artists that should be killed so that there are no artists in the room when Ilia calls.", "sample_inputs": ["1 1 10", "1 2 5", "2 3 9"], "sample_outputs": ["10", "2", "1"], "notes": "NoteTaymyr is a place in the north of Russia.In the first test the artists come each minute, as well as the calls, so we need to kill all of them.In the second test we need to kill artists which come on the second and the fourth minutes.In the third test — only the artist which comes on the sixth minute. "}, "src_uid": "e7ad55ce26fc8610639323af1de36c2d"}
{"nl": {"description": "Alice got many presents these days. So she decided to pack them into boxes and send them to her friends.There are $$$n$$$ kinds of presents. Presents of one kind are identical (i.e. there is no way to distinguish two gifts of the same kind). Presents of different kinds are different (i.e. that is, two gifts of different kinds are distinguishable). The number of presents of each kind, that Alice has is very big, so we can consider Alice has an infinite number of gifts of each kind.Also, there are $$$m$$$ boxes. All of them are for different people, so they are pairwise distinct (consider that the names of $$$m$$$ friends are written on the boxes). For example, putting the first kind of present into the first box but not into the second box, is different from putting the first kind of present into the second box but not into the first box.Alice wants to pack presents with the following rules:  She won't pack more than one present of each kind into the same box, so each box should contain presents of different kinds (i.e. each box contains a subset of $$$n$$$ kinds, empty boxes are allowed);  For each kind at least one present should be packed into some box. Now Alice wants to know how many different ways to pack the presents exists. Please, help her and calculate this number. Since the answer can be huge, output it by modulo $$$10^9+7$$$.See examples and their notes for clarification.", "input_spec": "The first line contains two integers $$$n$$$ and $$$m$$$, separated by spaces ($$$1 \\leq n,m \\leq 10^9$$$) — the number of kinds of presents and the number of boxes that Alice has.", "output_spec": "Print one integer  — the number of ways to pack the presents with Alice's rules, calculated by modulo $$$10^9+7$$$", "sample_inputs": ["1 3", "2 2"], "sample_outputs": ["7", "9"], "notes": "NoteIn the first example, there are seven ways to pack presents:$$$\\{1\\}\\{\\}\\{\\}$$$$$$\\{\\}\\{1\\}\\{\\}$$$$$$\\{\\}\\{\\}\\{1\\}$$$$$$\\{1\\}\\{1\\}\\{\\}$$$$$$\\{\\}\\{1\\}\\{1\\}$$$$$$\\{1\\}\\{\\}\\{1\\}$$$$$$\\{1\\}\\{1\\}\\{1\\}$$$In the second example there are nine ways to pack presents:$$$\\{\\}\\{1,2\\}$$$$$$\\{1\\}\\{2\\}$$$$$$\\{1\\}\\{1,2\\}$$$$$$\\{2\\}\\{1\\}$$$$$$\\{2\\}\\{1,2\\}$$$$$$\\{1,2\\}\\{\\}$$$$$$\\{1,2\\}\\{1\\}$$$$$$\\{1,2\\}\\{2\\}$$$$$$\\{1,2\\}\\{1,2\\}$$$For example, the way $$$\\{2\\}\\{2\\}$$$ is wrong, because presents of the first kind should be used in the least one box."}, "src_uid": "71029e5bf085b0f5f39d1835eb801891"}
{"nl": {"description": "You are given a rectangle grid. That grid's size is n × m. Let's denote the coordinate system on the grid. So, each point on the grid will have coordinates — a pair of integers (x, y) (0 ≤ x ≤ n, 0 ≤ y ≤ m).Your task is to find a maximum sub-rectangle on the grid (x1, y1, x2, y2) so that it contains the given point (x, y), and its length-width ratio is exactly (a, b). In other words the following conditions must hold: 0 ≤ x1 ≤ x ≤ x2 ≤ n, 0 ≤ y1 ≤ y ≤ y2 ≤ m, .The sides of this sub-rectangle should be parallel to the axes. And values x1, y1, x2, y2 should be integers.  If there are multiple solutions, find the rectangle which is closest to (x, y). Here \"closest\" means the Euclid distance between (x, y) and the center of the rectangle is as small as possible. If there are still multiple solutions, find the lexicographically minimum one. Here \"lexicographically minimum\" means that we should consider the sub-rectangle as sequence of integers (x1, y1, x2, y2), so we can choose the lexicographically minimum one.", "input_spec": "The first line contains six integers n, m, x, y, a, b (1 ≤ n, m ≤ 109, 0 ≤ x ≤ n, 0 ≤ y ≤ m, 1 ≤ a ≤ n, 1 ≤ b ≤ m).", "output_spec": "Print four integers x1, y1, x2, y2, which represent the founded sub-rectangle whose left-bottom point is (x1, y1) and right-up point is (x2, y2).", "sample_inputs": ["9 9 5 5 2 1", "100 100 52 50 46 56"], "sample_outputs": ["1 3 9 7", "17 8 86 92"], "notes": null}, "src_uid": "8f1211b995f35462ae83b2be27f54585"}
{"nl": {"description": "Iahub and Iahubina went to a picnic in a forest full of trees. Less than 5 minutes passed before Iahub remembered of trees from programming. Moreover, he invented a new problem and Iahubina has to solve it, otherwise Iahub won't give her the food. Iahub asks Iahubina: can you build a rooted tree, such that  each internal node (a node with at least one son) has at least two sons;  node i has ci nodes in its subtree? Iahubina has to guess the tree. Being a smart girl, she realized that it's possible no tree can follow Iahub's restrictions. In this way, Iahub will eat all the food. You need to help Iahubina: determine if there's at least one tree following Iahub's restrictions. The required tree must contain n nodes.", "input_spec": "The first line of the input contains integer n (1 ≤ n ≤ 24). Next line contains n positive integers: the i-th number represents ci (1 ≤ ci ≤ n).", "output_spec": "Output on the first line \"YES\" (without quotes) if there exist at least one tree following Iahub's restrictions, otherwise output \"NO\" (without quotes). ", "sample_inputs": ["4\n1 1 1 4", "5\n1 1 5 2 1"], "sample_outputs": ["YES", "NO"], "notes": null}, "src_uid": "ed0925cfaee961a3ceebd13b3c96a15a"}
{"nl": {"description": "You are given a sequence $$$a_1, a_2, \\dots, a_n$$$ consisting of $$$n$$$ integers.You can choose any non-negative integer $$$D$$$ (i.e. $$$D \\ge 0$$$), and for each $$$a_i$$$ you can:  add $$$D$$$ (only once), i. e. perform $$$a_i := a_i + D$$$, or  subtract $$$D$$$ (only once), i. e. perform $$$a_i := a_i - D$$$, or  leave the value of $$$a_i$$$ unchanged. It is possible that after an operation the value $$$a_i$$$ becomes negative.Your goal is to choose such minimum non-negative integer $$$D$$$ and perform changes in such a way, that all $$$a_i$$$ are equal (i.e. $$$a_1=a_2=\\dots=a_n$$$).Print the required $$$D$$$ or, if it is impossible to choose such value $$$D$$$, print -1.For example, for array $$$[2, 8]$$$ the value $$$D=3$$$ is minimum possible because you can obtain the array $$$[5, 5]$$$ if you will add $$$D$$$ to $$$2$$$ and subtract $$$D$$$ from $$$8$$$. And for array $$$[1, 4, 7, 7]$$$ the value $$$D=3$$$ is also minimum possible. You can add it to $$$1$$$ and subtract it from $$$7$$$ and obtain the array $$$[4, 4, 4, 4]$$$.", "input_spec": "The first line of the input contains one integer $$$n$$$ ($$$1 \\le n \\le 100$$$) — the number of elements in $$$a$$$. The second line of the input contains $$$n$$$ integers $$$a_1, a_2, \\dots, a_n$$$ ($$$1 \\le a_i \\le 100$$$) — the sequence $$$a$$$.", "output_spec": "Print one integer — the minimum non-negative integer value $$$D$$$ such that if you add this value to some $$$a_i$$$, subtract this value from some $$$a_i$$$ and leave some $$$a_i$$$ without changes, all obtained values become equal. If it is impossible to choose such value $$$D$$$, print -1.", "sample_inputs": ["6\n1 4 4 7 4 1", "5\n2 2 5 2 5", "4\n1 3 3 7", "2\n2 8"], "sample_outputs": ["3", "3", "-1", "3"], "notes": null}, "src_uid": "d486a88939c132848a7efdf257b9b066"}
{"nl": {"description": "Panic is rising in the committee for doggo standardization — the puppies of the new brood have been born multi-colored! In total there are 26 possible colors of puppies in the nature and they are denoted by letters from 'a' to 'z' inclusive.The committee rules strictly prohibit even the smallest diversity between doggos and hence all the puppies should be of the same color. Thus Slava, the committee employee, has been assigned the task to recolor some puppies into other colors in order to eliminate the difference and make all the puppies have one common color.Unfortunately, due to bureaucratic reasons and restricted budget, there's only one operation Slava can perform: he can choose a color $$$x$$$ such that there are currently at least two puppies of color $$$x$$$ and recolor all puppies of the color $$$x$$$ into some arbitrary color $$$y$$$. Luckily, this operation can be applied multiple times (including zero).For example, if the number of puppies is $$$7$$$ and their colors are represented as the string \"abababc\", then in one operation Slava can get the results \"zbzbzbc\", \"bbbbbbc\", \"aaaaaac\", \"acacacc\" and others. However, if the current color sequence is \"abababc\", then he can't choose $$$x$$$='c' right now, because currently only one puppy has the color 'c'.Help Slava and the committee determine whether it is possible to standardize all the puppies, i.e. after Slava's operations all the puppies should have the same color.", "input_spec": "The first line contains a single integer $$$n$$$ ($$$1 \\le n \\le 10^5$$$) — the number of puppies. The second line contains a string $$$s$$$ of length $$$n$$$ consisting of lowercase Latin letters, where the $$$i$$$-th symbol denotes the $$$i$$$-th puppy's color.", "output_spec": "If it's possible to recolor all puppies into one color, print \"Yes\". Otherwise print \"No\". Output the answer without quotation signs.", "sample_inputs": ["6\naabddc", "3\nabc", "3\njjj"], "sample_outputs": ["Yes", "No", "Yes"], "notes": "NoteIn the first example Slava can perform the following steps:   take all puppies of color 'a' (a total of two) and recolor them into 'b';  take all puppies of color 'd' (a total of two) and recolor them into 'c';  take all puppies of color 'b' (three puppies for now) and recolor them into 'c'. In the second example it's impossible to recolor any of the puppies.In the third example all the puppies' colors are the same; thus there's no need to recolor anything."}, "src_uid": "6b22e93f7e429693dcfe3c099346dcda"}
{"nl": {"description": "In a far away kingdom is the famous Lio Shan monastery. Gods constructed three diamond pillars on the monastery's lawn long ago. Gods also placed on one pillar n golden disks of different diameters (in the order of the diameters' decreasing from the bottom to the top). Besides, gods commanded to carry all the disks from the first pillar to the third one according to the following rules: you can carry only one disk in one move; you cannot put a larger disk on a smaller one. There was no universal opinion concerning what is to happen after the gods' will is done: some people promised world peace and eternal happiness to everyone, whereas others predicted that the kingdom will face communi… (gee, what am I rambling about?) the Armageddon. However, as everybody knew that it was impossible to solve the problem in less than 2n - 1 moves and the lazy Lio Shan monks never even started to solve it, everyone lives peacefully even though the problem was never solved and nobody was afraid of the Armageddon.However, the monastery wasn't doing so well lately and the wise prior Ku Sean Sun had to cut some disks at the edges and use the gold for the greater good. Wouldn't you think that the prior is entitled to have an air conditioning system? Besides, staying in the monastery all year is sooo dull… One has to have a go at something new now and then, go skiing, for example… Ku Sean Sun realize how big a mistake he had made only after a while: after he cut the edges, the diameters of some disks got the same; that means that some moves that used to be impossible to make, were at last possible (why, gods never prohibited to put a disk on a disk of the same diameter). Thus, the possible Armageddon can come earlier than was initially planned by gods. Much earlier. So much earlier, in fact, that Ku Sean Sun won't even have time to ski all he wants or relax under the air conditioner.The wise prior could never let that last thing happen and he asked one very old and very wise witch PikiWedia to help him. May be she can determine the least number of moves needed to solve the gods' problem. However, the witch laid out her cards and found no answer for the prior. Then he asked you to help him.Can you find the shortest solution of the problem, given the number of disks and their diameters? Keep in mind that it is allowed to place disks of the same diameter one on the other one, however, the order in which the disks are positioned on the third pillar in the end should match the initial order of the disks on the first pillar.", "input_spec": "The first line contains an integer n — the number of disks (1 ≤ n ≤ 20). The second line contains n integers di — the disks' diameters after Ku Sean Sun cut their edges. The diameters are given from the bottom to the top (1 ≤ di ≤ 20, besides, di ≥ di + 1 for any 1 ≤ i < n).", "output_spec": "Print on the first line number m — the smallest number of moves to solve the gods' problem. Print on the next m lines the description of moves: two space-separated positive integers si and ti that determine the number of the pillar from which the disk is moved and the number of pillar where the disk is moved, correspondingly (1 ≤ si, ti ≤ 3, si ≠ ti). ", "sample_inputs": ["3\n3 2 1", "3\n3 1 1", "3\n3 3 3"], "sample_outputs": ["7\n1 3\n1 2\n3 2\n1 3\n2 1\n2 3\n1 3", "5\n1 2\n1 2\n1 3\n2 3\n2 3", "5\n1 2\n1 2\n1 3\n2 3\n2 3"], "notes": "NotePay attention to the third test demonstrating that the order of disks should remain the same in the end, even despite the disks' same radius. If this condition was not necessary to fulfill, the gods' task could have been solved within a smaller number of moves (three — simply moving the three disks from the first pillar on the third one)."}, "src_uid": "4ea4ad10ef422a9cd45b8a7b25d359c5"}
{"nl": {"description": "Stepan is a very experienced olympiad participant. He has n cups for Physics olympiads and m cups for Informatics olympiads. Each cup is characterized by two parameters — its significance ci and width wi.Stepan decided to expose some of his cups on a shelf with width d in such a way, that:  there is at least one Physics cup and at least one Informatics cup on the shelf,  the total width of the exposed cups does not exceed d,  from each subjects (Physics and Informatics) some of the most significant cups are exposed (i. e. if a cup for some subject with significance x is exposed, then all the cups for this subject with significance greater than x must be exposed too). Your task is to determine the maximum possible total significance, which Stepan can get when he exposes cups on the shelf with width d, considering all the rules described above. The total significance is the sum of significances of all the exposed cups.", "input_spec": "The first line contains three integers n, m and d (1 ≤ n, m ≤ 100 000, 1 ≤ d ≤ 109) — the number of cups for Physics olympiads, the number of cups for Informatics olympiads and the width of the shelf. Each of the following n lines contains two integers ci and wi (1 ≤ ci, wi ≤ 109) — significance and width of the i-th cup for Physics olympiads. Each of the following m lines contains two integers cj and wj (1 ≤ cj, wj ≤ 109) — significance and width of the j-th cup for Informatics olympiads.", "output_spec": "Print the maximum possible total significance, which Stepan can get exposing cups on the shelf with width d, considering all the rules described in the statement. If there is no way to expose cups on the shelf, then print 0.", "sample_inputs": ["3 1 8\n4 2\n5 5\n4 2\n3 2", "4 3 12\n3 4\n2 4\n3 5\n3 4\n3 5\n5 2\n3 4", "2 2 2\n5 3\n6 3\n4 2\n8 1"], "sample_outputs": ["8", "11", "0"], "notes": "NoteIn the first example Stepan has only one Informatics cup which must be exposed on the shelf. Its significance equals 3 and width equals 2, so after Stepan exposes it, the width of free space on the shelf becomes equal to 6. Also, Stepan must expose the second Physics cup (which has width 5), because it is the most significant cup for Physics (its significance equals 5). After that Stepan can not expose more cups on the shelf, because there is no enough free space. Thus, the maximum total significance of exposed cups equals to 8."}, "src_uid": "da573a39459087ed7c42f70bc1d0e8ff"}
{"nl": {"description": "Zane the wizard had never loved anyone before, until he fell in love with a girl, whose name remains unknown to us.  The girl lives in house m of a village. There are n houses in that village, lining in a straight line from left to right: house 1, house 2, ..., house n. The village is also well-structured: house i and house i + 1 (1 ≤ i < n) are exactly 10 meters away. In this village, some houses are occupied, and some are not. Indeed, unoccupied houses can be purchased.You will be given n integers a1, a2, ..., an that denote the availability and the prices of the houses. If house i is occupied, and therefore cannot be bought, then ai equals 0. Otherwise, house i can be bought, and ai represents the money required to buy it, in dollars.As Zane has only k dollars to spare, it becomes a challenge for him to choose the house to purchase, so that he could live as near as possible to his crush. Help Zane determine the minimum distance from his crush's house to some house he can afford, to help him succeed in his love.", "input_spec": "The first line contains three integers n, m, and k (2 ≤ n ≤ 100, 1 ≤ m ≤ n, 1 ≤ k ≤ 100) — the number of houses in the village, the house where the girl lives, and the amount of money Zane has (in dollars), respectively. The second line contains n integers a1, a2, ..., an (0 ≤ ai ≤ 100) — denoting the availability and the prices of the houses. It is guaranteed that am = 0 and that it is possible to purchase some house with no more than k dollars.", "output_spec": "Print one integer — the minimum distance, in meters, from the house where the girl Zane likes lives to the house Zane can buy.", "sample_inputs": ["5 1 20\n0 27 32 21 19", "7 3 50\n62 0 0 0 99 33 22", "10 5 100\n1 0 1 0 0 0 0 0 1 1"], "sample_outputs": ["40", "30", "20"], "notes": "NoteIn the first sample, with k = 20 dollars, Zane can buy only house 5. The distance from house m = 1 to house 5 is 10 + 10 + 10 + 10 = 40 meters.In the second sample, Zane can buy houses 6 and 7. It is better to buy house 6 than house 7, since house m = 3 and house 6 are only 30 meters away, while house m = 3 and house 7 are 40 meters away."}, "src_uid": "57860e9a5342a29257ce506063d37624"}
{"nl": {"description": "Given an integer $$$x$$$, find 2 integers $$$a$$$ and $$$b$$$ such that:   $$$1 \\le a,b \\le x$$$  $$$b$$$ divides $$$a$$$ ($$$a$$$ is divisible by $$$b$$$).  $$$a \\cdot b>x$$$.  $$$\\frac{a}{b}<x$$$. ", "input_spec": "The only line contains the integer $$$x$$$ $$$(1 \\le x \\le 100)$$$.", "output_spec": "You should output two integers $$$a$$$ and $$$b$$$, satisfying the given conditions, separated by a space. If no pair of integers satisfy the conditions above, print \"-1\" (without quotes).", "sample_inputs": ["10", "1"], "sample_outputs": ["6 3", "-1"], "notes": null}, "src_uid": "883f67177474d23d7a320d9dbfa70dd3"}
{"nl": {"description": "At a geometry lesson Gerald was given a task: to get vector B out of vector A. Besides, the teacher permitted him to perform the following operations with vector А: Turn the vector by 90 degrees clockwise. Add to the vector a certain vector C.Operations could be performed in any order any number of times.Can Gerald cope with the task?", "input_spec": "The first line contains integers x1 и y1 — the coordinates of the vector A ( - 108 ≤ x1, y1 ≤ 108). The second and the third line contain in the similar manner vectors B and C (their coordinates are integers; their absolute value does not exceed 108).", "output_spec": "Print \"YES\" (without the quotes) if it is possible to get vector B using the given operations. Otherwise print \"NO\" (without the quotes).", "sample_inputs": ["0 0\n1 1\n0 1", "0 0\n1 1\n1 1", "0 0\n1 1\n2 2"], "sample_outputs": ["YES", "YES", "NO"], "notes": null}, "src_uid": "cc8a8af1ba2b19bf081e379139542883"}
{"nl": {"description": "You all know the Dirichlet principle, the point of which is that if n boxes have no less than n + 1 items, that leads to the existence of a box in which there are at least two items.Having heard of that principle, but having not mastered the technique of logical thinking, 8 year olds Stas and Masha invented a game. There are a different boxes and b different items, and each turn a player can either add a new box or a new item. The player, after whose turn the number of ways of putting b items into a boxes becomes no less then a certain given number n, loses. All the boxes and items are considered to be different. Boxes may remain empty.Who loses if both players play optimally and Stas's turn is first?", "input_spec": "The only input line has three integers a, b, n (1 ≤ a ≤ 10000, 1 ≤ b ≤ 30, 2 ≤ n ≤ 109) — the initial number of the boxes, the number of the items and the number which constrains the number of ways, respectively. Guaranteed that the initial number of ways is strictly less than n.", "output_spec": "Output \"Stas\" if Masha wins. Output \"Masha\" if Stas wins. In case of a draw, output \"Missing\".", "sample_inputs": ["2 2 10", "5 5 16808", "3 1 4", "1 4 10"], "sample_outputs": ["Masha", "Masha", "Stas", "Missing"], "notes": "NoteIn the second example the initial number of ways is equal to 3125.   If Stas increases the number of boxes, he will lose, as Masha may increase the number of boxes once more during her turn. After that any Stas's move will lead to defeat.  But if Stas increases the number of items, then any Masha's move will be losing. "}, "src_uid": "cffd5c0b7b659649f3bf9f2dbd20ad6b"}
{"nl": {"description": "There is the faculty of Computer Science in Berland. In the social net \"TheContact!\" for each course of this faculty there is the special group whose name equals the year of university entrance of corresponding course of students at the university. Each of students joins the group of his course and joins all groups for which the year of student's university entrance differs by no more than x from the year of university entrance of this student, where x — some non-negative integer. A value x is not given, but it can be uniquely determined from the available data. Note that students don't join other groups. You are given the list of groups which the student Igor joined. According to this information you need to determine the year of Igor's university entrance.", "input_spec": "The first line contains the positive odd integer n (1 ≤ n ≤ 5) — the number of groups which Igor joined.  The next line contains n distinct integers a1, a2, ..., an (2010 ≤ ai ≤ 2100) — years of student's university entrance for each group in which Igor is the member. It is guaranteed that the input data is correct and the answer always exists. Groups are given randomly.", "output_spec": "Print the year of Igor's university entrance. ", "sample_inputs": ["3\n2014 2016 2015", "1\n2050"], "sample_outputs": ["2015", "2050"], "notes": "NoteIn the first test the value x = 1. Igor entered the university in 2015. So he joined groups members of which are students who entered the university in 2014, 2015 and 2016.In the second test the value x = 0. Igor entered only the group which corresponds to the year of his university entrance. "}, "src_uid": "f03773118cca29ff8d5b4281d39e7c63"}
{"nl": {"description": "Ayoub had an array $$$a$$$ of integers of size $$$n$$$ and this array had two interesting properties:   All the integers in the array were between $$$l$$$ and $$$r$$$ (inclusive).  The sum of all the elements was divisible by $$$3$$$. Unfortunately, Ayoub has lost his array, but he remembers the size of the array $$$n$$$ and the numbers $$$l$$$ and $$$r$$$, so he asked you to find the number of ways to restore the array. Since the answer could be very large, print it modulo $$$10^9 + 7$$$ (i.e. the remainder when dividing by $$$10^9 + 7$$$). In case there are no satisfying arrays (Ayoub has a wrong memory), print $$$0$$$.", "input_spec": "The first and only line contains three integers $$$n$$$, $$$l$$$ and $$$r$$$ ($$$1 \\le n \\le 2 \\cdot 10^5 , 1 \\le l \\le r \\le 10^9$$$) — the size of the lost array and the range of numbers in the array.", "output_spec": "Print the remainder when dividing by $$$10^9 + 7$$$ the number of ways to restore the array.", "sample_inputs": ["2 1 3", "3 2 2", "9 9 99"], "sample_outputs": ["3", "1", "711426616"], "notes": "NoteIn the first example, the possible arrays are : $$$[1,2], [2,1], [3, 3]$$$.In the second example, the only possible array is $$$[2, 2, 2]$$$."}, "src_uid": "4c4852df62fccb0a19ad8bc41145de61"}
{"nl": {"description": "You are given two squares, one with sides parallel to the coordinate axes, and another one with sides at 45 degrees to the coordinate axes. Find whether the two squares intersect.The interior of the square is considered to be part of the square, i.e. if one square is completely inside another, they intersect. If the two squares only share one common point, they are also considered to intersect.", "input_spec": "The input data consists of two lines, one for each square, both containing 4 pairs of integers. Each pair represents coordinates of one vertex of the square. Coordinates within each line are either in clockwise or counterclockwise order. The first line contains the coordinates of the square with sides parallel to the coordinate axes, the second line contains the coordinates of the square at 45 degrees. All the values are integer and between $$$-100$$$ and $$$100$$$.", "output_spec": "Print \"Yes\" if squares intersect, otherwise print \"No\". You can print each letter in any case (upper or lower).", "sample_inputs": ["0 0 6 0 6 6 0 6\n1 3 3 5 5 3 3 1", "0 0 6 0 6 6 0 6\n7 3 9 5 11 3 9 1", "6 0 6 6 0 6 0 0\n7 4 4 7 7 10 10 7"], "sample_outputs": ["YES", "NO", "YES"], "notes": "NoteIn the first example the second square lies entirely within the first square, so they do intersect.In the second sample squares do not have any points in common.Here are images corresponding to the samples:      "}, "src_uid": "f6a3dd8b3bab58ff66055c61ddfdf06a"}
{"nl": {"description": "After finishing eating her bun, Alyona came up with two integers n and m. She decided to write down two columns of integers — the first column containing integers from 1 to n and the second containing integers from 1 to m. Now the girl wants to count how many pairs of integers she can choose, one from the first column and the other from the second column, such that their sum is divisible by 5.Formally, Alyona wants to count the number of pairs of integers (x, y) such that 1 ≤ x ≤ n, 1 ≤ y ≤ m and  equals 0.As usual, Alyona has some troubles and asks you to help.", "input_spec": "The only line of the input contains two integers n and m (1 ≤ n, m ≤ 1 000 000).", "output_spec": "Print the only integer — the number of pairs of integers (x, y) such that 1 ≤ x ≤ n, 1 ≤ y ≤ m and (x + y) is divisible by 5.", "sample_inputs": ["6 12", "11 14", "1 5", "3 8", "5 7", "21 21"], "sample_outputs": ["14", "31", "1", "5", "7", "88"], "notes": "NoteFollowing pairs are suitable in the first sample case:   for x = 1 fits y equal to 4 or 9;  for x = 2 fits y equal to 3 or 8;  for x = 3 fits y equal to 2, 7 or 12;  for x = 4 fits y equal to 1, 6 or 11;  for x = 5 fits y equal to 5 or 10;  for x = 6 fits y equal to 4 or 9. Only the pair (1, 4) is suitable in the third sample case."}, "src_uid": "df0879635b59e141c839d9599abd77d2"}
{"nl": {"description": "Absent-minded Masha got set of n cubes for her birthday.At each of 6 faces of each cube, there is exactly one digit from 0 to 9. Masha became interested what is the largest natural x such she can make using her new cubes all integers from 1 to x.To make a number Masha can rotate her cubes and put them in a row. After that, she looks at upper faces of cubes from left to right and reads the number.The number can't contain leading zeros. It's not required to use all cubes to build a number.Pay attention: Masha can't make digit 6 from digit 9 and vice-versa using cube rotations.", "input_spec": "In first line integer n is given (1 ≤ n ≤ 3) — the number of cubes, Masha got for her birthday. Each of next n lines contains 6 integers aij (0 ≤ aij ≤ 9) — number on j-th face of i-th cube.", "output_spec": "Print single integer — maximum number x such Masha can make any integers from 1 to x using her cubes or 0 if Masha can't make even 1.", "sample_inputs": ["3\n0 1 2 3 4 5\n6 7 8 9 0 1\n2 3 4 5 6 7", "3\n0 1 3 5 6 8\n1 2 4 5 7 8\n2 3 4 6 7 9"], "sample_outputs": ["87", "98"], "notes": "NoteIn the first test case, Masha can build all numbers from 1 to 87, but she can't make 88 because there are no two cubes with digit 8."}, "src_uid": "20aa53bffdfd47b4e853091ee6b11a4b"}
{"nl": {"description": "You are given an infinite checkered field. You should get from a square (x1; y1) to a square (x2; y2). Using the shortest path is not necessary. You can move on the field squares in four directions. That is, when you are positioned in any square, you can move to any other side-neighboring one. A square (x; y) is considered bad, if at least one of the two conditions is fulfilled: |x + y| ≡ 0 (mod 2a), |x - y| ≡ 0 (mod 2b). Your task is to find the minimum number of bad cells one will have to visit on the way from (x1; y1) to (x2; y2).", "input_spec": "The only line contains integers a, b, x1, y1, x2 and y2 — the parameters of the bad squares, the coordinates of the initial and the final squares correspondingly (2 ≤ a, b ≤ 109 and |x1|,|y1|,|x2|,|y2| ≤ 109). It is guaranteed that the initial and the final square aren't bad.", "output_spec": "Print a single number — the minimum number of bad cells that one will have to visit in order to travel from square (x1; y1) to square (x2; y2).", "sample_inputs": ["2 2 1 0 0 1", "2 2 10 11 0 1", "2 4 3 -1 3 7"], "sample_outputs": ["1", "5", "2"], "notes": "NoteIn the third sample one of the possible paths in (3;-1)->(3;0)->(3;1)->(3;2)->(4;2)->(4;3)->(4;4)->(4;5)->(4;6)->(4;7)->(3;7). Squares (3;1) and (4;4) are bad."}, "src_uid": "7219d1837c83b5920992aee5a60dc0d9"}
{"nl": {"description": "Two players play a simple game. Each player is provided with a box with balls. First player's box contains exactly n1 balls and second player's box contains exactly n2 balls. In one move first player can take from 1 to k1 balls from his box and throw them away. Similarly, the second player can take from 1 to k2 balls from his box in his move. Players alternate turns and the first player starts the game. The one who can't make a move loses. Your task is to determine who wins if both players play optimally.", "input_spec": "The first line contains four integers n1, n2, k1, k2. All numbers in the input are from 1 to 50. This problem doesn't have subproblems. You will get 3 points for the correct submission.", "output_spec": "Output \"First\" if the first player wins and \"Second\" otherwise.", "sample_inputs": ["2 2 1 2", "2 1 1 1"], "sample_outputs": ["Second", "First"], "notes": "NoteConsider the first sample test. Each player has a box with 2 balls. The first player draws a single ball from his box in one move and the second player can either take 1 or 2 balls from his box in one move. No matter how the first player acts, the second player can always win if he plays wisely."}, "src_uid": "aed24ebab3ed9fd1741eea8e4200f86b"}
{"nl": {"description": "One Martian boy called Zorg wants to present a string of beads to his friend from the Earth — Masha. He knows that Masha likes two colours: blue and red, — and right in the shop where he has come, there is a variety of adornments with beads of these two colours. All the strings of beads have a small fastener, and if one unfastens it, one might notice that all the strings of beads in the shop are of the same length. Because of the peculiarities of the Martian eyesight, if Zorg sees one blue-and-red string of beads first, and then the other with red beads instead of blue ones, and blue — instead of red, he regards these two strings of beads as identical. In other words, Zorg regards as identical not only those strings of beads that can be derived from each other by the string turnover, but as well those that can be derived from each other by a mutual replacement of colours and/or by the string turnover.It is known that all Martians are very orderly, and if a Martian sees some amount of objects, he tries to put them in good order. Zorg thinks that a red bead is smaller than a blue one. Let's put 0 for a red bead, and 1 — for a blue one. From two strings the Martian puts earlier the string with a red bead in the i-th position, providing that the second string has a blue bead in the i-th position, and the first two beads i - 1 are identical.At first Zorg unfastens all the strings of beads, and puts them into small heaps so, that in each heap strings are identical, in his opinion. Then he sorts out the heaps and chooses the minimum string in each heap, in his opinion. He gives the unnecassary strings back to the shop assistant and says he doesn't need them any more. Then Zorg sorts out the remaining strings of beads and buys the string with index k. All these manupulations will take Zorg a lot of time, that's why he asks you to help and find the string of beads for Masha.", "input_spec": "The input file contains two integers n and k (2 ≤ n ≤ 50;1 ≤ k ≤ 1016) —the length of a string of beads, and the index of the string, chosen by Zorg. ", "output_spec": "Output the k-th string of beads, putting 0 for a red bead, and 1 — for a blue one. If it s impossible to find the required string, output the only number -1.", "sample_inputs": ["4 4"], "sample_outputs": ["0101"], "notes": "NoteLet's consider the example of strings of length 4 — 0001, 0010, 0011, 0100, 0101, 0110, 0111, 1000, 1001, 1010, 1011, 1100, 1101, 1110. Zorg will divide them into heaps: {0001, 0111, 1000, 1110}, {0010, 0100, 1011, 1101}, {0011, 1100}, {0101, 1010}, {0110, 1001}. Then he will choose the minimum strings of beads in each heap: 0001, 0010, 0011, 0101, 0110. The forth string — 0101."}, "src_uid": "0a4a418dafaee71f1b31c928fc2ad24a"}
{"nl": {"description": "In Berland a money reform is being prepared. New coins are being introduced. After long economic calculations was decided that the most expensive coin should possess the denomination of exactly n Berland dollars. Also the following restriction has been introduced for comfort: the denomination of each coin should be divisible by the denomination of any cheaper coin. It is known that among all the possible variants the variant with the largest number of new coins will be chosen. Find this variant. Print in the order of decreasing of the coins' denominations.", "input_spec": "The first and only line contains an integer n (1 ≤ n ≤ 106) which represents the denomination of the most expensive coin. ", "output_spec": "Print the denominations of all the coins in the order of decreasing. The number of coins must be the largest possible (with the given denomination n of the most expensive coin). Also, the denomination of every coin must be divisible by the denomination of any cheaper coin. Naturally, the denominations of all the coins should be different. If there are several solutins to that problem, print any of them.", "sample_inputs": ["10", "4", "3"], "sample_outputs": ["10 5 1", "4 2 1", "3 1"], "notes": null}, "src_uid": "2fc946bb72f56b6d86eabfaf60f9fa63"}
{"nl": {"description": "Tonight is brain dinner night and all zombies will gather together to scarf down some delicious brains. The artful Heidi plans to crash the party, incognito, disguised as one of them. Her objective is to get away with at least one brain, so she can analyze the zombies' mindset back home and gain a strategic advantage.They will be N guests tonight: N - 1 real zombies and a fake one, our Heidi. The living-dead love hierarchies as much as they love brains: each one has a unique rank in the range 1 to N - 1, and Heidi, who still appears slightly different from the others, is attributed the highest rank, N. Tonight there will be a chest with brains on display and every attendee sees how many there are. These will then be split among the attendees according to the following procedure:The zombie of the highest rank makes a suggestion on who gets how many brains (every brain is an indivisible entity). A vote follows. If at least half of the attendees accept the offer, the brains are shared in the suggested way and the feast begins. But if majority is not reached, then the highest-ranked zombie is killed, and the next zombie in hierarchy has to make a suggestion. If he is killed too, then the third highest-ranked makes one, etc. (It's enough to have exactly half of the votes – in case of a tie, the vote of the highest-ranked alive zombie counts twice, and he will of course vote in favor of his own suggestion in order to stay alive.)You should know that zombies are very greedy and sly, and they know this too – basically all zombie brains are alike. Consequently, a zombie will never accept an offer which is suboptimal for him. That is, if an offer is not strictly better than a potential later offer, he will vote against it. And make no mistake: while zombies may normally seem rather dull, tonight their intellects are perfect. Each zombie's priorities for tonight are, in descending order:   survive the event (they experienced death already once and know it is no fun),  get as many brains as possible. Heidi goes first and must make an offer which at least half of the attendees will accept, and which allocates at least one brain for Heidi herself.What is the smallest number of brains that have to be in the chest for this to be possible?", "input_spec": "The only line of input contains one integer: N, the number of attendees (1 ≤ N ≤ 109).", "output_spec": "Output one integer: the smallest number of brains in the chest which allows Heidi to take one brain home.", "sample_inputs": ["1", "4"], "sample_outputs": ["1", "2"], "notes": "Note"}, "src_uid": "30e95770f12c631ce498a2b20c2931c7"}
{"nl": {"description": "Pasha has many hamsters and he makes them work out. Today, n hamsters (n is even) came to work out. The hamsters lined up and each hamster either sat down or stood up.For another exercise, Pasha needs exactly  hamsters to stand up and the other hamsters to sit down. In one minute, Pasha can make some hamster ether sit down or stand up. How many minutes will he need to get what he wants if he acts optimally well?", "input_spec": "The first line contains integer n (2 ≤ n ≤ 200; n is even). The next line contains n characters without spaces. These characters describe the hamsters' position: the i-th character equals 'X', if the i-th hamster in the row is standing, and 'x', if he is sitting.", "output_spec": "In the first line, print a single integer — the minimum required number of minutes. In the second line, print a string that describes the hamsters' position after Pasha makes the required changes. If there are multiple optimal positions, print any of them.", "sample_inputs": ["4\nxxXx", "2\nXX", "6\nxXXxXx"], "sample_outputs": ["1\nXxXx", "1\nxX", "0\nxXXxXx"], "notes": null}, "src_uid": "fa6311c72d90d8363d97854b903f849d"}
{"nl": {"description": "The new operating system BerOS has a nice feature. It is possible to use any number of characters '/' as a delimiter in path instead of one traditional '/'. For example, strings //usr///local//nginx/sbin// and /usr/local/nginx///sbin are equivalent. The character '/' (or some sequence of such characters) at the end of the path is required only in case of the path to the root directory, which can be represented as single character '/'.A path called normalized if it contains the smallest possible number of characters '/'.Your task is to transform a given path to the normalized form.", "input_spec": "The first line of the input contains only lowercase Latin letters and character '/' — the path to some directory. All paths start with at least one character '/'. The length of the given line is no more than 100 characters, it is not empty.", "output_spec": "The path in normalized form.", "sample_inputs": ["//usr///local//nginx/sbin"], "sample_outputs": ["/usr/local/nginx/sbin"], "notes": null}, "src_uid": "6c2e658ac3c3d6b0569dd373806fa031"}
{"nl": {"description": "An elephant decided to visit his friend. It turned out that the elephant's house is located at point 0 and his friend's house is located at point x(x > 0) of the coordinate line. In one step the elephant can move 1, 2, 3, 4 or 5 positions forward. Determine, what is the minimum number of steps he need to make in order to get to his friend's house.", "input_spec": "The first line of the input contains an integer x (1 ≤ x ≤ 1 000 000) — The coordinate of the friend's house.", "output_spec": "Print the minimum number of steps that elephant needs to make to get from point 0 to point x.", "sample_inputs": ["5", "12"], "sample_outputs": ["1", "3"], "notes": "NoteIn the first sample the elephant needs to make one step of length 5 to reach the point x.In the second sample the elephant can get to point x if he moves by 3, 5 and 4. There are other ways to get the optimal answer but the elephant cannot reach x in less than three moves."}, "src_uid": "4b3d65b1b593829e92c852be213922b6"}
{"nl": {"description": "Sereja adores trees. Today he came up with a revolutionary new type of binary root trees.His new tree consists of n levels, each vertex is indexed by two integers: the number of the level and the number of the vertex on the current level. The tree root is at level 1, its index is (1, 1). Here is a pseudo code of tree construction.//the global data are integer arrays cnt[], left[][], right[][]cnt[1] = 1;fill arrays left[][], right[][] with values -1;for(level = 1; level < n; level = level + 1){    cnt[level + 1] = 0;    for(position = 1; position <= cnt[level]; position = position + 1){        if(the value of position is a power of two){ // that is, 1, 2, 4, 8...            left[level][position] = cnt[level + 1] + 1;            right[level][position] = cnt[level + 1] + 2;            cnt[level + 1] = cnt[level + 1] + 2;                    }else{            right[level][position] = cnt[level + 1] + 1;            cnt[level + 1] = cnt[level + 1] + 1;        }    }}After the pseudo code is run, cell cnt[level] contains the number of vertices on level level. Cell left[level][position] contains the number of the vertex on the level level + 1, which is the left child of the vertex with index (level, position), or it contains -1, if the vertex doesn't have a left child. Similarly, cell right[level][position] is responsible for the right child. You can see how the tree with n = 4 looks like in the notes.Serja loves to make things complicated, so he first made a tree and then added an empty set A(level, position) for each vertex. Then Sereja executes m operations. Each operation is of one of the two following types:  The format of the operation is \"1 t l r x\". For all vertices level, position (level = t; l ≤ position ≤ r) add value x to set A(level, position).  The format of the operation is \"2 t v\". For vertex level, position (level = t, position = v), find the union of all sets of vertices that are in the subtree of vertex (level, position). Print the size of the union of these sets. Help Sereja execute the operations. In this problem a set contains only distinct values like std::set in C++.", "input_spec": "The first line contains integers n and m (1 ≤ n, m ≤ 7000).  Next m lines contain the descriptions of the operations. The operation of the first type is given by five integers: 1 t l r x (1 ≤ t ≤ n; 1 ≤ l ≤ r ≤ cnt[t]; 1 ≤ x ≤ 106). The operation of the second type is given by three integers: 2 t v (1 ≤ t ≤ n; 1 ≤ v ≤ cnt[t]).", "output_spec": "For each operation of the second type, print the answer on a single line.", "sample_inputs": ["4 5\n1 4 4 7 1\n1 3 1 2 2\n2 1 1\n2 4 1\n2 3 3"], "sample_outputs": ["2\n0\n1"], "notes": "NoteYou can find the definitions that are used while working with root trees by this link: http://en.wikipedia.org/wiki/Tree_(graph_theory)You can see an example of a constructed tree at n = 4 below.  "}, "src_uid": "9f239cfd29c1a2652a065bfe5c15476a"}
{"nl": {"description": "Nothing has changed since the last round. Dima and Inna still love each other and want to be together. They've made a deal with Seryozha and now they need to make a deal with the dorm guards...There are four guardposts in Dima's dorm. Each post contains two guards (in Russia they are usually elderly women). You can bribe a guard by a chocolate bar or a box of juice. For each guard you know the minimum price of the chocolate bar she can accept as a gift and the minimum price of the box of juice she can accept as a gift. If a chocolate bar for some guard costs less than the minimum chocolate bar price for this guard is, or if a box of juice for some guard costs less than the minimum box of juice price for this guard is, then the guard doesn't accept such a gift.In order to pass through a guardpost, one needs to bribe both guards.The shop has an unlimited amount of juice and chocolate of any price starting with 1. Dima wants to choose some guardpost, buy one gift for each guard from the guardpost and spend exactly n rubles on it.Help him choose a post through which he can safely sneak Inna or otherwise say that this is impossible. Mind you, Inna would be very sorry to hear that!", "input_spec": "The first line of the input contains integer n (1 ≤ n ≤ 105) — the money Dima wants to spend. Then follow four lines describing the guardposts. Each line contains four integers a, b, c, d (1 ≤ a, b, c, d ≤ 105) — the minimum price of the chocolate and the minimum price of the juice for the first guard and the minimum price of the chocolate and the minimum price of the juice for the second guard, correspondingly.", "output_spec": "In a single line of the output print three space-separated integers: the number of the guardpost, the cost of the first present and the cost of the second present. If there is no guardpost Dima can sneak Inna through at such conditions, print -1 in a single line.  The guardposts are numbered from 1 to 4 according to the order given in the input. If there are multiple solutions, you can print any of them.", "sample_inputs": ["10\n5 6 5 6\n6 6 7 7\n5 8 6 6\n9 9 9 9", "10\n6 6 6 6\n7 7 7 7\n4 4 4 4\n8 8 8 8", "5\n3 3 3 3\n3 3 3 3\n3 3 3 3\n3 3 3 3"], "sample_outputs": ["1 5 5", "3 4 6", "-1"], "notes": "NoteExplanation of the first example.The only way to spend 10 rubles to buy the gifts that won't be less than the minimum prices is to buy two 5 ruble chocolates to both guards from the first guardpost.Explanation of the second example.Dima needs 12 rubles for the first guardpost, 14 for the second one, 16 for the fourth one. So the only guardpost we can sneak through is the third one. So, Dima can buy 4 ruble chocolate for the first guard and 6 ruble juice of the second guard."}, "src_uid": "6e7ee0da980beb99ca49a5ddd04089a5"}
{"nl": {"description": "Recently a Golden Circle of Beetlovers was found in Byteland. It is a circle route going through $$$n \\cdot k$$$ cities. The cities are numerated from $$$1$$$ to $$$n \\cdot k$$$, the distance between the neighboring cities is exactly $$$1$$$ km.Sergey does not like beetles, he loves burgers. Fortunately for him, there are $$$n$$$ fast food restaurants on the circle, they are located in the $$$1$$$-st, the $$$(k + 1)$$$-st, the $$$(2k + 1)$$$-st, and so on, the $$$((n-1)k + 1)$$$-st cities, i.e. the distance between the neighboring cities with fast food restaurants is $$$k$$$ km.Sergey began his journey at some city $$$s$$$ and traveled along the circle, making stops at cities each $$$l$$$ km ($$$l > 0$$$), until he stopped in $$$s$$$ once again. Sergey then forgot numbers $$$s$$$ and $$$l$$$, but he remembers that the distance from the city $$$s$$$ to the nearest fast food restaurant was $$$a$$$ km, and the distance from the city he stopped at after traveling the first $$$l$$$ km from $$$s$$$ to the nearest fast food restaurant was $$$b$$$ km. Sergey always traveled in the same direction along the circle, but when he calculated distances to the restaurants, he considered both directions.Now Sergey is interested in two integers. The first integer $$$x$$$ is the minimum number of stops (excluding the first) Sergey could have done before returning to $$$s$$$. The second integer $$$y$$$ is the maximum number of stops (excluding the first) Sergey could have done before returning to $$$s$$$.", "input_spec": "The first line contains two integers $$$n$$$ and $$$k$$$ ($$$1 \\le n, k \\le 100\\,000$$$) — the number of fast food restaurants on the circle and the distance between the neighboring restaurants, respectively. The second line contains two integers $$$a$$$ and $$$b$$$ ($$$0 \\le a, b \\le \\frac{k}{2}$$$) — the distances to the nearest fast food restaurants from the initial city and from the city Sergey made the first stop at, respectively.", "output_spec": "Print the two integers $$$x$$$ and $$$y$$$.", "sample_inputs": ["2 3\n1 1", "3 2\n0 0", "1 10\n5 3"], "sample_outputs": ["1 6", "1 3", "5 5"], "notes": "NoteIn the first example the restaurants are located in the cities $$$1$$$ and $$$4$$$, the initial city $$$s$$$ could be $$$2$$$, $$$3$$$, $$$5$$$, or $$$6$$$. The next city Sergey stopped at could also be at cities $$$2, 3, 5, 6$$$. Let's loop through all possible combinations of these cities. If both $$$s$$$ and the city of the first stop are at the city $$$2$$$ (for example, $$$l = 6$$$), then Sergey is at $$$s$$$ after the first stop already, so $$$x = 1$$$. In other pairs Sergey needs $$$1, 2, 3$$$, or $$$6$$$ stops to return to $$$s$$$, so $$$y = 6$$$.In the second example Sergey was at cities with fast food restaurant both initially and after the first stop, so $$$l$$$ is $$$2$$$, $$$4$$$, or $$$6$$$. Thus $$$x = 1$$$, $$$y = 3$$$.In the third example there is only one restaurant, so the possible locations of $$$s$$$ and the first stop are: $$$(6, 8)$$$ and $$$(6, 4)$$$. For the first option $$$l = 2$$$, for the second $$$l = 8$$$. In both cases Sergey needs $$$x=y=5$$$ stops to go to $$$s$$$."}, "src_uid": "5bb4adff1b332f43144047955eefba0c"}
{"nl": {"description": "Vasya and Petya wrote down all integers from 1 to n to play the \"powers\" game (n can be quite large; however, Vasya and Petya are not confused by this fact).Players choose numbers in turn (Vasya chooses first). If some number x is chosen at the current turn, it is forbidden to choose x or all of its other positive integer powers (that is, x2, x3, ...) at the next turns. For instance, if the number 9 is chosen at the first turn, one cannot choose 9 or 81 later, while it is still allowed to choose 3 or 27. The one who cannot make a move loses.Who wins if both Vasya and Petya play optimally?", "input_spec": "Input contains single integer n (1 ≤ n ≤ 109).", "output_spec": "Print the name of the winner — \"Vasya\" or \"Petya\" (without quotes).", "sample_inputs": ["1", "2", "8"], "sample_outputs": ["Vasya", "Petya", "Petya"], "notes": "NoteIn the first sample Vasya will choose 1 and win immediately.In the second sample no matter which number Vasya chooses during his first turn, Petya can choose the remaining number and win."}, "src_uid": "0e22093668319217b7946e62afe32195"}
{"nl": {"description": "Anton has the integer x. He is interested what positive integer, which doesn't exceed x, has the maximum sum of digits.Your task is to help Anton and to find the integer that interests him. If there are several such integers, determine the biggest of them. ", "input_spec": "The first line contains the positive integer x (1 ≤ x ≤ 1018) — the integer which Anton has. ", "output_spec": "Print the positive integer which doesn't exceed x and has the maximum sum of digits. If there are several such integers, print the biggest of them. Printed integer must not contain leading zeros.", "sample_inputs": ["100", "48", "521"], "sample_outputs": ["99", "48", "499"], "notes": null}, "src_uid": "e55b0debbf33c266091e6634494356b8"}
{"nl": {"description": "Maxim has got a calculator. The calculator has two integer cells. Initially, the first cell contains number 1, and the second cell contains number 0. In one move you can perform one of the following operations:  Let's assume that at the current time the first cell contains number a, and the second cell contains number b. Write to the second cell number b + 1;  Let's assume that at the current time the first cell contains number a, and the second cell contains number b. Write to the first cell number a·b. Maxim is wondering, how many integers x (l ≤ x ≤ r) are there, such that we can write the number x to the first cell of the calculator, having performed at most p moves.", "input_spec": "The first line contains three integers: l, r, p (2 ≤ l ≤ r ≤ 109, 1 ≤ p ≤ 100).  The numbers in the line are separated by single spaces.", "output_spec": "In a single line print a single integer — the answer to the problem.", "sample_inputs": ["2 10 3", "2 111 100", "2 111 11"], "sample_outputs": ["1", "106", "47"], "notes": null}, "src_uid": "6d898638531e4713774bbd5d47e827bf"}
{"nl": {"description": "Being a nonconformist, Volodya is displeased with the current state of things, particularly with the order of natural numbers (natural number is positive integer number). He is determined to rearrange them. But there are too many natural numbers, so Volodya decided to start with the first n. He writes down the following sequence of numbers: firstly all odd integers from 1 to n (in ascending order), then all even integers from 1 to n (also in ascending order). Help our hero to find out which number will stand at the position number k.", "input_spec": "The only line of input contains integers n and k (1 ≤ k ≤ n ≤ 1012). Please, do not use the %lld specifier to read or write 64-bit integers in C++. It is preferred to use the cin, cout streams or the %I64d specifier.", "output_spec": "Print the number that will stand at the position number k after Volodya's manipulations.", "sample_inputs": ["10 3", "7 7"], "sample_outputs": ["5", "6"], "notes": "NoteIn the first sample Volodya's sequence will look like this: {1, 3, 5, 7, 9, 2, 4, 6, 8, 10}. The third place in the sequence is therefore occupied by the number 5."}, "src_uid": "1f8056884db00ad8294a7cc0be75fe97"}
{"nl": {"description": "The only difference between easy and hard versions is the constraints.Polycarp has to write a coursework. The coursework consists of $$$m$$$ pages.Polycarp also has $$$n$$$ cups of coffee. The coffee in the $$$i$$$-th cup has $$$a_i$$$ caffeine in it. Polycarp can drink some cups of coffee (each one no more than once). He can drink cups in any order. Polycarp drinks each cup instantly and completely (i.e. he cannot split any cup into several days).Surely, courseworks are not usually being written in a single day (in a perfect world of Berland, at least). Some of them require multiple days of hard work.Let's consider some day of Polycarp's work. Consider Polycarp drinks $$$k$$$ cups of coffee during this day and caffeine dosages of cups Polycarp drink during this day are $$$a_{i_1}, a_{i_2}, \\dots, a_{i_k}$$$. Then the first cup he drinks gives him energy to write $$$a_{i_1}$$$ pages of coursework, the second cup gives him energy to write $$$max(0, a_{i_2} - 1)$$$ pages, the third cup gives him energy to write $$$max(0, a_{i_3} - 2)$$$ pages, ..., the $$$k$$$-th cup gives him energy to write $$$max(0, a_{i_k} - k + 1)$$$ pages.If Polycarp doesn't drink coffee during some day, he cannot write coursework at all that day.Polycarp has to finish his coursework as soon as possible (spend the minimum number of days to do it). Your task is to find out this number of days or say that it is impossible.", "input_spec": "The first line of the input contains two integers $$$n$$$ and $$$m$$$ ($$$1 \\le n \\le 100$$$, $$$1 \\le m \\le 10^4$$$) — the number of cups of coffee and the number of pages in the coursework. The second line of the input contains $$$n$$$ integers $$$a_1, a_2, \\dots, a_n$$$ ($$$1 \\le a_i \\le 100$$$), where $$$a_i$$$ is the caffeine dosage of coffee in the $$$i$$$-th cup.", "output_spec": "If it is impossible to write the coursework, print -1. Otherwise print the minimum number of days Polycarp needs to do it.", "sample_inputs": ["5 8\n2 3 1 1 2", "7 10\n1 3 4 2 1 4 2", "5 15\n5 5 5 5 5", "5 16\n5 5 5 5 5", "5 26\n5 5 5 5 5"], "sample_outputs": ["4", "2", "1", "2", "-1"], "notes": "NoteIn the first example Polycarp can drink fourth cup during first day (and write $$$1$$$ page), first and second cups during second day (and write $$$2 + (3 - 1) = 4$$$ pages), fifth cup during the third day (and write $$$2$$$ pages) and third cup during the fourth day (and write $$$1$$$ page) so the answer is $$$4$$$. It is obvious that there is no way to write the coursework in three or less days in this test.In the second example Polycarp can drink third, fourth and second cups during first day (and write $$$4 + (2 - 1) + (3 - 2) = 6$$$ pages) and sixth cup during second day (and write $$$4$$$ pages) so the answer is $$$2$$$. It is obvious that Polycarp cannot write the whole coursework in one day in this test.In the third example Polycarp can drink all cups of coffee during first day and write $$$5 + (5 - 1) + (5 - 2) + (5 - 3) + (5 - 4) = 15$$$ pages of coursework.In the fourth example Polycarp cannot drink all cups during first day and should drink one of them during the second day. So during first day he will write $$$5 + (5 - 1) + (5 - 2) + (5 - 3) = 14$$$ pages of coursework and during second day he will write $$$5$$$ pages of coursework. This is enough to complete it.In the fifth example Polycarp cannot write the whole coursework at all, even if he will drink one cup of coffee during each day, so the answer is -1."}, "src_uid": "acb8a57c8cfdb849a55fa65aff86628d"}
{"nl": {"description": "At regular competition Vladik and Valera won a and b candies respectively. Vladik offered 1 his candy to Valera. After that Valera gave Vladik 2 his candies, so that no one thought that he was less generous. Vladik for same reason gave 3 candies to Valera in next turn.More formally, the guys take turns giving each other one candy more than they received in the previous turn.This continued until the moment when one of them couldn’t give the right amount of candy. Candies, which guys got from each other, they don’t consider as their own. You need to know, who is the first who can’t give the right amount of candy.", "input_spec": "Single line of input data contains two space-separated integers a, b (1 ≤ a, b ≤ 109) — number of Vladik and Valera candies respectively.", "output_spec": "Pring a single line \"Vladik’’ in case, if Vladik first who can’t give right amount of candy, or \"Valera’’ otherwise.", "sample_inputs": ["1 1", "7 6"], "sample_outputs": ["Valera", "Vladik"], "notes": "NoteIllustration for first test case:Illustration for second test case:"}, "src_uid": "87e37a82be7e39e433060fd8cdb03270"}
{"nl": {"description": "Petya studies positional notations. He has already learned to add and subtract numbers in the systems of notations with different radices and has moved on to a more complicated action — multiplication. To multiply large numbers one has to learn the multiplication table. Unfortunately, in the second grade students learn only the multiplication table of decimals (and some students even learn it in the first grade). Help Petya make a multiplication table for numbers in the system of notations with the radix k.", "input_spec": "The first line contains a single integer k (2 ≤ k ≤ 10) — the radix of the system.", "output_spec": "Output the multiplication table for the system of notations with the radix k. The table must contain k - 1 rows and k - 1 columns. The element on the crossing of the i-th row and the j-th column is equal to the product of i and j in the system of notations with the radix k. Each line may have any number of spaces between the numbers (the extra spaces in the samples are put for clarity).", "sample_inputs": ["10", "3"], "sample_outputs": ["1  2  3  4  5  6  7  8  9\n2  4  6  8 10 12 14 16 18\n3  6  9 12 15 18 21 24 27\n4  8 12 16 20 24 28 32 36\n5 10 15 20 25 30 35 40 45\n6 12 18 24 30 36 42 48 54\n7 14 21 28 35 42 49 56 63\n8 16 24 32 40 48 56 64 72\n9 18 27 36 45 54 63 72 81", "1  2\n2 11"], "notes": null}, "src_uid": "a705144ace798d6b41068aa284d99050"}
{"nl": {"description": "Paul is at the orchestra. The string section is arranged in an r × c rectangular grid and is filled with violinists with the exception of n violists. Paul really likes violas, so he would like to take a picture including at least k of them. Paul can take a picture of any axis-parallel rectangle in the orchestra. Count the number of possible pictures that Paul can take.Two pictures are considered to be different if the coordinates of corresponding rectangles are different.", "input_spec": "The first line of input contains four space-separated integers r, c, n, k (1 ≤ r, c, n ≤ 3000, 1 ≤ k ≤ min(n, 10)) — the number of rows and columns of the string section, the total number of violas, and the minimum number of violas Paul would like in his photograph, respectively. The next n lines each contain two integers xi and yi (1 ≤ xi ≤ r, 1 ≤ yi ≤ c): the position of the i-th viola. It is guaranteed that no location appears more than once in the input.", "output_spec": "Print a single integer — the number of photographs Paul can take which include at least k violas. ", "sample_inputs": ["2 2 1 1\n1 2", "3 2 3 3\n1 1\n3 1\n2 2", "3 2 3 2\n1 1\n3 1\n2 2"], "sample_outputs": ["4", "1", "4"], "notes": "NoteWe will use '*' to denote violinists and '#' to denote violists.In the first sample, the orchestra looks as follows: *#** Paul can take a photograph of just the viola, the 1 × 2 column containing the viola, the 2 × 1 row containing the viola, or the entire string section, for 4 pictures total.In the second sample, the orchestra looks as follows: #**##* Paul must take a photograph of the entire section.In the third sample, the orchestra looks the same as in the second sample."}, "src_uid": "9c766881f6415e2f53fb43b61f8f40b4"}
{"nl": {"description": "This night wasn't easy on Vasya. His favorite team lost, and he didn't find himself victorious either — although he played perfectly, his teammates let him down every time. He had to win at least one more time, but the losestreak only grew longer and longer... It's no wonder he didn't get any sleep this night at all.In the morning, Vasya was waiting the bus to the university on the bus stop. Vasya's thoughts were hazy and so he couldn't remember the right bus' number quite right and got onto the bus with the number $$$n$$$.In the bus, Vasya thought that he could get the order of the digits in the number of the bus wrong. Futhermore, he could \"see\" some digits several times, but the digits he saw were definitely in the real number of the bus. For example, if Vasya saw the number 2028, it could mean that the real bus number could be 2028, 8022, 2820 or just 820. However, numbers 80, 22208, 52 definitely couldn't be the number of the bus. Also, real bus number couldn't start with the digit 0, this meaning that, for example, number 082 couldn't be the real bus number too.Given $$$n$$$, determine the total number of possible bus number variants.", "input_spec": "The first line contains one integer $$$n$$$ ($$$1 \\leq n \\leq 10^{18}$$$) — the number of the bus that was seen by Vasya. It is guaranteed that this number does not start with $$$0$$$.", "output_spec": "Output a single integer — the amount of possible variants of the real bus number.", "sample_inputs": ["97", "2028"], "sample_outputs": ["2", "13"], "notes": "NoteIn the first sample, only variants $$$97$$$ and $$$79$$$ are possible.In the second sample, the variants (in the increasing order) are the following: $$$208$$$, $$$280$$$, $$$802$$$, $$$820$$$, $$$2028$$$, $$$2082$$$, $$$2208$$$, $$$2280$$$, $$$2802$$$, $$$2820$$$, $$$8022$$$, $$$8202$$$, $$$8220$$$."}, "src_uid": "7f4e533f49b73cc2b96b4c56847295f2"}
{"nl": {"description": "Vasya works as a watchman in the gallery. Unfortunately, one of the most expensive paintings was stolen while he was on duty. He doesn't want to be fired, so he has to quickly restore the painting. He remembers some facts about it.  The painting is a square 3 × 3, each cell contains a single integer from 1 to n, and different cells may contain either different or equal integers.  The sum of integers in each of four squares 2 × 2 is equal to the sum of integers in the top left square 2 × 2.  Four elements a, b, c and d are known and are located as shown on the picture below. Help Vasya find out the number of distinct squares the satisfy all the conditions above. Note, that this number may be equal to 0, meaning Vasya remembers something wrong.Two squares are considered to be different, if there exists a cell that contains two different integers in different squares.", "input_spec": "The first line of the input contains five integers n, a, b, c and d (1 ≤ n ≤ 100 000, 1 ≤ a, b, c, d ≤ n) — maximum possible value of an integer in the cell and four integers that Vasya remembers.", "output_spec": "Print one integer — the number of distinct valid squares.", "sample_inputs": ["2 1 1 1 2", "3 3 1 2 3"], "sample_outputs": ["2", "6"], "notes": "NoteBelow are all the possible paintings for the first sample.  In the second sample, only paintings displayed below satisfy all the rules.      "}, "src_uid": "b732869015baf3dee5094c51a309e32c"}
{"nl": {"description": "Recently, a chaotic virus Hexadecimal advanced a new theorem which will shake the Universe. She thinks that each Fibonacci number can be represented as sum of three not necessary different Fibonacci numbers.Let's remember how Fibonacci numbers can be calculated. F0 = 0, F1 = 1, and all the next numbers are Fi = Fi - 2 + Fi - 1.So, Fibonacci numbers make a sequence of numbers: 0, 1, 1, 2, 3, 5, 8, 13, ...If you haven't run away from the PC in fear, you have to help the virus. Your task is to divide given Fibonacci number n by three not necessary different Fibonacci numbers or say that it is impossible.", "input_spec": "The input contains of a single integer n (0 ≤ n < 109) — the number that should be represented by the rules described above. It is guaranteed that n is a Fibonacci number.", "output_spec": "Output three required numbers: a, b and c. If there is no answer for the test you have to print \"I'm too stupid to solve this problem\" without the quotes. If there are multiple answers, print any of them.", "sample_inputs": ["3", "13"], "sample_outputs": ["1 1 1", "2 3 8"], "notes": null}, "src_uid": "db46a6b0380df047aa34ea6a8f0f93c1"}
{"nl": {"description": "Bob is decorating his kitchen, more precisely, the floor. He has found a prime candidate for the tiles he will use. They come in a simple form factor — a square tile that is diagonally split into white and black part as depicted in the figure below.  The dimension of this tile is perfect for this kitchen, as he will need exactly $$$w \\times h$$$ tiles without any scraps. That is, the width of the kitchen is $$$w$$$ tiles, and the height is $$$h$$$ tiles. As each tile can be rotated in one of four ways, he still needs to decide on how exactly he will tile the floor. There is a single aesthetic criterion that he wants to fulfil: two adjacent tiles must not share a colour on the edge — i.e. one of the tiles must have a white colour on the shared border, and the second one must be black.    The picture on the left shows one valid tiling of a $$$3 \\times 2$$$ kitchen. The picture on the right shows an invalid arrangement, as the bottom two tiles touch with their white parts. Find the number of possible tilings. As this number may be large, output its remainder when divided by $$$998244353$$$ (a prime number). ", "input_spec": "The only line contains two space separated integers $$$w$$$, $$$h$$$ ($$$1 \\leq w,h \\leq 1\\,000$$$) — the width and height of the kitchen, measured in tiles.", "output_spec": "Output a single integer $$$n$$$ — the remainder of the number of tilings when divided by $$$998244353$$$.", "sample_inputs": ["2 2", "2 4"], "sample_outputs": ["16", "64"], "notes": null}, "src_uid": "8b2a9ae21740c89079a6011a30cd6aee"}
{"nl": {"description": "Have you ever tried to explain to the coordinator, why it is eight hours to the contest and not a single problem has been prepared yet? Misha had. And this time he has a really strong excuse: he faced a space-time paradox! Space and time replaced each other.The entire universe turned into an enormous clock face with three hands — hour, minute, and second. Time froze, and clocks now show the time h hours, m minutes, s seconds.Last time Misha talked with the coordinator at t1 o'clock, so now he stands on the number t1 on the clock face. The contest should be ready by t2 o'clock. In the terms of paradox it means that Misha has to go to number t2 somehow. Note that he doesn't have to move forward only: in these circumstances time has no direction.Clock hands are very long, and Misha cannot get round them. He also cannot step over as it leads to the collapse of space-time. That is, if hour clock points 12 and Misha stands at 11 then he cannot move to 1 along the top arc. He has to follow all the way round the clock center (of course, if there are no other hands on his way).Given the hands' positions, t1, and t2, find if Misha can prepare the contest on time (or should we say on space?). That is, find if he can move from t1 to t2 by the clock face.", "input_spec": "Five integers h, m, s, t1, t2 (1 ≤ h ≤ 12, 0 ≤ m, s ≤ 59, 1 ≤ t1, t2 ≤ 12, t1 ≠ t2). Misha's position and the target time do not coincide with the position of any hand.", "output_spec": "Print \"YES\" (quotes for clarity), if Misha can prepare the contest on time, and \"NO\" otherwise. You can print each character either upper- or lowercase (\"YeS\" and \"yes\" are valid when the answer is \"YES\").", "sample_inputs": ["12 30 45 3 11", "12 0 1 12 1", "3 47 0 4 9"], "sample_outputs": ["NO", "YES", "YES"], "notes": "NoteThe three examples are shown on the pictures below from left to right. The starting position of Misha is shown with green, the ending position is shown with pink. Note that the positions of the hands on the pictures are not exact, but are close to the exact and the answer is the same.  "}, "src_uid": "912c8f557a976bdedda728ba9f916c95"}
{"nl": {"description": "To get money for a new aeonic blaster, ranger Qwerty decided to engage in trade for a while. He wants to buy some number of items (or probably not to buy anything at all) on one of the planets, and then sell the bought items on another planet. Note that this operation is not repeated, that is, the buying and the selling are made only once. To carry out his plan, Qwerty is going to take a bank loan that covers all expenses and to return the loaned money at the end of the operation (the money is returned without the interest). At the same time, Querty wants to get as much profit as possible.The system has n planets in total. On each of them Qwerty can buy or sell items of m types (such as food, medicine, weapons, alcohol, and so on). For each planet i and each type of items j Qwerty knows the following: aij — the cost of buying an item;  bij — the cost of selling an item;  cij — the number of remaining items.It is not allowed to buy more than cij items of type j on planet i, but it is allowed to sell any number of items of any kind.Knowing that the hold of Qwerty's ship has room for no more than k items, determine the maximum profit which Qwerty can get.", "input_spec": "The first line contains three space-separated integers n, m and k (2 ≤ n ≤ 10, 1 ≤ m, k ≤ 100) — the number of planets, the number of question types and the capacity of Qwerty's ship hold, correspondingly. Then follow n blocks describing each planet. The first line of the i-th block has the planet's name as a string with length from 1 to 10 Latin letters. The first letter of the name is uppercase, the rest are lowercase. Then in the i-th block follow m lines, the j-th of them contains three integers aij, bij and cij (1 ≤ bij < aij ≤ 1000, 0 ≤ cij ≤ 100) — the numbers that describe money operations with the j-th item on the i-th planet. The numbers in the lines are separated by spaces. It is guaranteed that the names of all planets are different.", "output_spec": "Print a single number — the maximum profit Qwerty can get.", "sample_inputs": ["3 3 10\nVenus\n6 5 3\n7 6 5\n8 6 10\nEarth\n10 9 0\n8 6 4\n10 9 3\nMars\n4 3 0\n8 4 12\n7 2 5"], "sample_outputs": ["16"], "notes": "NoteIn the first test case you should fly to planet Venus, take a loan on 74 units of money and buy three items of the first type and 7 items of the third type (3·6 + 7·8 = 74). Then the ranger should fly to planet Earth and sell there all the items he has bought. He gets 3·9 + 7·9 = 90 units of money for the items, he should give 74 of them for the loan. The resulting profit equals 16 units of money. We cannot get more profit in this case."}, "src_uid": "7419c4268a9815282fadca6581f28ec1"}
{"nl": {"description": "zscoder wants to generate an input file for some programming competition problem.His input is a string consisting of n letters 'a'. He is too lazy to write a generator so he will manually generate the input in a text editor.Initially, the text editor is empty. It takes him x seconds to insert or delete a letter 'a' from the text file and y seconds to copy the contents of the entire text file, and duplicate it.zscoder wants to find the minimum amount of time needed for him to create the input file of exactly n letters 'a'. Help him to determine the amount of time needed to generate the input.", "input_spec": "The only line contains three integers n, x and y (1 ≤ n ≤ 107, 1 ≤ x, y ≤ 109) — the number of letters 'a' in the input file and the parameters from the problem statement.", "output_spec": "Print the only integer t — the minimum amount of time needed to generate the input file.", "sample_inputs": ["8 1 1", "8 1 10"], "sample_outputs": ["4", "8"], "notes": null}, "src_uid": "0f270af00be2a523515d5e7bd66800f6"}
{"nl": {"description": "The only king stands on the standard chess board. You are given his position in format \"cd\", where c is the column from 'a' to 'h' and d is the row from '1' to '8'. Find the number of moves permitted for the king.Check the king's moves here https://en.wikipedia.org/wiki/King_(chess).  King moves from the position e4 ", "input_spec": "The only line contains the king's position in the format \"cd\", where 'c' is the column from 'a' to 'h' and 'd' is the row from '1' to '8'.", "output_spec": "Print the only integer x — the number of moves permitted for the king.", "sample_inputs": ["e4"], "sample_outputs": ["8"], "notes": null}, "src_uid": "6994331ca6282669cbb7138eb7e55e01"}
{"nl": {"description": "Reca company makes monitors, the most popular of their models is AB999 with the screen size a × b centimeters. Because of some production peculiarities a screen parameters are integer numbers. Recently the screen sides ratio x: y became popular with users. That's why the company wants to reduce monitor AB999 size so that its screen sides ratio becomes x: y, at the same time they want its total area to be maximal of all possible variants. Your task is to find the screen parameters of the reduced size model, or find out that such a reduction can't be performed.", "input_spec": "The first line of the input contains 4 integers — a, b, x and y (1 ≤ a, b, x, y ≤ 2·109).", "output_spec": "If the answer exists, output 2 positive integers — screen parameters of the reduced size model. Output 0 0 otherwise.", "sample_inputs": ["800 600 4 3", "1920 1200 16 9", "1 1 1 2"], "sample_outputs": ["800 600", "1920 1080", "0 0"], "notes": null}, "src_uid": "97999cd7c6de79a4e39f56a41ff59e7a"}
{"nl": {"description": "The start of the new academic year brought about the problem of accommodation students into dormitories. One of such dormitories has a a × b square meter wonder room. The caretaker wants to accommodate exactly n students there. But the law says that there must be at least 6 square meters per student in a room (that is, the room for n students must have the area of at least 6n square meters). The caretaker can enlarge any (possibly both) side of the room by an arbitrary positive integer of meters. Help him change the room so as all n students could live in it and the total area of the room was as small as possible.", "input_spec": "The first line contains three space-separated integers n, a and b (1 ≤ n, a, b ≤ 109) — the number of students and the sizes of the room.", "output_spec": "Print three integers s, a1 and b1 (a ≤ a1; b ≤ b1) — the final area of the room and its sizes. If there are multiple optimal solutions, print any of them.", "sample_inputs": ["3 3 5", "2 4 4"], "sample_outputs": ["18\n3 6", "16\n4 4"], "notes": null}, "src_uid": "6a2a584d36008151d18e5080aea5029c"}
{"nl": {"description": "You can't possibly imagine how cold our friends are this winter in Nvodsk! Two of them play the following game to warm up: initially a piece of paper has an integer q. During a move a player should write any integer number that is a non-trivial divisor of the last written number. Then he should run this number of circles around the hotel. Let us remind you that a number's divisor is called non-trivial if it is different from one and from the divided number itself. The first person who can't make a move wins as he continues to lie in his warm bed under three blankets while the other one keeps running. Determine which player wins considering that both players play optimally. If the first player wins, print any winning first move.", "input_spec": "The first line contains the only integer q (1 ≤ q ≤ 1013). Please do not use the %lld specificator to read or write 64-bit integers in С++. It is preferred to use the cin, cout streams or the %I64d specificator.", "output_spec": "In the first line print the number of the winning player (1 or 2). If the first player wins then the second line should contain another integer — his first move (if the first player can't even make the first move, print 0). If there are multiple solutions, print any of them.", "sample_inputs": ["6", "30", "1"], "sample_outputs": ["2", "1\n6", "1\n0"], "notes": "NoteNumber 6 has only two non-trivial divisors: 2 and 3. It is impossible to make a move after the numbers 2 and 3 are written, so both of them are winning, thus, number 6 is the losing number. A player can make a move and write number 6 after number 30; 6, as we know, is a losing number. Thus, this move will bring us the victory."}, "src_uid": "f0a138b9f6ad979c5ca32437e05d6f43"}
{"nl": {"description": "Tomorrow Peter has a Biology exam. He does not like this subject much, but d days ago he learnt that he would have to take this exam. Peter's strict parents made him prepare for the exam immediately, for this purpose he has to study not less than minTimei and not more than maxTimei hours per each i-th day. Moreover, they warned Peter that a day before the exam they would check how he has followed their instructions.So, today is the day when Peter's parents ask him to show the timetable of his preparatory studies. But the boy has counted only the sum of hours sumTime spent him on preparation, and now he wants to know if he can show his parents a timetable sсhedule with d numbers, where each number sсhedulei stands for the time in hours spent by Peter each i-th day on biology studies, and satisfying the limitations imposed by his parents, and at the same time the sum total of all schedulei should equal to sumTime.", "input_spec": "The first input line contains two integer numbers d, sumTime (1 ≤ d ≤ 30, 0 ≤ sumTime ≤ 240) — the amount of days, during which Peter studied, and the total amount of hours, spent on preparation. Each of the following d lines contains two integer numbers minTimei, maxTimei (0 ≤ minTimei ≤ maxTimei ≤ 8), separated by a space — minimum and maximum amount of hours that Peter could spent in the i-th day.", "output_spec": "In the first line print YES, and in the second line print d numbers (separated by a space), each of the numbers — amount of hours, spent by Peter on preparation in the corresponding day, if he followed his parents' instructions; or print NO in the unique line. If there are many solutions, print any of them.", "sample_inputs": ["1 48\n5 7", "2 5\n0 1\n3 5"], "sample_outputs": ["NO", "YES\n1 4"], "notes": null}, "src_uid": "f48ff06e65b70f49eee3d7cba5a6aed0"}
{"nl": {"description": "Ted has a pineapple. This pineapple is able to bark like a bulldog! At time t (in seconds) it barks for the first time. Then every s seconds after it, it barks twice with 1 second interval. Thus it barks at times t, t + s, t + s + 1, t + 2s, t + 2s + 1, etc.  Barney woke up in the morning and wants to eat the pineapple, but he can't eat it when it's barking. Barney plans to eat it at time x (in seconds), so he asked you to tell him if it's gonna bark at that time.", "input_spec": "The first and only line of input contains three integers t, s and x (0 ≤ t, x ≤ 109, 2 ≤ s ≤ 109) — the time the pineapple barks for the first time, the pineapple barking interval, and the time Barney wants to eat the pineapple respectively.", "output_spec": "Print a single \"YES\" (without quotes) if the pineapple will bark at time x or a single \"NO\" (without quotes) otherwise in the only line of output.", "sample_inputs": ["3 10 4", "3 10 3", "3 8 51", "3 8 52"], "sample_outputs": ["NO", "YES", "YES", "YES"], "notes": "NoteIn the first and the second sample cases pineapple will bark at moments 3, 13, 14, ..., so it won't bark at the moment 4 and will bark at the moment 3.In the third and fourth sample cases pineapple will bark at moments 3, 11, 12, 19, 20, 27, 28, 35, 36, 43, 44, 51, 52, 59, ..., so it will bark at both moments 51 and 52."}, "src_uid": "3baf9d841ff7208c66f6de1b47b0f952"}
{"nl": {"description": "The Smart Beaver from ABBYY loves puzzles. One of his favorite puzzles is the magic square. He has recently had an idea to automate the solution of this puzzle. The Beaver decided to offer this challenge to the ABBYY Cup contestants.The magic square is a matrix of size n × n. The elements of this matrix are integers. The sum of numbers in each row of the matrix is equal to some number s. The sum of numbers in each column of the matrix is also equal to s. In addition, the sum of the elements on the main diagonal is equal to s and the sum of elements on the secondary diagonal is equal to s. Examples of magic squares are given in the following figure:   Magic squares  You are given a set of n2 integers ai. It is required to place these numbers into a square matrix of size n × n so that they form a magic square. Note that each number must occur in the matrix exactly the same number of times as it occurs in the original set.It is guaranteed that a solution exists!", "input_spec": "The first input line contains a single integer n. The next line contains n2 integers ai ( - 108 ≤ ai ≤ 108), separated by single spaces. The input limitations for getting 20 points are:    1 ≤ n ≤ 3  The input limitations for getting 50 points are:    1 ≤ n ≤ 4  It is guaranteed that there are no more than 9 distinct numbers among ai.  The input limitations for getting 100 points are:    1 ≤ n ≤ 4 ", "output_spec": "The first line of the output should contain a single integer s. In each of the following n lines print n integers, separated by spaces and describing the resulting magic square. In the resulting magic square the sums in the rows, columns and diagonals must be equal to s. If there are multiple solutions, you are allowed to print any of them.", "sample_inputs": ["3\n1 2 3 4 5 6 7 8 9", "3\n1 0 -1 0 2 -1 -2 0 1", "2\n5 5 5 5"], "sample_outputs": ["15\n2 7 6\n9 5 1\n4 3 8", "0\n1 0 -1\n-2 0 2\n1 0 -1", "10\n5 5\n5 5"], "notes": null}, "src_uid": "7c806fb163aaf23e1eef3e6570aea436"}
{"nl": {"description": "You are given a sequence a consisting of n integers. You may partition this sequence into two sequences b and c in such a way that every element belongs exactly to one of these sequences. Let B be the sum of elements belonging to b, and C be the sum of elements belonging to c (if some of these sequences is empty, then its sum is 0). What is the maximum possible value of B - C?", "input_spec": "The first line contains one integer n (1 ≤ n ≤ 100) — the number of elements in a. The second line contains n integers a1, a2, ..., an ( - 100 ≤ ai ≤ 100) — the elements of sequence a.", "output_spec": "Print the maximum possible value of B - C, where B is the sum of elements of sequence b, and C is the sum of elements of sequence c.", "sample_inputs": ["3\n1 -2 0", "6\n16 23 16 15 42 8"], "sample_outputs": ["3", "120"], "notes": "NoteIn the first example we may choose b = {1, 0}, c = { - 2}. Then B = 1, C =  - 2, B - C = 3.In the second example we choose b = {16, 23, 16, 15, 42, 8}, c = {} (an empty sequence). Then B = 120, C = 0, B - C = 120."}, "src_uid": "4b5d14833f9b51bfd336cc0e661243a5"}
{"nl": {"description": "Iahub got bored, so he invented a game to be played on paper. He writes n integers a1, a2, ..., an. Each of those integers can be either 0 or 1. He's allowed to do exactly one move: he chooses two indices i and j (1 ≤ i ≤ j ≤ n) and flips all values ak for which their positions are in range [i, j] (that is i ≤ k ≤ j). Flip the value of x means to apply operation x = 1 - x.The goal of the game is that after exactly one move to obtain the maximum number of ones. Write a program to solve the little game of Iahub.", "input_spec": "The first line of the input contains an integer n (1 ≤ n ≤ 100). In the second line of the input there are n integers: a1, a2, ..., an. It is guaranteed that each of those n values is either 0 or 1.", "output_spec": "Print an integer — the maximal number of 1s that can be obtained after exactly one move. ", "sample_inputs": ["5\n1 0 0 1 0", "4\n1 0 0 1"], "sample_outputs": ["4", "4"], "notes": "NoteIn the first case, flip the segment from 2 to 5 (i = 2, j = 5). That flip changes the sequence, it becomes: [1 1 1 0 1]. So, it contains four ones. There is no way to make the whole sequence equal to [1 1 1 1 1].In the second case, flipping only the second and the third element (i = 2, j = 3) will turn all numbers into 1."}, "src_uid": "9b543e07e805fe1dd8fa869d5d7c8b99"}
{"nl": {"description": "As a tradition, every year before IOI all the members of Natalia Fan Club are invited to Malek Dance Club to have a fun night together. Malek Dance Club has 2n members and coincidentally Natalia Fan Club also has 2n members. Each member of MDC is assigned a unique id i from 0 to 2n - 1. The same holds for each member of NFC.One of the parts of this tradition is one by one dance, where each member of MDC dances with a member of NFC. A dance pair is a pair of numbers (a, b) such that member a from MDC dances with member b from NFC.The complexity of a pairs' assignment is the number of pairs of dancing pairs (a, b) and (c, d) such that a < c and b > d.You are given a binary number of length n named x. We know that member i from MDC dances with member  from NFC. Your task is to calculate the complexity of this assignment modulo 1000000007 (109 + 7).Expression  denotes applying «XOR» to numbers x and y. This operation exists in all modern programming languages, for example, in C++ and Java it denotes as «^», in Pascal — «xor».", "input_spec": "The first line of input contains a binary number x of lenght n, (1 ≤ n ≤ 100). This number may contain leading zeros.", "output_spec": "Print the complexity of the given dance assignent modulo 1000000007 (109 + 7).", "sample_inputs": ["11", "01", "1"], "sample_outputs": ["6", "2", "1"], "notes": null}, "src_uid": "89b51a31e00424edd1385f2120028b9d"}
{"nl": {"description": "Polycarpus has recently got interested in sequences of pseudorandom numbers. He learned that many programming languages generate such sequences in a similar way:  (for i ≥ 1). Here a, b, m are constants, fixed for the given realization of the pseudorandom numbers generator, r0 is the so-called randseed (this value can be set from the program using functions like RandSeed(r) or srand(n)), and  denotes the operation of taking the remainder of division.For example, if a = 2, b = 6, m = 12, r0 = 11, the generated sequence will be: 4, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, ....Polycarpus realized that any such sequence will sooner or later form a cycle, but the cycle may occur not in the beginning, so there exist a preperiod and a period. The example above shows a preperiod equal to 1 and a period equal to 2.Your task is to find the period of a sequence defined by the given values of a, b, m and r0. Formally, you have to find such minimum positive integer t, for which exists such positive integer k, that for any i ≥ k: ri = ri + t.", "input_spec": "The single line of the input contains four integers a, b, m and r0 (1 ≤ m ≤ 105, 0 ≤ a, b ≤ 1000, 0 ≤ r0 < m), separated by single spaces.", "output_spec": "Print a single integer — the period of the sequence.", "sample_inputs": ["2 6 12 11", "2 3 5 1", "3 6 81 9"], "sample_outputs": ["2", "4", "1"], "notes": "NoteThe first sample is described above. In the second sample the sequence is (starting from the first element): 0, 3, 4, 1, 0, 3, 4, 1, 0, ...In the third sample the sequence is (starting from the first element): 33, 24, 78, 78, 78, 78, ..."}, "src_uid": "9137197ee1b781cd5cc77c46f50b9012"}
{"nl": {"description": "An n × n table a is defined as follows:  The first row and the first column contain ones, that is: ai, 1 = a1, i = 1 for all i = 1, 2, ..., n.  Each of the remaining numbers in the table is equal to the sum of the number above it and the number to the left of it. In other words, the remaining elements are defined by the formula ai, j = ai - 1, j + ai, j - 1. These conditions define all the values in the table.You are given a number n. You need to determine the maximum value in the n × n table defined by the rules above.", "input_spec": "The only line of input contains a positive integer n (1 ≤ n ≤ 10) — the number of rows and columns of the table.", "output_spec": "Print a single line containing a positive integer m — the maximum value in the table.", "sample_inputs": ["1", "5"], "sample_outputs": ["1", "70"], "notes": "NoteIn the second test the rows of the table look as follows: {1, 1, 1, 1, 1},  {1, 2, 3, 4, 5},  {1, 3, 6, 10, 15},  {1, 4, 10, 20, 35},  {1, 5, 15, 35, 70}."}, "src_uid": "2f650aae9dfeb02533149ced402b60dc"}
{"nl": {"description": "Devu wants to decorate his garden with flowers. He has purchased n boxes, where the i-th box contains fi flowers. All flowers in a single box are of the same color (hence they are indistinguishable). Also, no two boxes have flowers of the same color.Now Devu wants to select exactly s flowers from the boxes to decorate his garden. Devu would like to know, in how many different ways can he select the flowers from each box? Since this number may be very large, he asks you to find the number modulo (109 + 7). Devu considers two ways different if there is at least one box from which different number of flowers are selected in these two ways.", "input_spec": "The first line of input contains two space-separated integers n and s (1 ≤ n ≤ 20, 0 ≤ s ≤ 1014). The second line contains n space-separated integers f1, f2, ... fn (0 ≤ fi ≤ 1012).", "output_spec": "Output a single integer — the number of ways in which Devu can select the flowers modulo (109 + 7).", "sample_inputs": ["2 3\n1 3", "2 4\n2 2", "3 5\n1 3 2"], "sample_outputs": ["2", "1", "3"], "notes": "NoteSample 1. There are two ways of selecting 3 flowers: {1, 2} and {0, 3}.Sample 2. There is only one way of selecting 4 flowers: {2, 2}.Sample 3. There are three ways of selecting 5 flowers: {1, 2, 2}, {0, 3, 2}, and {1, 3, 1}."}, "src_uid": "8b883011eba9d15d284e54c7a85fcf74"}
{"nl": {"description": "Consider some square matrix A with side n consisting of zeros and ones. There are n rows numbered from 1 to n from top to bottom and n columns numbered from 1 to n from left to right in this matrix. We'll denote the element of the matrix which is located at the intersection of the i-row and the j-th column as Ai, j.Let's call matrix A clear if no two cells containing ones have a common side.Let's call matrix A symmetrical if it matches the matrices formed from it by a horizontal and/or a vertical reflection. Formally, for each pair (i, j) (1 ≤ i, j ≤ n) both of the following conditions must be met: Ai, j = An - i + 1, j and Ai, j = Ai, n - j + 1.Let's define the sharpness of matrix A as the number of ones in it.Given integer x, your task is to find the smallest positive integer n such that there exists a clear symmetrical matrix A with side n and sharpness x.", "input_spec": "The only line contains a single integer x (1 ≤ x ≤ 100) — the required sharpness of the matrix.", "output_spec": "Print a single number — the sought value of n.", "sample_inputs": ["4", "9"], "sample_outputs": ["3", "5"], "notes": "NoteThe figure below shows the matrices that correspond to the samples:  "}, "src_uid": "01eccb722b09a0474903b7e5abc4c47a"}
{"nl": {"description": "Polycarp and Vasiliy love simple logical games. Today they play a game with infinite chessboard and one pawn for each player. Polycarp and Vasiliy move in turns, Polycarp starts. In each turn Polycarp can move his pawn from cell (x, y) to (x - 1, y) or (x, y - 1). Vasiliy can move his pawn from (x, y) to one of cells: (x - 1, y), (x - 1, y - 1) and (x, y - 1). Both players are also allowed to skip move. There are some additional restrictions — a player is forbidden to move his pawn to a cell with negative x-coordinate or y-coordinate or to the cell containing opponent's pawn The winner is the first person to reach cell (0, 0). You are given the starting coordinates of both pawns. Determine who will win if both of them play optimally well.", "input_spec": "The first line contains four integers: xp, yp, xv, yv (0 ≤ xp, yp, xv, yv ≤ 105) — Polycarp's and Vasiliy's starting coordinates. It is guaranteed that in the beginning the pawns are in different cells and none of them is in the cell (0, 0).", "output_spec": "Output the name of the winner: \"Polycarp\" or \"Vasiliy\".", "sample_inputs": ["2 1 2 2", "4 7 7 4"], "sample_outputs": ["Polycarp", "Vasiliy"], "notes": "NoteIn the first sample test Polycarp starts in (2, 1) and will move to (1, 1) in the first turn. No matter what his opponent is doing, in the second turn Polycarp can move to (1, 0) and finally to (0, 0) in the third turn."}, "src_uid": "2637d57f7809ff8f922549c617709074"}
{"nl": {"description": "Throughout Igor K.'s life he has had many situations worthy of attention. We remember the story with the virus, the story of his mathematical career and of course, his famous programming achievements. However, one does not always adopt new hobbies, one can quit something as well.This time Igor K. got disappointed in one of his hobbies: editing and voicing videos. Moreover, he got disappointed in it so much, that he decided to destroy his secret archive for good. Igor K. use Pindows XR operation system which represents files and folders by small icons. At that, m icons can fit in a horizontal row in any window.Igor K.'s computer contains n folders in the D: disk's root catalog. The folders are numbered from 1 to n in the order from the left to the right and from top to bottom (see the images). At that the folders with secret videos have numbers from a to b inclusive. Igor K. wants to delete them forever, at that making as few frame selections as possible, and then pressing Shift+Delete exactly once. What is the minimum number of times Igor K. will have to select the folder in order to select folders from a to b and only them? Let us note that if some selected folder is selected repeatedly, then it is deselected. Each selection possesses the shape of some rectangle with sides parallel to the screen's borders.", "input_spec": "The only line contains four integers n, m, a, b (1 ≤ n, m ≤ 109, 1 ≤ a ≤ b ≤ n). They are the number of folders in Igor K.'s computer, the width of a window and the numbers of the first and the last folders that need to be deleted.", "output_spec": "Print a single number: the least possible number of times Igor K. will have to select the folders using frames to select only the folders with numbers from a to b.", "sample_inputs": ["11 4 3 9", "20 5 2 20"], "sample_outputs": ["3", "2"], "notes": "NoteThe images below illustrate statement tests.The first test:In this test we can select folders 3 and 4 with out first selection, folders 5, 6, 7, 8 with our second selection and folder 9 with our third, last selection.The second test:In this test we can first select all folders in the first row (2, 3, 4, 5), then — all other ones."}, "src_uid": "f256235c0b2815aae85a6f9435c69dac"}
{"nl": {"description": "John Doe has recently found a \"Free Market\" in his city — that is the place where you can exchange some of your possessions for other things for free. John knows that his city has n items in total (each item is unique). You can bring any number of items to the market and exchange them for any other one. Note that each item is one of a kind and that means that you cannot exchange set {a, b} for set {v, a}. However, you can always exchange set x for any set y, unless there is item p, such that p occurs in x and p occurs in y.For each item, John knows its value ci. John's sense of justice doesn't let him exchange a set of items x for a set of items y, if s(x) + d < s(y) (s(x) is the total price of items in the set x). During one day John can exchange only one set of items for something else. Initially, he has no items. John wants to get a set of items with the maximum total price. Find the cost of such set and the minimum number of days John can get it in. ", "input_spec": "The first line contains two space-separated integers n, d (1 ≤ n ≤ 50, 1 ≤ d ≤ 104) — the number of items on the market and John's sense of justice value, correspondingly. The second line contains n space-separated integers ci (1 ≤ ci ≤ 104).", "output_spec": "Print two space-separated integers: the maximum possible price in the set of items John can get and the minimum number of days needed to get such set.", "sample_inputs": ["3 2\n1 3 10", "3 5\n1 2 3", "10 10000\n10000 9999 1 10000 10000 10000 1 2 3 4"], "sample_outputs": ["4 3", "6 2", "50010 6"], "notes": "NoteIn the first sample John can act like this:   Take the first item (1 - 0 ≤ 2).  Exchange the first item for the second one (3 - 1 ≤ 2).  Take the first item (1 - 0 ≤ 2). "}, "src_uid": "65699ddec8d0db2f58b83a0f64de6f6f"}
{"nl": {"description": "The Rebel fleet is afraid that the Empire might want to strike back again. Princess Heidi needs to know if it is possible to assign R Rebel spaceships to guard B bases so that every base has exactly one guardian and each spaceship has exactly one assigned base (in other words, the assignment is a perfect matching). Since she knows how reckless her pilots are, she wants to be sure that any two (straight) paths – from a base to its assigned spaceship – do not intersect in the galaxy plane (that is, in 2D), and so there is no risk of collision.", "input_spec": "The first line contains two space-separated integers R, B(1 ≤ R, B ≤ 10). For 1 ≤ i ≤ R, the i + 1-th line contains two space-separated integers xi and yi (|xi|, |yi| ≤ 10000) denoting the coordinates of the i-th Rebel spaceship. The following B lines have the same format, denoting the position of bases. It is guaranteed that no two points coincide and that no three points are on the same line.", "output_spec": "If it is possible to connect Rebel spaceships and bases so as satisfy the constraint, output Yes, otherwise output No (without quote).", "sample_inputs": ["3 3\n0 0\n2 0\n3 1\n-2 1\n0 3\n2 2", "2 1\n1 0\n2 2\n3 1"], "sample_outputs": ["Yes", "No"], "notes": "NoteFor the first example, one possible way is to connect the Rebels and bases in order.For the second example, there is no perfect matching between Rebels and bases."}, "src_uid": "65f81f621c228c09915adcb05256c634"}
{"nl": {"description": "The Tower of Hanoi is a well-known mathematical puzzle. It consists of three rods, and a number of disks of different sizes which can slide onto any rod. The puzzle starts with the disks in a neat stack in ascending order of size on one rod, the smallest at the top, thus making a conical shape.The objective of the puzzle is to move the entire stack to another rod, obeying the following simple rules:   Only one disk can be moved at a time.  Each move consists of taking the upper disk from one of the stacks and placing it on top of another stack i.e. a disk can only be moved if it is the uppermost disk on a stack.  No disk may be placed on top of a smaller disk. With three disks, the puzzle can be solved in seven moves. The minimum number of moves required to solve a Tower of Hanoi puzzle is 2n - 1, where n is the number of disks. (c) Wikipedia.SmallY's puzzle is very similar to the famous Tower of Hanoi. In the Tower of Hanoi puzzle you need to solve a puzzle in minimum number of moves, in SmallY's puzzle each move costs some money and you need to solve the same puzzle but for minimal cost. At the beginning of SmallY's puzzle all n disks are on the first rod. Moving a disk from rod i to rod j (1 ≤ i, j ≤ 3) costs tij units of money. The goal of the puzzle is to move all the disks to the third rod.In the problem you are given matrix t and an integer n. You need to count the minimal cost of solving SmallY's puzzle, consisting of n disks.", "input_spec": "Each of the first three lines contains three integers — matrix t. The j-th integer in the i-th line is tij (1 ≤ tij ≤ 10000; i ≠ j). The following line contains a single integer n (1 ≤ n ≤ 40) — the number of disks. It is guaranteed that for all i (1 ≤ i ≤ 3), tii = 0.", "output_spec": "Print a single integer — the minimum cost of solving SmallY's puzzle.", "sample_inputs": ["0 1 1\n1 0 1\n1 1 0\n3", "0 2 2\n1 0 100\n1 2 0\n3", "0 2 1\n1 0 100\n1 2 0\n5"], "sample_outputs": ["7", "19", "87"], "notes": null}, "src_uid": "c4c20228624365e39299d0a6e8fe7095"}
{"nl": {"description": "You have $$$n$$$ coins, each of the same value of $$$1$$$.Distribute them into packets such that any amount $$$x$$$ ($$$1 \\leq x \\leq n$$$) can be formed using some (possibly one or all) number of these packets.Each packet may only be used entirely or not used at all. No packet may be used more than once in the formation of the single $$$x$$$, however it may be reused for the formation of other $$$x$$$'s.Find the minimum number of packets in such a distribution.", "input_spec": "The only line contains a single integer $$$n$$$ ($$$1 \\leq n \\leq 10^9$$$) — the number of coins you have.", "output_spec": "Output a single integer — the minimum possible number of packets, satisfying the condition above.", "sample_inputs": ["6", "2"], "sample_outputs": ["3", "2"], "notes": "NoteIn the first example, three packets with $$$1$$$, $$$2$$$ and $$$3$$$ coins can be made to get any amount $$$x$$$ ($$$1\\leq x\\leq 6$$$).  To get $$$1$$$ use the packet with $$$1$$$ coin.  To get $$$2$$$ use the packet with $$$2$$$ coins.  To get $$$3$$$ use the packet with $$$3$$$ coins.  To get $$$4$$$ use packets with $$$1$$$ and $$$3$$$ coins.  To get $$$5$$$ use packets with $$$2$$$ and $$$3$$$ coins  To get $$$6$$$ use all packets. In the second example, two packets with $$$1$$$ and $$$1$$$ coins can be made to get any amount $$$x$$$ ($$$1\\leq x\\leq 2$$$)."}, "src_uid": "95cb79597443461085e62d974d67a9a0"}
{"nl": {"description": "Today Patrick waits for a visit from his friend Spongebob. To prepare for the visit, Patrick needs to buy some goodies in two stores located near his house. There is a d1 meter long road between his house and the first shop and a d2 meter long road between his house and the second shop. Also, there is a road of length d3 directly connecting these two shops to each other. Help Patrick calculate the minimum distance that he needs to walk in order to go to both shops and return to his house.  Patrick always starts at his house. He should visit both shops moving only along the three existing roads and return back to his house. He doesn't mind visiting the same shop or passing the same road multiple times. The only goal is to minimize the total distance traveled.", "input_spec": "The first line of the input contains three integers d1, d2, d3 (1 ≤ d1, d2, d3 ≤ 108) — the lengths of the paths.    d1 is the length of the path connecting Patrick's house and the first shop;  d2 is the length of the path connecting Patrick's house and the second shop;  d3 is the length of the path connecting both shops. ", "output_spec": "Print the minimum distance that Patrick will have to walk in order to visit both shops and return to his house.", "sample_inputs": ["10 20 30", "1 1 5"], "sample_outputs": ["60", "4"], "notes": "NoteThe first sample is shown on the picture in the problem statement. One of the optimal routes is: house  first shop  second shop  house.In the second sample one of the optimal routes is: house  first shop  house  second shop  house."}, "src_uid": "26cd7954a21866dbb2824d725473673e"}
{"nl": {"description": "In Pavlopolis University where Noora studies it was decided to hold beauty contest \"Miss Pavlopolis University\". Let's describe the process of choosing the most beautiful girl in the university in more detail.The contest is held in several stages. Suppose that exactly n girls participate in the competition initially. All the participants are divided into equal groups, x participants in each group. Furthermore the number x is chosen arbitrarily, i. e. on every stage number x can be different. Within each group the jury of the contest compares beauty of the girls in the format \"each with each\". In this way, if group consists of x girls, then  comparisons occur. Then, from each group, the most beautiful participant is selected. Selected girls enter the next stage of the competition. Thus if n girls were divided into groups, x participants in each group, then exactly  participants will enter the next stage. The contest continues until there is exactly one girl left who will be \"Miss Pavlopolis University\"But for the jury this contest is a very tedious task. They would like to divide the girls into groups in each stage so that the total number of pairwise comparisons of the girls is as few as possible. Let f(n) be the minimal total number of comparisons that should be made to select the most beautiful participant, if we admit n girls to the first stage.The organizers of the competition are insane. They give Noora three integers t, l and r and ask the poor girl to calculate the value of the following expression: t0·f(l) + t1·f(l + 1) + ... + tr - l·f(r). However, since the value of this expression can be quite large the organizers ask her to calculate it modulo 109 + 7. If Noora can calculate the value of this expression the organizers promise her to help during the beauty contest. But the poor girl is not strong in mathematics, so she turned for help to Leha and he turned to you.", "input_spec": "The first and single line contains three integers t, l and r (1 ≤ t < 109 + 7, 2 ≤ l ≤ r ≤ 5·106).", "output_spec": "In the first line print single integer — the value of the expression modulo 109 + 7.", "sample_inputs": ["2 2 4"], "sample_outputs": ["19"], "notes": "NoteConsider the sample.It is necessary to find the value of .f(2) = 1. From two girls you can form only one group of two people, in which there will be one comparison.f(3) = 3. From three girls you can form only one group of three people, in which there will be three comparisons.f(4) = 3. From four girls you can form two groups of two girls each. Then at the first stage there will be two comparisons, one in each of the two groups. In the second stage there will be two girls and there will be one comparison between them. Total 2 + 1 = 3 comparisons. You can also leave all girls in same group in the first stage. Then  comparisons will occur. Obviously, it's better to split girls into groups in the first way.Then the value of the expression is ."}, "src_uid": "c9d45dac4a22f8f452d98d05eca2e79b"}
{"nl": {"description": "There are well-known formulas: , , . Also mathematicians found similar formulas for higher degrees.Find the value of the sum  modulo 109 + 7 (so you should find the remainder after dividing the answer by the value 109 + 7).", "input_spec": "The only line contains two integers n, k (1 ≤ n ≤ 109, 0 ≤ k ≤ 106).", "output_spec": "Print the only integer a — the remainder after dividing the value of the sum by the value 109 + 7.", "sample_inputs": ["4 1", "4 2", "4 3", "4 0"], "sample_outputs": ["10", "30", "100", "4"], "notes": null}, "src_uid": "6f6fc42a367cdce60d76fd1914e73f0c"}
{"nl": {"description": "Amr loves Geometry. One day he came up with a very interesting problem.Amr has a circle of radius r and center in point (x, y). He wants the circle center to be in new position (x', y').In one step Amr can put a pin to the border of the circle in a certain point, then rotate the circle around that pin by any angle and finally remove the pin.Help Amr to achieve his goal in minimum number of steps.", "input_spec": "Input consists of 5 space-separated integers r, x, y, x' y' (1 ≤ r ≤ 105,  - 105 ≤ x, y, x', y' ≤ 105), circle radius, coordinates of original center of the circle and coordinates of destination center of the circle respectively.", "output_spec": "Output a single integer — minimum number of steps required to move the center of the circle to the destination point.", "sample_inputs": ["2 0 0 0 4", "1 1 1 4 4", "4 5 6 5 6"], "sample_outputs": ["1", "3", "0"], "notes": "NoteIn the first sample test the optimal way is to put a pin at point (0, 2) and rotate the circle by 180 degrees counter-clockwise (or clockwise, no matter)."}, "src_uid": "698da80c7d24252b57cca4e4f0ca7031"}
{"nl": {"description": "Every true king during his life must conquer the world, hold the Codeforces world finals, win pink panda in the shooting gallery and travel all over his kingdom.King Copa has already done the first three things. Now he just needs to travel all over the kingdom. The kingdom is an infinite plane with Cartesian coordinate system on it. Every city is a point on this plane. There are n cities in the kingdom at points with coordinates (x1, 0), (x2, 0), ..., (xn, 0), and there is one city at point (xn + 1, yn + 1). King starts his journey in the city number k. Your task is to find such route for the king, which visits all cities (in any order) and has minimum possible length. It is allowed to visit a city twice. The king can end his journey in any city. Between any pair of cities there is a direct road with length equal to the distance between the corresponding points. No two cities may be located at the same point.", "input_spec": "The first line contains two integers n and k (1 ≤ n ≤ 105, 1 ≤ k ≤ n + 1) — amount of cities and index of the starting city. The second line contains n + 1 numbers xi. The third line contains yn + 1. All coordinates are integers and do not exceed 106 by absolute value. No two cities coincide.", "output_spec": "Output the minimum possible length of the journey. Your answer must have relative or absolute error less than 10 - 6.", "sample_inputs": ["3 1\n0 1 2 1\n1", "3 1\n1 0 2 1\n1", "4 5\n0 5 -1 -5 2\n3"], "sample_outputs": ["3.41421356237309490000", "3.82842712474619030000", "14.24264068711928400000"], "notes": null}, "src_uid": "f9ed5faca211e654d9d4e0a7557616f4"}
{"nl": {"description": "Once Vasya needed to transport m goats and m wolves from riverbank to the other as quickly as possible. The boat can hold n animals and Vasya, in addition, he is permitted to put less than n animals in the boat. If in one place (on one of the banks or in the boat) the wolves happen to strictly outnumber the goats, then the wolves eat the goats and Vasya gets upset. When Vasya swims on the boat from one shore to the other, he must take at least one animal to accompany him, otherwise he will get bored and he will, yet again, feel upset. When the boat reaches the bank, first all the animals get off simultaneously, and then the animals chosen by Vasya simultaneously get on the boat. That means that at the moment when the animals that have just arrived have already got off and the animals that are going to leave haven't yet got on, somebody might eat someone. Vasya needs to transport all the animals from one river bank to the other so that nobody eats anyone and Vasya doesn't get upset. What is the minimal number of times he will have to cross the river?", "input_spec": "The first line contains two space-separated numbers m and n (1 ≤ m, n ≤ 105) — the number of animals and the boat's capacity.", "output_spec": "If it is impossible to transport all the animals so that no one got upset, and all the goats survived, print -1. Otherwise print the single number — how many times Vasya will have to cross the river.", "sample_inputs": ["3 2", "33 3"], "sample_outputs": ["11", "-1"], "notes": "NoteThe first sample match to well-known problem for children."}, "src_uid": "83f1d50a1802e08dd154d4c9778e3d80"}
{"nl": {"description": "There is a sequence of colorful stones. The color of each stone is one of red, green, or blue. You are given a string s. The i-th (1-based) character of s represents the color of the i-th stone. If the character is \"R\", \"G\", or \"B\", the color of the corresponding stone is red, green, or blue, respectively.Initially Squirrel Liss is standing on the first stone. You perform instructions one or more times.Each instruction is one of the three types: \"RED\", \"GREEN\", or \"BLUE\". After an instruction c, if Liss is standing on a stone whose colors is c, Liss will move one stone forward, else she will not move.You are given a string t. The number of instructions is equal to the length of t, and the i-th character of t represents the i-th instruction.Calculate the final position of Liss (the number of the stone she is going to stand on in the end) after performing all the instructions, and print its 1-based position. It is guaranteed that Liss don't move out of the sequence.", "input_spec": "The input contains two lines. The first line contains the string s (1 ≤ |s| ≤ 50). The second line contains the string t (1 ≤ |t| ≤ 50). The characters of each string will be one of \"R\", \"G\", or \"B\". It is guaranteed that Liss don't move out of the sequence.", "output_spec": "Print the final 1-based position of Liss in a single line.", "sample_inputs": ["RGB\nRRR", "RRRBGBRBBB\nBBBRR", "BRRBGBRGRBGRGRRGGBGBGBRGBRGRGGGRBRRRBRBBBGRRRGGBBB\nBBRBGGRGRGBBBRBGRBRBBBBRBRRRBGBBGBBRRBBGGRBRRBRGRB"], "sample_outputs": ["2", "3", "15"], "notes": null}, "src_uid": "f5a907d6d35390b1fb11c8ce247d0252"}
{"nl": {"description": "Hideo Kojima has just quit his job at Konami. Now he is going to find a new place to work. Despite being such a well-known person, he still needs a CV to apply for a job.During all his career Hideo has produced n games. Some of them were successful, some were not. Hideo wants to remove several of them (possibly zero) from his CV to make a better impression on employers. As a result there should be no unsuccessful game which comes right after successful one in his CV.More formally, you are given an array s1, s2, ..., sn of zeros and ones. Zero corresponds to an unsuccessful game, one — to a successful one. Games are given in order they were produced, and Hideo can't swap these values. He should remove some elements from this array in such a way that no zero comes right after one.Besides that, Hideo still wants to mention as much games in his CV as possible. Help this genius of a man determine the maximum number of games he can leave in his CV.", "input_spec": "The first line contains one integer number n (1 ≤ n ≤ 100). The second line contains n space-separated integer numbers s1, s2, ..., sn (0 ≤ si ≤ 1). 0 corresponds to an unsuccessful game, 1 — to a successful one.", "output_spec": "Print one integer — the maximum number of games Hideo can leave in his CV so that no unsuccessful game comes after a successful one.", "sample_inputs": ["4\n1 1 0 1", "6\n0 1 0 0 1 0", "1\n0"], "sample_outputs": ["3", "4", "1"], "notes": null}, "src_uid": "c7b1f0b40e310f99936d1c33e4816b95"}
{"nl": {"description": "Nicholas has an array a that contains n distinct integers from 1 to n. In other words, Nicholas has a permutation of size n.Nicholas want the minimum element (integer 1) and the maximum element (integer n) to be as far as possible from each other. He wants to perform exactly one swap in order to maximize the distance between the minimum and the maximum elements. The distance between two elements is considered to be equal to the absolute difference between their positions.", "input_spec": "The first line of the input contains a single integer n (2 ≤ n ≤ 100) — the size of the permutation. The second line of the input contains n distinct integers a1, a2, ..., an (1 ≤ ai ≤ n), where ai is equal to the element at the i-th position.", "output_spec": "Print a single integer — the maximum possible distance between the minimum and the maximum elements Nicholas can achieve by performing exactly one swap.", "sample_inputs": ["5\n4 5 1 3 2", "7\n1 6 5 3 4 7 2", "6\n6 5 4 3 2 1"], "sample_outputs": ["3", "6", "5"], "notes": "NoteIn the first sample, one may obtain the optimal answer by swapping elements 1 and 2.In the second sample, the minimum and the maximum elements will be located in the opposite ends of the array if we swap 7 and 2.In the third sample, the distance between the minimum and the maximum elements is already maximum possible, so we just perform some unnecessary swap, for example, one can swap 5 and 2."}, "src_uid": "1d2b81ce842f8c97656d96bddff4e8b4"}
{"nl": {"description": "Sereja owns a restaurant for n people. The restaurant hall has a coat rack with n hooks. Each restaurant visitor can use a hook to hang his clothes on it. Using the i-th hook costs ai rubles. Only one person can hang clothes on one hook.Tonight Sereja expects m guests in the restaurant. Naturally, each guest wants to hang his clothes on an available hook with minimum price (if there are multiple such hooks, he chooses any of them). However if the moment a guest arrives the rack has no available hooks, Sereja must pay a d ruble fine to the guest. Help Sereja find out the profit in rubles (possibly negative) that he will get tonight. You can assume that before the guests arrive, all hooks on the rack are available, all guests come at different time, nobody besides the m guests is visiting Sereja's restaurant tonight.", "input_spec": "The first line contains two integers n and d (1 ≤ n, d ≤ 100). The next line contains integers a1, a2, ..., an (1 ≤ ai ≤ 100). The third line contains integer m (1 ≤ m ≤ 100).", "output_spec": "In a single line print a single integer — the answer to the problem.", "sample_inputs": ["2 1\n2 1\n2", "2 1\n2 1\n10"], "sample_outputs": ["3", "-5"], "notes": "NoteIn the first test both hooks will be used, so Sereja gets 1 + 2 = 3 rubles.In the second test both hooks will be used but Sereja pays a fine 8 times, so the answer is 3 - 8 =  - 5."}, "src_uid": "5c21e2dd658825580522af525142397d"}
{"nl": {"description": "Tattah is asleep if and only if Tattah is attending a lecture. This is a well-known formula among Tattah's colleagues.On a Wednesday afternoon, Tattah was attending Professor HH's lecture. At 12:21, right before falling asleep, he was staring at the digital watch around Saher's wrist. He noticed that the digits on the clock were the same when read from both directions i.e. a palindrome.In his sleep, he started dreaming about such rare moments of the day when the time displayed on a digital clock is a palindrome. As soon as he woke up, he felt destined to write a program that finds the next such moment.However, he still hasn't mastered the skill of programming while sleeping, so your task is to help him.", "input_spec": "The first and only line of the input starts with a string with the format \"HH:MM\" where \"HH\" is from \"00\" to \"23\" and \"MM\" is from \"00\" to \"59\". Both \"HH\" and \"MM\" have exactly two digits.", "output_spec": "Print the palindromic time of day that comes soonest after the time given in the input. If the input time is palindromic, output the soonest palindromic time after the input time.", "sample_inputs": ["12:21", "23:59"], "sample_outputs": ["13:31", "00:00"], "notes": null}, "src_uid": "158eae916daa3e0162d4eac0426fa87f"}
{"nl": {"description": "A burglar got into a matches warehouse and wants to steal as many matches as possible. In the warehouse there are m containers, in the i-th container there are ai matchboxes, and each matchbox contains bi matches. All the matchboxes are of the same size. The burglar's rucksack can hold n matchboxes exactly. Your task is to find out the maximum amount of matches that a burglar can carry away. He has no time to rearrange matches in the matchboxes, that's why he just chooses not more than n matchboxes so that the total amount of matches in them is maximal.", "input_spec": "The first line of the input contains integer n (1 ≤ n ≤ 2·108) and integer m (1 ≤ m ≤ 20). The i + 1-th line contains a pair of numbers ai and bi (1 ≤ ai ≤ 108, 1 ≤ bi ≤ 10). All the input numbers are integer.", "output_spec": "Output the only number — answer to the problem.", "sample_inputs": ["7 3\n5 10\n2 5\n3 6", "3 3\n1 3\n2 2\n3 1"], "sample_outputs": ["62", "7"], "notes": null}, "src_uid": "c052d85e402691b05e494b5283d62679"}
{"nl": {"description": "Petya studies at university. The current academic year finishes with $$$n$$$ special days. Petya needs to pass $$$m$$$ exams in those special days. The special days in this problem are numbered from $$$1$$$ to $$$n$$$.There are three values about each exam:  $$$s_i$$$ — the day, when questions for the $$$i$$$-th exam will be published,  $$$d_i$$$ — the day of the $$$i$$$-th exam ($$$s_i < d_i$$$),  $$$c_i$$$ — number of days Petya needs to prepare for the $$$i$$$-th exam. For the $$$i$$$-th exam Petya should prepare in days between $$$s_i$$$ and $$$d_i-1$$$, inclusive. There are three types of activities for Petya in each day: to spend a day doing nothing (taking a rest), to spend a day passing exactly one exam or to spend a day preparing for exactly one exam. So he can't pass/prepare for multiple exams in a day. He can't mix his activities in a day. If he is preparing for the $$$i$$$-th exam in day $$$j$$$, then $$$s_i \\le j < d_i$$$.It is allowed to have breaks in a preparation to an exam and to alternate preparations for different exams in consecutive days. So preparation for an exam is not required to be done in consecutive days.Find the schedule for Petya to prepare for all exams and pass them, or report that it is impossible.", "input_spec": "The first line contains two integers $$$n$$$ and $$$m$$$ $$$(2 \\le n \\le 100, 1 \\le m \\le n)$$$ — the number of days and the number of exams. Each of the following $$$m$$$ lines contains three integers $$$s_i$$$, $$$d_i$$$, $$$c_i$$$ $$$(1 \\le s_i < d_i \\le n, 1 \\le c_i \\le n)$$$ — the day, when questions for the $$$i$$$-th exam will be given, the day of the $$$i$$$-th exam, number of days Petya needs to prepare for the $$$i$$$-th exam.  Guaranteed, that all the exams will be in different days. Questions for different exams can be given in the same day. It is possible that, in the day of some exam, the questions for other exams are given.", "output_spec": "If Petya can not prepare and pass all the exams, print -1. In case of positive answer, print $$$n$$$ integers, where the $$$j$$$-th number is:   $$$(m + 1)$$$, if the $$$j$$$-th day is a day of some exam (recall that in each day no more than one exam is conducted),  zero, if in the $$$j$$$-th day Petya will have a rest,  $$$i$$$ ($$$1 \\le i \\le m$$$), if Petya will prepare for the $$$i$$$-th exam in the day $$$j$$$ (the total number of days Petya prepares for each exam should be strictly equal to the number of days needed to prepare for it).Assume that the exams are numbered in order of appearing in the input, starting from $$$1$$$.If there are multiple schedules, print any of them.", "sample_inputs": ["5 2\n1 3 1\n1 5 1", "3 2\n1 3 1\n1 2 1", "10 3\n4 7 2\n1 10 3\n8 9 1"], "sample_outputs": ["1 2 3 0 3", "-1", "2 2 2 1 1 0 4 3 4 4"], "notes": "NoteIn the first example Petya can, for example, prepare for exam $$$1$$$ in the first day, prepare for exam $$$2$$$ in the second day, pass exam $$$1$$$ in the third day, relax in the fourth day, and pass exam $$$2$$$ in the fifth day. So, he can prepare and pass all exams.In the second example, there are three days and two exams. So, Petya can prepare in only one day (because in two other days he should pass exams). Then Petya can not prepare and pass all exams."}, "src_uid": "02d8d403eb60ae77756ff96f71b662d3"}
{"nl": {"description": "Dima and Inna are doing so great! At the moment, Inna is sitting on the magic lawn playing with a pink pony. Dima wanted to play too. He brought an n × m chessboard, a very tasty candy and two numbers a and b.Dima put the chessboard in front of Inna and placed the candy in position (i, j) on the board. The boy said he would give the candy if it reaches one of the corner cells of the board. He's got one more condition. There can only be actions of the following types:  move the candy from position (x, y) on the board to position (x - a, y - b);  move the candy from position (x, y) on the board to position (x + a, y - b);  move the candy from position (x, y) on the board to position (x - a, y + b);  move the candy from position (x, y) on the board to position (x + a, y + b). Naturally, Dima doesn't allow to move the candy beyond the chessboard borders.Inna and the pony started shifting the candy around the board. They wonder what is the minimum number of allowed actions that they need to perform to move the candy from the initial position (i, j) to one of the chessboard corners. Help them cope with the task! ", "input_spec": "The first line of the input contains six integers n, m, i, j, a, b (1 ≤ n, m ≤ 106; 1 ≤ i ≤ n; 1 ≤ j ≤ m; 1 ≤ a, b ≤ 106). You can assume that the chessboard rows are numbered from 1 to n from top to bottom and the columns are numbered from 1 to m from left to right. Position (i, j) in the statement is a chessboard cell on the intersection of the i-th row and the j-th column. You can consider that the corners are: (1, m), (n, 1), (n, m), (1, 1).", "output_spec": "In a single line print a single integer — the minimum number of moves needed to get the candy. If Inna and the pony cannot get the candy playing by Dima's rules, print on a single line \"Poor Inna and pony!\" without the quotes.", "sample_inputs": ["5 7 1 3 2 2", "5 5 2 3 1 1"], "sample_outputs": ["2", "Poor Inna and pony!"], "notes": "NoteNote to sample 1:Inna and the pony can move the candy to position (1 + 2, 3 + 2) = (3, 5), from there they can move it to positions (3 - 2, 5 + 2) = (1, 7) and (3 + 2, 5 + 2) = (5, 7). These positions correspond to the corner squares of the chess board. Thus, the answer to the test sample equals two."}, "src_uid": "51155e9bfa90e0ff29d049cedc3e1862"}
{"nl": {"description": "The Little Elephant loves numbers. He has a positive integer x. The Little Elephant wants to find the number of positive integers d, such that d is the divisor of x, and x and d have at least one common (the same) digit in their decimal representations. Help the Little Elephant to find the described number.", "input_spec": "A single line contains a single integer x (1 ≤ x ≤ 109).", "output_spec": "In a single line print an integer — the answer to the problem.", "sample_inputs": ["1", "10"], "sample_outputs": ["1", "2"], "notes": null}, "src_uid": "ada94770281765f54ab264b4a1ef766e"}
{"nl": {"description": "You might have heard about the next game in Lara Croft series coming out this year. You also might have watched its trailer. Though you definitely missed the main idea about its plot, so let me lift the veil of secrecy.Lara is going to explore yet another dangerous dungeon. Game designers decided to use good old 2D environment. The dungeon can be represented as a rectangle matrix of n rows and m columns. Cell (x, y) is the cell in the x-th row in the y-th column. Lara can move between the neighbouring by side cells in all four directions.Moreover, she has even chosen the path for herself to avoid all the traps. She enters the dungeon in cell (1, 1), that is top left corner of the matrix. Then she goes down all the way to cell (n, 1) — the bottom left corner. Then she starts moving in the snake fashion — all the way to the right, one cell up, then to the left to the cell in 2-nd column, one cell up. She moves until she runs out of non-visited cells. n and m given are such that she always end up in cell (1, 2).Lara has already moved to a neighbouring cell k times. Can you determine her current position?", "input_spec": "The only line contains three integers n, m and k (2 ≤ n, m ≤ 109, n is always even, 0 ≤ k < n·m). Note that k doesn't fit into 32-bit integer type!", "output_spec": "Print the cell (the row and the column where the cell is situated) where Lara ends up after she moves k times.", "sample_inputs": ["4 3 0", "4 3 11", "4 3 7"], "sample_outputs": ["1 1", "1 2", "3 2"], "notes": "NoteHere is her path on matrix 4 by 3:  "}, "src_uid": "e88bb7621c7124c54e75109a00f96301"}
{"nl": {"description": "So many wall designs to choose from! Even modulo 106 + 3, it's an enormous number. Given that recently Heidi acquired an unlimited supply of bricks, her choices are endless! She really needs to do something to narrow them down.Heidi is quick to come up with criteria for a useful wall:  In a useful wall, at least one segment is wider than W bricks. This should give the zombies something to hit their heads against. Or,  in a useful wall, at least one column is higher than H bricks. This provides a lookout from which zombies can be spotted at a distance. This should rule out a fair amount of possibilities, right? Help Heidi compute the number of useless walls that do not confirm to either of these criteria. In other words, a wall is useless if every segment has width at most W and height at most H.Parameter C, the total width of the wall, has the same meaning as in the easy version. However, note that the number of bricks is now unlimited.Output the number of useless walls modulo 106 + 3.", "input_spec": "The first and the only line of the input contains three space-separated integers C, W and H (1 ≤ C ≤ 108, 1 ≤ W, H ≤ 100).", "output_spec": "Output the number of different walls, modulo 106 + 3, which are useless according to Heidi's criteria.", "sample_inputs": ["1 1 1", "1 2 2", "1 2 3", "3 2 2", "5 4 9", "40 37 65"], "sample_outputs": ["2", "3", "4", "19", "40951", "933869"], "notes": "NoteIf there is no brick in any of the columns, the structure is considered as a useless wall."}, "src_uid": "bb1c0ff47186e10e00b7dde6758ff1c1"}
{"nl": {"description": "Vasily the Programmer loves romance, so this year he decided to illuminate his room with candles.Vasily has a candles.When Vasily lights up a new candle, it first burns for an hour and then it goes out. Vasily is smart, so he can make b went out candles into a new candle. As a result, this new candle can be used like any other new candle.Now Vasily wonders: for how many hours can his candles light up the room if he acts optimally well? Help him find this number.", "input_spec": "The single line contains two integers, a and b (1 ≤ a ≤ 1000; 2 ≤ b ≤ 1000).", "output_spec": "Print a single integer — the number of hours Vasily can light up the room for.", "sample_inputs": ["4 2", "6 3"], "sample_outputs": ["7", "8"], "notes": "NoteConsider the first sample. For the first four hours Vasily lights up new candles, then he uses four burned out candles to make two new ones and lights them up. When these candles go out (stop burning), Vasily can make another candle. Overall, Vasily can light up the room for 7 hours."}, "src_uid": "a349094584d3fdc6b61e39bffe96dece"}
{"nl": {"description": "User ainta has a stack of n red and blue balls. He can apply a certain operation which changes the colors of the balls inside the stack.  While the top ball inside the stack is red, pop the ball from the top of the stack.  Then replace the blue ball on the top with a red ball.  And finally push some blue balls to the stack until the stack has total of n balls inside.   If there are no blue balls inside the stack, ainta can't apply this operation. Given the initial state of the stack, ainta wants to know the maximum number of operations he can repeatedly apply.", "input_spec": "The first line contains an integer n (1 ≤ n ≤ 50) — the number of balls inside the stack. The second line contains a string s (|s| = n) describing the initial state of the stack. The i-th character of the string s denotes the color of the i-th ball (we'll number the balls from top to bottom of the stack). If the character is \"R\", the color is red. If the character is \"B\", the color is blue.", "output_spec": "Print the maximum number of operations ainta can repeatedly apply. Please, do not write the %lld specifier to read or write 64-bit integers in С++. It is preferred to use the cin, cout streams or the %I64d specifier.", "sample_inputs": ["3\nRBR", "4\nRBBR", "5\nRBBRR"], "sample_outputs": ["2", "6", "6"], "notes": "NoteThe first example is depicted below.The explanation how user ainta applies the first operation. He pops out one red ball, changes the color of the ball in the middle from blue to red, and pushes one blue ball.  The explanation how user ainta applies the second operation. He will not pop out red balls, he simply changes the color of the ball on the top from blue to red.  From now on, ainta can't apply any operation because there are no blue balls inside the stack. ainta applied two operations, so the answer is 2.The second example is depicted below. The blue arrow denotes a single operation.  "}, "src_uid": "d86a1b5bf9fe9a985f7b030fedd29d58"}
{"nl": {"description": "Polycarp takes part in a math show. He is given n tasks, each consists of k subtasks, numbered 1 through k. It takes him tj minutes to solve the j-th subtask of any task. Thus, time required to solve a subtask depends only on its index, but not on the task itself. Polycarp can solve subtasks in any order.By solving subtask of arbitrary problem he earns one point. Thus, the number of points for task is equal to the number of solved subtasks in it. Moreover, if Polycarp completely solves the task (solves all k of its subtasks), he recieves one extra point. Thus, total number of points he recieves for the complete solution of the task is k + 1.Polycarp has M minutes of time. What is the maximum number of points he can earn?", "input_spec": "The first line contains three integer numbers n, k and M (1 ≤ n ≤ 45, 1 ≤ k ≤ 45, 0 ≤ M ≤ 2·109). The second line contains k integer numbers, values tj (1 ≤ tj ≤ 1000000), where tj is the time in minutes required to solve j-th subtask of any task.", "output_spec": "Print the maximum amount of points Polycarp can earn in M minutes.", "sample_inputs": ["3 4 11\n1 2 3 4", "5 5 10\n1 2 4 8 16"], "sample_outputs": ["6", "7"], "notes": "NoteIn the first example Polycarp can complete the first task and spend 1 + 2 + 3 + 4 = 10 minutes. He also has the time to solve one subtask of the second task in one minute.In the second example Polycarp can solve the first subtask of all five tasks and spend 5·1 = 5 minutes. Also he can solve the second subtasks of two tasks and spend 2·2 = 4 minutes. Thus, he earns 5 + 2 = 7 points in total."}, "src_uid": "d659e92a410c1bc836be64fc1c0db160"}
{"nl": {"description": "A soldier wants to buy w bananas in the shop. He has to pay k dollars for the first banana, 2k dollars for the second one and so on (in other words, he has to pay i·k dollars for the i-th banana). He has n dollars. How many dollars does he have to borrow from his friend soldier to buy w bananas?", "input_spec": "The first line contains three positive integers k, n, w (1  ≤  k, w  ≤  1000, 0 ≤ n ≤ 109), the cost of the first banana, initial number of dollars the soldier has and number of bananas he wants. ", "output_spec": "Output one integer — the amount of dollars that the soldier must borrow from his friend. If he doesn't have to borrow money, output 0.", "sample_inputs": ["3 17 4"], "sample_outputs": ["13"], "notes": null}, "src_uid": "e87d9798107734a885fd8263e1431347"}
{"nl": {"description": "Theatre Square in the capital city of Berland has a rectangular shape with the size n × m meters. On the occasion of the city's anniversary, a decision was taken to pave the Square with square granite flagstones. Each flagstone is of the size a × a.What is the least number of flagstones needed to pave the Square? It's allowed to cover the surface larger than the Theatre Square, but the Square has to be covered. It's not allowed to break the flagstones. The sides of flagstones should be parallel to the sides of the Square.", "input_spec": "The input contains three positive integer numbers in the first line: n,  m and a (1 ≤  n, m, a ≤ 109).", "output_spec": "Write the needed number of flagstones.", "sample_inputs": ["6 6 4"], "sample_outputs": ["4"], "notes": null}, "src_uid": "ef971874d8c4da37581336284b688517"}
{"nl": {"description": "A lot of people associate Logo programming language with turtle graphics. In this case the turtle moves along the straight line and accepts commands \"T\" (\"turn around\") and \"F\" (\"move 1 unit forward\").You are given a list of commands that will be given to the turtle. You have to change exactly n commands from the list (one command can be changed several times). How far from the starting point can the turtle move after it follows all the commands of the modified list?", "input_spec": "The first line of input contains a string commands — the original list of commands. The string commands contains between 1 and 100 characters, inclusive, and contains only characters \"T\" and \"F\". The second line contains an integer n (1 ≤ n ≤ 50) — the number of commands you have to change in the list.", "output_spec": "Output the maximum distance from the starting point to the ending point of the turtle's path. The ending point of the turtle's path is turtle's coordinate after it follows all the commands of the modified list.", "sample_inputs": ["FT\n1", "FFFTFFF\n2"], "sample_outputs": ["2", "6"], "notes": "NoteIn the first example the best option is to change the second command (\"T\") to \"F\" — this way the turtle will cover a distance of 2 units.In the second example you have to change two commands. One of the ways to cover maximal distance of 6 units is to change the fourth command and first or last one."}, "src_uid": "4a54971eb22e62b1d9e6b72f05ae361d"}
{"nl": {"description": "One day Alex was creating a contest about his friends, but accidentally deleted it. Fortunately, all the problems were saved, but now he needs to find them among other problems.But there are too many problems, to do it manually. Alex asks you to write a program, which will determine if a problem is from this contest by its name.It is known, that problem is from this contest if and only if its name contains one of Alex's friends' name exactly once. His friends' names are \"Danil\", \"Olya\", \"Slava\", \"Ann\" and \"Nikita\".Names are case sensitive.", "input_spec": "The only line contains string from lowercase and uppercase letters and \"_\" symbols of length, not more than 100 — the name of the problem.", "output_spec": "Print \"YES\", if problem is from this contest, and \"NO\" otherwise.", "sample_inputs": ["Alex_and_broken_contest", "NikitaAndString", "Danil_and_Olya"], "sample_outputs": ["NO", "YES", "NO"], "notes": null}, "src_uid": "db2dc7500ff4d84dcc1a37aebd2b3710"}
{"nl": {"description": "Let’s define a grid to be a set of tiles with 2 rows and 13 columns. Each tile has an English letter written in it. The letters don't have to be unique: there might be two or more tiles with the same letter written on them. Here is an example of a grid: ABCDEFGHIJKLMNOPQRSTUVWXYZ We say that two tiles are adjacent if they share a side or a corner. In the example grid above, the tile with the letter 'A' is adjacent only to the tiles with letters 'B', 'N', and 'O'. A tile is not adjacent to itself.A sequence of tiles is called a path if each tile in the sequence is adjacent to the tile which follows it (except for the last tile in the sequence, which of course has no successor). In this example, \"ABC\" is a path, and so is \"KXWIHIJK\". \"MAB\" is not a path because 'M' is not adjacent to 'A'. A single tile can be used more than once by a path (though the tile cannot occupy two consecutive places in the path because no tile is adjacent to itself).You’re given a string s which consists of 27 upper-case English letters. Each English letter occurs at least once in s. Find a grid that contains a path whose tiles, viewed in the order that the path visits them, form the string s. If there’s no solution, print \"Impossible\" (without the quotes).", "input_spec": "The only line of the input contains the string s, consisting of 27 upper-case English letters. Each English letter occurs at least once in s.", "output_spec": "Output two lines, each consisting of 13 upper-case English characters, representing the rows of the grid. If there are multiple solutions, print any of them. If there is no solution print \"Impossible\".", "sample_inputs": ["ABCDEFGHIJKLMNOPQRSGTUVWXYZ", "BUVTYZFQSNRIWOXXGJLKACPEMDH"], "sample_outputs": ["YXWVUTGHIJKLM\nZABCDEFSRQPON", "Impossible"], "notes": null}, "src_uid": "56c5ea443dec7a732802b16aed5b934d"}
{"nl": {"description": "Given a positive integer n, find k integers (not necessary distinct) such that all these integers are strictly greater than 1, and their product is equal to n.", "input_spec": "The first line contains two integers n and k (2 ≤ n ≤ 100000, 1 ≤ k ≤ 20).", "output_spec": "If it's impossible to find the representation of n as a product of k numbers, print -1. Otherwise, print k integers in any order. Their product must be equal to n. If there are multiple answers, print any of them.", "sample_inputs": ["100000 2", "100000 20", "1024 5"], "sample_outputs": ["2 50000", "-1", "2 64 2 2 2"], "notes": null}, "src_uid": "bd0bc809d52e0a17da07ccfd450a4d79"}
{"nl": {"description": "Pak Chanek has a grid that has $$$N$$$ rows and $$$M$$$ columns. Each row is numbered from $$$1$$$ to $$$N$$$ from top to bottom. Each column is numbered from $$$1$$$ to $$$M$$$ from left to right.Each tile in the grid contains a number. The numbers are arranged as follows:   Row $$$1$$$ contains integers from $$$1$$$ to $$$M$$$ from left to right.  Row $$$2$$$ contains integers from $$$M+1$$$ to $$$2 \\times M$$$ from left to right.  Row $$$3$$$ contains integers from $$$2 \\times M+1$$$ to $$$3 \\times M$$$ from left to right.  And so on until row $$$N$$$. A domino is defined as two different tiles in the grid that touch by their sides. A domino is said to be tight if and only if the two numbers in the domino have a difference of exactly $$$1$$$. Count the number of distinct tight dominoes in the grid.Two dominoes are said to be distinct if and only if there exists at least one tile that is in one domino, but not in the other.", "input_spec": "The only line contains two integers $$$N$$$ and $$$M$$$ ($$$1 \\leq N, M \\leq 10^9$$$) — the number of rows and columns in the grid.", "output_spec": "An integer representing the number of distinct tight dominoes in the grid.", "sample_inputs": ["3 4", "2 1"], "sample_outputs": ["9", "1"], "notes": "NoteThe picture below is the grid that Pak Chanek has in the first example.  The picture below is an example of a tight domino in the grid.  "}, "src_uid": "a91aab4c0618d036c81022232814ef44"}
{"nl": {"description": "String can be called correct if it consists of characters \"0\" and \"1\" and there are no redundant leading zeroes. Here are some examples: \"0\", \"10\", \"1001\".You are given a correct string s.You can perform two different operations on this string:   swap any pair of adjacent characters (for example, \"101\"  \"110\");  replace \"11\" with \"1\" (for example, \"110\"  \"10\"). Let val(s) be such a number that s is its binary representation.Correct string a is less than some other correct string b iff val(a) < val(b).Your task is to find the minimum correct string that you can obtain from the given one using the operations described above. You can use these operations any number of times in any order (or even use no operations at all).", "input_spec": "The first line contains integer number n (1 ≤ n ≤ 100) — the length of string s. The second line contains the string s consisting of characters \"0\" and \"1\". It is guaranteed that the string s is correct.", "output_spec": "Print one string — the minimum correct string that you can obtain from the given one.", "sample_inputs": ["4\n1001", "1\n1"], "sample_outputs": ["100", "1"], "notes": "NoteIn the first example you can obtain the answer by the following sequence of operations: \"1001\"  \"1010\"  \"1100\"  \"100\".In the second example you can't obtain smaller answer no matter what operations you use."}, "src_uid": "ac244791f8b648d672ed3de32ce0074d"}
{"nl": {"description": "Alice and Bob play 5-in-a-row game. They have a playing field of size 10 × 10. In turns they put either crosses or noughts, one at a time. Alice puts crosses and Bob puts noughts.In current match they have made some turns and now it's Alice's turn. She wonders if she can put cross in such empty cell that she wins immediately.Alice wins if some crosses in the field form line of length not smaller than 5. This line can be horizontal, vertical and diagonal.", "input_spec": "You are given matrix 10 × 10 (10 lines of 10 characters each) with capital Latin letters 'X' being a cross, letters 'O' being a nought and '.' being an empty cell. The number of 'X' cells is equal to the number of 'O' cells and there is at least one of each type. There is at least one empty cell. It is guaranteed that in the current arrangement nobody has still won.", "output_spec": "Print 'YES' if it's possible for Alice to win in one turn by putting cross in some empty cell. Otherwise print 'NO'.", "sample_inputs": ["XX.XX.....\n.....OOOO.\n..........\n..........\n..........\n..........\n..........\n..........\n..........\n..........", "XXOXX.....\nOO.O......\n..........\n..........\n..........\n..........\n..........\n..........\n..........\n.........."], "sample_outputs": ["YES", "NO"], "notes": null}, "src_uid": "d5541028a2753c758322c440bdbf9ec6"}
{"nl": {"description": "Two-gram is an ordered pair (i.e. string of length two) of capital Latin letters. For example, \"AZ\", \"AA\", \"ZA\" — three distinct two-grams.You are given a string $$$s$$$ consisting of $$$n$$$ capital Latin letters. Your task is to find any two-gram contained in the given string as a substring (i.e. two consecutive characters of the string) maximal number of times. For example, for string $$$s$$$ = \"BBAABBBA\" the answer is two-gram \"BB\", which contained in $$$s$$$ three times. In other words, find any most frequent two-gram.Note that occurrences of the two-gram can overlap with each other.", "input_spec": "The first line of the input contains integer number $$$n$$$ ($$$2 \\le n \\le 100$$$) — the length of string $$$s$$$. The second line of the input contains the string $$$s$$$ consisting of $$$n$$$ capital Latin letters.", "output_spec": "Print the only line containing exactly two capital Latin letters — any two-gram contained in the given string $$$s$$$ as a substring (i.e. two consecutive characters of the string) maximal number of times.", "sample_inputs": ["7\nABACABA", "5\nZZZAA"], "sample_outputs": ["AB", "ZZ"], "notes": "NoteIn the first example \"BA\" is also valid answer.In the second example the only two-gram \"ZZ\" can be printed because it contained in the string \"ZZZAA\" two times."}, "src_uid": "e78005d4be93dbaa518f3b40cca84ab1"}
{"nl": {"description": "You have a nuts and lots of boxes. The boxes have a wonderful feature: if you put x (x ≥ 0) divisors (the spacial bars that can divide a box) to it, you get a box, divided into x + 1 sections.You are minimalist. Therefore, on the one hand, you are against dividing some box into more than k sections. On the other hand, you are against putting more than v nuts into some section of the box. What is the minimum number of boxes you have to use if you want to put all the nuts in boxes, and you have b divisors?Please note that you need to minimize the number of used boxes, not sections. You do not have to minimize the number of used divisors.", "input_spec": "The first line contains four space-separated integers k, a, b, v (2 ≤ k ≤ 1000; 1 ≤ a, b, v ≤ 1000) — the maximum number of sections in the box, the number of nuts, the number of divisors and the capacity of each section of the box.", "output_spec": "Print a single integer — the answer to the problem.", "sample_inputs": ["3 10 3 3", "3 10 1 3", "100 100 1 1000"], "sample_outputs": ["2", "3", "1"], "notes": "NoteIn the first sample you can act like this:   Put two divisors to the first box. Now the first box has three sections and we can put three nuts into each section. Overall, the first box will have nine nuts.  Do not put any divisors into the second box. Thus, the second box has one section for the last nut. In the end we've put all the ten nuts into boxes.The second sample is different as we have exactly one divisor and we put it to the first box. The next two boxes will have one section each."}, "src_uid": "7cff20b1c63a694baca69bdf4bdb2652"}
{"nl": {"description": "Little Petya loves training spiders. Petya has a board n × m in size. Each cell of the board initially has a spider sitting on it. After one second Petya chooses a certain action for each spider, and all of them humbly perform its commands. There are 5 possible commands: to stay idle or to move from current cell to some of the four side-neighboring cells (that is, one command for each of the four possible directions). Petya gives the commands so that no spider leaves the field. It is allowed for spiders to pass through each other when they crawl towards each other in opposite directions. All spiders crawl simultaneously and several spiders may end up in one cell. Petya wants to know the maximum possible number of spider-free cells after one second.", "input_spec": "The first line contains two space-separated integers n and m (1 ≤ n, m ≤ 40, n·m ≤ 40) — the board sizes.", "output_spec": "In the first line print the maximum number of cells without spiders.", "sample_inputs": ["1 1", "2 3"], "sample_outputs": ["0", "4"], "notes": "NoteIn the first sample the only possible answer is:sIn the second sample one of the possible solutions is: rdlruls denotes command \"stay idle\", l, r, d, u denote commands \"crawl left\", \"crawl right\", \"crawl down\", \"crawl up\", correspondingly."}, "src_uid": "097674b4dd696b30e102938f71dd39b9"}
{"nl": {"description": "A group of university students wants to get to the top of a mountain to have a picnic there. For that they decided to use a cableway.A cableway is represented by some cablecars, hanged onto some cable stations by a cable. A cable is scrolled cyclically between the first and the last cable stations (the first of them is located at the bottom of the mountain and the last one is located at the top). As the cable moves, the cablecar attached to it move as well.The number of cablecars is divisible by three and they are painted three colors: red, green and blue, in such manner that after each red cablecar goes a green one, after each green cablecar goes a blue one and after each blue cablecar goes a red one. Each cablecar can transport no more than two people, the cablecars arrive with the periodicity of one minute (i. e. every minute) and it takes exactly 30 minutes for a cablecar to get to the top.All students are divided into three groups: r of them like to ascend only in the red cablecars, g of them prefer only the green ones and b of them prefer only the blue ones. A student never gets on a cablecar painted a color that he doesn't like,The first cablecar to arrive (at the moment of time 0) is painted red. Determine the least time it will take all students to ascend to the mountain top.", "input_spec": "The first line contains three integers r, g and b (0 ≤ r, g, b ≤ 100). It is guaranteed that r + g + b > 0, it means that the group consists of at least one student. ", "output_spec": "Print a single number — the minimal time the students need for the whole group to ascend to the top of the mountain.", "sample_inputs": ["1 3 2", "3 2 1"], "sample_outputs": ["34", "33"], "notes": "NoteLet's analyze the first sample.At the moment of time 0 a red cablecar comes and one student from the r group get on it and ascends to the top at the moment of time 30.At the moment of time 1 a green cablecar arrives and two students from the g group get on it; they get to the top at the moment of time 31.At the moment of time 2 comes the blue cablecar and two students from the b group get on it. They ascend to the top at the moment of time 32.At the moment of time 3 a red cablecar arrives but the only student who is left doesn't like red and the cablecar leaves empty.At the moment of time 4 a green cablecar arrives and one student from the g group gets on it. He ascends to top at the moment of time 34.Thus, all the students are on the top, overall the ascension took exactly 34 minutes."}, "src_uid": "a45daac108076102da54e07e1e2a37d7"}
{"nl": {"description": "Dreamoon loves summing up something for no reason. One day he obtains two integers a and b occasionally. He wants to calculate the sum of all nice integers. Positive integer x is called nice if  and , where k is some integer number in range [1, a].By  we denote the quotient of integer division of x and y. By  we denote the remainder of integer division of x and y. You can read more about these operations here: http://goo.gl/AcsXhT.The answer may be large, so please print its remainder modulo 1 000 000 007 (109 + 7). Can you compute it faster than Dreamoon?", "input_spec": "The single line of the input contains two integers a, b (1 ≤ a, b ≤ 107).", "output_spec": "Print a single integer representing the answer modulo 1 000 000 007 (109 + 7).", "sample_inputs": ["1 1", "2 2"], "sample_outputs": ["0", "8"], "notes": "NoteFor the first sample, there are no nice integers because  is always zero.For the second sample, the set of nice integers is {3, 5}."}, "src_uid": "cd351d1190a92d094b2d929bf1e5c44f"}
{"nl": {"description": "Petya loves lucky numbers. Everybody knows that lucky numbers are positive integers whose decimal representation contains only the lucky digits 4 and 7. For example, numbers 47, 744, 4 are lucky and 5, 17, 467 are not.Petya calls a number almost lucky if it could be evenly divided by some lucky number. Help him find out if the given number n is almost lucky.", "input_spec": "The single line contains an integer n (1 ≤ n ≤ 1000) — the number that needs to be checked.", "output_spec": "In the only line print \"YES\" (without the quotes), if number n is almost lucky. Otherwise, print \"NO\" (without the quotes).", "sample_inputs": ["47", "16", "78"], "sample_outputs": ["YES", "YES", "NO"], "notes": "NoteNote that all lucky numbers are almost lucky as any number is evenly divisible by itself.In the first sample 47 is a lucky number. In the second sample 16 is divisible by 4."}, "src_uid": "78cf8bc7660dbd0602bf6e499bc6bb0d"}
{"nl": {"description": "Let's denote d(n) as the number of divisors of a positive integer n. You are given three integers a, b and c. Your task is to calculate the following sum:Find the sum modulo 1073741824 (230).", "input_spec": "The first line contains three space-separated integers a, b and c (1 ≤ a, b, c ≤ 2000).", "output_spec": "Print a single integer — the required sum modulo 1073741824 (230).", "sample_inputs": ["2 2 2", "4 4 4", "10 10 10"], "sample_outputs": ["20", "328", "11536"], "notes": "NoteFor the first example.  d(1·1·1) = d(1) = 1;  d(1·1·2) = d(2) = 2;  d(1·2·1) = d(2) = 2;  d(1·2·2) = d(4) = 3;  d(2·1·1) = d(2) = 2;  d(2·1·2) = d(4) = 3;  d(2·2·1) = d(4) = 3;  d(2·2·2) = d(8) = 4. So the result is 1 + 2 + 2 + 3 + 2 + 3 + 3 + 4 = 20."}, "src_uid": "4fdd4027dd9cd688fcc70e1076c9b401"}
{"nl": {"description": "A system of n vessels with water is given. Several pairs of vessels are connected by tubes with transfusion mechanisms. One may transfer an integer amount of liters of water between two vessels connected by such tube (tube works in both directions). There might be multiple tubes between two vessels. Total number of tubes equals e. Volume of each vessel equals v liters. Of course, the amount of the water in any vessel cannot exceed v liters in the process of transfusions.Given the initial amounts ai of water in the vessels and the desired amounts bi find a sequence of transfusions that deals with the task. Total number of transfusions must not exceed 2·n2.", "input_spec": "First line of the input contains integers n, v, e (1 ≤ n ≤ 300, 1 ≤ v ≤ 109, 0 ≤ e ≤ 50000). Next two lines contain n integers each: initial ai and the desired amounts bi of water in corresponding vessels (0 ≤ ai, bi ≤ v). Next e lines describe one tube each in the format x y (1 ≤ x, y ≤ n, x ≠ y) for a tube between vessels number x and y. There might be multiple tubes between two vessels. You may assume that vessels are numbered from 1 to n in some way.", "output_spec": "Print \"NO\" (without quotes), if such sequence of transfusions does not exist. Otherwise print any suitable sequence in the following format. On the first line print the total number of transfusions k (k should not exceed 2·n2). In the following k lines print transfusions in the format x y d (transfusion of d liters from the vessel number x to the vessel number y, x and y must be distinct). For all transfusions d must be a non-negative integer.", "sample_inputs": ["2 10 1\n1 9\n5 5\n1 2", "2 10 0\n5 2\n4 2", "2 10 0\n4 2\n4 2"], "sample_outputs": ["1\n2 1 4", "NO", "0"], "notes": null}, "src_uid": "0939354d9bad8301efb79a1a934ded30"}
{"nl": {"description": "There are n walruses sitting in a circle. All of them are numbered in the clockwise order: the walrus number 2 sits to the left of the walrus number 1, the walrus number 3 sits to the left of the walrus number 2, ..., the walrus number 1 sits to the left of the walrus number n.The presenter has m chips. The presenter stands in the middle of the circle and starts giving the chips to the walruses starting from walrus number 1 and moving clockwise. The walrus number i gets i chips. If the presenter can't give the current walrus the required number of chips, then the presenter takes the remaining chips and the process ends. Determine by the given n and m how many chips the presenter will get in the end.", "input_spec": "The first line contains two integers n and m (1 ≤ n ≤ 50, 1 ≤ m ≤ 104) — the number of walruses and the number of chips correspondingly.", "output_spec": "Print the number of chips the presenter ended up with.", "sample_inputs": ["4 11", "17 107", "3 8"], "sample_outputs": ["0", "2", "1"], "notes": "NoteIn the first sample the presenter gives one chip to the walrus number 1, two chips to the walrus number 2, three chips to the walrus number 3, four chips to the walrus number 4, then again one chip to the walrus number 1. After that the presenter runs out of chips. He can't give anything to the walrus number 2 and the process finishes.In the third sample the presenter gives one chip to the walrus number 1, two chips to the walrus number 2, three chips to the walrus number 3, then again one chip to the walrus number 1. The presenter has one chip left and he can't give two chips to the walrus number 2, that's why the presenter takes the last chip."}, "src_uid": "5dd5ee90606d37cae5926eb8b8d250bb"}
{"nl": {"description": "Petya loves lucky numbers very much. Everybody knows that lucky numbers are positive integers whose decimal record contains only the lucky digits 4 and 7. For example, numbers 47, 744, 4 are lucky and 5, 17, 467 are not.Petya loves tickets very much. As we know, each ticket has a number that is a positive integer. Its length equals n (n is always even). Petya calls a ticket lucky if the ticket's number is a lucky number and the sum of digits in the first half (the sum of the first n / 2 digits) equals the sum of digits in the second half (the sum of the last n / 2 digits). Check if the given ticket is lucky.", "input_spec": "The first line contains an even integer n (2 ≤ n ≤ 50) — the length of the ticket number that needs to be checked. The second line contains an integer whose length equals exactly n — the ticket number. The number may contain leading zeros.", "output_spec": "On the first line print \"YES\" if the given ticket number is lucky. Otherwise, print \"NO\" (without the quotes).", "sample_inputs": ["2\n47", "4\n4738", "4\n4774"], "sample_outputs": ["NO", "NO", "YES"], "notes": "NoteIn the first sample the sum of digits in the first half does not equal the sum of digits in the second half (4 ≠ 7).In the second sample the ticket number is not the lucky number."}, "src_uid": "435b6d48f99d90caab828049a2c9e2a7"}
{"nl": {"description": "Malek lives in an apartment block with 100 floors numbered from 0 to 99. The apartment has an elevator with a digital counter showing the floor that the elevator is currently on. The elevator shows each digit of a number with 7 light sticks by turning them on or off. The picture below shows how the elevator shows each digit.One day when Malek wanted to go from floor 88 to floor 0 using the elevator he noticed that the counter shows number 89 instead of 88. Then when the elevator started moving the number on the counter changed to 87. After a little thinking Malek came to the conclusion that there is only one explanation for this: One of the sticks of the counter was broken. Later that day Malek was thinking about the broken stick and suddenly he came up with the following problem.Suppose the digital counter is showing number n. Malek calls an integer x (0 ≤ x ≤ 99) good if it's possible that the digital counter was supposed to show x but because of some(possibly none) broken sticks it's showing n instead. Malek wants to know number of good integers for a specific n. So you must write a program that calculates this number. Please note that the counter always shows two digits.", "input_spec": "The only line of input contains exactly two digits representing number n (0 ≤ n ≤ 99). Note that n may have a leading zero.", "output_spec": "In the only line of the output print the number of good integers.", "sample_inputs": ["89", "00", "73"], "sample_outputs": ["2", "4", "15"], "notes": "NoteIn the first sample the counter may be supposed to show 88 or 89.In the second sample the good integers are 00, 08, 80 and 88.In the third sample the good integers are 03, 08, 09, 33, 38, 39, 73, 78, 79, 83, 88, 89, 93, 98, 99."}, "src_uid": "76c8bfa6789db8364a8ece0574cd31f5"}
{"nl": {"description": "Tokitsukaze is one of the characters in the game \"Kantai Collection\". In this game, every character has a common attribute — health points, shortened to HP.In general, different values of HP are grouped into $$$4$$$ categories:  Category $$$A$$$ if HP is in the form of $$$(4 n + 1)$$$, that is, when divided by $$$4$$$, the remainder is $$$1$$$;  Category $$$B$$$ if HP is in the form of $$$(4 n + 3)$$$, that is, when divided by $$$4$$$, the remainder is $$$3$$$;  Category $$$C$$$ if HP is in the form of $$$(4 n + 2)$$$, that is, when divided by $$$4$$$, the remainder is $$$2$$$;  Category $$$D$$$ if HP is in the form of $$$4 n$$$, that is, when divided by $$$4$$$, the remainder is $$$0$$$. The above-mentioned $$$n$$$ can be any integer.These $$$4$$$ categories ordered from highest to lowest as $$$A > B > C > D$$$, which means category $$$A$$$ is the highest and category $$$D$$$ is the lowest.While playing the game, players can increase the HP of the character. Now, Tokitsukaze wants you to increase her HP by at most $$$2$$$ (that is, either by $$$0$$$, $$$1$$$ or $$$2$$$). How much should she increase her HP so that it has the highest possible category?", "input_spec": "The only line contains a single integer $$$x$$$ ($$$30 \\leq x \\leq 100$$$) — the value Tokitsukaze's HP currently.", "output_spec": "Print an integer $$$a$$$ ($$$0 \\leq a \\leq 2$$$) and an uppercase letter $$$b$$$ ($$$b \\in \\lbrace A, B, C, D \\rbrace$$$), representing that the best way is to increase her HP by $$$a$$$, and then the category becomes $$$b$$$. Note that the output characters are case-sensitive.", "sample_inputs": ["33", "98"], "sample_outputs": ["0 A", "1 B"], "notes": "NoteFor the first example, the category of Tokitsukaze's HP is already $$$A$$$, so you don't need to enhance her ability.For the second example:  If you don't increase her HP, its value is still $$$98$$$, which equals to $$$(4 \\times 24 + 2)$$$, and its category is $$$C$$$.  If you increase her HP by $$$1$$$, its value becomes $$$99$$$, which equals to $$$(4 \\times 24 + 3)$$$, and its category becomes $$$B$$$.  If you increase her HP by $$$2$$$, its value becomes $$$100$$$, which equals to $$$(4 \\times 25)$$$, and its category becomes $$$D$$$. Therefore, the best way is to increase her HP by $$$1$$$ so that the category of her HP becomes $$$B$$$."}, "src_uid": "488e809bd0c55531b0b47f577996627e"}
{"nl": {"description": "Vitaly is a diligent student who never missed a lesson in his five years of studying in the university. He always does his homework on time and passes his exams in time. During the last lesson the teacher has provided two strings s and t to Vitaly. The strings have the same length, they consist of lowercase English letters, string s is lexicographically smaller than string t. Vitaly wondered if there is such string that is lexicographically larger than string s and at the same is lexicographically smaller than string t. This string should also consist of lowercase English letters and have the length equal to the lengths of strings s and t. Let's help Vitaly solve this easy problem!", "input_spec": "The first line contains string s (1 ≤ |s| ≤ 100), consisting of lowercase English letters. Here, |s| denotes the length of the string. The second line contains string t (|t| = |s|), consisting of lowercase English letters. It is guaranteed that the lengths of strings s and t are the same and string s is lexicographically less than string t.", "output_spec": "If the string that meets the given requirements doesn't exist, print a single string \"No such string\" (without the quotes). If such string exists, print it. If there are multiple valid strings, you may print any of them.", "sample_inputs": ["a\nc", "aaa\nzzz", "abcdefg\nabcdefh"], "sample_outputs": ["b", "kkk", "No such string"], "notes": "NoteString s = s1s2... sn is said to be lexicographically smaller than t = t1t2... tn, if there exists such i, that s1 = t1, s2 = t2, ... si - 1 = ti - 1, si < ti."}, "src_uid": "47618510d2a17b1cc1e6a688201d51a3"}
{"nl": {"description": "Little Petya likes positive integers a lot. Recently his mom has presented him a positive integer a. There's only one thing Petya likes more than numbers: playing with little Masha. It turned out that Masha already has a positive integer b. Petya decided to turn his number a into the number b consecutively performing the operations of the following two types:  Subtract 1 from his number.  Choose any integer x from 2 to k, inclusive. Then subtract number (a mod x) from his number a. Operation a mod x means taking the remainder from division of number a by number x. Petya performs one operation per second. Each time he chooses an operation to perform during the current move, no matter what kind of operations he has performed by that moment. In particular, this implies that he can perform the same operation any number of times in a row.Now he wonders in what minimum number of seconds he could transform his number a into number b. Please note that numbers x in the operations of the second type are selected anew each time, independently of each other.", "input_spec": "The only line contains three integers a, b (1 ≤ b ≤ a ≤ 1018) and k (2 ≤ k ≤ 15). Please do not use the %lld specifier to read or write 64-bit integers in С++. It is preferred to use the cin, cout streams or the %I64d specifier.", "output_spec": "Print a single integer — the required minimum number of seconds needed to transform number a into number b.", "sample_inputs": ["10 1 4", "6 3 10", "1000000000000000000 1 3"], "sample_outputs": ["6", "2", "666666666666666667"], "notes": "NoteIn the first sample the sequence of numbers that Petya gets as he tries to obtain number b is as follows: 10  →  8  →  6  →  4  →  3  →  2  →  1.In the second sample one of the possible sequences is as follows: 6  →  4  →  3."}, "src_uid": "bd599d76c83cc1f30c1349ffb51b4273"}
{"nl": {"description": "A and B are preparing themselves for programming contests.To train their logical thinking and solve problems better, A and B decided to play chess. During the game A wondered whose position is now stronger.For each chess piece we know its weight:   the queen's weight is 9,  the rook's weight is 5,  the bishop's weight is 3,  the knight's weight is 3,  the pawn's weight is 1,  the king's weight isn't considered in evaluating position. The player's weight equals to the sum of weights of all his pieces on the board.As A doesn't like counting, he asked you to help him determine which player has the larger position weight.", "input_spec": "The input contains eight lines, eight characters each — the board's description. The white pieces on the board are marked with uppercase letters, the black pieces are marked with lowercase letters. The white pieces are denoted as follows: the queen is represented is 'Q', the rook — as 'R', the bishop — as'B', the knight — as 'N', the pawn — as 'P', the king — as 'K'. The black pieces are denoted as 'q', 'r', 'b', 'n', 'p', 'k', respectively. An empty square of the board is marked as '.' (a dot).  It is not guaranteed that the given chess position can be achieved in a real game. Specifically, there can be an arbitrary (possibly zero) number pieces of each type, the king may be under attack and so on.", "output_spec": "Print \"White\" (without quotes) if the weight of the position of the white pieces is more than the weight of the position of the black pieces, print \"Black\" if the weight of the black pieces is more than the weight of the white pieces and print \"Draw\" if the weights of the white and black pieces are equal.", "sample_inputs": ["...QK...\n........\n........\n........\n........\n........\n........\n...rk...", "rnbqkbnr\npppppppp\n........\n........\n........\n........\nPPPPPPPP\nRNBQKBNR", "rppppppr\n...k....\n........\n........\n........\n........\nK...Q...\n........"], "sample_outputs": ["White", "Draw", "Black"], "notes": "NoteIn the first test sample the weight of the position of the white pieces equals to 9, the weight of the position of the black pieces equals 5.In the second test sample the weights of the positions of the black and the white pieces are equal to 39.In the third test sample the weight of the position of the white pieces equals to 9, the weight of the position of the black pieces equals to 16."}, "src_uid": "44bed0ca7a8fb42fb72c1584d39a4442"}
{"nl": {"description": "Once upon a time in the Kingdom of Far Far Away lived Sir Lancelot, the chief Royal General. He was very proud of his men and he liked to invite the King to come and watch drill exercises which demonstrated the fighting techniques and tactics of the squad he was in charge of. But time went by and one day Sir Lancelot had a major argument with the Fairy Godmother (there were rumors that the argument occurred after the general spoke badly of the Godmother's flying techniques. That seemed to hurt the Fairy Godmother very deeply). As the result of the argument, the Godmother put a rather strange curse upon the general. It sounded all complicated and quite harmless: \"If the squared distance between some two soldiers equals to 5, then those soldiers will conflict with each other!\"The drill exercises are held on a rectangular n × m field, split into nm square 1 × 1 segments for each soldier. Thus, the square of the distance between the soldiers that stand on squares (x1, y1) and (x2, y2) equals exactly (x1 - x2)2 + (y1 - y2)2. Now not all nm squad soldiers can participate in the drill exercises as it was before the Fairy Godmother's curse. Unless, of course, the general wants the soldiers to fight with each other or even worse... For example, if he puts a soldier in the square (2, 2), then he cannot put soldiers in the squares (1, 4), (3, 4), (4, 1) and (4, 3) — each of them will conflict with the soldier in the square (2, 2).Your task is to help the general. You are given the size of the drill exercise field. You are asked to calculate the maximum number of soldiers that can be simultaneously positioned on this field, so that no two soldiers fall under the Fairy Godmother's curse.", "input_spec": "The single line contains space-separated integers n and m (1 ≤ n, m ≤ 1000) that represent the size of the drill exercise field.", "output_spec": "Print the desired maximum number of warriors.", "sample_inputs": ["2 4", "3 4"], "sample_outputs": ["4", "6"], "notes": "NoteIn the first sample test Sir Lancelot can place his 4 soldiers on the 2 × 4 court as follows (the soldiers' locations are marked with gray circles on the scheme):  In the second sample test he can place 6 soldiers on the 3 × 4 site in the following manner:  "}, "src_uid": "e858e7f22d91aaadd7a48a174d7b2dc9"}
{"nl": {"description": "\"QAQ\" is a word to denote an expression of crying. Imagine \"Q\" as eyes with tears and \"A\" as a mouth.Now Diamond has given Bort a string consisting of only uppercase English letters of length n. There is a great number of \"QAQ\" in the string (Diamond is so cute!).  illustration by 猫屋 https://twitter.com/nekoyaliu Bort wants to know how many subsequences \"QAQ\" are in the string Diamond has given. Note that the letters \"QAQ\" don't have to be consecutive, but the order of letters should be exact.", "input_spec": "The only line contains a string of length n (1 ≤ n ≤ 100). It's guaranteed that the string only contains uppercase English letters.", "output_spec": "Print a single integer — the number of subsequences \"QAQ\" in the string.", "sample_inputs": ["QAQAQYSYIOIWIN", "QAQQQZZYNOIWIN"], "sample_outputs": ["4", "3"], "notes": "NoteIn the first example there are 4 subsequences \"QAQ\": \"QAQAQYSYIOIWIN\", \"QAQAQYSYIOIWIN\", \"QAQAQYSYIOIWIN\", \"QAQAQYSYIOIWIN\"."}, "src_uid": "8aef4947322438664bd8610632fe0947"}
{"nl": {"description": "Today Vasya visited a widely known site and learned that the continuation of his favourite game Codecraft II will appear after exactly k months. He looked at the calendar and learned that at the moment is the month number s. Vasya immediately got interested in what month Codecraft III will appear. Help him understand that.All the twelve months in Vasya's calendar are named using their usual English names: January, February, March, April, May, June, July, August, September, October, November, December.", "input_spec": "The first input line contains the name of the current month. It is guaranteed that it is a proper English name of one of twelve months. The first letter is uppercase, the rest are lowercase. The second line contains integer k (0 ≤ k ≤ 100) — the number of months left till the appearance of Codecraft III.", "output_spec": "Print starting from an uppercase letter the name of the month in which the continuation of Codeforces II will appear. The printed name must be contained in the list January, February, March, April, May, June, July, August, September, October, November, December.", "sample_inputs": ["November\n3", "May\n24"], "sample_outputs": ["February", "May"], "notes": null}, "src_uid": "a307b402b20554ce177a73db07170691"}
{"nl": {"description": "Everyone knows what the Fibonacci sequence is. This sequence can be defined by the recurrence relation: F1 = 1, F2 = 2, Fi = Fi - 1 + Fi - 2 (i > 2).We'll define a new number sequence Ai(k) by the formula: Ai(k) = Fi × ik (i ≥ 1).In this problem, your task is to calculate the following sum: A1(k) + A2(k) + ... + An(k). The answer can be very large, so print it modulo 1000000007 (109 + 7).", "input_spec": "The first line contains two space-separated integers n, k (1 ≤ n ≤ 1017; 1 ≤ k ≤ 40).", "output_spec": "Print a single integer — the sum of the first n elements of the sequence Ai(k) modulo 1000000007 (109 + 7).", "sample_inputs": ["1 1", "4 1", "5 2", "7 4"], "sample_outputs": ["1", "34", "316", "73825"], "notes": null}, "src_uid": "14f50a111db268182e5927839a993118"}
{"nl": {"description": "Developing tools for creation of locations maps for turn-based fights in a new game, Petya faced the following problem.A field map consists of hexagonal cells. Since locations sizes are going to be big, a game designer wants to have a tool for quick filling of a field part with identical enemy units. This action will look like following: a game designer will select a rectangular area on the map, and each cell whose center belongs to the selected rectangle will be filled with the enemy unit.More formally, if a game designer selected cells having coordinates (x1, y1) and (x2, y2), where x1 ≤ x2 and y1 ≤ y2, then all cells having center coordinates (x, y) such that x1 ≤ x ≤ x2 and y1 ≤ y ≤ y2 will be filled. Orthogonal coordinates system is set up so that one of cell sides is parallel to OX axis, all hexagon centers have integer coordinates and for each integer x there are cells having center with such x coordinate and for each integer y there are cells having center with such y coordinate. It is guaranteed that difference x2 - x1 is divisible by 2.Working on the problem Petya decided that before painting selected units he wants to output number of units that will be painted on the map.Help him implement counting of these units before painting.  ", "input_spec": "The only line of input contains four integers x1, y1, x2, y2 ( - 109 ≤ x1 ≤ x2 ≤ 109,  - 109 ≤ y1 ≤ y2 ≤ 109) — the coordinates of the centers of two cells.", "output_spec": "Output one integer — the number of cells to be filled.", "sample_inputs": ["1 1 5 5"], "sample_outputs": ["13"], "notes": null}, "src_uid": "00cffd273df24d1676acbbfd9a39630d"}
{"nl": {"description": "Rikhail Mubinchik believes that the current definition of prime numbers is obsolete as they are too complex and unpredictable. A palindromic number is another matter. It is aesthetically pleasing, and it has a number of remarkable properties. Help Rikhail to convince the scientific community in this!Let us remind you that a number is called prime if it is integer larger than one, and is not divisible by any positive integer other than itself and one.Rikhail calls a number a palindromic if it is integer, positive, and its decimal representation without leading zeros is a palindrome, i.e. reads the same from left to right and right to left.One problem with prime numbers is that there are too many of them. Let's introduce the following notation: π(n) — the number of primes no larger than n, rub(n) — the number of palindromic numbers no larger than n. Rikhail wants to prove that there are a lot more primes than palindromic ones.He asked you to solve the following problem: for a given value of the coefficient A find the maximum n, such that π(n) ≤ A·rub(n).", "input_spec": "The input consists of two positive integers p, q, the numerator and denominator of the fraction that is the value of A (, ).", "output_spec": "If such maximum number exists, then print it. Otherwise, print \"Palindromic tree is better than splay tree\" (without the quotes).", "sample_inputs": ["1 1", "1 42", "6 4"], "sample_outputs": ["40", "1", "172"], "notes": null}, "src_uid": "e6e760164882b9e194a17663625be27d"}
{"nl": {"description": "Alex, Bob and Carl will soon participate in a team chess tournament. Since they are all in the same team, they have decided to practise really hard before the tournament. But it's a bit difficult for them because chess is a game for two players, not three.So they play with each other according to following rules:  Alex and Bob play the first game, and Carl is spectating;  When the game ends, the one who lost the game becomes the spectator in the next game, and the one who was spectating plays against the winner. Alex, Bob and Carl play in such a way that there are no draws.Today they have played n games, and for each of these games they remember who was the winner. They decided to make up a log of games describing who won each game. But now they doubt if the information in the log is correct, and they want to know if the situation described in the log they made up was possible (that is, no game is won by someone who is spectating if Alex, Bob and Carl play according to the rules). Help them to check it!", "input_spec": "The first line contains one integer n (1 ≤ n ≤ 100) — the number of games Alex, Bob and Carl played. Then n lines follow, describing the game log. i-th line contains one integer ai (1 ≤ ai ≤ 3) which is equal to 1 if Alex won i-th game, to 2 if Bob won i-th game and 3 if Carl won i-th game.", "output_spec": "Print YES if the situation described in the log was possible. Otherwise print NO.", "sample_inputs": ["3\n1\n1\n2", "2\n1\n2"], "sample_outputs": ["YES", "NO"], "notes": "NoteIn the first example the possible situation is:  Alex wins, Carl starts playing instead of Bob;  Alex wins, Bob replaces Carl;  Bob wins. The situation in the second example is impossible because Bob loses the first game, so he cannot win the second one."}, "src_uid": "6c7ab07abdf157c24be92f49fd1d8d87"}
{"nl": {"description": "Little Lesha loves listening to music via his smartphone. But the smartphone doesn't have much memory, so Lesha listens to his favorite songs in a well-known social network InTalk.Unfortunately, internet is not that fast in the city of Ekaterinozavodsk and the song takes a lot of time to download. But Lesha is quite impatient. The song's duration is T seconds. Lesha downloads the first S seconds of the song and plays it. When the playback reaches the point that has not yet been downloaded, Lesha immediately plays the song from the start (the loaded part of the song stays in his phone, and the download is continued from the same place), and it happens until the song is downloaded completely and Lesha listens to it to the end. For q seconds of real time the Internet allows you to download q - 1 seconds of the track.Tell Lesha, for how many times he will start the song, including the very first start.", "input_spec": "The single line contains three integers T, S, q (2 ≤ q ≤ 104, 1 ≤ S < T ≤ 105).", "output_spec": "Print a single integer — the number of times the song will be restarted.", "sample_inputs": ["5 2 2", "5 4 7", "6 2 3"], "sample_outputs": ["2", "1", "1"], "notes": "NoteIn the first test, the song is played twice faster than it is downloaded, which means that during four first seconds Lesha reaches the moment that has not been downloaded, and starts the song again. After another two seconds, the song is downloaded completely, and thus, Lesha starts the song twice.In the second test, the song is almost downloaded, and Lesha will start it only once.In the third sample test the download finishes and Lesha finishes listening at the same moment. Note that song isn't restarted in this case."}, "src_uid": "0d01bf286fb2c7950ce5d5fa59a17dd9"}
{"nl": {"description": "Winnie-the-Pooh likes honey very much! That is why he decided to visit his friends. Winnie has got three best friends: Rabbit, Owl and Eeyore, each of them lives in his own house. There are winding paths between each pair of houses. The length of a path between Rabbit's and Owl's houses is a meters, between Rabbit's and Eeyore's house is b meters, between Owl's and Eeyore's house is c meters.For enjoying his life and singing merry songs Winnie-the-Pooh should have a meal n times a day. Now he is in the Rabbit's house and has a meal for the first time. Each time when in the friend's house where Winnie is now the supply of honey is about to end, Winnie leaves that house. If Winnie has not had a meal the required amount of times, he comes out from the house and goes to someone else of his two friends. For this he chooses one of two adjacent paths, arrives to the house on the other end and visits his friend. You may assume that when Winnie is eating in one of his friend's house, the supply of honey in other friend's houses recover (most probably, they go to the supply store).Winnie-the-Pooh does not like physical activity. He wants to have a meal n times, traveling minimum possible distance. Help him to find this distance.", "input_spec": "First line contains an integer n (1 ≤ n ≤ 100) — number of visits. Second line contains an integer a (1 ≤ a ≤ 100) — distance between Rabbit's and Owl's houses. Third line contains an integer b (1 ≤ b ≤ 100) — distance between Rabbit's and Eeyore's houses. Fourth line contains an integer c (1 ≤ c ≤ 100) — distance between Owl's and Eeyore's houses.", "output_spec": "Output one number — minimum distance in meters Winnie must go through to have a meal n times.", "sample_inputs": ["3\n2\n3\n1", "1\n2\n3\n5"], "sample_outputs": ["3", "0"], "notes": "NoteIn the first test case the optimal path for Winnie is the following: first have a meal in Rabbit's house, then in Owl's house, then in Eeyore's house. Thus he will pass the distance 2 + 1 = 3.In the second test case Winnie has a meal in Rabbit's house and that is for him. So he doesn't have to walk anywhere at all."}, "src_uid": "6058529f0144c853e9e17ed7c661fc50"}
{"nl": {"description": "You will receive 3 points for solving this problem.Manao is designing the genetic code for a new type of algae to efficiently produce fuel. Specifically, Manao is focusing on a stretch of DNA that encodes one protein. The stretch of DNA is represented by a string containing only the characters 'A', 'T', 'G' and 'C'.Manao has determined that if the stretch of DNA contains a maximal sequence of consecutive identical nucleotides that is of even length, then the protein will be nonfunctional. For example, consider a protein described by DNA string \"GTTAAAG\". It contains four maximal sequences of consecutive identical nucleotides: \"G\", \"TT\", \"AAA\", and \"G\". The protein is nonfunctional because sequence \"TT\" has even length.Manao is trying to obtain a functional protein from the protein he currently has. Manao can insert additional nucleotides into the DNA stretch. Each additional nucleotide is a character from the set {'A', 'T', 'G', 'C'}. Manao wants to determine the minimum number of insertions necessary to make the DNA encode a functional protein.", "input_spec": "The input consists of a single line, containing a string s of length n (1 ≤ n ≤ 100). Each character of s will be from the set {'A', 'T', 'G', 'C'}. This problem doesn't have subproblems. You will get 3 points for the correct submission.", "output_spec": "The program should print on one line a single integer representing the minimum number of 'A', 'T', 'G', 'C' characters that are required to be inserted into the input string in order to make all runs of identical characters have odd length.", "sample_inputs": ["GTTAAAG", "AACCAACCAAAAC"], "sample_outputs": ["1", "5"], "notes": "NoteIn the first example, it is sufficient to insert a single nucleotide of any type between the two 'T's in the sequence to restore the functionality of the protein."}, "src_uid": "8b26ca1ca2b28166c3d25dceb1f3d49f"}
{"nl": {"description": "A little bear Limak plays a game. He has five cards. There is one number written on each card. Each number is a positive integer.Limak can discard (throw out) some cards. His goal is to minimize the sum of numbers written on remaining (not discarded) cards.He is allowed to at most once discard two or three cards with the same number. Of course, he won't discard cards if it's impossible to choose two or three cards with the same number.Given five numbers written on cards, cay you find the minimum sum of numbers on remaining cards?", "input_spec": "The only line of the input contains five integers t1, t2, t3, t4 and t5 (1 ≤ ti ≤ 100) — numbers written on cards.", "output_spec": "Print the minimum possible sum of numbers written on remaining cards.", "sample_inputs": ["7 3 7 3 20", "7 9 3 1 8", "10 10 10 10 10"], "sample_outputs": ["26", "28", "20"], "notes": "NoteIn the first sample, Limak has cards with numbers 7, 3, 7, 3 and 20. Limak can do one of the following.  Do nothing and the sum would be 7 + 3 + 7 + 3 + 20 = 40.  Remove two cards with a number 7. The remaining sum would be 3 + 3 + 20 = 26.  Remove two cards with a number 3. The remaining sum would be 7 + 7 + 20 = 34. You are asked to minimize the sum so the answer is 26.In the second sample, it's impossible to find two or three cards with the same number. Hence, Limak does nothing and the sum is 7 + 9 + 1 + 3 + 8 = 28.In the third sample, all cards have the same number. It's optimal to discard any three cards. The sum of two remaining numbers is 10 + 10 = 20."}, "src_uid": "a9c17ce5fd5f39ffd70917127ce3408a"}
{"nl": {"description": "Victor and Peter are playing hide-and-seek. Peter has hidden, and Victor is to find him. In the room where they are playing, there is only one non-transparent wall and one double-sided mirror. Victor and Peter are points with coordinates (xv, yv) and (xp, yp) respectively. The wall is a segment joining points with coordinates (xw, 1, yw, 1) and (xw, 2, yw, 2), the mirror — a segment joining points (xm, 1, ym, 1) and (xm, 2, ym, 2).If an obstacle has a common point with a line of vision, it's considered, that the boys can't see each other with this line of vision. If the mirror has a common point with the line of vision, it's considered, that the boys can see each other in the mirror, i.e. reflection takes place. The reflection process is governed by laws of physics — the angle of incidence is equal to the angle of reflection. The incident ray is in the same half-plane as the reflected ray, relative to the mirror. I.e. to see each other Victor and Peter should be to the same side of the line, containing the mirror (see example 1). If the line of vision is parallel to the mirror, reflection doesn't take place, and the mirror isn't regarded as an obstacle (see example 4).Victor got interested if he can see Peter, while standing at the same spot. Help him solve this problem.", "input_spec": "The first line contains two numbers xv and yv — coordinates of Victor. The second line contains two numbers xp and yp — coordinates of Peter. The third line contains 4 numbers xw, 1, yw, 1, xw, 2, yw, 2 — coordinates of the wall. The forth line contains 4 numbers xm, 1, ym, 1, xm, 2, ym, 2 — coordinates of the mirror. All the coordinates are integer numbers, and don't exceed 104 in absolute value. It's guaranteed, that the segments don't have common points, Victor and Peter are not on any of the segments, coordinates of Victor and Peter aren't the same, the segments don't degenerate into points.", "output_spec": "Output YES, if Victor can see Peter without leaving the initial spot. Otherwise output NO.", "sample_inputs": ["-1 3\n1 3\n0 2 0 4\n0 0 0 1", "0 0\n1 1\n0 1 1 0\n-100 -100 -101 -101", "0 0\n1 1\n0 1 1 0\n-1 1 1 3", "0 0\n10 0\n100 100 101 101\n1 0 3 0"], "sample_outputs": ["NO", "NO", "YES", "YES"], "notes": null}, "src_uid": "7539a41268b68238d644795bccaa0c0f"}
{"nl": {"description": "Polycarpus loves lucky numbers. Everybody knows that lucky numbers are positive integers, whose decimal representation (without leading zeroes) contain only the lucky digits x and y. For example, if x = 4, and y = 7, then numbers 47, 744, 4 are lucky.Let's call a positive integer a undoubtedly lucky, if there are such digits x and y (0 ≤ x, y ≤ 9), that the decimal representation of number a (without leading zeroes) contains only digits x and y.Polycarpus has integer n. He wants to know how many positive integers that do not exceed n, are undoubtedly lucky. Help him, count this number.", "input_spec": "The first line contains a single integer n (1 ≤ n ≤ 109) — Polycarpus's number.", "output_spec": "Print a single integer that says, how many positive integers that do not exceed n are undoubtedly lucky.", "sample_inputs": ["10", "123"], "sample_outputs": ["10", "113"], "notes": "NoteIn the first test sample all numbers that do not exceed 10 are undoubtedly lucky.In the second sample numbers 102, 103, 104, 105, 106, 107, 108, 109, 120, 123 are not undoubtedly lucky."}, "src_uid": "0f7f10557602c8c2f2eb80762709ffc4"}
{"nl": {"description": "Two bored soldiers are playing card war. Their card deck consists of exactly n cards, numbered from 1 to n, all values are different. They divide cards between them in some manner, it's possible that they have different number of cards. Then they play a \"war\"-like card game. The rules are following. On each turn a fight happens. Each of them picks card from the top of his stack and puts on the table. The one whose card value is bigger wins this fight and takes both cards from the table to the bottom of his stack. More precisely, he first takes his opponent's card and puts to the bottom of his stack, and then he puts his card to the bottom of his stack. If after some turn one of the player's stack becomes empty, he loses and the other one wins. You have to calculate how many fights will happen and who will win the game, or state that game won't end.", "input_spec": "First line contains a single integer n (2 ≤ n ≤ 10), the number of cards. Second line contains integer k1 (1 ≤ k1 ≤ n - 1), the number of the first soldier's cards. Then follow k1 integers that are the values on the first soldier's cards, from top to bottom of his stack. Third line contains integer k2 (k1 + k2 = n), the number of the second soldier's cards. Then follow k2 integers that are the values on the second soldier's cards, from top to bottom of his stack. All card values are different.", "output_spec": "If somebody wins in this game, print 2 integers where the first one stands for the number of fights before end of game and the second one is 1 or 2 showing which player has won. If the game won't end and will continue forever output  - 1.", "sample_inputs": ["4\n2 1 3\n2 4 2", "3\n1 2\n2 1 3"], "sample_outputs": ["6 2", "-1"], "notes": "NoteFirst sample:   Second sample:   "}, "src_uid": "f587b1867754e6958c3d7e0fe368ec6e"}
{"nl": {"description": "Translator's note: in Russia's most widespread grading system, there are four grades: 5, 4, 3, 2, the higher the better, roughly corresponding to A, B, C and F respectively in American grading system.The term is coming to an end and students start thinking about their grades. Today, a professor told his students that the grades for his course would be given out automatically  — he would calculate the simple average (arithmetic mean) of all grades given out for lab works this term and round to the nearest integer. The rounding would be done in favour of the student — $$$4.5$$$ would be rounded up to $$$5$$$ (as in example 3), but $$$4.4$$$ would be rounded down to $$$4$$$.This does not bode well for Vasya who didn't think those lab works would influence anything, so he may receive a grade worse than $$$5$$$ (maybe even the dreaded $$$2$$$). However, the professor allowed him to redo some of his works of Vasya's choosing to increase his average grade. Vasya wants to redo as as few lab works as possible in order to get $$$5$$$ for the course. Of course, Vasya will get $$$5$$$ for the lab works he chooses to redo.Help Vasya — calculate the minimum amount of lab works Vasya has to redo.", "input_spec": "The first line contains a single integer $$$n$$$ — the number of Vasya's grades ($$$1 \\leq n \\leq 100$$$). The second line contains $$$n$$$ integers from $$$2$$$ to $$$5$$$ — Vasya's grades for his lab works.", "output_spec": "Output a single integer — the minimum amount of lab works that Vasya has to redo. It can be shown that Vasya can always redo enough lab works to get a $$$5$$$.", "sample_inputs": ["3\n4 4 4", "4\n5 4 5 5", "4\n5 3 3 5"], "sample_outputs": ["2", "0", "1"], "notes": "NoteIn the first sample, it is enough to redo two lab works to make two $$$4$$$s into $$$5$$$s.In the second sample, Vasya's average is already $$$4.75$$$ so he doesn't have to redo anything to get a $$$5$$$.In the second sample Vasya has to redo one lab work to get rid of one of the $$$3$$$s, that will make the average exactly $$$4.5$$$ so the final grade would be $$$5$$$."}, "src_uid": "715608282b27a0a25b66f08574a6d5bd"}
{"nl": {"description": "Mishka got a six-faced dice. It has integer numbers from $$$2$$$ to $$$7$$$ written on its faces (all numbers on faces are different, so this is an almost usual dice).Mishka wants to get exactly $$$x$$$ points by rolling his dice. The number of points is just a sum of numbers written at the topmost face of the dice for all the rolls Mishka makes.Mishka doesn't really care about the number of rolls, so he just wants to know any number of rolls he can make to be able to get exactly $$$x$$$ points for them. Mishka is very lucky, so if the probability to get $$$x$$$ points with chosen number of rolls is non-zero, he will be able to roll the dice in such a way. Your task is to print this number. It is guaranteed that at least one answer exists.Mishka is also very curious about different number of points to score so you have to answer $$$t$$$ independent queries.", "input_spec": "The first line of the input contains one integer $$$t$$$ ($$$1 \\le t \\le 100$$$) — the number of queries. Each of the next $$$t$$$ lines contains one integer each. The $$$i$$$-th line contains one integer $$$x_i$$$ ($$$2 \\le x_i \\le 100$$$) — the number of points Mishka wants to get.", "output_spec": "Print $$$t$$$ lines. In the $$$i$$$-th line print the answer to the $$$i$$$-th query (i.e. any number of rolls Mishka can make to be able to get exactly $$$x_i$$$ points for them). It is guaranteed that at least one answer exists.", "sample_inputs": ["4\n2\n13\n37\n100"], "sample_outputs": ["1\n3\n8\n27"], "notes": "NoteIn the first query Mishka can roll a dice once and get $$$2$$$ points.In the second query Mishka can roll a dice $$$3$$$ times and get points $$$5$$$, $$$5$$$ and $$$3$$$ (for example).In the third query Mishka can roll a dice $$$8$$$ times and get $$$5$$$ points $$$7$$$ times and $$$2$$$ points with the remaining roll.In the fourth query Mishka can roll a dice $$$27$$$ times and get $$$2$$$ points $$$11$$$ times, $$$3$$$ points $$$6$$$ times and $$$6$$$ points $$$10$$$ times."}, "src_uid": "a661b6ce166fe4b2bbfd0ace56a7dc2c"}
{"nl": {"description": "Vasily the Bear loves beautiful strings. String s is beautiful if it meets the following criteria:   String s only consists of characters 0 and 1, at that character 0 must occur in string s exactly n times, and character 1 must occur exactly m times.  We can obtain character g from string s with some (possibly, zero) number of modifications. The character g equals either zero or one. A modification of string with length at least two is the following operation: we replace two last characters from the string by exactly one other character. This character equals one if it replaces two zeros, otherwise it equals zero. For example, one modification transforms string \"01010\" into string \"0100\", two modifications transform it to \"011\". It is forbidden to modify a string with length less than two.Help the Bear, count the number of beautiful strings. As the number of beautiful strings can be rather large, print the remainder after dividing the number by 1000000007 (109 + 7). ", "input_spec": "The first line of the input contains three space-separated integers n, m, g (0 ≤ n, m ≤ 105, n + m ≥ 1, 0 ≤ g ≤ 1).", "output_spec": "Print a single integer — the answer to the problem modulo 1000000007 (109 + 7).", "sample_inputs": ["1 1 0", "2 2 0", "1 1 1"], "sample_outputs": ["2", "4", "0"], "notes": "NoteIn the first sample the beautiful strings are: \"01\", \"10\".In the second sample the beautiful strings are: \"0011\", \"1001\", \"1010\", \"1100\".In the third sample there are no beautiful strings."}, "src_uid": "066dd9e6091238edf2912a6af4d29e7f"}
{"nl": {"description": "Lenny is playing a game on a 3 × 3 grid of lights. In the beginning of the game all lights are switched on. Pressing any of the lights will toggle it and all side-adjacent lights. The goal of the game is to switch all the lights off. We consider the toggling as follows: if the light was switched on then it will be switched off, if it was switched off then it will be switched on.Lenny has spent some time playing with the grid and by now he has pressed each light a certain number of times. Given the number of times each light is pressed, you have to print the current state of each light.", "input_spec": "The input consists of three rows. Each row contains three integers each between 0 to 100 inclusive. The j-th number in the i-th row is the number of times the j-th light of the i-th row of the grid is pressed.", "output_spec": "Print three lines, each containing three characters. The j-th character of the i-th line is \"1\" if and only if the corresponding light is switched on, otherwise it's \"0\".", "sample_inputs": ["1 0 0\n0 0 0\n0 0 1", "1 0 1\n8 8 8\n2 0 3"], "sample_outputs": ["001\n010\n100", "010\n011\n100"], "notes": null}, "src_uid": "b045abf40c75bb66a80fd6148ecc5bd6"}
{"nl": {"description": "Maxim loves to fill in a matrix in a special manner. Here is a pseudocode of filling in a matrix of size (m + 1) × (m + 1):Maxim asks you to count, how many numbers m (1 ≤ m ≤ n) are there, such that the sum of values in the cells in the row number m + 1 of the resulting matrix equals t.Expression (x xor y) means applying the operation of bitwise excluding \"OR\" to numbers x and y. The given operation exists in all modern programming languages. For example, in languages C++ and Java it is represented by character \"^\", in Pascal — by \"xor\".", "input_spec": "A single line contains two integers n and t (1 ≤ n, t ≤ 1012, t ≤ n + 1). Please, do not use the %lld specifier to read or write 64-bit integers in C++. It is preferred to use the cin, cout streams or the %I64d specifier.", "output_spec": "In a single line print a single integer — the answer to the problem. ", "sample_inputs": ["1 1", "3 2", "3 3", "1000000000000 1048576"], "sample_outputs": ["1", "1", "0", "118606527258"], "notes": null}, "src_uid": "727d5b601694e5e0f0cf3a9ca25323fc"}
{"nl": {"description": "Mislove had an array $$$a_1$$$, $$$a_2$$$, $$$\\cdots$$$, $$$a_n$$$ of $$$n$$$ positive integers, but he has lost it. He only remembers the following facts about it: The number of different numbers in the array is not less than $$$l$$$ and is not greater than $$$r$$$; For each array's element $$$a_i$$$ either $$$a_i = 1$$$ or $$$a_i$$$ is even and there is a number $$$\\dfrac{a_i}{2}$$$ in the array.For example, if $$$n=5$$$, $$$l=2$$$, $$$r=3$$$ then an array could be $$$[1,2,2,4,4]$$$ or $$$[1,1,1,1,2]$$$; but it couldn't be $$$[1,2,2,4,8]$$$ because this array contains $$$4$$$ different numbers; it couldn't be $$$[1,2,2,3,3]$$$ because $$$3$$$ is odd and isn't equal to $$$1$$$; and it couldn't be $$$[1,1,2,2,16]$$$ because there is a number $$$16$$$ in the array but there isn't a number $$$\\frac{16}{2} = 8$$$.According to these facts, he is asking you to count the minimal and the maximal possible sums of all elements in an array. ", "input_spec": "The only input line contains three integers $$$n$$$, $$$l$$$ and $$$r$$$ ($$$1 \\leq n \\leq 1\\,000$$$, $$$1 \\leq l \\leq r \\leq \\min(n, 20)$$$) — an array's size, the minimal number and the maximal number of distinct elements in an array.", "output_spec": "Output two numbers — the minimal and the maximal possible sums of all elements in an array.", "sample_inputs": ["4 2 2", "5 1 5"], "sample_outputs": ["5 7", "5 31"], "notes": "NoteIn the first example, an array could be the one of the following: $$$[1,1,1,2]$$$, $$$[1,1,2,2]$$$ or $$$[1,2,2,2]$$$. In the first case the minimal sum is reached and in the last case the maximal sum is reached.In the second example, the minimal sum is reached at the array $$$[1,1,1,1,1]$$$, and the maximal one is reached at the array $$$[1,2,4,8,16]$$$."}, "src_uid": "ce220726392fb0cacf0ec44a7490084a"}
{"nl": {"description": "One quite ordinary day Valera went to school (there's nowhere else he should go on a week day). In a maths lesson his favorite teacher Ms. Evans told students about divisors. Despite the fact that Valera loved math, he didn't find this particular topic interesting. Even more, it seemed so boring that he fell asleep in the middle of a lesson. And only a loud ringing of a school bell could interrupt his sweet dream. Of course, the valuable material and the teacher's explanations were lost. However, Valera will one way or another have to do the homework. As he does not know the new material absolutely, he cannot do the job himself. That's why he asked you to help. You're his best friend after all, you just cannot refuse to help. Valera's home task has only one problem, which, though formulated in a very simple way, has not a trivial solution. Its statement looks as follows: if we consider all positive integers in the interval [a;b] then it is required to count the amount of such numbers in this interval that their smallest divisor will be a certain integer k (you do not have to consider divisor equal to one). In other words, you should count the amount of such numbers from the interval [a;b], that are not divisible by any number between 2 and k - 1 and yet are divisible by k. ", "input_spec": "The first and only line contains three positive integers a, b, k (1 ≤ a ≤ b ≤ 2·109, 2 ≤ k ≤ 2·109). ", "output_spec": "Print on a single line the answer to the given problem. ", "sample_inputs": ["1 10 2", "12 23 3", "6 19 5"], "sample_outputs": ["5", "2", "0"], "notes": "NoteComments to the samples from the statement: In the first sample the answer is numbers 2, 4, 6, 8, 10.In the second one — 15, 21In the third one there are no such numbers."}, "src_uid": "04a26f1d1013b6e6b4b0bdcf225475f2"}
{"nl": {"description": "We define $$$x \\bmod y$$$ as the remainder of division of $$$x$$$ by $$$y$$$ ($$$\\%$$$ operator in C++ or Java, mod operator in Pascal).Let's call an array of positive integers $$$[a_1, a_2, \\dots, a_k]$$$ stable if for every permutation $$$p$$$ of integers from $$$1$$$ to $$$k$$$, and for every non-negative integer $$$x$$$, the following condition is met: $$$ (((x \\bmod a_1) \\bmod a_2) \\dots \\bmod a_{k - 1}) \\bmod a_k = (((x \\bmod a_{p_1}) \\bmod a_{p_2}) \\dots \\bmod a_{p_{k - 1}}) \\bmod a_{p_k} $$$ That is, for each non-negative integer $$$x$$$, the value of $$$(((x \\bmod a_1) \\bmod a_2) \\dots \\bmod a_{k - 1}) \\bmod a_k$$$ does not change if we reorder the elements of the array $$$a$$$.For two given integers $$$n$$$ and $$$k$$$, calculate the number of stable arrays $$$[a_1, a_2, \\dots, a_k]$$$ such that $$$1 \\le a_1 < a_2 < \\dots < a_k \\le n$$$.", "input_spec": "The only line contains two integers $$$n$$$ and $$$k$$$ ($$$1 \\le n, k \\le 5 \\cdot 10^5$$$).", "output_spec": "Print one integer — the number of stable arrays $$$[a_1, a_2, \\dots, a_k]$$$ such that $$$1 \\le a_1 < a_2 < \\dots < a_k \\le n$$$. Since the answer may be large, print it modulo $$$998244353$$$.", "sample_inputs": ["7 3", "3 7", "1337 42", "1 1", "500000 1"], "sample_outputs": ["16", "0", "95147305", "1", "500000"], "notes": null}, "src_uid": "8e8eb64a047cb970a549ee870c3d280d"}
{"nl": {"description": "Just in case somebody missed it: this winter is totally cold in Nvodsk! It is so cold that one gets funny thoughts. For example, let's say there are strings with the length exactly n, based on the alphabet of size m. Any its substring with length equal to k is a palindrome. How many such strings exist? Your task is to find their quantity modulo 1000000007 (109 + 7). Be careful and don't miss a string or two!Let us remind you that a string is a palindrome if it can be read the same way in either direction, from the left to the right and from the right to the left.", "input_spec": "The first and only line contains three integers: n, m and k (1 ≤ n, m, k ≤ 2000).", "output_spec": "Print a single integer — the number of strings of the described type modulo 1000000007 (109 + 7).", "sample_inputs": ["1 1 1", "5 2 4"], "sample_outputs": ["1", "2"], "notes": "NoteIn the first sample only one string is valid: \"a\" (let's denote the only letter of our alphabet as \"a\").In the second sample (if we denote the alphabet letters as \"a\" and \"b\") the following strings are valid: \"aaaaa\" and \"bbbbb\"."}, "src_uid": "1f9107e8d1d8aebb1f4a1707a6cdeb6d"}
{"nl": {"description": "How horrible! The empire of galactic chickens tries to conquer a beautiful city \"Z\", they have built a huge incubator that produces millions of chicken soldiers a day, and fenced it around. The huge incubator looks like a polygon on the plane Oxy with n vertices. Naturally, DravDe can't keep still, he wants to destroy the chicken empire. For sure, he will start with the incubator.DravDe is strictly outside the incubator's territory in point A(xa, ya), and wants to get inside and kill all the chickens working there. But it takes a lot of doing! The problem is that recently DravDe went roller skating and has broken both his legs. He will get to the incubator's territory in his jet airplane LEVAP-41.LEVAP-41 flies at speed V(xv, yv, zv). DravDe can get on the plane in point A, fly for some time, and then air drop himself. DravDe is very heavy, that's why he falls vertically at speed Fdown, but in each point of his free fall DravDe can open his parachute, and from that moment he starts to fall at the wind speed U(xu, yu, zu) until he lands. Unfortunately, DravDe isn't good at mathematics. Would you help poor world's saviour find such an air dropping plan, that allows him to land on the incubator's territory? If the answer is not unique, DravDe wants to find the plan with the minimum time of his flight on the plane. If the answers are still multiple, he wants to find the one with the minimum time of his free fall before opening his parachute", "input_spec": "The first line contains the number n (3 ≤ n ≤ 104) — the amount of vertices of the fence. Then there follow n lines containing the coordinates of these vertices (two integer numbers xi, yi) in clockwise or counter-clockwise order. It's guaranteed, that the fence does not contain self-intersections. The following four lines contain coordinates of point A(xa, ya), speeds V(xv, yv, zv), Fdown and speed U(xu, yu, zu). All the input numbers are integer. All the coordinates don't exceed 104 in absolute value. It's guaranteed, that zv > 0 and Fdown, zu < 0, and point A is strictly outside the incubator's territory.", "output_spec": "In the first line output two numbers t1, t2 such, that if DravDe air drops at time t1 (counting from the beginning of the flight), he lands on the incubator's territory (landing on the border is regarder as landing on the territory). If DravDe doesn't open his parachute, the second number should be equal to the duration of DravDe's falling down. If it's impossible for DravDe to get to the incubator's territory, output -1 -1. If the answer is not unique, output the answer with the minimum t1. If the answers are still multiple, output the answer with the minimum t2. Your answer must have an absolute or relative error less than 10 - 6.", "sample_inputs": ["4\n0 0\n1 0\n1 1\n0 1\n0 -1\n1 0 1\n-1\n0 1 -1", "4\n0 0\n0 1\n1 1\n1 0\n0 -1\n-1 -1 1\n-1\n0 1 -1", "4\n0 0\n1 0\n1 1\n0 1\n0 -1\n1 1 1\n-1\n1 1 -1"], "sample_outputs": ["1.00000000 0.00000000", "-1.00000000 -1.00000000", "0.50000000 0.00000000"], "notes": null}, "src_uid": "d6afa6a515fc0adde11891e81cb179d7"}
{"nl": {"description": "Pasha has two hamsters: Arthur and Alexander. Pasha put n apples in front of them. Pasha knows which apples Arthur likes. Similarly, Pasha knows which apples Alexander likes. Pasha doesn't want any conflict between the hamsters (as they may like the same apple), so he decided to distribute the apples between the hamsters on his own. He is going to give some apples to Arthur and some apples to Alexander. It doesn't matter how many apples each hamster gets but it is important that each hamster gets only the apples he likes. It is possible that somebody doesn't get any apples.Help Pasha distribute all the apples between the hamsters. Note that Pasha wants to distribute all the apples, not just some of them.", "input_spec": "The first line contains integers n, a, b (1 ≤ n ≤ 100; 1 ≤ a, b ≤ n) — the number of apples Pasha has, the number of apples Arthur likes and the number of apples Alexander likes, correspondingly. The next line contains a distinct integers — the numbers of the apples Arthur likes. The next line contains b distinct integers — the numbers of the apples Alexander likes. Assume that the apples are numbered from 1 to n. The input is such that the answer exists.", "output_spec": "Print n characters, each of them equals either 1 or 2. If the i-h character equals 1, then the i-th apple should be given to Arthur, otherwise it should be given to Alexander. If there are multiple correct answers, you are allowed to print any of them.", "sample_inputs": ["4 2 3\n1 2\n2 3 4", "5 5 2\n3 4 1 2 5\n2 3"], "sample_outputs": ["1 1 2 2", "1 1 1 1 1"], "notes": null}, "src_uid": "a35a27754c9c095c6f1b2d4adccbfe93"}
{"nl": {"description": "The math faculty of Berland State University has suffered the sudden drop in the math skills of enrolling students. This year the highest grade on the entrance math test was 8. Out of 100! Thus, the decision was made to make the test easier.Future students will be asked just a single question. They are given a sequence of integer numbers $$$a_1, a_2, \\dots, a_n$$$, each number is from $$$1$$$ to $$$3$$$ and $$$a_i \\ne a_{i + 1}$$$ for each valid $$$i$$$. The $$$i$$$-th number represents a type of the $$$i$$$-th figure:  circle;  isosceles triangle with the length of height equal to the length of base;  square. The figures of the given sequence are placed somewhere on a Cartesian plane in such a way that:  $$$(i + 1)$$$-th figure is inscribed into the $$$i$$$-th one;  each triangle base is parallel to OX;  the triangle is oriented in such a way that the vertex opposite to its base is at the top;  each square sides are parallel to the axes;  for each $$$i$$$ from $$$2$$$ to $$$n$$$ figure $$$i$$$ has the maximum possible length of side for triangle and square and maximum radius for circle. Note that the construction is unique for some fixed position and size of just the first figure.The task is to calculate the number of distinct points (not necessarily with integer coordinates) where figures touch. The trick is, however, that the number is sometimes infinite. But that won't make the task difficult for you, will it?So can you pass the math test and enroll into Berland State University?", "input_spec": "The first line contains a single integer $$$n$$$ ($$$2 \\le n \\le 100$$$) — the number of figures. The second line contains $$$n$$$ integer numbers $$$a_1, a_2, \\dots, a_n$$$ ($$$1 \\le a_i \\le 3$$$, $$$a_i \\ne a_{i + 1}$$$) — types of the figures.", "output_spec": "The first line should contain either the word \"Infinite\" if the number of distinct points where figures touch is infinite or \"Finite\" otherwise. If the number is finite than print it in the second line. It's guaranteed that the number fits into 32-bit integer type.", "sample_inputs": ["3\n2 1 3", "3\n1 2 3"], "sample_outputs": ["Finite\n7", "Infinite"], "notes": "NoteHere are the glorious pictures for the examples. Note that the triangle is not equilateral but just isosceles with the length of height equal to the length of base. Thus it fits into a square in a unique way.The distinct points where figures touch are marked red.In the second example the triangle and the square touch each other for the whole segment, it contains infinite number of points.  "}, "src_uid": "6c8f028f655cc77b05ed89a668273702"}
{"nl": {"description": "Duff is in love with lovely numbers! A positive integer x is called lovely if and only if there is no such positive integer a > 1 such that a2 is a divisor of x.  Malek has a number store! In his store, he has only divisors of positive integer n (and he has all of them). As a birthday present, Malek wants to give her a lovely number from his store. He wants this number to be as big as possible.Malek always had issues in math, so he asked for your help. Please tell him what is the biggest lovely number in his store.", "input_spec": "The first and only line of input contains one integer, n (1 ≤ n ≤ 1012).", "output_spec": "Print the answer in one line.", "sample_inputs": ["10", "12"], "sample_outputs": ["10", "6"], "notes": "NoteIn first sample case, there are numbers 1, 2, 5 and 10 in the shop. 10 isn't divisible by any perfect square, so 10 is lovely.In second sample case, there are numbers 1, 2, 3, 4, 6 and 12 in the shop. 12 is divisible by 4 = 22, so 12 is not lovely, while 6 is indeed lovely."}, "src_uid": "6d0da975fa0961acfdbe75f2f29aeb92"}
{"nl": {"description": "Andrey received a postcard from Irina. It contained only the words \"Hello, Andrey!\", and a strange string consisting of lowercase Latin letters, snowflakes and candy canes. Andrey thought that this string is an encrypted message, and decided to decrypt it.Andrey noticed that snowflakes and candy canes always stand after the letters, so he supposed that the message was encrypted as follows. Candy cane means that the letter before it can be removed, or can be left. A snowflake means that the letter before it can be removed, left, or repeated several times.For example, consider the following string:   This string can encode the message «happynewyear». For this, candy canes and snowflakes should be used as follows:   candy cane 1: remove the letter w,  snowflake 1: repeat the letter p twice,  candy cane 2: leave the letter n,  snowflake 2: remove the letter w,  snowflake 3: leave the letter e.   Please note that the same string can encode different messages. For example, the string above can encode «hayewyar», «happpppynewwwwwyear», and other messages.Andrey knows that messages from Irina usually have a length of $$$k$$$ letters. Help him to find out if a given string can encode a message of $$$k$$$ letters, and if so, give an example of such a message.", "input_spec": "The first line contains the string received in the postcard. The string consists only of lowercase Latin letters, as well as the characters «*» and «?», meaning snowflake and candy cone, respectively. These characters can only appear immediately after the letter. The length of the string does not exceed $$$200$$$. The second line contains an integer number $$$k$$$ ($$$1 \\leq k \\leq 200$$$), the required message length.", "output_spec": "Print any message of length $$$k$$$ that the given string can encode, or «Impossible» if such a message does not exist.", "sample_inputs": ["hw?ap*yn?eww*ye*ar\n12", "ab?a\n2", "ab?a\n3", "ababb\n5", "ab?a\n1"], "sample_outputs": ["happynewyear", "aa", "aba", "ababb", "Impossible"], "notes": null}, "src_uid": "90ad5e6bb5839f9b99a125ccb118a276"}
{"nl": {"description": "Everybody in Russia uses Gregorian calendar. In this calendar there are 31 days in January, 28 or 29 days in February (depending on whether the year is leap or not), 31 days in March, 30 days in April, 31 days in May, 30 in June, 31 in July, 31 in August, 30 in September, 31 in October, 30 in November, 31 in December.A year is leap in one of two cases: either its number is divisible by 4, but not divisible by 100, or is divisible by 400. For example, the following years are leap: 2000, 2004, but years 1900 and 2018 are not leap.In this problem you are given n (1 ≤ n ≤ 24) integers a1, a2, ..., an, and you have to check if these integers could be durations in days of n consecutive months, according to Gregorian calendar. Note that these months could belong to several consecutive years. In other words, check if there is a month in some year, such that its duration is a1 days, duration of the next month is a2 days, and so on.", "input_spec": "The first line contains single integer n (1 ≤ n ≤ 24) — the number of integers. The second line contains n integers a1, a2, ..., an (28 ≤ ai ≤ 31) — the numbers you are to check.", "output_spec": "If there are several consecutive months that fit the sequence, print \"YES\" (without quotes). Otherwise, print \"NO\" (without quotes). You can print each letter in arbitrary case (small or large).", "sample_inputs": ["4\n31 31 30 31", "2\n30 30", "5\n29 31 30 31 30", "3\n31 28 30", "3\n31 31 28"], "sample_outputs": ["Yes", "No", "Yes", "No", "Yes"], "notes": "NoteIn the first example the integers can denote months July, August, September and October.In the second example the answer is no, because there are no two consecutive months each having 30 days.In the third example the months are: February (leap year) — March — April – May — June.In the fourth example the number of days in the second month is 28, so this is February. March follows February and has 31 days, but not 30, so the answer is NO.In the fifth example the months are: December — January — February (non-leap year)."}, "src_uid": "d60c8895cebcc5d0c6459238edbdb945"}
{"nl": {"description": "Petya studies in a school and he adores Maths. His class has been studying arithmetic expressions. On the last class the teacher wrote three positive integers a, b, c on the blackboard. The task was to insert signs of operations '+' and '*', and probably brackets between the numbers so that the value of the resulting expression is as large as possible. Let's consider an example: assume that the teacher wrote numbers 1, 2 and 3 on the blackboard. Here are some ways of placing signs and brackets:  1+2*3=7  1*(2+3)=5  1*2*3=6  (1+2)*3=9 Note that you can insert operation signs only between a and b, and between b and c, that is, you cannot swap integers. For instance, in the given sample you cannot get expression (1+3)*2.It's easy to see that the maximum value that you can obtain is 9.Your task is: given a, b and c print the maximum value that you can get.", "input_spec": "The input contains three integers a, b and c, each on a single line (1 ≤ a, b, c ≤ 10).", "output_spec": "Print the maximum value of the expression that you can obtain.", "sample_inputs": ["1\n2\n3", "2\n10\n3"], "sample_outputs": ["9", "60"], "notes": null}, "src_uid": "1cad9e4797ca2d80a12276b5a790ef27"}
{"nl": {"description": "There is a building consisting of $$$10~000$$$ apartments numbered from $$$1$$$ to $$$10~000$$$, inclusive.Call an apartment boring, if its number consists of the same digit. Examples of boring apartments are $$$11, 2, 777, 9999$$$ and so on.Our character is a troublemaker, and he calls the intercoms of all boring apartments, till someone answers the call, in the following order:  First he calls all apartments consisting of digit $$$1$$$, in increasing order ($$$1, 11, 111, 1111$$$).  Next he calls all apartments consisting of digit $$$2$$$, in increasing order ($$$2, 22, 222, 2222$$$)  And so on. The resident of the boring apartment $$$x$$$ answers the call, and our character stops calling anyone further.Our character wants to know how many digits he pressed in total and your task is to help him to count the total number of keypresses.For example, if the resident of boring apartment $$$22$$$ answered, then our character called apartments with numbers $$$1, 11, 111, 1111, 2, 22$$$ and the total number of digits he pressed is $$$1 + 2 + 3 + 4 + 1 + 2 = 13$$$.You have to answer $$$t$$$ independent test cases.", "input_spec": "The first line of the input contains one integer $$$t$$$ ($$$1 \\le t \\le 36$$$) — the number of test cases. The only line of the test case contains one integer $$$x$$$ ($$$1 \\le x \\le 9999$$$) — the apartment number of the resident who answered the call. It is guaranteed that $$$x$$$ consists of the same digit.", "output_spec": "For each test case, print the answer: how many digits our character pressed in total.", "sample_inputs": ["4\n22\n9999\n1\n777"], "sample_outputs": ["13\n90\n1\n66"], "notes": null}, "src_uid": "289a55128be89bb86a002d218d31b57f"}
{"nl": {"description": "Katie, Kuro and Shiro are best friends. They have known each other since kindergarten. That's why they often share everything with each other and work together on some very hard problems.Today is Shiro's birthday. She really loves pizza so she wants to invite her friends to the pizza restaurant near her house to celebrate her birthday, including her best friends Katie and Kuro.She has ordered a very big round pizza, in order to serve her many friends. Exactly $$$n$$$ of Shiro's friends are here. That's why she has to divide the pizza into $$$n + 1$$$ slices (Shiro also needs to eat). She wants the slices to be exactly the same size and shape. If not, some of her friends will get mad and go home early, and the party will be over.Shiro is now hungry. She wants to cut the pizza with minimum of straight cuts. A cut is a straight segment, it might have ends inside or outside the pizza. But she is too lazy to pick up the calculator.As usual, she will ask Katie and Kuro for help. But they haven't come yet. Could you help Shiro with this problem?", "input_spec": "A single line contains one non-negative integer $$$n$$$ ($$$0 \\le n \\leq 10^{18}$$$) — the number of Shiro's friends. The circular pizza has to be sliced into $$$n + 1$$$ pieces.", "output_spec": "A single integer — the number of straight cuts Shiro needs.", "sample_inputs": ["3", "4"], "sample_outputs": ["2", "5"], "notes": "NoteTo cut the round pizza into quarters one has to make two cuts through the center with angle $$$90^{\\circ}$$$ between them.To cut the round pizza into five equal parts one has to make five cuts."}, "src_uid": "236177ff30dafe68295b5d33dc501828"}
{"nl": {"description": "Awruk is taking part in elections in his school. It is the final round. He has only one opponent — Elodreip. The are $$$n$$$ students in the school. Each student has exactly $$$k$$$ votes and is obligated to use all of them. So Awruk knows that if a person gives $$$a_i$$$ votes for Elodreip, than he will get exactly $$$k - a_i$$$ votes from this person. Of course $$$0 \\le k - a_i$$$ holds.Awruk knows that if he loses his life is over. He has been speaking a lot with his friends and now he knows $$$a_1, a_2, \\dots, a_n$$$ — how many votes for Elodreip each student wants to give. Now he wants to change the number $$$k$$$ to win the elections. Of course he knows that bigger $$$k$$$ means bigger chance that somebody may notice that he has changed something and then he will be disqualified.So, Awruk knows $$$a_1, a_2, \\dots, a_n$$$ — how many votes each student will give to his opponent. Help him select the smallest winning number $$$k$$$. In order to win, Awruk needs to get strictly more votes than Elodreip.", "input_spec": "The first line contains integer $$$n$$$ ($$$1 \\le n \\le 100$$$) — the number of students in the school. The second line contains $$$n$$$ integers $$$a_1, a_2, \\ldots, a_n$$$ ($$$1 \\leq a_i \\leq 100$$$) — the number of votes each student gives to Elodreip.", "output_spec": "Output the smallest integer $$$k$$$ ($$$k \\ge \\max a_i$$$) which gives Awruk the victory. In order to win, Awruk needs to get strictly more votes than Elodreip.", "sample_inputs": ["5\n1 1 1 5 1", "5\n2 2 3 2 2"], "sample_outputs": ["5", "5"], "notes": "NoteIn the first example, Elodreip gets $$$1 + 1 + 1 + 5 + 1 = 9$$$ votes. The smallest possible $$$k$$$ is $$$5$$$ (it surely can't be less due to the fourth person), and it leads to $$$4 + 4 + 4 + 0 + 4 = 16$$$ votes for Awruk, which is enough to win.In the second example, Elodreip gets $$$11$$$ votes. If $$$k = 4$$$, Awruk gets $$$9$$$ votes and loses to Elodreip."}, "src_uid": "d215b3541d6d728ad01b166aae64faa2"}
{"nl": {"description": "Today, Mezo is playing a game. Zoma, a character in that game, is initially at position $$$x = 0$$$. Mezo starts sending $$$n$$$ commands to Zoma. There are two possible commands:  'L' (Left) sets the position $$$x: =x - 1$$$;  'R' (Right) sets the position $$$x: =x + 1$$$. Unfortunately, Mezo's controller malfunctions sometimes. Some commands are sent successfully and some are ignored. If the command is ignored then the position $$$x$$$ doesn't change and Mezo simply proceeds to the next command.For example, if Mezo sends commands \"LRLR\", then here are some possible outcomes (underlined commands are sent successfully):   \"LRLR\" — Zoma moves to the left, to the right, to the left again and to the right for the final time, ending up at position $$$0$$$;  \"LRLR\" — Zoma recieves no commands, doesn't move at all and ends up at position $$$0$$$ as well;  \"LRLR\" — Zoma moves to the left, then to the left again and ends up in position $$$-2$$$. Mezo doesn't know which commands will be sent successfully beforehand. Thus, he wants to know how many different positions may Zoma end up at.", "input_spec": "The first line contains $$$n$$$ $$$(1 \\le n \\le 10^5)$$$ — the number of commands Mezo sends. The second line contains a string $$$s$$$ of $$$n$$$ commands, each either 'L' (Left) or 'R' (Right).", "output_spec": "Print one integer — the number of different positions Zoma may end up at.", "sample_inputs": ["4\nLRLR"], "sample_outputs": ["5"], "notes": "NoteIn the example, Zoma may end up anywhere between $$$-2$$$ and $$$2$$$."}, "src_uid": "098ade88ed90664da279fe8a5a54b5ba"}
{"nl": {"description": "You are given a permutation p of numbers 1, 2, ..., n. Let's define f(p) as the following sum:Find the lexicographically m-th permutation of length n in the set of permutations having the maximum possible value of f(p).", "input_spec": "The single line of input contains two integers n and m (1 ≤ m ≤ cntn), where cntn is the number of permutations of length n with maximum possible value of f(p). The problem consists of two subproblems. The subproblems have different constraints on the input. You will get some score for the correct submission of the subproblem. The description of the subproblems follows.   In subproblem B1 (3 points), the constraint 1 ≤ n ≤ 8 will hold.  In subproblem B2 (4 points), the constraint 1 ≤ n ≤ 50 will hold. ", "output_spec": "Output n number forming the required permutation.", "sample_inputs": ["2 2", "3 2"], "sample_outputs": ["2 1", "1 3 2"], "notes": "NoteIn the first example, both permutations of numbers {1, 2} yield maximum possible f(p) which is equal to 4. Among them, (2, 1) comes second in lexicographical order."}, "src_uid": "a8da7cbd9ddaec8e0468c6cce884e7a2"}
{"nl": {"description": "Since Grisha behaved well last year, at New Year's Eve he was visited by Ded Moroz who brought an enormous bag of gifts with him! The bag contains n sweet candies from the good ol' bakery, each labeled from 1 to n corresponding to its tastiness. No two candies have the same tastiness.The choice of candies has a direct effect on Grisha's happiness. One can assume that he should take the tastiest ones — but no, the holiday magic turns things upside down. It is the xor-sum of tastinesses that matters, not the ordinary sum!A xor-sum of a sequence of integers a1, a2, ..., am is defined as the bitwise XOR of all its elements: , here  denotes the bitwise XOR operation; more about bitwise XOR can be found here.Ded Moroz warned Grisha he has more houses to visit, so Grisha can take no more than k candies from the bag. Help Grisha determine the largest xor-sum (largest xor-sum means maximum happiness!) he can obtain.", "input_spec": "The sole string contains two integers n and k (1 ≤ k ≤ n ≤ 1018).", "output_spec": "Output one number — the largest possible xor-sum.", "sample_inputs": ["4 3", "6 6"], "sample_outputs": ["7", "7"], "notes": "NoteIn the first sample case, one optimal answer is 1, 2 and 4, giving the xor-sum of 7.In the second sample case, one can, for example, take all six candies and obtain the xor-sum of 7."}, "src_uid": "16bc089f5ef6b68bebe8eda6ead2eab9"}
{"nl": {"description": "Several months later Alex finally got his brother Bob's creation by post. And now, in his turn, Alex wants to boast about something to his brother. He thought for a while, and came to the conclusion that he has no ready creations, and decided to write a program for rectangles detection. According to his plan, the program detects if the four given segments form a rectangle of a positive area and with sides parallel to coordinate axes. As Alex does badly at school and can't write this program by himself, he asks you to help him.", "input_spec": "The input data contain four lines. Each of these lines contains four integers x1, y1, x2, y2 ( - 109 ≤ x1, y1, x2, y2 ≤ 109) — coordinates of segment's beginning and end positions. The given segments can degenerate into points.", "output_spec": "Output the word «YES», if the given four segments form the required rectangle, otherwise output «NO».", "sample_inputs": ["1 1 6 1\n1 0 6 0\n6 0 6 1\n1 1 1 0", "0 0 0 3\n2 0 0 0\n2 2 2 0\n0 2 2 2"], "sample_outputs": ["YES", "NO"], "notes": null}, "src_uid": "ad105c08f63e9761fe90f69630628027"}
{"nl": {"description": "Vasya has n days of vacations! So he decided to improve his IT skills and do sport. Vasya knows the following information about each of this n days: whether that gym opened and whether a contest was carried out in the Internet on that day. For the i-th day there are four options:  on this day the gym is closed and the contest is not carried out;  on this day the gym is closed and the contest is carried out;  on this day the gym is open and the contest is not carried out;  on this day the gym is open and the contest is carried out. On each of days Vasya can either have a rest or write the contest (if it is carried out on this day), or do sport (if the gym is open on this day).Find the minimum number of days on which Vasya will have a rest (it means, he will not do sport and write the contest at the same time). The only limitation that Vasya has — he does not want to do the same activity on two consecutive days: it means, he will not do sport on two consecutive days, and write the contest on two consecutive days.", "input_spec": "The first line contains a positive integer n (1 ≤ n ≤ 100) — the number of days of Vasya's vacations. The second line contains the sequence of integers a1, a2, ..., an (0 ≤ ai ≤ 3) separated by space, where:    ai equals 0, if on the i-th day of vacations the gym is closed and the contest is not carried out;  ai equals 1, if on the i-th day of vacations the gym is closed, but the contest is carried out;  ai equals 2, if on the i-th day of vacations the gym is open and the contest is not carried out;  ai equals 3, if on the i-th day of vacations the gym is open and the contest is carried out.", "output_spec": "Print the minimum possible number of days on which Vasya will have a rest. Remember that Vasya refuses:   to do sport on any two consecutive days,  to write the contest on any two consecutive days. ", "sample_inputs": ["4\n1 3 2 0", "7\n1 3 3 2 1 2 3", "2\n2 2"], "sample_outputs": ["2", "0", "1"], "notes": "NoteIn the first test Vasya can write the contest on the day number 1 and do sport on the day number 3. Thus, he will have a rest for only 2 days.In the second test Vasya should write contests on days number 1, 3, 5 and 7, in other days do sport. Thus, he will not have a rest for a single day.In the third test Vasya can do sport either on a day number 1 or number 2. He can not do sport in two days, because it will be contrary to the his limitation. Thus, he will have a rest for only one day."}, "src_uid": "08f1ba79ced688958695a7cfcfdda035"}
{"nl": {"description": "Vasya has a pack of 54 cards (52 standard cards and 2 distinct jokers). That is all he has at the moment. Not to die from boredom, Vasya plays Solitaire with them.Vasya lays out nm cards as a rectangle n × m. If there are jokers among them, then Vasya should change them with some of the rest of 54 - nm cards (which are not layed out) so that there were no jokers left. Vasya can pick the cards to replace the jokers arbitrarily. Remember, that each card presents in pack exactly once (i. e. in a single copy). Vasya tries to perform the replacements so that the solitaire was solved.Vasya thinks that the solitaire is solved if after the jokers are replaced, there exist two non-overlapping squares 3 × 3, inside each of which all the cards either have the same suit, or pairwise different ranks.Determine by the initial position whether the solitaire can be solved or not. If it can be solved, show the way in which it is possible.", "input_spec": "The first line contains integers n and m (3 ≤ n, m ≤ 17, n × m ≤ 52). Next n lines contain m words each. Each word consists of two letters. The jokers are defined as \"J1\" and \"J2\" correspondingly. For the rest of the cards, the first letter stands for the rank and the second one — for the suit. The possible ranks are: \"2\", \"3\", \"4\", \"5\", \"6\", \"7\", \"8\", \"9\", \"T\", \"J\", \"Q\", \"K\" and \"A\". The possible suits are: \"C\", \"D\", \"H\" and \"S\". All the cards are different.", "output_spec": "If the Solitaire can be solved, print on the first line \"Solution exists.\" without the quotes. On the second line print in what way the jokers can be replaced. Three variants are possible:   \"There are no jokers.\", if there are no jokers in the input data. \"Replace Jx with y.\", if there is one joker. x is its number, and y is the card it should be replaced with. \"Replace J1 with x and J2 with y.\", if both jokers are present in the input data. x and y here represent distinct cards with which one should replace the first and the second jokers correspondingly. On the third line print the coordinates of the upper left corner of the first square 3 × 3 in the format \"Put the first square to (r, c).\", where r and c are the row and the column correspondingly. In the same manner print on the fourth line the coordinates of the second square 3 × 3 in the format \"Put the second square to (r, c).\". If there are several solutions to that problem, print any of them. If there are no solutions, print of the single line \"No solution.\" without the quotes. See the samples to understand the output format better.", "sample_inputs": ["4 6\n2S 3S 4S 7S 8S AS\n5H 6H 7H 5S TC AC\n8H 9H TH 7C 8C 9C\n2D 2C 3C 4C 5C 6C", "4 6\n2S 3S 4S 7S 8S AS\n5H 6H 7H J1 TC AC\n8H 9H TH 7C 8C 9C\n2D 2C 3C 4C 5C 6C", "4 6\n2S 3S 4S 7S 8S AS\n5H 6H 7H QC TC AC\n8H 9H TH 7C 8C 9C\n2D 2C 3C 4C 5C 6C"], "sample_outputs": ["No solution.", "Solution exists.\nReplace J1 with 2H.\nPut the first square to (1, 1).\nPut the second square to (2, 4).", "Solution exists.\nThere are no jokers.\nPut the first square to (1, 1).\nPut the second square to (2, 4)."], "notes": "NoteThe pretests cover all the possible output formats."}, "src_uid": "b3f29d9c27cbfeadb96b6ac9ffd6bc8f"}
{"nl": {"description": "Consider a playoff tournament where $$$2^n$$$ athletes compete. The athletes are numbered from $$$1$$$ to $$$2^n$$$.The tournament is held in $$$n$$$ stages. In each stage, the athletes are split into pairs in such a way that each athlete belongs exactly to one pair. In each pair, the athletes compete against each other, and exactly one of them wins. The winner of each pair advances to the next stage, the athlete who was defeated gets eliminated from the tournament.The pairs are formed as follows:  in the first stage, athlete $$$1$$$ competes against athlete $$$2$$$; $$$3$$$ competes against $$$4$$$; $$$5$$$ competes against $$$6$$$, and so on;  in the second stage, the winner of the match \"$$$1$$$–$$$2$$$\" competes against the winner of the match \"$$$3$$$–$$$4$$$\"; the winner of the match \"$$$5$$$–$$$6$$$\" competes against the winner of the match \"$$$7$$$–$$$8$$$\", and so on;  the next stages are held according to the same rules. When athletes $$$x$$$ and $$$y$$$ compete, the winner is decided as follows:  if $$$x+y$$$ is odd, the athlete with the lower index wins (i. e. if $$$x < y$$$, then $$$x$$$ wins, otherwise $$$y$$$ wins);  if $$$x+y$$$ is even, the athlete with the higher index wins. The following picture describes the way the tournament with $$$n = 3$$$ goes.  Your task is the following one: given the integer $$$n$$$, determine the index of the athlete who wins the tournament.", "input_spec": "The first line contains one integer $$$t$$$ ($$$1 \\le t \\le 30$$$) — the number of test cases. Each test case consists of one line containing one integer $$$n$$$ ($$$1 \\le n \\le 30$$$).", "output_spec": "For each test case, print one integer — the index of the winner of the tournament.", "sample_inputs": ["2\n3\n1"], "sample_outputs": ["7\n1"], "notes": "NoteThe case $$$n = 3$$$ is shown in the picture from the statement.If $$$n = 1$$$, then there's only one match between athletes $$$1$$$ and $$$2$$$. Since $$$1 + 2 = 3$$$ is an odd number, the athlete with the lower index wins. So, the athlete $$$1$$$ is the winner."}, "src_uid": "d5e66e34601cad6d78c3f02898fa09f4"}
{"nl": {"description": "Once upon a time a child got a test consisting of multiple-choice questions as homework. A multiple-choice question consists of four choices: A, B, C and D. Each choice has a description, and the child should find out the only one that is correct.Fortunately the child knows how to solve such complicated test. The child will follow the algorithm:  If there is some choice whose description at least twice shorter than all other descriptions, or at least twice longer than all other descriptions, then the child thinks the choice is great.  If there is exactly one great choice then the child chooses it. Otherwise the child chooses C (the child think it is the luckiest choice). You are given a multiple-choice questions, can you predict child's choose?", "input_spec": "The first line starts with \"A.\" (without quotes), then followed the description of choice A. The next three lines contains the descriptions of the other choices in the same format. They are given in order: B, C, D. Please note, that the description goes after prefix \"X.\", so the prefix mustn't be counted in description's length. Each description is non-empty and consists of at most 100 characters. Each character can be either uppercase English letter or lowercase English letter, or \"_\". ", "output_spec": "Print a single line with the child's choice: \"A\", \"B\", \"C\" or \"D\" (without quotes).", "sample_inputs": ["A.VFleaKing_is_the_author_of_this_problem\nB.Picks_is_the_author_of_this_problem\nC.Picking_is_the_author_of_this_problem\nD.Ftiasch_is_cute", "A.ab\nB.abcde\nC.ab\nD.abc", "A.c\nB.cc\nC.c\nD.c"], "sample_outputs": ["D", "C", "B"], "notes": "NoteIn the first sample, the first choice has length 39, the second one has length 35, the third one has length 37, and the last one has length 15. The choice D (length 15) is twice shorter than all other choices', so it is great choice. There is no other great choices so the child will choose D.In the second sample, no choice is great, so the child will choose the luckiest choice C.In the third sample, the choice B (length 2) is twice longer than all other choices', so it is great choice. There is no other great choices so the child will choose B."}, "src_uid": "30725e340dc07f552f0cce359af226a4"}
{"nl": {"description": "One day Misha and Andrew were playing a very simple game. First, each player chooses an integer in the range from 1 to n. Let's assume that Misha chose number m, and Andrew chose number a.Then, by using a random generator they choose a random integer c in the range between 1 and n (any integer from 1 to n is chosen with the same probability), after which the winner is the player, whose number was closer to c. The boys agreed that if m and a are located on the same distance from c, Misha wins.Andrew wants to win very much, so he asks you to help him. You know the number selected by Misha, and number n. You need to determine which value of a Andrew must choose, so that the probability of his victory is the highest possible.More formally, you need to find such integer a (1 ≤ a ≤ n), that the probability that  is maximal, where c is the equiprobably chosen integer from 1 to n (inclusive).", "input_spec": "The first line contains two integers n and m (1 ≤ m ≤ n ≤ 109) — the range of numbers in the game, and the number selected by Misha respectively.", "output_spec": "Print a single number — such value a, that probability that Andrew wins is the highest. If there are multiple such values, print the minimum of them.", "sample_inputs": ["3 1", "4 3"], "sample_outputs": ["2", "2"], "notes": "NoteIn the first sample test: Andrew wins if c is equal to 2 or 3. The probability that Andrew wins is 2 / 3. If Andrew chooses a = 3, the probability of winning will be 1 / 3. If a = 1, the probability of winning is 0.In the second sample test: Andrew wins if c is equal to 1 and 2. The probability that Andrew wins is 1 / 2. For other choices of a the probability of winning is less."}, "src_uid": "f6a80c0f474cae1e201032e1df10e9f7"}
{"nl": {"description": "Memory and his friend Lexa are competing to get higher score in one popular computer game. Memory starts with score a and Lexa starts with score b. In a single turn, both Memory and Lexa get some integer in the range [ - k;k] (i.e. one integer among  - k,  - k + 1,  - k + 2, ...,  - 2,  - 1, 0, 1, 2, ..., k - 1, k) and add them to their current scores. The game has exactly t turns. Memory and Lexa, however, are not good at this game, so they both always get a random integer at their turn.Memory wonders how many possible games exist such that he ends with a strictly higher score than Lexa. Two games are considered to be different if in at least one turn at least one player gets different score. There are (2k + 1)2t games in total. Since the answer can be very large, you should print it modulo 109 + 7. Please solve this problem for Memory.", "input_spec": "The first and only line of input contains the four integers a, b, k, and t (1 ≤ a, b ≤ 100, 1 ≤ k ≤ 1000, 1 ≤ t ≤ 100) — the amount Memory and Lexa start with, the number k, and the number of turns respectively.", "output_spec": "Print the number of possible games satisfying the conditions modulo 1 000 000 007 (109 + 7) in one line.", "sample_inputs": ["1 2 2 1", "1 1 1 2", "2 12 3 1"], "sample_outputs": ["6", "31", "0"], "notes": "NoteIn the first sample test, Memory starts with 1 and Lexa starts with 2. If Lexa picks  - 2, Memory can pick 0, 1, or 2 to win. If Lexa picks  - 1, Memory can pick 1 or 2 to win. If Lexa picks 0, Memory can pick 2 to win. If Lexa picks 1 or 2, Memory cannot win. Thus, there are 3 + 2 + 1 = 6 possible games in which Memory wins."}, "src_uid": "8b8327512a318a5b5afd531ff7223bd0"}
{"nl": {"description": "Let's introduce some definitions that will be needed later.Let $$$prime(x)$$$ be the set of prime divisors of $$$x$$$. For example, $$$prime(140) = \\{ 2, 5, 7 \\}$$$, $$$prime(169) = \\{ 13 \\}$$$.Let $$$g(x, p)$$$ be the maximum possible integer $$$p^k$$$ where $$$k$$$ is an integer such that $$$x$$$ is divisible by $$$p^k$$$. For example:  $$$g(45, 3) = 9$$$ ($$$45$$$ is divisible by $$$3^2=9$$$ but not divisible by $$$3^3=27$$$),  $$$g(63, 7) = 7$$$ ($$$63$$$ is divisible by $$$7^1=7$$$ but not divisible by $$$7^2=49$$$). Let $$$f(x, y)$$$ be the product of $$$g(y, p)$$$ for all $$$p$$$ in $$$prime(x)$$$. For example:  $$$f(30, 70) = g(70, 2) \\cdot g(70, 3) \\cdot g(70, 5) = 2^1 \\cdot 3^0 \\cdot 5^1 = 10$$$,  $$$f(525, 63) = g(63, 3) \\cdot g(63, 5) \\cdot g(63, 7) = 3^2 \\cdot 5^0 \\cdot 7^1 = 63$$$. You have integers $$$x$$$ and $$$n$$$. Calculate $$$f(x, 1) \\cdot f(x, 2) \\cdot \\ldots \\cdot f(x, n) \\bmod{(10^{9} + 7)}$$$.", "input_spec": "The only line contains integers $$$x$$$ and $$$n$$$ ($$$2 \\le x \\le 10^{9}$$$, $$$1 \\le n \\le 10^{18}$$$) — the numbers used in formula.", "output_spec": "Print the answer.", "sample_inputs": ["10 2", "20190929 1605", "947 987654321987654321"], "sample_outputs": ["2", "363165664", "593574252"], "notes": "NoteIn the first example, $$$f(10, 1) = g(1, 2) \\cdot g(1, 5) = 1$$$, $$$f(10, 2) = g(2, 2) \\cdot g(2, 5) = 2$$$.In the second example, actual value of formula is approximately $$$1.597 \\cdot 10^{171}$$$. Make sure you print the answer modulo $$$(10^{9} + 7)$$$.In the third example, be careful about overflow issue."}, "src_uid": "04610fbaa746c083dda30e21fa6e1a0c"}
{"nl": {"description": "The King of Flatland will organize a knights' tournament! The winner will get half the kingdom and the favor of the princess of legendary beauty and wisdom. The final test of the applicants' courage and strength will be a fencing tournament. The tournament is held by the following rules: the participants fight one on one, the winner (or rather, the survivor) transfers to the next round.Before the battle both participants stand at the specified points on the Ox axis with integer coordinates. Then they make moves in turn. The first participant moves first, naturally. During a move, the first participant can transfer from the point x to any integer point of the interval [x + a; x + b]. The second participant can transfer during a move to any integer point of the interval [x - b; x - a]. That is, the options for the players' moves are symmetric (note that the numbers a and b are not required to be positive, and if a ≤ 0 ≤ b, then staying in one place is a correct move). At any time the participants can be located arbitrarily relative to each other, that is, it is allowed to \"jump\" over the enemy in any direction. A participant wins if he uses his move to transfer to the point where his opponent is.Of course, the princess has already chosen a husband and now she wants to make her sweetheart win the tournament. He has already reached the tournament finals and he is facing the last battle. The princess asks the tournament manager to arrange the tournament finalists in such a way that her sweetheart wins the tournament, considering that both players play optimally. However, the initial location of the participants has already been announced, and we can only pull some strings and determine which participant will be first and which one will be second. But how do we know which participant can secure the victory? Alas, the princess is not learned in the military affairs... Therefore, she asks you to determine how the battle will end considering that both opponents play optimally. Also, if the first player wins, your task is to determine his winning move.", "input_spec": "The first line contains four space-separated integers — x1, x2, a and b (x1 ≠ x2, a ≤ b,  - 109 ≤ x1, x2, a, b ≤ 109) — coordinates of the points where the first and the second participant start, and the numbers that determine the players' moves, correspondingly.", "output_spec": "On the first line print the outcome of the battle as \"FIRST\" (without the quotes), if both players play optimally and the first player wins. Print \"SECOND\" (without the quotes) if the second player wins and print \"DRAW\" (without the quotes), if nobody is able to secure the victory. If the first player wins, print on the next line the single integer x — the coordinate of the point where the first player should transfer to win. The indicated move should be valid, that is, it should meet the following condition: x1 + a ≤ x ≤ x1 + b. If there are several winning moves, print any of them. If the first participant can't secure the victory, then you do not have to print anything.", "sample_inputs": ["0 2 0 4", "0 2 1 1", "0 2 0 1"], "sample_outputs": ["FIRST\n2", "SECOND", "DRAW"], "notes": "NoteIn the first sample the first player can win in one move.In the second sample the first participant must go to point 1, where the second participant immediately goes and wins. In the third sample changing the position isn't profitable to either participant, so nobody wins."}, "src_uid": "4ea8cc3305a0ee2c1e580b43e5bc46c6"}
{"nl": {"description": "Famous Brazil city Rio de Janeiro holds a tennis tournament and Ostap Bender doesn't want to miss this event. There will be n players participating, and the tournament will follow knockout rules from the very first game. That means, that if someone loses a game he leaves the tournament immediately.Organizers are still arranging tournament grid (i.e. the order games will happen and who is going to play with whom) but they have already fixed one rule: two players can play against each other only if the number of games one of them has already played differs by no more than one from the number of games the other one has already played. Of course, both players had to win all their games in order to continue participating in the tournament.Tournament hasn't started yet so the audience is a bit bored. Ostap decided to find out what is the maximum number of games the winner of the tournament can take part in (assuming the rule above is used). However, it is unlikely he can deal with this problem without your help.", "input_spec": "The only line of the input contains a single integer n (2 ≤ n ≤ 1018) — the number of players to participate in the tournament.", "output_spec": "Print the maximum number of games in which the winner of the tournament can take part.", "sample_inputs": ["2", "3", "4", "10"], "sample_outputs": ["1", "2", "2", "4"], "notes": "NoteIn all samples we consider that player number 1 is the winner.In the first sample, there would be only one game so the answer is 1.In the second sample, player 1 can consequently beat players 2 and 3. In the third sample, player 1 can't play with each other player as after he plays with players 2 and 3 he can't play against player 4, as he has 0 games played, while player 1 already played 2. Thus, the answer is 2 and to achieve we make pairs (1, 2) and (3, 4) and then clash the winners."}, "src_uid": "3d3432b4f7c6a3b901161fa24b415b14"}
{"nl": {"description": "You are given a text of single-space separated words, consisting of small and capital Latin letters.Volume of the word is number of capital letters in the word. Volume of the text is maximum volume of all words in the text.Calculate the volume of the given text.", "input_spec": "The first line contains one integer number n (1 ≤ n ≤ 200) — length of the text. The second line contains text of single-space separated words s1, s2, ..., si, consisting only of small and capital Latin letters.", "output_spec": "Print one integer number — volume of text.", "sample_inputs": ["7\nNonZERO", "24\nthis is zero answer text", "24\nHarbour Space University"], "sample_outputs": ["5", "0", "1"], "notes": "NoteIn the first example there is only one word, there are 5 capital letters in it.In the second example all of the words contain 0 capital letters."}, "src_uid": "d3929a9acf1633475ab16f5dfbead13c"}
{"nl": {"description": "Your friend recently gave you some slimes for your birthday. You have n slimes all initially with value 1.You are going to play a game with these slimes. Initially, you put a single slime by itself in a row. Then, you will add the other n - 1 slimes one by one. When you add a slime, you place it at the right of all already placed slimes. Then, while the last two slimes in the row have the same value v, you combine them together to create a slime with value v + 1.You would like to see what the final state of the row is after you've added all n slimes. Please print the values of the slimes in the row from left to right.", "input_spec": "The first line of the input will contain a single integer, n (1 ≤ n ≤ 100 000).", "output_spec": "Output a single line with k integers, where k is the number of slimes in the row after you've finished the procedure described in the problem statement. The i-th of these numbers should be the value of the i-th slime from the left.", "sample_inputs": ["1", "2", "3", "8"], "sample_outputs": ["1", "2", "2 1", "4"], "notes": "NoteIn the first sample, we only have a single slime with value 1. The final state of the board is just a single slime with value 1.In the second sample, we perform the following steps:Initially we place a single slime in a row by itself. Thus, row is initially 1.Then, we will add another slime. The row is now 1 1. Since two rightmost slimes have the same values, we should replace these slimes with one with value 2. Thus, the final state of the board is 2.In the third sample, after adding the first two slimes, our row is 2. After adding one more slime, the row becomes 2 1.In the last sample, the steps look as follows:   1  2  2 1  3  3 1  3 2  3 2 1  4 "}, "src_uid": "757cd804aba01dc4bc108cb0722f68dc"}
{"nl": {"description": "Amr is a young coder who likes music a lot. He always wanted to learn how to play music but he was busy coding so he got an idea.Amr has n instruments, it takes ai days to learn i-th instrument. Being busy, Amr dedicated k days to learn how to play the maximum possible number of instruments.Amr asked for your help to distribute his free days between instruments so that he can achieve his goal.", "input_spec": "The first line contains two numbers n, k (1 ≤ n ≤ 100, 0 ≤ k ≤ 10 000), the number of instruments and number of days respectively. The second line contains n integers ai (1 ≤ ai ≤ 100), representing number of days required to learn the i-th instrument.", "output_spec": "In the first line output one integer m representing the maximum number of instruments Amr can learn. In the second line output m space-separated integers: the indices of instruments to be learnt. You may output indices in any order. if there are multiple optimal solutions output any. It is not necessary to use all days for studying.", "sample_inputs": ["4 10\n4 3 1 2", "5 6\n4 3 1 1 2", "1 3\n4"], "sample_outputs": ["4\n1 2 3 4", "3\n1 3 4", "0"], "notes": "NoteIn the first test Amr can learn all 4 instruments.In the second test other possible solutions are: {2, 3, 5} or {3, 4, 5}.In the third test Amr doesn't have enough time to learn the only presented instrument."}, "src_uid": "dbb164a8dd190e63cceba95a31690a7c"}
{"nl": {"description": "Daenerys Targaryen has an army consisting of k groups of soldiers, the i-th group contains ai soldiers. She wants to bring her army to the other side of the sea to get the Iron Throne. She has recently bought an airplane to carry her army through the sea. The airplane has n rows, each of them has 8 seats. We call two seats neighbor, if they are in the same row and in seats {1, 2}, {3, 4}, {4, 5}, {5, 6} or {7, 8}.  A row in the airplane Daenerys Targaryen wants to place her army in the plane so that there are no two soldiers from different groups sitting on neighboring seats.Your task is to determine if there is a possible arranging of her army in the airplane such that the condition above is satisfied.", "input_spec": "The first line contains two integers n and k (1 ≤ n ≤ 10000, 1 ≤ k ≤ 100) — the number of rows and the number of groups of soldiers, respectively. The second line contains k integers a1, a2, a3, ..., ak (1 ≤ ai ≤ 10000), where ai denotes the number of soldiers in the i-th group. It is guaranteed that a1 + a2 + ... + ak ≤ 8·n.", "output_spec": "If we can place the soldiers in the airplane print \"YES\" (without quotes). Otherwise print \"NO\" (without quotes). You can choose the case (lower or upper) for each letter arbitrary.", "sample_inputs": ["2 2\n5 8", "1 2\n7 1", "1 2\n4 4", "1 4\n2 2 1 2"], "sample_outputs": ["YES", "NO", "YES", "YES"], "notes": "NoteIn the first sample, Daenerys can place the soldiers like in the figure below:  In the second sample, there is no way to place the soldiers in the plane since the second group soldier will always have a seat neighboring to someone from the first group.In the third example Daenerys can place the first group on seats (1, 2, 7, 8), and the second group an all the remaining seats.In the fourth example she can place the first two groups on seats (1, 2) and (7, 8), the third group on seats (3), and the fourth group on seats (5, 6)."}, "src_uid": "d1f88a97714d6c13309c88fcf7d86821"}
{"nl": {"description": "Stepan has n pens. Every day he uses them, and on the i-th day he uses the pen number i. On the (n + 1)-th day again he uses the pen number 1, on the (n + 2)-th — he uses the pen number 2 and so on.On every working day (from Monday to Saturday, inclusive) Stepan spends exactly 1 milliliter of ink of the pen he uses that day. On Sunday Stepan has a day of rest, he does not stend the ink of the pen he uses that day. Stepan knows the current volume of ink in each of his pens. Now it's the Monday morning and Stepan is going to use the pen number 1 today. Your task is to determine which pen will run out of ink before all the rest (that is, there will be no ink left in it), if Stepan will use the pens according to the conditions described above.", "input_spec": "The first line contains the integer n (1 ≤ n ≤ 50 000) — the number of pens Stepan has. The second line contains the sequence of integers a1, a2, ..., an (1 ≤ ai ≤ 109), where ai is equal to the number of milliliters of ink which the pen number i currently has.", "output_spec": "Print the index of the pen which will run out of ink before all (it means that there will be no ink left in it), if Stepan will use pens according to the conditions described above.  Pens are numbered in the order they are given in input data. The numeration begins from one.  Note that the answer is always unambiguous, since several pens can not end at the same time.", "sample_inputs": ["3\n3 3 3", "5\n5 4 5 4 4"], "sample_outputs": ["2", "5"], "notes": "NoteIn the first test Stepan uses ink of pens as follows:   on the day number 1 (Monday) Stepan will use the pen number 1, after that there will be 2 milliliters of ink in it;  on the day number 2 (Tuesday) Stepan will use the pen number 2, after that there will be 2 milliliters of ink in it;  on the day number 3 (Wednesday) Stepan will use the pen number 3, after that there will be 2 milliliters of ink in it;  on the day number 4 (Thursday) Stepan will use the pen number 1, after that there will be 1 milliliters of ink in it;  on the day number 5 (Friday) Stepan will use the pen number 2, after that there will be 1 milliliters of ink in it;  on the day number 6 (Saturday) Stepan will use the pen number 3, after that there will be 1 milliliters of ink in it;  on the day number 7 (Sunday) Stepan will use the pen number 1, but it is a day of rest so he will not waste ink of this pen in it;  on the day number 8 (Monday) Stepan will use the pen number 2, after that this pen will run out of ink. So, the first pen which will not have ink is the pen number 2."}, "src_uid": "8054dc5dd09d600d7fb8d9f5db4dcaca"}
{"nl": {"description": "The Fair Nut lives in $$$n$$$ story house. $$$a_i$$$ people live on the $$$i$$$-th floor of the house. Every person uses elevator twice a day: to get from the floor where he/she lives to the ground (first) floor and to get from the first floor to the floor where he/she lives, when he/she comes back home in the evening. It was decided that elevator, when it is not used, will stay on the $$$x$$$-th floor, but $$$x$$$ hasn't been chosen yet. When a person needs to get from floor $$$a$$$ to floor $$$b$$$, elevator follows the simple algorithm:   Moves from the $$$x$$$-th floor (initially it stays on the $$$x$$$-th floor) to the $$$a$$$-th and takes the passenger.  Moves from the $$$a$$$-th floor to the $$$b$$$-th floor and lets out the passenger (if $$$a$$$ equals $$$b$$$, elevator just opens and closes the doors, but still comes to the floor from the $$$x$$$-th floor).  Moves from the $$$b$$$-th floor back to the $$$x$$$-th.  The elevator never transposes more than one person and always goes back to the floor $$$x$$$ before transposing a next passenger. The elevator spends one unit of electricity to move between neighboring floors. So moving from the $$$a$$$-th floor to the $$$b$$$-th floor requires $$$|a - b|$$$ units of electricity.Your task is to help Nut to find the minimum number of electricity units, that it would be enough for one day, by choosing an optimal the $$$x$$$-th floor. Don't forget than elevator initially stays on the $$$x$$$-th floor. ", "input_spec": "The first line contains one integer $$$n$$$ ($$$1 \\leq n \\leq 100$$$) — the number of floors. The second line contains $$$n$$$ integers $$$a_1, a_2, \\ldots, a_n$$$ ($$$0 \\leq a_i \\leq 100$$$) — the number of people on each floor.", "output_spec": "In a single line, print the answer to the problem — the minimum number of electricity units.", "sample_inputs": ["3\n0 2 1", "2\n1 1"], "sample_outputs": ["16", "4"], "notes": "NoteIn the first example, the answer can be achieved by choosing the second floor as the $$$x$$$-th floor. Each person from the second floor (there are two of them) would spend $$$4$$$ units of electricity per day ($$$2$$$ to get down and $$$2$$$ to get up), and one person from the third would spend $$$8$$$ units of electricity per day ($$$4$$$ to get down and $$$4$$$ to get up). $$$4 \\cdot 2 + 8 \\cdot 1 = 16$$$.In the second example, the answer can be achieved by choosing the first floor as the $$$x$$$-th floor."}, "src_uid": "a5002ddf9e792cb4b4685e630f1e1b8f"}
{"nl": {"description": "Meg the Rabbit decided to do something nice, specifically — to determine the shortest distance between two points on the surface of our planet. But Meg... what can you say, she wants everything simple. So, she already regards our planet as a two-dimensional circle. No, wait, it's even worse — as a square of side n. Thus, the task has been reduced to finding the shortest path between two dots on a square (the path should go through the square sides). To simplify the task let us consider the vertices of the square to lie at points whose coordinates are: (0, 0), (n, 0), (0, n) and (n, n).", "input_spec": "The single line contains 5 space-separated integers: n, x1, y1, x2, y2 (1 ≤ n ≤ 1000, 0 ≤ x1, y1, x2, y2 ≤ n) which correspondingly represent a side of the square, the coordinates of the first point and the coordinates of the second point. It is guaranteed that the points lie on the sides of the square.", "output_spec": "You must print on a single line the shortest distance between the points.", "sample_inputs": ["2 0 0 1 0", "2 0 1 2 1", "100 0 0 100 100"], "sample_outputs": ["1", "4", "200"], "notes": null}, "src_uid": "685fe16c217b5b71eafdb4198822250e"}
{"nl": {"description": "Polycarpus loves hamburgers very much. He especially adores the hamburgers he makes with his own hands. Polycarpus thinks that there are only three decent ingredients to make hamburgers from: a bread, sausage and cheese. He writes down the recipe of his favorite \"Le Hamburger de Polycarpus\" as a string of letters 'B' (bread), 'S' (sausage) и 'C' (cheese). The ingredients in the recipe go from bottom to top, for example, recipe \"ВSCBS\" represents the hamburger where the ingredients go from bottom to top as bread, sausage, cheese, bread and sausage again.Polycarpus has nb pieces of bread, ns pieces of sausage and nc pieces of cheese in the kitchen. Besides, the shop nearby has all three ingredients, the prices are pb rubles for a piece of bread, ps for a piece of sausage and pc for a piece of cheese.Polycarpus has r rubles and he is ready to shop on them. What maximum number of hamburgers can he cook? You can assume that Polycarpus cannot break or slice any of the pieces of bread, sausage or cheese. Besides, the shop has an unlimited number of pieces of each ingredient.", "input_spec": "The first line of the input contains a non-empty string that describes the recipe of \"Le Hamburger de Polycarpus\". The length of the string doesn't exceed 100, the string contains only letters 'B' (uppercase English B), 'S' (uppercase English S) and 'C' (uppercase English C). The second line contains three integers nb, ns, nc (1 ≤ nb, ns, nc ≤ 100) — the number of the pieces of bread, sausage and cheese on Polycarpus' kitchen. The third line contains three integers pb, ps, pc (1 ≤ pb, ps, pc ≤ 100) — the price of one piece of bread, sausage and cheese in the shop. Finally, the fourth line contains integer r (1 ≤ r ≤ 1012) — the number of rubles Polycarpus has. Please, do not write the %lld specifier to read or write 64-bit integers in С++. It is preferred to use the cin, cout streams or the %I64d specifier.", "output_spec": "Print the maximum number of hamburgers Polycarpus can make. If he can't make any hamburger, print 0.", "sample_inputs": ["BBBSSC\n6 4 1\n1 2 3\n4", "BBC\n1 10 1\n1 10 1\n21", "BSC\n1 1 1\n1 1 3\n1000000000000"], "sample_outputs": ["2", "7", "200000000001"], "notes": null}, "src_uid": "8126a4232188ae7de8e5a7aedea1a97e"}
{"nl": {"description": "Bomboslav likes to look out of the window in his room and watch lads outside playing famous shell game. The game is played by two persons: operator and player. Operator takes three similar opaque shells and places a ball beneath one of them. Then he shuffles the shells by swapping some pairs and the player has to guess the current position of the ball.Bomboslav noticed that guys are not very inventive, so the operator always swaps the left shell with the middle one during odd moves (first, third, fifth, etc.) and always swaps the middle shell with the right one during even moves (second, fourth, etc.).Let's number shells from 0 to 2 from left to right. Thus the left shell is assigned number 0, the middle shell is 1 and the right shell is 2. Bomboslav has missed the moment when the ball was placed beneath the shell, but he knows that exactly n movements were made by the operator and the ball was under shell x at the end. Now he wonders, what was the initial position of the ball?", "input_spec": "The first line of the input contains an integer n (1 ≤ n ≤ 2·109) — the number of movements made by the operator. The second line contains a single integer x (0 ≤ x ≤ 2) — the index of the shell where the ball was found after n movements.", "output_spec": "Print one integer from 0 to 2 — the index of the shell where the ball was initially placed.", "sample_inputs": ["4\n2", "1\n1"], "sample_outputs": ["1", "0"], "notes": "NoteIn the first sample, the ball was initially placed beneath the middle shell and the operator completed four movements.  During the first move operator swapped the left shell and the middle shell. The ball is now under the left shell.  During the second move operator swapped the middle shell and the right one. The ball is still under the left shell.  During the third move operator swapped the left shell and the middle shell again. The ball is again in the middle.  Finally, the operators swapped the middle shell and the right shell. The ball is now beneath the right shell. "}, "src_uid": "7853e03d520cd71571a6079cdfc4c4b0"}
{"nl": {"description": "Little Petya loves presents. His mum bought him two strings of the same size for his birthday. The strings consist of uppercase and lowercase Latin letters. Now Petya wants to compare those two strings lexicographically. The letters' case does not matter, that is an uppercase letter is considered equivalent to the corresponding lowercase letter. Help Petya perform the comparison.", "input_spec": "Each of the first two lines contains a bought string. The strings' lengths range from 1 to 100 inclusive. It is guaranteed that the strings are of the same length and also consist of uppercase and lowercase Latin letters.", "output_spec": "If the first string is less than the second one, print \"-1\". If the second string is less than the first one, print \"1\". If the strings are equal, print \"0\". Note that the letters' case is not taken into consideration when the strings are compared.", "sample_inputs": ["aaaa\naaaA", "abs\nAbz", "abcdefg\nAbCdEfF"], "sample_outputs": ["0", "-1", "1"], "notes": "NoteIf you want more formal information about the lexicographical order (also known as the \"dictionary order\" or \"alphabetical order\"), you can visit the following site: http://en.wikipedia.org/wiki/Lexicographical_order"}, "src_uid": "ffeae332696a901813677bd1033cf01e"}
{"nl": {"description": "Little Petya loves counting. He wants to count the number of ways to paint a rectangular checkered board of size n × m (n rows, m columns) in k colors. Besides, the coloring should have the following property: for any vertical line that passes along the grid lines and divides the board in two non-empty parts the number of distinct colors in both these parts should be the same. Help Petya to count these colorings.", "input_spec": "The first line contains space-separated integers n, m and k (1 ≤ n, m ≤ 1000, 1 ≤ k ≤ 106) — the board's vertical and horizontal sizes and the number of colors respectively.", "output_spec": "Print the answer to the problem. As the answer can be quite a large number, you should print it modulo 109 + 7 (1000000007).", "sample_inputs": ["2 2 1", "2 2 2", "3 2 2"], "sample_outputs": ["1", "8", "40"], "notes": null}, "src_uid": "f22f28e2d8933f4199ba5ccfc0de8cda"}
{"nl": {"description": "You are given two set of points. The first set is determined by the equation A1x + B1y + C1 = 0, and the second one is determined by the equation A2x + B2y + C2 = 0.Write the program which finds the number of points in the intersection of two given sets.", "input_spec": "The first line of the input contains three integer numbers A1, B1, C1 separated by space. The second line contains three integer numbers A2, B2, C2 separated by space. All the numbers are between -100 and 100, inclusive.", "output_spec": "Print the number of points in the intersection or -1 if there are infinite number of points.", "sample_inputs": ["1 1 0\n2 2 0", "1 1 0\n2 -2 0"], "sample_outputs": ["-1", "1"], "notes": null}, "src_uid": "c8e869cb17550e888733551c749f2e1a"}
{"nl": {"description": "The final round of Bayan Programming Contest will be held in Tehran, and the participants will be carried around with a yellow bus. The bus has 34 passenger seats: 4 seats in the last row and 3 seats in remaining rows.   The event coordinator has a list of k participants who should be picked up at the airport. When a participant gets on the bus, he will sit in the last row with an empty seat. If there is more than one empty seat in that row, he will take the leftmost one. In order to keep track of the people who are on the bus, the event coordinator needs a figure showing which seats are going to be taken by k participants. Your task is to draw the figure representing occupied seats.", "input_spec": "The only line of input contains integer k, (0 ≤ k ≤ 34), denoting the number of participants.", "output_spec": "Print the figure of a bus with k passengers as described in sample tests. Character '#' denotes an empty seat, while 'O' denotes a taken seat. 'D' is the bus driver and other characters in the output are for the purpose of beautifying the figure. Strictly follow the sample test cases output format. Print exactly six lines. Do not output extra space or other characters.", "sample_inputs": ["9", "20"], "sample_outputs": ["+------------------------+\n|O.O.O.#.#.#.#.#.#.#.#.|D|)\n|O.O.O.#.#.#.#.#.#.#.#.|.|\n|O.......................|\n|O.O.#.#.#.#.#.#.#.#.#.|.|)\n+------------------------+", "+------------------------+\n|O.O.O.O.O.O.O.#.#.#.#.|D|)\n|O.O.O.O.O.O.#.#.#.#.#.|.|\n|O.......................|\n|O.O.O.O.O.O.#.#.#.#.#.|.|)\n+------------------------+"], "notes": null}, "src_uid": "075f83248f6d4d012e0ca1547fc67993"}
{"nl": {"description": "Let's define the permutation of length n as an array p = [p1, p2, ..., pn] consisting of n distinct integers from range from 1 to n. We say that this permutation maps value 1 into the value p1, value 2 into the value p2 and so on.Kyota Ootori has just learned about cyclic representation of a permutation. A cycle is a sequence of numbers such that each element of this sequence is being mapped into the next element of this sequence (and the last element of the cycle is being mapped into the first element of the cycle). The cyclic representation is a representation of p as a collection of cycles forming p. For example, permutation p = [4, 1, 6, 2, 5, 3] has a cyclic representation that looks like (142)(36)(5) because 1 is replaced by 4, 4 is replaced by 2, 2 is replaced by 1, 3 and 6 are swapped, and 5 remains in place. Permutation may have several cyclic representations, so Kyoya defines the standard cyclic representation of a permutation as follows. First, reorder the elements within each cycle so the largest element is first. Then, reorder all of the cycles so they are sorted by their first element. For our example above, the standard cyclic representation of [4, 1, 6, 2, 5, 3] is (421)(5)(63).Now, Kyoya notices that if we drop the parenthesis in the standard cyclic representation, we get another permutation! For instance, [4, 1, 6, 2, 5, 3] will become [4, 2, 1, 5, 6, 3].Kyoya notices that some permutations don't change after applying operation described above at all. He wrote all permutations of length n that do not change in a list in lexicographic order. Unfortunately, his friend Tamaki Suoh lost this list. Kyoya wishes to reproduce the list and he needs your help. Given the integers n and k, print the permutation that was k-th on Kyoya's list.", "input_spec": "The first line will contain two integers n, k (1 ≤ n ≤ 50, 1 ≤ k ≤ min{1018, l} where l is the length of the Kyoya's list).", "output_spec": "Print n space-separated integers, representing the permutation that is the answer for the question. ", "sample_inputs": ["4 3", "10 1"], "sample_outputs": ["1 3 2 4", "1 2 3 4 5 6 7 8 9 10"], "notes": "NoteThe standard cycle representation is (1)(32)(4), which after removing parenthesis gives us the original permutation. The first permutation on the list would be [1, 2, 3, 4], while the second permutation would be [1, 2, 4, 3]."}, "src_uid": "e03c6d3bb8cf9119530668765691a346"}
{"nl": {"description": "The only difference between easy and hard versions is constraints.Ivan plays a computer game that contains some microtransactions to make characters look cooler. Since Ivan wants his character to be really cool, he wants to use some of these microtransactions — and he won't start playing until he gets all of them.Each day (during the morning) Ivan earns exactly one burle.There are $$$n$$$ types of microtransactions in the game. Each microtransaction costs $$$2$$$ burles usually and $$$1$$$ burle if it is on sale. Ivan has to order exactly $$$k_i$$$ microtransactions of the $$$i$$$-th type (he orders microtransactions during the evening).Ivan can order any (possibly zero) number of microtransactions of any types during any day (of course, if he has enough money to do it). If the microtransaction he wants to order is on sale then he can buy it for $$$1$$$ burle and otherwise he can buy it for $$$2$$$ burles.There are also $$$m$$$ special offers in the game shop. The $$$j$$$-th offer $$$(d_j, t_j)$$$ means that microtransactions of the $$$t_j$$$-th type are on sale during the $$$d_j$$$-th day.Ivan wants to order all microtransactions as soon as possible. Your task is to calculate the minimum day when he can buy all microtransactions he want and actually start playing.", "input_spec": "The first line of the input contains two integers $$$n$$$ and $$$m$$$ ($$$1 \\le n, m \\le 1000$$$) — the number of types of microtransactions and the number of special offers in the game shop. The second line of the input contains $$$n$$$ integers $$$k_1, k_2, \\dots, k_n$$$ ($$$0 \\le k_i \\le 1000$$$), where $$$k_i$$$ is the number of copies of microtransaction of the $$$i$$$-th type Ivan has to order. It is guaranteed that sum of all $$$k_i$$$ is not less than $$$1$$$ and not greater than $$$1000$$$. The next $$$m$$$ lines contain special offers. The $$$j$$$-th of these lines contains the $$$j$$$-th special offer. It is given as a pair of integers $$$(d_j, t_j)$$$ ($$$1 \\le d_j \\le 1000, 1 \\le t_j \\le n$$$) and means that microtransactions of the $$$t_j$$$-th type are on sale during the $$$d_j$$$-th day.", "output_spec": "Print one integer — the minimum day when Ivan can order all microtransactions he wants and actually start playing.", "sample_inputs": ["5 6\n1 2 0 2 0\n2 4\n3 3\n1 5\n1 2\n1 5\n2 3", "5 3\n4 2 1 3 2\n3 5\n4 2\n2 5"], "sample_outputs": ["8", "20"], "notes": null}, "src_uid": "2eb101dcfcc487fe6e44c9b4c0e4024d"}
{"nl": {"description": "One day Vasya was lying in bed watching his electronic clock to fall asleep quicker.Vasya lives in a strange country, where days have h hours, and every hour has m minutes. Clock shows time in decimal number system, in format H:M, where the string H always has a fixed length equal to the number of digits in the decimal representation of number h - 1. To achieve this, leading zeros are added if necessary. The string M has a similar format, and its length is always equal to the number of digits in the decimal representation of number m - 1. For example, if h = 17, m = 1000, then time equal to 13 hours and 75 minutes will be displayed as \"13:075\".Vasya had been watching the clock from h1 hours m1 minutes to h2 hours m2 minutes inclusive, and then he fell asleep. Now he asks you to count how many times he saw the moment at which at least k digits changed on the clock simultaneously.For example, when switching 04:19  →  04:20 two digits change. When switching 23:59  →  00:00, four digits change.Consider that Vasya has been watching the clock for strictly less than one day. Note that the last time Vasya saw on the clock before falling asleep was \"h2:m2\". That is, Vasya didn't see the moment at which time \"h2:m2\" switched to the next value.", "input_spec": "The first line of the input file contains three space-separated integers h, m and k (2 ≤ h, m ≤ 109, 1 ≤ k ≤ 20). The second line contains space-separated integers h1, m1 (0 ≤ h1 < h, 0 ≤ m1 < m). The third line contains space-separated integers h2, m2 (0 ≤ h2 < h, 0 ≤ m2 < m).", "output_spec": "Print a single number — the number of times Vasya saw the moment of changing at least k digits simultaneously. Please do not use the %lld specificator to read or write 64-bit integers in C++. It is preferred to use the cin stream (also you may use the %I64d specificator).", "sample_inputs": ["5 5 2\n4 4\n2 1", "24 60 1\n0 0\n23 59", "24 60 3\n23 59\n23 59"], "sample_outputs": ["3", "1439", "0"], "notes": "NoteIn the first example Vasya will see the following moments of time: 4:4  0:0  →  0:1  →  0:2  →  0:3  →  0:4  1:0  →  1:1  →  1:2  →  1:3  →  1:4  2:0  →  2:1  →  2:2  →  2:3  →  2:4. Double arrow () marks the sought moments of time (in this example — when Vasya sees two numbers changing simultaneously).In the second example k = 1. Any switching time can be accepted, since during switching of the clock at least one digit is changed. Total switching equals to 24·60 = 1440, but Vasya have not seen one of them — the switching of 23:59  00:00.In the third example Vasya fell asleep immediately after he began to look at the clock, so he did not see any change."}, "src_uid": "e2782743229645ad3a0f8e815d86dc5f"}
{"nl": {"description": "In the city of Ultima Thule job applicants are often offered an IQ test. The test is as follows: the person gets a piece of squared paper with a 4 × 4 square painted on it. Some of the square's cells are painted black and others are painted white. Your task is to repaint at most one cell the other color so that the picture has a 2 × 2 square, completely consisting of cells of the same color. If the initial picture already has such a square, the person should just say so and the test will be completed. Your task is to write a program that determines whether it is possible to pass the test. You cannot pass the test if either repainting any cell or no action doesn't result in a 2 × 2 square, consisting of cells of the same color.", "input_spec": "Four lines contain four characters each: the j-th character of the i-th line equals \".\" if the cell in the i-th row and the j-th column of the square is painted white, and \"#\", if the cell is black.", "output_spec": "Print \"YES\" (without the quotes), if the test can be passed and \"NO\" (without the quotes) otherwise.", "sample_inputs": ["####\n.#..\n####\n....", "####\n....\n####\n...."], "sample_outputs": ["YES", "NO"], "notes": "NoteIn the first test sample it is enough to repaint the first cell in the second row. After such repainting the required 2 × 2 square is on the intersection of the 1-st and 2-nd row with the 1-st and 2-nd column."}, "src_uid": "01b145e798bbdf0ca2ecc383676d79f3"}
{"nl": {"description": "Let's denote a function $$$f(x)$$$ in such a way: we add $$$1$$$ to $$$x$$$, then, while there is at least one trailing zero in the resulting number, we remove that zero. For example,   $$$f(599) = 6$$$: $$$599 + 1 = 600 \\rightarrow 60 \\rightarrow 6$$$;  $$$f(7) = 8$$$: $$$7 + 1 = 8$$$;  $$$f(9) = 1$$$: $$$9 + 1 = 10 \\rightarrow 1$$$;  $$$f(10099) = 101$$$: $$$10099 + 1 = 10100 \\rightarrow 1010 \\rightarrow 101$$$. We say that some number $$$y$$$ is reachable from $$$x$$$ if we can apply function $$$f$$$ to $$$x$$$ some (possibly zero) times so that we get $$$y$$$ as a result. For example, $$$102$$$ is reachable from $$$10098$$$ because $$$f(f(f(10098))) = f(f(10099)) = f(101) = 102$$$; and any number is reachable from itself.You are given a number $$$n$$$; your task is to count how many different numbers are reachable from $$$n$$$.", "input_spec": "The first line contains one integer $$$n$$$ ($$$1 \\le n \\le 10^9$$$).", "output_spec": "Print one integer: the number of different numbers that are reachable from $$$n$$$.", "sample_inputs": ["1098", "10"], "sample_outputs": ["20", "19"], "notes": "NoteThe numbers that are reachable from $$$1098$$$ are:$$$1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 14, 15, 16, 17, 18, 19, 1098, 1099$$$."}, "src_uid": "055fbbde4b9ffd4473e6e716da6da899"}
{"nl": {"description": "Vasya is studying number theory. He has denoted a function f(a, b) such that:  f(a, 0) = 0;  f(a, b) = 1 + f(a, b - gcd(a, b)), where gcd(a, b) is the greatest common divisor of a and b. Vasya has two numbers x and y, and he wants to calculate f(x, y). He tried to do it by himself, but found out that calculating this function the way he wants to do that might take very long time. So he decided to ask you to implement a program that will calculate this function swiftly.", "input_spec": "The first line contains two integer numbers x and y (1 ≤ x, y ≤ 1012).", "output_spec": "Print f(x, y).", "sample_inputs": ["3 5", "6 3"], "sample_outputs": ["3", "1"], "notes": null}, "src_uid": "ea92cd905e9725e7fcb87b9ed4f64c2e"}
{"nl": {"description": "Those days, many boys use beautiful girls' photos as avatars in forums. So it is pretty hard to tell the gender of a user at the first glance. Last year, our hero went to a forum and had a nice chat with a beauty (he thought so). After that they talked very often and eventually they became a couple in the network. But yesterday, he came to see \"her\" in the real world and found out \"she\" is actually a very strong man! Our hero is very sad and he is too tired to love again now. So he came up with a way to recognize users' genders by their user names.This is his method: if the number of distinct characters in one's user name is odd, then he is a male, otherwise she is a female. You are given the string that denotes the user name, please help our hero to determine the gender of this user by his method.", "input_spec": "The first line contains a non-empty string, that contains only lowercase English letters — the user name. This string contains at most 100 letters.", "output_spec": "If it is a female by our hero's method, print \"CHAT WITH HER!\" (without the quotes), otherwise, print \"IGNORE HIM!\" (without the quotes).", "sample_inputs": ["wjmzbmr", "xiaodao", "sevenkplus"], "sample_outputs": ["CHAT WITH HER!", "IGNORE HIM!", "CHAT WITH HER!"], "notes": "NoteFor the first example. There are 6 distinct characters in \"wjmzbmr\". These characters are: \"w\", \"j\", \"m\", \"z\", \"b\", \"r\". So wjmzbmr is a female and you should print \"CHAT WITH HER!\"."}, "src_uid": "a8c14667b94b40da087501fd4bdd7818"}
{"nl": {"description": "There are $$$n + 2$$$ towns located on a coordinate line, numbered from $$$0$$$ to $$$n + 1$$$. The $$$i$$$-th town is located at the point $$$i$$$.You build a radio tower in each of the towns $$$1, 2, \\dots, n$$$ with probability $$$\\frac{1}{2}$$$ (these events are independent). After that, you want to set the signal power on each tower to some integer from $$$1$$$ to $$$n$$$ (signal powers are not necessarily the same, but also not necessarily different). The signal from a tower located in a town $$$i$$$ with signal power $$$p$$$ reaches every city $$$c$$$ such that $$$|c - i| < p$$$.After building the towers, you want to choose signal powers in such a way that:  towns $$$0$$$ and $$$n + 1$$$ don't get any signal from the radio towers;  towns $$$1, 2, \\dots, n$$$ get signal from exactly one radio tower each. For example, if $$$n = 5$$$, and you have built the towers in towns $$$2$$$, $$$4$$$ and $$$5$$$, you may set the signal power of the tower in town $$$2$$$ to $$$2$$$, and the signal power of the towers in towns $$$4$$$ and $$$5$$$ to $$$1$$$. That way, towns $$$0$$$ and $$$n + 1$$$ don't get the signal from any tower, towns $$$1$$$, $$$2$$$ and $$$3$$$ get the signal from the tower in town $$$2$$$, town $$$4$$$ gets the signal from the tower in town $$$4$$$, and town $$$5$$$ gets the signal from the tower in town $$$5$$$.Calculate the probability that, after building the towers, you will have a way to set signal powers to meet all constraints.", "input_spec": "The first (and only) line of the input contains one integer $$$n$$$ ($$$1 \\le n \\le 2 \\cdot 10^5$$$).", "output_spec": "Print one integer — the probability that there will be a way to set signal powers so that all constraints are met, taken modulo $$$998244353$$$. Formally, the probability can be expressed as an irreducible fraction $$$\\frac{x}{y}$$$. You have to print the value of $$$x \\cdot y^{-1} \\bmod 998244353$$$, where $$$y^{-1}$$$ is an integer such that $$$y \\cdot y^{-1} \\bmod 998244353 = 1$$$.", "sample_inputs": ["2", "3", "5", "200000"], "sample_outputs": ["748683265", "748683265", "842268673", "202370013"], "notes": "NoteThe real answer for the first example is $$$\\frac{1}{4}$$$:  with probability $$$\\frac{1}{4}$$$, the towers are built in both towns $$$1$$$ and $$$2$$$, so we can set their signal powers to $$$1$$$. The real answer for the second example is $$$\\frac{1}{4}$$$:   with probability $$$\\frac{1}{8}$$$, the towers are built in towns $$$1$$$, $$$2$$$ and $$$3$$$, so we can set their signal powers to $$$1$$$;  with probability $$$\\frac{1}{8}$$$, only one tower in town $$$2$$$ is built, and we can set its signal power to $$$2$$$. The real answer for the third example is $$$\\frac{5}{32}$$$. Note that even though the previous explanations used equal signal powers for all towers, it is not necessarily so. For example, if $$$n = 5$$$ and the towers are built in towns $$$2$$$, $$$4$$$ and $$$5$$$, you may set the signal power of the tower in town $$$2$$$ to $$$2$$$, and the signal power of the towers in towns $$$4$$$ and $$$5$$$ to $$$1$$$."}, "src_uid": "cec37432956bb0a1ce62a0188fe2d805"}
{"nl": {"description": "In Berland each high school student is characterized by academic performance — integer value between 1 and 5.In high school 0xFF there are two groups of pupils: the group A and the group B. Each group consists of exactly n students. An academic performance of each student is known — integer value between 1 and 5.The school director wants to redistribute students between groups so that each of the two groups has the same number of students whose academic performance is equal to 1, the same number of students whose academic performance is 2 and so on. In other words, the purpose of the school director is to change the composition of groups, so that for each value of academic performance the numbers of students in both groups are equal.To achieve this, there is a plan to produce a series of exchanges of students between groups. During the single exchange the director selects one student from the class A and one student of class B. After that, they both change their groups.Print the least number of exchanges, in order to achieve the desired equal numbers of students for each academic performance.", "input_spec": "The first line of the input contains integer number n (1 ≤ n ≤ 100) — number of students in both groups. The second line contains sequence of integer numbers a1, a2, ..., an (1 ≤ ai ≤ 5), where ai is academic performance of the i-th student of the group A. The third line contains sequence of integer numbers b1, b2, ..., bn (1 ≤ bi ≤ 5), where bi is academic performance of the i-th student of the group B.", "output_spec": "Print the required minimum number of exchanges or -1, if the desired distribution of students can not be obtained.", "sample_inputs": ["4\n5 4 4 4\n5 5 4 5", "6\n1 1 1 1 1 1\n5 5 5 5 5 5", "1\n5\n3", "9\n3 2 5 5 2 3 3 3 2\n4 1 4 1 1 2 4 4 1"], "sample_outputs": ["1", "3", "-1", "4"], "notes": null}, "src_uid": "47da1dd95cd015acb8c7fd6ae5ec22a3"}
{"nl": {"description": "Sagheer is walking in the street when he comes to an intersection of two roads. Each road can be represented as two parts where each part has 3 lanes getting into the intersection (one for each direction) and 3 lanes getting out of the intersection, so we have 4 parts in total. Each part has 4 lights, one for each lane getting into the intersection (l — left, s — straight, r — right) and a light p for a pedestrian crossing.   An accident is possible if a car can hit a pedestrian. This can happen if the light of a pedestrian crossing of some part and the light of a lane that can get to or from that same part are green at the same time.Now, Sagheer is monitoring the configuration of the traffic lights. Your task is to help him detect whether an accident is possible.", "input_spec": "The input consists of four lines with each line describing a road part given in a counter-clockwise order. Each line contains four integers l, s, r, p — for the left, straight, right and pedestrian lights, respectively. The possible values are 0 for red light and 1 for green light.", "output_spec": "On a single line, print \"YES\" if an accident is possible, and \"NO\" otherwise.", "sample_inputs": ["1 0 0 1\n0 1 0 0\n0 0 1 0\n0 0 0 1", "0 1 1 0\n1 0 1 0\n1 1 0 0\n0 0 0 1", "1 0 0 0\n0 0 0 1\n0 0 0 0\n1 0 1 0"], "sample_outputs": ["YES", "NO", "NO"], "notes": "NoteIn the first example, some accidents are possible because cars of part 1 can hit pedestrians of parts 1 and 4. Also, cars of parts 2 and 3 can hit pedestrians of part 4.In the second example, no car can pass the pedestrian crossing of part 4 which is the only green pedestrian light. So, no accident can occur."}, "src_uid": "44fdf71d56bef949ec83f00d17c29127"}
{"nl": {"description": "Simon and Antisimon play a game. Initially each player receives one fixed positive integer that doesn't change throughout the game. Simon receives number a and Antisimon receives number b. They also have a heap of n stones. The players take turns to make a move and Simon starts. During a move a player should take from the heap the number of stones equal to the greatest common divisor of the fixed number he has received and the number of stones left in the heap. A player loses when he cannot take the required number of stones (i. e. the heap has strictly less stones left than one needs to take). Your task is to determine by the given a, b and n who wins the game.", "input_spec": "The only string contains space-separated integers a, b and n (1 ≤ a, b, n ≤ 100) — the fixed numbers Simon and Antisimon have received correspondingly and the initial number of stones in the pile.", "output_spec": "If Simon wins, print \"0\" (without the quotes), otherwise print \"1\" (without the quotes).", "sample_inputs": ["3 5 9", "1 1 100"], "sample_outputs": ["0", "1"], "notes": "NoteThe greatest common divisor of two non-negative integers a and b is such maximum positive integer k, that a is divisible by k without remainder and similarly, b is divisible by k without remainder. Let gcd(a, b) represent the operation of calculating the greatest common divisor of numbers a and b. Specifically, gcd(x, 0) = gcd(0, x) = x.In the first sample the game will go like that: Simon should take gcd(3, 9) = 3 stones from the heap. After his move the heap has 6 stones left. Antisimon should take gcd(5, 6) = 1 stone from the heap. After his move the heap has 5 stones left. Simon should take gcd(3, 5) = 1 stone from the heap. After his move the heap has 4 stones left. Antisimon should take gcd(5, 4) = 1 stone from the heap. After his move the heap has 3 stones left. Simon should take gcd(3, 3) = 3 stones from the heap. After his move the heap has 0 stones left. Antisimon should take gcd(5, 0) = 5 stones from the heap. As 0 < 5, it is impossible and Antisimon loses.In the second sample each player during each move takes one stone from the heap. As n is even, Antisimon takes the last stone and Simon can't make a move after that."}, "src_uid": "0bd6fbb6b0a2e7e5f080a70553149ac2"}
{"nl": {"description": "As you have noticed, there are lovely girls in Arpa’s land.People in Arpa's land are numbered from 1 to n. Everyone has exactly one crush, i-th person's crush is person with the number crushi.  Someday Arpa shouted Owf loudly from the top of the palace and a funny game started in Arpa's land. The rules are as follows.The game consists of rounds. Assume person x wants to start a round, he calls crushx and says: \"Oww...wwf\" (the letter w is repeated t times) and cuts off the phone immediately. If t > 1 then crushx calls crushcrushx and says: \"Oww...wwf\" (the letter w is repeated t - 1 times) and cuts off the phone immediately. The round continues until some person receives an \"Owf\" (t = 1). This person is called the Joon-Joon of the round. There can't be two rounds at the same time.Mehrdad has an evil plan to make the game more funny, he wants to find smallest t (t ≥ 1) such that for each person x, if x starts some round and y becomes the Joon-Joon of the round, then by starting from y, x would become the Joon-Joon of the round. Find such t for Mehrdad if it's possible.Some strange fact in Arpa's land is that someone can be himself's crush (i.e. crushi = i).", "input_spec": "The first line of input contains integer n (1 ≤ n ≤ 100) — the number of people in Arpa's land. The second line contains n integers, i-th of them is crushi (1 ≤ crushi ≤ n) — the number of i-th person's crush.", "output_spec": "If there is no t satisfying the condition, print -1. Otherwise print such smallest t.", "sample_inputs": ["4\n2 3 1 4", "4\n4 4 4 4", "4\n2 1 4 3"], "sample_outputs": ["3", "-1", "1"], "notes": "NoteIn the first sample suppose t = 3. If the first person starts some round:The first person calls the second person and says \"Owwwf\", then the second person calls the third person and says \"Owwf\", then the third person calls the first person and says \"Owf\", so the first person becomes Joon-Joon of the round. So the condition is satisfied if x is 1.The process is similar for the second and the third person.If the fourth person starts some round:The fourth person calls himself and says \"Owwwf\", then he calls himself again and says \"Owwf\", then he calls himself for another time and says \"Owf\", so the fourth person becomes Joon-Joon of the round. So the condition is satisfied when x is 4.In the last example if the first person starts a round, then the second person becomes the Joon-Joon, and vice versa."}, "src_uid": "149221131a978298ac56b58438df46c9"}
{"nl": {"description": "Mr. Kitayuta has kindly given you a string s consisting of lowercase English letters. You are asked to insert exactly n lowercase English letters into s to make it a palindrome. (A palindrome is a string that reads the same forward and backward. For example, \"noon\", \"testset\" and \"a\" are all palindromes, while \"test\" and \"kitayuta\" are not.) You can choose any n lowercase English letters, and insert each of them to any position of s, possibly to the beginning or the end of s. You have to insert exactly n letters even if it is possible to turn s into a palindrome by inserting less than n letters.Find the number of the palindromes that can be obtained in this way, modulo 10007.", "input_spec": "The first line contains a string s (1 ≤ |s| ≤ 200). Each character in s is a lowercase English letter. The second line contains an integer n (1 ≤ n ≤ 109).", "output_spec": "Print the number of the palindromes that can be obtained, modulo 10007.", "sample_inputs": ["revive\n1", "add\n2"], "sample_outputs": ["1", "28"], "notes": "NoteFor the first sample, you can obtain the palindrome \"reviver\" by inserting 'r' to the end of \"revive\".For the second sample, the following 28 palindromes can be obtained: \"adada\", \"adbda\", ..., \"adzda\", \"dadad\" and \"ddadd\"."}, "src_uid": "2ae6f17e0dd0bc93090d939f4f49d7a8"}
{"nl": {"description": "Little Dima misbehaved during a math lesson a lot and the nasty teacher Mr. Pickles gave him the following problem as a punishment. Find all integer solutions x (0 < x < 109) of the equation:x = b·s(x)a + c,  where a, b, c are some predetermined constant values and function s(x) determines the sum of all digits in the decimal representation of number x.The teacher gives this problem to Dima for each lesson. He changes only the parameters of the equation: a, b, c. Dima got sick of getting bad marks and he asks you to help him solve this challenging problem.", "input_spec": "The first line contains three space-separated integers: a, b, c (1 ≤ a ≤ 5; 1 ≤ b ≤ 10000;  - 10000 ≤ c ≤ 10000).", "output_spec": "Print integer n — the number of the solutions that you've found. Next print n integers in the increasing order — the solutions of the given equation. Print only integer solutions that are larger than zero and strictly less than 109.", "sample_inputs": ["3 2 8", "1 2 -18", "2 2 -1"], "sample_outputs": ["3\n10 2008 13726", "0", "4\n1 31 337 967"], "notes": null}, "src_uid": "e477185b94f93006d7ae84c8f0817009"}
{"nl": {"description": "Fox Ciel is playing a game with numbers now. Ciel has n positive integers: x1, x2, ..., xn. She can do the following operation as many times as needed: select two different indexes i and j such that xi > xj hold, and then apply assignment xi = xi - xj. The goal is to make the sum of all numbers as small as possible.Please help Ciel to find this minimal sum.", "input_spec": "The first line contains an integer n (2 ≤ n ≤ 100). Then the second line contains n integers: x1, x2, ..., xn (1 ≤ xi ≤ 100).", "output_spec": "Output a single integer — the required minimal sum.", "sample_inputs": ["2\n1 2", "3\n2 4 6", "2\n12 18", "5\n45 12 27 30 18"], "sample_outputs": ["2", "6", "12", "15"], "notes": "NoteIn the first example the optimal way is to do the assignment: x2 = x2 - x1.In the second example the optimal sequence of operations is: x3 = x3 - x2, x2 = x2 - x1."}, "src_uid": "042cf938dc4a0f46ff33d47b97dc6ad4"}
{"nl": {"description": "Please note that the memory limit differs from the standard.You really love to listen to music. During the each of next s days you will listen to exactly m songs from the playlist that consists of exactly n songs. Let's number the songs from the playlist with numbers from 1 to n, inclusive. The quality of song number i is ai.On the i-th day you choose some integer v (li ≤ v ≤ ri) and listen to songs number v, v + 1, ..., v + m - 1. On the i-th day listening to one song with quality less than qi increases your displeasure by exactly one.Determine what minimum displeasure you can get on each of the s next days. ", "input_spec": "The first line contains two positive integers n, m (1 ≤ m ≤ n ≤ 2·105). The second line contains n positive integers a1, a2, ..., an (0 ≤ ai < 230) — the description of songs from the playlist.  The next line contains a single number s (1 ≤ s ≤ 2·105) — the number of days that you consider. The next s lines contain three integers each li, ri, xi (1 ≤ li ≤ ri ≤ n - m + 1; 0 ≤ xi < 230) — the description of the parameters for the i-th day. In order to calculate value qi, you need to use formula: , where ansi is the answer to the problem for day i. Assume that ans0 = 0. ", "output_spec": "Print exactly s integers ans1, ans2, ..., anss, where ansi is the minimum displeasure that you can get on day i.", "sample_inputs": ["5 3\n1 2 1 2 3\n5\n1 1 2\n1 3 2\n1 3 3\n1 3 5\n1 3 1"], "sample_outputs": ["2\n0\n2\n3\n1"], "notes": null}, "src_uid": "92c773d61414ec6a13cdfbdcd24a2b0d"}
{"nl": {"description": "There are n boys and m girls attending a theatre club. To set a play \"The Big Bang Theory\", they need to choose a group containing exactly t actors containing no less than 4 boys and no less than one girl. How many ways are there to choose a group? Of course, the variants that only differ in the composition of the troupe are considered different.Perform all calculations in the 64-bit type: long long for С/С++, int64 for Delphi and long for Java.", "input_spec": "The only line of the input data contains three integers n, m, t (4 ≤ n ≤ 30, 1 ≤ m ≤ 30, 5 ≤ t ≤ n + m).", "output_spec": "Find the required number of ways. Please do not use the %lld specificator to read or write 64-bit integers in С++. It is preferred to use cin, cout streams or the %I64d specificator.", "sample_inputs": ["5 2 5", "4 3 5"], "sample_outputs": ["10", "3"], "notes": null}, "src_uid": "489e69c7a2fba5fac34e89d7388ed4b8"}
{"nl": {"description": "Ilya is an experienced player in tic-tac-toe on the 4 × 4 field. He always starts and plays with Xs. He played a lot of games today with his friend Arseny. The friends became tired and didn't finish the last game. It was Ilya's turn in the game when they left it. Determine whether Ilya could have won the game by making single turn or not. The rules of tic-tac-toe on the 4 × 4 field are as follows. Before the first turn all the field cells are empty. The two players take turns placing their signs into empty cells (the first player places Xs, the second player places Os). The player who places Xs goes first, the another one goes second. The winner is the player who first gets three of his signs in a row next to each other (horizontal, vertical or diagonal).", "input_spec": "The tic-tac-toe position is given in four lines. Each of these lines contains four characters. Each character is '.' (empty cell), 'x' (lowercase English letter x), or 'o' (lowercase English letter o). It is guaranteed that the position is reachable playing tic-tac-toe, and it is Ilya's turn now (in particular, it means that the game is not finished). It is possible that all the cells are empty, it means that the friends left without making single turn.", "output_spec": "Print single line: \"YES\" in case Ilya could have won by making single turn, and \"NO\" otherwise.", "sample_inputs": ["xx..\n.oo.\nx...\noox.", "x.ox\nox..\nx.o.\noo.x", "x..x\n..oo\no...\nx.xo", "o.x.\no...\n.x..\nooxx"], "sample_outputs": ["YES", "NO", "YES", "NO"], "notes": "NoteIn the first example Ilya had two winning moves: to the empty cell in the left column and to the leftmost empty cell in the first row.In the second example it wasn't possible to win by making single turn.In the third example Ilya could have won by placing X in the last row between two existing Xs.In the fourth example it wasn't possible to win by making single turn."}, "src_uid": "ca4a77fe9718b8bd0b3cc3d956e22917"}
{"nl": {"description": "A long time ago (probably even in the first book), Nicholas Flamel, a great alchemist and the creator of the Philosopher's Stone, taught Harry Potter three useful spells. The first one allows you to convert a grams of sand into b grams of lead, the second one allows you to convert c grams of lead into d grams of gold and third one allows you to convert e grams of gold into f grams of sand. When Harry told his friends about these spells, Ron Weasley was amazed. After all, if they succeed in turning sand into lead, lead into gold, and then turning part of the gold into sand again and so on, then it will be possible to start with a small amount of sand and get huge amounts of gold! Even an infinite amount of gold! Hermione Granger, by contrast, was skeptical about that idea. She argues that according to the law of conservation of matter getting an infinite amount of matter, even using magic, is impossible. On the contrary, the amount of matter may even decrease during transformation, being converted to magical energy. Though Hermione's theory seems convincing, Ron won't believe her. As far as Ron is concerned, Hermione made up her law of conservation of matter to stop Harry and Ron wasting their time with this nonsense, and to make them go and do homework instead. That's why Ron has already collected a certain amount of sand for the experiments. A quarrel between the friends seems unavoidable...Help Harry to determine which one of his friends is right, and avoid the quarrel after all. To do this you have to figure out whether it is possible to get the amount of gold greater than any preassigned number from some finite amount of sand.", "input_spec": "The first line contains 6 integers a, b, c, d, e, f (0 ≤ a, b, c, d, e, f ≤ 1000).", "output_spec": "Print \"Ron\", if it is possible to get an infinitely large amount of gold having a certain finite amount of sand (and not having any gold and lead at all), i.e., Ron is right. Otherwise, print \"Hermione\".", "sample_inputs": ["100 200 250 150 200 250", "100 50 50 200 200 100", "100 10 200 20 300 30", "0 0 0 0 0 0", "1 1 0 1 1 1", "1 0 1 2 1 2", "100 1 100 1 0 1"], "sample_outputs": ["Ron", "Hermione", "Hermione", "Hermione", "Ron", "Hermione", "Ron"], "notes": "NoteConsider the first sample. Let's start with the 500 grams of sand. Apply the first spell 5 times and turn the sand into 1000 grams of lead. Then apply the second spell 4 times to get 600 grams of gold. Let’s take 400 grams from the resulting amount of gold turn them back into sand. We get 500 grams of sand and 200 grams of gold. If we apply the same operations to 500 grams of sand again, we can get extra 200 grams of gold every time. Thus, you can get 200, 400, 600 etc. grams of gold, i.e., starting with a finite amount of sand (500 grams), you can get the amount of gold which is greater than any preassigned number.In the forth sample it is impossible to get sand, or lead, or gold, applying the spells.In the fifth sample an infinitely large amount of gold can be obtained by using only the second spell, which allows you to receive 1 gram of gold out of nothing. Note that if such a second spell is available, then the first and the third one do not affect the answer at all.The seventh sample is more interesting. We can also start with a zero amount of sand there. With the aid of the third spell you can get sand out of nothing. We get 10000 grams of sand in this manner. Let's get 100 grams of lead using the first spell 100 times. Then make 1 gram of gold from them. We managed to receive 1 gram of gold, starting with a zero amount of sand! Clearly, in this manner you can get an infinitely large amount of gold."}, "src_uid": "44d608de3e1447f89070e707ba550150"}
{"nl": {"description": "Count the number of distinct sequences a1, a2, ..., an (1 ≤ ai) consisting of positive integers such that gcd(a1, a2, ..., an) = x and . As this number could be large, print the answer modulo 109 + 7.gcd here means the greatest common divisor.", "input_spec": "The only line contains two positive integers x and y (1 ≤ x, y ≤ 109).", "output_spec": "Print the number of such sequences modulo 109 + 7.", "sample_inputs": ["3 9", "5 8"], "sample_outputs": ["3", "0"], "notes": "NoteThere are three suitable sequences in the first test: (3, 3, 3), (3, 6), (6, 3).There are no suitable sequences in the second test."}, "src_uid": "de7731ce03735b962ee033613192f7bc"}
{"nl": {"description": "You've got a 5 × 5 matrix, consisting of 24 zeroes and a single number one. Let's index the matrix rows by numbers from 1 to 5 from top to bottom, let's index the matrix columns by numbers from 1 to 5 from left to right. In one move, you are allowed to apply one of the two following transformations to the matrix:  Swap two neighboring matrix rows, that is, rows with indexes i and i + 1 for some integer i (1 ≤ i < 5).  Swap two neighboring matrix columns, that is, columns with indexes j and j + 1 for some integer j (1 ≤ j < 5). You think that a matrix looks beautiful, if the single number one of the matrix is located in its middle (in the cell that is on the intersection of the third row and the third column). Count the minimum number of moves needed to make the matrix beautiful.", "input_spec": "The input consists of five lines, each line contains five integers: the j-th integer in the i-th line of the input represents the element of the matrix that is located on the intersection of the i-th row and the j-th column. It is guaranteed that the matrix consists of 24 zeroes and a single number one.", "output_spec": "Print a single integer — the minimum number of moves needed to make the matrix beautiful.", "sample_inputs": ["0 0 0 0 0\n0 0 0 0 1\n0 0 0 0 0\n0 0 0 0 0\n0 0 0 0 0", "0 0 0 0 0\n0 0 0 0 0\n0 1 0 0 0\n0 0 0 0 0\n0 0 0 0 0"], "sample_outputs": ["3", "1"], "notes": null}, "src_uid": "8ba7cedc3f6ae478a0bb3f902440c8e9"}
{"nl": {"description": "Tonio has a keyboard with only two letters, \"V\" and \"K\".One day, he has typed out a string s with only these two letters. He really likes it when the string \"VK\" appears, so he wishes to change at most one letter in the string (or do no changes) to maximize the number of occurrences of that string. Compute the maximum number of times \"VK\" can appear as a substring (i. e. a letter \"K\" right after a letter \"V\") in the resulting string.", "input_spec": "The first line will contain a string s consisting only of uppercase English letters \"V\" and \"K\" with length not less than 1 and not greater than 100.", "output_spec": "Output a single integer, the maximum number of times \"VK\" can appear as a substring of the given string after changing at most one character.", "sample_inputs": ["VK", "VV", "V", "VKKKKKKKKKVVVVVVVVVK", "KVKV"], "sample_outputs": ["1", "1", "0", "3", "1"], "notes": "NoteFor the first case, we do not change any letters. \"VK\" appears once, which is the maximum number of times it could appear.For the second case, we can change the second character from a \"V\" to a \"K\". This will give us the string \"VK\". This has one occurrence of the string \"VK\" as a substring.For the fourth case, we can change the fourth character from a \"K\" to a \"V\". This will give us the string \"VKKVKKKKKKVVVVVVVVVK\". This has three occurrences of the string \"VK\" as a substring. We can check no other moves can give us strictly more occurrences."}, "src_uid": "578bae0fe6634882227ac371ebb38fc9"}
{"nl": {"description": "There are n students who have taken part in an olympiad. Now it's time to award the students.Some of them will receive diplomas, some wiil get certificates, and others won't receive anything. Students with diplomas and certificates are called winners. But there are some rules of counting the number of diplomas and certificates. The number of certificates must be exactly k times greater than the number of diplomas. The number of winners must not be greater than half of the number of all students (i.e. not be greater than half of n). It's possible that there are no winners.You have to identify the maximum possible number of winners, according to these rules. Also for this case you have to calculate the number of students with diplomas, the number of students with certificates and the number of students who are not winners.", "input_spec": "The first (and the only) line of input contains two integers n and k (1 ≤ n, k ≤ 1012), where n is the number of students and k is the ratio between the number of certificates and the number of diplomas.", "output_spec": "Output three numbers: the number of students with diplomas, the number of students with certificates and the number of students who are not winners in case when the number of winners is maximum possible. It's possible that there are no winners.", "sample_inputs": ["18 2", "9 10", "1000000000000 5", "1000000000000 499999999999"], "sample_outputs": ["3 6 9", "0 0 9", "83333333333 416666666665 500000000002", "1 499999999999 500000000000"], "notes": null}, "src_uid": "405a70c3b3f1561a9546910ab3fb5c80"}
{"nl": {"description": "In this task Anna and Maria play a game with a very unpleasant rival. Anna and Maria are in the opposite squares of a chessboard (8 × 8): Anna is in the upper right corner, and Maria is in the lower left one. Apart from them, the board has several statues. Each statue occupies exactly one square. A square that contains a statue cannot have anything or anyone — neither any other statues, nor Anna, nor Maria.Anna is present on the board as a figurant (she stands still and never moves), and Maria has been actively involved in the game. Her goal is — to come to Anna's square. Maria and statues move in turn, Maria moves first. During one move Maria can go to any adjacent on the side or diagonal cell in which there is no statue, or she can stay in the cell where she is. The statues during their move must go one square down simultaneously, and those statues that were in the bottom row fall from the board and are no longer appeared.At that moment, when one of the statues is in the cell in which the Maria is, the statues are declared winners. At the moment when Maria comes into the cell where Anna has been waiting, Maria is declared the winner.Obviously, nothing depends on the statues, so it all depends on Maria. Determine who will win, if Maria does not make a strategic error.", "input_spec": "You are given the 8 strings whose length equals 8, describing the initial position on the board. The first line represents the top row of the board, the next one — for the second from the top, and so on, the last line represents the bottom row. Each character string matches a single cell board in the appropriate row, and the characters are in the same manner as that of the corresponding cell. If the cell is empty, the corresponding character is \".\". If a cell has Maria, then it is represented by character \"M\". If a cell has Anna, it is represented by the character \"A\". If a cell has a statue, then the cell is represented by character \"S\". It is guaranteed that the last character of the first row is always \"A\", the first character of the last line is always \"M\". The remaining characters are \".\" or \"S\".", "output_spec": "If Maria wins, print string \"WIN\". If the statues win, print string \"LOSE\".", "sample_inputs": [".......A\n........\n........\n........\n........\n........\n........\nM.......", ".......A\n........\n........\n........\n........\n........\nSS......\nM.......", ".......A\n........\n........\n........\n........\n.S......\nS.......\nMS......"], "sample_outputs": ["WIN", "LOSE", "LOSE"], "notes": null}, "src_uid": "f47e4ab041288ba9567c19930eb9a090"}
{"nl": {"description": "Ehab is interested in the bitwise-xor operation and the special graphs. Mahmoud gave him a problem that combines both. He has a complete graph consisting of n vertices numbered from 0 to n - 1. For all 0 ≤ u < v < n, vertex u and vertex v are connected with an undirected edge that has weight  (where  is the bitwise-xor operation). Can you find the weight of the minimum spanning tree of that graph?You can read about complete graphs in https://en.wikipedia.org/wiki/Complete_graphYou can read about the minimum spanning tree in https://en.wikipedia.org/wiki/Minimum_spanning_treeThe weight of the minimum spanning tree is the sum of the weights on the edges included in it.", "input_spec": "The only line contains an integer n (2 ≤ n ≤ 1012), the number of vertices in the graph.", "output_spec": "The only line contains an integer x, the weight of the graph's minimum spanning tree.", "sample_inputs": ["4"], "sample_outputs": ["4"], "notes": "NoteIn the first sample:  The weight of the minimum spanning tree is 1+2+1=4."}, "src_uid": "a98f0d924ea52cafe0048f213f075891"}
{"nl": {"description": "Karl likes Codeforces and subsequences. He wants to find a string of lowercase English letters that contains at least $$$k$$$ subsequences codeforces. Out of all possible strings, Karl wants to find a shortest one.Formally, a codeforces subsequence of a string $$$s$$$ is a subset of ten characters of $$$s$$$ that read codeforces from left to right. For example, codeforces contains codeforces a single time, while codeforcesisawesome contains codeforces four times: codeforcesisawesome, codeforcesisawesome, codeforcesisawesome, codeforcesisawesome.Help Karl find any shortest string that contains at least $$$k$$$ codeforces subsequences.", "input_spec": "The only line contains a single integer $$$k$$$ ($$$1 \\leq k \\leq 10^{16})$$$.", "output_spec": "Print a shortest string of lowercase English letters that contains at least $$$k$$$ codeforces subsequences. If there are several such strings, print any of them.", "sample_inputs": ["1", "3"], "sample_outputs": ["codeforces", "codeforcesss"], "notes": null}, "src_uid": "8001a7570766cadcc538217e941b3031"}
{"nl": {"description": "Bran and his older sister Arya are from the same house. Bran like candies so much, so Arya is going to give him some Candies.At first, Arya and Bran have 0 Candies. There are n days, at the i-th day, Arya finds ai candies in a box, that is given by the Many-Faced God. Every day she can give Bran at most 8 of her candies. If she don't give him the candies at the same day, they are saved for her and she can give them to him later.Your task is to find the minimum number of days Arya needs to give Bran k candies before the end of the n-th day. Formally, you need to output the minimum day index to the end of which k candies will be given out (the days are indexed from 1 to n).Print -1 if she can't give him k candies during n given days.", "input_spec": "The first line contains two integers n and k (1 ≤ n ≤ 100, 1 ≤ k ≤ 10000). The second line contains n integers a1, a2, a3, ..., an (1 ≤ ai ≤ 100).", "output_spec": "If it is impossible for Arya to give Bran k candies within n days, print -1. Otherwise print a single integer — the minimum number of days Arya needs to give Bran k candies before the end of the n-th day.", "sample_inputs": ["2 3\n1 2", "3 17\n10 10 10", "1 9\n10"], "sample_outputs": ["2", "3", "-1"], "notes": "NoteIn the first sample, Arya can give Bran 3 candies in 2 days.In the second sample, Arya can give Bran 17 candies in 3 days, because she can give him at most 8 candies per day.In the third sample, Arya can't give Bran 9 candies, because she can give him at most 8 candies per day and she must give him the candies within 1 day."}, "src_uid": "24695b6a2aa573e90f0fe661b0c0bd3a"}
{"nl": {"description": "Mister B once received a gift: it was a book about aliens, which he started read immediately. This book had c pages.At first day Mister B read v0 pages, but after that he started to speed up. Every day, starting from the second, he read a pages more than on the previous day (at first day he read v0 pages, at second — v0 + a pages, at third — v0 + 2a pages, and so on). But Mister B is just a human, so he physically wasn't able to read more than v1 pages per day.Also, to refresh his memory, every day, starting from the second, Mister B had to reread last l pages he read on the previous day. Mister B finished the book when he read the last page for the first time.Help Mister B to calculate how many days he needed to finish the book.", "input_spec": "First and only line contains five space-separated integers: c, v0, v1, a and l (1 ≤ c ≤ 1000, 0 ≤ l < v0 ≤ v1 ≤ 1000, 0 ≤ a ≤ 1000) — the length of the book in pages, the initial reading speed, the maximum reading speed, the acceleration in reading speed and the number of pages for rereading.", "output_spec": "Print one integer — the number of days Mister B needed to finish the book.", "sample_inputs": ["5 5 10 5 4", "12 4 12 4 1", "15 1 100 0 0"], "sample_outputs": ["1", "3", "15"], "notes": "NoteIn the first sample test the book contains 5 pages, so Mister B read it right at the first day.In the second sample test at first day Mister B read pages number 1 - 4, at second day — 4 - 11, at third day — 11 - 12 and finished the book.In third sample test every day Mister B read 1 page of the book, so he finished in 15 days."}, "src_uid": "b743110117ce13e2090367fd038d3b50"}
{"nl": {"description": "We consider a positive integer perfect, if and only if the sum of its digits is exactly $$$10$$$. Given a positive integer $$$k$$$, your task is to find the $$$k$$$-th smallest perfect positive integer.", "input_spec": "A single line with a positive integer $$$k$$$ ($$$1 \\leq k \\leq 10\\,000$$$).", "output_spec": "A single number, denoting the $$$k$$$-th smallest perfect integer.", "sample_inputs": ["1", "2"], "sample_outputs": ["19", "28"], "notes": "NoteThe first perfect integer is $$$19$$$ and the second one is $$$28$$$."}, "src_uid": "0a98a6a15e553ce11cb468d3330fc86a"}
{"nl": {"description": "Bizon the Champion isn't just charming, he also is very smart.While some of us were learning the multiplication table, Bizon the Champion had fun in his own manner. Bizon the Champion painted an n × m multiplication table, where the element on the intersection of the i-th row and j-th column equals i·j (the rows and columns of the table are numbered starting from 1). Then he was asked: what number in the table is the k-th largest number? Bizon the Champion always answered correctly and immediately. Can you repeat his success?Consider the given multiplication table. If you write out all n·m numbers from the table in the non-decreasing order, then the k-th number you write out is called the k-th largest number.", "input_spec": "The single line contains integers n, m and k (1 ≤ n, m ≤ 5·105; 1 ≤ k ≤ n·m).", "output_spec": "Print the k-th largest number in a n × m multiplication table.", "sample_inputs": ["2 2 2", "2 3 4", "1 10 5"], "sample_outputs": ["2", "3", "5"], "notes": "NoteA 2 × 3 multiplication table looks like this:1 2 32 4 6"}, "src_uid": "13a918eca30799b240ceb9de47507a26"}
{"nl": {"description": "Jzzhu has invented a kind of sequences, they meet the following property:You are given x and y, please calculate fn modulo 1000000007 (109 + 7).", "input_spec": "The first line contains two integers x and y (|x|, |y| ≤ 109). The second line contains a single integer n (1 ≤ n ≤ 2·109).", "output_spec": "Output a single integer representing fn modulo 1000000007 (109 + 7).", "sample_inputs": ["2 3\n3", "0 -1\n2"], "sample_outputs": ["1", "1000000006"], "notes": "NoteIn the first sample, f2 = f1 + f3, 3 = 2 + f3, f3 = 1.In the second sample, f2 =  - 1;  - 1 modulo (109 + 7) equals (109 + 6)."}, "src_uid": "2ff85140e3f19c90e587ce459d64338b"}
{"nl": {"description": "The whole world got obsessed with robots,and to keep pace with the progress, great Berland's programmer Draude decided to build his own robot. He was working hard at the robot. He taught it to walk the shortest path from one point to another, to record all its movements, but like in many Draude's programs, there was a bug — the robot didn't always walk the shortest path. Fortunately, the robot recorded its own movements correctly. Now Draude wants to find out when his robot functions wrong. Heh, if Draude only remembered the map of the field, where he tested the robot, he would easily say if the robot walked in the right direction or not. But the field map was lost never to be found, that's why he asks you to find out if there exist at least one map, where the path recorded by the robot is the shortest.The map is an infinite checkered field, where each square is either empty, or contains an obstruction. It is also known that the robot never tries to run into the obstruction. By the recorded robot's movements find out if there exist at least one such map, that it is possible to choose for the robot a starting square (the starting square should be empty) such that when the robot moves from this square its movements coincide with the recorded ones (the robot doesn't run into anything, moving along empty squares only), and the path from the starting square to the end one is the shortest.In one movement the robot can move into the square (providing there are no obstrutions in this square) that has common sides with the square the robot is currently in.", "input_spec": "The first line of the input file contains the recording of the robot's movements. This recording is a non-empty string, consisting of uppercase Latin letters L, R, U and D, standing for movements left, right, up and down respectively. The length of the string does not exceed 100.", "output_spec": "In the first line output the only word OK (if the above described map exists), or BUG (if such a map does not exist).", "sample_inputs": ["LLUUUR", "RRUULLDD"], "sample_outputs": ["OK", "BUG"], "notes": null}, "src_uid": "bb7805cc9d1cc907b64371b209c564b3"}
{"nl": {"description": "A classroom in a school has six rows with 3 desks in each row. Two people can use the same desk: one sitting on the left and one sitting on the right. Some places are already occupied, and some places are vacant. Petya has just entered the class and wants to occupy the most convenient place. The conveniences of the places are shown on the picture:  Here, the desks in the top row are the closest to the blackboard, while the desks in the bottom row are the furthest from the blackboard.You are given a plan of the class, where '*' denotes an occupied place, '.' denotes a vacant place, and the aisles are denoted by '-'. Find any of the most convenient vacant places for Petya.", "input_spec": "The input consists of 6 lines. Each line describes one row of desks, starting from the closest to the blackboard. Each line is given in the following format: two characters, each is '*' or '.' — the description of the left desk in the current row; a character '-' — the aisle; two characters, each is '*' or '.' — the description of the center desk in the current row; a character '-' — the aisle; two characters, each is '*' or '.' — the description of the right desk in the current row. So, the length of each of the six lines is 8. It is guaranteed that there is at least one vacant place in the classroom.", "output_spec": "Print the plan of the classroom after Petya takes one of the most convenient for him places. Mark this place with the letter 'P'. There should be exactly one letter 'P' in the plan. Petya can only take a vacant place. In all other places the output should coincide with the input. If there are multiple answers, print any.", "sample_inputs": ["..-**-..\n..-**-..\n..-..-..\n..-..-..\n..-..-..\n..-..-..", "**-**-**\n**-**-**\n..-**-.*\n**-**-**\n..-..-..\n..-**-..", "**-**-*.\n*.-*.-**\n**-**-**\n**-**-**\n..-..-..\n..-**-.."], "sample_outputs": ["..-**-..\n..-**-..\n..-..-..\n..-P.-..\n..-..-..\n..-..-..", "**-**-**\n**-**-**\n..-**-.*\n**-**-**\n..-P.-..\n..-**-..", "**-**-*.\n*.-*P-**\n**-**-**\n**-**-**\n..-..-..\n..-**-.."], "notes": "NoteIn the first example the maximum convenience is 3.In the second example the maximum convenience is 2.In the third example the maximum convenience is 4."}, "src_uid": "35503a2aeb18c8c1b3eda9de2c6ce33e"}
{"nl": {"description": "A group of $$$n$$$ dancers rehearses a performance for the closing ceremony. The dancers are arranged in a row, they've studied their dancing moves and can't change positions. For some of them, a white dancing suit is already bought, for some of them — a black one, and for the rest the suit will be bought in the future.On the day when the suits were to be bought, the director was told that the participants of the olympiad will be happy if the colors of the suits on the scene will form a palindrome. A palindrome is a sequence that is the same when read from left to right and when read from right to left. The director liked the idea, and she wants to buy suits so that the color of the leftmost dancer's suit is the same as the color of the rightmost dancer's suit, the 2nd left is the same as 2nd right, and so on.The director knows how many burls it costs to buy a white suit, and how many burls to buy a black suit. You need to find out whether it is possible to buy suits to form a palindrome, and if it's possible, what's the minimal cost of doing so. Remember that dancers can not change positions, and due to bureaucratic reasons it is not allowed to buy new suits for the dancers who already have suits, even if it reduces the overall spending.", "input_spec": "The first line contains three integers $$$n$$$, $$$a$$$, and $$$b$$$ ($$$1 \\leq n \\leq 20$$$, $$$1 \\leq a, b \\leq 100$$$) — the number of dancers, the cost of a white suit, and the cost of a black suit. The next line contains $$$n$$$ numbers $$$c_i$$$, $$$i$$$-th of which denotes the color of the suit of the $$$i$$$-th dancer. Number $$$0$$$ denotes the white color, $$$1$$$ — the black color, and $$$2$$$ denotes that a suit for this dancer is still to be bought.", "output_spec": "If it is not possible to form a palindrome without swapping dancers and buying new suits for those who have one, then output -1. Otherwise, output the minimal price to get the desired visual effect.", "sample_inputs": ["5 100 1\n0 1 2 1 2", "3 10 12\n1 2 0", "3 12 1\n0 1 0"], "sample_outputs": ["101", "-1", "0"], "notes": "NoteIn the first sample, the cheapest way to obtain palindromic colors is to buy a black suit for the third from left dancer and a white suit for the rightmost dancer.In the second sample, the leftmost dancer's suit already differs from the rightmost dancer's suit so there is no way to obtain the desired coloring.In the third sample, all suits are already bought and their colors form a palindrome."}, "src_uid": "af07223819aeb5bd6ded4340c472b2b6"}
{"nl": {"description": "Petya wrote a programme on C++ that calculated a very interesting function f(n). Petya ran the program with a certain value of n and went to the kitchen to have some tea. The history has no records concerning how long the program had been working. By the time Petya returned, it had completed the calculations and had the result. However while Petya was drinking tea, a sly virus managed to destroy the input file so that Petya can't figure out for which value of n the program was run. Help Petya, carry out the inverse function!Mostly, the program consists of a function in C++ with the following simplified syntax:  function ::= int f(int n) {operatorSequence} operatorSequence ::= operator | operator operatorSequence operator ::= return arithmExpr; | if (logicalExpr) return arithmExpr; logicalExpr ::= arithmExpr > arithmExpr | arithmExpr < arithmExpr | arithmExpr == arithmExpr arithmExpr ::= sum sum ::= product | sum + product | sum - product product ::= multiplier | product * multiplier | product / multiplier multiplier ::= n | number | f(arithmExpr) number ::= 0|1|2|... |32767 The whitespaces in a operatorSequence are optional.Thus, we have a function, in which body there are two kinds of operators. There is the operator \"return arithmExpr;\" that returns the value of the expression as the value of the function, and there is the conditional operator \"if (logicalExpr) return arithmExpr;\" that returns the value of the arithmetical expression when and only when the logical expression is true. Guaranteed that no other constructions of C++ language — cycles, assignment operators, nested conditional operators etc, and other variables except the n parameter are used in the function. All the constants are integers in the interval [0..32767].The operators are performed sequentially. After the function has returned a value other operators in the sequence are not performed. Arithmetical expressions are performed taking into consideration the standard priority of the operations. It means that first all the products that are part of the sum are calculated. During the calculation of the products the operations of multiplying and division are performed from the left to the right. Then the summands are summed, and the addition and the subtraction are also performed from the left to the right. Operations \">\" (more), \"<\" (less) and \"==\" (equals) also have standard meanings.Now you've got to pay close attention! The program is compiled with the help of 15-bit Berland C++ compiler invented by a Berland company BerSoft, that's why arithmetical operations are performed in a non-standard way. Addition, subtraction and multiplication are performed modulo 32768 (if the result of subtraction is negative, then 32768 is added to it until the number belongs to the interval [0..32767]). Division \"/\" is a usual integer division where the remainder is omitted.Examples of arithmetical operations: Guaranteed that for all values of n from 0 to 32767 the given function is performed correctly. That means that:1. Division by 0 never occures.2. When performing a function for the value n = N recursive calls of the function f may occur only for the parameter value of 0, 1, ..., N - 1. Consequently, the program never has an infinite recursion.3. As the result of the sequence of the operators, the function always returns a value.We have to mention that due to all the limitations the value returned by the function f is independent from either global variables or the order of performing the calculations of arithmetical expressions as part of the logical one, or from anything else except the value of n parameter. That's why the f function can be regarded as a function in its mathematical sense, i.e. as a unique correspondence between any value of n from the interval [0..32767] and a value of f(n) from the same interval.Given the value of f(n), and you should find n. If the suitable n value is not unique, you should find the maximal one (from the interval [0..32767]).", "input_spec": "The first line has an integer f(n) from the interval [0..32767]. The next lines have the description of the function f. In the description can be found extra spaces and line breaks (see the examples) which, of course, can’t break key words int, if, return and numbers. The size of input data can’t exceed 100 bytes.", "output_spec": "Output a single number — the answer to the problem. If there’s no answer, output \"-1\" (without quotes).", "sample_inputs": ["17\nint f(int n)\n{\nif (n < 100) return 17;\nif (n > 99) return 27;\n}", "13\nint f(int n)\n{\nif (n == 0) return 0;\nreturn f(n - 1) + 1;\n}", "144\nint f(int n)\n{\nif (n == 0) return 0;\nif (n == 1) return n;\nreturn f(n - 1) + f(n - 2);\n}"], "sample_outputs": ["99", "13", "24588"], "notes": null}, "src_uid": "698c5a87f9adbe6af60d9f70519c9672"}
{"nl": {"description": "The Little Elephant very much loves sums on intervals.This time he has a pair of integers l and r (l ≤ r). The Little Elephant has to find the number of such integers x (l ≤ x ≤ r), that the first digit of integer x equals the last one (in decimal notation). For example, such numbers as 101, 477474 or 9 will be included in the answer and 47, 253 or 1020 will not.Help him and count the number of described numbers x for a given pair l and r.", "input_spec": "The single line contains a pair of integers l and r (1 ≤ l ≤ r ≤ 1018) — the boundaries of the interval. Please, do not use the %lld specifier to read or write 64-bit integers in С++. It is preferred to use cin, cout streams or the %I64d specifier.", "output_spec": "On a single line print a single integer — the answer to the problem.", "sample_inputs": ["2 47", "47 1024"], "sample_outputs": ["12", "98"], "notes": "NoteIn the first sample the answer includes integers 2, 3, 4, 5, 6, 7, 8, 9, 11, 22, 33, 44. "}, "src_uid": "9642368dc4ffe2fc6fe6438c7406c1bd"}
{"nl": {"description": "Valera is a coder. Recently he wrote a funny program. The pseudo code for this program is given below://input: integers x, k, pa = x;for(step = 1; step <= k; step = step + 1){    rnd = [random integer from 1 to 100];    if(rnd <= p)        a = a * 2;    else        a = a + 1;}s = 0;while(remainder after dividing a by 2 equals 0){    a = a / 2;    s = s + 1;}Now Valera wonders: given the values x, k and p, what is the expected value of the resulting number s?", "input_spec": "The first line of the input contains three integers x, k, p (1 ≤ x ≤ 109; 1 ≤ k ≤ 200; 0 ≤ p ≤ 100).", "output_spec": "Print the required expected value. Your answer will be considered correct if the absolute or relative error doesn't exceed 10 - 6.", "sample_inputs": ["1 1 50", "5 3 0", "5 3 25"], "sample_outputs": ["1.0000000000000", "3.0000000000000", "1.9218750000000"], "notes": "NoteIf the concept of expected value is new to you, you can read about it by the link: http://en.wikipedia.org/wiki/Expected_value"}, "src_uid": "c9274249c26b1a85c19ab70d91c1c3e0"}
{"nl": {"description": "The New Year tree is an infinite perfect binary tree rooted in the node 1. Each node v has two children: nodes indexed (2·v) and (2·v + 1).  Polar bears love decorating the New Year tree and Limak is no exception. As he is only a little bear, he was told to decorate only one simple path between some pair of nodes. Though he was given an opportunity to pick the pair himself! Now he wants to know the number of unordered pairs of indices (u, v) (u ≤ v), such that the sum of indices of all nodes along the simple path between u and v (including endpoints) is equal to s. Can you help him and count this value?", "input_spec": "The only line of the input contains a single integer s (1 ≤ s ≤ 1015).", "output_spec": "Print one integer, denoting the number of unordered pairs of nodes indices defining simple paths with the sum of indices of vertices equal to s.", "sample_inputs": ["10"], "sample_outputs": ["4"], "notes": "NoteIn sample test, there are 4 paths with the sum of indices equal to 10:  "}, "src_uid": "c142f8bc5252e739035992926545c251"}
{"nl": {"description": "The only difference between easy and hard versions is constraints.A session has begun at Beland State University. Many students are taking exams.Polygraph Poligrafovich is going to examine a group of $$$n$$$ students. Students will take the exam one-by-one in order from $$$1$$$-th to $$$n$$$-th. Rules of the exam are following:  The $$$i$$$-th student randomly chooses a ticket.  if this ticket is too hard to the student, he doesn't answer and goes home immediately (this process is so fast that it's considered no time elapses). This student fails the exam.  if the student finds the ticket easy, he spends exactly $$$t_i$$$ minutes to pass the exam. After it, he immediately gets a mark and goes home. Students take the exam in the fixed order, one-by-one, without any interruption. At any moment of time, Polygraph Poligrafovich takes the answer from one student.The duration of the whole exam for all students is $$$M$$$ minutes ($$$\\max t_i \\le M$$$), so students at the end of the list have a greater possibility to run out of time to pass the exam.For each student $$$i$$$, you should count the minimum possible number of students who need to fail the exam so the $$$i$$$-th student has enough time to pass the exam.For each student $$$i$$$, find the answer independently. That is, if when finding the answer for the student $$$i_1$$$ some student $$$j$$$ should leave, then while finding the answer for $$$i_2$$$ ($$$i_2>i_1$$$) the student $$$j$$$ student does not have to go home.", "input_spec": "The first line of the input contains two integers $$$n$$$ and $$$M$$$ ($$$1 \\le n \\le 100$$$, $$$1 \\le M \\le 100$$$) — the number of students and the total duration of the exam in minutes, respectively. The second line of the input contains $$$n$$$ integers $$$t_i$$$ ($$$1 \\le t_i \\le 100$$$) — time in minutes that $$$i$$$-th student spends to answer to a ticket. It's guaranteed that all values of $$$t_i$$$ are not greater than $$$M$$$.", "output_spec": "Print $$$n$$$ numbers: the $$$i$$$-th number must be equal to the minimum number of students who have to leave the exam in order to $$$i$$$-th student has enough time to pass the exam.", "sample_inputs": ["7 15\n1 2 3 4 5 6 7", "5 100\n80 40 40 40 60"], "sample_outputs": ["0 0 0 0 0 2 3", "0 1 1 2 3"], "notes": "NoteThe explanation for the example 1.Please note that the sum of the first five exam times does not exceed $$$M=15$$$ (the sum is $$$1+2+3+4+5=15$$$). Thus, the first five students can pass the exam even if all the students before them also pass the exam. In other words, the first five numbers in the answer are $$$0$$$.In order for the $$$6$$$-th student to pass the exam, it is necessary that at least $$$2$$$ students must fail it before (for example, the $$$3$$$-rd and $$$4$$$-th, then the $$$6$$$-th will finish its exam in $$$1+2+5+6=14$$$ minutes, which does not exceed $$$M$$$).In order for the $$$7$$$-th student to pass the exam, it is necessary that at least $$$3$$$ students must fail it before (for example, the $$$2$$$-nd, $$$5$$$-th and $$$6$$$-th, then the $$$7$$$-th will finish its exam in $$$1+3+4+7=15$$$ minutes, which does not exceed $$$M$$$)."}, "src_uid": "d3c1dc3ed7af2b51b4c49c9b5052c346"}
{"nl": {"description": "Jamie loves sleeping. One day, he decides that he needs to wake up at exactly hh: mm. However, he hates waking up, so he wants to make waking up less painful by setting the alarm at a lucky time. He will then press the snooze button every x minutes until hh: mm is reached, and only then he will wake up. He wants to know what is the smallest number of times he needs to press the snooze button.A time is considered lucky if it contains a digit '7'. For example, 13: 07 and 17: 27 are lucky, while 00: 48 and 21: 34 are not lucky.Note that it is not necessary that the time set for the alarm and the wake-up time are on the same day. It is guaranteed that there is a lucky time Jamie can set so that he can wake at hh: mm.Formally, find the smallest possible non-negative integer y such that the time representation of the time x·y minutes before hh: mm contains the digit '7'.Jamie uses 24-hours clock, so after 23: 59 comes 00: 00.", "input_spec": "The first line contains a single integer x (1 ≤ x ≤ 60). The second line contains two two-digit integers, hh and mm (00 ≤ hh ≤ 23, 00 ≤ mm ≤ 59).", "output_spec": "Print the minimum number of times he needs to press the button.", "sample_inputs": ["3\n11 23", "5\n01 07"], "sample_outputs": ["2", "0"], "notes": "NoteIn the first sample, Jamie needs to wake up at 11:23. So, he can set his alarm at 11:17. He would press the snooze button when the alarm rings at 11:17 and at 11:20.In the second sample, Jamie can set his alarm at exactly at 01:07 which is lucky."}, "src_uid": "5ecd569e02e0164a5da9ff549fca3ceb"}
{"nl": {"description": "Alice has a string $$$s$$$. She really likes the letter \"a\". She calls a string good if strictly more than half of the characters in that string are \"a\"s. For example \"aaabb\", \"axaa\" are good strings, and \"baca\", \"awwwa\", \"\" (empty string) are not.Alice can erase some characters from her string $$$s$$$. She would like to know what is the longest string remaining after erasing some characters (possibly zero) to get a good string. It is guaranteed that the string has at least one \"a\" in it, so the answer always exists.", "input_spec": "The first line contains a string $$$s$$$ ($$$1 \\leq |s| \\leq 50$$$) consisting of lowercase English letters. It is guaranteed that there is at least one \"a\" in $$$s$$$.", "output_spec": "Print a single integer, the length of the longest good string that Alice can get after erasing some characters from $$$s$$$.", "sample_inputs": ["xaxxxxa", "aaabaa"], "sample_outputs": ["3", "6"], "notes": "NoteIn the first example, it's enough to erase any four of the \"x\"s. The answer is $$$3$$$ since that is the maximum number of characters that can remain.In the second example, we don't need to erase any characters."}, "src_uid": "84cb9ad2ae3ba7e912920d7feb4f6219"}
{"nl": {"description": "The football season has just ended in Berland. According to the rules of Berland football, each match is played between two teams. The result of each match is either a draw, or a victory of one of the playing teams. If a team wins the match, it gets $$$w$$$ points, and the opposing team gets $$$0$$$ points. If the game results in a draw, both teams get $$$d$$$ points.The manager of the Berland capital team wants to summarize the results of the season, but, unfortunately, all information about the results of each match is lost. The manager only knows that the team has played $$$n$$$ games and got $$$p$$$ points for them.You have to determine three integers $$$x$$$, $$$y$$$ and $$$z$$$ — the number of wins, draws and loses of the team. If there are multiple answers, print any of them. If there is no suitable triple $$$(x, y, z)$$$, report about it.", "input_spec": "The first line contains four integers $$$n$$$, $$$p$$$, $$$w$$$ and $$$d$$$ $$$(1 \\le n \\le 10^{12}, 0 \\le p \\le 10^{17}, 1 \\le d < w \\le 10^{5})$$$ — the number of games, the number of points the team got, the number of points awarded for winning a match, and the number of points awarded for a draw, respectively. Note that $$$w > d$$$, so the number of points awarded for winning is strictly greater than the number of points awarded for draw.", "output_spec": "If there is no answer, print $$$-1$$$. Otherwise print three non-negative integers $$$x$$$, $$$y$$$ and $$$z$$$ — the number of wins, draws and losses of the team. If there are multiple possible triples $$$(x, y, z)$$$, print any of them. The numbers should meet the following conditions:    $$$x \\cdot w + y \\cdot d = p$$$,  $$$x + y + z = n$$$. ", "sample_inputs": ["30 60 3 1", "10 51 5 4", "20 0 15 5"], "sample_outputs": ["17 9 4", "-1", "0 0 20"], "notes": "NoteOne of the possible answers in the first example — $$$17$$$ wins, $$$9$$$ draws and $$$4$$$ losses. Then the team got $$$17 \\cdot 3 + 9 \\cdot 1 = 60$$$ points in $$$17 + 9 + 4 = 30$$$ games.In the second example the maximum possible score is $$$10 \\cdot 5 = 50$$$. Since $$$p = 51$$$, there is no answer.In the third example the team got $$$0$$$ points, so all $$$20$$$ games were lost."}, "src_uid": "503116e144d19eb953954d99c5526a7d"}
{"nl": {"description": "Little X has met the following problem recently. Let's define f(x) as the sum of digits in decimal representation of number x (for example, f(1234) = 1 + 2 + 3 + 4). You are to calculate Of course Little X has solved this problem quickly, has locked it, and then has tried to hack others. He has seen the following C++ code:     ans = solve(l, r) % a;    if (ans <= 0)      ans += a; This code will fail only on the test with . You are given number a, help Little X to find a proper test for hack.", "input_spec": "The first line contains a single integer a (1 ≤ a ≤ 1018).", "output_spec": "Print two integers: l, r (1 ≤ l ≤ r < 10200) — the required test data. Leading zeros aren't allowed. It's guaranteed that the solution exists.", "sample_inputs": ["46", "126444381000032"], "sample_outputs": ["1 10", "2333333 2333333333333"], "notes": null}, "src_uid": "52b8d97f216ea22693bc16fadcd46dae"}
{"nl": {"description": "A car moves from point A to point B at speed v meters per second. The action takes place on the X-axis. At the distance d meters from A there are traffic lights. Starting from time 0, for the first g seconds the green light is on, then for the following r seconds the red light is on, then again the green light is on for the g seconds, and so on.The car can be instantly accelerated from 0 to v and vice versa, can instantly slow down from the v to 0. Consider that it passes the traffic lights at the green light instantly. If the car approaches the traffic lights at the moment when the red light has just turned on, it doesn't have time to pass it. But if it approaches the traffic lights at the moment when the green light has just turned on, it can move. The car leaves point A at the time 0.What is the minimum time for the car to get from point A to point B without breaking the traffic rules?", "input_spec": "The first line contains integers l, d, v, g, r (1 ≤ l, d, v, g, r ≤ 1000, d < l) — the distance between A and B (in meters), the distance from A to the traffic lights, car's speed, the duration of green light and the duration of red light.", "output_spec": "Output a single number — the minimum time that the car needs to get from point A to point B. Your output must have relative or absolute error less than 10 - 6.", "sample_inputs": ["2 1 3 4 5", "5 4 3 1 1"], "sample_outputs": ["0.66666667", "2.33333333"], "notes": null}, "src_uid": "e4a4affb439365c843c9f9828d81b42c"}
{"nl": {"description": "Vasya is very upset that many people on the Net mix uppercase and lowercase letters in one word. That's why he decided to invent an extension for his favorite browser that would change the letters' register in every word so that it either only consisted of lowercase letters or, vice versa, only of uppercase ones. At that as little as possible letters should be changed in the word. For example, the word HoUse must be replaced with house, and the word ViP — with VIP. If a word contains an equal number of uppercase and lowercase letters, you should replace all the letters with lowercase ones. For example, maTRIx should be replaced by matrix. Your task is to use the given method on one given word.", "input_spec": "The first line contains a word s — it consists of uppercase and lowercase Latin letters and possesses the length from 1 to 100.", "output_spec": "Print the corrected word s. If the given word s has strictly more uppercase letters, make the word written in the uppercase register, otherwise - in the lowercase one.", "sample_inputs": ["HoUse", "ViP", "maTRIx"], "sample_outputs": ["house", "VIP", "matrix"], "notes": null}, "src_uid": "b432dfa66bae2b542342f0b42c0a2598"}
{"nl": {"description": "You are given the current time in 24-hour format hh:mm. Find and print the time after a minutes.Note that you should find only the time after a minutes, see the examples to clarify the problem statement.You can read more about 24-hour format here https://en.wikipedia.org/wiki/24-hour_clock.", "input_spec": "The first line contains the current time in the format hh:mm (0 ≤ hh < 24, 0 ≤ mm < 60). The hours and the minutes are given with two digits (the hours or the minutes less than 10 are given with the leading zeroes). The second line contains integer a (0 ≤ a ≤ 104) — the number of the minutes passed.", "output_spec": "The only line should contain the time after a minutes in the format described in the input. Note that you should print exactly two digits for the hours and the minutes (add leading zeroes to the numbers if needed). See the examples to check the input/output format.", "sample_inputs": ["23:59\n10", "20:20\n121", "10:10\n0"], "sample_outputs": ["00:09", "22:21", "10:10"], "notes": null}, "src_uid": "20c2d9da12d6b88f300977d74287a15d"}
{"nl": {"description": "Our good friend Mole is trying to code a big message. He is typing on an unusual keyboard with characters arranged in following way:qwertyuiopasdfghjkl;zxcvbnm,./Unfortunately Mole is blind, so sometimes it is problem for him to put his hands accurately. He accidentally moved both his hands with one position to the left or to the right. That means that now he presses not a button he wants, but one neighboring button (left or right, as specified in input).We have a sequence of characters he has typed and we want to find the original message.", "input_spec": "First line of the input contains one letter describing direction of shifting ('L' or 'R' respectively for left or right). Second line contains a sequence of characters written by Mole. The size of this sequence will be no more than 100. Sequence contains only symbols that appear on Mole's keyboard. It doesn't contain spaces as there is no space on Mole's keyboard. It is guaranteed that even though Mole hands are moved, he is still pressing buttons on keyboard and not hitting outside it.", "output_spec": "Print a line that contains the original message.", "sample_inputs": ["R\ns;;upimrrfod;pbr"], "sample_outputs": ["allyouneedislove"], "notes": null}, "src_uid": "df49c0c257903516767fdb8ac9c2bfd6"}
{"nl": {"description": "Ternary numeric notation is quite popular in Berland. To telegraph the ternary number the Borze alphabet is used. Digit 0 is transmitted as «.», 1 as «-.» and 2 as «--». You are to decode the Borze code, i.e. to find out the ternary number given its representation in Borze alphabet.", "input_spec": "The first line contains a number in Borze code. The length of the string is between 1 and 200 characters. It's guaranteed that the given string is a valid Borze code of some ternary number (this number can have leading zeroes).", "output_spec": "Output the decoded ternary number. It can have leading zeroes.", "sample_inputs": [".-.--", "--.", "-..-.--"], "sample_outputs": ["012", "20", "1012"], "notes": null}, "src_uid": "46b5a1cd1bd2985f2752662b7dbb1869"}
{"nl": {"description": "Luke Skywalker gave Chewbacca an integer number x. Chewbacca isn't good at numbers but he loves inverting digits in them. Inverting digit t means replacing it with digit 9 - t. Help Chewbacca to transform the initial number x to the minimum possible positive number by inverting some (possibly, zero) digits. The decimal representation of the final number shouldn't start with a zero.", "input_spec": "The first line contains a single integer x (1 ≤ x ≤ 1018) — the number that Luke Skywalker gave to Chewbacca.", "output_spec": "Print the minimum possible positive number that Chewbacca can obtain after inverting some digits. The number shouldn't contain leading zeroes.", "sample_inputs": ["27", "4545"], "sample_outputs": ["22", "4444"], "notes": null}, "src_uid": "d5de5052b4e9bbdb5359ac6e05a18b61"}
{"nl": {"description": "Santa Claus is the first who came to the Christmas Olympiad, and he is going to be the first to take his place at a desk! In the classroom there are n lanes of m desks each, and there are two working places at each of the desks. The lanes are numbered from 1 to n from the left to the right, the desks in a lane are numbered from 1 to m starting from the blackboard. Note that the lanes go perpendicularly to the blackboard, not along it (see picture).The organizers numbered all the working places from 1 to 2nm. The places are numbered by lanes (i. e. all the places of the first lane go first, then all the places of the second lane, and so on), in a lane the places are numbered starting from the nearest to the blackboard (i. e. from the first desk in the lane), at each desk, the place on the left is numbered before the place on the right.    The picture illustrates the first and the second samples. Santa Clause knows that his place has number k. Help him to determine at which lane at which desk he should sit, and whether his place is on the left or on the right!", "input_spec": "The only line contains three integers n, m and k (1 ≤ n, m ≤ 10 000, 1 ≤ k ≤ 2nm) — the number of lanes, the number of desks in each lane and the number of Santa Claus' place.", "output_spec": "Print two integers: the number of lane r, the number of desk d, and a character s, which stands for the side of the desk Santa Claus. The character s should be \"L\", if Santa Clause should sit on the left, and \"R\" if his place is on the right.", "sample_inputs": ["4 3 9", "4 3 24", "2 4 4"], "sample_outputs": ["2 2 L", "4 3 R", "1 2 R"], "notes": "NoteThe first and the second samples are shown on the picture. The green place corresponds to Santa Claus' place in the first example, the blue place corresponds to Santa Claus' place in the second example.In the third sample there are two lanes with four desks in each, and Santa Claus has the fourth place. Thus, his place is in the first lane at the second desk on the right."}, "src_uid": "d6929926b44c2d5b1a8e6b7f965ca1bb"}
{"nl": {"description": "Bob likes to draw camels: with a single hump, two humps, three humps, etc. He draws a camel by connecting points on a coordinate plane. Now he's drawing camels with t humps, representing them as polylines in the plane. Each polyline consists of n vertices with coordinates (x1, y1), (x2, y2), ..., (xn, yn). The first vertex has a coordinate x1 = 1, the second — x2 = 2, etc. Coordinates yi might be any, but should satisfy the following conditions:  there should be t humps precisely, i.e. such indexes j (2 ≤ j ≤ n - 1), so that yj - 1 < yj > yj + 1,  there should be precisely t - 1 such indexes j (2 ≤ j ≤ n - 1), so that yj - 1 > yj < yj + 1,  no segment of a polyline should be parallel to the Ox-axis,  all yi are integers between 1 and 4. For a series of his drawings of camels with t humps Bob wants to buy a notebook, but he doesn't know how many pages he will need. Output the amount of different polylines that can be drawn to represent camels with t humps for a given number n.", "input_spec": "The first line contains a pair of integers n and t (3 ≤ n ≤ 20, 1 ≤ t ≤ 10).", "output_spec": "Output the required amount of camels with t humps.", "sample_inputs": ["6 1", "4 2"], "sample_outputs": ["6", "0"], "notes": "NoteIn the first sample test sequences of y-coordinates for six camels are: 123421, 123431, 123432, 124321, 134321 и 234321 (each digit corresponds to one value of yi)."}, "src_uid": "6d67559744583229455c5eafe68f7952"}
{"nl": {"description": "Uncle Fyodor, Matroskin the Cat and Sharic the Dog live their simple but happy lives in Prostokvashino. Sometimes they receive parcels from Uncle Fyodor’s parents and sometimes from anonymous benefactors, in which case it is hard to determine to which one of them the package has been sent. A photographic rifle is obviously for Sharic who loves hunting and fish is for Matroskin, but for whom was a new video game console meant? Every one of the three friends claimed that the present is for him and nearly quarreled. Uncle Fyodor had an idea how to solve the problem justly: they should suppose that the console was sent to all three of them and play it in turns. Everybody got relieved but then yet another burning problem popped up — who will play first? This time Matroskin came up with a brilliant solution, suggesting the most fair way to find it out: play rock-paper-scissors together. The rules of the game are very simple. On the count of three every player shows a combination with his hand (or paw). The combination corresponds to one of three things: a rock, scissors or paper. Some of the gestures win over some other ones according to well-known rules: the rock breaks the scissors, the scissors cut the paper, and the paper gets wrapped over the stone. Usually there are two players. Yet there are three friends, that’s why they decided to choose the winner like that: If someone shows the gesture that wins over the other two players, then that player wins. Otherwise, another game round is required. Write a program that will determine the winner by the gestures they have shown.", "input_spec": "The first input line contains the name of the gesture that Uncle Fyodor showed, the second line shows which gesture Matroskin showed and the third line shows Sharic’s gesture. ", "output_spec": "Print \"F\" (without quotes) if Uncle Fyodor wins. Print \"M\" if Matroskin wins and \"S\" if Sharic wins. If it is impossible to find the winner, print \"?\".", "sample_inputs": ["rock\nrock\nrock", "paper\nrock\nrock", "scissors\nrock\nrock", "scissors\npaper\nrock"], "sample_outputs": ["?", "F", "?", "?"], "notes": null}, "src_uid": "072c7d29a1b338609a72ab6b73988282"}
{"nl": {"description": "Someday, Drazil wanted to go on date with Varda. Drazil and Varda live on Cartesian plane. Drazil's home is located in point (0, 0) and Varda's home is located in point (a, b). In each step, he can move in a unit distance in horizontal or vertical direction. In other words, from position (x, y) he can go to positions (x + 1, y), (x - 1, y), (x, y + 1) or (x, y - 1). Unfortunately, Drazil doesn't have sense of direction. So he randomly chooses the direction he will go to in each step. He may accidentally return back to his house during his travel. Drazil may even not notice that he has arrived to (a, b) and continue travelling. Luckily, Drazil arrived to the position (a, b) successfully. Drazil said to Varda: \"It took me exactly s steps to travel from my house to yours\". But Varda is confused about his words, she is not sure that it is possible to get from (0, 0) to (a, b) in exactly s steps. Can you find out if it is possible for Varda?", "input_spec": "You are given three integers a, b, and s ( - 109 ≤ a, b ≤ 109, 1 ≤ s ≤ 2·109) in a single line.", "output_spec": "If you think Drazil made a mistake and it is impossible to take exactly s steps and get from his home to Varda's home, print \"No\" (without quotes). Otherwise, print \"Yes\".", "sample_inputs": ["5 5 11", "10 15 25", "0 5 1", "0 0 2"], "sample_outputs": ["No", "Yes", "No", "Yes"], "notes": "NoteIn fourth sample case one possible route is: ."}, "src_uid": "9a955ce0775018ff4e5825700c13ed36"}
{"nl": {"description": "Neko loves divisors. During the latest number theory lesson, he got an interesting exercise from his math teacher.Neko has two integers $$$a$$$ and $$$b$$$. His goal is to find a non-negative integer $$$k$$$ such that the least common multiple of $$$a+k$$$ and $$$b+k$$$ is the smallest possible. If there are multiple optimal integers $$$k$$$, he needs to choose the smallest one.Given his mathematical talent, Neko had no trouble getting Wrong Answer on this problem. Can you help him solve it?", "input_spec": "The only line contains two integers $$$a$$$ and $$$b$$$ ($$$1 \\le a, b \\le 10^9$$$).", "output_spec": "Print the smallest non-negative integer $$$k$$$ ($$$k \\ge 0$$$) such that the lowest common multiple of $$$a+k$$$ and $$$b+k$$$ is the smallest possible. If there are many possible integers $$$k$$$ giving the same value of the least common multiple, print the smallest one.", "sample_inputs": ["6 10", "21 31", "5 10"], "sample_outputs": ["2", "9", "0"], "notes": "NoteIn the first test, one should choose $$$k = 2$$$, as the least common multiple of $$$6 + 2$$$ and $$$10 + 2$$$ is $$$24$$$, which is the smallest least common multiple possible."}, "src_uid": "414149fadebe25ab6097fc67663177c3"}
{"nl": {"description": "One day Kefa found n baloons. For convenience, we denote color of i-th baloon as si — lowercase letter of the Latin alphabet. Also Kefa has k friends. Friend will be upset, If he get two baloons of the same color. Kefa want to give out all baloons to his friends. Help Kefa to find out, can he give out all his baloons, such that no one of his friens will be upset — print «YES», if he can, and «NO», otherwise. Note, that Kefa's friend will not upset, if he doesn't get baloons at all.", "input_spec": "The first line contains two integers n and k (1 ≤ n, k ≤ 100) — the number of baloons and friends. Next line contains string s — colors of baloons.", "output_spec": "Answer to the task — «YES» or «NO» in a single line. You can choose the case (lower or upper) for each letter arbitrary.", "sample_inputs": ["4 2\naabb", "6 3\naacaab"], "sample_outputs": ["YES", "NO"], "notes": "NoteIn the first sample Kefa can give 1-st and 3-rd baloon to the first friend, and 2-nd and 4-th to the second.In the second sample Kefa needs to give to all his friends baloons of color a, but one baloon will stay, thats why answer is «NO»."}, "src_uid": "ceb3807aaffef60bcdbcc9a17a1391be"}
{"nl": {"description": "Johny likes numbers n and k very much. Now Johny wants to find the smallest integer x greater than n, so it is divisible by the number k.", "input_spec": "The only line contains two integers n and k (1 ≤ n, k ≤ 109).", "output_spec": "Print the smallest integer x > n, so it is divisible by the number k.", "sample_inputs": ["5 3", "25 13", "26 13"], "sample_outputs": ["6", "26", "39"], "notes": null}, "src_uid": "75f3835c969c871a609b978e04476542"}
{"nl": {"description": "Gerald has been selling state secrets at leisure. All the secrets cost the same: n marks. The state which secrets Gerald is selling, has no paper money, only coins. But there are coins of all positive integer denominations that are powers of three: 1 mark, 3 marks, 9 marks, 27 marks and so on. There are no coins of other denominations. Of course, Gerald likes it when he gets money without the change. And all buyers respect him and try to give the desired sum without change, if possible. But this does not always happen.One day an unlucky buyer came. He did not have the desired sum without change. Then he took out all his coins and tried to give Gerald a larger than necessary sum with as few coins as possible. What is the maximum number of coins he could get?The formal explanation of the previous paragraph: we consider all the possible combinations of coins for which the buyer can not give Gerald the sum of n marks without change. For each such combination calculate the minimum number of coins that can bring the buyer at least n marks. Among all combinations choose the maximum of the minimum number of coins. This is the number we want.", "input_spec": "The single line contains a single integer n (1 ≤ n ≤ 1017). Please, do not use the %lld specifier to read or write 64 bit integers in С++. It is preferred to use the cin, cout streams or the %I64d specifier.", "output_spec": "In a single line print an integer: the maximum number of coins the unlucky buyer could have paid with.", "sample_inputs": ["1", "4"], "sample_outputs": ["1", "2"], "notes": "NoteIn the first test case, if a buyer has exactly one coin of at least 3 marks, then, to give Gerald one mark, he will have to give this coin. In this sample, the customer can not have a coin of one mark, as in this case, he will be able to give the money to Gerald without any change.In the second test case, if the buyer had exactly three coins of 3 marks, then, to give Gerald 4 marks, he will have to give two of these coins. The buyer cannot give three coins as he wants to minimize the number of coins that he gives."}, "src_uid": "7e7b59f2112fd200ee03255c0c230ebd"}
{"nl": {"description": "The numbers of all offices in the new building of the Tax Office of IT City will have lucky numbers.Lucky number is a number that consists of digits 7 and 8 only. Find the maximum number of offices in the new building of the Tax Office given that a door-plate can hold a number not longer than n digits.", "input_spec": "The only line of input contains one integer n (1 ≤ n ≤ 55) — the maximum length of a number that a door-plate can hold.", "output_spec": "Output one integer — the maximum number of offices, than can have unique lucky numbers not longer than n digits.", "sample_inputs": ["2"], "sample_outputs": ["6"], "notes": null}, "src_uid": "f1b43baa14d4c262ba616d892525dfde"}
{"nl": {"description": "You are given three positive integers x, y, n. Your task is to find the nearest fraction to fraction  whose denominator is no more than n. Formally, you should find such pair of integers a, b (1 ≤ b ≤ n; 0 ≤ a) that the value  is as minimal as possible.If there are multiple \"nearest\" fractions, choose the one with the minimum denominator. If there are multiple \"nearest\" fractions with the minimum denominator, choose the one with the minimum numerator.", "input_spec": "A single line contains three integers x, y, n (1 ≤ x, y, n ≤ 105).", "output_spec": "Print the required fraction in the format \"a/b\" (without quotes).", "sample_inputs": ["3 7 6", "7 2 4"], "sample_outputs": ["2/5", "7/2"], "notes": null}, "src_uid": "827bc6f120aff6a6f04271bc84e863ee"}
{"nl": {"description": "A positive integer is called a 2-3-integer, if it is equal to 2x·3y for some non-negative integers x and y. In other words, these integers are such integers that only have 2 and 3 among their prime divisors. For example, integers 1, 6, 9, 16 and 108 — are 2-3 integers, while 5, 10, 21 and 120 are not.Print the number of 2-3-integers on the given segment [l, r], i. e. the number of sich 2-3-integers t that l ≤ t ≤ r.", "input_spec": "The only line contains two integers l and r (1 ≤ l ≤ r ≤ 2·109).", "output_spec": "Print a single integer the number of 2-3-integers on the segment [l, r].", "sample_inputs": ["1 10", "100 200", "1 2000000000"], "sample_outputs": ["7", "5", "326"], "notes": "NoteIn the first example the 2-3-integers are 1, 2, 3, 4, 6, 8 and 9.In the second example the 2-3-integers are 108, 128, 144, 162 and 192."}, "src_uid": "05fac54ed2064b46338bb18f897a4411"}
{"nl": {"description": "Vanya has a scales for weighing loads and weights of masses w0, w1, w2, ..., w100 grams where w is some integer not less than 2 (exactly one weight of each nominal value). Vanya wonders whether he can weight an item with mass m using the given weights, if the weights can be put on both pans of the scales. Formally speaking, your task is to determine whether it is possible to place an item of mass m and some weights on the left pan of the scales, and some weights on the right pan of the scales so that the pans of the scales were in balance.", "input_spec": "The first line contains two integers w, m (2 ≤ w ≤ 109, 1 ≤ m ≤ 109) — the number defining the masses of the weights and the mass of the item.", "output_spec": "Print word 'YES' if the item can be weighted and 'NO' if it cannot.", "sample_inputs": ["3 7", "100 99", "100 50"], "sample_outputs": ["YES", "YES", "NO"], "notes": "NoteNote to the first sample test. One pan can have an item of mass 7 and a weight of mass 3, and the second pan can have two weights of masses 9 and 1, correspondingly. Then 7 + 3 = 9 + 1.Note to the second sample test. One pan of the scales can have an item of mass 99 and the weight of mass 1, and the second pan can have the weight of mass 100.Note to the third sample test. It is impossible to measure the weight of the item in the manner described in the input. "}, "src_uid": "a74adcf0314692f8ac95f54d165d9582"}
{"nl": {"description": "A tennis tournament with n participants is running. The participants are playing by an olympic system, so the winners move on and the losers drop out.The tournament takes place in the following way (below, m is the number of the participants of the current round):  let k be the maximal power of the number 2 such that k ≤ m,  k participants compete in the current round and a half of them passes to the next round, the other m - k participants pass to the next round directly,  when only one participant remains, the tournament finishes. Each match requires b bottles of water for each participant and one bottle for the judge. Besides p towels are given to each participant for the whole tournament.Find the number of bottles and towels needed for the tournament.Note that it's a tennis tournament so in each match two participants compete (one of them will win and the other will lose).", "input_spec": "The only line contains three integers n, b, p (1 ≤ n, b, p ≤ 500) — the number of participants and the parameters described in the problem statement.", "output_spec": "Print two integers x and y — the number of bottles and towels need for the tournament.", "sample_inputs": ["5 2 3", "8 2 4"], "sample_outputs": ["20 15", "35 32"], "notes": "NoteIn the first example will be three rounds:  in the first round will be two matches and for each match 5 bottles of water are needed (two for each of the participants and one for the judge),  in the second round will be only one match, so we need another 5 bottles of water,  in the third round will also be only one match, so we need another 5 bottles of water. So in total we need 20 bottles of water.In the second example no participant will move on to some round directly."}, "src_uid": "eb815f35e9f29793a120d120968cfe34"}
{"nl": {"description": "You are at a water bowling training. There are l people who play with their left hand, r people, who play with their right hand, and a ambidexters, who can play with left or right hand.The coach decided to form a team of even number of players, exactly half of the players should play with their right hand, and exactly half of the players should play with their left hand. One player should use only on of his hands.Ambidexters play as well with their right hand as with their left hand. In the team, an ambidexter can play with their left hand, or with their right hand.Please find the maximum possible size of the team, where equal number of players use their left and right hands, respectively.", "input_spec": "The only line contains three integers l, r and a (0 ≤ l, r, a ≤ 100) — the number of left-handers, the number of right-handers and the number of ambidexters at the training. ", "output_spec": "Print a single even integer — the maximum number of players in the team. It is possible that the team can only have zero number of players.", "sample_inputs": ["1 4 2", "5 5 5", "0 2 0"], "sample_outputs": ["6", "14", "0"], "notes": "NoteIn the first example you can form a team of 6 players. You should take the only left-hander and two ambidexters to play with left hand, and three right-handers to play with right hand. The only person left can't be taken into the team.In the second example you can form a team of 14 people. You have to take all five left-handers, all five right-handers, two ambidexters to play with left hand and two ambidexters to play with right hand."}, "src_uid": "e8148140e61baffd0878376ac5f3857c"}
{"nl": {"description": "You have a rectangular n × m-cell board. Some cells are already painted some of k colors. You need to paint each uncolored cell one of the k colors so that any path from the upper left square to the lower right one doesn't contain any two cells of the same color. The path can go only along side-adjacent cells and can only go down or right.Print the number of possible paintings modulo 1000000007 (109 + 7).", "input_spec": "The first line contains three integers n, m, k (1 ≤ n, m ≤ 1000, 1 ≤ k ≤ 10). The next n lines contain m integers each — the board. The first of them contains m uppermost cells of the board from the left to the right and the second one contains m cells from the second uppermost row and so on. If a number in a line equals 0, then the corresponding cell isn't painted. Otherwise, this number represents the initial color of the board cell — an integer from 1 to k. Consider all colors numbered from 1 to k in some manner.", "output_spec": "Print the number of possible paintings modulo 1000000007 (109 + 7).", "sample_inputs": ["2 2 4\n0 0\n0 0", "2 2 4\n1 2\n2 1", "5 6 10\n0 0 0 0 0 0\n0 0 0 0 0 0\n0 0 0 0 0 0\n0 0 0 0 0 0\n0 0 0 0 0 0", "2 6 10\n1 2 3 4 5 6\n0 0 0 0 0 0"], "sample_outputs": ["48", "0", "3628800", "4096"], "notes": null}, "src_uid": "5bb21f49d976cfa16a239593a95c53b5"}
{"nl": {"description": "IT City company developing computer games decided to upgrade its way to reward its employees. Now it looks the following way. After a new game release users start buying it actively, and the company tracks the number of sales with precision to each transaction. Every time when the next number of sales is not divisible by any number from 2 to 10 every developer of this game gets a small bonus.A game designer Petya knows that the company is just about to release a new game that was partly developed by him. On the basis of his experience he predicts that n people will buy the game during the first month. Now Petya wants to determine how many times he will get the bonus. Help him to know it.", "input_spec": "The only line of the input contains one integer n (1 ≤ n ≤ 1018) — the prediction on the number of people who will buy the game.", "output_spec": "Output one integer showing how many numbers from 1 to n are not divisible by any number from 2 to 10.", "sample_inputs": ["12"], "sample_outputs": ["2"], "notes": null}, "src_uid": "e392be5411ffccc1df50e65ec1f5c589"}
{"nl": {"description": "Little Elephant loves magic squares very much.A magic square is a 3 × 3 table, each cell contains some positive integer. At that the sums of integers in all rows, columns and diagonals of the table are equal. The figure below shows the magic square, the sum of integers in all its rows, columns and diagonals equals 15.  The Little Elephant remembered one magic square. He started writing this square on a piece of paper, but as he wrote, he forgot all three elements of the main diagonal of the magic square. Fortunately, the Little Elephant clearly remembered that all elements of the magic square did not exceed 105. Help the Little Elephant, restore the original magic square, given the Elephant's notes.", "input_spec": "The first three lines of the input contain the Little Elephant's notes. The first line contains elements of the first row of the magic square. The second line contains the elements of the second row, the third line is for the third row. The main diagonal elements that have been forgotten by the Elephant are represented by zeroes. It is guaranteed that the notes contain exactly three zeroes and they are all located on the main diagonal. It is guaranteed that all positive numbers in the table do not exceed 105.", "output_spec": "Print three lines, in each line print three integers — the Little Elephant's magic square. If there are multiple magic squares, you are allowed to print any of them. Note that all numbers you print must be positive and not exceed 105. It is guaranteed that there exists at least one magic square that meets the conditions.", "sample_inputs": ["0 1 1\n1 0 1\n1 1 0", "0 3 6\n5 0 5\n4 7 0"], "sample_outputs": ["1 1 1\n1 1 1\n1 1 1", "6 3 6\n5 5 5\n4 7 4"], "notes": null}, "src_uid": "0c42eafb73d1e30f168958a06a0f9bca"}
{"nl": {"description": "The year 2015 is almost over.Limak is a little polar bear. He has recently learnt about the binary system. He noticed that the passing year has exactly one zero in its representation in the binary system — 201510 = 111110111112. Note that he doesn't care about the number of zeros in the decimal representation.Limak chose some interval of years. He is going to count all years from this interval that have exactly one zero in the binary representation. Can you do it faster?Assume that all positive integers are always written without leading zeros.", "input_spec": "The only line of the input contains two integers a and b (1 ≤ a ≤ b ≤ 1018) — the first year and the last year in Limak's interval respectively.", "output_spec": "Print one integer – the number of years Limak will count in his chosen interval.", "sample_inputs": ["5 10", "2015 2015", "100 105", "72057594000000000 72057595000000000"], "sample_outputs": ["2", "1", "0", "26"], "notes": "NoteIn the first sample Limak's interval contains numbers 510 = 1012, 610 = 1102, 710 = 1112, 810 = 10002, 910 = 10012 and 1010 = 10102. Two of them (1012 and 1102) have the described property."}, "src_uid": "581f61b1f50313bf4c75833cefd4d022"}
{"nl": {"description": "Mr. Bender has a digital table of size n × n, each cell can be switched on or off. He wants the field to have at least c switched on squares. When this condition is fulfilled, Mr Bender will be happy.We'll consider the table rows numbered from top to bottom from 1 to n, and the columns — numbered from left to right from 1 to n. Initially there is exactly one switched on cell with coordinates (x, y) (x is the row number, y is the column number), and all other cells are switched off. Then each second we switch on the cells that are off but have the side-adjacent cells that are on.For a cell with coordinates (x, y) the side-adjacent cells are cells with coordinates (x - 1, y), (x + 1, y), (x, y - 1), (x, y + 1).In how many seconds will Mr. Bender get happy?", "input_spec": "The first line contains four space-separated integers n, x, y, c (1 ≤ n, c ≤ 109; 1 ≤ x, y ≤ n; c ≤ n2).", "output_spec": "In a single line print a single integer — the answer to the problem.", "sample_inputs": ["6 4 3 1", "9 3 8 10"], "sample_outputs": ["0", "2"], "notes": "NoteInitially the first test has one painted cell, so the answer is 0. In the second test all events will go as is shown on the figure. ."}, "src_uid": "232c5206ee7c1903556c3625e0b0efc6"}
{"nl": {"description": "Little Joty has got a task to do. She has a line of n tiles indexed from 1 to n. She has to paint them in a strange pattern.An unpainted tile should be painted Red if it's index is divisible by a and an unpainted tile should be painted Blue if it's index is divisible by b. So the tile with the number divisible by a and b can be either painted Red or Blue.After her painting is done, she will get p chocolates for each tile that is painted Red and q chocolates for each tile that is painted Blue.Note that she can paint tiles in any order she wants.Given the required information, find the maximum number of chocolates Joty can get.", "input_spec": "The only line contains five integers n, a, b, p and q (1 ≤ n, a, b, p, q ≤ 109).", "output_spec": "Print the only integer s — the maximum number of chocolates Joty can get. Note that the answer can be too large, so you should use 64-bit integer type to store it. In C++ you can use the long long integer type and in Java you can use long integer type.", "sample_inputs": ["5 2 3 12 15", "20 2 3 3 5"], "sample_outputs": ["39", "51"], "notes": null}, "src_uid": "35d8a9f0d5b5ab22929ec050b55ec769"}
{"nl": {"description": "We all know that GukiZ often plays with arrays. Now he is thinking about this problem: how many arrays a, of length n, with non-negative elements strictly less then 2l meet the following condition: ? Here operation  means bitwise AND (in Pascal it is equivalent to and, in C/C++/Java/Python it is equivalent to &), operation  means bitwise OR (in Pascal it is equivalent to , in C/C++/Java/Python it is equivalent to |). Because the answer can be quite large, calculate it modulo m. This time GukiZ hasn't come up with solution, and needs you to help him!", "input_spec": "First and the only line of input contains four integers n, k, l, m (2 ≤ n ≤ 1018, 0 ≤ k ≤ 1018, 0 ≤ l ≤ 64, 1 ≤ m ≤ 109 + 7).", "output_spec": "In the single line print the number of arrays satisfying the condition above modulo m.", "sample_inputs": ["2 1 2 10", "2 1 1 3", "3 3 2 10"], "sample_outputs": ["3", "1", "9"], "notes": "NoteIn the first sample, satisfying arrays are {1, 1}, {3, 1}, {1, 3}.In the second sample, only satisfying array is {1, 1}.In the third sample, satisfying arrays are {0, 3, 3}, {1, 3, 2}, {1, 3, 3}, {2, 3, 1}, {2, 3, 3}, {3, 3, 0}, {3, 3, 1}, {3, 3, 2}, {3, 3, 3}."}, "src_uid": "2163eec2ea1eed5da8231d1882cb0f8e"}
{"nl": {"description": "While playing with geometric figures Alex has accidentally invented a concept of a $$$n$$$-th order rhombus in a cell grid.A $$$1$$$-st order rhombus is just a square $$$1 \\times 1$$$ (i.e just a cell).A $$$n$$$-th order rhombus for all $$$n \\geq 2$$$ one obtains from a $$$n-1$$$-th order rhombus adding all cells which have a common side with it to it (look at the picture to understand it better).    Alex asks you to compute the number of cells in a $$$n$$$-th order rhombus.", "input_spec": "The first and only input line contains integer $$$n$$$ ($$$1 \\leq n \\leq 100$$$) — order of a rhombus whose numbers of cells should be computed.", "output_spec": "Print exactly one integer — the number of cells in a $$$n$$$-th order rhombus.", "sample_inputs": ["1", "2", "3"], "sample_outputs": ["1", "5", "13"], "notes": "NoteImages of rhombus corresponding to the examples are given in the statement."}, "src_uid": "758d342c1badde6d0b4db81285be780c"}
{"nl": {"description": "Vasya has a non-negative integer n. He wants to round it to nearest integer, which ends up with 0. If n already ends up with 0, Vasya considers it already rounded.For example, if n = 4722 answer is 4720. If n = 5 Vasya can round it to 0 or to 10. Both ways are correct.For given n find out to which integer will Vasya round it.", "input_spec": "The first line contains single integer n (0 ≤ n ≤ 109) — number that Vasya has.", "output_spec": "Print result of rounding n. Pay attention that in some cases answer isn't unique. In that case print any correct answer.", "sample_inputs": ["5", "113", "1000000000", "5432359"], "sample_outputs": ["0", "110", "1000000000", "5432360"], "notes": "NoteIn the first example n = 5. Nearest integers, that ends up with zero are 0 and 10. Any of these answers is correct, so you can print 0 or 10."}, "src_uid": "29c4d5fdf1328bbc943fa16d54d97aa9"}
{"nl": {"description": "It is the easy version of the problem. The difference is that in this version, there are no nodes with already chosen colors.Theofanis is starving, and he wants to eat his favorite food, sheftalia. However, he should first finish his homework. Can you help him with this problem?You have a perfect binary tree of $$$2^k - 1$$$ nodes — a binary tree where all vertices $$$i$$$ from $$$1$$$ to $$$2^{k - 1} - 1$$$ have exactly two children: vertices $$$2i$$$ and $$$2i + 1$$$. Vertices from $$$2^{k - 1}$$$ to $$$2^k - 1$$$ don't have any children. You want to color its vertices with the $$$6$$$ Rubik's cube colors (White, Green, Red, Blue, Orange and Yellow).Let's call a coloring good when all edges connect nodes with colors that are neighboring sides in the Rubik's cube.  A picture of Rubik's cube and its 2D map. More formally:   a white node can not be neighboring with white and yellow nodes;  a yellow node can not be neighboring with white and yellow nodes;  a green node can not be neighboring with green and blue nodes;  a blue node can not be neighboring with green and blue nodes;  a red node can not be neighboring with red and orange nodes;  an orange node can not be neighboring with red and orange nodes; You want to calculate the number of the good colorings of the binary tree. Two colorings are considered different if at least one node is colored with a different color.The answer may be too large, so output the answer modulo $$$10^9+7$$$.", "input_spec": "The first and only line contains the integers $$$k$$$ ($$$1 \\le k \\le 60$$$) — the number of levels in the perfect binary tree you need to color.", "output_spec": "Print one integer — the number of the different colorings modulo $$$10^9+7$$$.", "sample_inputs": ["3", "14"], "sample_outputs": ["24576", "934234"], "notes": "NoteIn the picture below, you can see one of the correct colorings of the first example.  "}, "src_uid": "5144b9b281ea4087d8334d91c3c8bda4"}
{"nl": {"description": "On his free time, Chouti likes doing some housework. He has got one new task, paint some bricks in the yard.There are $$$n$$$ bricks lined in a row on the ground. Chouti has got $$$m$$$ paint buckets of different colors at hand, so he painted each brick in one of those $$$m$$$ colors.Having finished painting all bricks, Chouti was satisfied. He stood back and decided to find something fun with these bricks. After some counting, he found there are $$$k$$$ bricks with a color different from the color of the brick on its left (the first brick is not counted, for sure).So as usual, he needs your help in counting how many ways could he paint the bricks. Two ways of painting bricks are different if there is at least one brick painted in different colors in these two ways. Because the answer might be quite big, you only need to output the number of ways modulo $$$998\\,244\\,353$$$.", "input_spec": "The first and only line contains three integers $$$n$$$, $$$m$$$ and $$$k$$$ ($$$1 \\leq n,m \\leq 2000, 0 \\leq k \\leq n-1$$$) — the number of bricks, the number of colors, and the number of bricks, such that its color differs from the color of brick to the left of it.", "output_spec": "Print one integer — the number of ways to color bricks modulo $$$998\\,244\\,353$$$.", "sample_inputs": ["3 3 0", "3 2 1"], "sample_outputs": ["3", "4"], "notes": "NoteIn the first example, since $$$k=0$$$, the color of every brick should be the same, so there will be exactly $$$m=3$$$ ways to color the bricks.In the second example, suppose the two colors in the buckets are yellow and lime, the following image shows all $$$4$$$ possible colorings.  "}, "src_uid": "b2b9bee53e425fab1aa4d5468b9e578b"}
{"nl": {"description": "Misha and Vasya participated in a Codeforces contest. Unfortunately, each of them solved only one problem, though successfully submitted it at the first attempt. Misha solved the problem that costs a points and Vasya solved the problem that costs b points. Besides, Misha submitted the problem c minutes after the contest started and Vasya submitted the problem d minutes after the contest started. As you know, on Codeforces the cost of a problem reduces as a round continues. That is, if you submit a problem that costs p points t minutes after the contest started, you get  points. Misha and Vasya are having an argument trying to find out who got more points. Help them to find out the truth.", "input_spec": "The first line contains four integers a, b, c, d (250 ≤ a, b ≤ 3500, 0 ≤ c, d ≤ 180).  It is guaranteed that numbers a and b are divisible by 250 (just like on any real Codeforces round).", "output_spec": "Output on a single line:  \"Misha\" (without the quotes), if Misha got more points than Vasya. \"Vasya\" (without the quotes), if Vasya got more points than Misha. \"Tie\" (without the quotes), if both of them got the same number of points.", "sample_inputs": ["500 1000 20 30", "1000 1000 1 1", "1500 1000 176 177"], "sample_outputs": ["Vasya", "Tie", "Misha"], "notes": null}, "src_uid": "95b19d7569d6b70bd97d46a8541060d0"}
{"nl": {"description": "To celebrate the opening of the Winter Computer School the organizers decided to buy in n liters of cola. However, an unexpected difficulty occurred in the shop: it turned out that cola is sold in bottles 0.5, 1 and 2 liters in volume. At that, there are exactly a bottles 0.5 in volume, b one-liter bottles and c of two-liter ones. The organizers have enough money to buy any amount of cola. What did cause the heated arguments was how many bottles of every kind to buy, as this question is pivotal for the distribution of cola among the participants (and organizers as well).Thus, while the organizers are having the argument, discussing different variants of buying cola, the Winter School can't start. Your task is to count the number of all the possible ways to buy exactly n liters of cola and persuade the organizers that this number is too large, and if they keep on arguing, then the Winter Computer School will have to be organized in summer.All the bottles of cola are considered indistinguishable, i.e. two variants of buying are different from each other only if they differ in the number of bottles of at least one kind.", "input_spec": "The first line contains four integers — n, a, b, c (1 ≤ n ≤ 10000, 0 ≤ a, b, c ≤ 5000).", "output_spec": "Print the unique number — the solution to the problem. If it is impossible to buy exactly n liters of cola, print 0. ", "sample_inputs": ["10 5 5 5", "3 0 0 2"], "sample_outputs": ["9", "0"], "notes": null}, "src_uid": "474e527d41040446a18186596e8bdd83"}
{"nl": {"description": "The first ship with the Earth settlers landed on Mars. The colonists managed to build n necessary structures on the surface of the planet (which can be regarded as a plane, and the construction can be regarded as points on it). But one day the scanners recorded suspicious activity on the outskirts of the colony. It was decided to use the protective force field generating system to protect the colony against possible trouble.The system works as follows: the surface contains a number of generators of the field (they can also be considered as points). The active range of each generator is a circle of radius r centered at the location of the generator (the boundary of the circle is also included in the range). After the system is activated, it stretches the protective force field only over the part of the surface, which is within the area of all generators' activity. That is, the protected part is the intersection of the generators' active ranges.The number of generators available to the colonists is not limited, but the system of field generation consumes a lot of energy. More precisely, the energy consumption does not depend on the number of generators, but it is directly proportional to the area, which is protected by the field. Also, it is necessary that all the existing buildings are located within the protected area.Determine the smallest possible area of the protected part of the surface containing all the buildings.", "input_spec": "The first line contains two integers n and r (1 ≤ n ≤ 105, 1 ≤ r ≤ 50000) — the number of buildings and the active ranges of the generators, correspondingly. Next n lines contains the buildings' coordinates. The i + 1-th (1 ≤ i ≤ n) line contains two real numbers with at most three digits after the decimal point xi and yi (|xi|, |yi| ≤ 50000) — coordinates of the i-th building. It is guaranteed that no two buildings are located at the same point, and no two different buildings are located closer than 1. It is guaranteed that there exists a circle with radius r that contains all the buildings.", "output_spec": "Print the single real number — the minimum area of the protected part containing all the buildings. The answer is accepted if absolute or relative error doesn't exceed 10 - 4.", "sample_inputs": ["3 5\n0.00 0.000\n0.0 8.00\n6 8.00", "4 1000\n0.0 0.0\n0 2.00\n2.00 2\n2.0 0.00", "4 5\n3.00 0.0\n-3 0.00\n0.000 1\n0.0 -1.00"], "sample_outputs": ["78.5398163397", "4.0026666140", "8.1750554397"], "notes": "NoteIn the first sample the given radius equals the radius of the circle circumscribed around the given points. That's why the circle that corresponds to it is the sought area. The answer is 25π.In the second sample the area nearly coincides with the square which has vertexes in the given points.The area for the third sample is shown on the picture below.  "}, "src_uid": "5f2a0960bab9bdc91b190ed07d6adcf7"}
{"nl": {"description": "Mishka started participating in a programming contest. There are $$$n$$$ problems in the contest. Mishka's problem-solving skill is equal to $$$k$$$.Mishka arranges all problems from the contest into a list. Because of his weird principles, Mishka only solves problems from one of the ends of the list. Every time, he chooses which end (left or right) he will solve the next problem from. Thus, each problem Mishka solves is either the leftmost or the rightmost problem in the list.Mishka cannot solve a problem with difficulty greater than $$$k$$$. When Mishka solves the problem, it disappears from the list, so the length of the list decreases by $$$1$$$. Mishka stops when he is unable to solve any problem from any end of the list.How many problems can Mishka solve?", "input_spec": "The first line of input contains two integers $$$n$$$ and $$$k$$$ ($$$1 \\le n, k \\le 100$$$) — the number of problems in the contest and Mishka's problem-solving skill. The second line of input contains $$$n$$$ integers $$$a_1, a_2, \\dots, a_n$$$ ($$$1 \\le a_i \\le 100$$$), where $$$a_i$$$ is the difficulty of the $$$i$$$-th problem. The problems are given in order from the leftmost to the rightmost in the list.", "output_spec": "Print one integer — the maximum number of problems Mishka can solve.", "sample_inputs": ["8 4\n4 2 3 1 5 1 6 4", "5 2\n3 1 2 1 3", "5 100\n12 34 55 43 21"], "sample_outputs": ["5", "0", "5"], "notes": "NoteIn the first example, Mishka can solve problems in the following order: $$$[4, 2, 3, 1, 5, 1, 6, 4] \\rightarrow [2, 3, 1, 5, 1, 6, 4] \\rightarrow [2, 3, 1, 5, 1, 6] \\rightarrow [3, 1, 5, 1, 6] \\rightarrow [1, 5, 1, 6] \\rightarrow [5, 1, 6]$$$, so the number of solved problems will be equal to $$$5$$$.In the second example, Mishka can't solve any problem because the difficulties of problems from both ends are greater than $$$k$$$.In the third example, Mishka's solving skill is so amazing that he can solve all the problems."}, "src_uid": "ecf0ead308d8a581dd233160a7e38173"}
{"nl": {"description": "It is known that fleas in Berland can jump only vertically and horizontally, and the length of the jump is always equal to s centimeters. A flea has found herself at the center of some cell of the checked board of the size n × m centimeters (each cell is 1 × 1 centimeters). She can jump as she wishes for an arbitrary number of times, she can even visit a cell more than once. The only restriction is that she cannot jump out of the board.The flea can count the amount of cells that she can reach from the starting position (x, y). Let's denote this amount by dx, y. Your task is to find the number of such starting positions (x, y), which have the maximum possible value of dx, y.", "input_spec": "The first line contains three integers n, m, s (1 ≤ n, m, s ≤ 106) — length of the board, width of the board and length of the flea's jump.", "output_spec": "Output the only integer — the number of the required starting positions of the flea.", "sample_inputs": ["2 3 1000000", "3 3 2"], "sample_outputs": ["6", "4"], "notes": null}, "src_uid": "e853733fb2ed87c56623ff9a5ac09c36"}
{"nl": {"description": "Chloe, the same as Vladik, is a competitive programmer. She didn't have any problems to get to the olympiad like Vladik, but she was confused by the task proposed on the olympiad.Let's consider the following algorithm of generating a sequence of integers. Initially we have a sequence consisting of a single element equal to 1. Then we perform (n - 1) steps. On each step we take the sequence we've got on the previous step, append it to the end of itself and insert in the middle the minimum positive integer we haven't used before. For example, we get the sequence [1, 2, 1] after the first step, the sequence [1, 2, 1, 3, 1, 2, 1] after the second step.The task is to find the value of the element with index k (the elements are numbered from 1) in the obtained sequence, i. e. after (n - 1) steps.Please help Chloe to solve the problem!", "input_spec": "The only line contains two integers n and k (1 ≤ n ≤ 50, 1 ≤ k ≤ 2n - 1).", "output_spec": "Print single integer — the integer at the k-th position in the obtained sequence.", "sample_inputs": ["3 2", "4 8"], "sample_outputs": ["2", "4"], "notes": "NoteIn the first sample the obtained sequence is [1, 2, 1, 3, 1, 2, 1]. The number on the second position is 2.In the second sample the obtained sequence is [1, 2, 1, 3, 1, 2, 1, 4, 1, 2, 1, 3, 1, 2, 1]. The number on the eighth position is 4."}, "src_uid": "0af400ea8e25b1a36adec4cc08912b71"}
{"nl": {"description": "One cold winter evening Alice and her older brother Bob was sitting at home near the fireplace and giving each other interesting problems to solve. When it was Alice's turn, she told the number n to Bob and said:—Shuffle the digits in this number in order to obtain the smallest possible number without leading zeroes.—No problem! — said Bob and immediately gave her an answer.Alice said a random number, so she doesn't know whether Bob's answer is correct. Help her to find this out, because impatient brother is waiting for the verdict.", "input_spec": "The first line contains one integer n (0 ≤ n ≤ 109) without leading zeroes. The second lines contains one integer m (0 ≤ m ≤ 109) — Bob's answer, possibly with leading zeroes.", "output_spec": "Print OK if Bob's answer is correct and WRONG_ANSWER otherwise.", "sample_inputs": ["3310\n1033", "4\n5"], "sample_outputs": ["OK", "WRONG_ANSWER"], "notes": null}, "src_uid": "d1e381b72a6c09a0723cfe72c0917372"}
{"nl": {"description": "One day a highly important task was commissioned to Vasya — writing a program in a night. The program consists of n lines of code. Vasya is already exhausted, so he works like that: first he writes v lines of code, drinks a cup of tea, then he writes as much as  lines, drinks another cup of tea, then he writes  lines and so on: , , , ...The expression  is regarded as the integral part from dividing number a by number b.The moment the current value  equals 0, Vasya immediately falls asleep and he wakes up only in the morning, when the program should already be finished.Vasya is wondering, what minimum allowable value v can take to let him write not less than n lines of code before he falls asleep.", "input_spec": "The input consists of two integers n and k, separated by spaces — the size of the program in lines and the productivity reduction coefficient, 1 ≤ n ≤ 109, 2 ≤ k ≤ 10.", "output_spec": "Print the only integer — the minimum value of v that lets Vasya write the program in one night.", "sample_inputs": ["7 2", "59 9"], "sample_outputs": ["4", "54"], "notes": "NoteIn the first sample the answer is v = 4. Vasya writes the code in the following portions: first 4 lines, then 2, then 1, and then Vasya falls asleep. Thus, he manages to write 4 + 2 + 1 = 7 lines in a night and complete the task.In the second sample the answer is v = 54. Vasya writes the code in the following portions: 54, 6. The total sum is 54 + 6 = 60, that's even more than n = 59."}, "src_uid": "41dfc86d341082dd96e089ac5433dc04"}
{"nl": {"description": "The following problem is well-known: given integers n and m, calculate , where 2n = 2·2·...·2 (n factors), and  denotes the remainder of division of x by y.You are asked to solve the \"reverse\" problem. Given integers n and m, calculate . ", "input_spec": "The first line contains a single integer n (1 ≤ n ≤ 108). The second line contains a single integer m (1 ≤ m ≤ 108).", "output_spec": "Output a single integer — the value of .", "sample_inputs": ["4\n42", "1\n58", "98765432\n23456789"], "sample_outputs": ["10", "0", "23456789"], "notes": "NoteIn the first example, the remainder of division of 42 by 24 = 16 is equal to 10.In the second example, 58 is divisible by 21 = 2 without remainder, and the answer is 0."}, "src_uid": "c649052b549126e600691931b512022f"}
{"nl": {"description": "Gerald bought two very rare paintings at the Sotheby's auction and he now wants to hang them on the wall. For that he bought a special board to attach it to the wall and place the paintings on the board. The board has shape of an a1 × b1 rectangle, the paintings have shape of a a2 × b2 and a3 × b3 rectangles.Since the paintings are painted in the style of abstract art, it does not matter exactly how they will be rotated, but still, one side of both the board, and each of the paintings must be parallel to the floor. The paintings can touch each other and the edges of the board, but can not overlap or go beyond the edge of the board. Gerald asks whether it is possible to place the paintings on the board, or is the board he bought not large enough?", "input_spec": "The first line contains two space-separated numbers a1 and b1 — the sides of the board. Next two lines contain numbers a2, b2, a3 and b3 — the sides of the paintings. All numbers ai, bi in the input are integers and fit into the range from 1 to 1000.", "output_spec": "If the paintings can be placed on the wall, print \"YES\" (without the quotes), and if they cannot, print \"NO\" (without the quotes).", "sample_inputs": ["3 2\n1 3\n2 1", "5 5\n3 3\n3 3", "4 2\n2 3\n1 2"], "sample_outputs": ["YES", "NO", "YES"], "notes": "NoteThat's how we can place the pictures in the first test:And that's how we can do it in the third one."}, "src_uid": "2ff30d9c4288390fd7b5b37715638ad9"}
{"nl": {"description": "Nauuo is a girl who loves writing comments.One day, she posted a comment on Codeforces, wondering whether she would get upvotes or downvotes.It's known that there were $$$x$$$ persons who would upvote, $$$y$$$ persons who would downvote, and there were also another $$$z$$$ persons who would vote, but you don't know whether they would upvote or downvote. Note that each of the $$$x+y+z$$$ people would vote exactly one time.There are three different results: if there are more people upvote than downvote, the result will be \"+\"; if there are more people downvote than upvote, the result will be \"-\"; otherwise the result will be \"0\".Because of the $$$z$$$ unknown persons, the result may be uncertain (i.e. there are more than one possible results). More formally, the result is uncertain if and only if there exist two different situations of how the $$$z$$$ persons vote, that the results are different in the two situations.Tell Nauuo the result or report that the result is uncertain.", "input_spec": "The only line contains three integers $$$x$$$, $$$y$$$, $$$z$$$ ($$$0\\le x,y,z\\le100$$$), corresponding to the number of persons who would upvote, downvote or unknown.", "output_spec": "If there is only one possible result, print the result : \"+\", \"-\" or \"0\". Otherwise, print \"?\" to report that the result is uncertain.", "sample_inputs": ["3 7 0", "2 0 1", "1 1 0", "0 0 1"], "sample_outputs": ["-", "+", "0", "?"], "notes": "NoteIn the first example, Nauuo would definitely get three upvotes and seven downvotes, so the only possible result is \"-\".In the second example, no matter the person unknown downvotes or upvotes, Nauuo would get more upvotes than downvotes. So the only possible result is \"+\".In the third example, Nauuo would definitely get one upvote and one downvote, so the only possible result is \"0\".In the fourth example, if the only one person upvoted, the result would be \"+\", otherwise, the result would be \"-\". There are two possible results, so the result is uncertain."}, "src_uid": "66398694a4a142b4a4e709d059aca0fa"}
{"nl": {"description": "In this problem you will meet the simplified model of game King of Thieves.In a new ZeptoLab game called \"King of Thieves\" your aim is to reach a chest with gold by controlling your character, avoiding traps and obstacles on your way.  An interesting feature of the game is that you can design your own levels that will be available to other players. Let's consider the following simple design of a level.A dungeon consists of n segments located at a same vertical level, each segment is either a platform that character can stand on, or a pit with a trap that makes player lose if he falls into it. All segments have the same length, platforms on the scheme of the level are represented as '*' and pits are represented as '.'. One of things that affects speedrun characteristics of the level is a possibility to perform a series of consecutive jumps of the same length. More formally, when the character is on the platform number i1, he can make a sequence of jumps through the platforms i1 < i2 < ... < ik, if i2 - i1 = i3 - i2 = ... = ik - ik - 1. Of course, all segments i1, i2, ... ik should be exactly the platforms, not pits. Let's call a level to be good if you can perform a sequence of four jumps of the same length or in the other words there must be a sequence i1, i2, ..., i5, consisting of five platforms so that the intervals between consecutive platforms are of the same length. Given the scheme of the level, check if it is good.", "input_spec": "The first line contains integer n (1 ≤ n ≤ 100) — the number of segments on the level. Next line contains the scheme of the level represented as a string of n characters '*' and '.'.", "output_spec": "If the level is good, print the word \"yes\" (without the quotes), otherwise print the word \"no\" (without the quotes).", "sample_inputs": ["16\n.**.*..*.***.**.", "11\n.*.*...*.*."], "sample_outputs": ["yes", "no"], "notes": "NoteIn the first sample test you may perform a sequence of jumps through platforms 2, 5, 8, 11, 14."}, "src_uid": "12d451eb1b401a8f426287c4c6909e4b"}
{"nl": {"description": "You are solving the crossword problem K from IPSC 2014. You solved all the clues except for one: who does Eevee evolve into? You are not very into pokemons, but quick googling helped you find out, that Eevee can evolve into eight different pokemons: Vaporeon, Jolteon, Flareon, Espeon, Umbreon, Leafeon, Glaceon, and Sylveon.You know the length of the word in the crossword, and you already know some letters. Designers of the crossword made sure that the answer is unambiguous, so you can assume that exactly one pokemon out of the 8 that Eevee evolves into fits the length and the letters given. Your task is to find it.", "input_spec": "First line contains an integer n (6 ≤ n ≤ 8) – the length of the string. Next line contains a string consisting of n characters, each of which is either a lower case english letter (indicating a known letter) or a dot character (indicating an empty cell in the crossword).", "output_spec": "Print a name of the pokemon that Eevee can evolve into that matches the pattern in the input. Use lower case letters only to print the name (in particular, do not capitalize the first letter).", "sample_inputs": ["7\nj......", "7\n...feon", "7\n.l.r.o."], "sample_outputs": ["jolteon", "leafeon", "flareon"], "notes": "NoteHere's a set of names in a form you can paste into your solution:[\"vaporeon\", \"jolteon\", \"flareon\", \"espeon\", \"umbreon\", \"leafeon\", \"glaceon\", \"sylveon\"]{\"vaporeon\", \"jolteon\", \"flareon\", \"espeon\", \"umbreon\", \"leafeon\", \"glaceon\", \"sylveon\"}"}, "src_uid": "ec3d15ff198d1e4ab9fd04dd3b12e6c0"}
{"nl": {"description": "The protection of a popular program developed by one of IT City companies is organized the following way. After installation it outputs a random five digit number which should be sent in SMS to a particular phone number. In response an SMS activation code arrives.A young hacker Vasya disassembled the program and found the algorithm that transforms the shown number into the activation code. Note: it is clear that Vasya is a law-abiding hacker, and made it for a noble purpose — to show the developer the imperfection of their protection.The found algorithm looks the following way. At first the digits of the number are shuffled in the following order <first digit><third digit><fifth digit><fourth digit><second digit>. For example the shuffle of 12345 should lead to 13542. On the second stage the number is raised to the fifth power. The result of the shuffle and exponentiation of the number 12345 is 455 422 043 125 550 171 232. The answer is the 5 last digits of this result. For the number 12345 the answer should be 71232.Vasya is going to write a keygen program implementing this algorithm. Can you do the same?", "input_spec": "The only line of the input contains a positive integer five digit number for which the activation code should be found.", "output_spec": "Output exactly 5 digits without spaces between them — the found activation code of the program.", "sample_inputs": ["12345"], "sample_outputs": ["71232"], "notes": null}, "src_uid": "51b1c216948663fff721c28d131bf18f"}
{"nl": {"description": "Imagine that you are in a building that has exactly n floors. You can move between the floors in a lift. Let's number the floors from bottom to top with integers from 1 to n. Now you're on the floor number a. You are very bored, so you want to take the lift. Floor number b has a secret lab, the entry is forbidden. However, you already are in the mood and decide to make k consecutive trips in the lift.Let us suppose that at the moment you are on the floor number x (initially, you were on floor a). For another trip between floors you choose some floor with number y (y ≠ x) and the lift travels to this floor. As you cannot visit floor b with the secret lab, you decided that the distance from the current floor x to the chosen y must be strictly less than the distance from the current floor x to floor b with the secret lab. Formally, it means that the following inequation must fulfill: |x - y| < |x - b|. After the lift successfully transports you to floor y, you write down number y in your notepad.Your task is to find the number of distinct number sequences that you could have written in the notebook as the result of k trips in the lift. As the sought number of trips can be rather large, find the remainder after dividing the number by 1000000007 (109 + 7).", "input_spec": "The first line of the input contains four space-separated integers n, a, b, k (2 ≤ n ≤ 5000, 1 ≤ k ≤ 5000, 1 ≤ a, b ≤ n, a ≠ b).", "output_spec": "Print a single integer — the remainder after dividing the sought number of sequences by 1000000007 (109 + 7).", "sample_inputs": ["5 2 4 1", "5 2 4 2", "5 3 4 1"], "sample_outputs": ["2", "2", "0"], "notes": "NoteTwo sequences p1, p2, ..., pk and q1, q2, ..., qk are distinct, if there is such integer j (1 ≤ j ≤ k), that pj ≠ qj.Notes to the samples:  In the first sample after the first trip you are either on floor 1, or on floor 3, because |1 - 2| < |2 - 4| and |3 - 2| < |2 - 4|.  In the second sample there are two possible sequences: (1, 2); (1, 3). You cannot choose floor 3 for the first trip because in this case no floor can be the floor for the second trip.  In the third sample there are no sought sequences, because you cannot choose the floor for the first trip. "}, "src_uid": "142b06ed43b3473513995de995e19fc3"}
{"nl": {"description": "Fox Ciel has some flowers: r red flowers, g green flowers and b blue flowers. She wants to use these flowers to make several bouquets. There are 4 types of bouquets:  To make a \"red bouquet\", it needs 3 red flowers.  To make a \"green bouquet\", it needs 3 green flowers.  To make a \"blue bouquet\", it needs 3 blue flowers.  To make a \"mixing bouquet\", it needs 1 red, 1 green and 1 blue flower. Help Fox Ciel to find the maximal number of bouquets she can make.", "input_spec": "The first line contains three integers r, g and b (0 ≤ r, g, b ≤ 109) — the number of red, green and blue flowers.", "output_spec": "Print the maximal number of bouquets Fox Ciel can make.", "sample_inputs": ["3 6 9", "4 4 4", "0 0 0"], "sample_outputs": ["6", "4", "0"], "notes": "NoteIn test case 1, we can make 1 red bouquet, 2 green bouquets and 3 blue bouquets.In test case 2, we can make 1 red, 1 green, 1 blue and 1 mixing bouquet."}, "src_uid": "acddc9b0db312b363910a84bd4f14d8e"}
{"nl": {"description": "Polycarpus is sure that his life fits the description: \"first there is a white stripe, then a black one, then a white one again\". So, Polycarpus is sure that this rule is going to fulfill during the next n days. Polycarpus knows that he is in for w good events and b not-so-good events. At least one event is going to take place during each day. As each day is unequivocally characterizes as a part of a white or a black stripe, then each day is going to have events of the same type only (ether good or not-so-good).What is the number of distinct ways this scenario can develop over the next n days if Polycarpus is in for a white stripe (a stripe that has good events only, the stripe's length is at least 1 day), the a black stripe (a stripe that has not-so-good events only, the stripe's length is at least 1 day) and a white stripe again (a stripe that has good events only, the stripe's length is at least 1 day). Each of n days will belong to one of the three stripes only.Note that even the events of the same type are distinct from each other. Even if some events occur on the same day, they go in some order (there are no simultaneous events).Write a code that prints the number of possible configurations to sort the events into days. See the samples for clarifications on which scenarios should be considered distinct. Print the answer modulo 1000000009 (109 + 9).", "input_spec": "The single line of the input contains integers n, w and b (3 ≤ n ≤ 4000, 2 ≤ w ≤ 4000, 1 ≤ b ≤ 4000) — the number of days, the number of good events and the number of not-so-good events. It is guaranteed that w + b ≥ n.", "output_spec": "Print the required number of ways modulo 1000000009 (109 + 9).", "sample_inputs": ["3 2 1", "4 2 2", "3 2 2"], "sample_outputs": ["2", "4", "4"], "notes": "NoteWe'll represent the good events by numbers starting from 1 and the not-so-good events — by letters starting from 'a'. Vertical lines separate days.In the first sample the possible ways are: \"1|a|2\" and \"2|a|1\". In the second sample the possible ways are: \"1|a|b|2\", \"2|a|b|1\", \"1|b|a|2\" and \"2|b|a|1\". In the third sample the possible ways are: \"1|ab|2\", \"2|ab|1\", \"1|ba|2\" and \"2|ba|1\"."}, "src_uid": "63e93a161bbff623323e66c98d5e20ac"}
{"nl": {"description": "Ari the monster always wakes up very early with the first ray of the sun and the first thing she does is feeding her squirrel.Ari draws a regular convex polygon on the floor and numbers it's vertices 1, 2, ..., n in clockwise order. Then starting from the vertex 1 she draws a ray in the direction of each other vertex. The ray stops when it reaches a vertex or intersects with another ray drawn before. Ari repeats this process for vertex 2, 3, ..., n (in this particular order). And then she puts a walnut in each region inside the polygon.  Ada the squirrel wants to collect all the walnuts, but she is not allowed to step on the lines drawn by Ari. That means Ada have to perform a small jump if she wants to go from one region to another. Ada can jump from one region P to another region Q if and only if P and Q share a side or a corner.Assuming that Ada starts from outside of the picture, what is the minimum number of jumps she has to perform in order to collect all the walnuts?", "input_spec": "The first and only line of the input contains a single integer n (3 ≤ n ≤ 54321) - the number of vertices of the regular polygon drawn by Ari.", "output_spec": "Print the minimum number of jumps Ada should make to collect all the walnuts. Note, that she doesn't need to leave the polygon after.", "sample_inputs": ["5", "3"], "sample_outputs": ["9", "1"], "notes": "NoteOne of the possible solutions for the first sample is shown on the picture above."}, "src_uid": "efa8e7901a3084d34cfb1a6b18067f2b"}
{"nl": {"description": "Do you remember a kind cartoon \"Beauty and the Beast\"? No, no, there was no firing from machine guns or radiation mutants time-travels!There was a beauty named Belle. Once she had violated the Beast's order and visited the West Wing. After that she was banished from the castle... Everybody was upset. The beautiful Belle was upset, so was the Beast, so was Lumiere the candlestick. But the worst thing was that Cogsworth was upset. Cogsworth is not a human, but is the mantel clock, which was often used as an alarm clock.Due to Cogsworth's frustration all the inhabitants of the castle were in trouble: now they could not determine when it was time to drink morning tea, and when it was time for an evening stroll. Fortunately, deep in the basement are lying digital clock showing the time in the format HH:MM. Now the residents of the castle face a difficult task. They should turn Cogsworth's hour and minute mustache hands in such a way, that Cogsworth began to show the correct time. Moreover they need to find turn angles in degrees for each mustache hands. The initial time showed by Cogsworth is 12:00.You can only rotate the hands forward, that is, as is shown in the picture:   As since there are many ways too select such angles because of full rotations, choose the smallest angles in the right (non-negative) direction.Note that Cogsworth's hour and minute mustache hands move evenly and continuously. Hands are moving independently, so when turning one hand the other hand remains standing still.", "input_spec": "The only line of input contains current time according to the digital clock, formatted as HH:MM (00 ≤ HH ≤ 23, 00 ≤ MM ≤ 59). The mantel clock initially shows 12:00. Pretests contain times of the beginning of some morning TV programs of the Channel One Russia.", "output_spec": "Print two numbers x and y — the angles of turning the hour and minute hands, respectively (0 ≤ x, y < 360). The absolute or relative error in the answer should not exceed 10 - 9.", "sample_inputs": ["12:00", "04:30", "08:17"], "sample_outputs": ["0 0", "135 180", "248.5 102"], "notes": "NoteA note to the second example: the hour hand will be positioned exactly in the middle, between 4 and 5."}, "src_uid": "175dc0bdb5c9513feb49be6644d0d150"}
{"nl": {"description": "Polycarpus plays with red and blue marbles. He put n marbles from the left to the right in a row. As it turned out, the marbles form a zebroid.A non-empty sequence of red and blue marbles is a zebroid, if the colors of the marbles in this sequence alternate. For example, sequences (red; blue; red) and (blue) are zebroids and sequence (red; red) is not a zebroid.Now Polycarpus wonders, how many ways there are to pick a zebroid subsequence from this sequence. Help him solve the problem, find the number of ways modulo 1000000007 (109 + 7).", "input_spec": "The first line contains a single integer n (1 ≤ n ≤ 106) — the number of marbles in Polycarpus's sequence.", "output_spec": "Print a single number — the answer to the problem modulo 1000000007 (109 + 7).", "sample_inputs": ["3", "4"], "sample_outputs": ["6", "11"], "notes": "NoteLet's consider the first test sample. Let's assume that Polycarpus initially had sequence (red; blue; red), so there are six ways to pick a zebroid:   pick the first marble;  pick the second marble;  pick the third marble;  pick the first and second marbles;  pick the second and third marbles;  pick the first, second and third marbles. It can be proven that if Polycarpus picks (blue; red; blue) as the initial sequence, the number of ways won't change."}, "src_uid": "5c4bd12df3915186a7b506c2060db125"}
{"nl": {"description": "Limak and Radewoosh are going to compete against each other in the upcoming algorithmic contest. They are equally skilled but they won't solve problems in the same order.There will be n problems. The i-th problem has initial score pi and it takes exactly ti minutes to solve it. Problems are sorted by difficulty — it's guaranteed that pi < pi + 1 and ti < ti + 1.A constant c is given too, representing the speed of loosing points. Then, submitting the i-th problem at time x (x minutes after the start of the contest) gives max(0,  pi - c·x) points.Limak is going to solve problems in order 1, 2, ..., n (sorted increasingly by pi). Radewoosh is going to solve them in order n, n - 1, ..., 1 (sorted decreasingly by pi). Your task is to predict the outcome — print the name of the winner (person who gets more points at the end) or a word \"Tie\" in case of a tie.You may assume that the duration of the competition is greater or equal than the sum of all ti. That means both Limak and Radewoosh will accept all n problems.", "input_spec": "The first line contains two integers n and c (1 ≤ n ≤ 50, 1 ≤ c ≤ 1000) — the number of problems and the constant representing the speed of loosing points. The second line contains n integers p1, p2, ..., pn (1 ≤ pi ≤ 1000, pi < pi + 1) — initial scores. The third line contains n integers t1, t2, ..., tn (1 ≤ ti ≤ 1000, ti < ti + 1) where ti denotes the number of minutes one needs to solve the i-th problem.", "output_spec": "Print \"Limak\" (without quotes) if Limak will get more points in total. Print \"Radewoosh\" (without quotes) if Radewoosh will get more points in total. Print \"Tie\" (without quotes) if Limak and Radewoosh will get the same total number of points.", "sample_inputs": ["3 2\n50 85 250\n10 15 25", "3 6\n50 85 250\n10 15 25", "8 1\n10 20 30 40 50 60 70 80\n8 10 58 63 71 72 75 76"], "sample_outputs": ["Limak", "Radewoosh", "Tie"], "notes": "NoteIn the first sample, there are 3 problems. Limak solves them as follows:  Limak spends 10 minutes on the 1-st problem and he gets 50 - c·10 = 50 - 2·10 = 30 points.  Limak spends 15 minutes on the 2-nd problem so he submits it 10 + 15 = 25 minutes after the start of the contest. For the 2-nd problem he gets 85 - 2·25 = 35 points.  He spends 25 minutes on the 3-rd problem so he submits it 10 + 15 + 25 = 50 minutes after the start. For this problem he gets 250 - 2·50 = 150 points. So, Limak got 30 + 35 + 150 = 215 points.Radewoosh solves problem in the reversed order:  Radewoosh solves 3-rd problem after 25 minutes so he gets 250 - 2·25 = 200 points.  He spends 15 minutes on the 2-nd problem so he submits it 25 + 15 = 40 minutes after the start. He gets 85 - 2·40 = 5 points for this problem.  He spends 10 minutes on the 1-st problem so he submits it 25 + 15 + 10 = 50 minutes after the start. He gets max(0, 50 - 2·50) = max(0,  - 50) = 0 points. Radewoosh got 200 + 5 + 0 = 205 points in total. Limak has 215 points so Limak wins.In the second sample, Limak will get 0 points for each problem and Radewoosh will first solve the hardest problem and he will get 250 - 6·25 = 100 points for that. Radewoosh will get 0 points for other two problems but he is the winner anyway.In the third sample, Limak will get 2 points for the 1-st problem and 2 points for the 2-nd problem. Radewoosh will get 4 points for the 8-th problem. They won't get points for other problems and thus there is a tie because 2 + 2 = 4."}, "src_uid": "8c704de75ab85f9e2c04a926143c8b4a"}
{"nl": {"description": "The Holmes children are fighting over who amongst them is the cleverest.Mycroft asked Sherlock and Eurus to find value of f(n), where f(1) = 1 and for n ≥ 2, f(n) is the number of distinct ordered positive integer pairs (x, y) that satisfy x + y = n and gcd(x, y) = 1. The integer gcd(a, b) is the greatest common divisor of a and b.Sherlock said that solving this was child's play and asked Mycroft to instead get the value of . Summation is done over all positive integers d that divide n.Eurus was quietly observing all this and finally came up with her problem to astonish both Sherlock and Mycroft.She defined a k-composite function Fk(n) recursively as follows:She wants them to tell the value of Fk(n) modulo 1000000007.", "input_spec": "A single line of input contains two space separated integers n (1 ≤ n ≤ 1012) and k (1 ≤ k ≤ 1012) indicating that Eurus asks Sherlock and Mycroft to find the value of Fk(n) modulo 1000000007.", "output_spec": "Output a single integer — the value of Fk(n) modulo 1000000007.", "sample_inputs": ["7 1", "10 2"], "sample_outputs": ["6", "4"], "notes": "NoteIn the first case, there are 6 distinct ordered pairs (1, 6), (2, 5), (3, 4), (4, 3), (5, 2) and (6, 1) satisfying x + y = 7 and gcd(x, y) = 1. Hence, f(7) = 6. So, F1(7) = f(g(7)) = f(f(7) + f(1)) = f(6 + 1) = f(7) = 6."}, "src_uid": "0591ade5f9a69afcbecd80402493f975"}
{"nl": {"description": "Having stayed home alone, Petya decided to watch forbidden films on the Net in secret. \"What ungentlemanly behavior!\" — you can say that, of course, but don't be too harsh on the kid. In his country films about the Martians and other extraterrestrial civilizations are forbidden. It was very unfair to Petya as he adored adventure stories that featured lasers and robots. Today Petya is watching a shocking blockbuster about the Martians called \"R2:D2\". What can \"R2:D2\" possibly mean? It might be the Martian time represented in the Martian numeral system. Petya knows that time on Mars is counted just like on the Earth (that is, there are 24 hours and each hour has 60 minutes). The time is written as \"a:b\", where the string a stands for the number of hours (from 0 to 23 inclusive), and string b stands for the number of minutes (from 0 to 59 inclusive). The only thing Petya doesn't know is in what numeral system the Martian time is written.Your task is to print the radixes of all numeral system which can contain the time \"a:b\".", "input_spec": "The first line contains a single string as \"a:b\" (without the quotes). There a is a non-empty string, consisting of numbers and uppercase Latin letters. String a shows the number of hours. String b is a non-empty string that consists of numbers and uppercase Latin letters. String b shows the number of minutes. The lengths of strings a and b are from 1 to 5 characters, inclusive. Please note that strings a and b can have leading zeroes that do not influence the result in any way (for example, string \"008:1\" in decimal notation denotes correctly written time). We consider characters 0, 1, ..., 9 as denoting the corresponding digits of the number's representation in some numeral system, and characters A, B, ..., Z correspond to numbers 10, 11, ..., 35.", "output_spec": "Print the radixes of the numeral systems that can represent the time \"a:b\" in the increasing order. Separate the numbers with spaces or line breaks. If there is no numeral system that can represent time \"a:b\", print the single integer 0. If there are infinitely many numeral systems that can represent the time \"a:b\", print the single integer -1. Note that on Mars any positional numeral systems with positive radix strictly larger than one are possible.", "sample_inputs": ["11:20", "2A:13", "000B:00001"], "sample_outputs": ["3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22", "0", "-1"], "notes": "NoteLet's consider the first sample. String \"11:20\" can be perceived, for example, as time 4:6, represented in the ternary numeral system or as time 17:32 in hexadecimal system. Let's consider the second sample test. String \"2A:13\" can't be perceived as correct time in any notation. For example, let's take the base-11 numeral notation. There the given string represents time 32:14 that isn't a correct time.Let's consider the third sample. String \"000B:00001\" can be perceived as a correct time in the infinite number of numeral systems. If you need an example, you can take any numeral system with radix no less than 12."}, "src_uid": "c02dfe5b8d9da2818a99c3afbe7a5293"}
{"nl": {"description": "As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as , where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!", "input_spec": "The first input line contains an integer n (1 ≤ n ≤ 109).", "output_spec": "Print \"YES\" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print \"NO\" (without the quotes).", "sample_inputs": ["256", "512"], "sample_outputs": ["YES", "NO"], "notes": "NoteIn the first sample number .In the second sample number 512 can not be represented as a sum of two triangular numbers."}, "src_uid": "245ec0831cd817714a4e5c531bffd099"}
{"nl": {"description": "For some experiments little Petya needs a synchrophasotron. He has already got the device, all that's left is to set the fuel supply. Fuel comes through a system of nodes numbered from 1 to n and connected by pipes. Pipes go from every node with smaller number to every node with greater number. Fuel can only flow through pipes in direction from node with smaller number to node with greater number. Any amount of fuel can enter through the first node and the last node is connected directly to the synchrophasotron. It is known that every pipe has three attributes: the minimum amount of fuel that should go through it, the maximum amount of fuel that can possibly go through it and the cost of pipe activation. If cij units of fuel (cij > 0) flow from node i to node j, it will cost aij + cij2 tugriks (aij is the cost of pipe activation), and if fuel doesn't flow through the pipe, it doesn't cost anything. Only integer number of units of fuel can flow through each pipe.Constraints on the minimal and the maximal fuel capacity of a pipe take place always, not only if it is active. You may assume that the pipe is active if and only if the flow through it is strictly greater than zero.Petya doesn't want the pipe system to be overloaded, so he wants to find the minimal amount of fuel, that, having entered the first node, can reach the synchrophasotron. Besides that he wants to impress the sponsors, so the sum of money needed to be paid for fuel to go through each pipe, must be as big as possible.", "input_spec": "First line contains integer n (2 ≤ n ≤ 6), which represents the number of nodes. Each of the next n(n - 1) / 2 lines contains five integers s, f, l, h, a that describe pipes — the first node of the pipe, the second node of the pipe, the minimum and the maximum amount of fuel that can flow through the pipe and the the activation cost, respectively. (1 ≤ s < f ≤ n, 0 ≤ l ≤ h ≤ 5, 0 ≤ a ≤ 6). It is guaranteed that for each pair of nodes with distinct numbers there will be exactly one pipe between them described in the input.", "output_spec": "Output in the first line two space-separated numbers: the minimum possible amount of fuel that can flow into the synchrophasotron, and the maximum possible sum that needs to be paid in order for that amount of fuel to reach synchrophasotron. If there is no amount of fuel that can reach synchrophasotron, output \"-1 -1\". The amount of fuel which will flow into synchrophasotron is not neccessary positive. It could be equal to zero if the minimum constraint of every pipe is equal to zero.", "sample_inputs": ["2\n1 2 1 2 3", "3\n1 2 1 2 3\n1 3 0 0 0\n2 3 3 4 5", "4\n1 2 0 2 1\n2 3 0 2 1\n1 3 0 2 6\n1 4 0 0 1\n2 4 0 0 0\n3 4 2 3 0", "3\n1 2 0 2 1\n1 3 1 2 1\n2 3 1 2 1"], "sample_outputs": ["1 4", "-1 -1", "2 15", "2 6"], "notes": "NoteIn the first test, we can either pass 1 or 2 units of fuel from node 1 to node 2. The minimum possible amount is 1, it costs a12 + 12 = 4.In the second test, you can pass at most 2 units from node 1 to node 2, and at you have to pass at least 3 units from node 2 to node 3. It is impossible.In the third test, the minimum possible amount is 2. You can pass each unit of fuel through two different paths: either 1->2->3->4 or 1->3->4. If you use the first path twice, it will cost a12 + 22 + a23 + 22 + a34 + 22=14. If you use the second path twice, it will cost a13 + 22 + a34 + 22=14. However, if you use each path (allowing one unit of fuel go through pipes 1->2, 2->3, 1->3, and two units go through 3->4) it will cost a12 + 12 + a23 + 12 + a13 + 12 + a34 + 22=15 and it is the maximum possible cost.Also note that since no fuel flows from node 1 to node 4, activation cost for that pipe is not added to the answer."}, "src_uid": "38886ad7b0d83e66b77348be34828426"}
{"nl": {"description": "Vasily has a number a, which he wants to turn into a number b. For this purpose, he can do two types of operations:  multiply the current number by 2 (that is, replace the number x by 2·x);  append the digit 1 to the right of current number (that is, replace the number x by 10·x + 1). You need to help Vasily to transform the number a into the number b using only the operations described above, or find that it is impossible.Note that in this task you are not required to minimize the number of operations. It suffices to find any way to transform a into b.", "input_spec": "The first line contains two positive integers a and b (1 ≤ a < b ≤ 109) — the number which Vasily has and the number he wants to have.", "output_spec": "If there is no way to get b from a, print \"NO\" (without quotes). Otherwise print three lines. On the first line print \"YES\" (without quotes). The second line should contain single integer k — the length of the transformation sequence. On the third line print the sequence of transformations x1, x2, ..., xk, where:   x1 should be equal to a,  xk should be equal to b,  xi should be obtained from xi - 1 using any of two described operations (1 < i ≤ k).  If there are multiple answers, print any of them.", "sample_inputs": ["2 162", "4 42", "100 40021"], "sample_outputs": ["YES\n5\n2 4 8 81 162", "NO", "YES\n5\n100 200 2001 4002 40021"], "notes": null}, "src_uid": "fc3adb1a9a7f1122b567b4d8afd7b3f3"}
{"nl": {"description": "Once Max found an electronic calculator from his grandfather Dovlet's chest. He noticed that the numbers were written with seven-segment indicators (https://en.wikipedia.org/wiki/Seven-segment_display).  Max starts to type all the values from a to b. After typing each number Max resets the calculator. Find the total number of segments printed on the calculator.For example if a = 1 and b = 3 then at first the calculator will print 2 segments, then — 5 segments and at last it will print 5 segments. So the total number of printed segments is 12.", "input_spec": "The only line contains two integers a, b (1 ≤ a ≤ b ≤ 106) — the first and the last number typed by Max.", "output_spec": "Print the only integer a — the total number of printed segments.", "sample_inputs": ["1 3", "10 15"], "sample_outputs": ["12", "39"], "notes": null}, "src_uid": "1193de6f80a9feee8522a404d16425b9"}
{"nl": {"description": "Vasya studies divisibility rules at school. Here are some of them: Divisibility by 2. A number is divisible by 2 if and only if its last digit is divisible by 2 or in other words, is even. Divisibility by 3. A number is divisible by 3 if and only if the sum of its digits is divisible by 3. Divisibility by 4. A number is divisible by 4 if and only if its last two digits form a number that is divisible by 4. Divisibility by 5. A number is divisible by 5 if and only if its last digit equals 5 or 0. Divisibility by 6. A number is divisible by 6 if and only if it is divisible by 2 and 3 simultaneously (that is, if the last digit is even and the sum of all digits is divisible by 3). Divisibility by 7. Vasya doesn't know such divisibility rule. Divisibility by 8. A number is divisible by 8 if and only if its last three digits form a number that is divisible by 8. Divisibility by 9. A number is divisible by 9 if and only if the sum of its digits is divisible by 9. Divisibility by 10. A number is divisible by 10 if and only if its last digit is a zero. Divisibility by 11. A number is divisible by 11 if and only if the sum of digits on its odd positions either equals to the sum of digits on the even positions, or they differ in a number that is divisible by 11.Vasya got interested by the fact that some divisibility rules resemble each other. In fact, to check a number's divisibility by 2, 4, 5, 8 and 10 it is enough to check fulfiling some condition for one or several last digits. Vasya calls such rules the 2-type rules.If checking divisibility means finding a sum of digits and checking whether the sum is divisible by the given number, then Vasya calls this rule the 3-type rule (because it works for numbers 3 and 9).If we need to find the difference between the sum of digits on odd and even positions and check whether the difference is divisible by the given divisor, this rule is called the 11-type rule (it works for number 11).In some cases we should divide the divisor into several factors and check whether rules of different types (2-type, 3-type or 11-type) work there. For example, for number 6 we check 2-type and 3-type rules, for number 66 we check all three types. Such mixed divisibility rules are called 6-type rules. And finally, there are some numbers for which no rule works: neither 2-type, nor 3-type, nor 11-type, nor 6-type. The least such number is number 7, so we'll say that in such cases the mysterious 7-type rule works, the one that Vasya hasn't discovered yet. Vasya's dream is finding divisibility rules for all possible numbers. He isn't going to stop on the decimal numbers only. As there are quite many numbers, ha can't do it all by himself. Vasya asked you to write a program that determines the divisibility rule type in the b-based notation for the given divisor d.", "input_spec": "The first input line contains two integers b and d (2 ≤ b, d ≤ 100) — the notation system base and the divisor. Both numbers are given in the decimal notation.", "output_spec": "On the first output line print the type of the rule in the b-based notation system, where the divisor is d: \"2-type\", \"3-type\", \"11-type\", \"6-type\" or \"7-type\". If there are several such types, print the one that goes earlier in the given sequence. If a number belongs to the 2-type, print on the second line the least number of the last b-based digits that we will need to use to check the divisibility.", "sample_inputs": ["10 10", "2 3"], "sample_outputs": ["2-type\n1", "11-type"], "notes": "NoteThe divisibility rule for number 3 in binary notation looks as follows: \"A number is divisible by 3 if and only if the sum of its digits that occupy the even places differs from the sum of digits that occupy the odd places, in a number that is divisible by 3\". That's an 11-type rule. For example, 2110 = 101012. For it the sum of digits on odd positions equals 1 + 1 + 1 = 3, an on even positions — 0 + 0 = 0. The rule works and the number is divisible by 3. In some notations a number can fit into the 3-type rule and the 11-type rule. In this case the correct answer is \"3-type\"."}, "src_uid": "809e1c78b0a5a16f7f2115b046a20bde"}
{"nl": {"description": "You have a positive integer m and a non-negative integer s. Your task is to find the smallest and the largest of the numbers that have length m and sum of digits s. The required numbers should be non-negative integers written in the decimal base without leading zeroes.", "input_spec": "The single line of the input contains a pair of integers m, s (1 ≤ m ≤ 100, 0 ≤ s ≤ 900) — the length and the sum of the digits of the required numbers.", "output_spec": "In the output print the pair of the required non-negative integer numbers — first the minimum possible number, then — the maximum possible number. If no numbers satisfying conditions required exist, print the pair of numbers \"-1 -1\" (without the quotes).", "sample_inputs": ["2 15", "3 0"], "sample_outputs": ["69 96", "-1 -1"], "notes": null}, "src_uid": "75d062cece5a2402920d6706c655cad7"}
{"nl": {"description": "A long time ago somewhere in the depths of America existed a powerful tribe governed by the great leader Pinnie-the-Wooh. Once the tribe conquered three Maya cities. Pinnie-the-Wooh grew concerned: there had to be some control over the conquered territories. That's why he appealed to the priests of the supreme god Mogohu-Rea for help.The priests conveyed the god's will to him: to control these three cities he should put an idol to Mogohu-Rea — that will create a religious field over the cities. However, the idol is so powerful that it can easily drive the people around it mad unless it is balanced by exactly three sacrifice altars, placed one in each city. To balance the idol the altars should be placed so that the center of mass of the system of these three points coincided with the idol. When counting the center of mass consider that all the altars have the same mass.Now Pinnie-the-Wooh is thinking where to put the idol. He has a list of hills, that are suitable to put an idol there. Help him to identify on which of them you can put an idol without risking to fry off the brains of the cities' population with the religious field.Each city has a shape of a convex polygon such that no three vertexes lie on a straight line. The cities can intersect. Each altar should be attached to the city through a special ceremony, besides, it must be situated on the city's territory (possibly at the border). Thus, there may be several altars on a city's territory, but exactly one of them will be attached to the city. The altars, the idol and the hills are points on the plane, some of them may coincide.The hills are taken into consideration independently from each other, the altars' location for different hills may also be different.", "input_spec": "First follow descriptions of the three cities, divided by empty lines. The descriptions are in the following format: The first line contains an integer n, which represent the number of the polygon's vertexes (3 ≤ n ≤ 5·104). Next n lines contain two integers xi, yi each, they are the coordinates of the polygon's i-th vertex in the counterclockwise order. After the cities' description follows the integer m (1 ≤ m ≤ 105), which represents the number of hills. Next m lines each contain two integers xj, yj, they are the coordinates of the j-th hill. All the coordinates in the input data do not exceed 5·108 in the absolute value.", "output_spec": "For each hill print on a single line \"YES\" (without the quotes) or \"NO\" (without the quotes), depending on whether the three sacrifice altars can be put to balance the idol or not.", "sample_inputs": ["3\n0 0\n1 0\n1 1\n\n4\n8 8\n5 5\n6 4\n8 4\n\n3\n-1 -1\n-3 -1\n-2 -2\n\n5\n0 0\n2 1\n7 1\n1 1\n5 3"], "sample_outputs": ["NO\nYES\nNO\nYES\nNO"], "notes": "NoteFor the hill at (2, 1) the altars can be placed at the points (1, 0), (7, 5), ( - 2,  - 2), for the hill at (1, 1) — at the points (0, 0), (6, 4), ( - 3,  - 1). Many other groups of three points can do the trick. There are no suitable points for other hills."}, "src_uid": "a764daf8e19e48a0735811a4f67485c3"}
{"nl": {"description": "Two positive integers a and b have a sum of s and a bitwise XOR of x. How many possible values are there for the ordered pair (a, b)?", "input_spec": "The first line of the input contains two integers s and x (2 ≤ s ≤ 1012, 0 ≤ x ≤ 1012), the sum and bitwise xor of the pair of positive integers, respectively.", "output_spec": "Print a single integer, the number of solutions to the given conditions. If no solutions exist, print 0.", "sample_inputs": ["9 5", "3 3", "5 2"], "sample_outputs": ["4", "2", "0"], "notes": "NoteIn the first sample, we have the following solutions: (2, 7), (3, 6), (6, 3), (7, 2).In the second sample, the only solutions are (1, 2) and (2, 1)."}, "src_uid": "18410980789b14c128dd6adfa501aea5"}
{"nl": {"description": "To make a paper airplane, one has to use a rectangular piece of paper. From a sheet of standard size you can make $$$s$$$ airplanes.A group of $$$k$$$ people decided to make $$$n$$$ airplanes each. They are going to buy several packs of paper, each of them containing $$$p$$$ sheets, and then distribute the sheets between the people. Each person should have enough sheets to make $$$n$$$ airplanes. How many packs should they buy?", "input_spec": "The only line contains four integers $$$k$$$, $$$n$$$, $$$s$$$, $$$p$$$ ($$$1 \\le k, n, s, p \\le 10^4$$$) — the number of people, the number of airplanes each should make, the number of airplanes that can be made using one sheet and the number of sheets in one pack, respectively.", "output_spec": "Print a single integer — the minimum number of packs they should buy.", "sample_inputs": ["5 3 2 3", "5 3 100 1"], "sample_outputs": ["4", "5"], "notes": "NoteIn the first sample they have to buy $$$4$$$ packs of paper: there will be $$$12$$$ sheets in total, and giving $$$2$$$ sheets to each person is enough to suit everyone's needs.In the second sample they have to buy a pack for each person as they can't share sheets."}, "src_uid": "73f0c7cfc06a9b04e4766d6aa61fc780"}
{"nl": {"description": "Ilya got tired of sports programming, left university and got a job in the subway. He was given the task to determine the escalator load factor. Let's assume that n people stand in the queue for the escalator. At each second one of the two following possibilities takes place: either the first person in the queue enters the escalator with probability p, or the first person in the queue doesn't move with probability (1 - p), paralyzed by his fear of escalators and making the whole queue wait behind him.Formally speaking, the i-th person in the queue cannot enter the escalator until people with indices from 1 to i - 1 inclusive enter it. In one second only one person can enter the escalator. The escalator is infinite, so if a person enters it, he never leaves it, that is he will be standing on the escalator at any following second. Ilya needs to count the expected value of the number of people standing on the escalator after t seconds. Your task is to help him solve this complicated task.", "input_spec": "The first line of the input contains three numbers n, p, t (1 ≤ n, t ≤ 2000, 0 ≤ p ≤ 1). Numbers n and t are integers, number p is real, given with exactly two digits after the decimal point.", "output_spec": "Print a single real number — the expected number of people who will be standing on the escalator after t seconds. The absolute or relative error mustn't exceed 10 - 6.", "sample_inputs": ["1 0.50 1", "1 0.50 4", "4 0.20 2"], "sample_outputs": ["0.5", "0.9375", "0.4"], "notes": null}, "src_uid": "20873b1e802c7aa0e409d9f430516c1e"}
{"nl": {"description": "Certainly, everyone is familiar with tic-tac-toe game. The rules are very simple indeed. Two players take turns marking the cells in a 3 × 3 grid (one player always draws crosses, the other — noughts). The player who succeeds first in placing three of his marks in a horizontal, vertical or diagonal line wins, and the game is finished. The player who draws crosses goes first. If the grid is filled, but neither Xs, nor 0s form the required line, a draw is announced.You are given a 3 × 3 grid, each grid cell is empty, or occupied by a cross or a nought. You have to find the player (first or second), whose turn is next, or print one of the verdicts below:   illegal — if the given board layout can't appear during a valid game;  the first player won — if in the given board layout the first player has just won;  the second player won — if in the given board layout the second player has just won;  draw — if the given board layout has just let to a draw. ", "input_spec": "The input consists of three lines, each of the lines contains characters \".\", \"X\" or \"0\" (a period, a capital letter X, or a digit zero).", "output_spec": "Print one of the six verdicts: first, second, illegal, the first player won, the second player won or draw.", "sample_inputs": ["X0X\n.0.\n.X."], "sample_outputs": ["second"], "notes": null}, "src_uid": "892680e26369325fb00d15543a96192c"}
{"nl": {"description": "One spring day on his way to university Lesha found an array A. Lesha likes to split arrays into several parts. This time Lesha decided to split the array A into several, possibly one, new arrays so that the sum of elements in each of the new arrays is not zero. One more condition is that if we place the new arrays one after another they will form the old array A.Lesha is tired now so he asked you to split the array. Help Lesha!", "input_spec": "The first line contains single integer n (1 ≤ n ≤ 100) — the number of elements in the array A. The next line contains n integers a1, a2, ..., an ( - 103 ≤ ai ≤ 103) — the elements of the array A.", "output_spec": "If it is not possible to split the array A and satisfy all the constraints, print single line containing \"NO\" (without quotes). Otherwise in the first line print \"YES\" (without quotes). In the next line print single integer k — the number of new arrays. In each of the next k lines print two integers li and ri which denote the subarray A[li... ri] of the initial array A being the i-th new array. Integers li, ri should satisfy the following conditions:   l1 = 1  rk = n  ri + 1 = li + 1 for each 1 ≤ i < k.  If there are multiple answers, print any of them.", "sample_inputs": ["3\n1 2 -3", "8\n9 -12 3 4 -4 -10 7 3", "1\n0", "4\n1 2 3 -5"], "sample_outputs": ["YES\n2\n1 2\n3 3", "YES\n2\n1 2\n3 8", "NO", "YES\n4\n1 1\n2 2\n3 3\n4 4"], "notes": null}, "src_uid": "3a9258070ff179daf33a4515def9897a"}
{"nl": {"description": "— This is not playing but duty as allies of justice, Nii-chan!— Not allies but justice itself, Onii-chan!With hands joined, go everywhere at a speed faster than our thoughts! This time, the Fire Sisters — Karen and Tsukihi — is heading for somewhere they've never reached — water-surrounded islands!There are three clusters of islands, conveniently coloured red, blue and purple. The clusters consist of a, b and c distinct islands respectively.Bridges have been built between some (possibly all or none) of the islands. A bridge bidirectionally connects two different islands and has length 1. For any two islands of the same colour, either they shouldn't be reached from each other through bridges, or the shortest distance between them is at least 3, apparently in order to prevent oddities from spreading quickly inside a cluster.The Fire Sisters are ready for the unknown, but they'd also like to test your courage. And you're here to figure out the number of different ways to build all bridges under the constraints, and give the answer modulo 998 244 353. Two ways are considered different if a pair of islands exist, such that there's a bridge between them in one of them, but not in the other.", "input_spec": "The first and only line of input contains three space-separated integers a, b and c (1 ≤ a, b, c ≤ 5 000) — the number of islands in the red, blue and purple clusters, respectively.", "output_spec": "Output one line containing an integer — the number of different ways to build bridges, modulo 998 244 353.", "sample_inputs": ["1 1 1", "1 2 2", "1 3 5", "6 2 9"], "sample_outputs": ["8", "63", "3264", "813023575"], "notes": "NoteIn the first example, there are 3 bridges that can possibly be built, and no setup of bridges violates the restrictions. Thus the answer is 23 = 8.In the second example, the upper two structures in the figure below are instances of valid ones, while the lower two are invalid due to the blue and purple clusters, respectively.  "}, "src_uid": "b6dc5533fbf285d5ef4cf60ef6300383"}
{"nl": {"description": "We've got no test cases. A big olympiad is coming up. But the problemsetters' number one priority should be adding another problem to the round. The diameter of a multiset of points on the line is the largest distance between two points from this set. For example, the diameter of the multiset {1, 3, 2, 1} is 2.Diameter of multiset consisting of one point is 0.You are given n points on the line. What is the minimum number of points you have to remove, so that the diameter of the multiset of the remaining points will not exceed d?", "input_spec": "The first line contains two integers n and d (1 ≤ n ≤ 100, 0 ≤ d ≤ 100) — the amount of points and the maximum allowed diameter respectively. The second line contains n space separated integers (1 ≤ xi ≤ 100) — the coordinates of the points.", "output_spec": "Output a single integer — the minimum number of points you have to remove.", "sample_inputs": ["3 1\n2 1 4", "3 0\n7 7 7", "6 3\n1 3 4 6 9 10"], "sample_outputs": ["1", "0", "3"], "notes": "NoteIn the first test case the optimal strategy is to remove the point with coordinate 4. The remaining points will have coordinates 1 and 2, so the diameter will be equal to 2 - 1 = 1.In the second test case the diameter is equal to 0, so its is unnecessary to remove any points. In the third test case the optimal strategy is to remove points with coordinates 1, 9 and 10. The remaining points will have coordinates 3, 4 and 6, so the diameter will be equal to 6 - 3 = 3."}, "src_uid": "6bcb324c072f796f4d50bafea5f624b2"}
{"nl": {"description": "Modern text editors usually show some information regarding the document being edited. For example, the number of words, the number of pages, or the number of characters.In this problem you should implement the similar functionality.You are given a string which only consists of:  uppercase and lowercase English letters,  underscore symbols (they are used as separators),  parentheses (both opening and closing). It is guaranteed that each opening parenthesis has a succeeding closing parenthesis. Similarly, each closing parentheses has a preceding opening parentheses matching it. For each pair of matching parentheses there are no other parenthesis between them. In other words, each parenthesis in the string belongs to a matching \"opening-closing\" pair, and such pairs can't be nested.For example, the following string is valid: \"_Hello_Vasya(and_Petya)__bye_(and_OK)\".Word is a maximal sequence of consecutive letters, i.e. such sequence that the first character to the left and the first character to the right of it is an underscore, a parenthesis, or it just does not exist. For example, the string above consists of seven words: \"Hello\", \"Vasya\", \"and\", \"Petya\", \"bye\", \"and\" and \"OK\". Write a program that finds:  the length of the longest word outside the parentheses (print 0, if there is no word outside the parentheses),  the number of words inside the parentheses (print 0, if there is no word inside the parentheses). ", "input_spec": "The first line of the input contains a single integer n (1 ≤ n ≤ 255) — the length of the given string. The second line contains the string consisting of only lowercase and uppercase English letters, parentheses and underscore symbols. ", "output_spec": "Print two space-separated integers:   the length of the longest word outside the parentheses (print 0, if there is no word outside the parentheses),  the number of words inside the parentheses (print 0, if there is no word inside the parentheses). ", "sample_inputs": ["37\n_Hello_Vasya(and_Petya)__bye_(and_OK)", "37\n_a_(_b___c)__de_f(g_)__h__i(j_k_l)m__", "27\n(LoooonG)__shOrt__(LoooonG)", "5\n(___)"], "sample_outputs": ["5 4", "2 6", "5 2", "0 0"], "notes": "NoteIn the first sample, the words \"Hello\", \"Vasya\" and \"bye\" are outside any of the parentheses, and the words \"and\", \"Petya\", \"and\" and \"OK\" are inside. Note, that the word \"and\" is given twice and you should count it twice in the answer."}, "src_uid": "fc86df4931e787fa3a1a40e2aecf0b92"}
{"nl": {"description": "A sequence of non-negative integers a1, a2, ..., an of length n is called a wool sequence if and only if there exists two integers l and r (1 ≤ l ≤ r ≤ n) such that . In other words each wool sequence contains a subsequence of consecutive elements with xor equal to 0.The expression  means applying the operation of a bitwise xor to numbers x and y. The given operation exists in all modern programming languages, for example, in languages C++ and Java it is marked as \"^\", in Pascal — as \"xor\".In this problem you are asked to compute the number of sequences made of n integers from 0 to 2m - 1 that are not a wool sequence. You should print this number modulo 1000000009 (109 + 9).", "input_spec": "The only line of input contains two space-separated integers n and m (1 ≤ n, m ≤ 105).", "output_spec": "Print the required number of sequences modulo 1000000009 (109 + 9) on the only line of output.", "sample_inputs": ["3 2"], "sample_outputs": ["6"], "notes": "NoteSequences of length 3 made of integers 0, 1, 2 and 3 that are not a wool sequence are (1, 3, 1), (1, 2, 1), (2, 1, 2), (2, 3, 2), (3, 1, 3) and (3, 2, 3)."}, "src_uid": "fef4d9c94a93fcf6d536f33503b1d4b8"}
{"nl": {"description": "$$$k$$$ people want to split $$$n$$$ candies between them. Each candy should be given to exactly one of them or be thrown away.The people are numbered from $$$1$$$ to $$$k$$$, and Arkady is the first of them. To split the candies, Arkady will choose an integer $$$x$$$ and then give the first $$$x$$$ candies to himself, the next $$$x$$$ candies to the second person, the next $$$x$$$ candies to the third person and so on in a cycle. The leftover (the remainder that is not divisible by $$$x$$$) will be thrown away.Arkady can't choose $$$x$$$ greater than $$$M$$$ as it is considered greedy. Also, he can't choose such a small $$$x$$$ that some person will receive candies more than $$$D$$$ times, as it is considered a slow splitting.Please find what is the maximum number of candies Arkady can receive by choosing some valid $$$x$$$.", "input_spec": "The only line contains four integers $$$n$$$, $$$k$$$, $$$M$$$ and $$$D$$$ ($$$2 \\le n \\le 10^{18}$$$, $$$2 \\le k \\le n$$$, $$$1 \\le M \\le n$$$, $$$1 \\le D \\le \\min{(n, 1000)}$$$, $$$M \\cdot D \\cdot k \\ge n$$$) — the number of candies, the number of people, the maximum number of candies given to a person at once, the maximum number of times a person can receive candies.", "output_spec": "Print a single integer — the maximum possible number of candies Arkady can give to himself. Note that it is always possible to choose some valid $$$x$$$.", "sample_inputs": ["20 4 5 2", "30 9 4 1"], "sample_outputs": ["8", "4"], "notes": "NoteIn the first example Arkady should choose $$$x = 4$$$. He will give $$$4$$$ candies to himself, $$$4$$$ candies to the second person, $$$4$$$ candies to the third person, then $$$4$$$ candies to the fourth person and then again $$$4$$$ candies to himself. No person is given candies more than $$$2$$$ times, and Arkady receives $$$8$$$ candies in total.Note that if Arkady chooses $$$x = 5$$$, he will receive only $$$5$$$ candies, and if he chooses $$$x = 3$$$, he will receive only $$$3 + 3 = 6$$$ candies as well as the second person, the third and the fourth persons will receive $$$3$$$ candies, and $$$2$$$ candies will be thrown away. He can't choose $$$x = 1$$$ nor $$$x = 2$$$ because in these cases he will receive candies more than $$$2$$$ times.In the second example Arkady has to choose $$$x = 4$$$, because any smaller value leads to him receiving candies more than $$$1$$$ time."}, "src_uid": "ac2e795cd44061db8da13e3947ba791b"}
{"nl": {"description": "Your security guard friend recently got a new job at a new security company. The company requires him to patrol an area of the city encompassing exactly N city blocks, but they let him choose which blocks. That is, your friend must walk the perimeter of a region whose area is exactly N blocks. Your friend is quite lazy and would like your help to find the shortest possible route that meets the requirements. The city is laid out in a square grid pattern, and is large enough that for the sake of the problem it can be considered infinite.", "input_spec": "Input will consist of a single integer N (1 ≤ N ≤ 106), the number of city blocks that must be enclosed by the route.", "output_spec": "Print the minimum perimeter that can be achieved.", "sample_inputs": ["4", "11", "22"], "sample_outputs": ["8", "14", "20"], "notes": "NoteHere are some possible shapes for the examples:"}, "src_uid": "414cc57550e31d98c1a6a56be6722a12"}
{"nl": {"description": "The three friends, Kuro, Shiro, and Katie, met up again! It's time for a party...What the cats do when they unite? Right, they have a party. Since they wanted to have as much fun as possible, they invited all their friends. Now $$$n$$$ cats are at the party, sitting in a circle and eating soup. The rules are simple: anyone having finished their soup leaves the circle.Katie suddenly notices that whenever a cat leaves, the place where she was sitting becomes an empty space, which means the circle is divided into smaller continuous groups of cats sitting next to each other. At the moment Katie observes, there are $$$m$$$ cats who left the circle. This raises a question for Katie: what is the maximum possible number of groups the circle is divided into at the moment?Could you help her with this curiosity?You can see the examples and their descriptions with pictures in the \"Note\" section.", "input_spec": "The only line contains two integers $$$n$$$ and $$$m$$$ ($$$2 \\leq n \\leq 1000$$$, $$$0 \\leq m \\leq n$$$) — the initial number of cats at the party and the number of cats who left the circle at the moment Katie observes, respectively.", "output_spec": "Print a single integer — the maximum number of groups of cats at the moment Katie observes.", "sample_inputs": ["7 4", "6 2", "3 0", "2 2"], "sample_outputs": ["3", "2", "1", "0"], "notes": "NoteIn the first example, originally there are $$$7$$$ cats sitting as shown below, creating a single group:  At the observed moment, $$$4$$$ cats have left the table. Suppose the cats $$$2$$$, $$$3$$$, $$$5$$$ and $$$7$$$ have left, then there are $$$3$$$ groups remaining. It is possible to show that it is the maximum possible number of groups remaining.  In the second example, there are $$$6$$$ cats sitting as shown below:  At the observed moment, $$$2$$$ cats have left the table. Suppose the cats numbered $$$3$$$ and $$$6$$$ left, then there will be $$$2$$$ groups remaining ($$$\\{1, 2\\}$$$ and $$$\\{4, 5\\}$$$). It is impossible to have more than $$$2$$$ groups of cats remaining.  In the third example, no cats have left, so there is $$$1$$$ group consisting of all cats.In the fourth example, all cats have left the circle, so there are $$$0$$$ groups."}, "src_uid": "c05d0a9cabe04d8fb48c76d2ce033648"}
{"nl": {"description": "Statistics claims that students sleep no more than three hours a day. But even in the world of their dreams, while they are snoring peacefully, the sense of impending doom is still upon them.A poor student is dreaming that he is sitting the mathematical analysis exam. And he is examined by the most formidable professor of all times, a three times Soviet Union Hero, a Noble Prize laureate in student expulsion, venerable Petr Palych.The poor student couldn't answer a single question. Thus, instead of a large spacious office he is going to apply for a job to thorium mines. But wait a minute! Petr Palych decided to give the student the last chance! Yes, that is possible only in dreams. So the professor began: \"Once a Venusian girl and a Marsian boy met on the Earth and decided to take a walk holding hands. But the problem is the girl has al fingers on her left hand and ar fingers on the right one. The boy correspondingly has bl and br fingers. They can only feel comfortable when holding hands, when no pair of the girl's fingers will touch each other. That is, they are comfortable when between any two girl's fingers there is a boy's finger. And in addition, no three fingers of the boy should touch each other. Determine if they can hold hands so that the both were comfortable.\"The boy any the girl don't care who goes to the left and who goes to the right. The difference is only that if the boy goes to the left of the girl, he will take her left hand with his right one, and if he goes to the right of the girl, then it is vice versa.", "input_spec": "The first line contains two positive integers not exceeding 100. They are the number of fingers on the Venusian girl's left and right hand correspondingly. The second line contains two integers not exceeding 100. They are the number of fingers on the Marsian boy's left and right hands correspondingly.", "output_spec": "Print YES or NO, that is, the answer to Petr Palych's question.", "sample_inputs": ["5 1\n10 5", "4 5\n3 3", "1 2\n11 6"], "sample_outputs": ["YES", "YES", "NO"], "notes": "NoteThe boy and the girl don't really care who goes to the left."}, "src_uid": "36b7478e162be6e985613b2dad0974dd"}
{"nl": {"description": "Tavak and Seyyed are good friends. Seyyed is very funny and he told Tavak to solve the following problem instead of longest-path.You are given l and r. For all integers from l to r, inclusive, we wrote down all of their integer divisors except 1. Find the integer that we wrote down the maximum number of times.Solve the problem to show that it's not a NP problem.", "input_spec": "The first line contains two integers l and r (2 ≤ l ≤ r ≤ 109).", "output_spec": "Print single integer, the integer that appears maximum number of times in the divisors.  If there are multiple answers, print any of them.", "sample_inputs": ["19 29", "3 6"], "sample_outputs": ["2", "3"], "notes": "NoteDefinition of a divisor: https://www.mathsisfun.com/definitions/divisor-of-an-integer-.htmlThe first example: from 19 to 29 these numbers are divisible by 2: {20, 22, 24, 26, 28}.The second example: from 3 to 6 these numbers are divisible by 3: {3, 6}."}, "src_uid": "a8d992ab26a528f0be327c93fb499c15"}
{"nl": {"description": "In order to put away old things and welcome a fresh new year, a thorough cleaning of the house is a must.Little Tommy finds an old polynomial and cleaned it up by taking it modulo another. But now he regrets doing this...Given two integers p and k, find a polynomial f(x) with non-negative integer coefficients strictly less than k, whose remainder is p when divided by (x + k). That is, f(x) = q(x)·(x + k) + p, where q(x) is a polynomial (not necessarily with integer coefficients).", "input_spec": "The only line of input contains two space-separated integers p and k (1 ≤ p ≤ 1018, 2 ≤ k ≤ 2 000).", "output_spec": "If the polynomial does not exist, print a single integer -1, or output two lines otherwise. In the first line print a non-negative integer d — the number of coefficients in the polynomial. In the second line print d space-separated integers a0, a1, ..., ad - 1, describing a polynomial  fulfilling the given requirements. Your output should satisfy 0 ≤ ai < k for all 0 ≤ i ≤ d - 1, and ad - 1 ≠ 0. If there are many possible solutions, print any of them.", "sample_inputs": ["46 2", "2018 214"], "sample_outputs": ["7\n0 1 0 0 1 1 1", "3\n92 205 1"], "notes": "NoteIn the first example, f(x) = x6 + x5 + x4 + x = (x5 - x4 + 3x3 - 6x2 + 12x - 23)·(x + 2) + 46.In the second example, f(x) = x2 + 205x + 92 = (x - 9)·(x + 214) + 2018."}, "src_uid": "f4dbaa8deb2bd5c054fe34bb83bc6cd5"}
{"nl": {"description": "A monster is attacking the Cyberland!Master Yang, a braver, is going to beat the monster. Yang and the monster each have 3 attributes: hitpoints (HP), offensive power (ATK) and defensive power (DEF).During the battle, every second the monster's HP decrease by max(0, ATKY - DEFM), while Yang's HP decreases by max(0, ATKM - DEFY), where index Y denotes Master Yang and index M denotes monster. Both decreases happen simultaneously Once monster's HP ≤ 0 and the same time Master Yang's HP > 0, Master Yang wins.Master Yang can buy attributes from the magic shop of Cyberland: h bitcoins per HP, a bitcoins per ATK, and d bitcoins per DEF.Now Master Yang wants to know the minimum number of bitcoins he can spend in order to win.", "input_spec": "The first line contains three integers HPY, ATKY, DEFY, separated by a space, denoting the initial HP, ATK and DEF of Master Yang. The second line contains three integers HPM, ATKM, DEFM, separated by a space, denoting the HP, ATK and DEF of the monster. The third line contains three integers h, a, d, separated by a space, denoting the price of 1 HP, 1 ATK and 1 DEF. All numbers in input are integer and lie between 1 and 100 inclusively.", "output_spec": "The only output line should contain an integer, denoting the minimum bitcoins Master Yang should spend in order to win.", "sample_inputs": ["1 2 1\n1 100 1\n1 100 100", "100 100 100\n1 1 1\n1 1 1"], "sample_outputs": ["99", "0"], "notes": "NoteFor the first sample, prices for ATK and DEF are extremely high. Master Yang can buy 99 HP, then he can beat the monster with 1 HP left.For the second sample, Master Yang is strong enough to beat the monster, so he doesn't need to buy anything."}, "src_uid": "bf8a133154745e64a547de6f31ddc884"}
{"nl": {"description": "During the break the schoolchildren, boys and girls, formed a queue of n people in the canteen. Initially the children stood in the order they entered the canteen. However, after a while the boys started feeling awkward for standing in front of the girls in the queue and they started letting the girls move forward each second. Let's describe the process more precisely. Let's say that the positions in the queue are sequentially numbered by integers from 1 to n, at that the person in the position number 1 is served first. Then, if at time x a boy stands on the i-th position and a girl stands on the (i + 1)-th position, then at time x + 1 the i-th position will have a girl and the (i + 1)-th position will have a boy. The time is given in seconds.You've got the initial position of the children, at the initial moment of time. Determine the way the queue is going to look after t seconds.", "input_spec": "The first line contains two integers n and t (1 ≤ n, t ≤ 50), which represent the number of children in the queue and the time after which the queue will transform into the arrangement you need to find.  The next line contains string s, which represents the schoolchildren's initial arrangement. If the i-th position in the queue contains a boy, then the i-th character of string s equals \"B\", otherwise the i-th character equals \"G\".", "output_spec": "Print string a, which describes the arrangement after t seconds. If the i-th position has a boy after the needed time, then the i-th character a must equal \"B\", otherwise it must equal \"G\".", "sample_inputs": ["5 1\nBGGBG", "5 2\nBGGBG", "4 1\nGGGB"], "sample_outputs": ["GBGGB", "GGBGB", "GGGB"], "notes": null}, "src_uid": "964ed316c6e6715120039b0219cc653a"}
{"nl": {"description": "George woke up and saw the current time s on the digital clock. Besides, George knows that he has slept for time t. Help George! Write a program that will, given time s and t, determine the time p when George went to bed. Note that George could have gone to bed yesterday relatively to the current time (see the second test sample). ", "input_spec": "The first line contains current time s as a string in the format \"hh:mm\". The second line contains time t in the format \"hh:mm\" — the duration of George's sleep. It is guaranteed that the input contains the correct time in the 24-hour format, that is, 00 ≤ hh ≤ 23, 00 ≤ mm ≤ 59.", "output_spec": "In the single line print time p — the time George went to bed in the format similar to the format of the time in the input.", "sample_inputs": ["05:50\n05:44", "00:00\n01:00", "00:01\n00:00"], "sample_outputs": ["00:06", "23:00", "00:01"], "notes": "NoteIn the first sample George went to bed at \"00:06\". Note that you should print the time only in the format \"00:06\". That's why answers \"0:06\", \"00:6\" and others will be considered incorrect. In the second sample, George went to bed yesterday.In the third sample, George didn't do to bed at all."}, "src_uid": "595c4a628c261104c8eedad767e85775"}
{"nl": {"description": "Today in the scientific lyceum of the Kingdom of Kremland, there was a biology lesson. The topic of the lesson was the genomes. Let's call the genome the string \"ACTG\".Maxim was very boring to sit in class, so the teacher came up with a task for him: on a given string $$$s$$$ consisting of uppercase letters and length of at least $$$4$$$, you need to find the minimum number of operations that you need to apply, so that the genome appears in it as a substring. For one operation, you can replace any letter in the string $$$s$$$ with the next or previous in the alphabet. For example, for the letter \"D\" the previous one will be \"C\", and the next — \"E\". In this problem, we assume that for the letter \"A\", the previous one will be the letter \"Z\", and the next one will be \"B\", and for the letter \"Z\", the previous one is the letter \"Y\", and the next one is the letter \"A\".Help Maxim solve the problem that the teacher gave him.A string $$$a$$$ is a substring of a string $$$b$$$ if $$$a$$$ can be obtained from $$$b$$$ by deletion of several (possibly, zero or all) characters from the beginning and several (possibly, zero or all) characters from the end.", "input_spec": "The first line contains a single integer $$$n$$$ ($$$4 \\leq n \\leq 50$$$) — the length of the string $$$s$$$. The second line contains the string $$$s$$$, consisting of exactly $$$n$$$ uppercase letters of the Latin alphabet.", "output_spec": "Output the minimum number of operations that need to be applied to the string $$$s$$$ so that the genome appears as a substring in it.", "sample_inputs": ["4\nZCTH", "5\nZDATG", "6\nAFBAKC"], "sample_outputs": ["2", "5", "16"], "notes": "NoteIn the first example, you should replace the letter \"Z\" with \"A\" for one operation, the letter \"H\" — with the letter \"G\" for one operation. You will get the string \"ACTG\", in which the genome is present as a substring.In the second example, we replace the letter \"A\" with \"C\" for two operations, the letter \"D\" — with the letter \"A\" for three operations. You will get the string \"ZACTG\", in which there is a genome."}, "src_uid": "ee4f88abe4c9fa776abd15c5f3a94543"}
{"nl": {"description": "Holidays have finished. Thanks to the help of the hacker Leha, Noora managed to enter the university of her dreams which is located in a town Pavlopolis. It's well known that universities provide students with dormitory for the period of university studies. Consequently Noora had to leave Vičkopolis and move to Pavlopolis. Thus Leha was left completely alone in a quiet town Vičkopolis. He almost even fell into a depression from boredom!Leha came up with a task for himself to relax a little. He chooses two integers A and B and then calculates the greatest common divisor of integers \"A factorial\" and \"B factorial\". Formally the hacker wants to find out GCD(A!, B!). It's well known that the factorial of an integer x is a product of all positive integers less than or equal to x. Thus x! = 1·2·3·...·(x - 1)·x. For example 4! = 1·2·3·4 = 24. Recall that GCD(x, y) is the largest positive integer q that divides (without a remainder) both x and y.Leha has learned how to solve this task very effective. You are able to cope with it not worse, aren't you?", "input_spec": "The first and single line contains two integers A and B (1 ≤ A, B ≤ 109, min(A, B) ≤ 12).", "output_spec": "Print a single integer denoting the greatest common divisor of integers A! and B!.", "sample_inputs": ["4 3"], "sample_outputs": ["6"], "notes": "NoteConsider the sample.4! = 1·2·3·4 = 24. 3! = 1·2·3 = 6. The greatest common divisor of integers 24 and 6 is exactly 6."}, "src_uid": "7bf30ceb24b66d91382e97767f9feeb6"}
{"nl": {"description": "Once Petya and Vasya invented a new game and called it \"Smart Boy\". They located a certain set of words — the dictionary — for the game. It is admissible for the dictionary to contain similar words. The rules of the game are as follows: first the first player chooses any letter (a word as long as 1) from any word from the dictionary and writes it down on a piece of paper. The second player adds some other letter to this one's initial or final position, thus making a word as long as 2, then it's the first player's turn again, he adds a letter in the beginning or in the end thus making a word as long as 3 and so on. But the player mustn't break one condition: the newly created word must be a substring of a word from a dictionary. The player who can't add a letter to the current word without breaking the condition loses.Also if by the end of a turn a certain string s is written on paper, then the player, whose turn it just has been, gets a number of points according to the formula:where    is a sequence number of symbol c in Latin alphabet, numbered starting from 1. For example, , and .   is the number of words from the dictionary where the line s occurs as a substring at least once. Your task is to learn who will win the game and what the final score will be. Every player plays optimally and most of all tries to win, then — to maximize the number of his points, then — to minimize the number of the points of the opponent.", "input_spec": "The first input line contains an integer n which is the number of words in the located dictionary (1 ≤ n ≤ 30). The n lines contain the words from the dictionary — one word is written on one line. Those lines are nonempty, consisting of Latin lower-case characters no longer than 30 characters. Equal words can be in the list of words.", "output_spec": "On the first output line print a line \"First\" or \"Second\" which means who will win the game. On the second line output the number of points of the first player and the number of points of the second player after the game ends. Separate the numbers by a single space.", "sample_inputs": ["2\naba\nabac", "3\nartem\nnik\nmax"], "sample_outputs": ["Second\n29 35", "First\n2403 1882"], "notes": null}, "src_uid": "d0f8976d9b847f7426dc56cb59b5b5b9"}
{"nl": {"description": "Two polar bears Menshykov and Uslada from the St.Petersburg zoo and elephant Horace from the Kiev zoo got six sticks to play with and assess the animals' creativity. Menshykov, Uslada and Horace decided to make either an elephant or a bear from those sticks. They can make an animal from sticks in the following way:   Four sticks represent the animal's legs, these sticks should have the same length.  Two remaining sticks represent the animal's head and body. The bear's head stick must be shorter than the body stick. The elephant, however, has a long trunk, so his head stick must be as long as the body stick. Note that there are no limits on the relations between the leg sticks and the head and body sticks. Your task is to find out which animal can be made from the given stick set. The zoo keeper wants the sticks back after the game, so they must never be broken, even bears understand it.", "input_spec": "The single line contains six space-separated integers li (1 ≤ li ≤ 9) — the lengths of the six sticks. It is guaranteed that the input is such that you cannot make both animals from the sticks.", "output_spec": "If you can make a bear from the given set, print string \"Bear\" (without the quotes). If you can make an elephant, print string \"Elephant\" (wıthout the quotes). If you can make neither a bear nor an elephant, print string \"Alien\" (without the quotes).", "sample_inputs": ["4 2 5 4 4 4", "4 4 5 4 4 5", "1 2 3 4 5 6"], "sample_outputs": ["Bear", "Elephant", "Alien"], "notes": "NoteIf you're out of creative ideas, see instructions below which show how to make a bear and an elephant in the first two samples. The stick of length 2 is in red, the sticks of length 4 are in green, the sticks of length 5 are in blue.   "}, "src_uid": "43308fa25e8578fd9f25328e715d4dd6"}
{"nl": {"description": "On the Literature lesson Sergei noticed an awful injustice, it seems that some students are asked more often than others.Seating in the class looks like a rectangle, where n rows with m pupils in each. The teacher asks pupils in the following order: at first, she asks all pupils from the first row in the order of their seating, then she continues to ask pupils from the next row. If the teacher asked the last row, then the direction of the poll changes, it means that she asks the previous row. The order of asking the rows looks as follows: the 1-st row, the 2-nd row, ..., the n - 1-st row, the n-th row, the n - 1-st row, ..., the 2-nd row, the 1-st row, the 2-nd row, ...The order of asking of pupils on the same row is always the same: the 1-st pupil, the 2-nd pupil, ..., the m-th pupil.During the lesson the teacher managed to ask exactly k questions from pupils in order described above. Sergei seats on the x-th row, on the y-th place in the row. Sergei decided to prove to the teacher that pupils are asked irregularly, help him count three values:  the maximum number of questions a particular pupil is asked,  the minimum number of questions a particular pupil is asked,  how many times the teacher asked Sergei. If there is only one row in the class, then the teacher always asks children from this row.", "input_spec": "The first and the only line contains five integers n, m, k, x and y (1 ≤ n, m ≤ 100, 1 ≤ k ≤ 1018, 1 ≤ x ≤ n, 1 ≤ y ≤ m).", "output_spec": "Print three integers:   the maximum number of questions a particular pupil is asked,  the minimum number of questions a particular pupil is asked,  how many times the teacher asked Sergei. ", "sample_inputs": ["1 3 8 1 1", "4 2 9 4 2", "5 5 25 4 3", "100 100 1000000000000000000 100 100"], "sample_outputs": ["3 2 3", "2 1 1", "1 1 1", "101010101010101 50505050505051 50505050505051"], "notes": "NoteThe order of asking pupils in the first test:   the pupil from the first row who seats at the first table, it means it is Sergei;  the pupil from the first row who seats at the second table;  the pupil from the first row who seats at the third table;  the pupil from the first row who seats at the first table, it means it is Sergei;  the pupil from the first row who seats at the second table;  the pupil from the first row who seats at the third table;  the pupil from the first row who seats at the first table, it means it is Sergei;  the pupil from the first row who seats at the second table; The order of asking pupils in the second test:   the pupil from the first row who seats at the first table;  the pupil from the first row who seats at the second table;  the pupil from the second row who seats at the first table;  the pupil from the second row who seats at the second table;  the pupil from the third row who seats at the first table;  the pupil from the third row who seats at the second table;  the pupil from the fourth row who seats at the first table;  the pupil from the fourth row who seats at the second table, it means it is Sergei;  the pupil from the third row who seats at the first table; "}, "src_uid": "e61debcad37eaa9a6e21d7a2122b8b21"}
{"nl": {"description": "Eighth-grader Vova is on duty today in the class. After classes, he went into the office to wash the board, and found on it the number n. He asked what is this number and the teacher of mathematics Inna Petrovna answered Vova that n is the answer to the arithmetic task for first-graders. In the textbook, a certain positive integer x was given. The task was to add x to the sum of the digits of the number x written in decimal numeral system.Since the number n on the board was small, Vova quickly guessed which x could be in the textbook. Now he wants to get a program which will search for arbitrary values of the number n for all suitable values of x or determine that such x does not exist. Write such a program for Vova.", "input_spec": "The first line contains integer n (1 ≤ n ≤ 109).", "output_spec": "In the first line print one integer k — number of different values of x satisfying the condition.  In next k lines print these values in ascending order.", "sample_inputs": ["21", "20"], "sample_outputs": ["1\n15", "0"], "notes": "NoteIn the first test case x = 15 there is only one variant: 15 + 1 + 5 = 21.In the second test case there are no such x."}, "src_uid": "ae20ae2a16273a0d379932d6e973f878"}
{"nl": {"description": "In problems on strings one often has to find a string with some particular properties. The problem authors were reluctant to waste time on thinking of a name for some string so they called it good. A string is good if it doesn't have palindrome substrings longer than or equal to d. You are given string s, consisting only of lowercase English letters. Find a good string t with length |s|, consisting of lowercase English letters, which is lexicographically larger than s. Of all such strings string t must be lexicographically minimum.We will call a non-empty string s[a ... b] = sasa + 1... sb (1 ≤ a ≤ b ≤ |s|) a substring of string s = s1s2... s|s|.A non-empty string s = s1s2... sn is called a palindrome if for all i from 1 to n the following fulfills: si = sn - i + 1. In other words, palindrome read the same in both directions.String x = x1x2... x|x| is lexicographically larger than string y = y1y2... y|y|, if either |x| > |y| and x1 = y1, x2 = y2, ... , x|y| = y|y|, or there exists such number r (r < |x|, r < |y|), that x1 = y1, x2 = y2, ... , xr = yr and xr + 1 > yr + 1. Characters in such strings are compared like their ASCII codes.", "input_spec": "The first line contains integer d (1 ≤ d ≤ |s|). The second line contains a non-empty string s, its length is no more than 4·105 characters. The string consists of lowercase English letters.", "output_spec": "Print the good string that lexicographically follows s, has the same length and consists of only lowercase English letters. If such string does not exist, print \"Impossible\" (without the quotes).", "sample_inputs": ["3\naaaaaaa", "3\nzzyzzzz", "4\nabbabbbabbb"], "sample_outputs": ["aabbcaa", "Impossible", "abbbcaaabab"], "notes": null}, "src_uid": "959a274a06219f4a8c061cd6f5b17160"}
{"nl": {"description": "Arkady decided to buy roses for his girlfriend.A flower shop has white, orange and red roses, and the total amount of them is n. Arkady thinks that red roses are not good together with white roses, so he won't buy a bouquet containing both red and white roses. Also, Arkady won't buy a bouquet where all roses have the same color. Arkady wants to buy exactly k roses. For each rose in the shop he knows its beauty and color: the beauty of the i-th rose is bi, and its color is ci ('W' for a white rose, 'O' for an orange rose and 'R' for a red rose). Compute the maximum possible total beauty of a bouquet of k roses satisfying the constraints above or determine that it is not possible to make such a bouquet.", "input_spec": "The first line contains two integers n and k (1 ≤ k ≤ n ≤ 200 000) — the number of roses in the show and the number of roses Arkady wants to buy. The second line contains a sequence of integers b1, b2, ..., bn (1 ≤ bi ≤ 10 000), where bi equals the beauty of the i-th rose. The third line contains a string c of length n, consisting of uppercase English letters 'W', 'O' and 'R', where ci denotes the color of the i-th rose: 'W' denotes white, 'O'  — orange, 'R' — red.", "output_spec": "Print the maximum possible total beauty of a bouquet of k roses that satisfies the constraints above. If it is not possible to make a single such bouquet, print -1.", "sample_inputs": ["5 3\n4 3 4 1 6\nRROWW", "5 2\n10 20 14 20 11\nRRRRR", "11 5\n5 6 3 2 3 4 7 5 4 5 6\nRWOORWORROW"], "sample_outputs": ["11", "-1", "28"], "notes": "NoteIn the first example Arkady wants to buy 3 roses. He can, for example, buy both red roses (their indices are 1 and 2, and their total beauty is 7) and the only orange rose (its index is 3, its beauty is 4). This way the total beauty of the bouquet is 11. In the second example Arkady can not buy a bouquet because all roses have the same color."}, "src_uid": "104cf5253e027929f257364b3874c38b"}
{"nl": {"description": "Nick likes strings very much, he likes to rotate them, sort them, rearrange characters within a string... Once he wrote a random string of characters a, b, c on a piece of paper and began to perform the following operations:   to take two adjacent characters and replace the second character with the first one,  to take two adjacent characters and replace the first character with the second one To understand these actions better, let's take a look at a string «abc». All of the following strings can be obtained by performing one of the described operations on «abc»: «bbc», «abb», «acc». Let's denote the frequency of a character for each of the characters a, b and c as the number of occurrences of this character in the string. For example, for string «abc»: |a| = 1, |b| = 1, |c| = 1, and for string «bbc»: |a| = 0, |b| = 2, |c| = 1. While performing the described operations, Nick sometimes got balanced strings. Let's say that a string is balanced, if the frequencies of each character differ by at most 1. That is  - 1 ≤ |a| - |b| ≤ 1,  - 1 ≤ |a| - |c| ≤ 1 и  - 1 ≤ |b| - |c| ≤ 1. Would you help Nick find the number of different balanced strings that can be obtained by performing the operations described above, perhaps multiple times, on the given string s. This number should be calculated modulo 51123987.", "input_spec": "The first line contains integer n (1 ≤ n ≤ 150) — the length of the given string s. Next line contains the given string s. The initial string can be balanced as well, in this case it should be counted too. The given string s consists only of characters a, b and c.", "output_spec": "Output the only number — the number of different balanced strings that can be obtained by performing the described operations, perhaps multiple times, on the given string s, modulo 51123987.", "sample_inputs": ["4\nabca", "4\nabbc", "2\nab"], "sample_outputs": ["7", "3", "1"], "notes": "NoteIn the first sample it is possible to get 51 different strings through the described operations, but only 7 of them are balanced: «abca», «bbca», «bcca», «bcaa», «abcc», «abbc», «aabc». In the second sample: «abbc», «aabc», «abcc». In the third sample there is only one balanced string — «ab» itself."}, "src_uid": "64fada10630906e052ff05f2afbf337e"}
{"nl": {"description": "A string is a palindrome if it reads the same from the left to the right and from the right to the left. For example, the strings \"kek\", \"abacaba\", \"r\" and \"papicipap\" are palindromes, while the strings \"abb\" and \"iq\" are not.A substring $$$s[l \\ldots r]$$$ ($$$1 \\leq l \\leq r \\leq |s|$$$) of a string $$$s = s_{1}s_{2} \\ldots s_{|s|}$$$ is the string $$$s_{l}s_{l + 1} \\ldots s_{r}$$$.Anna does not like palindromes, so she makes her friends call her Ann. She also changes all the words she reads in a similar way. Namely, each word $$$s$$$ is changed into its longest substring that is not a palindrome. If all the substrings of $$$s$$$ are palindromes, she skips the word at all.Some time ago Ann read the word $$$s$$$. What is the word she changed it into?", "input_spec": "The first line contains a non-empty string $$$s$$$ with length at most $$$50$$$ characters, containing lowercase English letters only.", "output_spec": "If there is such a substring in $$$s$$$ that is not a palindrome, print the maximum length of such a substring. Otherwise print $$$0$$$. Note that there can be multiple longest substrings that are not palindromes, but their length is unique.", "sample_inputs": ["mew", "wuffuw", "qqqqqqqq"], "sample_outputs": ["3", "5", "0"], "notes": "Note\"mew\" is not a palindrome, so the longest substring of it that is not a palindrome, is the string \"mew\" itself. Thus, the answer for the first example is $$$3$$$.The string \"uffuw\" is one of the longest non-palindrome substrings (of length $$$5$$$) of the string \"wuffuw\", so the answer for the second example is $$$5$$$.All substrings of the string \"qqqqqqqq\" consist of equal characters so they are palindromes. This way, there are no non-palindrome substrings. Thus, the answer for the third example is $$$0$$$."}, "src_uid": "6c85175d334f811617e7030e0403f706"}
{"nl": {"description": "Nothing is eternal in the world, Kostya understood it on the 7-th of January when he saw partially dead four-color garland.Now he has a goal to replace dead light bulbs, however he doesn't know how many light bulbs for each color are required. It is guaranteed that for each of four colors at least one light is working.It is known that the garland contains light bulbs of four colors: red, blue, yellow and green. The garland is made as follows: if you take any four consecutive light bulbs then there will not be light bulbs with the same color among them. For example, the garland can look like \"RYBGRYBGRY\", \"YBGRYBGRYBG\", \"BGRYB\", but can not look like \"BGRYG\", \"YBGRYBYGR\" or \"BGYBGY\". Letters denote colors: 'R' — red, 'B' — blue, 'Y' — yellow, 'G' — green.Using the information that for each color at least one light bulb still works count the number of dead light bulbs of each four colors.", "input_spec": "The first and the only line contains the string s (4 ≤ |s| ≤ 100), which describes the garland, the i-th symbol of which describes the color of the i-th light bulb in the order from the beginning of garland:    'R' — the light bulb is red,  'B' — the light bulb is blue,  'Y' — the light bulb is yellow,  'G' — the light bulb is green,  '!' — the light bulb is dead.  The string s can not contain other symbols except those five which were described.  It is guaranteed that in the given string at least once there is each of four letters 'R', 'B', 'Y' and 'G'.  It is guaranteed that the string s is correct garland with some blown light bulbs, it means that for example the line \"GRBY!!!B\" can not be in the input data. ", "output_spec": "In the only line print four integers kr, kb, ky, kg — the number of dead light bulbs of red, blue, yellow and green colors accordingly.", "sample_inputs": ["RYBGRYBGR", "!RGYB", "!!!!YGRB", "!GB!RG!Y!"], "sample_outputs": ["0 0 0 0", "0 1 0 0", "1 1 1 1", "2 1 1 0"], "notes": "NoteIn the first example there are no dead light bulbs.In the second example it is obvious that one blue bulb is blown, because it could not be light bulbs of other colors on its place according to the statements."}, "src_uid": "64fc6e9b458a9ece8ad70a8c72126b33"}
{"nl": {"description": "Little Johnny Bubbles enjoys spending hours in front of his computer playing video games. His favorite game is Bubble Strike, fast-paced bubble shooting online game for two players.Each game is set in one of the N maps, each having different terrain configuration. First phase of each game decides on which map the game will be played. The game system randomly selects three maps and shows them to the players. Each player must pick one of those three maps to be discarded. The game system then randomly selects one of the maps that were not picked by any of the players and starts the game.Johnny is deeply enthusiastic about the game and wants to spend some time studying maps, thus increasing chances to win games played on those maps. However, he also needs to do his homework, so he does not have time to study all the maps. That is why he asked himself the following question: \"What is the minimum number of maps I have to study, so that the probability to play one of those maps is at least $$$P$$$\"?Can you help Johnny find the answer for this question? You can assume Johnny's opponents do not know him, and they will randomly pick maps.", "input_spec": "The first line contains two integers $$$N$$$ ($$$3$$$ $$$\\leq$$$ $$$N$$$ $$$\\leq$$$ $$$10^{3}$$$) and $$$P$$$ ($$$0$$$ $$$\\leq$$$ $$$P$$$ $$$\\leq$$$ $$$1$$$) – total number of maps in the game and probability to play map Johnny has studied. $$$P$$$ will have at most four digits after the decimal point.", "output_spec": "Output contains one integer number – minimum number of maps Johnny has to study.", "sample_inputs": ["7 1.0000"], "sample_outputs": ["6"], "notes": null}, "src_uid": "788ed59a964264bd0e755e155a37e14d"}
{"nl": {"description": "There are n children in Jzzhu's school. Jzzhu is going to give some candies to them. Let's number all the children from 1 to n. The i-th child wants to get at least ai candies.Jzzhu asks children to line up. Initially, the i-th child stands at the i-th place of the line. Then Jzzhu start distribution of the candies. He follows the algorithm:  Give m candies to the first child of the line.  If this child still haven't got enough candies, then the child goes to the end of the line, else the child go home.  Repeat the first two steps while the line is not empty. Consider all the children in the order they go home. Jzzhu wants to know, which child will be the last in this order?", "input_spec": "The first line contains two integers n, m (1 ≤ n ≤ 100; 1 ≤ m ≤ 100). The second line contains n integers a1, a2, ..., an (1 ≤ ai ≤ 100).", "output_spec": "Output a single integer, representing the number of the last child.", "sample_inputs": ["5 2\n1 3 1 4 2", "6 4\n1 1 2 2 3 3"], "sample_outputs": ["4", "6"], "notes": "NoteLet's consider the first sample. Firstly child 1 gets 2 candies and go home. Then child 2 gets 2 candies and go to the end of the line. Currently the line looks like [3, 4, 5, 2] (indices of the children in order of the line). Then child 3 gets 2 candies and go home, and then child 4 gets 2 candies and goes to the end of the line. Currently the line looks like [5, 2, 4]. Then child 5 gets 2 candies and goes home. Then child 2 gets two candies and goes home, and finally child 4 gets 2 candies and goes home.Child 4 is the last one who goes home."}, "src_uid": "c0ef1e4d7df360c5c1e52bc6f16ca87c"}
{"nl": {"description": "In this task Anna and Maria play the following game. Initially they have a checkered piece of paper with a painted n × m rectangle (only the border, no filling). Anna and Maria move in turns and Anna starts. During each move one should paint inside the last-painted rectangle a new lesser rectangle (along the grid lines). The new rectangle should have no common points with the previous one. Note that when we paint a rectangle, we always paint only the border, the rectangles aren't filled.Nobody wins the game — Anna and Maria simply play until they have done k moves in total. Count the number of different ways to play this game.", "input_spec": "The first and only line contains three integers: n, m, k (1 ≤ n, m, k ≤ 1000).", "output_spec": "Print the single number — the number of the ways to play the game. As this number can be very big, print the value modulo 1000000007 (109 + 7).", "sample_inputs": ["3 3 1", "4 4 1", "6 7 2"], "sample_outputs": ["1", "9", "75"], "notes": "NoteTwo ways to play the game are considered different if the final pictures are different. In other words, if one way contains a rectangle that is not contained in the other way.In the first sample Anna, who performs her first and only move, has only one possible action plan — insert a 1 × 1 square inside the given 3 × 3 square.In the second sample Anna has as much as 9 variants: 4 ways to paint a 1 × 1 square, 2 ways to insert a 1 × 2 rectangle vertically, 2 more ways to insert it horizontally and one more way is to insert a 2 × 2 square."}, "src_uid": "309d2d46086d526d160292717dfef308"}
{"nl": {"description": "One day Vasya heard a story: \"In the city of High Bertown a bus number 62 left from the bus station. It had n grown-ups and m kids...\"The latter events happen to be of no importance to us. Vasya is an accountant and he loves counting money. So he wondered what maximum and minimum sum of money these passengers could have paid for the ride.The bus fare equals one berland ruble in High Bertown. However, not everything is that easy — no more than one child can ride for free with each grown-up passenger. That means that a grown-up passenger who rides with his k (k > 0) children, pays overall k rubles: a ticket for himself and (k - 1) tickets for his children. Also, a grown-up can ride without children, in this case he only pays one ruble.We know that in High Bertown children can't ride in a bus unaccompanied by grown-ups.Help Vasya count the minimum and the maximum sum in Berland rubles, that all passengers of this bus could have paid in total.", "input_spec": "The input file consists of a single line containing two space-separated numbers n and m (0 ≤ n, m ≤ 105) — the number of the grown-ups and the number of the children in the bus, correspondingly.", "output_spec": "If n grown-ups and m children could have ridden in the bus, then print on a single line two space-separated integers — the minimum and the maximum possible total bus fare, correspondingly.  Otherwise, print \"Impossible\" (without the quotes).", "sample_inputs": ["1 2", "0 5", "2 2"], "sample_outputs": ["2 2", "Impossible", "2 3"], "notes": "NoteIn the first sample a grown-up rides with two children and pays two rubles.In the second sample there are only children in the bus, so the situation is impossible. In the third sample there are two cases:  Each of the two grown-ups rides with one children and pays one ruble for the tickets. In this case the passengers pay two rubles in total.  One of the grown-ups ride with two children's and pays two rubles, the another one rides alone and pays one ruble for himself. So, they pay three rubles in total. "}, "src_uid": "1e865eda33afe09302bda9077d613763"}
{"nl": {"description": "Petr wants to make a calendar for current month. For this purpose he draws a table in which columns correspond to weeks (a week is seven consequent days from Monday to Sunday), rows correspond to weekdays, and cells contain dates. For example, a calendar for January 2017 should look like on the picture:  Petr wants to know how many columns his table should have given the month and the weekday of the first date of that month? Assume that the year is non-leap.", "input_spec": "The only line contain two integers m and d (1 ≤ m ≤ 12, 1 ≤ d ≤ 7) — the number of month (January is the first month, December is the twelfth) and the weekday of the first date of this month (1 is Monday, 7 is Sunday).", "output_spec": "Print single integer: the number of columns the table should have.", "sample_inputs": ["1 7", "1 1", "11 6"], "sample_outputs": ["6", "5", "5"], "notes": "NoteThe first example corresponds to the January 2017 shown on the picture in the statements.In the second example 1-st January is Monday, so the whole month fits into 5 columns.In the third example 1-st November is Saturday and 5 columns is enough."}, "src_uid": "5b969b6f564df6f71e23d4adfb2ded74"}
{"nl": {"description": "You've decided to carry out a survey in the theory of prime numbers. Let us remind you that a prime number is a positive integer that has exactly two distinct positive integer divisors.Consider positive integers a, a + 1, ..., b (a ≤ b). You want to find the minimum integer l (1 ≤ l ≤ b - a + 1) such that for any integer x (a ≤ x ≤ b - l + 1) among l integers x, x + 1, ..., x + l - 1 there are at least k prime numbers. Find and print the required minimum l. If no value l meets the described limitations, print -1.", "input_spec": "A single line contains three space-separated integers a, b, k (1 ≤ a, b, k ≤ 106; a ≤ b).", "output_spec": "In a single line print a single integer — the required minimum l. If there's no solution, print -1.", "sample_inputs": ["2 4 2", "6 13 1", "1 4 3"], "sample_outputs": ["3", "4", "-1"], "notes": null}, "src_uid": "3e1751a2990134f2132d743afe02a10e"}
{"nl": {"description": "Vitya has just started learning Berlanese language. It is known that Berlanese uses the Latin alphabet. Vowel letters are \"a\", \"o\", \"u\", \"i\", and \"e\". Other letters are consonant.In Berlanese, there has to be a vowel after every consonant, but there can be any letter after any vowel. The only exception is a consonant \"n\"; after this letter, there can be any letter (not only a vowel) or there can be no letter at all. For example, the words \"harakiri\", \"yupie\", \"man\", and \"nbo\" are Berlanese while the words \"horse\", \"king\", \"my\", and \"nz\" are not.Help Vitya find out if a word $$$s$$$ is Berlanese.", "input_spec": "The first line of the input contains the string $$$s$$$ consisting of $$$|s|$$$ ($$$1\\leq |s|\\leq 100$$$) lowercase Latin letters.", "output_spec": "Print \"YES\" (without quotes) if there is a vowel after every consonant except \"n\", otherwise print \"NO\". You can print each letter in any case (upper or lower).", "sample_inputs": ["sumimasen", "ninja", "codeforces"], "sample_outputs": ["YES", "YES", "NO"], "notes": "NoteIn the first and second samples, a vowel goes after each consonant except \"n\", so the word is Berlanese.In the third sample, the consonant \"c\" goes after the consonant \"r\", and the consonant \"s\" stands on the end, so the word is not Berlanese."}, "src_uid": "a83144ba7d4906b7692456f27b0ef7d4"}
{"nl": {"description": "Dima came to the horse land. There are n horses living in the land. Each horse in the horse land has several enemies (enmity is a symmetric relationship). The horse land isn't very hostile, so the number of enemies of each horse is at most 3.Right now the horse land is going through an election campaign. So the horses trusted Dima to split them into two parts. At that the horses want the following condition to hold: a horse shouldn't have more than one enemy in its party.Help Dima split the horses into parties. Note that one of the parties can turn out to be empty.", "input_spec": "The first line contains two integers n, m  — the number of horses in the horse land and the number of enemy pairs. Next m lines define the enemy pairs. The i-th line contains integers ai, bi (1 ≤ ai, bi ≤ n; ai ≠ bi), which mean that horse ai is the enemy of horse bi. Consider the horses indexed in some way from 1 to n. It is guaranteed that each horse has at most three enemies. No pair of enemies occurs more than once in the input.", "output_spec": "Print a line, consisting of n characters: the i-th character of the line must equal \"0\", if the horse number i needs to go to the first party, otherwise this character should equal \"1\". If there isn't a way to divide the horses as required, print -1.", "sample_inputs": ["3 3\n1 2\n3 2\n3 1", "2 1\n2 1", "10 6\n1 2\n1 3\n1 4\n2 3\n2 4\n3 4"], "sample_outputs": ["100", "00", "0110000000"], "notes": null}, "src_uid": "7017f2c81d5aed716b90e46480f96582"}
{"nl": {"description": "There are three points marked on the coordinate plane. The goal is to make a simple polyline, without self-intersections and self-touches, such that it passes through all these points. Also, the polyline must consist of only segments parallel to the coordinate axes. You are to find the minimum number of segments this polyline may consist of.", "input_spec": "Each of the three lines of the input contains two integers. The i-th line contains integers xi and yi ( - 109 ≤ xi, yi ≤ 109) — the coordinates of the i-th point. It is guaranteed that all points are distinct.", "output_spec": "Print a single number — the minimum possible number of segments of the polyline.", "sample_inputs": ["1 -1\n1 1\n1 2", "-1 -1\n-1 3\n4 3", "1 1\n2 3\n3 2"], "sample_outputs": ["1", "2", "3"], "notes": "NoteThe variant of the polyline in the first sample:  The variant of the polyline in the second sample:  The variant of the polyline in the third sample: "}, "src_uid": "36fe960550e59b046202b5811343590d"}
{"nl": {"description": "A frog lives on the axis Ox and needs to reach home which is in the point n. She starts from the point 1. The frog can jump to the right at a distance not more than d. So, after she jumped from the point x she can reach the point x + a, where a is an integer from 1 to d.For each point from 1 to n is known if there is a lily flower in it. The frog can jump only in points with a lilies. Guaranteed that there are lilies in the points 1 and n.Determine the minimal number of jumps that the frog needs to reach home which is in the point n from the point 1. Consider that initially the frog is in the point 1. If the frog can not reach home, print -1.", "input_spec": "The first line contains two integers n and d (2 ≤ n ≤ 100, 1 ≤ d ≤ n - 1) — the point, which the frog wants to reach, and the maximal length of the frog jump. The second line contains a string s of length n, consisting of zeros and ones. If a character of the string s equals to zero, then in the corresponding point there is no lily flower. In the other case, in the corresponding point there is a lily flower. Guaranteed that the first and the last characters of the string s equal to one.", "output_spec": "If the frog can not reach the home, print -1. In the other case, print the minimal number of jumps that the frog needs to reach the home which is in the point n from the point 1.", "sample_inputs": ["8 4\n10010101", "4 2\n1001", "8 4\n11100101", "12 3\n101111100101"], "sample_outputs": ["2", "-1", "3", "4"], "notes": "NoteIn the first example the from can reach home in two jumps: the first jump from the point 1 to the point 4 (the length of the jump is three), and the second jump from the point 4 to the point 8 (the length of the jump is four).In the second example the frog can not reach home, because to make it she need to jump on a distance three, but the maximum length of her jump equals to two."}, "src_uid": "c08d2ecdfc66cd07fbbd461b1f069c9e"}
{"nl": {"description": "Soon a school Olympiad in Informatics will be held in Berland, n schoolchildren will participate there.At a meeting of the jury of the Olympiad it was decided that each of the n participants, depending on the results, will get a diploma of the first, second or third degree. Thus, each student will receive exactly one diploma.They also decided that there must be given at least min1 and at most max1 diplomas of the first degree, at least min2 and at most max2 diplomas of the second degree, and at least min3 and at most max3 diplomas of the third degree.After some discussion it was decided to choose from all the options of distributing diplomas satisfying these limitations the one that maximizes the number of participants who receive diplomas of the first degree. Of all these options they select the one which maximizes the number of the participants who receive diplomas of the second degree. If there are multiple of these options, they select the option that maximizes the number of diplomas of the third degree.Choosing the best option of distributing certificates was entrusted to Ilya, one of the best programmers of Berland. However, he found more important things to do, so it is your task now to choose the best option of distributing of diplomas, based on the described limitations.It is guaranteed that the described limitations are such that there is a way to choose such an option of distributing diplomas that all n participants of the Olympiad will receive a diploma of some degree.", "input_spec": "The first line of the input contains a single integer n (3 ≤ n ≤ 3·106) — the number of schoolchildren who will participate in the Olympiad. The next line of the input contains two integers min1 and max1 (1 ≤ min1 ≤ max1 ≤ 106) — the minimum and maximum limits on the number of diplomas of the first degree that can be distributed. The third line of the input contains two integers min2 and max2 (1 ≤ min2 ≤ max2 ≤ 106) — the minimum and maximum limits on the number of diplomas of the second degree that can be distributed.  The next line of the input contains two integers min3 and max3 (1 ≤ min3 ≤ max3 ≤ 106) — the minimum and maximum limits on the number of diplomas of the third degree that can be distributed.  It is guaranteed that min1 + min2 + min3 ≤ n ≤ max1 + max2 + max3.", "output_spec": "In the first line of the output print three numbers, showing how many diplomas of the first, second and third degree will be given to students in the optimal variant of distributing diplomas. The optimal variant of distributing diplomas is the one that maximizes the number of students who receive diplomas of the first degree. Of all the suitable options, the best one is the one which maximizes the number of participants who receive diplomas of the second degree. If there are several of these options, the best one is the one that maximizes the number of diplomas of the third degree.", "sample_inputs": ["6\n1 5\n2 6\n3 7", "10\n1 2\n1 3\n1 5", "6\n1 3\n2 2\n2 2"], "sample_outputs": ["1 2 3", "2 3 5", "2 2 2"], "notes": null}, "src_uid": "3cd092b6507079518cf206deab21cf97"}
{"nl": {"description": "The final match of the Berland Football Cup has been held recently. The referee has shown $$$n$$$ yellow cards throughout the match. At the beginning of the match there were $$$a_1$$$ players in the first team and $$$a_2$$$ players in the second team.The rules of sending players off the game are a bit different in Berland football. If a player from the first team receives $$$k_1$$$ yellow cards throughout the match, he can no longer participate in the match — he's sent off. And if a player from the second team receives $$$k_2$$$ yellow cards, he's sent off. After a player leaves the match, he can no longer receive any yellow cards. Each of $$$n$$$ yellow cards was shown to exactly one player. Even if all players from one team (or even from both teams) leave the match, the game still continues.The referee has lost his records on who has received each yellow card. Help him to determine the minimum and the maximum number of players that could have been thrown out of the game.", "input_spec": "The first line contains one integer $$$a_1$$$ $$$(1 \\le a_1 \\le 1\\,000)$$$ — the number of players in the first team. The second line contains one integer $$$a_2$$$ $$$(1 \\le a_2 \\le 1\\,000)$$$ — the number of players in the second team. The third line contains one integer $$$k_1$$$ $$$(1 \\le k_1 \\le 1\\,000)$$$ — the maximum number of yellow cards a player from the first team can receive (after receiving that many yellow cards, he leaves the game). The fourth line contains one integer $$$k_2$$$ $$$(1 \\le k_2 \\le 1\\,000)$$$ — the maximum number of yellow cards a player from the second team can receive (after receiving that many yellow cards, he leaves the game). The fifth line contains one integer $$$n$$$ $$$(1 \\le n \\le a_1 \\cdot k_1 + a_2 \\cdot k_2)$$$ — the number of yellow cards that have been shown during the match.", "output_spec": "Print two integers — the minimum and the maximum number of players that could have been thrown out of the game.", "sample_inputs": ["2\n3\n5\n1\n8", "3\n1\n6\n7\n25", "6\n4\n9\n10\n89"], "sample_outputs": ["0 4", "4 4", "5 9"], "notes": "NoteIn the first example it could be possible that no player left the game, so the first number in the output is $$$0$$$. The maximum possible number of players that could have been forced to leave the game is $$$4$$$ — one player from the first team, and three players from the second.In the second example the maximum possible number of yellow cards has been shown $$$(3 \\cdot 6 + 1 \\cdot 7 = 25)$$$, so in any case all players were sent off."}, "src_uid": "2be8e0b8ad4d3de2930576c0209e8b91"}
{"nl": {"description": "Vasya has got many devices that work on electricity. He's got n supply-line filters to plug the devices, the i-th supply-line filter has ai sockets.Overall Vasya has got m devices and k electrical sockets in his flat, he can plug the devices or supply-line filters directly. Of course, he can plug the supply-line filter to any other supply-line filter. The device (or the supply-line filter) is considered plugged to electricity if it is either plugged to one of k electrical sockets, or if it is plugged to some supply-line filter that is in turn plugged to electricity. What minimum number of supply-line filters from the given set will Vasya need to plug all the devices he has to electricity? Note that all devices and supply-line filters take one socket for plugging and that he can use one socket to plug either one device or one supply-line filter.", "input_spec": "The first line contains three integers n, m, k (1 ≤ n, m, k ≤ 50) — the number of supply-line filters, the number of devices and the number of sockets that he can plug to directly, correspondingly. The second line contains n space-separated integers a1, a2, ..., an (1 ≤ ai ≤ 50) — number ai stands for the number of sockets on the i-th supply-line filter.", "output_spec": "Print a single number — the minimum number of supply-line filters that is needed to plug all the devices to electricity. If it is impossible to plug all the devices even using all the supply-line filters, print -1.", "sample_inputs": ["3 5 3\n3 1 2", "4 7 2\n3 3 2 4", "5 5 1\n1 3 1 2 1"], "sample_outputs": ["1", "2", "-1"], "notes": "NoteIn the first test case he can plug the first supply-line filter directly to electricity. After he plug it, he get 5 (3 on the supply-line filter and 2 remaining sockets for direct plugging) available sockets to plug. Thus, one filter is enough to plug 5 devices.One of the optimal ways in the second test sample is to plug the second supply-line filter directly and plug the fourth supply-line filter to one of the sockets in the second supply-line filter. Thus, he gets exactly 7 sockets, available to plug: one to plug to the electricity directly, 2 on the second supply-line filter, 4 on the fourth supply-line filter. There's no way he can plug 7 devices if he use one supply-line filter."}, "src_uid": "b32ab27503ee3c4196d6f0d0f133d13c"}
{"nl": {"description": "The Smart Beaver from ABBYY decided to have a day off. But doing nothing the whole day turned out to be too boring, and he decided to play a game with pebbles. Initially, the Beaver has n pebbles. He arranges them in a equal rows, each row has b pebbles (a > 1). Note that the Beaver must use all the pebbles he has, i. e. n = a·b.   10 pebbles are arranged in two rows, each row has 5 pebbles  Once the Smart Beaver has arranged the pebbles, he takes back any of the resulting rows (that is, b pebbles) and discards all other pebbles. Then he arranges all his pebbles again (possibly choosing other values of a and b) and takes back one row, and so on. The game continues until at some point the Beaver ends up with exactly one pebble. The game process can be represented as a finite sequence of integers c1, ..., ck, where:   c1 = n  ci + 1 is the number of pebbles that the Beaver ends up with after the i-th move, that is, the number of pebbles in a row after some arrangement of ci pebbles (1 ≤ i < k). Note that ci > ci + 1.  ck = 1 The result of the game is the sum of numbers ci. You are given n. Find the maximum possible result of the game.", "input_spec": "The single line of the input contains a single integer n — the initial number of pebbles the Smart Beaver has. The input limitations for getting 30 points are:    2 ≤ n ≤ 50  The input limitations for getting 100 points are:    2 ≤ n ≤ 109 ", "output_spec": "Print a single number — the maximum possible result of the game.", "sample_inputs": ["10", "8"], "sample_outputs": ["16", "15"], "notes": "NoteConsider the first example (c1 = 10). The possible options for the game development are:  Arrange the pebbles in 10 rows, one pebble per row. Then c2 = 1, and the game ends after the first move with the result of 11.  Arrange the pebbles in 5 rows, two pebbles per row. Then c2 = 2, and the game continues. During the second move we have two pebbles which can be arranged in a unique way (remember that you are not allowed to put all the pebbles in the same row!) — 2 rows, one pebble per row. c3 = 1, and the game ends with the result of 13.  Finally, arrange the pebbles in two rows, five pebbles per row. The same logic leads us to c2 = 5, c3 = 1, and the game ends with the result of 16 — the maximum possible result. "}, "src_uid": "821c0e3b5fad197a47878bba5e520b6e"}
{"nl": {"description": "You are given a string s consisting of |s| small english letters.In one move you can replace any character of this string to the next character in alphabetical order (a will be replaced with b, s will be replaced with t, etc.). You cannot replace letter z with any other letter.Your target is to make some number of moves (not necessary minimal) to get string abcdefghijklmnopqrstuvwxyz (english alphabet) as a subsequence. Subsequence of the string is the string that is obtained by deleting characters at some positions. You need to print the string that will be obtained from the given string and will be contain english alphabet as a subsequence or say that it is impossible.", "input_spec": "The only one line of the input consisting of the string s consisting of |s| (1 ≤ |s| ≤ 105) small english letters.", "output_spec": "If you can get a string that can be obtained from the given string and will contain english alphabet as a subsequence, print it. Otherwise print «-1» (without quotes).", "sample_inputs": ["aacceeggiikkmmooqqssuuwwyy", "thereisnoanswer"], "sample_outputs": ["abcdefghijklmnopqrstuvwxyz", "-1"], "notes": null}, "src_uid": "f8ad543d499bcc0da0121a71a26db854"}
{"nl": {"description": "The gym leaders were fascinated by the evolutions which took place at Felicity camp. So, they were curious to know about the secret behind evolving Pokemon. The organizers of the camp gave the gym leaders a PokeBlock, a sequence of n ingredients. Each ingredient can be of type 0 or 1. Now the organizers told the gym leaders that to evolve a Pokemon of type k (k ≥ 2), they need to make a valid set of k cuts on the PokeBlock to get smaller blocks.Suppose the given PokeBlock sequence is b0b1b2... bn - 1. You have a choice of making cuts at n + 1 places, i.e., Before b0, between b0 and b1, between b1 and b2, ..., between bn - 2 and bn - 1, and after bn - 1.The n + 1 choices of making cuts are as follows (where a | denotes a possible cut):| b0 | b1 | b2 | ... | bn - 2 | bn - 1 |Consider a sequence of k cuts. Now each pair of consecutive cuts will contain a binary string between them, formed from the ingredient types. The ingredients before the first cut and after the last cut are wasted, which is to say they are not considered. So there will be exactly k - 1 such binary substrings. Every substring can be read as a binary number. Let m be the maximum number out of the obtained numbers. If all the obtained numbers are positive and the set of the obtained numbers contains all integers from 1 to m, then this set of cuts is said to be a valid set of cuts.For example, suppose the given PokeBlock sequence is 101101001110 and we made 5 cuts in the following way:10 | 11 | 010 | 01 | 1 | 10So the 4 binary substrings obtained are: 11, 010, 01 and 1, which correspond to the numbers 3, 2, 1 and 1 respectively. Here m = 3, as it is the maximum value among the obtained numbers. And all the obtained numbers are positive and we have obtained all integers from 1 to m. Hence this set of cuts is a valid set of 5 cuts.A Pokemon of type k will evolve only if the PokeBlock is cut using a valid set of k cuts. There can be many valid sets of the same size. Two valid sets of k cuts are considered different if there is a cut in one set which is not there in the other set.Let f(k) denote the number of valid sets of k cuts. Find the value of . Since the value of s can be very large, output s modulo 109 + 7.", "input_spec": "The input consists of two lines. The first line consists an integer n (1 ≤ n ≤ 75) — the length of the PokeBlock. The next line contains the PokeBlock, a binary string of length n.", "output_spec": "Output a single integer, containing the answer to the problem, i.e., the value of s modulo 109 + 7.", "sample_inputs": ["4\n1011", "2\n10"], "sample_outputs": ["10", "1"], "notes": "NoteIn the first sample, the sets of valid cuts are:Size 2: |1|011, 1|01|1, 10|1|1, 101|1|.Size 3: |1|01|1, |10|1|1, 10|1|1|, 1|01|1|.Size 4: |10|1|1|, |1|01|1|.Hence, f(2) = 4, f(3) = 4 and f(4) = 2. So, the value of s = 10.In the second sample, the set of valid cuts is:Size 2: |1|0.Hence, f(2) = 1 and f(3) = 0. So, the value of s = 1."}, "src_uid": "61f88159762cbc7c51c36e7b56ecde48"}
{"nl": {"description": "When new students come to the Specialized Educational and Scientific Centre (SESC) they need to start many things from the beginning. Sometimes the teachers say (not always unfairly) that we cannot even count. So our teachers decided to teach us arithmetics from the start. And what is the best way to teach students add and subtract? — That's right, using counting sticks! An here's our new task: An expression of counting sticks is an expression of type:[ A sticks][sign +][B sticks][sign =][C sticks] (1 ≤ A, B, C).  Sign + consists of two crossed sticks: one vertical and one horizontal. Sign = consists of two horizontal sticks. The expression is arithmetically correct if A + B = C.We've got an expression that looks like A + B = C given by counting sticks. Our task is to shift at most one stick (or we can shift nothing) so that the expression became arithmetically correct. Note that we cannot remove the sticks from the expression, also we cannot shift the sticks from the signs + and =.We really aren't fabulous at arithmetics. Can you help us?", "input_spec": "The single line contains the initial expression. It is guaranteed that the expression looks like A + B = C, where 1 ≤ A, B, C ≤ 100.", "output_spec": "If there isn't a way to shift the stick so the expression becomes correct, print on a single line \"Impossible\" (without the quotes). If there is a way, print the resulting expression. Follow the format of the output from the test samples. Don't print extra space characters. If there are multiple correct answers, print any of them. For clarifications, you are recommended to see the test samples.", "sample_inputs": ["||+|=|||||", "|||||+||=||", "|+|=||||||", "||||+||=||||||"], "sample_outputs": ["|||+|=||||", "Impossible", "Impossible", "||||+||=||||||"], "notes": "NoteIn the first sample we can shift stick from the third group of sticks to the first one.In the second sample we cannot shift vertical stick from + sign to the second group of sticks. So we cannot make a - sign.There is no answer in the third sample because we cannot remove sticks from the expression.In the forth sample the initial expression is already arithmetically correct and that is why we don't have to shift sticks."}, "src_uid": "ee0aaa7acf127e9f3a9edafc58f4e2d6"}
{"nl": {"description": "The only difference between the easy and the hard versions is constraints.A subsequence is a string that can be derived from another string by deleting some or no symbols without changing the order of the remaining symbols. Characters to be deleted are not required to go successively, there can be any gaps between them. For example, for the string \"abaca\" the following strings are subsequences: \"abaca\", \"aba\", \"aaa\", \"a\" and \"\" (empty string). But the following strings are not subsequences: \"aabaca\", \"cb\" and \"bcaa\".You are given a string $$$s$$$ consisting of $$$n$$$ lowercase Latin letters.In one move you can take any subsequence $$$t$$$ of the given string and add it to the set $$$S$$$. The set $$$S$$$ can't contain duplicates. This move costs $$$n - |t|$$$, where $$$|t|$$$ is the length of the added subsequence (i.e. the price equals to the number of the deleted characters).Your task is to find out the minimum possible total cost to obtain a set $$$S$$$ of size $$$k$$$ or report that it is impossible to do so.", "input_spec": "The first line of the input contains two integers $$$n$$$ and $$$k$$$ ($$$1 \\le n, k \\le 100$$$) — the length of the string and the size of the set, correspondingly. The second line of the input contains a string $$$s$$$ consisting of $$$n$$$ lowercase Latin letters.", "output_spec": "Print one integer — if it is impossible to obtain the set $$$S$$$ of size $$$k$$$, print -1. Otherwise, print the minimum possible total cost to do it.", "sample_inputs": ["4 5\nasdf", "5 6\naaaaa", "5 7\naaaaa", "10 100\najihiushda"], "sample_outputs": ["4", "15", "-1", "233"], "notes": "NoteIn the first example we can generate $$$S$$$ = { \"asdf\", \"asd\", \"adf\", \"asf\", \"sdf\" }. The cost of the first element in $$$S$$$ is $$$0$$$ and the cost of the others is $$$1$$$. So the total cost of $$$S$$$ is $$$4$$$."}, "src_uid": "ae5d21919ecac431ea7507cb1b6dc72b"}
{"nl": {"description": "Little Chris is having a nightmare. Even in dreams all he thinks about is math.Chris dreams about m binary strings of length n, indexed with numbers from 1 to m. The most horrifying part is that the bits of each string are ordered in either ascending or descending order. For example, Chris could be dreaming about the following 4 strings of length 5:  The Hamming distance H(a, b) between two strings a and b of length n is the number of positions at which the corresponding symbols are different. Сhris thinks that each three strings with different indices constitute a single triple. Chris's delusion is that he will wake up only if he counts the number of such string triples a, b, c that the sum H(a, b) + H(b, c) + H(c, a) is maximal among all the string triples constructed from the dreamed strings.Help Chris wake up from this nightmare!", "input_spec": "The first line of input contains two space-separated integers n and m (1 ≤ n ≤ 109; 3 ≤ m ≤ 105), the length and the number of strings. The next m lines contain the description of the strings. The i-th line contains two space-separated integers si and fi (0 ≤ si ≤ 1; 1 ≤ fi ≤ n), the description of the string with index i; that means that the first fi bits of the i-th string are equal to si, and the remaining n - fi bits are equal to 1 - si. There can be multiple equal strings in Chris's dream.", "output_spec": "Output a single integer, the number of such string triples among the given that the sum of the Hamming distances between the strings of the triple is maximal.", "sample_inputs": ["5 4\n0 3\n0 5\n1 4\n1 5", "10 4\n1 5\n0 5\n0 5\n1 5"], "sample_outputs": ["3", "4"], "notes": null}, "src_uid": "bfc61d3e967fc28e1ab5b9028856125b"}
{"nl": {"description": "Bike is a smart boy who loves math very much. He invented a number called \"Rotatable Number\" inspired by 142857. As you can see, 142857 is a magic number because any of its rotatings can be got by multiplying that number by 1, 2, ..., 6 (numbers from one to number's length). Rotating a number means putting its last several digit into first. For example, by rotating number 12345 you can obtain any numbers: 12345, 51234, 45123, 34512, 23451. It's worth mentioning that leading-zeroes are allowed. So both 4500123 and 0123450 can be obtained by rotating 0012345. You can see why 142857 satisfies the condition. All of the 6 equations are under base 10.  142857·1 = 142857;  142857·2 = 285714;  142857·3 = 428571;  142857·4 = 571428;  142857·5 = 714285;  142857·6 = 857142. Now, Bike has a problem. He extends \"Rotatable Number\" under any base b. As is mentioned above, 142857 is a \"Rotatable Number\" under base 10. Another example is 0011 under base 2. All of the 4 equations are under base 2.  0011·1 = 0011;  0011·10 = 0110;  0011·11 = 1001;  0011·100 = 1100. So, he wants to find the largest b (1 < b < x) so that there is a positive \"Rotatable Number\" (leading-zeroes allowed) of length n under base b.Note that any time you multiply a rotatable number by numbers from 1 to its length you should get a rotating of that number.", "input_spec": "The only line contains two space-separated integers n, x (1 ≤ n ≤ 5·106, 2 ≤ x ≤ 109). ", "output_spec": "Print a single integer — the largest b you found. If no such b exists, print -1 instead. ", "sample_inputs": ["6 11", "5 8"], "sample_outputs": ["10", "-1"], "notes": null}, "src_uid": "29dda6a3f057e5bccdc076d7e492ac9a"}
{"nl": {"description": "Polycarpus is an amateur businessman. Recently he was surprised to find out that the market for paper scissors is completely free! Without further ado, Polycarpus decided to start producing and selling such scissors.Polycaprus calculated that the optimal celling price for such scissors would be p bourles. However, he read somewhere that customers are attracted by prices that say something like \"Special Offer! Super price 999 bourles!\". So Polycarpus decided to lower the price a little if it leads to the desired effect.Polycarpus agrees to lower the price by no more than d bourles so that the number of nines at the end of the resulting price is maximum. If there are several ways to do it, he chooses the maximum possible price.Note, Polycarpus counts only the trailing nines in a price.", "input_spec": "The first line contains two integers p and d (1 ≤ p ≤ 1018; 0 ≤ d < p) — the initial price of scissors and the maximum possible price reduction. Please, do not use the %lld specifier to read or write 64-bit integers in С++. It is preferred to use cin, cout streams or the %I64d specifier.", "output_spec": "Print the required price — the maximum price that ends with the largest number of nines and that is less than p by no more than d. The required number shouldn't have leading zeroes.", "sample_inputs": ["1029 102", "27191 17"], "sample_outputs": ["999", "27189"], "notes": null}, "src_uid": "c706cfcd4c37fbc1b1631aeeb2c02b6a"}
{"nl": {"description": "Vasya has found a strange device. On the front panel of a device there are: a red button, a blue button and a display showing some positive integer. After clicking the red button, device multiplies the displayed number by two. After clicking the blue button, device subtracts one from the number on the display. If at some point the number stops being positive, the device breaks down. The display can show arbitrarily large numbers. Initially, the display shows number n.Bob wants to get number m on the display. What minimum number of clicks he has to make in order to achieve this result?", "input_spec": "The first and the only line of the input contains two distinct integers n and m (1 ≤ n, m ≤ 104), separated by a space .", "output_spec": "Print a single number — the minimum number of times one needs to push the button required to get the number m out of number n.", "sample_inputs": ["4 6", "10 1"], "sample_outputs": ["2", "9"], "notes": "NoteIn the first example you need to push the blue button once, and then push the red button once.In the second example, doubling the number is unnecessary, so we need to push the blue button nine times."}, "src_uid": "861f8edd2813d6d3a5ff7193a804486f"}
{"nl": {"description": "Everyone loves a freebie. Especially students.It is well-known that if in the night before exam a student opens window, opens the student's record-book and shouts loudly three times \"Fly, freebie, fly!\" — then flown freebie helps him to pass the upcoming exam.In the night before the exam on mathematical analysis n students living in dormitory shouted treasured words. The i-th student made a sacrament at the time ti, where ti is the number of seconds elapsed since the beginning of the night.It is known that the freebie is a capricious and willful lady. That night the freebie was near dormitory only for T seconds. Therefore, if for two students their sacrament times differ for more than T, then the freebie didn't visit at least one of them.Since all students are optimists, they really want to know what is the maximal number of students visited by the freebie can be.", "input_spec": "The first line of the input contains integer n (1 ≤ n ≤ 100), where n — the number of students shouted \"Fly, freebie, fly!\" The second line contains n positive integers ti (1 ≤ ti ≤ 1000). The last line contains integer T (1 ≤ T ≤ 1000) — the time interval during which the freebie was near the dormitory.", "output_spec": "Print a single integer — the largest number of people who will pass exam tomorrow because of the freebie visit.", "sample_inputs": ["6\n4 1 7 8 3 8\n1"], "sample_outputs": ["3"], "notes": null}, "src_uid": "086d07bd6f9031df09bd6a6e8fe8f25c"}
{"nl": {"description": "Smart Beaver decided to be not only smart, but also a healthy beaver! And so he began to attend physical education classes at school X. In this school, physical education has a very creative teacher. One of his favorite warm-up exercises is throwing balls. Students line up. Each one gets a single ball in the beginning. The balls are numbered from 1 to n (by the demand of the inventory commission).   Figure 1. The initial position for n = 5.  After receiving the balls the students perform the warm-up exercise. The exercise takes place in a few throws. For each throw the teacher chooses any two arbitrary different students who will participate in it. The selected students throw their balls to each other. Thus, after each throw the students remain in their positions, and the two balls are swapped.   Figure 2. The example of a throw.  In this case there was a throw between the students, who were holding the 2-nd and the 4-th balls. Since the warm-up has many exercises, each of them can only continue for little time. Therefore, for each student we know the maximum number of throws he can participate in. For this lessons maximum number of throws will be 1 or 2.Note that after all phases of the considered exercise any ball can end up with any student. Smart Beaver decided to formalize it and introduced the concept of the \"ball order\". The ball order is a sequence of n numbers that correspond to the order of balls in the line. The first number will match the number of the ball of the first from the left student in the line, the second number will match the ball of the second student, and so on. For example, in figure 2 the order of the balls was (1, 2, 3, 4, 5), and after the throw it was (1, 4, 3, 2, 5). Smart beaver knows the number of students and for each student he knows the maximum number of throws in which he can participate. And now he is wondering: what is the number of distinct ways of ball orders by the end of the exercise.", "input_spec": "The first line contains a single number n — the number of students in the line and the number of balls. The next line contains exactly n space-separated integers. Each number corresponds to a student in the line (the i-th number corresponds to the i-th from the left student in the line) and shows the number of throws he can participate in. The input limits for scoring 30 points are (subproblem D1):    1 ≤ n ≤ 10.  The input limits for scoring 70 points are (subproblems D1+D2):    1 ≤ n ≤ 500.  The input limits for scoring 100 points are (subproblems D1+D2+D3):    1 ≤ n ≤ 1000000. ", "output_spec": "The output should contain a single integer — the number of variants of ball orders after the warm up exercise is complete. As the number can be rather large, print it modulo 1000000007 (109 + 7).", "sample_inputs": ["5\n1 2 2 1 2", "8\n1 2 2 1 2 1 1 2"], "sample_outputs": ["120", "16800"], "notes": null}, "src_uid": "91e8dbe94273e255182aca0f94117bb9"}
{"nl": {"description": "Valera the Horse is going to the party with friends. He has been following the fashion trends for a while, and he knows that it is very popular to wear all horseshoes of different color. Valera has got four horseshoes left from the last year, but maybe some of them have the same color. In this case he needs to go to the store and buy some few more horseshoes, not to lose face in front of his stylish comrades.Fortunately, the store sells horseshoes of all colors under the sun and Valera has enough money to buy any four of them. However, in order to save the money, he would like to spend as little money as possible, so you need to help Valera and determine what is the minimum number of horseshoes he needs to buy to wear four horseshoes of different colors to a party.", "input_spec": "The first line contains four space-separated integers s1, s2, s3, s4 (1 ≤ s1, s2, s3, s4 ≤ 109) — the colors of horseshoes Valera has. Consider all possible colors indexed with integers.", "output_spec": "Print a single integer — the minimum number of horseshoes Valera needs to buy.", "sample_inputs": ["1 7 3 3", "7 7 7 7"], "sample_outputs": ["1", "3"], "notes": null}, "src_uid": "38c4864937e57b35d3cce272f655e20f"}
{"nl": {"description": "Consider a linear function f(x) = Ax + B. Let's define g(0)(x) = x and g(n)(x) = f(g(n - 1)(x)) for n > 0. For the given integer values A, B, n and x find the value of g(n)(x) modulo 109 + 7.", "input_spec": "The only line contains four integers A, B, n and x (1 ≤ A, B, x ≤ 109, 1 ≤ n ≤ 1018) — the parameters from the problem statement. Note that the given value n can be too large, so you should use 64-bit integer type to store it. In C++ you can use the long long integer type and in Java you can use long integer type.", "output_spec": "Print the only integer s — the value g(n)(x) modulo 109 + 7.", "sample_inputs": ["3 4 1 1", "3 4 2 1", "3 4 3 1"], "sample_outputs": ["7", "25", "79"], "notes": null}, "src_uid": "e22a1fc38c8b2a4cc30ce3b9f893028e"}
{"nl": {"description": "Vasya plays the Power Defence. He must pass the last level of the game. In order to do this he must kill the Main Villain, who moves in a straight line at speed 1 meter per second from the point ( - ∞, 0) to the point ( + ∞, 0) of the game world. In the points (x, 1) and (x,  - 1), where x is an integer number, Vasya can build towers of three types: fire-tower, electric-tower or freezing-tower. However, it is not allowed to build two towers at the same point. Towers of each type have a certain action radius and the value of damage per second (except freezing-tower). If at some point the Main Villain is in the range of action of k freezing towers then his speed is decreased by k + 1 times.The allowed number of towers of each type is known. It is necessary to determine the maximum possible damage we can inflict on the Main Villain.All distances in the problem are given in meters. The size of the Main Villain and the towers are so small, that they can be considered as points on the plane. The Main Villain is in the action radius of a tower if the distance between him and tower is less than or equal to the action radius of the tower.", "input_spec": "The first line contains three integer numbers nf, ne and ns — the maximum number of fire-towers, electric-towers and freezing-towers that can be built (0 ≤ nf, ne, ns ≤ 20, 1 ≤ nf + ne + ns ≤ 20). The numbers are separated with single spaces. The second line contains three integer numbers rf, re and rs (1 ≤ rf, re, rs ≤ 1000) — the action radii of fire-towers, electric-towers and freezing-towers. The numbers are separated with single spaces. The third line contains two integer numbers df and de (1 ≤ df, de ≤ 1000) — the damage a fire-tower and an electronic-tower can inflict on the Main Villain per second (in the case when the Main Villain is in the action radius of the tower). The numbers are separated with single space.", "output_spec": "Print the only real number — the maximum possible damage to the Main Villain with absolute or relative error not more than 10 - 6.", "sample_inputs": ["1 0 0\n10 10 10\n100 100", "1 0 1\n10 10 10\n100 100"], "sample_outputs": ["1989.97487421", "3979.94974843"], "notes": "NoteIn the first sample we've got one fire-tower that always inflicts the same damage, independently of its position. In the second sample we've got another freezing-tower of the same action radius. If we build the two towers opposite each other, then the Main Villain's speed will be two times lower, whenever he enters the fire-tower's action radius. That means that the enemy will be inflicted with twice more damage."}, "src_uid": "de5a42225714552cc5422d8a45734d58"}
{"nl": {"description": "Moamen and Ezzat are playing a game. They create an array $$$a$$$ of $$$n$$$ non-negative integers where every element is less than $$$2^k$$$.Moamen wins if $$$a_1 \\,\\&\\, a_2 \\,\\&\\, a_3 \\,\\&\\, \\ldots \\,\\&\\, a_n \\ge a_1 \\oplus a_2 \\oplus a_3 \\oplus \\ldots \\oplus a_n$$$.Here $$$\\&$$$ denotes the bitwise AND operation, and $$$\\oplus$$$ denotes the bitwise XOR operation.Please calculate the number of winning for Moamen arrays $$$a$$$.As the result may be very large, print the value modulo $$$1\\,000\\,000\\,007$$$ ($$$10^9 + 7$$$).", "input_spec": "The first line contains a single integer $$$t$$$ ($$$1 \\le t \\le 5$$$)— the number of test cases.  Each test case consists of one line containing two integers $$$n$$$ and $$$k$$$ ($$$1 \\le n\\le 2\\cdot 10^5$$$, $$$0 \\le k \\le 2\\cdot 10^5$$$).", "output_spec": "For each test case, print a single value — the number of different arrays that Moamen wins with. Print the result modulo $$$1\\,000\\,000\\,007$$$ ($$$10^9 + 7$$$).", "sample_inputs": ["3\n3 1\n2 1\n4 0"], "sample_outputs": ["5\n2\n1"], "notes": "NoteIn the first example, $$$n = 3$$$, $$$k = 1$$$. As a result, all the possible arrays are $$$[0,0,0]$$$, $$$[0,0,1]$$$, $$$[0,1,0]$$$, $$$[1,0,0]$$$, $$$[1,1,0]$$$, $$$[0,1,1]$$$, $$$[1,0,1]$$$, and $$$[1,1,1]$$$.Moamen wins in only $$$5$$$ of them: $$$[0,0,0]$$$, $$$[1,1,0]$$$, $$$[0,1,1]$$$, $$$[1,0,1]$$$, and $$$[1,1,1]$$$."}, "src_uid": "02f5fe43ea60939dd4a53299b5fa0881"}
{"nl": {"description": "This is an easy version of the problem. The actual problems are different, but the easy version is almost a subtask of the hard version. Note that the constraints and the output format are different.You are given a string $$$s$$$ consisting of $$$n$$$ lowercase Latin letters.You have to color all its characters one of the two colors (each character to exactly one color, the same letters can be colored the same or different colors, i.e. you can choose exactly one color for each index in $$$s$$$).After coloring, you can swap any two neighboring characters of the string that are colored different colors. You can perform such an operation arbitrary (possibly, zero) number of times.The goal is to make the string sorted, i.e. all characters should be in alphabetical order.Your task is to say if it is possible to color the given string so that after coloring it can become sorted by some sequence of swaps. Note that you have to restore only coloring, not the sequence of swaps.", "input_spec": "The first line of the input contains one integer $$$n$$$ ($$$1 \\le n \\le 200$$$) — the length of $$$s$$$. The second line of the input contains the string $$$s$$$ consisting of exactly $$$n$$$ lowercase Latin letters.", "output_spec": "If it is impossible to color the given string so that after coloring it can become sorted by some sequence of swaps, print \"NO\" (without quotes) in the first line. Otherwise, print \"YES\" in the first line and any correct coloring in the second line (the coloring is the string consisting of $$$n$$$ characters, the $$$i$$$-th character should be '0' if the $$$i$$$-th character is colored the first color and '1' otherwise).", "sample_inputs": ["9\nabacbecfd", "8\naaabbcbb", "7\nabcdedc", "5\nabcde"], "sample_outputs": ["YES\n001010101", "YES\n01011011", "NO", "YES\n00000"], "notes": null}, "src_uid": "9bd31827cda83eacfcf5e46cdeaabe2b"}
{"nl": {"description": "Есть n-подъездный дом, в каждом подъезде по m этажей, и на каждом этаже каждого подъезда ровно k квартир. Таким образом, в доме всего n·m·k квартир. Они пронумерованы естественным образом от 1 до n·m·k, то есть первая квартира на первом этаже в первом подъезде имеет номер 1, первая квартира на втором этаже первого подъезда имеет номер k + 1 и так далее. Особенность этого дома состоит в том, что он круглый. То есть если обходить его по часовой стрелке, то после подъезда номер 1 следует подъезд номер 2, затем подъезд номер 3 и так далее до подъезда номер n. После подъезда номер n снова идёт подъезд номер 1.Эдвард живёт в квартире номер a, а Наташа — в квартире номер b. Переход на 1 этаж вверх или вниз по лестнице занимает 5 секунд, переход от двери подъезда к двери соседнего подъезда — 15 секунд, а переход в пределах одного этажа одного подъезда происходит мгновенно. Также в каждом подъезде дома есть лифт. Он устроен следующим образом: он всегда приезжает ровно через 10 секунд после вызова, а чтобы переместить пассажира на один этаж вверх или вниз, лифт тратит ровно 1 секунду. Посадка и высадка происходят мгновенно.Помогите Эдварду найти минимальное время, за которое он сможет добраться до квартиры Наташи. Считайте, что Эдвард может выйти из подъезда только с первого этажа соответствующего подъезда (это происходит мгновенно). Если Эдвард стоит перед дверью какого-то подъезда, он может зайти в него и сразу окажется на первом этаже этого подъезда (это также происходит мгновенно). Эдвард может выбирать, в каком направлении идти вокруг дома.", "input_spec": "В первой строке входных данных следуют три числа n, m, k (1 ≤ n, m, k ≤ 1000) — количество подъездов в доме, количество этажей в каждом подъезде и количество квартир на каждом этаже каждого подъезда соответственно. Во второй строке входных данных записаны два числа a и b (1 ≤ a, b ≤ n·m·k) — номера квартир, в которых живут Эдвард и Наташа, соответственно. Гарантируется, что эти номера различны. ", "output_spec": "Выведите единственное целое число — минимальное время (в секундах), за которое Эдвард сможет добраться от своей квартиры до квартиры Наташи.", "sample_inputs": ["4 10 5\n200 6", "3 1 5\n7 2"], "sample_outputs": ["39", "15"], "notes": "ПримечаниеВ первом тестовом примере Эдвард находится в 4 подъезде на 10 этаже, а Наташа находится в 1 подъезде на 2 этаже. Поэтому Эдварду выгодно сначала спуститься на лифте на первый этаж (на это он потратит 19 секунд, из которых 10 — на ожидание и 9 — на поездку на лифте), затем обойти дом против часовой стрелки до подъезда номер 1 (на это он потратит 15 секунд), и наконец подняться по лестнице на этаж номер 2 (на это он потратит 5 секунд). Таким образом, ответ равен 19 + 15 + 5 = 39.Во втором тестовом примере Эдвард живёт в подъезде 2 на этаже 1, а Наташа находится в подъезде 1 на этаже 1. Поэтому Эдварду выгодно просто обойти дом по часовой стрелке до подъезда 1, на это он потратит 15 секунд."}, "src_uid": "c37b46851abcf7eb472869bd1ab9f793"}
{"nl": {"description": "Sometimes one has to spell email addresses over the phone. Then one usually pronounces a dot as dot, an at sign as at. As a result, we get something like vasyaatgmaildotcom. Your task is to transform it into a proper email address (vasya@gmail.com). It is known that a proper email address contains only such symbols as . @ and lower-case Latin letters, doesn't start with and doesn't end with a dot. Also, a proper email address doesn't start with and doesn't end with an at sign. Moreover, an email address contains exactly one such symbol as @, yet may contain any number (possible, zero) of dots. You have to carry out a series of replacements so that the length of the result was as short as possible and it was a proper email address. If the lengths are equal, you should print the lexicographically minimal result. Overall, two variants of replacement are possible: dot can be replaced by a dot, at can be replaced by an at. ", "input_spec": "The first line contains the email address description. It is guaranteed that that is a proper email address with all the dots replaced by dot an the at signs replaced by at. The line is not empty and its length does not exceed 100 symbols.", "output_spec": "Print the shortest email address, from which the given line could be made by the described above replacements. If there are several solutions to that problem, print the lexicographically minimal one (the lexicographical comparison of the lines are implemented with an operator < in modern programming languages). In the ASCII table the symbols go in this order: . @ ab...z", "sample_inputs": ["vasyaatgmaildotcom", "dotdotdotatdotdotat", "aatt"], "sample_outputs": ["vasya@gmail.com", "dot..@..at", "a@t"], "notes": null}, "src_uid": "a11c9679d8e2dca51be17d466202df6e"}
{"nl": {"description": "You are given a rectangular cake, represented as an r × c grid. Each cell either has an evil strawberry, or is empty. For example, a 3 × 4 cake may look as follows:  The cakeminator is going to eat the cake! Each time he eats, he chooses a row or a column that does not contain any evil strawberries and contains at least one cake cell that has not been eaten before, and eats all the cake cells there. He may decide to eat any number of times.Please output the maximum number of cake cells that the cakeminator can eat.", "input_spec": "The first line contains two integers r and c (2 ≤ r, c ≤ 10), denoting the number of rows and the number of columns of the cake. The next r lines each contains c characters — the j-th character of the i-th line denotes the content of the cell at row i and column j, and is either one of these:    '.' character denotes a cake cell with no evil strawberry;  'S' character denotes a cake cell with an evil strawberry. ", "output_spec": "Output the maximum number of cake cells that the cakeminator can eat.", "sample_inputs": ["3 4\nS...\n....\n..S."], "sample_outputs": ["8"], "notes": "NoteFor the first example, one possible way to eat the maximum number of cake cells is as follows (perform 3 eats).      "}, "src_uid": "ebaf7d89c623d006a6f1ffd025892102"}
{"nl": {"description": "There is a legend in the IT City college. A student that failed to answer all questions on the game theory exam is given one more chance by his professor. The student has to play a game with the professor.The game is played on a square field consisting of n × n cells. Initially all cells are empty. On each turn a player chooses and paint an empty cell that has no common sides with previously painted cells. Adjacent corner of painted cells is allowed. On the next turn another player does the same, then the first one and so on. The player with no cells to paint on his turn loses.The professor have chosen the field size n and allowed the student to choose to be the first or the second player in the game. What should the student choose to win the game? Both players play optimally.", "input_spec": "The only line of the input contains one integer n (1 ≤ n ≤ 1018) — the size of the field.", "output_spec": "Output number 1, if the player making the first turn wins when both players play optimally, otherwise print number 2.", "sample_inputs": ["1", "2"], "sample_outputs": ["1", "2"], "notes": null}, "src_uid": "816ec4cd9736f3113333ef05405b8e81"}
{"nl": {"description": "Melody Pond was stolen from her parents as a newborn baby by Madame Kovarian, to become a weapon of the Silence in their crusade against the Doctor. Madame Kovarian changed Melody's name to River Song, giving her a new identity that allowed her to kill the Eleventh Doctor.Heidi figured out that Madame Kovarian uses a very complicated hashing function in order to change the names of the babies she steals. In order to prevent this from happening to future Doctors, Heidi decided to prepare herself by learning some basic hashing techniques.The first hashing function she designed is as follows.Given two positive integers $$$(x, y)$$$ she defines $$$H(x,y):=x^2+2xy+x+1$$$.Now, Heidi wonders if the function is reversible. That is, given a positive integer $$$r$$$, can you find a pair $$$(x, y)$$$ (of positive integers) such that $$$H(x, y) = r$$$?If multiple such pairs exist, output the one with smallest possible $$$x$$$. If there is no such pair, output \"NO\".", "input_spec": "The first and only line contains an integer $$$r$$$ ($$$1 \\le r \\le 10^{12}$$$).", "output_spec": "Output integers $$$x, y$$$ such that $$$H(x,y) = r$$$ and $$$x$$$ is smallest possible, or \"NO\" if no such pair exists.", "sample_inputs": ["19", "16"], "sample_outputs": ["1 8", "NO"], "notes": null}, "src_uid": "3ff1c25a1026c90aeb14d148d7fb96ba"}
{"nl": {"description": "There are n people, sitting in a line at the table. For each person we know that he always tells either the truth or lies.Little Serge asked them: how many of you always tell the truth? Each of the people at the table knows everything (who is an honest person and who is a liar) about all the people at the table. The honest people are going to say the correct answer, the liars are going to say any integer from 1 to n, which is not the correct answer. Every liar chooses his answer, regardless of the other liars, so two distinct liars may give distinct answer.Serge does not know any information about the people besides their answers to his question. He took a piece of paper and wrote n integers a1, a2, ..., an, where ai is the answer of the i-th person in the row. Given this sequence, Serge determined that exactly k people sitting at the table apparently lie.Serge wonders, how many variants of people's answers (sequences of answers a of length n) there are where one can say that exactly k people sitting at the table apparently lie. As there can be rather many described variants of answers, count the remainder of dividing the number of the variants by 777777777.", "input_spec": "The first line contains two integers n, k, (1 ≤ k ≤ n ≤ 28). It is guaranteed that n — is the power of number 2.", "output_spec": "Print a single integer — the answer to the problem modulo 777777777.", "sample_inputs": ["1 1", "2 1"], "sample_outputs": ["0", "2"], "notes": null}, "src_uid": "cfe19131644e5925e32084a581e23286"}
{"nl": {"description": "The dragon and the princess are arguing about what to do on the New Year's Eve. The dragon suggests flying to the mountains to watch fairies dancing in the moonlight, while the princess thinks they should just go to bed early. They are desperate to come to an amicable agreement, so they decide to leave this up to chance.They take turns drawing a mouse from a bag which initially contains w white and b black mice. The person who is the first to draw a white mouse wins. After each mouse drawn by the dragon the rest of mice in the bag panic, and one of them jumps out of the bag itself (the princess draws her mice carefully and doesn't scare other mice). Princess draws first. What is the probability of the princess winning?If there are no more mice in the bag and nobody has drawn a white mouse, the dragon wins. Mice which jump out of the bag themselves are not considered to be drawn (do not define the winner). Once a mouse has left the bag, it never returns to it. Every mouse is drawn from the bag with the same probability as every other one, and every mouse jumps out of the bag with the same probability as every other one.", "input_spec": "The only line of input data contains two integers w and b (0 ≤ w, b ≤ 1000).", "output_spec": "Output the probability of the princess winning. The answer is considered to be correct if its absolute or relative error does not exceed 10 - 9.", "sample_inputs": ["1 3", "5 5"], "sample_outputs": ["0.500000000", "0.658730159"], "notes": "NoteLet's go through the first sample. The probability of the princess drawing a white mouse on her first turn and winning right away is 1/4. The probability of the dragon drawing a black mouse and not winning on his first turn is 3/4 * 2/3 = 1/2. After this there are two mice left in the bag — one black and one white; one of them jumps out, and the other is drawn by the princess on her second turn. If the princess' mouse is white, she wins (probability is 1/2 * 1/2 = 1/4), otherwise nobody gets the white mouse, so according to the rule the dragon wins."}, "src_uid": "7adb8bf6879925955bf187c3d05fde8c"}
{"nl": {"description": "Dima and Anya love playing different games. Now Dima has imagined a new game that he wants to play with Anya.Dima writes n pairs of integers on a piece of paper (li, ri) (1 ≤ li < ri ≤ p). Then players take turns. On his turn the player can do the following actions:  choose the number of the pair i (1 ≤ i ≤ n), such that ri - li > 2;  replace pair number i by pair  or by pair . Notation ⌊x⌋ means rounding down to the closest integer. The player who can't make a move loses.Of course, Dima wants Anya, who will move first, to win. That's why Dima should write out such n pairs of integers (li, ri) (1 ≤ li < ri ≤ p), that if both players play optimally well, the first one wins. Count the number of ways in which Dima can do it. Print the remainder after dividing the answer by number 1000000007 (109 + 7).Two ways are considered distinct, if the ordered sequences of the written pairs are distinct.", "input_spec": "The first line contains two integers n, p (1 ≤ n ≤ 1000, 1 ≤ p ≤ 109). The numbers are separated by a single space.", "output_spec": "In a single line print the remainder after dividing the answer to the problem by number 1000000007 (109 + 7).", "sample_inputs": ["2 2", "4 4", "100 1000"], "sample_outputs": ["0", "520", "269568947"], "notes": null}, "src_uid": "c03b6379e9d186874ac3d97c6968fbd0"}
{"nl": {"description": "Madoka decided to entrust the organization of a major computer game tournament \"OSU\"!In this tournament, matches are held according to the \"Olympic system\". In other words, there are $$$2^n$$$ participants in the tournament, numbered with integers from $$$1$$$ to $$$2^n$$$. There are $$$n$$$ rounds in total in the tournament. In the $$$i$$$-th round there are $$$2^{n - i}$$$ matches between two players (one of whom is right, the other is left), after which the winners go further along the tournament grid, and the losing participants are eliminated from the tournament. Herewith, the relative order in the next round does not change. And the winner of the tournament — is the last remaining participant.But the smaller the participant's number, the more he will pay Madoka if he wins, so Madoka wants the participant with the lowest number to win. To do this, she can arrange the participants in the first round as she likes, and also determine for each match who will win — the participant on the left or right.But Madoka knows that tournament sponsors can change the winner in matches no more than $$$k$$$ times. (That is, if the participant on the left won before the change, then the participant on the right will win after the change, and if the participant on the right won, then the participant on the left will win after the change).  So, the first image shows the tournament grid that Madoka made, where the red lines denote who should win the match. And the second one shows the tournament grid, after one change in the outcome of the match by sponsors (a match between $$$1$$$ and $$$3$$$ players). Print the minimum possible number of the winner in the tournament, which Madoka can get regardless of changes in sponsors. But since the answer can be very large, output it modulo $$$10^9 + 7$$$. Note that we need to minimize the answer, and only then take it modulo.", "input_spec": "The first and the only line contains two integers $$$n$$$ and $$$k$$$ ($$$1 \\le n \\le 10^5, 1 \\le k \\le \\min(2^n - 1, 10^9)$$$) — the number of rounds in the tournament and the number of outcomes that sponsors can change.", "output_spec": "Print exactly one integer — the minimum number of the winner modulo $$$10^9 + 7$$$", "sample_inputs": ["1 1", "2 1", "3 2"], "sample_outputs": ["2", "3", "7"], "notes": "NoteIn the first example, there is only one match between players $$$1$$$ and $$$2$$$, so the sponsors can always make player $$$2$$$ wins.The tournament grid from the second example is shown in the picture in the statement."}, "src_uid": "dc7b887afcc2e95c4e90619ceda63071"}
{"nl": {"description": "Arkady the air traffic controller is now working with n planes in the air. All planes move along a straight coordinate axis with Arkady's station being at point 0 on it. The i-th plane, small enough to be represented by a point, currently has a coordinate of xi and is moving with speed vi. It's guaranteed that xi·vi < 0, i.e., all planes are moving towards the station.Occasionally, the planes are affected by winds. With a wind of speed vwind (not necessarily positive or integral), the speed of the i-th plane becomes vi + vwind.According to weather report, the current wind has a steady speed falling inside the range [ - w, w] (inclusive), but the exact value cannot be measured accurately since this value is rather small — smaller than the absolute value of speed of any plane.Each plane should contact Arkady at the exact moment it passes above his station. And you are to help Arkady count the number of pairs of planes (i, j) (i < j) there are such that there is a possible value of wind speed, under which planes i and j contact Arkady at the same moment. This value needn't be the same across different pairs.The wind speed is the same for all planes. You may assume that the wind has a steady speed and lasts arbitrarily long.", "input_spec": "The first line contains two integers n and w (1 ≤ n ≤ 100 000, 0 ≤ w < 105) — the number of planes and the maximum wind speed. The i-th of the next n lines contains two integers xi and vi (1 ≤ |xi| ≤ 105, w + 1 ≤ |vi| ≤ 105, xi·vi < 0) — the initial position and speed of the i-th plane. Planes are pairwise distinct, that is, no pair of (i, j) (i < j) exists such that both xi = xj and vi = vj.", "output_spec": "Output a single integer — the number of unordered pairs of planes that can contact Arkady at the same moment.", "sample_inputs": ["5 1\n-3 2\n-3 3\n-1 2\n1 -3\n3 -5", "6 1\n-3 2\n-2 2\n-1 2\n1 -2\n2 -2\n3 -2"], "sample_outputs": ["3", "9"], "notes": "NoteIn the first example, the following 3 pairs of planes satisfy the requirements:   (2, 5) passes the station at time 3 / 4 with vwind = 1;  (3, 4) passes the station at time 2 / 5 with vwind = 1 / 2;  (3, 5) passes the station at time 4 / 7 with vwind =  - 1 / 4. In the second example, each of the 3 planes with negative coordinates can form a valid pair with each of the other 3, totaling 9 pairs."}, "src_uid": "d073d41f7e184e9bc4a12219d86e7184"}
{"nl": {"description": "The stardate is 1977 and the science and art of detecting Death Stars is in its infancy. Princess Heidi has received information about the stars in the nearby solar system from the Rebel spies and now, to help her identify the exact location of the Death Star, she needs to know whether this information is correct. Two rebel spies have provided her with the maps of the solar system. Each map is an N × N grid, where each cell is either occupied by a star or empty. To see whether the information is correct, Heidi needs to know whether the two maps are of the same solar system, or if possibly one of the spies is actually an Empire double agent, feeding her false information.Unfortunately, spies may have accidentally rotated a map by 90, 180, or 270 degrees, or flipped it along the vertical or the horizontal axis, before delivering it to Heidi. If Heidi can rotate or flip the maps so that two of them become identical, then those maps are of the same solar system. Otherwise, there are traitors in the Rebel ranks! Help Heidi find out.", "input_spec": "The first line of the input contains one number N (1 ≤ N ≤ 10) – the dimension of each map. Next N lines each contain N characters, depicting the first map: 'X' indicates a star, while 'O' indicates an empty quadrant of space. Next N lines each contain N characters, depicting the second map in the same format.", "output_spec": "The only line of output should contain the word Yes if the maps are identical, or No if it is impossible to match them by performing rotations and translations.", "sample_inputs": ["4\nXOOO\nXXOO\nOOOO\nXXXX\nXOOO\nXOOO\nXOXO\nXOXX", "2\nXX\nOO\nXO\nOX"], "sample_outputs": ["Yes", "No"], "notes": "NoteIn the first test, you can match the first map to the second map by first flipping the first map along the vertical axis, and then by rotating it 90 degrees clockwise. "}, "src_uid": "2e793c9f476d03e8ba7df262db1c06e4"}
{"nl": {"description": "Vasya studies positional numeral systems. Unfortunately, he often forgets to write the base of notation in which the expression is written. Once he saw a note in his notebook saying a + b = ?, and that the base of the positional notation wasn’t written anywhere. Now Vasya has to choose a base p and regard the expression as written in the base p positional notation. Vasya understood that he can get different results with different bases, and some bases are even invalid. For example, expression 78 + 87 in the base 16 positional notation is equal to FF16, in the base 15 positional notation it is equal to 11015, in the base 10 one — to 16510, in the base 9 one — to 1769, and in the base 8 or lesser-based positional notations the expression is invalid as all the numbers should be strictly less than the positional notation base. Vasya got interested in what is the length of the longest possible expression value. Help him to find this length.The length of a number should be understood as the number of numeric characters in it. For example, the length of the longest answer for 78 + 87 = ? is 3. It is calculated like that in the base 15 (11015), base 10 (16510), base 9 (1769) positional notations, for example, and in some other ones.", "input_spec": "The first letter contains two space-separated numbers a and b (1 ≤ a, b ≤ 1000) which represent the given summands.", "output_spec": "Print a single number — the length of the longest answer.", "sample_inputs": ["78 87", "1 1"], "sample_outputs": ["3", "2"], "notes": null}, "src_uid": "8ccfb9b1fef6a992177cc49bd56fab7b"}
{"nl": {"description": "The only difference between easy and hard versions is constraints.Polycarp loves to listen to music, so he never leaves the player, even on the way home from the university. Polycarp overcomes the distance from the university to the house in exactly $$$T$$$ minutes.In the player, Polycarp stores $$$n$$$ songs, each of which is characterized by two parameters: $$$t_i$$$ and $$$g_i$$$, where $$$t_i$$$ is the length of the song in minutes ($$$1 \\le t_i \\le 15$$$), $$$g_i$$$ is its genre ($$$1 \\le g_i \\le 3$$$).Polycarp wants to create such a playlist so that he can listen to music all the time on the way from the university to his home, and at the time of his arrival home, the playlist is over. Polycarp never interrupts songs and always listens to them from beginning to end. Thus, if he started listening to the $$$i$$$-th song, he would spend exactly $$$t_i$$$ minutes on its listening. Polycarp also does not like when two songs of the same genre play in a row (i.e. successively/adjacently) or when the songs in his playlist are repeated.Help Polycarpus count the number of different sequences of songs (their order matters), the total duration is exactly $$$T$$$, such that there are no two consecutive songs of the same genre in them and all the songs in the playlist are different.", "input_spec": "The first line of the input contains two integers $$$n$$$ and $$$T$$$ ($$$1 \\le n \\le 15, 1 \\le T \\le 225$$$) — the number of songs in the player and the required total duration, respectively. Next, the $$$n$$$ lines contain descriptions of songs: the $$$i$$$-th line contains two integers $$$t_i$$$ and $$$g_i$$$ ($$$1 \\le t_i \\le 15, 1 \\le g_i \\le 3$$$) — the duration of the $$$i$$$-th song and its genre, respectively.", "output_spec": "Output one integer — the number of different sequences of songs, the total length of exactly $$$T$$$, such that there are no two consecutive songs of the same genre in them and all the songs in the playlist are different. Since the answer may be huge, output it modulo $$$10^9 + 7$$$ (that is, the remainder when dividing the quantity by $$$10^9 + 7$$$).", "sample_inputs": ["3 3\n1 1\n1 2\n1 3", "3 3\n1 1\n1 1\n1 3", "4 10\n5 3\n2 1\n3 2\n5 1"], "sample_outputs": ["6", "2", "10"], "notes": "NoteIn the first example, Polycarp can make any of the $$$6$$$ possible playlist by rearranging the available songs: $$$[1, 2, 3]$$$, $$$[1, 3, 2]$$$, $$$[2, 1, 3]$$$, $$$[2, 3, 1]$$$, $$$[3, 1, 2]$$$ and $$$[3, 2, 1]$$$ (indices of the songs are given).In the second example, the first and second songs cannot go in succession (since they have the same genre). Thus, Polycarp can create a playlist in one of $$$2$$$ possible ways: $$$[1, 3, 2]$$$ and $$$[2, 3, 1]$$$ (indices of the songs are given).In the third example, Polycarp can make the following playlists: $$$[1, 2, 3]$$$, $$$[1, 3, 2]$$$, $$$[2, 1, 3]$$$, $$$[2, 3, 1]$$$, $$$[3, 1, 2]$$$, $$$[3, 2, 1]$$$, $$$[1, 4]$$$, $$$[4, 1]$$$, $$$[2, 3, 4]$$$ and $$$[4, 3, 2]$$$ (indices of the songs are given)."}, "src_uid": "ac2a37ff4c7e89a345b189e4891bbf56"}
{"nl": {"description": "Drazil is playing a math game with Varda.Let's define  for positive integer x as a product of factorials of its digits. For example, .First, they choose a decimal number a consisting of n digits that contains at least one digit larger than 1. This number may possibly start with leading zeroes. Then they should find maximum positive number x satisfying following two conditions:1. x doesn't contain neither digit 0 nor digit 1.2.  = .Help friends find such number.", "input_spec": "The first line contains an integer n (1 ≤ n ≤ 15) — the number of digits in a. The second line contains n digits of a. There is at least one digit in a that is larger than 1. Number a may possibly contain leading zeroes.", "output_spec": "Output a maximum possible integer satisfying the conditions above. There should be no zeroes and ones in this number decimal representation.", "sample_inputs": ["4\n1234", "3\n555"], "sample_outputs": ["33222", "555"], "notes": "NoteIn the first case, "}, "src_uid": "60dbfc7a65702ae8bd4a587db1e06398"}
{"nl": {"description": "In the year 2500 the annual graduation ceremony in the German University in Cairo (GUC) has run smoothly for almost 500 years so far.The most important part of the ceremony is related to the arrangement of the professors in the ceremonial hall.Traditionally GUC has n professors. Each professor has his seniority level. All seniorities are different. Let's enumerate the professors from 1 to n, with 1 being the most senior professor and n being the most junior professor.The ceremonial hall has n seats, one seat for each professor. Some places in this hall are meant for more senior professors than the others. More specifically, m pairs of seats are in \"senior-junior\" relation, and the tradition requires that for all m pairs of seats (ai, bi) the professor seated in \"senior\" position ai should be more senior than the professor seated in \"junior\" position bi.GUC is very strict about its traditions, which have been carefully observed starting from year 2001. The tradition requires that:   The seating of the professors changes every year.  Year 2001 ceremony was using lexicographically first arrangement of professors in the ceremonial hall.  Each consecutive year lexicographically next arrangement of the professors is used. The arrangement of the professors is the list of n integers, where the first integer is the seniority of the professor seated in position number one, the second integer is the seniority of the professor seated in position number two, etc.Given n, the number of professors, y, the current year and m pairs of restrictions, output the arrangement of the professors for this year.", "input_spec": "The first line contains three integers n, y and m (1 ≤ n ≤ 16, 2001 ≤ y ≤ 1018, 0 ≤ m ≤ 100) — the number of professors, the year for which the arrangement should be computed, and the number of pairs of seats for which the seniority relation should be kept, respectively. The next m lines contain one pair of integers each, \"ai bi\", indicating that professor on the ai-th seat is more senior than professor on the bi-th seat (1 ≤ ai, bi ≤ n, ai ≠ bi). Some pair may be listed more than once. Please, do not use the %lld specificator to read or write 64-bit integers in С++. It is preferred to use the cin stream (you may also use the %I64d specificator).", "output_spec": "Print the order in which the professors should be seated in the requested year. If by this year the GUC would have ran out of arrangements, or the given \"senior-junior\" relation are contradictory, print \"The times have changed\" (without quotes).", "sample_inputs": ["3 2001 2\n1 2\n2 3", "7 2020 6\n1 2\n1 3\n2 4\n2 5\n3 6\n3 7", "10 3630801 0", "3 2001 3\n1 2\n2 3\n3 1"], "sample_outputs": ["1 2 3", "1 2 3 7 4 6 5", "The times have changed", "The times have changed"], "notes": "NoteIn the first example the lexicographically first order of seating is 1 2 3.In the third example the GUC will run out of arrangements after the year 3630800.In the fourth example there are no valid arrangements for the seating.The lexicographical comparison of arrangements is performed by the < operator in modern programming languages. The arrangement a is lexicographically less that the arrangement b, if there exists such i (1 ≤ i ≤ n), that ai < bi, and for any j (1 ≤ j < i) aj = bj."}, "src_uid": "e9db8d048e9763cf38c584342dea9f53"}
{"nl": {"description": "Vasya has recently finished writing a book. Now he faces the problem of giving it the title. Vasya wants the title to be vague and mysterious for his book to be noticeable among others. That's why the title should be represented by a single word containing at least once each of the first k Latin letters and not containing any other ones. Also, the title should be a palindrome, that is it should be read similarly from the left to the right and from the right to the left.Vasya has already composed the approximate variant of the title. You are given the title template s consisting of lowercase Latin letters and question marks. Your task is to replace all the question marks by lowercase Latin letters so that the resulting word satisfies the requirements, described above. Each question mark should be replaced by exactly one letter, it is not allowed to delete characters or add new ones to the template. If there are several suitable titles, choose the first in the alphabetical order, for Vasya's book to appear as early as possible in all the catalogues.", "input_spec": "The first line contains an integer k (1 ≤ k ≤ 26) which is the number of allowed alphabet letters. The second line contains s which is the given template. In s only the first k lowercase letters of Latin alphabet and question marks can be present, the length of s is from 1 to 100 characters inclusively.", "output_spec": "If there is no solution, print IMPOSSIBLE. Otherwise, a single line should contain the required title, satisfying the given template. The title should be a palindrome and it can only contain the first k letters of the Latin alphabet. At that, each of those k letters must be present at least once. If there are several suitable titles, print the lexicographically minimal one.  The lexicographical comparison is performed by the standard < operator in modern programming languages. The line a is lexicographically smaller than the line b, if exists such an i (1 ≤ i ≤ |s|), that ai < bi, and for any j (1 ≤ j < i) aj = bj. |s| stands for the length of the given template.", "sample_inputs": ["3\na?c", "2\na??a", "2\n?b?a"], "sample_outputs": ["IMPOSSIBLE", "abba", "abba"], "notes": null}, "src_uid": "9d1dd9d722e5fe46823224334b3b208a"}
{"nl": {"description": "Vasya came up with his own weather forecasting method. He knows the information about the average air temperature for each of the last n days. Assume that the average air temperature for each day is integral.Vasya believes that if the average temperatures over the last n days form an arithmetic progression, where the first term equals to the average temperature on the first day, the second term equals to the average temperature on the second day and so on, then the average temperature of the next (n + 1)-th day will be equal to the next term of the arithmetic progression. Otherwise, according to Vasya's method, the temperature of the (n + 1)-th day will be equal to the temperature of the n-th day.Your task is to help Vasya predict the average temperature for tomorrow, i. e. for the (n + 1)-th day.", "input_spec": "The first line contains a single integer n (2 ≤ n ≤ 100) — the number of days for which the average air temperature is known. The second line contains a sequence of integers t1, t2, ..., tn ( - 1000 ≤ ti ≤ 1000) — where ti is the average temperature in the i-th day.", "output_spec": "Print the average air temperature in the (n + 1)-th day, which Vasya predicts according to his method. Note that the absolute value of the predicted temperature can exceed 1000.", "sample_inputs": ["5\n10 5 0 -5 -10", "4\n1 1 1 1", "3\n5 1 -5", "2\n900 1000"], "sample_outputs": ["-15", "1", "-5", "1100"], "notes": "NoteIn the first example the sequence of the average temperatures is an arithmetic progression where the first term is 10 and each following terms decreases by 5. So the predicted average temperature for the sixth day is  - 10 - 5 =  - 15.In the second example the sequence of the average temperatures is an arithmetic progression where the first term is 1 and each following terms equals to the previous one. So the predicted average temperature in the fifth day is 1.In the third example the average temperatures do not form an arithmetic progression, so the average temperature of the fourth day equals to the temperature of the third day and equals to  - 5.In the fourth example the sequence of the average temperatures is an arithmetic progression where the first term is 900 and each the following terms increase by 100. So predicted average temperature in the third day is 1000 + 100 = 1100."}, "src_uid": "d04fa4322a1b300bdf4a56f09681b17f"}
{"nl": {"description": "Alice likes word \"nineteen\" very much. She has a string s and wants the string to contain as many such words as possible. For that reason she can rearrange the letters of the string.For example, if she has string \"xiineteenppnnnewtnee\", she can get string \"xnineteenppnineteenw\", containing (the occurrences marked) two such words. More formally, word \"nineteen\" occurs in the string the number of times you can read it starting from some letter of the string. Of course, you shouldn't skip letters.Help her to find the maximum number of \"nineteen\"s that she can get in her string.", "input_spec": "The first line contains a non-empty string s, consisting only of lowercase English letters. The length of string s doesn't exceed 100.", "output_spec": "Print a single integer — the maximum number of \"nineteen\"s that she can get in her string.", "sample_inputs": ["nniinneetteeeenn", "nneteenabcnneteenabcnneteenabcnneteenabcnneteenabcii", "nineteenineteen"], "sample_outputs": ["2", "2", "2"], "notes": null}, "src_uid": "bb433cdb8299afcf46cb2797cbfbf724"}
{"nl": {"description": "Baby Badawy's first words were \"AND 0 SUM BIG\", so he decided to solve the following problem. Given two integers $$$n$$$ and $$$k$$$, count the number of arrays of length $$$n$$$ such that:  all its elements are integers between $$$0$$$ and $$$2^k-1$$$ (inclusive);  the bitwise AND of all its elements is $$$0$$$;  the sum of its elements is as large as possible. Since the answer can be very large, print its remainder when divided by $$$10^9+7$$$.", "input_spec": "The first line contains an integer $$$t$$$ ($$$1 \\le t \\le 10$$$) — the number of test cases you need to solve. Each test case consists of a line containing two integers $$$n$$$ and $$$k$$$ ($$$1 \\le n \\le 10^{5}$$$, $$$1 \\le k \\le 20$$$).", "output_spec": "For each test case, print the number of arrays satisfying the conditions. Since the answer can be very large, print its remainder when divided by $$$10^9+7$$$.", "sample_inputs": ["2\n2 2\n100000 20"], "sample_outputs": ["4\n226732710"], "notes": "NoteIn the first example, the $$$4$$$ arrays are:  $$$[3,0]$$$,  $$$[0,3]$$$,  $$$[1,2]$$$,  $$$[2,1]$$$. "}, "src_uid": "2e7a9f3a97938e4a7e036520d812b97a"}
{"nl": {"description": "Yakko, Wakko and Dot, world-famous animaniacs, decided to rest from acting in cartoons, and take a leave to travel a bit. Yakko dreamt to go to Pennsylvania, his Motherland and the Motherland of his ancestors. Wakko thought about Tasmania, its beaches, sun and sea. Dot chose Transylvania as the most mysterious and unpredictable place.But to their great regret, the leave turned to be very short, so it will be enough to visit one of the three above named places. That's why Yakko, as the cleverest, came up with a truly genius idea: let each of the three roll an ordinary six-sided die, and the one with the highest amount of points will be the winner, and will take the other two to the place of his/her dreams.Yakko thrown a die and got Y points, Wakko — W points. It was Dot's turn. But she didn't hurry. Dot wanted to know for sure what were her chances to visit Transylvania.It is known that Yakko and Wakko are true gentlemen, that's why if they have the same amount of points with Dot, they will let Dot win.", "input_spec": "The only line of the input file contains two natural numbers Y and W — the results of Yakko's and Wakko's die rolls.", "output_spec": "Output the required probability in the form of irreducible fraction in format «A/B», where A — the numerator, and B — the denominator. If the required probability equals to zero, output «0/1». If the required probability equals to 1, output «1/1». ", "sample_inputs": ["4 2"], "sample_outputs": ["1/2"], "notes": "NoteDot will go to Transylvania, if she is lucky to roll 4, 5 or 6 points."}, "src_uid": "f97eb4ecffb6cbc8679f0c621fd59414"}
{"nl": {"description": "There is a square box 6 × 6 in size. It contains 36 chips 1 × 1 in size. Those chips contain 36 different characters — \"0\"-\"9\" and \"A\"-\"Z\". There is exactly one chip with each character.You are allowed to make the following operations: you may choose one of 6 rows or one of 6 columns and cyclically shift the chips there to one position to the left or to the right (for the row) or upwards or downwards (for the column). Those operations are allowed to perform several times. To solve the puzzle is to shift the chips using the above described operations so that they were written in the increasing order (exactly equal to the right picture). An example of solving the puzzle is shown on a picture below.  Write a program that finds the sequence of operations that solves the puzzle. That sequence should not necessarily be shortest, but you should not exceed the limit of 10000 operations. It is guaranteed that the solution always exists.", "input_spec": "The input data are represented by 6 lines containing 6 characters each. They are the puzzle's initial position. Those lines contain each character from the string \"0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ\" exactly once.", "output_spec": "On the first line print number n, which is the number of operations. On the next n lines print the sequence of operations one per line. An operation is described by a word consisting of two characters. The first character shows the direction where the row or the column will be shifted. The possible directions are \"L\", \"R\" (to the left, to the right correspondingly, we shift a row), \"U\", \"D\" (upwards, downwards correspondingly, we shift a column). The second character is the number of the row (or the column), it is an integer from \"1\" to \"6\". The rows are numbered from the top to the bottom, the columns are numbered from the left to the right. The number of operations should not exceed 104. If there are several solutions, print any of them.", "sample_inputs": ["01W345\n729AB6\nCD8FGH\nIJELMN\nOPKRST\nUVQXYZ"], "sample_outputs": ["2\nR2\nU3"], "notes": null}, "src_uid": "10b2c1c53580dd382c41a56f7413e709"}
{"nl": {"description": "Robbers, who attacked the Gerda's cab, are very successful in covering from the kingdom police. To make the goal of catching them even harder, they use their own watches.First, as they know that kingdom police is bad at math, robbers use the positional numeral system with base 7. Second, they divide one day in n hours, and each hour in m minutes. Personal watches of each robber are divided in two parts: first of them has the smallest possible number of places that is necessary to display any integer from 0 to n - 1, while the second has the smallest possible number of places that is necessary to display any integer from 0 to m - 1. Finally, if some value of hours or minutes can be displayed using less number of places in base 7 than this watches have, the required number of zeroes is added at the beginning of notation.Note that to display number 0 section of the watches is required to have at least one place.Little robber wants to know the number of moments of time (particular values of hours and minutes), such that all digits displayed on the watches are distinct. Help her calculate this number.", "input_spec": "The first line of the input contains two integers, given in the decimal notation, n and m (1 ≤ n, m ≤ 109) — the number of hours in one day and the number of minutes in one hour, respectively.", "output_spec": "Print one integer in decimal notation — the number of different pairs of hour and minute, such that all digits displayed on the watches are distinct.", "sample_inputs": ["2 3", "8 2"], "sample_outputs": ["4", "5"], "notes": "NoteIn the first sample, possible pairs are: (0: 1), (0: 2), (1: 0), (1: 2).In the second sample, possible pairs are: (02: 1), (03: 1), (04: 1), (05: 1), (06: 1)."}, "src_uid": "0930c75f57dd88a858ba7bb0f11f1b1c"}
{"nl": {"description": "Kolya got string s for his birthday, the string consists of small English letters. He immediately added k more characters to the right of the string.Then Borya came and said that the new string contained a tandem repeat of length l as a substring. How large could l be?See notes for definition of a tandem repeat.", "input_spec": "The first line contains s (1 ≤ |s| ≤ 200). This string contains only small English letters. The second line contains number k (1 ≤ k ≤ 200) — the number of the added characters.", "output_spec": "Print a single number — the maximum length of the tandem repeat that could have occurred in the new string.", "sample_inputs": ["aaba\n2", "aaabbbb\n2", "abracadabra\n10"], "sample_outputs": ["6", "6", "20"], "notes": "NoteA tandem repeat of length 2n is string s, where for any position i (1 ≤ i ≤ n) the following condition fulfills: si = si + n.In the first sample Kolya could obtain a string aabaab, in the second — aaabbbbbb, in the third — abracadabrabracadabra."}, "src_uid": "bb65667b65ff069a9c0c9e8fe31da8ab"}
{"nl": {"description": "Petya and Vasya decided to play a little. They found n red cubes and m blue cubes. The game goes like that: the players take turns to choose a cube of some color (red or blue) and put it in a line from left to right (overall the line will have n + m cubes). Petya moves first. Petya's task is to get as many pairs of neighbouring cubes of the same color as possible. Vasya's task is to get as many pairs of neighbouring cubes of different colors as possible. The number of Petya's points in the game is the number of pairs of neighboring cubes of the same color in the line, the number of Vasya's points in the game is the number of neighbouring cubes of the different color in the line. Your task is to calculate the score at the end of the game (Petya's and Vasya's points, correspondingly), if both boys are playing optimally well. To \"play optimally well\" first of all means to maximize the number of one's points, and second — to minimize the number of the opponent's points.", "input_spec": "The only line contains two space-separated integers n and m (1 ≤ n, m ≤ 105) — the number of red and blue cubes, correspondingly.", "output_spec": "On a single line print two space-separated integers — the number of Petya's and Vasya's points correspondingly provided that both players play optimally well.", "sample_inputs": ["3 1", "2 4"], "sample_outputs": ["2 1", "3 2"], "notes": "NoteIn the first test sample the optimal strategy for Petya is to put the blue cube in the line. After that there will be only red cubes left, so by the end of the game the line of cubes from left to right will look as [blue, red, red, red]. So, Petya gets 2 points and Vasya gets 1 point. If Petya would choose the red cube during his first move, then, provided that both boys play optimally well, Petya would get 1 point and Vasya would get 2 points."}, "src_uid": "c8378e6fcaab30d15469a55419f38b39"}
{"nl": {"description": "You are given n rectangles. The corners of rectangles have integer coordinates and their edges are parallel to the Ox and Oy axes. The rectangles may touch each other, but they do not overlap (that is, there are no points that belong to the interior of more than one rectangle). Your task is to determine if the rectangles form a square. In other words, determine if the set of points inside or on the border of at least one rectangle is precisely equal to the set of points inside or on the border of some square.", "input_spec": "The first line contains a single integer n (1 ≤ n ≤ 5). Next n lines contain four integers each, describing a single rectangle: x1, y1, x2, y2 (0 ≤ x1 < x2 ≤ 31400, 0 ≤ y1 < y2 ≤ 31400) — x1 and x2 are x-coordinates of the left and right edges of the rectangle, and y1 and y2 are y-coordinates of the bottom and top edges of the rectangle.  No two rectangles overlap (that is, there are no points that belong to the interior of more than one rectangle).", "output_spec": "In a single line print \"YES\", if the given rectangles form a square, or \"NO\" otherwise.", "sample_inputs": ["5\n0 0 2 3\n0 3 3 5\n2 0 5 2\n3 2 5 5\n2 2 3 3", "4\n0 0 2 3\n0 3 3 5\n2 0 5 2\n3 2 5 5"], "sample_outputs": ["YES", "NO"], "notes": null}, "src_uid": "f63fc2d97fd88273241fce206cc217f2"}
{"nl": {"description": "Little Petya was given this problem for homework:You are given function  (here  represents the operation of taking the remainder). His task is to count the number of integers x in range [a;b] with property f(x) = x.It is a pity that Petya forgot the order in which the remainders should be taken and wrote down only 4 numbers. Each of 24 possible orders of taking the remainder has equal probability of being chosen. For example, if Petya has numbers 1, 2, 3, 4 then he can take remainders in that order or first take remainder modulo 4, then modulo 2, 3, 1. There also are 22 other permutations of these numbers that represent orders in which remainder can be taken. In this problem 4 numbers wrote down by Petya will be pairwise distinct.Now it is impossible for Petya to complete the task given by teacher but just for fun he decided to find the number of integers  with property that probability that f(x) = x is not less than 31.4159265352718281828459045%. In other words, Petya will pick up the number x if there exist at least 7 permutations of numbers p1, p2, p3, p4, for which f(x) = x.", "input_spec": "First line of the input will contain 6 integers, separated by spaces: p1, p2, p3, p4, a, b (1 ≤ p1, p2, p3, p4 ≤ 1000, 0 ≤ a ≤ b ≤ 31415).  It is guaranteed that numbers p1, p2, p3, p4 will be pairwise distinct.", "output_spec": "Output the number of integers in the given range that have the given property.", "sample_inputs": ["2 7 1 8 2 8", "20 30 40 50 0 100", "31 41 59 26 17 43"], "sample_outputs": ["0", "20", "9"], "notes": null}, "src_uid": "63b9dc70e6ad83d89a487ffebe007b0a"}
{"nl": {"description": "Mashmokh's boss, Bimokh, didn't like Mashmokh. So he fired him. Mashmokh decided to go to university and participate in ACM instead of finding a new job. He wants to become a member of Bamokh's team. In order to join he was given some programming tasks and one week to solve them. Mashmokh is not a very experienced programmer. Actually he is not a programmer at all. So he wasn't able to solve them. That's why he asked you to help him with these tasks. One of these tasks is the following.A sequence of l integers b1, b2, ..., bl (1 ≤ b1 ≤ b2 ≤ ... ≤ bl ≤ n) is called good if each number divides (without a remainder) by the next number in the sequence. More formally  for all i (1 ≤ i ≤ l - 1).Given n and k find the number of good sequences of length k. As the answer can be rather large print it modulo 1000000007 (109 + 7).", "input_spec": "The first line of input contains two space-separated integers n, k (1 ≤ n, k ≤ 2000).", "output_spec": "Output a single integer — the number of good sequences of length k modulo 1000000007 (109 + 7).", "sample_inputs": ["3 2", "6 4", "2 1"], "sample_outputs": ["5", "39", "2"], "notes": "NoteIn the first sample the good sequences are: [1, 1], [2, 2], [3, 3], [1, 2], [1, 3]."}, "src_uid": "c8cbd155d9f20563d37537ef68dde5aa"}
{"nl": {"description": "Trouble came from the overseas lands: a three-headed dragon Gorynych arrived. The dragon settled at point C and began to terrorize the residents of the surrounding villages.A brave hero decided to put an end to the dragon. He moved from point A to fight with Gorynych. The hero rode from point A along a straight road and met point B on his way. The hero knows that in this land for every pair of roads it is true that they are either parallel to each other, or lie on a straight line, or are perpendicular to each other. He also knows well that points B and C are connected by a road. So the hero must either turn 90 degrees to the left or continue riding straight ahead or turn 90 degrees to the right. But he forgot where the point C is located.Fortunately, a Brave Falcon flew right by. It can see all three points from the sky. The hero asked him what way to go to get to the dragon's lair.If you have not got it, you are the falcon. Help the hero and tell him how to get him to point C: turn left, go straight or turn right.At this moment the hero is believed to stand at point B, turning his back to point A.", "input_spec": "The first input line contains two space-separated integers xa, ya (|xa|, |ya| ≤ 109) — the coordinates of point A. The second line contains the coordinates of point B in the same form, the third line contains the coordinates of point C. It is guaranteed that all points are pairwise different. It is also guaranteed that either point B lies on segment AC, or angle ABC is right.", "output_spec": "Print a single line. If a hero must turn left, print \"LEFT\" (without the quotes); If he must go straight ahead, print \"TOWARDS\" (without the quotes); if he should turn right, print \"RIGHT\" (without the quotes).", "sample_inputs": ["0 0\n0 1\n1 1", "-1 -1\n-3 -3\n-4 -4", "-4 -6\n-3 -7\n-2 -6"], "sample_outputs": ["RIGHT", "TOWARDS", "LEFT"], "notes": "NoteThe picture to the first sample: The red color shows points A, B and C. The blue arrow shows the hero's direction. The green color shows the hero's trajectory.The picture to the second sample: "}, "src_uid": "f6e132d1969863e9f28c87e5a44c2b69"}
{"nl": {"description": "You are given a rectangular board of M × N squares. Also you are given an unlimited number of standard domino pieces of 2 × 1 squares. You are allowed to rotate the pieces. You are asked to place as many dominoes as possible on the board so as to meet the following conditions:1. Each domino completely covers two squares.2. No two dominoes overlap.3. Each domino lies entirely inside the board. It is allowed to touch the edges of the board.Find the maximum number of dominoes, which can be placed under these restrictions.", "input_spec": "In a single line you are given two integers M and N — board sizes in squares (1 ≤ M ≤ N ≤ 16).", "output_spec": "Output one number — the maximal number of dominoes, which can be placed.", "sample_inputs": ["2 4", "3 3"], "sample_outputs": ["4", "4"], "notes": null}, "src_uid": "e840e7bfe83764bee6186fcf92a1b5cd"}
{"nl": {"description": "Okabe needs bananas for one of his experiments for some strange reason. So he decides to go to the forest and cut banana trees.Consider the point (x, y) in the 2D plane such that x and y are integers and 0 ≤ x, y. There is a tree in such a point, and it has x + y bananas. There are no trees nor bananas in other points. Now, Okabe draws a line with equation . Okabe can select a single rectangle with axis aligned sides with all points on or under the line and cut all the trees in all points that are inside or on the border of this rectangle and take their bananas. Okabe's rectangle can be degenerate; that is, it can be a line segment or even a point.Help Okabe and find the maximum number of bananas he can get if he chooses the rectangle wisely.Okabe is sure that the answer does not exceed 1018. You can trust him.", "input_spec": "The first line of input contains two space-separated integers m and b (1 ≤ m ≤ 1000, 1 ≤ b ≤ 10000).", "output_spec": "Print the maximum number of bananas Okabe can get from the trees he cuts.", "sample_inputs": ["1 5", "2 3"], "sample_outputs": ["30", "25"], "notes": "Note  The graph above corresponds to sample test 1. The optimal rectangle is shown in red and has 30 bananas."}, "src_uid": "9300f1c07dd36e0cf7e6cb7911df4cf2"}
{"nl": {"description": "The elections to Berland parliament are happening today. Voting is in full swing!Totally there are n candidates, they are numbered from 1 to n. Based on election results k (1 ≤ k ≤ n) top candidates will take seats in the parliament.After the end of the voting the number of votes for each candidate is calculated. In the resulting table the candidates are ordered by the number of votes. In case of tie (equal number of votes) they are ordered by the time of the last vote given. The candidate with ealier last vote stands higher in the resulting table.So in the resulting table candidates are sorted by the number of votes (more votes stand for the higher place) and if two candidates have equal number of votes they are sorted by the time of last vote (earlier last vote stands for the higher place).There is no way for a candidate with zero votes to take a seat in the parliament. So it is possible that less than k candidates will take a seat in the parliament.In Berland there are m citizens who can vote. Each of them will vote for some candidate. Each citizen will give a vote to exactly one of n candidates. There is no option \"against everyone\" on the elections. It is not accepted to spoil bulletins or not to go to elections. So each of m citizens will vote for exactly one of n candidates.At the moment a citizens have voted already (1 ≤ a ≤ m). This is an open election, so for each citizen it is known the candidate for which the citizen has voted. Formally, the j-th citizen voted for the candidate gj. The citizens who already voted are numbered in chronological order; i.e. the (j + 1)-th citizen voted after the j-th.The remaining m - a citizens will vote before the end of elections, each of them will vote for one of n candidates.Your task is to determine for each of n candidates one of the three possible outcomes:  a candidate will be elected to the parliament regardless of votes of the remaining m - a citizens;  a candidate has chance to be elected to the parliament after all n citizens have voted;  a candidate has no chances to be elected to the parliament regardless of votes of the remaining m - a citizens. ", "input_spec": "The first line contains four integers n, k, m and a (1 ≤ k ≤ n ≤ 100, 1 ≤ m ≤ 100, 1 ≤ a ≤ m) — the number of candidates, the number of seats in the parliament, the number of Berland citizens and the number of citizens who already have voted. The second line contains a sequence of a integers g1, g2, ..., ga (1 ≤ gj ≤ n), where gj is the candidate for which the j-th citizen has voted. Citizens who already voted are numbered in increasing order of voting times.", "output_spec": "Print the sequence consisting of n integers r1, r2, ..., rn where:   ri = 1 means that the i-th candidate is guaranteed to take seat in the parliament regardless of votes of the remaining m - a citizens;  ri = 2 means that the i-th candidate has a chance to take a seat in the parliament, i.e. the remaining m - a citizens can vote in such a way that the candidate will take a seat in the parliament;  ri = 3 means that the i-th candidate will not take a seat in the parliament regardless of votes of the remaining m - a citizens. ", "sample_inputs": ["3 1 5 4\n1 2 1 3", "3 1 5 3\n1 3 1", "3 2 5 3\n1 3 1"], "sample_outputs": ["1 3 3", "2 3 2", "1 2 2"], "notes": null}, "src_uid": "81a890bd542963bbcec7a041dde5c247"}
{"nl": {"description": "Yet another Armageddon is coming! This time the culprit is the Julya tribe calendar. The beavers in this tribe knew math very well. Smart Beaver, an archaeologist, got a sacred plate with a magic integer on it. The translation from Old Beaverish is as follows: \"May the Great Beaver bless you! May your chacres open and may your third eye never turn blind from beholding the Truth! Take the magic number, subtract a digit from it (the digit must occur in the number) and get a new magic number. Repeat this operation until a magic number equals zero. The Earth will stand on Three Beavers for the time, equal to the number of subtractions you perform!\"Distinct subtraction sequences can obviously get you different number of operations. But the Smart Beaver is ready to face the worst and is asking you to count the minimum number of operations he needs to reduce the magic number to zero.", "input_spec": "The single line contains the magic integer n, 0 ≤ n.   to get 20 points, you need to solve the problem with constraints: n ≤ 106 (subproblem C1);  to get 40 points, you need to solve the problem with constraints: n ≤ 1012 (subproblems C1+C2);  to get 100 points, you need to solve the problem with constraints: n ≤ 1018 (subproblems C1+C2+C3). ", "output_spec": "Print a single integer — the minimum number of subtractions that turns the magic number to a zero.", "sample_inputs": ["24"], "sample_outputs": ["5"], "notes": "NoteIn the first test sample the minimum number of operations can be reached by the following sequence of subtractions:  24 → 20 → 18 → 10 → 9 → 0 "}, "src_uid": "fc5765b9bd18dc7555fa76e91530c036"}
{"nl": {"description": "Two best friends Serozha and Gena play a game.Initially there is one pile consisting of n stones on the table. During one move one pile should be taken and divided into an arbitrary number of piles consisting of a1 > a2 > ... > ak > 0 stones. The piles should meet the condition a1 - a2 = a2 - a3 = ... = ak - 1 - ak = 1. Naturally, the number of piles k should be no less than two.The friends play in turns. The player who cannot make a move loses. Serozha makes the first move. Who will win if both players play in the optimal way?", "input_spec": "The single line contains a single integer n (1 ≤ n ≤ 105).", "output_spec": "If Serozha wins, print k, which represents the minimal number of piles into which he can split the initial one during the first move in order to win the game. If Gena wins, print \"-1\" (without the quotes).", "sample_inputs": ["3", "6", "100"], "sample_outputs": ["2", "-1", "8"], "notes": null}, "src_uid": "63262317ba572d78163c91b853c05506"}
{"nl": {"description": "Alice and Bob are playing a game with $$$n$$$ piles of stones. It is guaranteed that $$$n$$$ is an even number. The $$$i$$$-th pile has $$$a_i$$$ stones.Alice and Bob will play a game alternating turns with Alice going first.On a player's turn, they must choose exactly $$$\\frac{n}{2}$$$ nonempty piles and independently remove a positive number of stones from each of the chosen piles. They can remove a different number of stones from the piles in a single turn. The first player unable to make a move loses (when there are less than $$$\\frac{n}{2}$$$ nonempty piles).Given the starting configuration, determine who will win the game.", "input_spec": "The first line contains one integer $$$n$$$ ($$$2 \\leq n \\leq 50$$$) — the number of piles. It is guaranteed that $$$n$$$ is an even number. The second line contains $$$n$$$ integers $$$a_1, a_2, \\ldots, a_n$$$ ($$$1 \\leq a_i \\leq 50$$$) — the number of stones in the piles.", "output_spec": "Print a single string \"Alice\" if Alice wins; otherwise, print \"Bob\" (without double quotes).", "sample_inputs": ["2\n8 8", "4\n3 1 4 1"], "sample_outputs": ["Bob", "Alice"], "notes": "NoteIn the first example, each player can only remove stones from one pile ($$$\\frac{2}{2}=1$$$). Alice loses, since Bob can copy whatever Alice does on the other pile, so Alice will run out of moves first.In the second example, Alice can remove $$$2$$$ stones from the first pile and $$$3$$$ stones from the third pile on her first move to guarantee a win."}, "src_uid": "4b9cf82967aa8441e9af3db3101161e9"}
{"nl": {"description": "A new delivery of clothing has arrived today to the clothing store. This delivery consists of $$$a$$$ ties, $$$b$$$ scarves, $$$c$$$ vests and $$$d$$$ jackets.The store does not sell single clothing items — instead, it sells suits of two types:  a suit of the first type consists of one tie and one jacket;  a suit of the second type consists of one scarf, one vest and one jacket. Each suit of the first type costs $$$e$$$ coins, and each suit of the second type costs $$$f$$$ coins.Calculate the maximum possible cost of a set of suits that can be composed from the delivered clothing items. Note that one item cannot be used in more than one suit (though some items may be left unused).", "input_spec": "The first line contains one integer $$$a$$$ $$$(1 \\le a \\le 100\\,000)$$$ — the number of ties. The second line contains one integer $$$b$$$ $$$(1 \\le b \\le 100\\,000)$$$ — the number of scarves. The third line contains one integer $$$c$$$ $$$(1 \\le c \\le 100\\,000)$$$ — the number of vests. The fourth line contains one integer $$$d$$$ $$$(1 \\le d \\le 100\\,000)$$$ — the number of jackets. The fifth line contains one integer $$$e$$$ $$$(1 \\le e \\le 1\\,000)$$$ — the cost of one suit of the first type. The sixth line contains one integer $$$f$$$ $$$(1 \\le f \\le 1\\,000)$$$ — the cost of one suit of the second type.", "output_spec": "Print one integer — the maximum total cost of some set of suits that can be composed from the delivered items. ", "sample_inputs": ["4\n5\n6\n3\n1\n2", "12\n11\n13\n20\n4\n6", "17\n14\n5\n21\n15\n17"], "sample_outputs": ["6", "102", "325"], "notes": "NoteIt is possible to compose three suits of the second type in the first example, and their total cost will be $$$6$$$. Since all jackets will be used, it's impossible to add anything to this set.The best course of action in the second example is to compose nine suits of the first type and eleven suits of the second type. The total cost is $$$9 \\cdot 4 + 11 \\cdot 6 = 102$$$."}, "src_uid": "84d9e7e9c9541d997e6573edb421ae0a"}
{"nl": {"description": "While most students still sit their exams, the tractor college has completed the summer exam session. In fact, students study only one subject at this college — the Art of Operating a Tractor. Therefore, at the end of a term a student gets only one mark, a three (satisfactory), a four (good) or a five (excellent). Those who score lower marks are unfortunately expelled.The college has n students, and oddly enough, each of them can be on scholarship. The size of the scholarships varies each term. Since the end-of-the-term exam has just ended, it's time to determine the size of the scholarship to the end of next term.The monthly budget for the scholarships of the Tractor college is s rubles. To distribute the budget optimally, you must follow these rules:  The students who received the same mark for the exam, should receive the same scholarship; Let us denote the size of the scholarship (in roubles) for students who have received marks 3, 4 and 5 for the exam, as k3, k4 and k5, respectively. The values k3, k4 and k5 must be integers and satisfy the inequalities 0 ≤ k3 ≤ k4 ≤ k5; Let's assume that c3, c4, c5 show how many students received marks 3, 4 and 5 for the exam, respectively. The budget of the scholarship should be fully spent on them, that is, c3·k3 + c4·k4 + c5·k5 = s; Let's introduce function  — the value that shows how well the scholarships are distributed between students. In the optimal distribution function f(k3, k4, k5) takes the minimum possible value. Given the results of the exam, and the budget size s, you have to find the optimal distribution of the scholarship.", "input_spec": "The first line has two integers n, s (3 ≤ n ≤ 300, 1 ≤ s ≤ 3·105) — the number of students and the budget size for the scholarship, respectively. The second line contains n integers, where the i-th number represents the mark that the i-th student got for the exam. It is guaranteed that at each mark was given to at least one student.", "output_spec": "On a single line print three integers k3, k4 and k5 — the sought values that represent the optimal distribution of the scholarships. If there are multiple optimal answers, print any of them. If there is no answer, print -1.", "sample_inputs": ["5 11\n3 4 3 5 5", "6 15\n5 3 3 4 4 5"], "sample_outputs": ["1 3 3", "-1"], "notes": null}, "src_uid": "3f3eb49a127768139283ac04ee44950f"}
{"nl": {"description": "Fafa owns a company that works on huge projects. There are n employees in Fafa's company. Whenever the company has a new project to start working on, Fafa has to divide the tasks of this project among all the employees.Fafa finds doing this every time is very tiring for him. So, he decided to choose the best l employees in his company as team leaders. Whenever there is a new project, Fafa will divide the tasks among only the team leaders and each team leader will be responsible of some positive number of employees to give them the tasks. To make this process fair for the team leaders, each one of them should be responsible for the same number of employees. Moreover, every employee, who is not a team leader, has to be under the responsibility of exactly one team leader, and no team leader is responsible for another team leader.Given the number of employees n, find in how many ways Fafa could choose the number of team leaders l in such a way that it is possible to divide employees between them evenly.", "input_spec": "The input consists of a single line containing a positive integer n (2 ≤ n ≤ 105) — the number of employees in Fafa's company.", "output_spec": "Print a single integer representing the answer to the problem.", "sample_inputs": ["2", "10"], "sample_outputs": ["1", "3"], "notes": "NoteIn the second sample Fafa has 3 ways:  choose only 1 employee as a team leader with 9 employees under his responsibility.  choose 2 employees as team leaders with 4 employees under the responsibility of each of them.  choose 5 employees as team leaders with 1 employee under the responsibility of each of them. "}, "src_uid": "89f6c1659e5addbf909eddedb785d894"}
{"nl": {"description": "One Sunday Petr went to a bookshop and bought a new book on sports programming. The book had exactly n pages.Petr decided to start reading it starting from the next day, that is, from Monday. Petr's got a very tight schedule and for each day of the week he knows how many pages he will be able to read on that day. Some days are so busy that Petr will have no time to read whatsoever. However, we know that he will be able to read at least one page a week.Assuming that Petr will not skip days and will read as much as he can every day, determine on which day of the week he will read the last page of the book.", "input_spec": "The first input line contains the single integer n (1 ≤ n ≤ 1000) — the number of pages in the book. The second line contains seven non-negative space-separated integers that do not exceed 1000 — those integers represent how many pages Petr can read on Monday, Tuesday, Wednesday, Thursday, Friday, Saturday and Sunday correspondingly. It is guaranteed that at least one of those numbers is larger than zero.", "output_spec": "Print a single number — the number of the day of the week, when Petr will finish reading the book. The days of the week are numbered starting with one in the natural order: Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday.", "sample_inputs": ["100\n15 20 20 15 10 30 45", "2\n1 0 0 0 0 0 0"], "sample_outputs": ["6", "1"], "notes": "NoteNote to the first sample:By the end of Monday and therefore, by the beginning of Tuesday Petr has 85 pages left. He has 65 pages left by Wednesday, 45 by Thursday, 30 by Friday, 20 by Saturday and on Saturday Petr finishes reading the book (and he also has time to read 10 pages of something else).Note to the second sample:On Monday of the first week Petr will read the first page. On Monday of the second week Petr will read the second page and will finish reading the book."}, "src_uid": "007a779d966e2e9219789d6d9da7002c"}
{"nl": {"description": "You can not just take the file and send it. When Polycarp trying to send a file in the social network \"Codehorses\", he encountered an unexpected problem. If the name of the file contains three or more \"x\" (lowercase Latin letters \"x\") in a row, the system considers that the file content does not correspond to the social network topic. In this case, the file is not sent and an error message is displayed.Determine the minimum number of characters to remove from the file name so after that the name does not contain \"xxx\" as a substring. Print 0 if the file name does not initially contain a forbidden substring \"xxx\".You can delete characters in arbitrary positions (not necessarily consecutive). If you delete a character, then the length of a string is reduced by $$$1$$$. For example, if you delete the character in the position $$$2$$$ from the string \"exxxii\", then the resulting string is \"exxii\".", "input_spec": "The first line contains integer $$$n$$$ $$$(3 \\le n \\le 100)$$$ — the length of the file name. The second line contains a string of length $$$n$$$ consisting of lowercase Latin letters only — the file name.", "output_spec": "Print the minimum number of characters to remove from the file name so after that the name does not contain \"xxx\" as a substring. If initially the file name dost not contain a forbidden substring \"xxx\", print 0.", "sample_inputs": ["6\nxxxiii", "5\nxxoxx", "10\nxxxxxxxxxx"], "sample_outputs": ["1", "0", "8"], "notes": "NoteIn the first example Polycarp tried to send a file with name contains number $$$33$$$, written in Roman numerals. But he can not just send the file, because it name contains three letters \"x\" in a row. To send the file he needs to remove any one of this letters."}, "src_uid": "8de14db41d0acee116bd5d8079cb2b02"}
{"nl": {"description": "Calvin the robot lies in an infinite rectangular grid. Calvin's source code contains a list of n commands, each either 'U', 'R', 'D', or 'L' — instructions to move a single square up, right, down, or left, respectively. How many ways can Calvin execute a non-empty contiguous substrings of commands and return to the same square he starts in? Two substrings are considered different if they have different starting or ending indices.", "input_spec": "The first line of the input contains a single positive integer, n (1 ≤ n ≤ 200) — the number of commands. The next line contains n characters, each either 'U', 'R', 'D', or 'L' — Calvin's source code.", "output_spec": "Print a single integer — the number of contiguous substrings that Calvin can execute and return to his starting square.", "sample_inputs": ["6\nURLLDR", "4\nDLUU", "7\nRLRLRLR"], "sample_outputs": ["2", "0", "12"], "notes": "NoteIn the first case, the entire source code works, as well as the \"RL\" substring in the second and third characters.Note that, in the third case, the substring \"LR\" appears three times, and is therefore counted three times to the total result."}, "src_uid": "7bd5521531950e2de9a7b0904353184d"}
{"nl": {"description": "The recent All-Berland Olympiad in Informatics featured n participants with each scoring a certain amount of points.As the head of the programming committee, you are to determine the set of participants to be awarded with diplomas with respect to the following criteria:   At least one participant should get a diploma.  None of those with score equal to zero should get awarded.  When someone is awarded, all participants with score not less than his score should also be awarded. Determine the number of ways to choose a subset of participants that will receive the diplomas.", "input_spec": "The first line contains a single integer n (1 ≤ n ≤ 100) — the number of participants. The next line contains a sequence of n integers a1, a2, ..., an (0 ≤ ai ≤ 600) — participants' scores. It's guaranteed that at least one participant has non-zero score.", "output_spec": "Print a single integer — the desired number of ways.", "sample_inputs": ["4\n1 3 3 2", "3\n1 1 1", "4\n42 0 0 42"], "sample_outputs": ["3", "1", "1"], "notes": "NoteThere are three ways to choose a subset in sample case one.  Only participants with 3 points will get diplomas.  Participants with 2 or 3 points will get diplomas.  Everyone will get a diploma! The only option in sample case two is to award everyone.Note that in sample case three participants with zero scores cannot get anything."}, "src_uid": "3b520c15ea9a11b16129da30dcfb5161"}
{"nl": {"description": "Arthur and Alexander are number busters. Today they've got a competition. Arthur took a group of four integers a, b, w, x (0 ≤ b < w, 0 < x < w) and Alexander took integer с. Arthur and Alexander use distinct approaches to number bustings. Alexander is just a regular guy. Each second, he subtracts one from his number. In other words, he performs the assignment: c = c - 1. Arthur is a sophisticated guy. Each second Arthur performs a complex operation, described as follows: if b ≥ x, perform the assignment b = b - x, if b < x, then perform two consecutive assignments a = a - 1; b = w - (x - b).You've got numbers a, b, w, x, c. Determine when Alexander gets ahead of Arthur if both guys start performing the operations at the same time. Assume that Alexander got ahead of Arthur if c ≤ a.", "input_spec": "The first line contains integers a, b, w, x, c (1 ≤ a ≤ 2·109, 1 ≤ w ≤ 1000, 0 ≤ b < w, 0 < x < w, 1 ≤ c ≤ 2·109).", "output_spec": "Print a single integer — the minimum time in seconds Alexander needs to get ahead of Arthur. You can prove that the described situation always occurs within the problem's limits.", "sample_inputs": ["4 2 3 1 6", "4 2 3 1 7", "1 2 3 2 6", "1 1 2 1 1"], "sample_outputs": ["2", "4", "13", "0"], "notes": null}, "src_uid": "a1db3dd9f8d0f0cad7bdeb1780707143"}
{"nl": {"description": "Amr bought a new video game \"Guess Your Way Out!\". The goal of the game is to find an exit from the maze that looks like a perfect binary tree of height h. The player is initially standing at the root of the tree and the exit from the tree is located at some leaf node. Let's index all the leaf nodes from the left to the right from 1 to 2h. The exit is located at some node n where 1 ≤ n ≤ 2h, the player doesn't know where the exit is so he has to guess his way out!Amr follows simple algorithm to choose the path. Let's consider infinite command string \"LRLRLRLRL...\" (consisting of alternating characters 'L' and 'R'). Amr sequentially executes the characters of the string using following rules:  Character 'L' means \"go to the left child of the current node\";  Character 'R' means \"go to the right child of the current node\";  If the destination node is already visited, Amr skips current command, otherwise he moves to the destination node;  If Amr skipped two consecutive commands, he goes back to the parent of the current node before executing next command;  If he reached a leaf node that is not the exit, he returns to the parent of the current node;  If he reaches an exit, the game is finished. Now Amr wonders, if he follows this algorithm, how many nodes he is going to visit before reaching the exit?", "input_spec": "Input consists of two integers h, n (1 ≤ h ≤ 50, 1 ≤ n ≤ 2h).", "output_spec": "Output a single integer representing the number of nodes (excluding the exit node) Amr is going to visit before reaching the exit by following this algorithm.", "sample_inputs": ["1 2", "2 3", "3 6", "10 1024"], "sample_outputs": ["2", "5", "10", "2046"], "notes": "NoteA perfect binary tree of height h is a binary tree consisting of h + 1 levels. Level 0 consists of a single node called root, level h consists of 2h nodes called leaves. Each node that is not a leaf has exactly two children, left and right one. Following picture illustrates the sample test number 3. Nodes are labeled according to the order of visit."}, "src_uid": "3dc25ccb394e2d5ceddc6b3a26cb5781"}
{"nl": {"description": "Not so long ago as a result of combat operations the main Berland place of interest — the magic clock — was damaged. The cannon's balls made several holes in the clock, that's why the residents are concerned about the repair. The magic clock can be represented as an infinite Cartesian plane, where the origin corresponds to the clock center. The clock was painted two colors as is shown in the picture:  The picture shows only the central part of the clock. This coloring naturally extends to infinity.The balls can be taken to be points on the plane. Your task is to find the color of the area, damaged by the given ball.All the points located on the border of one of the areas have to be considered painted black.", "input_spec": "The first and single line contains two integers x and y — the coordinates of the hole made in the clock by the ball. Each of the numbers x and y has an absolute value that does not exceed 1000.", "output_spec": "Find the required color. All the points between which and the origin of coordinates the distance is integral-value are painted black.", "sample_inputs": ["-2 1", "2 1", "4 3"], "sample_outputs": ["white", "black", "black"], "notes": null}, "src_uid": "8c92aac1bef5822848a136a1328346c6"}
{"nl": {"description": "The hero of our story, Valera, and his best friend Arcady are still in school, and therefore they spend all the free time playing turn-based strategy \"GAGA: Go And Go Again\". The gameplay is as follows. There are two armies on the playing field each of which consists of n men (n is always even). The current player specifies for each of her soldiers an enemy's soldier he will shoot (a target) and then all the player's soldiers shot simultaneously. This is a game world, and so each soldier shoots perfectly, that is he absolutely always hits the specified target. If an enemy soldier is hit, he will surely die. It may happen that several soldiers had been indicated the same target. Killed soldiers do not participate in the game anymore. The game \"GAGA\" consists of three steps: first Valera makes a move, then Arcady, then Valera again and the game ends. You are asked to calculate the maximum total number of soldiers that may be killed during the game. ", "input_spec": "The input data consist of a single integer n (2 ≤ n ≤ 108, n is even). Please note that before the game starts there are 2n soldiers on the fields. ", "output_spec": "Print a single number — a maximum total number of soldiers that could be killed in the course of the game in three turns.", "sample_inputs": ["2", "4"], "sample_outputs": ["3", "6"], "notes": "NoteThe first sample test:1) Valera's soldiers 1 and 2 shoot at Arcady's soldier 1.2) Arcady's soldier 2 shoots at Valera's soldier 1.3) Valera's soldier 1 shoots at Arcady's soldier 2.There are 3 soldiers killed in total: Valera's soldier 1 and Arcady's soldiers 1 and 2."}, "src_uid": "031e53952e76cff8fdc0988bb0d3239c"}
{"nl": {"description": "Fox Ciel has a robot on a 2D plane. Initially it is located in (0, 0). Fox Ciel code a command to it. The command was represented by string s. Each character of s is one move operation. There are four move operations at all:  'U': go up, (x, y)  →  (x, y+1);  'D': go down, (x, y)  →  (x, y-1);  'L': go left, (x, y)  →  (x-1, y);  'R': go right, (x, y)  →  (x+1, y). The robot will do the operations in s from left to right, and repeat it infinite times. Help Fox Ciel to determine if after some steps the robot will located in (a, b).", "input_spec": "The first line contains two integers a and b, ( - 109 ≤ a, b ≤ 109). The second line contains a string s (1 ≤ |s| ≤ 100, s only contains characters 'U', 'D', 'L', 'R') — the command.", "output_spec": "Print \"Yes\" if the robot will be located at (a, b), and \"No\" otherwise.", "sample_inputs": ["2 2\nRU", "1 2\nRU", "-1 1000000000\nLRRLU", "0 0\nD"], "sample_outputs": ["Yes", "No", "Yes", "Yes"], "notes": "NoteIn the first and second test case, command string is \"RU\", so the robot will go right, then go up, then right, and then up and so on.The locations of its moves are (0, 0)  →  (1, 0)  →  (1, 1)  →  (2, 1)  →  (2, 2)  →  ...So it can reach (2, 2) but not (1, 2)."}, "src_uid": "5d6212e28c7942e9ff4d096938b782bf"}
{"nl": {"description": "There are $$$n$$$ students in a university. The number of students is even. The $$$i$$$-th student has programming skill equal to $$$a_i$$$. The coach wants to form $$$\\frac{n}{2}$$$ teams. Each team should consist of exactly two students, and each student should belong to exactly one team. Two students can form a team only if their skills are equal (otherwise they cannot understand each other and cannot form a team).Students can solve problems to increase their skill. One solved problem increases the skill by one.The coach wants to know the minimum total number of problems students should solve to form exactly $$$\\frac{n}{2}$$$ teams (i.e. each pair of students should form a team). Your task is to find this number.", "input_spec": "The first line of the input contains one integer $$$n$$$ ($$$2 \\le n \\le 100$$$) — the number of students. It is guaranteed that $$$n$$$ is even. The second line of the input contains $$$n$$$ integers $$$a_1, a_2, \\dots, a_n$$$ ($$$1 \\le a_i \\le 100$$$), where $$$a_i$$$ is the skill of the $$$i$$$-th student.", "output_spec": "Print one number — the minimum total number of problems students should solve to form exactly $$$\\frac{n}{2}$$$ teams.", "sample_inputs": ["6\n5 10 2 3 14 5", "2\n1 100"], "sample_outputs": ["5", "99"], "notes": "NoteIn the first example the optimal teams will be: $$$(3, 4)$$$, $$$(1, 6)$$$ and $$$(2, 5)$$$, where numbers in brackets are indices of students. Then, to form the first team the third student should solve $$$1$$$ problem, to form the second team nobody needs to solve problems and to form the third team the second student should solve $$$4$$$ problems so the answer is $$$1 + 4 = 5$$$.In the second example the first student should solve $$$99$$$ problems to form a team with the second one."}, "src_uid": "55485fe203a114374f0aae93006278d3"}
{"nl": {"description": "Alice is the leader of the State Refactoring Party, and she is about to become the prime minister. The elections have just taken place. There are $$$n$$$ parties, numbered from $$$1$$$ to $$$n$$$. The $$$i$$$-th party has received $$$a_i$$$ seats in the parliament.Alice's party has number $$$1$$$. In order to become the prime minister, she needs to build a coalition, consisting of her party and possibly some other parties. There are two conditions she needs to fulfil:   The total number of seats of all parties in the coalition must be a strict majority of all the seats, i.e. it must have strictly more than half of the seats. For example, if the parliament has $$$200$$$ (or $$$201$$$) seats, then the majority is $$$101$$$ or more seats.  Alice's party must have at least $$$2$$$ times more seats than any other party in the coalition. For example, to invite a party with $$$50$$$ seats, Alice's party must have at least $$$100$$$ seats. For example, if $$$n=4$$$ and $$$a=[51, 25, 99, 25]$$$ (note that Alice'a party has $$$51$$$ seats), then the following set $$$[a_1=51, a_2=25, a_4=25]$$$ can create a coalition since both conditions will be satisfied. However, the following sets will not create a coalition:  $$$[a_2=25, a_3=99, a_4=25]$$$ since Alice's party is not there;  $$$[a_1=51, a_2=25]$$$ since coalition should have a strict majority;  $$$[a_1=51, a_2=25, a_3=99]$$$ since Alice's party should have at least $$$2$$$ times more seats than any other party in the coalition. Alice does not have to minimise the number of parties in a coalition. If she wants, she can invite as many parties as she wants (as long as the conditions are satisfied). If Alice's party has enough people to create a coalition on her own, she can invite no parties.Note that Alice can either invite a party as a whole or not at all. It is not possible to invite only some of the deputies (seats) from another party. In other words, if Alice invites a party, she invites all its deputies.Find and print any suitable coalition.", "input_spec": "The first line contains a single integer $$$n$$$ ($$$2 \\leq n \\leq 100$$$) — the number of parties. The second line contains $$$n$$$ space separated integers $$$a_1, a_2, \\dots, a_n$$$ ($$$1 \\leq a_i \\leq 100$$$) — the number of seats the $$$i$$$-th party has.", "output_spec": "If no coalition satisfying both conditions is possible, output a single line with an integer $$$0$$$. Otherwise, suppose there are $$$k$$$ ($$$1 \\leq k \\leq n$$$) parties in the coalition (Alice does not have to minimise the number of parties in a coalition), and their indices are $$$c_1, c_2, \\dots, c_k$$$ ($$$1 \\leq c_i \\leq n$$$). Output two lines, first containing the integer $$$k$$$, and the second the space-separated indices $$$c_1, c_2, \\dots, c_k$$$.  You may print the parties in any order. Alice's party (number $$$1$$$) must be on that list. If there are multiple solutions, you may print any of them.", "sample_inputs": ["3\n100 50 50", "3\n80 60 60", "2\n6 5", "4\n51 25 99 25"], "sample_outputs": ["2\n1 2", "0", "1\n1", "3\n1 2 4"], "notes": "NoteIn the first example, Alice picks the second party. Note that she can also pick the third party or both of them. However, she cannot become prime minister without any of them, because $$$100$$$ is not a strict majority out of $$$200$$$.In the second example, there is no way of building a majority, as both other parties are too large to become a coalition partner.In the third example, Alice already has the majority. The fourth example is described in the problem statement."}, "src_uid": "0a71fdaaf08c18396324ad762b7379d7"}
{"nl": {"description": "Petya is a big fan of mathematics, especially its part related to fractions. Recently he learned that a fraction  is called proper iff its numerator is smaller than its denominator (a < b) and that the fraction is called irreducible if its numerator and its denominator are coprime (they do not have positive common divisors except 1).During his free time, Petya thinks about proper irreducible fractions and converts them to decimals using the calculator. One day he mistakenly pressed addition button ( + ) instead of division button (÷) and got sum of numerator and denominator that was equal to n instead of the expected decimal notation. Petya wanted to restore the original fraction, but soon he realized that it might not be done uniquely. That's why he decided to determine maximum possible proper irreducible fraction  such that sum of its numerator and denominator equals n. Help Petya deal with this problem. ", "input_spec": "In the only line of input there is an integer n (3 ≤ n ≤ 1000), the sum of numerator and denominator of the fraction.", "output_spec": "Output two space-separated positive integers a and b, numerator and denominator of the maximum possible proper irreducible fraction satisfying the given sum.", "sample_inputs": ["3", "4", "12"], "sample_outputs": ["1 2", "1 3", "5 7"], "notes": null}, "src_uid": "0af3515ed98d9d01ce00546333e98e77"}
{"nl": {"description": "There are $$$b$$$ boys and $$$g$$$ girls participating in Olympiad of Metropolises. There will be a board games tournament in the evening and $$$n$$$ participants have accepted the invitation. The organizers do not know how many boys and girls are among them.Organizers are preparing red badges for girls and blue ones for boys.Vasya prepared $$$n+1$$$ decks of badges. The $$$i$$$-th (where $$$i$$$ is from $$$0$$$ to $$$n$$$, inclusive) deck contains $$$i$$$ blue badges and $$$n-i$$$ red ones. The total number of badges in any deck is exactly $$$n$$$.Determine the minimum number of decks among these $$$n+1$$$ that Vasya should take, so that there will be a suitable deck no matter how many girls and boys there will be among the participants of the tournament.", "input_spec": "The first line contains an integer $$$b$$$ ($$$1 \\le b \\le 300$$$), the number of boys.  The second line contains an integer $$$g$$$ ($$$1 \\le g \\le 300$$$), the number of girls.  The third line contains an integer $$$n$$$ ($$$1 \\le n \\le b + g$$$), the number of the board games tournament participants.", "output_spec": "Output the only integer, the minimum number of badge decks that Vasya could take.", "sample_inputs": ["5\n6\n3", "5\n3\n5"], "sample_outputs": ["4", "4"], "notes": "NoteIn the first example, each of 4 decks should be taken: (0 blue, 3 red), (1 blue, 2 red), (2 blue, 1 red), (3 blue, 0 red).In the second example, 4 decks should be taken: (2 blue, 3 red), (3 blue, 2 red), (4 blue, 1 red), (5 blue, 0 red). Piles (0 blue, 5 red) and (1 blue, 4 red) can not be used."}, "src_uid": "9266a69e767df299569986151852e7b1"}
{"nl": {"description": "Gennady owns a small hotel in the countryside where he lives a peaceful life. He loves to take long walks, watch sunsets and play cards with tourists staying in his hotel. His favorite game is called \"Mau-Mau\".To play Mau-Mau, you need a pack of $$$52$$$ cards. Each card has a suit (Diamonds — D, Clubs — C, Spades — S, or Hearts — H), and a rank (2, 3, 4, 5, 6, 7, 8, 9, T, J, Q, K, or A).At the start of the game, there is one card on the table and you have five cards in your hand. You can play a card from your hand if and only if it has the same rank or the same suit as the card on the table.In order to check if you'd be a good playing partner, Gennady has prepared a task for you. Given the card on the table and five cards in your hand, check if you can play at least one card.", "input_spec": "The first line of the input contains one string which describes the card on the table. The second line contains five strings which describe the cards in your hand. Each string is two characters long. The first character denotes the rank and belongs to the set $$$\\{{\\tt 2}, {\\tt 3}, {\\tt 4}, {\\tt 5}, {\\tt 6}, {\\tt 7}, {\\tt 8}, {\\tt 9}, {\\tt T}, {\\tt J}, {\\tt Q}, {\\tt K}, {\\tt A}\\}$$$. The second character denotes the suit and belongs to the set $$$\\{{\\tt D}, {\\tt C}, {\\tt S}, {\\tt H}\\}$$$. All the cards in the input are different.", "output_spec": "If it is possible to play a card from your hand, print one word \"YES\". Otherwise, print \"NO\". You can print each letter in any case (upper or lower).", "sample_inputs": ["AS\n2H 4C TH JH AD", "2H\n3D 4C AC KD AS", "4D\nAS AC AD AH 5H"], "sample_outputs": ["YES", "NO", "YES"], "notes": "NoteIn the first example, there is an Ace of Spades (AS) on the table. You can play an Ace of Diamonds (AD) because both of them are Aces.In the second example, you cannot play any card.In the third example, you can play an Ace of Diamonds (AD) because it has the same suit as a Four of Diamonds (4D), which lies on the table."}, "src_uid": "699444eb6366ad12bc77e7ac2602d74b"}
{"nl": {"description": "Anna's got a birthday today. She invited many guests and cooked a huge (nearly infinite) birthday cake decorated by n banana circles of different sizes. Maria's birthday is about to start in 7 minutes too, and while Anna is older, she decided to play the boss a little. She told Maria to cut the cake by k straight-line cuts (the cutting lines can intersect) to divide banana circles into banana pieces. Anna has many guests and she wants everyone to get at least one banana piece. That's why she told Maria to make the total number of banana pieces maximum. It's not a problem if some banana pieces end up on the same cake piece — the key is to make the maximum number of banana pieces. Determine what result Maria will achieve.", "input_spec": "The first line contains two integers n and k — the number of banana circles and the number of cuts Maria should perform (1 ≤ n ≤ 1000, 1 ≤ k ≤ 105). Next n lines contain the positions and sizes of the banana circles (all banana circles are round). On the cake the Cartesian coordinate system is defined. Each line contains three integers x, y and r — the coordinates of the center of the corresponding banana piece and its radius ( - 1000 ≤ x, y ≤ 1000, 1 ≤ r ≤ 1000). It is guaranteed that the banana circles do not intersect, do not touch each other and do not overlap with each other. Pretest 10 is big test with n = k = 1000.", "output_spec": "Print the only integer — the largest number of banana pieces that Maria can get after she performs the k straight-line cuts. Please do not use the %lld specificator to read or write 64-bit integers in C++. It is preferred to use the cin, cout streams or the %I64d specificator.", "sample_inputs": ["1 1\n0 0 1", "3 1\n0 0 1\n3 0 1\n6 0 1", "1 3\n0 0 1"], "sample_outputs": ["2", "6", "7"], "notes": null}, "src_uid": "06ec7e481c963e635a6303503ffccc8b"}
{"nl": {"description": "You are given an integer $$$n$$$ from $$$1$$$ to $$$10^{18}$$$ without leading zeroes.In one move you can swap any two adjacent digits in the given number in such a way that the resulting number will not contain leading zeroes. In other words, after each move the number you have cannot contain any leading zeroes.What is the minimum number of moves you have to make to obtain a number that is divisible by $$$25$$$? Print -1 if it is impossible to obtain a number that is divisible by $$$25$$$.", "input_spec": "The first line contains an integer $$$n$$$ ($$$1 \\le n \\le 10^{18}$$$). It is guaranteed that the first (left) digit of the number $$$n$$$ is not a zero.", "output_spec": "If it is impossible to obtain a number that is divisible by $$$25$$$, print -1. Otherwise print the minimum number of moves required to obtain such number. Note that you can swap only adjacent digits in the given number.", "sample_inputs": ["5071", "705", "1241367"], "sample_outputs": ["4", "1", "-1"], "notes": "NoteIn the first example one of the possible sequences of moves is 5071 $$$\\rightarrow$$$ 5701 $$$\\rightarrow$$$ 7501 $$$\\rightarrow$$$ 7510 $$$\\rightarrow$$$ 7150."}, "src_uid": "ea1c737956f88be94107f2565ca8bbfd"}
{"nl": {"description": "Some country is populated by wizards. They want to organize a demonstration.There are n people living in the city, x of them are the wizards who will surely go to the demonstration. Other city people (n - x people) do not support the wizards and aren't going to go to the demonstration. We know that the city administration will react only to the demonstration involving at least y percent of the city people. Having considered the matter, the wizards decided to create clone puppets which can substitute the city people on the demonstration. So all in all, the demonstration will involve only the wizards and their puppets. The city administration cannot tell the difference between a puppet and a person, so, as they calculate the percentage, the administration will consider the city to be consisting of only n people and not containing any clone puppets. Help the wizards and find the minimum number of clones to create to that the demonstration had no less than y percent of the city people.", "input_spec": "The first line contains three space-separated integers, n, x, y (1 ≤ n, x, y ≤ 104, x ≤ n) — the number of citizens in the city, the number of wizards and the percentage the administration needs, correspondingly. Please note that y can exceed 100 percent, that is, the administration wants to see on a demonstration more people that actually live in the city ( > n).", "output_spec": "Print a single integer — the answer to the problem, the minimum number of clones to create, so that the demonstration involved no less than y percent of n (the real total city population). ", "sample_inputs": ["10 1 14", "20 10 50", "1000 352 146"], "sample_outputs": ["1", "0", "1108"], "notes": "NoteIn the first sample it is necessary that at least 14% of 10 people came to the demonstration. As the number of people should be integer, then at least two people should come. There is only one wizard living in the city and he is going to come. That isn't enough, so he needs to create one clone. In the second sample 10 people should come to the demonstration. The city has 10 wizards. They will all come to the demonstration, so nobody has to create any clones."}, "src_uid": "7038d7b31e1900588da8b61b325e4299"}
{"nl": {"description": "На координатной прямой сидит n собачек, i-я собачка находится в точке xi. Кроме того, на прямой есть m мисок с едой, для каждой известна её координата на прямой uj и время tj, через которое еда в миске остынет и станет невкусной. Это значит, что если собачка прибежит к миске в момент времени, строго больший tj, то еда уже остынет, и собачка кушать её не станет.Считая, что каждая собачка бежит со скоростью 1, найдите максимальное количество собачек, которые смогут покушать. Считайте, что собачки побегут к тем мискам, на которые вы им укажете. Из одной миски не могут кушать две или более собачки.Собачки могут обгонять друг друга, то есть, если одна из них остановится покушать, другая может пройти мимо неё, чтобы попасть к другой миске.", "input_spec": "В первой строке находится пара целых чисел n и m (1 ≤ n, m ≤ 200 000) — количество собачек и мисок соответственно. Во второй строке находятся n целых чисел xi ( - 109 ≤ xi ≤ 109) — координата i-й собачки. В следующих m строках находятся пары целых чисел uj и tj ( - 109 ≤ uj ≤ 109, 1 ≤ tj ≤ 109) — координата j-й миски и время, когда остынет еда в ней, соответственно. Гарантируется, что никакие две собачки не находятся в одной точке. Никакие две миски также не могут находиться в одной точке.", "output_spec": "Выведите одно целое число a — максимальное количество собачек, которые смогут покушать.", "sample_inputs": ["5 4\n-2 0 4 8 13\n-1 1\n4 3\n6 3\n11 2", "3 3\n-1 3 7\n1 1\n4 1\n7 1", "4 4\n20 1 10 30\n1 1\n2 5\n22 2\n40 10"], "sample_outputs": ["4", "2", "3"], "notes": "ПримечаниеВ первом примере первая собачка побежит направо к первой миске, третья собачка сразу начнёт есть из второй миски, четвёртая собачка побежит влево к третьей миске, а пятая собачка побежит влево к четвёртой миске."}, "src_uid": "04375596477fc65a2093554ff7b7934d"}
{"nl": {"description": "Polycarp decided to relax on his weekend and visited to the performance of famous ropewalkers: Agafon, Boniface and Konrad.The rope is straight and infinite in both directions. At the beginning of the performance, Agafon, Boniface and Konrad are located in positions $$$a$$$, $$$b$$$ and $$$c$$$ respectively. At the end of the performance, the distance between each pair of ropewalkers was at least $$$d$$$.Ropewalkers can walk on the rope. In one second, only one ropewalker can change his position. Every ropewalker can change his position exactly by $$$1$$$ (i. e. shift by $$$1$$$ to the left or right direction on the rope). Agafon, Boniface and Konrad can not move at the same time (Only one of them can move at each moment). Ropewalkers can be at the same positions at the same time and can \"walk past each other\".You should find the minimum duration (in seconds) of the performance. In other words, find the minimum number of seconds needed so that the distance between each pair of ropewalkers can be greater or equal to $$$d$$$.Ropewalkers can walk to negative coordinates, due to the rope is infinite to both sides.", "input_spec": "The only line of the input contains four integers $$$a$$$, $$$b$$$, $$$c$$$, $$$d$$$ ($$$1 \\le a, b, c, d \\le 10^9$$$). It is possible that any two (or all three) ropewalkers are in the same position at the beginning of the performance.", "output_spec": "Output one integer — the minimum duration (in seconds) of the performance.", "sample_inputs": ["5 2 6 3", "3 1 5 6", "8 3 3 2", "2 3 10 4"], "sample_outputs": ["2", "8", "2", "3"], "notes": "NoteIn the first example: in the first two seconds Konrad moves for 2 positions to the right (to the position $$$8$$$), while Agafon and Boniface stay at their positions. Thus, the distance between Agafon and Boniface will be $$$|5 - 2| = 3$$$, the distance between Boniface and Konrad will be $$$|2 - 8| = 6$$$ and the distance between Agafon and Konrad will be $$$|5 - 8| = 3$$$. Therefore, all three pairwise distances will be at least $$$d=3$$$, so the performance could be finished within 2 seconds."}, "src_uid": "47c07e46517dbc937e2e779ec0d74eb3"}
{"nl": {"description": "Limak is a little polar bear. He plays by building towers from blocks. Every block is a cube with positive integer length of side. Limak has infinitely many blocks of each side length.A block with side a has volume a3. A tower consisting of blocks with sides a1, a2, ..., ak has the total volume a13 + a23 + ... + ak3.Limak is going to build a tower. First, he asks you to tell him a positive integer X — the required total volume of the tower. Then, Limak adds new blocks greedily, one by one. Each time he adds the biggest block such that the total volume doesn't exceed X.Limak asks you to choose X not greater than m. Also, he wants to maximize the number of blocks in the tower at the end (however, he still behaves greedily). Secondarily, he wants to maximize X.Can you help Limak? Find the maximum number of blocks his tower can have and the maximum X ≤ m that results this number of blocks.", "input_spec": "The only line of the input contains one integer m (1 ≤ m ≤ 1015), meaning that Limak wants you to choose X between 1 and m, inclusive.", "output_spec": "Print two integers — the maximum number of blocks in the tower and the maximum required total volume X, resulting in the maximum number of blocks.", "sample_inputs": ["48", "6"], "sample_outputs": ["9 42", "6 6"], "notes": "NoteIn the first sample test, there will be 9 blocks if you choose X = 23 or X = 42. Limak wants to maximize X secondarily so you should choose 42.In more detail, after choosing X = 42 the process of building a tower is:  Limak takes a block with side 3 because it's the biggest block with volume not greater than 42. The remaining volume is 42 - 27 = 15.  The second added block has side 2, so the remaining volume is 15 - 8 = 7.  Finally, Limak adds 7 blocks with side 1, one by one. So, there are 9 blocks in the tower. The total volume is is 33 + 23 + 7·13 = 27 + 8 + 7 = 42."}, "src_uid": "385cf3c40c96f0879788b766eeb25139"}
{"nl": {"description": "So nearly half of the winter is over and Maria is dreaming about summer. She's fed up with skates and sleds, she was dreaming about Hopscotch all night long. It's a very popular children's game. The game field, the court, looks as is shown in the figure (all blocks are square and are numbered from bottom to top, blocks in the same row are numbered from left to right). Let us describe the hopscotch with numbers that denote the number of squares in the row, staring from the lowest one: 1-1-2-1-2-1-2-(1-2)..., where then the period is repeated (1-2).  The coordinate system is defined as shown in the figure. Side of all the squares are equal and have length a.Maria is a very smart and clever girl, and she is concerned with quite serious issues: if she throws a stone into a point with coordinates (x, y), then will she hit some square? If the answer is positive, you are also required to determine the number of the square.It is believed that the stone has fallen into the square if it is located strictly inside it. In other words a stone that has fallen on the square border is not considered a to hit a square.", "input_spec": "The only input line contains three integers: a, x, y, where a (1 ≤ a ≤ 100) is the side of the square, x and y ( - 106 ≤ x ≤ 106, 0 ≤ y ≤ 106) are coordinates of the stone.", "output_spec": "Print the number of the square, inside which the stone fell. If the stone is on a border of some stone or outside the court, print \"-1\" without the quotes.", "sample_inputs": ["1 0 0", "3 1 1", "3 0 10", "3 0 7", "3 4 0"], "sample_outputs": ["-1", "1", "5", "-1", "-1"], "notes": null}, "src_uid": "cf48ff6ba3e77ba5d4afccb8f775fb02"}
{"nl": {"description": "One day, Hongcow goes to the store and sees a brand new deck of n special cards. Each individual card is either red or blue. He decides he wants to buy them immediately. To do this, he needs to play a game with the owner of the store.This game takes some number of turns to complete. On a turn, Hongcow may do one of two things:   Collect tokens. Hongcow collects 1 red token and 1 blue token by choosing this option (thus, 2 tokens in total per one operation).  Buy a card. Hongcow chooses some card and spends tokens to purchase it as specified below. The i-th card requires ri red resources and bi blue resources. Suppose Hongcow currently has A red cards and B blue cards. Then, the i-th card will require Hongcow to spend max(ri - A, 0) red tokens, and max(bi - B, 0) blue tokens. Note, only tokens disappear, but the cards stay with Hongcow forever. Each card can be bought only once.Given a description of the cards and their costs determine the minimum number of turns Hongcow needs to purchase all cards.", "input_spec": "The first line of input will contain a single integer n (1 ≤ n ≤ 16). The next n lines of input will contain three tokens ci, ri and bi. ci will be 'R' or 'B', denoting the color of the card as red or blue. ri will be an integer denoting the amount of red resources required to obtain the card, and bi will be an integer denoting the amount of blue resources required to obtain the card (0 ≤ ri, bi ≤ 107).", "output_spec": "Output a single integer, denoting the minimum number of turns needed to acquire all the cards.", "sample_inputs": ["3\nR 0 1\nB 1 0\nR 1 1", "3\nR 3 0\nR 2 0\nR 1 0"], "sample_outputs": ["4", "6"], "notes": "NoteFor the first sample, Hongcow's four moves are as follows:   Collect tokens  Buy card 1  Buy card 2  Buy card 3  Note, at the fourth step, Hongcow is able to buy card 3 because Hongcow already has one red and one blue card, so we don't need to collect tokens.For the second sample, one optimal strategy is as follows:   Collect tokens  Collect tokens  Buy card 2  Collect tokens  Buy card 3  Buy card 1  At the fifth step, even though Hongcow has a red token, Hongcow doesn't actually need to spend it, since Hongcow has a red card already."}, "src_uid": "25a77f2b7cb281ff3c7800a20b3e5969"}
{"nl": {"description": "You have a given integer $$$n$$$. Find the number of ways to fill all $$$3 \\times n$$$ tiles with the shape described in the picture below. Upon filling, no empty spaces are allowed. Shapes cannot overlap.  This picture describes when $$$n = 4$$$. The left one is the shape and the right one is $$$3 \\times n$$$ tiles. ", "input_spec": "The only line contains one integer $$$n$$$ ($$$1 \\le n \\le 60$$$) — the length.", "output_spec": "Print the number of ways to fill.", "sample_inputs": ["4", "1"], "sample_outputs": ["4", "0"], "notes": "NoteIn the first example, there are $$$4$$$ possible cases of filling.In the second example, you cannot fill the shapes in $$$3 \\times 1$$$ tiles."}, "src_uid": "4b7ff467ed5907e32fd529fb39b708db"}
{"nl": {"description": "Several ages ago Berland was a kingdom. The King of Berland adored math. That's why, when he first visited one of his many palaces, he first of all paid attention to the floor in one hall. The floor was tiled with hexagonal tiles.The hall also turned out hexagonal in its shape. The King walked along the perimeter of the hall and concluded that each of the six sides has a, b, c, a, b and c adjacent tiles, correspondingly.To better visualize the situation, look at the picture showing a similar hexagon for a = 2, b = 3 and c = 4.  According to the legend, as the King of Berland obtained the values a, b and c, he almost immediately calculated the total number of tiles on the hall floor. Can you do the same?", "input_spec": "The first line contains three integers: a, b and c (2 ≤ a, b, c ≤ 1000).", "output_spec": "Print a single number — the total number of tiles on the hall floor.", "sample_inputs": ["2 3 4"], "sample_outputs": ["18"], "notes": null}, "src_uid": "8ab25ed4955d978fe20f6872cb94b0da"}
{"nl": {"description": "Two players are playing a game. First each of them writes an integer from 1 to 6, and then a dice is thrown. The player whose written number got closer to the number on the dice wins. If both payers have the same difference, it's a draw.The first player wrote number a, the second player wrote number b. How many ways to throw a dice are there, at which the first player wins, or there is a draw, or the second player wins?", "input_spec": "The single line contains two integers a and b (1 ≤ a, b ≤ 6) — the numbers written on the paper by the first and second player, correspondingly.", "output_spec": "Print three integers: the number of ways to throw the dice at which the first player wins, the game ends with a draw or the second player wins, correspondingly.", "sample_inputs": ["2 5", "2 4"], "sample_outputs": ["3 0 3", "2 1 3"], "notes": "NoteThe dice is a standard cube-shaped six-sided object with each side containing a number from 1 to 6, and where all numbers on all sides are distinct.You can assume that number a is closer to number x than number b, if |a - x| < |b - x|."}, "src_uid": "504b8aae3a3abedf873a3b8b127c5dd8"}
{"nl": {"description": "There is a new TV game on BerTV. In this game two players get a number A consisting of 2n digits. Before each turn players determine who will make the next move. Each player should make exactly n moves. On it's turn i-th player takes the leftmost digit of A and appends it to his or her number Si. After that this leftmost digit is erased from A. Initially the numbers of both players (S1 and S2) are «empty». Leading zeroes in numbers A, S1, S2 are allowed. In the end of the game the first player gets S1 dollars, and the second gets S2 dollars.One day Homer and Marge came to play the game. They managed to know the number A beforehand. They want to find such sequence of their moves that both of them makes exactly n moves and which maximizes their total prize. Help them.", "input_spec": "The first line contains integer n (1 ≤ n ≤ 18). The second line contains integer A consisting of exactly 2n digits. This number can have leading zeroes.", "output_spec": "Output the line of 2n characters «H» and «M» — the sequence of moves of Homer and Marge, which gives them maximum possible total prize. Each player must make exactly n moves. If there are several solutions, output any of them.", "sample_inputs": ["2\n1234", "2\n9911"], "sample_outputs": ["HHMM", "HMHM"], "notes": null}, "src_uid": "98489fe54488dcfb45f8ae7b5c473d88"}
{"nl": {"description": "Little Petya very much likes computers. Recently he has received a new \"Ternatron IV\" as a gift from his mother. Unlike other modern computers, \"Ternatron IV\" operates with ternary and not binary logic. Petya immediately wondered how the xor operation is performed on this computer (and whether there is anything like it).It turned out that the operation does exist (however, it is called tor) and it works like this. Suppose that we need to calculate the value of the expression a tor b. Both numbers a and b are written in the ternary notation one under the other one (b under a). If they have a different number of digits, then leading zeroes are added to the shorter number until the lengths are the same. Then the numbers are summed together digit by digit. The result of summing each two digits is calculated modulo 3. Note that there is no carry between digits (i. e. during this operation the digits aren't transferred). For example: 1410 tor 5010 = 01123 tor 12123 = 10213 = 3410.Petya wrote numbers a and c on a piece of paper. Help him find such number b, that a tor b = c. If there are several such numbers, print the smallest one.", "input_spec": "The first line contains two integers a and c (0 ≤ a, c ≤ 109). Both numbers are written in decimal notation.", "output_spec": "Print the single integer b, such that a tor b = c. If there are several possible numbers b, print the smallest one. You should print the number in decimal notation.", "sample_inputs": ["14 34", "50 34", "387420489 225159023", "5 5"], "sample_outputs": ["50", "14", "1000000001", "0"], "notes": null}, "src_uid": "5fb635d52ddccf6a4d5103805da02a88"}
{"nl": {"description": "Tanechka is shopping in the toy shop. There are exactly $$$n$$$ toys in the shop for sale, the cost of the $$$i$$$-th toy is $$$i$$$ burles. She wants to choose two toys in such a way that their total cost is $$$k$$$ burles. How many ways to do that does she have?Each toy appears in the shop exactly once. Pairs $$$(a, b)$$$ and $$$(b, a)$$$ are considered equal. Pairs $$$(a, b)$$$, where $$$a=b$$$, are not allowed.", "input_spec": "The first line of the input contains two integers $$$n$$$, $$$k$$$ ($$$1 \\le n, k \\le 10^{14}$$$) — the number of toys and the expected total cost of the pair of toys.", "output_spec": "Print the number of ways to choose the pair of toys satisfying the condition above. Print 0, if Tanechka can choose no pair of toys in such a way that their total cost is $$$k$$$ burles.", "sample_inputs": ["8 5", "8 15", "7 20", "1000000000000 1000000000001"], "sample_outputs": ["2", "1", "0", "500000000000"], "notes": "NoteIn the first example Tanechka can choose the pair of toys ($$$1, 4$$$) or the pair of toys ($$$2, 3$$$).In the second example Tanechka can choose only the pair of toys ($$$7, 8$$$).In the third example choosing any pair of toys will lead to the total cost less than $$$20$$$. So the answer is 0.In the fourth example she can choose the following pairs: $$$(1, 1000000000000)$$$, $$$(2, 999999999999)$$$, $$$(3, 999999999998)$$$, ..., $$$(500000000000, 500000000001)$$$. The number of such pairs is exactly $$$500000000000$$$."}, "src_uid": "98624ab2fcd2a50a75788a29e04999ad"}
{"nl": {"description": "Dima loves making pictures on a piece of squared paper. And yet more than that Dima loves the pictures that depict one of his favorite figures. A piece of squared paper of size n × m is represented by a table, consisting of n rows and m columns. All squares are white on blank squared paper. Dima defines a picture as an image on a blank piece of paper, obtained by painting some squares black.The picture portrays one of Dima's favorite figures, if the following conditions hold:  The picture contains at least one painted cell;  All painted cells form a connected set, that is, you can get from any painted cell to any other one (you can move from one cell to a side-adjacent one);  The minimum number of moves needed to go from the painted cell at coordinates (x1, y1) to the painted cell at coordinates (x2, y2), moving only through the colored cells, equals |x1 - x2| + |y1 - y2|. Now Dima is wondering: how many paintings are on an n × m piece of paper, that depict one of his favorite figures? Count this number modulo 1000000007 (109 + 7).", "input_spec": "The first line contains two integers n and m — the sizes of the piece of paper (1 ≤ n, m ≤ 150).", "output_spec": "In a single line print the remainder after dividing the answer to the problem by number 1000000007 (109 + 7).", "sample_inputs": ["2 2", "3 4"], "sample_outputs": ["13", "571"], "notes": null}, "src_uid": "740eceed59d3c6ac55c1bf9d3d4160c7"}
{"nl": {"description": "Mikhail walks on a 2D plane. He can go either up or right. You are given a sequence of Mikhail's moves. He thinks that this sequence is too long and he wants to make it as short as possible.In the given sequence moving up is described by character U and moving right is described by character R. Mikhail can replace any pair of consecutive moves RU or UR with a diagonal move (described as character D). After that, he can go on and do some other replacements, until there is no pair of consecutive moves RU or UR left.Your problem is to print the minimum possible length of the sequence of moves after the replacements.", "input_spec": "The first line of the input contains one integer n (1 ≤ n ≤ 100) — the length of the sequence. The second line contains the sequence consisting of n characters U and R.", "output_spec": "Print the minimum possible length of the sequence of moves after all replacements are done.", "sample_inputs": ["5\nRUURU", "17\nUUURRRRRUUURURUUU"], "sample_outputs": ["3", "13"], "notes": "NoteIn the first test the shortened sequence of moves may be DUD (its length is 3).In the second test the shortened sequence of moves can be UUDRRRDUDDUUU (its length is 13)."}, "src_uid": "986ae418ce82435badadb0bd5588f45b"}
{"nl": {"description": "Last week, Hamed learned about a new type of equations in his math class called Modular Equations. Lets define i modulo j as the remainder of division of i by j and denote it by . A Modular Equation, as Hamed's teacher described, is an equation of the form  in which a and b are two non-negative integers and x is a variable. We call a positive integer x for which  a solution of our equation.Hamed didn't pay much attention to the class since he was watching a movie. He only managed to understand the definitions of these equations.Now he wants to write his math exercises but since he has no idea how to do that, he asked you for help. He has told you all he knows about Modular Equations and asked you to write a program which given two numbers a and b determines how many answers the Modular Equation  has.", "input_spec": "In the only line of the input two space-separated integers a and b (0 ≤ a, b ≤ 109) are given.", "output_spec": "If there is an infinite number of answers to our equation, print \"infinity\" (without the quotes). Otherwise print the number of solutions of the Modular Equation .", "sample_inputs": ["21 5", "9435152 272", "10 10"], "sample_outputs": ["2", "282", "infinity"], "notes": "NoteIn the first sample the answers of the Modular Equation are 8 and 16 since "}, "src_uid": "6e0715f9239787e085b294139abb2475"}
{"nl": {"description": "Natasha is planning an expedition to Mars for $$$n$$$ people. One of the important tasks is to provide food for each participant.The warehouse has $$$m$$$ daily food packages. Each package has some food type $$$a_i$$$.Each participant must eat exactly one food package each day. Due to extreme loads, each participant must eat the same food type throughout the expedition. Different participants may eat different (or the same) types of food.Formally, for each participant $$$j$$$ Natasha should select his food type $$$b_j$$$ and each day $$$j$$$-th participant will eat one food package of type $$$b_j$$$. The values $$$b_j$$$ for different participants may be different.What is the maximum possible number of days the expedition can last, following the requirements above?", "input_spec": "The first line contains two integers $$$n$$$ and $$$m$$$ ($$$1 \\le n \\le 100$$$, $$$1 \\le m \\le 100$$$) — the number of the expedition participants and the number of the daily food packages available. The second line contains sequence of integers $$$a_1, a_2, \\dots, a_m$$$ ($$$1 \\le a_i \\le 100$$$), where $$$a_i$$$ is the type of $$$i$$$-th food package.", "output_spec": "Print the single integer — the number of days the expedition can last. If it is not possible to plan the expedition for even one day, print 0.", "sample_inputs": ["4 10\n1 5 2 1 1 1 2 5 7 2", "100 1\n1", "2 5\n5 4 3 2 1", "3 9\n42 42 42 42 42 42 42 42 42"], "sample_outputs": ["2", "0", "1", "3"], "notes": "NoteIn the first example, Natasha can assign type $$$1$$$ food to the first participant, the same type $$$1$$$ to the second, type $$$5$$$ to the third and type $$$2$$$ to the fourth. In this case, the expedition can last for $$$2$$$ days, since each participant can get two food packages of his food type (there will be used $$$4$$$ packages of type $$$1$$$, two packages of type $$$2$$$ and two packages of type $$$5$$$).In the second example, there are $$$100$$$ participants and only $$$1$$$ food package. In this case, the expedition can't last even $$$1$$$ day."}, "src_uid": "b7ef696a11ff96f2e9c31becc2ff50fe"}
{"nl": {"description": "The weather is fine today and hence it's high time to climb the nearby pine and enjoy the landscape.The pine's trunk includes several branches, located one above another and numbered from 2 to y. Some of them (more precise, from 2 to p) are occupied by tiny vile grasshoppers which you're at war with. These grasshoppers are known for their awesome jumping skills: the grasshopper at branch x can jump to branches .Keeping this in mind, you wisely decided to choose such a branch that none of the grasshoppers could interrupt you. At the same time you wanna settle as high as possible since the view from up there is simply breathtaking.In other words, your goal is to find the highest branch that cannot be reached by any of the grasshoppers or report that it's impossible.", "input_spec": "The only line contains two integers p and y (2 ≤ p ≤ y ≤ 109).", "output_spec": "Output the number of the highest suitable branch. If there are none, print -1 instead.", "sample_inputs": ["3 6", "3 4"], "sample_outputs": ["5", "-1"], "notes": "NoteIn the first sample case grasshopper from branch 2 reaches branches 2, 4 and 6 while branch 3 is initially settled by another grasshopper. Therefore the answer is 5.It immediately follows that there are no valid branches in second sample case."}, "src_uid": "b533203f488fa4caf105f3f46dd5844d"}
{"nl": {"description": "To quickly hire highly skilled specialists one of the new IT City companies made an unprecedented move. Every employee was granted a car, and an employee can choose one of four different car makes.The parking lot before the office consists of one line of (2n - 2) parking spaces. Unfortunately the total number of cars is greater than the parking lot capacity. Furthermore even amount of cars of each make is greater than the amount of parking spaces! That's why there are no free spaces on the parking lot ever.Looking on the straight line of cars the company CEO thought that parking lot would be more beautiful if it contained exactly n successive cars of the same make. Help the CEO determine the number of ways to fill the parking lot this way.", "input_spec": "The only line of the input contains one integer n (3 ≤ n ≤ 30) — the amount of successive cars of the same make.", "output_spec": "Output one integer — the number of ways to fill the parking lot by cars of four makes using the described way.", "sample_inputs": ["3"], "sample_outputs": ["24"], "notes": "NoteLet's denote car makes in the following way: A — Aston Martin, B —   Bentley, M — Mercedes-Maybach, Z — Zaporozhets. For n = 3 there are the following appropriate ways to fill the parking lot: AAAB AAAM AAAZ ABBB AMMM AZZZ BBBA BBBM BBBZ BAAA BMMM BZZZ MMMA MMMB MMMZ MAAA MBBB MZZZ ZZZA ZZZB ZZZM ZAAA ZBBB ZMMMOriginally it was planned to grant sport cars of Ferrari, Lamborghini, Maserati and Bugatti makes but this idea was renounced because it is impossible to drive these cars having small road clearance on the worn-down roads of IT City."}, "src_uid": "3b02cbb38d0b4ddc1a6467f7647d53a9"}
{"nl": {"description": "Bob loves everything sweet. His favorite chocolate bar consists of pieces, each piece may contain a nut. Bob wants to break the bar of chocolate into multiple pieces so that each part would contain exactly one nut and any break line goes between two adjacent pieces.You are asked to calculate the number of ways he can do it. Two ways to break chocolate are considered distinct if one of them contains a break between some two adjacent pieces and the other one doesn't. Please note, that if Bob doesn't make any breaks, all the bar will form one piece and it still has to have exactly one nut.", "input_spec": "The first line of the input contains integer n (1 ≤ n ≤ 100) — the number of pieces in the chocolate bar. The second line contains n integers ai (0 ≤ ai ≤ 1), where 0 represents a piece without the nut and 1 stands for a piece with the nut.", "output_spec": "Print the number of ways to break the chocolate into multiple parts so that each part would contain exactly one nut.", "sample_inputs": ["3\n0 1 0", "5\n1 0 1 0 1"], "sample_outputs": ["1", "4"], "notes": "NoteIn the first sample there is exactly one nut, so the number of ways equals 1 — Bob shouldn't make any breaks.In the second sample you can break the bar in four ways:10|10|11|010|110|1|011|01|01"}, "src_uid": "58242665476f1c4fa723848ff0ecda98"}
{"nl": {"description": "Dante is engaged in a fight with \"The Savior\". Before he can fight it with his sword, he needs to break its shields. He has two guns, Ebony and Ivory, each of them is able to perform any non-negative number of shots.For every bullet that hits the shield, Ebony deals a units of damage while Ivory deals b units of damage. In order to break the shield Dante has to deal exactly c units of damage. Find out if this is possible.", "input_spec": "The first line of the input contains three integers a, b, c (1 ≤ a, b ≤ 100, 1 ≤ c ≤ 10 000) — the number of units of damage dealt by Ebony gun and Ivory gun, and the total number of damage required to break the shield, respectively.", "output_spec": "Print \"Yes\" (without quotes) if Dante can deal exactly c damage to the shield and \"No\" (without quotes) otherwise.", "sample_inputs": ["4 6 15", "3 2 7", "6 11 6"], "sample_outputs": ["No", "Yes", "Yes"], "notes": "NoteIn the second sample, Dante can fire 1 bullet from Ebony and 2 from Ivory to deal exactly 1·3 + 2·2 = 7 damage. In the third sample, Dante can fire 1 bullet from ebony and no bullets from ivory to do 1·6 + 0·11 = 6 damage. "}, "src_uid": "e66ecb0021a34042885442b336f3d911"}
{"nl": {"description": "Grandma Laura came to the market to sell some apples. During the day she sold all the apples she had. But grandma is old, so she forgot how many apples she had brought to the market.She precisely remembers she had n buyers and each of them bought exactly half of the apples she had at the moment of the purchase and also she gave a half of an apple to some of them as a gift (if the number of apples at the moment of purchase was odd), until she sold all the apples she had.So each buyer took some integral positive number of apples, but maybe he didn't pay for a half of an apple (if the number of apples at the moment of the purchase was odd).For each buyer grandma remembers if she gave a half of an apple as a gift or not. The cost of an apple is p (the number p is even).Print the total money grandma should have at the end of the day to check if some buyers cheated her.", "input_spec": "The first line contains two integers n and p (1 ≤ n ≤ 40, 2 ≤ p ≤ 1000) — the number of the buyers and the cost of one apple. It is guaranteed that the number p is even. The next n lines contains the description of buyers. Each buyer is described with the string half if he simply bought half of the apples and with the string halfplus if grandma also gave him a half of an apple as a gift. It is guaranteed that grandma has at least one apple at the start of the day and she has no apples at the end of the day.", "output_spec": "Print the only integer a — the total money grandma should have at the end of the day. Note that the answer can be too large, so you should use 64-bit integer type to store it. In C++ you can use the long long integer type and in Java you can use long integer type.", "sample_inputs": ["2 10\nhalf\nhalfplus", "3 10\nhalfplus\nhalfplus\nhalfplus"], "sample_outputs": ["15", "55"], "notes": "NoteIn the first sample at the start of the day the grandma had two apples. First she sold one apple and then she sold a half of the second apple and gave a half of the second apple as a present to the second buyer."}, "src_uid": "6330891dd05bb70241e2a052f5bf5a58"}
{"nl": {"description": "Vasya decided to learn to play chess. Classic chess doesn't seem interesting to him, so he plays his own sort of chess.The queen is the piece that captures all squares on its vertical, horizontal and diagonal lines. If the cell is located on the same vertical, horizontal or diagonal line with queen, and the cell contains a piece of the enemy color, the queen is able to move to this square. After that the enemy's piece is removed from the board. The queen cannot move to a cell containing an enemy piece if there is some other piece between it and the queen. There is an n × n chessboard. We'll denote a cell on the intersection of the r-th row and c-th column as (r, c). The square (1, 1) contains the white queen and the square (1, n) contains the black queen. All other squares contain green pawns that don't belong to anyone.The players move in turns. The player that moves first plays for the white queen, his opponent plays for the black queen.On each move the player has to capture some piece with his queen (that is, move to a square that contains either a green pawn or the enemy queen). The player loses if either he cannot capture any piece during his move or the opponent took his queen during the previous move. Help Vasya determine who wins if both players play with an optimal strategy on the board n × n.", "input_spec": "The input contains a single number n (2 ≤ n ≤ 109) — the size of the board.", "output_spec": "On the first line print the answer to problem — string \"white\" or string \"black\", depending on who wins if the both players play optimally.  If the answer is \"white\", then you should also print two integers r and c representing the cell (r, c), where the first player should make his first move to win. If there are multiple such cells, print the one with the minimum r. If there are still multiple squares, print the one with the minimum c.", "sample_inputs": ["2", "3"], "sample_outputs": ["white\n1 2", "black"], "notes": "NoteIn the first sample test the white queen can capture the black queen at the first move, so the white player wins.In the second test from the statement if the white queen captures the green pawn located on the central vertical line, then it will be captured by the black queen during the next move. So the only move for the white player is to capture the green pawn located at (2, 1). Similarly, the black queen doesn't have any other options but to capture the green pawn located at (2, 3), otherwise if it goes to the middle vertical line, it will be captured by the white queen.During the next move the same thing happens — neither the white, nor the black queen has other options rather than to capture green pawns situated above them. Thus, the white queen ends up on square (3, 1), and the black queen ends up on square (3, 3). In this situation the white queen has to capture any of the green pawns located on the middle vertical line, after that it will be captured by the black queen. Thus, the player who plays for the black queen wins."}, "src_uid": "52e07d176aa1d370788f94ee2e61df93"}
{"nl": {"description": "The Smart Beaver from ABBYY got hooked on square matrices. Now he is busy studying an n × n size matrix, where n is odd. The Smart Beaver considers the following matrix elements good:    Elements of the main diagonal.   Elements of the secondary diagonal.   Elements of the \"middle\" row — the row which has exactly  rows above it and the same number of rows below it.   Elements of the \"middle\" column — the column that has exactly  columns to the left of it and the same number of columns to the right of it.    The figure shows a 5 × 5 matrix.   The good elements are marked with green.  Help the Smart Beaver count the sum of good elements of the given matrix.", "input_spec": "The first line of input data contains a single odd integer n. Each of the next n lines contains n integers aij (0 ≤ aij ≤ 100) separated by single spaces — the elements of the given matrix. The input limitations for getting 30 points are:    1 ≤ n ≤ 5  The input limitations for getting 100 points are:   1 ≤ n ≤ 101 ", "output_spec": "Print a single integer — the sum of good matrix elements.", "sample_inputs": ["3\n1 2 3\n4 5 6\n7 8 9", "5\n1 1 1 1 1\n1 1 1 1 1\n1 1 1 1 1\n1 1 1 1 1\n1 1 1 1 1"], "sample_outputs": ["45", "17"], "notes": "NoteIn the first sample all matrix elements will be good. Good elements in the second sample are shown on the figure."}, "src_uid": "5ebfad36e56d30c58945c5800139b880"}
{"nl": {"description": "Each student eagerly awaits the day he would pass the exams successfully. Thus, Vasya was ready to celebrate, but, alas, he didn't pass it. However, many of Vasya's fellow students from the same group were more successful and celebrated after the exam.Some of them celebrated in the BugDonalds restaurant, some of them — in the BeaverKing restaurant, the most successful ones were fast enough to celebrate in both of restaurants. Students which didn't pass the exam didn't celebrate in any of those restaurants and elected to stay home to prepare for their reexamination. However, this quickly bored Vasya and he started checking celebration photos on the Kilogramm. He found out that, in total, BugDonalds was visited by $$$A$$$ students, BeaverKing — by $$$B$$$ students and $$$C$$$ students visited both restaurants. Vasya also knows that there are $$$N$$$ students in his group.Based on this info, Vasya wants to determine either if his data contradicts itself or, if it doesn't, how many students in his group didn't pass the exam. Can you help him so he won't waste his valuable preparation time?", "input_spec": "The first line contains four integers — $$$A$$$, $$$B$$$, $$$C$$$ and $$$N$$$ ($$$0 \\leq A, B, C, N \\leq 100$$$).", "output_spec": "If a distribution of $$$N$$$ students exists in which $$$A$$$ students visited BugDonalds, $$$B$$$ — BeaverKing, $$$C$$$ — both of the restaurants and at least one student is left home (it is known that Vasya didn't pass the exam and stayed at home), output one integer — amount of students (including Vasya) who did not pass the exam.  If such a distribution does not exist and Vasya made a mistake while determining the numbers $$$A$$$, $$$B$$$, $$$C$$$ or $$$N$$$ (as in samples 2 and 3), output $$$-1$$$.", "sample_inputs": ["10 10 5 20", "2 2 0 4", "2 2 2 1"], "sample_outputs": ["5", "-1", "-1"], "notes": "NoteThe first sample describes following situation: $$$5$$$ only visited BugDonalds, $$$5$$$ students only visited BeaverKing, $$$5$$$ visited both of them and $$$5$$$ students (including Vasya) didn't pass the exam.In the second sample $$$2$$$ students only visited BugDonalds and $$$2$$$ only visited BeaverKing, but that means all $$$4$$$ students in group passed the exam which contradicts the fact that Vasya didn't pass meaning that this situation is impossible.The third sample describes a situation where $$$2$$$ students visited BugDonalds but the group has only $$$1$$$ which makes it clearly impossible."}, "src_uid": "959d56affbe2ff5dd999a7e8729f60ce"}
{"nl": {"description": "You are given two arithmetic progressions: a1k + b1 and a2l + b2. Find the number of integers x such that L ≤ x ≤ R and x = a1k' + b1 = a2l' + b2, for some integers k', l' ≥ 0.", "input_spec": "The only line contains six integers a1, b1, a2, b2, L, R (0 < a1, a2 ≤ 2·109,  - 2·109 ≤ b1, b2, L, R ≤ 2·109, L ≤ R).", "output_spec": "Print the desired number of integers x.", "sample_inputs": ["2 0 3 3 5 21", "2 4 3 0 6 17"], "sample_outputs": ["3", "2"], "notes": null}, "src_uid": "b08ee0cd6f5cb574086fa02f07d457a4"}
{"nl": {"description": "Given a positive integer $$$m$$$, we say that a sequence $$$x_1, x_2, \\dots, x_n$$$ of positive integers is $$$m$$$-cute if for every index $$$i$$$ such that $$$2 \\le i \\le n$$$ it holds that $$$x_i = x_{i - 1} + x_{i - 2} + \\dots + x_1 + r_i$$$ for some positive integer $$$r_i$$$ satisfying $$$1 \\le r_i \\le m$$$.You will be given $$$q$$$ queries consisting of three positive integers $$$a$$$, $$$b$$$ and $$$m$$$. For each query you must determine whether or not there exists an $$$m$$$-cute sequence whose first term is $$$a$$$ and whose last term is $$$b$$$. If such a sequence exists, you must additionally find an example of it.", "input_spec": "The first line contains an integer number $$$q$$$ ($$$1 \\le q \\le 10^3$$$) — the number of queries. Each of the following $$$q$$$ lines contains three integers $$$a$$$, $$$b$$$, and $$$m$$$ ($$$1 \\le a, b, m \\le 10^{14}$$$, $$$a \\leq b$$$), describing a single query.", "output_spec": "For each query, if no $$$m$$$-cute sequence whose first term is $$$a$$$ and whose last term is $$$b$$$ exists, print $$$-1$$$. Otherwise print an integer $$$k$$$ ($$$1 \\le k \\leq 50$$$), followed by $$$k$$$ integers $$$x_1, x_2, \\dots, x_k$$$ ($$$1 \\le x_i \\le 10^{14}$$$). These integers must satisfy $$$x_1 = a$$$, $$$x_k = b$$$, and that the sequence $$$x_1, x_2, \\dots, x_k$$$ is $$$m$$$-cute. It can be shown that under the problem constraints, for each query either no $$$m$$$-cute sequence exists, or there exists one with at most $$$50$$$ terms. If there are multiple possible sequences, you may print any of them.", "sample_inputs": ["2\n5 26 2\n3 9 1"], "sample_outputs": ["4 5 6 13 26\n-1"], "notes": "NoteConsider the sample. In the first query, the sequence $$$5, 6, 13, 26$$$ is valid since $$$6 = 5 + \\bf{\\color{blue} 1}$$$, $$$13 = 6 + 5 + {\\bf\\color{blue} 2}$$$ and $$$26 = 13 + 6 + 5 + {\\bf\\color{blue} 2}$$$ have the bold values all between $$$1$$$ and $$$2$$$, so the sequence is $$$2$$$-cute. Other valid sequences, such as $$$5, 7, 13, 26$$$ are also accepted.In the second query, the only possible $$$1$$$-cute sequence starting at $$$3$$$ is $$$3, 4, 8, 16, \\dots$$$, which does not contain $$$9$$$."}, "src_uid": "c9d646762e2e78064bc0670ec7c173c6"}
{"nl": {"description": "The Cybermen and the Daleks have long been the Doctor's main enemies. Everyone knows that both these species enjoy destroying everything they encounter. However, a little-known fact about them is that they both also love taking Turing tests!Heidi designed a series of increasingly difficult tasks for them to spend their time on, which would allow the Doctor enough time to save innocent lives!The funny part is that these tasks would be very easy for a human to solve.The first task is as follows. There are some points on the plane. All but one of them are on the boundary of an axis-aligned square (its sides are parallel to the axes). Identify that point.", "input_spec": "The first line contains an integer $$$n$$$ ($$$2 \\le n \\le 10$$$). Each of the following $$$4n + 1$$$ lines contains two integers $$$x_i, y_i$$$ ($$$0 \\leq x_i, y_i \\leq 50$$$), describing the coordinates of the next point. It is guaranteed that there are at least $$$n$$$ points on each side of the square and all $$$4n + 1$$$ points are distinct.", "output_spec": "Print two integers — the coordinates of the point that is not on the boundary of the square.", "sample_inputs": ["2\n0 0\n0 1\n0 2\n1 0\n1 1\n1 2\n2 0\n2 1\n2 2", "2\n0 0\n0 1\n0 2\n0 3\n1 0\n1 2\n2 0\n2 1\n2 2"], "sample_outputs": ["1 1", "0 3"], "notes": "NoteIn both examples, the square has four sides $$$x=0$$$, $$$x=2$$$, $$$y=0$$$, $$$y=2$$$."}, "src_uid": "1f9153088dcba9383b1a2dbe592e4d06"}
{"nl": {"description": "The Little Elephant is playing with the Cartesian coordinates' system. Most of all he likes playing with integer points. The Little Elephant defines an integer point as a pair of integers (x; y), such that 0 ≤ x ≤ w and 0 ≤ y ≤ h. Thus, the Little Elephant knows only (w + 1)·(h + 1) distinct integer points.The Little Elephant wants to paint a triangle with vertexes at integer points, the triangle's area must be a positive integer. For that, he needs to find the number of groups of three points that form such triangle. At that, the order of points in a group matters, that is, the group of three points (0;0), (0;2), (2;2) isn't equal to the group (0;2), (0;0), (2;2).Help the Little Elephant to find the number of groups of three integer points that form a nondegenerate triangle with integer area.", "input_spec": "A single line contains two integers w and h (1 ≤ w, h ≤ 4000).", "output_spec": "In a single output line print an integer — the remainder of dividing the answer to the problem by 1000000007 (109 + 7).", "sample_inputs": ["2 1", "2 2"], "sample_outputs": ["36", "240"], "notes": null}, "src_uid": "984788e4b4925c15c9c6f31e42f2f8fa"}
{"nl": {"description": "Ivan's classes at the university have just finished, and now he wants to go to the local CFK cafe and eat some fried chicken.CFK sells chicken chunks in small and large portions. A small portion contains 3 chunks; a large one — 7 chunks. Ivan wants to eat exactly x chunks. Now he wonders whether he can buy exactly this amount of chicken.Formally, Ivan wants to know if he can choose two non-negative integers a and b in such a way that a small portions and b large ones contain exactly x chunks.Help Ivan to answer this question for several values of x!", "input_spec": "The first line contains one integer n (1 ≤ n ≤ 100) — the number of testcases. The i-th of the following n lines contains one integer xi (1 ≤ xi ≤ 100) — the number of chicken chunks Ivan wants to eat.", "output_spec": "Print n lines, in i-th line output YES if Ivan can buy exactly xi chunks. Otherwise, print NO.", "sample_inputs": ["2\n6\n5"], "sample_outputs": ["YES\nNO"], "notes": "NoteIn the first example Ivan can buy two small portions.In the second example Ivan cannot buy exactly 5 chunks, since one small portion is not enough, but two small portions or one large is too much."}, "src_uid": "cfd1182be98fb5f0c426f8b68e48d452"}
{"nl": {"description": "Polycarpus has a ribbon, its length is n. He wants to cut the ribbon in a way that fulfils the following two conditions:   After the cutting each ribbon piece should have length a, b or c.  After the cutting the number of ribbon pieces should be maximum. Help Polycarpus and find the number of ribbon pieces after the required cutting.", "input_spec": "The first line contains four space-separated integers n, a, b and c (1 ≤ n, a, b, c ≤ 4000) — the length of the original ribbon and the acceptable lengths of the ribbon pieces after the cutting, correspondingly. The numbers a, b and c can coincide.", "output_spec": "Print a single number — the maximum possible number of ribbon pieces. It is guaranteed that at least one correct ribbon cutting exists.", "sample_inputs": ["5 5 3 2", "7 5 5 2"], "sample_outputs": ["2", "2"], "notes": "NoteIn the first example Polycarpus can cut the ribbon in such way: the first piece has length 2, the second piece has length 3.In the second example Polycarpus can cut the ribbon in such way: the first piece has length 5, the second piece has length 2."}, "src_uid": "062a171cc3ea717ea95ede9d7a1c3a43"}
{"nl": {"description": "You are given two positive integer numbers a and b. Permute (change order) of the digits of a to construct maximal number not exceeding b. No number in input and/or output can start with the digit 0.It is allowed to leave a as it is.", "input_spec": "The first line contains integer a (1 ≤ a ≤ 1018). The second line contains integer b (1 ≤ b ≤ 1018). Numbers don't have leading zeroes. It is guaranteed that answer exists.", "output_spec": "Print the maximum possible number that is a permutation of digits of a and is not greater than b. The answer can't have any leading zeroes. It is guaranteed that the answer exists. The number in the output should have exactly the same length as number a. It should be a permutation of digits of a.", "sample_inputs": ["123\n222", "3921\n10000", "4940\n5000"], "sample_outputs": ["213", "9321", "4940"], "notes": null}, "src_uid": "bc31a1d4a02a0011eb9f5c754501cd44"}
{"nl": {"description": "Ann has recently started commuting by subway. We know that a one ride subway ticket costs a rubles. Besides, Ann found out that she can buy a special ticket for m rides (she can buy it several times). It costs b rubles. Ann did the math; she will need to use subway n times. Help Ann, tell her what is the minimum sum of money she will have to spend to make n rides?", "input_spec": "The single line contains four space-separated integers n, m, a, b (1 ≤ n, m, a, b ≤ 1000) — the number of rides Ann has planned, the number of rides covered by the m ride ticket, the price of a one ride ticket and the price of an m ride ticket. ", "output_spec": "Print a single integer — the minimum sum in rubles that Ann will need to spend.", "sample_inputs": ["6 2 1 2", "5 2 2 3"], "sample_outputs": ["6", "8"], "notes": "NoteIn the first sample one of the optimal solutions is: each time buy a one ride ticket. There are other optimal solutions. For example, buy three m ride tickets."}, "src_uid": "faa343ad6028c5a069857a38fa19bb24"}
{"nl": {"description": "You are given two integers $$$n$$$ and $$$k$$$.You need to construct $$$k$$$ regular polygons having same circumcircle, with distinct number of sides $$$l$$$ between $$$3$$$ and $$$n$$$.   Illustration for the first example. You can rotate them to minimize the total number of distinct points on the circle. Find the minimum number of such points.", "input_spec": "The only line of input contains two integers $$$n$$$ and $$$k$$$ ($$$3 \\le n \\le 10^{6}$$$, $$$1 \\le k \\le n-2$$$), the maximum number of sides of a polygon and the number of polygons to construct, respectively.", "output_spec": "Print a single integer — the minimum number of points required for $$$k$$$ polygons.", "sample_inputs": ["6 2", "200 50"], "sample_outputs": ["6", "708"], "notes": "NoteIn the first example, we have $$$n = 6$$$ and $$$k = 2$$$. So, we have $$$4$$$ polygons with number of sides $$$3$$$, $$$4$$$, $$$5$$$ and $$$6$$$ to choose from and if we choose the triangle and the hexagon, then we can arrange them as shown in the picture in the statement.Hence, the minimum number of points required on the circle is $$$6$$$, which is also the minimum overall possible sets."}, "src_uid": "c2f7012082c84d773c2f4b1858c17110"}
{"nl": {"description": "A New Year party is not a New Year party without lemonade! As usual, you are expecting a lot of guests, and buying lemonade has already become a pleasant necessity.Your favorite store sells lemonade in bottles of n different volumes at different costs. A single bottle of type i has volume 2i - 1 liters and costs ci roubles. The number of bottles of each type in the store can be considered infinite.You want to buy at least L liters of lemonade. How many roubles do you have to spend?", "input_spec": "The first line contains two integers n and L (1 ≤ n ≤ 30; 1 ≤ L ≤ 109) — the number of types of bottles in the store and the required amount of lemonade in liters, respectively. The second line contains n integers c1, c2, ..., cn (1 ≤ ci ≤ 109) — the costs of bottles of different types.", "output_spec": "Output a single integer — the smallest number of roubles you have to pay in order to buy at least L liters of lemonade.", "sample_inputs": ["4 12\n20 30 70 90", "4 3\n10000 1000 100 10", "4 3\n10 100 1000 10000", "5 787787787\n123456789 234567890 345678901 456789012 987654321"], "sample_outputs": ["150", "10", "30", "44981600785557577"], "notes": "NoteIn the first example you should buy one 8-liter bottle for 90 roubles and two 2-liter bottles for 30 roubles each. In total you'll get 12 liters of lemonade for just 150 roubles.In the second example, even though you need only 3 liters, it's cheaper to buy a single 8-liter bottle for 10 roubles.In the third example it's best to buy three 1-liter bottles for 10 roubles each, getting three liters for 30 roubles."}, "src_uid": "04ca137d0383c03944e3ce1c502c635b"}
{"nl": {"description": "One day Vasya came across three Berland coins. They didn't have any numbers that's why Vasya didn't understand how their denominations differ. He supposed that if one coin is heavier than the other one, then it should be worth more. Vasya weighed all the three pairs of coins on pan balance scales and told you the results. Find out how the deminations of the coins differ or if Vasya has a mistake in the weighting results. No two coins are equal.", "input_spec": "The input data contains the results of all the weighting, one result on each line. It is guaranteed that every coin pair was weighted exactly once. Vasya labelled the coins with letters «A», «B» and «C». Each result is a line that appears as (letter)(> or < sign)(letter). For example, if coin \"A\" proved lighter than coin \"B\", the result of the weighting is A<B.", "output_spec": "It the results are contradictory, print Impossible. Otherwise, print without spaces the rearrangement of letters «A», «B» and «C» which represent the coins in the increasing order of their weights.", "sample_inputs": ["A>B\nC<B\nA>C", "A<B\nB>C\nC>A"], "sample_outputs": ["CBA", "ACB"], "notes": null}, "src_uid": "97fd9123d0fb511da165b900afbde5dc"}
{"nl": {"description": "Bizon the Champion is called the Champion for a reason. Bizon the Champion has recently got a present — a new glass cupboard with n shelves and he decided to put all his presents there. All the presents can be divided into two types: medals and cups. Bizon the Champion has a1 first prize cups, a2 second prize cups and a3 third prize cups. Besides, he has b1 first prize medals, b2 second prize medals and b3 third prize medals. Naturally, the rewards in the cupboard must look good, that's why Bizon the Champion decided to follow the rules:  any shelf cannot contain both cups and medals at the same time;  no shelf can contain more than five cups;  no shelf can have more than ten medals. Help Bizon the Champion find out if we can put all the rewards so that all the conditions are fulfilled.", "input_spec": "The first line contains integers a1, a2 and a3 (0 ≤ a1, a2, a3 ≤ 100). The second line contains integers b1, b2 and b3 (0 ≤ b1, b2, b3 ≤ 100). The third line contains integer n (1 ≤ n ≤ 100). The numbers in the lines are separated by single spaces.", "output_spec": "Print \"YES\" (without the quotes) if all the rewards can be put on the shelves in the described manner. Otherwise, print \"NO\" (without the quotes).", "sample_inputs": ["1 1 1\n1 1 1\n4", "1 1 3\n2 3 4\n2", "1 0 0\n1 0 0\n1"], "sample_outputs": ["YES", "YES", "NO"], "notes": null}, "src_uid": "fe6301816dea7d9cea1c3a06a7d1ea7e"}
{"nl": {"description": "Little Petya loves playing with squares. Mum bought him a square 2n × 2n in size. Petya marked a cell inside the square and now he is solving the following task.The task is to draw a broken line that would go along the grid lines and that would cut the square into two equal parts. The cutting line should not have any common points with the marked cell and the resulting two parts should be equal up to rotation.Petya wants to determine whether it is possible to cut the square in the required manner given the sizes of the square side and the coordinates of the marked cell. Help him.", "input_spec": "The first line contains three space-separated integers 2n, x and y (2 ≤ 2n ≤ 100, 1 ≤ x, y ≤ 2n), representing the length of a square's side and the coordinates of the marked cell. It is guaranteed that 2n is even. The coordinates of the marked cell are represented by a pair of numbers x y, where x represents the number of the row and y represents the number of the column. The rows and columns are numbered by consecutive integers from 1 to 2n. The rows are numbered from top to bottom and the columns are numbered from the left to the right.", "output_spec": "If the square is possible to cut, print \"YES\", otherwise print \"NO\" (without the quotes).", "sample_inputs": ["4 1 1", "2 2 2"], "sample_outputs": ["YES", "NO"], "notes": "NoteA sample test from the statement and one of the possible ways of cutting the square are shown in the picture:   "}, "src_uid": "dc891d57bcdad3108dcb4ccf9c798789"}
{"nl": {"description": "John Doe has a list of all Fibonacci numbers modulo 1013. This list is infinite, it starts with numbers 0 and 1. Each number in the list, apart from the first two, is a sum of previous two modulo 1013. That is, John's list is made from the Fibonacci numbers' list by replacing each number there by the remainder when divided by 1013. John got interested in number f (0 ≤ f < 1013) and now wants to find its first occurrence in the list given above. Help John and find the number of the first occurence of number f in the list or otherwise state that number f does not occur in the list. The numeration in John's list starts from zero. There, the 0-th position is the number 0, the 1-st position is the number 1, the 2-nd position is the number 1, the 3-rd position is the number 2, the 4-th position is the number 3 and so on. Thus, the beginning of the list looks like this: 0, 1, 1, 2, 3, 5, 8, 13, 21, ...", "input_spec": "The first line contains the single integer f (0 ≤ f < 1013) — the number, which position in the list we should find. Please, do not use the %lld specifier to read or write 64-bit integers in С++. It is preferred to use the cin, cout streams or the %I64d specifier. ", "output_spec": "Print a single number — the number of the first occurrence of the given number in John's list. If this number doesn't occur in John's list, print -1.", "sample_inputs": ["13", "377"], "sample_outputs": ["7", "14"], "notes": null}, "src_uid": "cbf786abfceeb8df29732c8a872f7f8a"}
{"nl": {"description": "The only difference between easy and hard versions is on constraints. In this version constraints are lower. You can make hacks only if all versions of the problem are solved.Koa the Koala is at the beach!The beach consists (from left to right) of a shore, $$$n+1$$$ meters of sea and an island at $$$n+1$$$ meters from the shore.She measured the depth of the sea at $$$1, 2, \\dots, n$$$ meters from the shore and saved them in array $$$d$$$. $$$d_i$$$ denotes the depth of the sea at $$$i$$$ meters from the shore for $$$1 \\le i \\le n$$$.Like any beach this one has tide, the intensity of the tide is measured by parameter $$$k$$$ and affects all depths from the beginning at time $$$t=0$$$ in the following way:  For a total of $$$k$$$ seconds, each second, tide increases all depths by $$$1$$$.  Then, for a total of $$$k$$$ seconds, each second, tide decreases all depths by $$$1$$$.  This process repeats again and again (ie. depths increase for $$$k$$$ seconds then decrease for $$$k$$$ seconds and so on ...).Formally, let's define $$$0$$$-indexed array $$$p = [0, 1, 2, \\ldots, k - 2, k - 1, k, k - 1, k - 2, \\ldots, 2, 1]$$$ of length $$$2k$$$. At time $$$t$$$ ($$$0 \\le t$$$) depth at $$$i$$$ meters from the shore equals $$$d_i + p[t \\bmod 2k]$$$ ($$$t \\bmod 2k$$$ denotes the remainder of the division of $$$t$$$ by $$$2k$$$). Note that the changes occur instantaneously after each second, see the notes for better understanding. At time $$$t=0$$$ Koa is standing at the shore and wants to get to the island. Suppose that at some time $$$t$$$ ($$$0 \\le t$$$) she is at $$$x$$$ ($$$0 \\le x \\le n$$$) meters from the shore:  In one second Koa can swim $$$1$$$ meter further from the shore ($$$x$$$ changes to $$$x+1$$$) or not swim at all ($$$x$$$ stays the same), in both cases $$$t$$$ changes to $$$t+1$$$.  As Koa is a bad swimmer, the depth of the sea at the point where she is can't exceed $$$l$$$ at integer points of time (or she will drown). More formally, if Koa is at $$$x$$$ ($$$1 \\le x \\le n$$$) meters from the shore at the moment $$$t$$$ (for some integer $$$t\\ge 0$$$), the depth of the sea at this point  — $$$d_x + p[t \\bmod 2k]$$$  — can't exceed $$$l$$$. In other words, $$$d_x + p[t \\bmod 2k] \\le l$$$ must hold always.  Once Koa reaches the island at $$$n+1$$$ meters from the shore, she stops and can rest.Note that while Koa swims tide doesn't have effect on her (ie. she can't drown while swimming). Note that Koa can choose to stay on the shore for as long as she needs and neither the shore or the island are affected by the tide (they are solid ground and she won't drown there). Koa wants to know whether she can go from the shore to the island. Help her!", "input_spec": "The first line of the input contains one integer $$$t$$$ ($$$1 \\le t \\le 100$$$)  — the number of test cases. Description of the test cases follows. The first line of each test case contains three integers $$$n$$$, $$$k$$$ and $$$l$$$ ($$$1 \\le n \\le 100; 1 \\le k \\le 100; 1 \\le l \\le 100$$$) — the number of meters of sea Koa measured and parameters $$$k$$$ and $$$l$$$. The second line of each test case contains $$$n$$$ integers $$$d_1, d_2, \\ldots, d_n$$$ ($$$0 \\le d_i \\le 100$$$)  — the depths of each meter of sea Koa measured. It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$100$$$.", "output_spec": "For each test case: Print Yes if Koa can get from the shore to the island, and No otherwise. You may print each letter in any case (upper or lower).", "sample_inputs": ["7\n2 1 1\n1 0\n5 2 3\n1 2 3 2 2\n4 3 4\n0 2 4 3\n2 3 5\n3 0\n7 2 3\n3 0 2 1 3 0 1\n7 1 4\n4 4 3 0 2 4 2\n5 2 3\n1 2 3 2 2"], "sample_outputs": ["Yes\nNo\nYes\nYes\nYes\nNo\nNo"], "notes": "NoteIn the following $$$s$$$ denotes the shore, $$$i$$$ denotes the island, $$$x$$$ denotes distance from Koa to the shore, the underline denotes the position of Koa, and values in the array below denote current depths, affected by tide, at $$$1, 2, \\dots, n$$$ meters from the shore.In test case $$$1$$$ we have $$$n = 2, k = 1, l = 1, p = [ 0, 1 ]$$$.Koa wants to go from shore (at $$$x = 0$$$) to the island (at $$$x = 3$$$). Let's describe a possible solution:  Initially at $$$t = 0$$$ the beach looks like this: $$$[\\underline{s}, 1, 0, i]$$$.  At $$$t = 0$$$ if Koa would decide to swim to $$$x = 1$$$, beach would look like: $$$[s, \\underline{2}, 1, i]$$$ at $$$t = 1$$$, since $$$2 > 1$$$ she would drown. So Koa waits $$$1$$$ second instead and beach looks like $$$[\\underline{s}, 2, 1, i]$$$ at $$$t = 1$$$.  At $$$t = 1$$$ Koa swims to $$$x = 1$$$, beach looks like $$$[s, \\underline{1}, 0, i]$$$ at $$$t = 2$$$. Koa doesn't drown because $$$1 \\le 1$$$.  At $$$t = 2$$$ Koa swims to $$$x = 2$$$, beach looks like $$$[s, 2, \\underline{1}, i]$$$ at $$$t = 3$$$. Koa doesn't drown because $$$1 \\le 1$$$.  At $$$t = 3$$$ Koa swims to $$$x = 3$$$, beach looks like $$$[s, 1, 0, \\underline{i}]$$$ at $$$t = 4$$$.  At $$$t = 4$$$ Koa is at $$$x = 3$$$ and she made it! We can show that in test case $$$2$$$ Koa can't get to the island."}, "src_uid": "4941b0a365f86b2e2cf686cdf5d532f8"}
{"nl": {"description": "Pasha has a wooden stick of some positive integer length n. He wants to perform exactly three cuts to get four parts of the stick. Each part must have some positive integer length and the sum of these lengths will obviously be n. Pasha likes rectangles but hates squares, so he wonders, how many ways are there to split a stick into four parts so that it's possible to form a rectangle using these parts, but is impossible to form a square.Your task is to help Pasha and count the number of such ways. Two ways to cut the stick are considered distinct if there exists some integer x, such that the number of parts of length x in the first way differ from the number of parts of length x in the second way.", "input_spec": "The first line of the input contains a positive integer n (1 ≤ n ≤ 2·109) — the length of Pasha's stick.", "output_spec": "The output should contain a single integer — the number of ways to split Pasha's stick into four parts of positive integer length so that it's possible to make a rectangle by connecting the ends of these parts, but is impossible to form a square. ", "sample_inputs": ["6", "20"], "sample_outputs": ["1", "4"], "notes": "NoteThere is only one way to divide the stick in the first sample {1, 1, 2, 2}.Four ways to divide the stick in the second sample are {1, 1, 9, 9}, {2, 2, 8, 8}, {3, 3, 7, 7} and {4, 4, 6, 6}. Note that {5, 5, 5, 5} doesn't work."}, "src_uid": "32b59d23f71800bc29da74a3fe2e2b37"}
{"nl": {"description": "It's that time of the year when the Russians flood their countryside summer cottages (dachas) and the bus stop has a lot of people. People rarely go to the dacha on their own, it's usually a group, so the people stand in queue by groups.The bus stop queue has n groups of people. The i-th group from the beginning has ai people. Every 30 minutes an empty bus arrives at the bus stop, it can carry at most m people. Naturally, the people from the first group enter the bus first. Then go the people from the second group and so on. Note that the order of groups in the queue never changes. Moreover, if some group cannot fit all of its members into the current bus, it waits for the next bus together with other groups standing after it in the queue.Your task is to determine how many buses is needed to transport all n groups to the dacha countryside.", "input_spec": "The first line contains two integers n and m (1 ≤ n, m ≤ 100). The next line contains n integers: a1, a2, ..., an (1 ≤ ai ≤ m).", "output_spec": "Print a single integer — the number of buses that is needed to transport all n groups to the dacha countryside.", "sample_inputs": ["4 3\n2 3 2 1", "3 4\n1 2 1"], "sample_outputs": ["3", "1"], "notes": null}, "src_uid": "5c73d6e3770dff034d210cdd572ccf0f"}
{"nl": {"description": "Recently, Vladimir got bad mark in algebra again. To avoid such unpleasant events in future he decided to train his arithmetic skills. He wrote four integer numbers a, b, c, d on the blackboard. During each of the next three minutes he took two numbers from the blackboard (not necessarily adjacent) and replaced them with their sum or their product. In the end he got one number. Unfortunately, due to the awful memory he forgot that number, but he remembers four original numbers, sequence of the operations and his surprise because of the very small result. Help Vladimir remember the forgotten number: find the smallest number that can be obtained from the original numbers by the given sequence of operations.", "input_spec": "First line contains four integers separated by space: 0 ≤ a, b, c, d ≤ 1000 — the original numbers. Second line contains three signs ('+' or '*' each) separated by space — the sequence of the operations in the order of performing. ('+' stands for addition, '*' — multiplication)", "output_spec": "Output one integer number — the minimal result which can be obtained. Please, do not use %lld specificator to read or write 64-bit integers in C++. It is preffered to use cin (also you may use %I64d).", "sample_inputs": ["1 1 1 1\n+ + *", "2 2 2 2\n* * +", "1 2 3 4\n* + +"], "sample_outputs": ["3", "8", "9"], "notes": null}, "src_uid": "7a66fae63d9b27e444d84447012e484c"}
{"nl": {"description": "Reforms have started in Berland again! At this time, the Parliament is discussing the reform of the calendar. To make the lives of citizens of Berland more varied, it was decided to change the calendar. As more and more people are complaining that \"the years fly by...\", it was decided that starting from the next year the number of days per year will begin to grow. So the coming year will have exactly a days, the next after coming year will have a + 1 days, the next one will have a + 2 days and so on. This schedule is planned for the coming n years (in the n-th year the length of the year will be equal a + n - 1 day).No one has yet decided what will become of months. An MP Palevny made the following proposal.   The calendar for each month is comfortable to be printed on a square sheet of paper. We are proposed to make the number of days in each month be the square of some integer. The number of days per month should be the same for each month of any year, but may be different for different years.  The number of days in each year must be divisible by the number of days per month in this year. This rule ensures that the number of months in each year is an integer.  The number of days per month for each year must be chosen so as to save the maximum amount of paper to print the calendars. In other words, the number of days per month should be as much as possible. These rules provide an unambiguous method for choosing the number of days in each month for any given year length. For example, according to Palevny's proposition, a year that consists of 108 days will have three months, 36 days each. The year that consists of 99 days will have 11 months, 9 days each, and a year of 365 days will have 365 months, one day each.The proposal provoked heated discussion in the community, the famous mathematician Perelmanov quickly calculated that if the proposal is supported, then in a period of n years, beginning with the year that has a days, the country will spend p sheets of paper to print a set of calendars for these years. Perelmanov's calculations take into account the fact that the set will contain one calendar for each year and each month will be printed on a separate sheet.Repeat Perelmanov's achievement and print the required number p. You are given positive integers a and n. Perelmanov warns you that your program should not work longer than four seconds at the maximum test.", "input_spec": "The only input line contains a pair of integers a, n (1 ≤ a, n ≤ 107; a + n - 1 ≤ 107).", "output_spec": "Print the required number p.  Please, do not use the %lld specifier to read or write 64-bit integers in C++. It is preferred to use cin, cout streams or the %I64d specifier.", "sample_inputs": ["25 3", "50 5"], "sample_outputs": ["30", "125"], "notes": "NoteA note to the first sample test. A year of 25 days will consist of one month containing 25 days. A year of 26 days will consist of 26 months, one day each. A year of 27 days will have three months, 9 days each."}, "src_uid": "915081861e391958dce6ee2a117abd4e"}
{"nl": {"description": "Valera came to Japan and bought many robots for his research. He's already at the airport, the plane will fly very soon and Valera urgently needs to bring all robots to the luggage compartment.The robots are self-propelled (they can potentially move on their own), some of them even have compartments to carry other robots. More precisely, for the i-th robot we know value ci — the number of robots it can carry. In this case, each of ci transported robots can additionally carry other robots.However, the robots need to be filled with fuel to go, so Valera spent all his last money and bought S liters of fuel. He learned that each robot has a restriction on travel distances. Thus, in addition to features ci, the i-th robot has two features fi and li — the amount of fuel (in liters) needed to move the i-th robot, and the maximum distance that the robot can go.Due to the limited amount of time and fuel, Valera wants to move the maximum number of robots to the luggage compartment. He operates as follows.   First Valera selects some robots that will travel to the luggage compartment on their own. In this case the total amount of fuel required to move all these robots must not exceed S.  Then Valera seats the robots into the compartments, so as to transport as many robots as possible. Note that if a robot doesn't move by itself, you can put it in another not moving robot that is moved directly or indirectly by a moving robot.  After that all selected and seated robots along with Valera go to the luggage compartment and the rest robots will be lost. There are d meters to the luggage compartment. Therefore, the robots that will carry the rest, must have feature li of not less than d. During the moving Valera cannot stop or change the location of the robots in any way.Help Valera calculate the maximum number of robots that he will be able to take home, and the minimum amount of fuel he will have to spend, because the remaining fuel will come in handy in Valera's research.", "input_spec": "The first line contains three space-separated integers n, d, S (1 ≤ n ≤ 105, 1 ≤ d, S ≤ 109). The first number represents the number of robots, the second one — the distance to the luggage compartment and the third one — the amount of available fuel. Next n lines specify the robots. The i-th line contains three space-separated integers ci, fi, li (0 ≤ ci, fi, li ≤ 109) — the i-th robot's features. The first number is the number of robots the i-th robot can carry, the second number is the amount of fuel needed for the i-th robot to move and the third one shows the maximum distance the i-th robot can go.", "output_spec": "Print two space-separated integers — the maximum number of robots Valera can transport to the luggage compartment and the minimum amount of fuel he will need for that. If Valera won't manage to get any robots to the luggage compartment, print two zeroes.", "sample_inputs": ["3 10 10\n0 12 10\n1 6 10\n0 1 1", "2 7 10\n3 12 10\n5 16 8", "4 8 10\n0 12 3\n1 1 0\n0 3 11\n1 6 9"], "sample_outputs": ["2 6", "0 0", "4 9"], "notes": null}, "src_uid": "e69f42403f3b0357e06a14523025b34a"}
{"nl": {"description": "As technologies develop, manufacturers are making the process of unlocking a phone as user-friendly as possible. To unlock its new phone, Arkady's pet dog Mu-mu has to bark the password once. The phone represents a password as a string of two lowercase English letters.Mu-mu's enemy Kashtanka wants to unlock Mu-mu's phone to steal some sensible information, but it can only bark n distinct words, each of which can be represented as a string of two lowercase English letters. Kashtanka wants to bark several words (not necessarily distinct) one after another to pronounce a string containing the password as a substring. Tell if it's possible to unlock the phone in this way, or not.", "input_spec": "The first line contains two lowercase English letters — the password on the phone. The second line contains single integer n (1 ≤ n ≤ 100) — the number of words Kashtanka knows. The next n lines contain two lowercase English letters each, representing the words Kashtanka knows. The words are guaranteed to be distinct.", "output_spec": "Print \"YES\" if Kashtanka can bark several words in a line forming a string containing the password, and \"NO\" otherwise. You can print each letter in arbitrary case (upper or lower).", "sample_inputs": ["ya\n4\nah\noy\nto\nha", "hp\n2\nht\ntp", "ah\n1\nha"], "sample_outputs": ["YES", "NO", "YES"], "notes": "NoteIn the first example the password is \"ya\", and Kashtanka can bark \"oy\" and then \"ah\", and then \"ha\" to form the string \"oyahha\" which contains the password. So, the answer is \"YES\".In the second example Kashtanka can't produce a string containing password as a substring. Note that it can bark \"ht\" and then \"tp\" producing \"http\", but it doesn't contain the password \"hp\" as a substring.In the third example the string \"hahahaha\" contains \"ah\" as a substring."}, "src_uid": "cad8283914da16bc41680857bd20fe9f"}
{"nl": {"description": "You are given a chessboard of size 1 × n. It is guaranteed that n is even. The chessboard is painted like this: \"BWBW...BW\".Some cells of the board are occupied by the chess pieces. Each cell contains no more than one chess piece. It is known that the total number of pieces equals to .In one step you can move one of the pieces one cell to the left or to the right. You cannot move pieces beyond the borders of the board. You also cannot move pieces to the cells that are already occupied.Your task is to place all the pieces in the cells of the same color using the minimum number of moves (all the pieces must occupy only the black cells or only the white cells after all the moves are made).", "input_spec": "The first line of the input contains one integer n (2 ≤ n ≤ 100, n is even) — the size of the chessboard.  The second line of the input contains  integer numbers  (1 ≤ pi ≤ n) — initial positions of the pieces. It is guaranteed that all the positions are distinct.", "output_spec": "Print one integer — the minimum number of moves you have to make to place all the pieces in the cells of the same color.", "sample_inputs": ["6\n1 2 6", "10\n1 2 3 4 5"], "sample_outputs": ["2", "10"], "notes": "NoteIn the first example the only possible strategy is to move the piece at the position 6 to the position 5 and move the piece at the position 2 to the position 3. Notice that if you decide to place the pieces in the white cells the minimum number of moves will be 3.In the second example the possible strategy is to move  in 4 moves, then  in 3 moves,  in 2 moves and  in 1 move."}, "src_uid": "0efe9afd8e6be9e00f7949be93f0ca1a"}
{"nl": {"description": "The last stage of Football World Cup is played using the play-off system.There are n teams left in this stage, they are enumerated from 1 to n. Several rounds are held, in each round the remaining teams are sorted in the order of their ids, then the first in this order plays with the second, the third — with the fourth, the fifth — with the sixth, and so on. It is guaranteed that in each round there is even number of teams. The winner of each game advances to the next round, the loser is eliminated from the tournament, there are no draws. In the last round there is the only game with two remaining teams: the round is called the Final, the winner is called the champion, and the tournament is over.Arkady wants his two favorite teams to play in the Final. Unfortunately, the team ids are already determined, and it may happen that it is impossible for teams to meet in the Final, because they are to meet in some earlier stage, if they are strong enough. Determine, in which round the teams with ids a and b can meet.", "input_spec": "The only line contains three integers n, a and b (2 ≤ n ≤ 256, 1 ≤ a, b ≤ n) — the total number of teams, and the ids of the teams that Arkady is interested in.  It is guaranteed that n is such that in each round an even number of team advance, and that a and b are not equal.", "output_spec": "In the only line print \"Final!\" (without quotes), if teams a and b can meet in the Final. Otherwise, print a single integer — the number of the round in which teams a and b can meet. The round are enumerated from 1.", "sample_inputs": ["4 1 2", "8 2 6", "8 7 5"], "sample_outputs": ["1", "Final!", "2"], "notes": "NoteIn the first example teams 1 and 2 meet in the first round.In the second example teams 2 and 6 can only meet in the third round, which is the Final, if they win all their opponents in earlier rounds.In the third example the teams with ids 7 and 5 can meet in the second round, if they win their opponents in the first round."}, "src_uid": "a753bfa7bde157e108f34a28240f441f"}
{"nl": {"description": "Kitahara Haruki has bought n apples for Touma Kazusa and Ogiso Setsuna. Now he wants to divide all the apples between the friends.Each apple weights 100 grams or 200 grams. Of course Kitahara Haruki doesn't want to offend any of his friend. Therefore the total weight of the apples given to Touma Kazusa must be equal to the total weight of the apples given to Ogiso Setsuna.But unfortunately Kitahara Haruki doesn't have a knife right now, so he cannot split any apple into some parts. Please, tell him: is it possible to divide all the apples in a fair way between his friends?", "input_spec": "The first line contains an integer n (1 ≤ n ≤ 100) — the number of apples. The second line contains n integers w1, w2, ..., wn (wi = 100 or wi = 200), where wi is the weight of the i-th apple.", "output_spec": "In a single line print \"YES\" (without the quotes) if it is possible to divide all the apples between his friends. Otherwise print \"NO\" (without the quotes).", "sample_inputs": ["3\n100 200 100", "4\n100 100 100 200"], "sample_outputs": ["YES", "NO"], "notes": "NoteIn the first test sample Kitahara Haruki can give the first and the last apple to Ogiso Setsuna and the middle apple to Touma Kazusa."}, "src_uid": "9679acef82356004e47b1118f8fc836a"}
{"nl": {"description": "Furik loves writing all sorts of problems, especially such that he can't solve himself. You've got one of his problems, the one Furik gave to Rubik. And Rubik asks you to solve it.There is integer n and array a, consisting of ten integers, indexed by numbers from 0 to 9. Your task is to count the number of positive integers with the following properties:  the number's length does not exceed n;  the number doesn't have leading zeroes;  digit i (0 ≤ i ≤ 9) occurs in the number at least a[i] times. ", "input_spec": "The first line contains integer n (1 ≤ n ≤ 100). The next line contains 10 integers a[0], a[1], ..., a[9] (0 ≤ a[i] ≤ 100) — elements of array a. The numbers are separated by spaces.", "output_spec": "On a single line print the remainder of dividing the answer to the problem by 1000000007 (109 + 7).", "sample_inputs": ["1\n0 0 0 0 0 0 0 0 0 1", "2\n1 1 0 0 0 0 0 0 0 0", "3\n1 1 0 0 0 0 0 0 0 0"], "sample_outputs": ["1", "1", "36"], "notes": "NoteIn the first sample number 9 meets the requirements.In the second sample number 10 meets the requirements.In the third sample numbers 10, 110, 210, 120, 103 meet the requirements. There are other suitable numbers, 36 in total."}, "src_uid": "c1b5169a5c3b1bd4a2f1df1069ee7755"}
{"nl": {"description": "There are n stones on the table in a row, each of them can be red, green or blue. Count the minimum number of stones to take from the table so that any two neighboring stones had different colors. Stones in a row are considered neighboring if there are no other stones between them.", "input_spec": "The first line contains integer n (1 ≤ n ≤ 50) — the number of stones on the table.  The next line contains string s, which represents the colors of the stones. We'll consider the stones in the row numbered from 1 to n from left to right. Then the i-th character s equals \"R\", if the i-th stone is red, \"G\", if it's green and \"B\", if it's blue.", "output_spec": "Print a single integer — the answer to the problem.", "sample_inputs": ["3\nRRG", "5\nRRRRR", "4\nBRBG"], "sample_outputs": ["1", "4", "0"], "notes": null}, "src_uid": "d561436e2ddc9074b98ebbe49b9e27b8"}
{"nl": {"description": "The translation from the Berland language into the Birland language is not an easy task. Those languages are very similar: a berlandish word differs from a birlandish word with the same meaning a little: it is spelled (and pronounced) reversely. For example, a Berlandish word code corresponds to a Birlandish word edoc. However, it's easy to make a mistake during the «translation». Vasya translated word s from Berlandish into Birlandish as t. Help him: find out if he translated the word correctly.", "input_spec": "The first line contains word s, the second line contains word t. The words consist of lowercase Latin letters. The input data do not consist unnecessary spaces. The words are not empty and their lengths do not exceed 100 symbols.", "output_spec": "If the word t is a word s, written reversely, print YES, otherwise print NO.", "sample_inputs": ["code\nedoc", "abb\naba", "code\ncode"], "sample_outputs": ["YES", "NO", "NO"], "notes": null}, "src_uid": "35a4be326690b58bf9add547fb63a5a5"}
{"nl": {"description": "Polycarpus enjoys studying Berland hieroglyphs. Once Polycarp got hold of two ancient Berland pictures, on each of which was drawn a circle of hieroglyphs. We know that no hieroglyph occurs twice in either the first or the second circle (but in can occur once in each of them).Polycarpus wants to save these pictures on his laptop, but the problem is, laptops do not allow to write hieroglyphs circles. So Polycarp had to break each circle and write down all of its hieroglyphs in a clockwise order in one line. A line obtained from the first circle will be called a, and the line obtained from the second one will be called b.There are quite many ways to break hieroglyphic circles, so Polycarpus chooses the method, that makes the length of the largest substring of string a, which occurs as a subsequence in string b, maximum.Help Polycarpus — find the maximum possible length of the desired substring (subsequence) if the first and the second circles are broken optimally.The length of string s is the number of characters in it. If we denote the length of string s as |s|, we can write the string as s = s1s2... s|s|.A substring of s is a non-empty string x = s[a... b] = sasa + 1... sb (1 ≤ a ≤ b ≤ |s|). For example, \"code\" and \"force\" are substrings of \"codeforces\", while \"coders\" is not. A subsequence of s is a non-empty string y = s[p1p2... p|y|] = sp1sp2... sp|y| (1 ≤ p1 < p2 < ... < p|y| ≤ |s|). For example, \"coders\" is a subsequence of \"codeforces\".", "input_spec": "The first line contains two integers la and lb (1 ≤ la, lb ≤ 1000000) — the number of hieroglyphs in the first and second circles, respectively. Below, due to difficulties with encoding of Berland hieroglyphs, they are given as integers from 1 to 106. The second line contains la integers — the hieroglyphs in the first picture, in the clockwise order, starting with one of them. The third line contains lb integers — the hieroglyphs in the second picture, in the clockwise order, starting with one of them. It is guaranteed that the first circle doesn't contain a hieroglyph, which occurs twice. The second circle also has this property.", "output_spec": "Print a single number — the maximum length of the common substring and subsequence. If at any way of breaking the circles it does not exist, print 0.", "sample_inputs": ["5 4\n1 2 3 4 5\n1 3 5 6", "4 6\n1 3 5 2\n1 2 3 4 5 6", "3 3\n1 2 3\n3 2 1"], "sample_outputs": ["2", "3", "2"], "notes": "NoteIn the first test Polycarpus picks a string that consists of hieroglyphs 5 and 1, and in the second sample — from hieroglyphs 1, 3 and 5."}, "src_uid": "13cd1aafbb1ba76be9ee10eaf8d8aef5"}
{"nl": {"description": "Arpa is taking a geometry exam. Here is the last problem of the exam.You are given three points a, b, c.Find a point and an angle such that if we rotate the page around the point by the angle, the new position of a is the same as the old position of b, and the new position of b is the same as the old position of c.Arpa is doubting if the problem has a solution or not (i.e. if there exists a point and an angle satisfying the condition). Help Arpa determine if the question has a solution or not.", "input_spec": "The only line contains six integers ax, ay, bx, by, cx, cy (|ax|, |ay|, |bx|, |by|, |cx|, |cy| ≤ 109). It's guaranteed that the points are distinct.", "output_spec": "Print \"Yes\" if the problem has a solution, \"No\" otherwise. You can print each letter in any case (upper or lower).", "sample_inputs": ["0 1 1 1 1 0", "1 1 0 0 1000 1000"], "sample_outputs": ["Yes", "No"], "notes": "NoteIn the first sample test, rotate the page around (0.5, 0.5) by .In the second sample test, you can't find any solution."}, "src_uid": "05ec6ec3e9ffcc0e856dc0d461e6eeab"}
{"nl": {"description": "Devu is a renowned classical singer. He is invited to many big functions/festivals. Recently he was invited to \"All World Classical Singing Festival\". Other than Devu, comedian Churu was also invited.Devu has provided organizers a list of the songs and required time for singing them. He will sing n songs, ith song will take ti minutes exactly. The Comedian, Churu will crack jokes. All his jokes are of 5 minutes exactly.People have mainly come to listen Devu. But you know that he needs rest of 10 minutes after each song. On the other hand, Churu being a very active person, doesn't need any rest.You as one of the organizers should make an optimal sсhedule for the event. For some reasons you must follow the conditions:  The duration of the event must be no more than d minutes;  Devu must complete all his songs;  With satisfying the two previous conditions the number of jokes cracked by Churu should be as many as possible. If it is not possible to find a way to conduct all the songs of the Devu, output -1. Otherwise find out maximum number of jokes that Churu can crack in the grand event.", "input_spec": "The first line contains two space separated integers n, d (1 ≤ n ≤ 100; 1 ≤ d ≤ 10000). The second line contains n space-separated integers: t1, t2, ..., tn (1 ≤ ti ≤ 100).", "output_spec": "If there is no way to conduct all the songs of Devu, output -1. Otherwise output the maximum number of jokes that Churu can crack in the grand event.", "sample_inputs": ["3 30\n2 2 1", "3 20\n2 1 1"], "sample_outputs": ["5", "-1"], "notes": "NoteConsider the first example. The duration of the event is 30 minutes. There could be maximum 5 jokes in the following way:  First Churu cracks a joke in 5 minutes.  Then Devu performs the first song for 2 minutes.  Then Churu cracks 2 jokes in 10 minutes.  Now Devu performs second song for 2 minutes.  Then Churu cracks 2 jokes in 10 minutes.  Now finally Devu will perform his last song in 1 minutes.  Total time spent is 5 + 2 + 10 + 2 + 10 + 1 = 30 minutes.Consider the second example. There is no way of organizing Devu's all songs. Hence the answer is -1. "}, "src_uid": "b16f5f5c4eeed2a3700506003e8ea8ea"}
{"nl": {"description": "In Omkar's last class of math, he learned about the least common multiple, or $$$LCM$$$. $$$LCM(a, b)$$$ is the smallest positive integer $$$x$$$ which is divisible by both $$$a$$$ and $$$b$$$.Omkar, having a laudably curious mind, immediately thought of a problem involving the $$$LCM$$$ operation: given an integer $$$n$$$, find positive integers $$$a$$$ and $$$b$$$ such that $$$a + b = n$$$ and $$$LCM(a, b)$$$ is the minimum value possible.Can you help Omkar solve his ludicrously challenging math problem?", "input_spec": "Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \\leq t \\leq 10$$$). Description of the test cases follows. Each test case consists of a single integer $$$n$$$ ($$$2 \\leq n \\leq 10^{9}$$$).", "output_spec": "For each test case, output two positive integers $$$a$$$ and $$$b$$$, such that $$$a + b = n$$$ and $$$LCM(a, b)$$$ is the minimum possible.", "sample_inputs": ["3\n4\n6\n9"], "sample_outputs": ["2 2\n3 3\n3 6"], "notes": "NoteFor the first test case, the numbers we can choose are $$$1, 3$$$ or $$$2, 2$$$. $$$LCM(1, 3) = 3$$$ and $$$LCM(2, 2) = 2$$$, so we output $$$2 \\ 2$$$.For the second test case, the numbers we can choose are $$$1, 5$$$, $$$2, 4$$$, or $$$3, 3$$$. $$$LCM(1, 5) = 5$$$, $$$LCM(2, 4) = 4$$$, and $$$LCM(3, 3) = 3$$$, so we output $$$3 \\ 3$$$.For the third test case, $$$LCM(3, 6) = 6$$$. It can be shown that there are no other pairs of numbers which sum to $$$9$$$ that have a lower $$$LCM$$$."}, "src_uid": "3fd60db24b1873e906d6dee9c2508ac5"}
{"nl": {"description": "You are locked in a room with a door that has a keypad with 10 keys corresponding to digits from 0 to 9. To escape from the room, you need to enter a correct code. You also have a sequence of digits.Some keys on the keypad have fingerprints. You believe the correct code is the longest not necessarily contiguous subsequence of the sequence you have that only contains digits with fingerprints on the corresponding keys. Find such code.", "input_spec": "The first line contains two integers $$$n$$$ and $$$m$$$ ($$$1 \\le n, m \\le 10$$$) representing the number of digits in the sequence you have and the number of keys on the keypad that have fingerprints. The next line contains $$$n$$$ distinct space-separated integers $$$x_1, x_2, \\ldots, x_n$$$ ($$$0 \\le x_i \\le 9$$$) representing the sequence. The next line contains $$$m$$$ distinct space-separated integers $$$y_1, y_2, \\ldots, y_m$$$ ($$$0 \\le y_i \\le 9$$$) — the keys with fingerprints.", "output_spec": "In a single line print a space-separated sequence of integers representing the code. If the resulting sequence is empty, both printing nothing and printing a single line break is acceptable.", "sample_inputs": ["7 3\n3 5 7 1 6 2 8\n1 2 7", "4 4\n3 4 1 0\n0 1 7 9"], "sample_outputs": ["7 1 2", "1 0"], "notes": "NoteIn the first example, the only digits with fingerprints are $$$1$$$, $$$2$$$ and $$$7$$$. All three of them appear in the sequence you know, $$$7$$$ first, then $$$1$$$ and then $$$2$$$. Therefore the output is 7 1 2. Note that the order is important, and shall be the same as the order in the original sequence.In the second example digits $$$0$$$, $$$1$$$, $$$7$$$ and $$$9$$$ have fingerprints, however only $$$0$$$ and $$$1$$$ appear in the original sequence. $$$1$$$ appears earlier, so the output is 1 0. Again, the order is important."}, "src_uid": "f9044a4b4c3a0c2751217d9b31cd0c72"}
{"nl": {"description": "Vasya has got an undirected graph consisting of $$$n$$$ vertices and $$$m$$$ edges. This graph doesn't contain any self-loops or multiple edges. Self-loop is an edge connecting a vertex to itself. Multiple edges are a pair of edges such that they connect the same pair of vertices. Since the graph is undirected, the pair of edges $$$(1, 2)$$$ and $$$(2, 1)$$$ is considered to be multiple edges. Isolated vertex of the graph is a vertex such that there is no edge connecting this vertex to any other vertex.Vasya wants to know the minimum and maximum possible number of isolated vertices in an undirected graph consisting of $$$n$$$ vertices and $$$m$$$ edges. ", "input_spec": "The only line contains two integers $$$n$$$ and $$$m~(1 \\le n \\le 10^5, 0 \\le m \\le \\frac{n (n - 1)}{2})$$$. It is guaranteed that there exists a graph without any self-loops or multiple edges with such number of vertices and edges.", "output_spec": "In the only line print two numbers $$$min$$$ and $$$max$$$ — the minimum and maximum number of isolated vertices, respectively.", "sample_inputs": ["4 2", "3 1"], "sample_outputs": ["0 1", "1 1"], "notes": "NoteIn the first example it is possible to construct a graph with $$$0$$$ isolated vertices: for example, it should contain edges $$$(1, 2)$$$ and $$$(3, 4)$$$. To get one isolated vertex, we may construct a graph with edges $$$(1, 2)$$$ and $$$(1, 3)$$$. In the second example the graph will always contain exactly one isolated vertex."}, "src_uid": "daf0dd781bf403f7c1bb668925caa64d"}
{"nl": {"description": "Vasya studies music. He has learned lots of interesting stuff. For example, he knows that there are 12 notes: C, C#, D, D#, E, F, F#, G, G#, A, B, H. He also knows that the notes are repeated cyclically: after H goes C again, and before C stands H. We will consider the C note in the row's beginning and the C note after the H similar and we will identify them with each other. The distance between the notes along the musical scale is measured in tones: between two consecutive notes there's exactly one semitone, that is, 0.5 tone. The distance is taken from the lowest tone to the uppest one, that is, the distance between C and E is 4 semitones and between E and C is 8 semitonesVasya also knows what a chord is. A chord is an unordered set of no less than three notes. However, for now Vasya only works with triads, that is with the chords that consist of exactly three notes. He can already distinguish between two types of triads — major and minor.Let's define a major triad. Let the triad consist of notes X, Y and Z. If we can order the notes so as the distance along the musical scale between X and Y equals 4 semitones and the distance between Y and Z is 3 semitones, then the triad is major. The distance between X and Z, accordingly, equals 7 semitones.A minor triad is different in that the distance between X and Y should be 3 semitones and between Y and Z — 4 semitones.For example, the triad \"C E G\" is major: between C and E are 4 semitones, and between E and G are 3 semitones. And the triplet \"C# B F\" is minor, because if we order the notes as \"B C# F\", than between B and C# will be 3 semitones, and between C# and F — 4 semitones.Help Vasya classify the triad the teacher has given to him.", "input_spec": "The only line contains 3 space-separated notes in the above-given notation.", "output_spec": "Print \"major\" if the chord is major, \"minor\" if it is minor, and \"strange\" if the teacher gave Vasya some weird chord which is neither major nor minor. Vasya promises you that the answer will always be unambiguous. That is, there are no chords that are both major and minor simultaneously.", "sample_inputs": ["C E G", "C# B F", "A B H"], "sample_outputs": ["major", "minor", "strange"], "notes": null}, "src_uid": "6aa83c2f6e095848bc63aba7d013aa58"}
{"nl": {"description": "In the city of Saint Petersburg, a day lasts for $$$2^{100}$$$ minutes. From the main station of Saint Petersburg, a train departs after $$$1$$$ minute, $$$4$$$ minutes, $$$16$$$ minutes, and so on; in other words, the train departs at time $$$4^k$$$ for each integer $$$k \\geq 0$$$. Team BowWow has arrived at the station at the time $$$s$$$ and it is trying to count how many trains have they missed; in other words, the number of trains that have departed strictly before time $$$s$$$. For example if $$$s = 20$$$, then they missed trains which have departed at $$$1$$$, $$$4$$$ and $$$16$$$. As you are the only one who knows the time, help them!Note that the number $$$s$$$ will be given you in a binary representation without leading zeroes.", "input_spec": "The first line contains a single binary number $$$s$$$ ($$$0 \\leq s < 2^{100}$$$) without leading zeroes.", "output_spec": "Output a single number — the number of trains which have departed strictly before the time $$$s$$$.", "sample_inputs": ["100000000", "101", "10100"], "sample_outputs": ["4", "2", "3"], "notes": "NoteIn the first example $$$100000000_2 = 256_{10}$$$, missed trains have departed at $$$1$$$, $$$4$$$, $$$16$$$ and $$$64$$$.In the second example $$$101_2 = 5_{10}$$$, trains have departed at $$$1$$$ and $$$4$$$.The third example is explained in the statements."}, "src_uid": "d8ca1c83b431466eff6054d3b422ab47"}
{"nl": {"description": "After a probationary period in the game development company of IT City Petya was included in a group of the programmers that develops a new turn-based strategy game resembling the well known \"Heroes of Might & Magic\". A part of the game is turn-based fights of big squadrons of enemies on infinite fields where every cell is in form of a hexagon.Some of magic effects are able to affect several field cells at once, cells that are situated not farther than n cells away from the cell in which the effect was applied. The distance between cells is the minimum number of cell border crosses on a path from one cell to another.It is easy to see that the number of cells affected by a magic effect grows rapidly when n increases, so it can adversely affect the game performance. That's why Petya decided to write a program that can, given n, determine the number of cells that should be repainted after effect application, so that game designers can balance scale of the effects and the game performance. Help him to do it. Find the number of hexagons situated not farther than n cells away from a given cell.  ", "input_spec": "The only line of the input contains one integer n (0 ≤ n ≤ 109).", "output_spec": "Output one integer — the number of hexagons situated not farther than n cells away from a given cell.", "sample_inputs": ["2"], "sample_outputs": ["19"], "notes": null}, "src_uid": "c046895a90f2e1381a7c1867020453bd"}
{"nl": {"description": "As you know, lemmings like jumping. For the next spectacular group jump n lemmings gathered near a high rock with k comfortable ledges on it. The first ledge is situated at the height of h meters, the second one is at the height of 2h meters, and so on (the i-th ledge is at the height of i·h meters). The lemmings are going to jump at sunset, and there's not much time left.Each lemming is characterized by its climbing speed of vi meters per minute and its weight mi. This means that the i-th lemming can climb to the j-th ledge in  minutes.To make the jump beautiful, heavier lemmings should jump from higher ledges: if a lemming of weight mi jumps from ledge i, and a lemming of weight mj jumps from ledge j (for i < j), then the inequation mi ≤ mj should be fulfilled.Since there are n lemmings and only k ledges (k ≤ n), the k lemmings that will take part in the jump need to be chosen. The chosen lemmings should be distributed on the ledges from 1 to k, one lemming per ledge. The lemmings are to be arranged in the order of non-decreasing weight with the increasing height of the ledge. In addition, each lemming should have enough time to get to his ledge, that is, the time of his climb should not exceed t minutes. The lemmings climb to their ledges all at the same time and they do not interfere with each other.Find the way to arrange the lemmings' jump so that time t is minimized.", "input_spec": "The first line contains space-separated integers n, k and h (1 ≤ k ≤ n ≤ 105, 1 ≤ h ≤ 104) — the total number of lemmings, the number of ledges and the distance between adjacent ledges. The second line contains n space-separated integers m1, m2, ..., mn (1 ≤ mi ≤ 109), where mi is the weight of i-th lemming. The third line contains n space-separated integers v1, v2, ..., vn (1 ≤ vi ≤ 109), where vi is the speed of i-th lemming.", "output_spec": "Print k different numbers from 1 to n — the numbers of the lemmings who go to ledges at heights h, 2h, ..., kh, correspondingly, if the jump is organized in an optimal way. If there are multiple ways to select the lemmings, pick any of them.", "sample_inputs": ["5 3 2\n1 2 3 2 1\n1 2 1 2 10", "5 3 10\n3 4 3 2 1\n5 4 3 2 1"], "sample_outputs": ["5 2 4", "4 3 1"], "notes": "NoteLet's consider the first sample case. The fifth lemming (speed 10) gets to the ledge at height 2 in  minutes; the second lemming (speed 2) gets to the ledge at height 4 in 2 minutes; the fourth lemming (speed 2) gets to the ledge at height 6 in 3 minutes. All lemmings manage to occupy their positions in 3 minutes. "}, "src_uid": "6861128fcd83c752b0ea0286869901c2"}
{"nl": {"description": "Reziba has many magic gems. Each magic gem can be split into $$$M$$$ normal gems. The amount of space each magic (and normal) gem takes is $$$1$$$ unit. A normal gem cannot be split.Reziba wants to choose a set of magic gems and split some of them, so the total space occupied by the resulting set of gems is $$$N$$$ units. If a magic gem is chosen and split, it takes $$$M$$$ units of space (since it is split into $$$M$$$ gems); if a magic gem is not split, it takes $$$1$$$ unit.How many different configurations of the resulting set of gems can Reziba have, such that the total amount of space taken is $$$N$$$ units? Print the answer modulo $$$1000000007$$$ ($$$10^9+7$$$). Two configurations are considered different if the number of magic gems Reziba takes to form them differs, or the indices of gems Reziba has to split differ.", "input_spec": "The input contains a single line consisting of $$$2$$$ integers $$$N$$$ and $$$M$$$ ($$$1 \\le N \\le 10^{18}$$$, $$$2 \\le M \\le 100$$$).", "output_spec": "Print one integer, the total number of configurations of the resulting set of gems, given that the total amount of space taken is $$$N$$$ units. Print the answer modulo $$$1000000007$$$ ($$$10^9+7$$$).", "sample_inputs": ["4 2", "3 2"], "sample_outputs": ["5", "3"], "notes": "NoteIn the first example each magic gem can split into $$$2$$$ normal gems, and we know that the total amount of gems are $$$4$$$.Let $$$1$$$ denote a magic gem, and $$$0$$$ denote a normal gem.The total configurations you can have is:   $$$1 1 1 1$$$ (None of the gems split);  $$$0 0 1 1$$$ (First magic gem splits into $$$2$$$ normal gems);  $$$1 0 0 1$$$ (Second magic gem splits into $$$2$$$ normal gems);  $$$1 1 0 0$$$ (Third magic gem splits into $$$2$$$ normal gems);  $$$0 0 0 0$$$ (First and second magic gems split into total $$$4$$$ normal gems). Hence, answer is $$$5$$$."}, "src_uid": "e7b9eec21d950f5d963ff50619c6f119"}
{"nl": {"description": "You are given two positive integers $$$x$$$ and $$$y$$$. You can perform the following operation with $$$x$$$: write it in its binary form without leading zeros, add $$$0$$$ or $$$1$$$ to the right of it, reverse the binary form and turn it into a decimal number which is assigned as the new value of $$$x$$$.For example:   $$$34$$$ can be turned into $$$81$$$ via one operation: the binary form of $$$34$$$ is $$$100010$$$, if you add $$$1$$$, reverse it and remove leading zeros, you will get $$$1010001$$$, which is the binary form of $$$81$$$.  $$$34$$$ can be turned into $$$17$$$ via one operation: the binary form of $$$34$$$ is $$$100010$$$, if you add $$$0$$$, reverse it and remove leading zeros, you will get $$$10001$$$, which is the binary form of $$$17$$$.  $$$81$$$ can be turned into $$$69$$$ via one operation: the binary form of $$$81$$$ is $$$1010001$$$, if you add $$$0$$$, reverse it and remove leading zeros, you will get $$$1000101$$$, which is the binary form of $$$69$$$.  $$$34$$$ can be turned into $$$69$$$ via two operations: first you turn $$$34$$$ into $$$81$$$ and then $$$81$$$ into $$$69$$$. Your task is to find out whether $$$x$$$ can be turned into $$$y$$$ after a certain number of operations (possibly zero).", "input_spec": "The only line of the input contains two integers $$$x$$$ and $$$y$$$ ($$$1 \\le x, y \\le 10^{18}$$$).", "output_spec": "Print YES if you can make $$$x$$$ equal to $$$y$$$ and NO if you can't.", "sample_inputs": ["3 3", "7 4", "2 8", "34 69", "8935891487501725 71487131900013807"], "sample_outputs": ["YES", "NO", "NO", "YES", "YES"], "notes": "NoteIn the first example, you don't even need to do anything.The fourth example is described in the statement."}, "src_uid": "9f39a3c160087beb0efab2e3cb510e89"}
{"nl": {"description": "Year 2118. Androids are in mass production for decades now, and they do all the work for humans. But androids have to go to school to be able to solve creative tasks. Just like humans before.It turns out that high school struggles are not gone. If someone is not like others, he is bullied. Vasya-8800 is an economy-class android which is produced by a little-known company. His design is not perfect, his characteristics also could be better. So he is bullied by other androids.One of the popular pranks on Vasya is to force him to compare $$$x^y$$$ with $$$y^x$$$. Other androids can do it in milliseconds while Vasya's memory is too small to store such big numbers.Please help Vasya! Write a fast program to compare $$$x^y$$$ with $$$y^x$$$ for Vasya, maybe then other androids will respect him.", "input_spec": "On the only line of input there are two integers $$$x$$$ and $$$y$$$ ($$$1 \\le x, y \\le 10^{9}$$$).", "output_spec": "If $$$x^y < y^x$$$, then print '<' (without quotes). If $$$x^y > y^x$$$, then print '>' (without quotes). If $$$x^y = y^x$$$, then print '=' (without quotes).", "sample_inputs": ["5 8", "10 3", "6 6"], "sample_outputs": [">", "<", "="], "notes": "NoteIn the first example $$$5^8 = 5 \\cdot 5 \\cdot 5 \\cdot 5 \\cdot 5 \\cdot 5 \\cdot 5 \\cdot 5 = 390625$$$, and $$$8^5 = 8 \\cdot 8 \\cdot 8 \\cdot 8 \\cdot 8 = 32768$$$. So you should print '>'.In the second example $$$10^3 = 1000 < 3^{10} = 59049$$$.In the third example $$$6^6 = 46656 = 6^6$$$."}, "src_uid": "ec1e44ff41941f0e6436831b5ae543c6"}
{"nl": {"description": "Noora is a student of one famous high school. It's her final year in school — she is going to study in university next year. However, she has to get an «A» graduation certificate in order to apply to a prestigious one.In school, where Noora is studying, teachers are putting down marks to the online class register, which are integers from 1 to k. The worst mark is 1, the best is k. Mark that is going to the certificate, is calculated as an average of all the marks, rounded to the closest integer. If several answers are possible, rounding up is produced. For example, 7.3 is rounded to 7, but 7.5 and 7.8784 — to 8. For instance, if Noora has marks [8, 9], then the mark to the certificate is 9, because the average is equal to 8.5 and rounded to 9, but if the marks are [8, 8, 9], Noora will have graduation certificate with 8.To graduate with «A» certificate, Noora has to have mark k.Noora got n marks in register this year. However, she is afraid that her marks are not enough to get final mark k. Noora decided to ask for help in the internet, where hacker Leha immediately responded to her request. He is ready to hack class register for Noora and to add Noora any number of additional marks from 1 to k. At the same time, Leha want his hack be unseen to everyone, so he decided to add as less as possible additional marks. Please help Leha to calculate the minimal number of marks he has to add, so that final Noora's mark will become equal to k.", "input_spec": "The first line contains two integers n and k (1 ≤ n ≤ 100, 1 ≤ k ≤ 100) denoting the number of marks, received by Noora and the value of highest possible mark. The second line contains n integers a1, a2, ..., an (1 ≤ ai ≤ k) denoting marks received by Noora before Leha's hack.", "output_spec": "Print a single integer — minimal number of additional marks, that Leha has to add in order to change Noora's final mark to k.", "sample_inputs": ["2 10\n8 9", "3 5\n4 4 4"], "sample_outputs": ["4", "3"], "notes": "NoteConsider the first example testcase.Maximal mark is 10, Noora received two marks — 8 and 9, so current final mark is 9. To fix it, Leha can add marks [10, 10, 10, 10] (4 marks in total) to the registry, achieving Noora having average mark equal to . Consequently, new final mark is 10. Less number of marks won't fix the situation.In the second example Leha can add [5, 5, 5] to the registry, so that making average mark equal to 4.5, which is enough to have 5 in the certificate."}, "src_uid": "f22267bf3fad0bf342ecf4c27ad3a900"}
{"nl": {"description": "Doctor prescribed medicine to his patient. The medicine is represented by pills. Each pill consists of a shell and healing powder. The shell consists of two halves; each half has one of four colors — blue, red, white or yellow.The doctor wants to put 28 pills in a rectangular box 7 × 8 in size. Besides, each pill occupies exactly two neighboring cells and any cell contains exactly one half of a pill. Thus, the result is a four colored picture 7 × 8 in size.The doctor thinks that a patient will recover sooner if the picture made by the pills will be special. Unfortunately, putting the pills in the box so as to get the required picture is not a very easy task. That's why doctor asks you to help. Doctor has some amount of pills of each of 10 painting types. They all contain the same medicine, that's why it doesn't matter which 28 of them will be stored inside the box.Place the pills in the box so that the required picture was formed. If it is impossible to place the pills in the required manner, then place them so that the number of matching colors in all 56 cells in the final arrangement and the doctor's picture were maximum.", "input_spec": "First 7 lines contain the doctor's picture. Each line contains 8 characters, each character can be \"B\", \"R\", \"W\" and \"Y\" that stands for blue, red, white and yellow colors correspondingly. Next four lines contain 10 numbers that stand for, correspondingly, the number of pills painted: \"BY\" \"BW\" \"BR\" \"BB\" \"RY\" \"RW\" \"RR\" \"WY\" \"WW\" \"YY\" Those numbers lie within range from 0 to 28 inclusively. It is guaranteed that the total number of pills in no less than 28.", "output_spec": "Print on the first line the maximal number cells for which the colors match. Then print 13 lines each containing 15 characters — the pills' position in the optimal arrangement. The intersections of odd lines and odd columns should contain characters \"B\", \"R\", \"W\" and \"Y\". All other positions should contain characters \".\", \"-\" and \"|\". Use \"-\" and \"|\" to show which halves belong to one pill. See the samples for more clarification. If there are several possible solutions, print any of them.", "sample_inputs": ["WWWBBWWW\nWWWBBWWW\nYYWBBWWW\nYYWBBWRR\nYYWBBWRR\nYYWBBWRR\nYYWBBWRR\n0 0 0 8\n0 1 5\n1 10\n5", "WWWWWWWW\nWBYWRBBY\nBRYRBWYY\nWWBRYWBB\nBWWRWBYW\nRBWRBWYY\nWWWWWWWW\n0 0 0 1\n0 0 1\n0 1\n25"], "sample_outputs": ["53\nW.W.W.B.B.W.W.W\n|.|.|.|.|.|.|.|\nW.W.W.B.B.W.W.W\n...............\nY.Y.W.B.B.W.W-W\n|.|.|.|.|.|....\nY.Y.W.B.B.W.R.R\n............|.|\nY.Y.W.B.B.R.R.R\n|.|.|.|.|.|....\nY.Y.W.B.B.W.R.R\n............|.|\nY-Y.B-B.B-B.R.R", "15\nW.Y.Y-Y.Y-Y.Y-Y\n|.|............\nW.Y.Y.Y.Y.B-B.Y\n....|.|.|.....|\nY-Y.Y.Y.Y.Y-Y.Y\n...............\nY.Y.Y.R.Y.Y.Y-Y\n|.|.|.|.|.|....\nY.Y.Y.R.Y.Y.Y.Y\n............|.|\nY-Y.Y.Y-Y.Y.Y.Y\n....|.....|....\nY-Y.Y.Y-Y.Y.Y-Y"], "notes": null}, "src_uid": "cb56e7578ec5e04118993444283ad1eb"}
{"nl": {"description": "Alice has a lovely piece of cloth. It has the shape of a square with a side of length $$$a$$$ centimeters. Bob also wants such piece of cloth. He would prefer a square with a side of length $$$b$$$ centimeters (where $$$b < a$$$). Alice wanted to make Bob happy, so she cut the needed square out of the corner of her piece and gave it to Bob. Now she is left with an ugly L shaped cloth (see pictures below).Alice would like to know whether the area of her cloth expressed in square centimeters is prime. Could you help her to determine it?", "input_spec": "The first line contains a number $$$t$$$ ($$$1 \\leq t \\leq 5$$$) — the number of test cases. Each of the next $$$t$$$ lines describes the $$$i$$$-th test case. It contains two integers $$$a$$$ and $$$b~(1 \\leq b < a \\leq 10^{11})$$$ — the side length of Alice's square and the side length of the square that Bob wants.", "output_spec": "Print $$$t$$$ lines, where the $$$i$$$-th line is the answer to the $$$i$$$-th test case. Print \"YES\" (without quotes) if the area of the remaining piece of cloth is prime, otherwise print \"NO\". You can print each letter in an arbitrary case (upper or lower).", "sample_inputs": ["4\n6 5\n16 13\n61690850361 24777622630\n34 33"], "sample_outputs": ["YES\nNO\nNO\nYES"], "notes": "NoteThe figure below depicts the first test case. The blue part corresponds to the piece which belongs to Bob, and the red part is the piece that Alice keeps for herself. The area of the red part is $$$6^2 - 5^2 = 36 - 25 = 11$$$, which is prime, so the answer is \"YES\".  In the second case, the area is $$$16^2 - 13^2 = 87$$$, which is divisible by $$$3$$$.  In the third case, the area of the remaining piece is $$$61690850361^2 - 24777622630^2 = 3191830435068605713421$$$. This number is not prime because $$$3191830435068605713421 = 36913227731 \\cdot 86468472991 $$$.In the last case, the area is $$$34^2 - 33^2 = 67$$$."}, "src_uid": "5a052e4e6c64333d94c83df890b1183c"}
{"nl": {"description": "Let's assume that set S consists of m distinct intervals [l1, r1], [l2, r2], ..., [lm, rm] (1 ≤ li ≤ ri ≤ n; li, ri are integers).Let's assume that f(S) is the maximum number of intervals that you can choose from the set S, such that every two of them do not intersect. We assume that two intervals, [l1, r1] and [l2, r2], intersect if there is an integer x, which meets two inequalities: l1 ≤ x ≤ r1 and l2 ≤ x ≤ r2.Sereja wonders, how many sets S are there, such that f(S) = k? Count this number modulo 1000000007 (109 + 7).", "input_spec": "The first line contains integers n, k (1 ≤ n ≤ 500; 0 ≤ k ≤ 500).", "output_spec": "In a single line, print the answer to the problem modulo 1000000007 (109 + 7).", "sample_inputs": ["3 1", "3 2", "2 0", "2 2"], "sample_outputs": ["23", "32", "1", "2"], "notes": null}, "src_uid": "111673158df2e37ac6c019bb99225ccb"}
{"nl": {"description": "You have unlimited number of coins with values $$$1, 2, \\ldots, n$$$. You want to select some set of coins having the total value of $$$S$$$. It is allowed to have multiple coins with the same value in the set. What is the minimum number of coins required to get sum $$$S$$$?", "input_spec": "The only line of the input contains two integers $$$n$$$ and $$$S$$$ ($$$1 \\le n \\le 100\\,000$$$, $$$1 \\le S \\le 10^9$$$)", "output_spec": "Print exactly one integer — the minimum number of coins required to obtain sum $$$S$$$.", "sample_inputs": ["5 11", "6 16"], "sample_outputs": ["3", "3"], "notes": "NoteIn the first example, some of the possible ways to get sum $$$11$$$ with $$$3$$$ coins are:   $$$(3, 4, 4)$$$ $$$(2, 4, 5)$$$ $$$(1, 5, 5)$$$ $$$(3, 3, 5)$$$ It is impossible to get sum $$$11$$$ with less than $$$3$$$ coins.In the second example, some of the possible ways to get sum $$$16$$$ with $$$3$$$ coins are:   $$$(5, 5, 6)$$$ $$$(4, 6, 6)$$$ It is impossible to get sum $$$16$$$ with less than $$$3$$$ coins."}, "src_uid": "04c067326ec897091c3dbcf4d134df96"}
{"nl": {"description": "Vasily the bear has a favorite rectangle, it has one vertex at point (0, 0), and the opposite vertex at point (x, y). Of course, the sides of Vasya's favorite rectangle are parallel to the coordinate axes. Vasya also loves triangles, if the triangles have one vertex at point B = (0, 0). That's why today he asks you to find two points A = (x1, y1) and C = (x2, y2), such that the following conditions hold:  the coordinates of points: x1, x2, y1, y2 are integers. Besides, the following inequation holds: x1 < x2;  the triangle formed by point A, B and C is rectangular and isosceles ( is right);  all points of the favorite rectangle are located inside or on the border of triangle ABC;  the area of triangle ABC is as small as possible. Help the bear, find the required points. It is not so hard to proof that these points are unique.", "input_spec": "The first line contains two integers x, y ( - 109 ≤ x, y ≤ 109, x ≠ 0, y ≠ 0).", "output_spec": "Print in the single line four integers x1, y1, x2, y2 — the coordinates of the required points.", "sample_inputs": ["10 5", "-10 5"], "sample_outputs": ["0 15 15 0", "-15 0 0 15"], "notes": "NoteFigure to the first sample"}, "src_uid": "e2f15a9d9593eec2e19be3140a847712"}
{"nl": {"description": "Mike is trying rock climbing but he is awful at it. There are n holds on the wall, i-th hold is at height ai off the ground. Besides, let the sequence ai increase, that is, ai < ai + 1 for all i from 1 to n - 1; we will call such sequence a track. Mike thinks that the track a1, ..., an has difficulty . In other words, difficulty equals the maximum distance between two holds that are adjacent in height.Today Mike decided to cover the track with holds hanging on heights a1, ..., an. To make the problem harder, Mike decided to remove one hold, that is, remove one element of the sequence (for example, if we take the sequence (1, 2, 3, 4, 5) and remove the third element from it, we obtain the sequence (1, 2, 4, 5)). However, as Mike is awful at climbing, he wants the final difficulty (i.e. the maximum difference of heights between adjacent holds after removing the hold) to be as small as possible among all possible options of removing a hold. The first and last holds must stay at their positions.Help Mike determine the minimum difficulty of the track after removing one hold.", "input_spec": "The first line contains a single integer n (3 ≤ n ≤ 100) — the number of holds. The next line contains n space-separated integers ai (1 ≤ ai ≤ 1000), where ai is the height where the hold number i hangs. The sequence ai is increasing (i.e. each element except for the first one is strictly larger than the previous one).", "output_spec": "Print a single number — the minimum difficulty of the track after removing a single hold.", "sample_inputs": ["3\n1 4 6", "5\n1 2 3 4 5", "5\n1 2 3 7 8"], "sample_outputs": ["5", "2", "4"], "notes": "NoteIn the first sample you can remove only the second hold, then the sequence looks like (1, 6), the maximum difference of the neighboring elements equals 5.In the second test after removing every hold the difficulty equals 2.In the third test you can obtain sequences (1, 3, 7, 8), (1, 2, 7, 8), (1, 2, 3, 8), for which the difficulty is 4, 5 and 5, respectively. Thus, after removing the second element we obtain the optimal answer — 4."}, "src_uid": "8a8013f960814040ac4bf229a0bd5437"}
{"nl": {"description": "Santa Claus has n candies, he dreams to give them as gifts to children.What is the maximal number of children for whose he can give candies if Santa Claus want each kid should get distinct positive integer number of candies. Santa Class wants to give all n candies he has.", "input_spec": "The only line contains positive integer number n (1 ≤ n ≤ 1000) — number of candies Santa Claus has.", "output_spec": "Print to the first line integer number k — maximal number of kids which can get candies. Print to the second line k distinct integer numbers: number of candies for each of k kid. The sum of k printed numbers should be exactly n. If there are many solutions, print any of them.", "sample_inputs": ["5", "9", "2"], "sample_outputs": ["2\n2 3", "3\n3 5 1", "1\n2"], "notes": null}, "src_uid": "356a7bcebbbd354c268cddbb5454d5fc"}
{"nl": {"description": "Jabber ID on the national Berland service «Babber» has a form <username>@<hostname>[/resource], where   <username> — is a sequence of Latin letters (lowercase or uppercase), digits or underscores characters «_», the length of <username> is between 1 and 16, inclusive.  <hostname> — is a sequence of word separated by periods (characters «.»), where each word should contain only characters allowed for <username>, the length of each word is between 1 and 16, inclusive. The length of <hostname> is between 1 and 32, inclusive.  <resource> — is a sequence of Latin letters (lowercase or uppercase), digits or underscores characters «_», the length of <resource> is between 1 and 16, inclusive. The content of square brackets is optional — it can be present or can be absent.There are the samples of correct Jabber IDs: mike@codeforces.com, 007@en.codeforces.com/contest.Your task is to write program which checks if given string is a correct Jabber ID.", "input_spec": "The input contains of a single line. The line has the length between 1 and 100 characters, inclusive. Each characters has ASCII-code between 33 and 127, inclusive.", "output_spec": "Print YES or NO.", "sample_inputs": ["mike@codeforces.com", "john.smith@codeforces.ru/contest.icpc/12"], "sample_outputs": ["YES", "NO"], "notes": null}, "src_uid": "2a68157e327f92415067f127feb31e24"}
{"nl": {"description": "  Walking through the streets of Marshmallow City, Slastyona have spotted some merchants selling a kind of useless toy which is very popular nowadays – caramel spinner! Wanting to join the craze, she has immediately bought the strange contraption.Spinners in Sweetland have the form of V-shaped pieces of caramel. Each spinner can, well, spin around an invisible magic axis. At a specific point in time, a spinner can take 4 positions shown below (each one rotated 90 degrees relative to the previous, with the fourth one followed by the first one):  After the spinner was spun, it starts its rotation, which is described by a following algorithm: the spinner maintains its position for a second then majestically switches to the next position in clockwise or counter-clockwise order, depending on the direction the spinner was spun in.Slastyona managed to have spinner rotating for exactly n seconds. Being fascinated by elegance of the process, she completely forgot the direction the spinner was spun in! Lucky for her, she managed to recall the starting position, and wants to deduct the direction given the information she knows. Help her do this.", "input_spec": "There are two characters in the first string – the starting and the ending position of a spinner. The position is encoded with one of the following characters: v (ASCII code 118, lowercase v), < (ASCII code 60), ^ (ASCII code 94) or > (ASCII code 62) (see the picture above for reference). Characters are separated by a single space. In the second strings, a single number n is given (0 ≤ n ≤ 109) – the duration of the rotation. It is guaranteed that the ending position of a spinner is a result of a n second spin in any of the directions, assuming the given starting position.", "output_spec": "Output cw, if the direction is clockwise, ccw – if counter-clockwise, and undefined otherwise.", "sample_inputs": ["^ >\n1", "< ^\n3", "^ v\n6"], "sample_outputs": ["cw", "ccw", "undefined"], "notes": null}, "src_uid": "fb99ef80fd21f98674fe85d80a2e5298"}
{"nl": {"description": "Do you remember how Kai constructed the word \"eternity\" using pieces of ice as components?Little Sheldon plays with pieces of ice, each piece has exactly one digit between 0 and 9. He wants to construct his favourite number t. He realized that digits 6 and 9 are very similar, so he can rotate piece of ice with 6 to use as 9 (and vice versa). Similary, 2 and 5 work the same. There is no other pair of digits with similar effect. He called this effect \"Digital Mimicry\".Sheldon favourite number is t. He wants to have as many instances of t as possible. How many instances he can construct using the given sequence of ice pieces. He can use any piece at most once. ", "input_spec": "The first line contains integer t (1 ≤ t ≤ 10000). The second line contains the sequence of digits on the pieces. The length of line is equal to the number of pieces and between 1 and 200, inclusive. It contains digits between 0 and 9.", "output_spec": "Print the required number of instances.", "sample_inputs": ["42\n23454", "169\n12118999"], "sample_outputs": ["2", "1"], "notes": "NoteThis problem contains very weak pretests."}, "src_uid": "72a196044787cb8dbd8d350cb60ccc32"}
{"nl": {"description": "Barney is standing in a bar and starring at a pretty girl. He wants to shoot her with his heart arrow but he needs to know the distance between him and the girl to make his shot accurate.  Barney asked the bar tender Carl about this distance value, but Carl was so busy talking to the customers so he wrote the distance value (it's a real number) on a napkin. The problem is that he wrote it in scientific notation. The scientific notation of some real number x is the notation of form AeB, where A is a real number and B is an integer and x = A × 10B is true. In our case A is between 0 and 9 and B is non-negative.Barney doesn't know anything about scientific notation (as well as anything scientific at all). So he asked you to tell him the distance value in usual decimal representation with minimal number of digits after the decimal point (and no decimal point if it is an integer). See the output format for better understanding.", "input_spec": "The first and only line of input contains a single string of form a.deb where a, d and b are integers and e is usual character 'e' (0 ≤ a ≤ 9, 0 ≤ d < 10100, 0 ≤ b ≤ 100) — the scientific notation of the desired distance value. a and b contain no leading zeros and d contains no trailing zeros (but may be equal to 0). Also, b can not be non-zero if a is zero.", "output_spec": "Print the only real number x (the desired distance value) in the only line in its decimal notation.  Thus if x is an integer, print it's integer value without decimal part and decimal point and without leading zeroes.  Otherwise print x in a form of p.q such that p is an integer that have no leading zeroes (but may be equal to zero), and q is an integer that have no trailing zeroes (and may not be equal to zero).", "sample_inputs": ["8.549e2", "8.549e3", "0.33e0"], "sample_outputs": ["854.9", "8549", "0.33"], "notes": null}, "src_uid": "a79358099f08f3ec50c013d47d910eef"}
{"nl": {"description": "What joy! Petya's parents went on a business trip for the whole year and the playful kid is left all by himself. Petya got absolutely happy. He jumped on the bed and threw pillows all day long, until... Today Petya opened the cupboard and found a scary note there. His parents had left him with duties: he should water their favourite flower all year, each day, in the morning, in the afternoon and in the evening. \"Wait a second!\" — thought Petya. He know for a fact that if he fulfills the parents' task in the i-th (1 ≤ i ≤ 12) month of the year, then the flower will grow by ai centimeters, and if he doesn't water the flower in the i-th month, then the flower won't grow this month. Petya also knows that try as he might, his parents won't believe that he has been watering the flower if it grows strictly less than by k centimeters. Help Petya choose the minimum number of months when he will water the flower, given that the flower should grow no less than by k centimeters.", "input_spec": "The first line contains exactly one integer k (0 ≤ k ≤ 100). The next line contains twelve space-separated integers: the i-th (1 ≤ i ≤ 12) number in the line represents ai (0 ≤ ai ≤ 100). ", "output_spec": "Print the only integer — the minimum number of months when Petya has to water the flower so that the flower grows no less than by k centimeters. If the flower can't grow by k centimeters in a year, print -1.", "sample_inputs": ["5\n1 1 1 1 2 2 3 2 2 1 1 1", "0\n0 0 0 0 0 0 0 1 1 2 3 0", "11\n1 1 4 1 1 5 1 1 4 1 1 1"], "sample_outputs": ["2", "0", "3"], "notes": "NoteLet's consider the first sample test. There it is enough to water the flower during the seventh and the ninth month. Then the flower grows by exactly five centimeters.In the second sample Petya's parents will believe him even if the flower doesn't grow at all (k = 0). So, it is possible for Petya not to water the flower at all."}, "src_uid": "59dfa7a4988375febc5dccc27aca90a8"}
{"nl": {"description": "Fangy collects cookies. Once he decided to take a box and put cookies into it in some way. If we take a square k × k in size, divided into blocks 1 × 1 in size and paint there the main diagonal together with cells, which lie above it, then the painted area will be equal to the area occupied by one cookie k in size. Fangy also has a box with a square base 2n × 2n, divided into blocks 1 × 1 in size. In a box the cookies should not overlap, and they should not be turned over or rotated. See cookies of sizes 2 and 4 respectively on the figure:    To stack the cookies the little walrus uses the following algorithm. He takes out of the repository the largest cookie which can fit in some place in the box and puts it there. Everything could be perfect but alas, in the repository the little walrus has infinitely many cookies of size 2 and larger, and there are no cookies of size 1, therefore, empty cells will remain in the box. Fangy wants to know how many empty cells will be left in the end.", "input_spec": "The first line contains a single integer n (0 ≤ n ≤ 1000).", "output_spec": "Print the single number, equal to the number of empty cells in the box. The answer should be printed modulo 106 + 3.", "sample_inputs": ["3"], "sample_outputs": ["9"], "notes": "NoteIf the box possesses the base of 23 × 23 (as in the example), then the cookies will be put there in the following manner: "}, "src_uid": "1a335a9638523ca0315282a67e18eec7"}
{"nl": {"description": "The cows have just learned what a primitive root is! Given a prime p, a primitive root  is an integer x (1 ≤ x < p) such that none of integers x - 1, x2 - 1, ..., xp - 2 - 1 are divisible by p, but xp - 1 - 1 is. Unfortunately, computing primitive roots can be time consuming, so the cows need your help. Given a prime p, help the cows find the number of primitive roots .", "input_spec": "The input contains a single line containing an integer p (2 ≤ p < 2000). It is guaranteed that p is a prime.", "output_spec": "Output on a single line the number of primitive roots .", "sample_inputs": ["3", "5"], "sample_outputs": ["1", "2"], "notes": "NoteThe only primitive root  is 2.The primitive roots  are 2 and 3."}, "src_uid": "3bed682b6813f1ddb54410218c233cff"}
{"nl": {"description": "Polycarp invited all his friends to the tea party to celebrate the holiday. He has n cups, one for each of his n friends, with volumes a1, a2, ..., an. His teapot stores w milliliters of tea (w ≤ a1 + a2 + ... + an). Polycarp wants to pour tea in cups in such a way that:  Every cup will contain tea for at least half of its volume  Every cup will contain integer number of milliliters of tea  All the tea from the teapot will be poured into cups  All friends will be satisfied. Friend with cup i won't be satisfied, if there exists such cup j that cup i contains less tea than cup j but ai > aj.For each cup output how many milliliters of tea should be poured in it. If it's impossible to pour all the tea and satisfy all conditions then output -1.", "input_spec": "The first line contains two integer numbers n and w (1 ≤ n ≤ 100, ). The second line contains n numbers a1, a2, ..., an (1 ≤ ai ≤ 100).", "output_spec": "Output how many milliliters of tea every cup should contain. If there are multiple answers, print any of them. If it's impossible to pour all the tea and satisfy all conditions then output -1.", "sample_inputs": ["2 10\n8 7", "4 4\n1 1 1 1", "3 10\n9 8 10"], "sample_outputs": ["6 4", "1 1 1 1", "-1"], "notes": "NoteIn the third example you should pour to the first cup at least 5 milliliters, to the second one at least 4, to the third one at least 5. It sums up to 14, which is greater than 10 milliliters available."}, "src_uid": "5d3bb9e03f4c5c8ecb6233bd5f90f3a3"}
{"nl": {"description": "The Fat Rat and his friend Сerealguy have had a bet whether at least a few oats are going to descend to them by some clever construction. The figure below shows the clever construction.  A more formal description of the clever construction is as follows. The clever construction consists of n rows with scales. The first row has n scales, the second row has (n - 1) scales, the i-th row has (n - i + 1) scales, the last row has exactly one scale. Let's number the scales in each row from the left to the right, starting from 1. Then the value of wi, k in kilograms (1 ≤ i ≤ n; 1 ≤ k ≤ n - i + 1) is the weight capacity parameter of the k-th scale in the i-th row. If a body whose mass is not less than wi, k falls on the scale with weight capacity wi, k, then the scale breaks. At that anything that the scale has on it, either falls one level down to the left (if possible) or one level down to the right (if possible). In other words, if the scale wi, k (i < n) breaks, then there are at most two possible variants in which the contents of the scale's pan can fall out: all contents of scale wi, k falls either on scale wi + 1, k - 1 (if it exists), or on scale wi + 1, k (if it exists). If scale wn, 1 breaks, then all its contents falls right in the Fat Rat's claws. Please note that the scales that are the first and the last in a row, have only one variant of dropping the contents.Initially, oats are simultaneously put on all scales of the first level. The i-th scale has ai kilograms of oats put on it. After that the scales start breaking and the oats start falling down in some way. You can consider everything to happen instantly. That is, the scale breaks instantly and the oats also fall instantly.The Fat Rat is sure that whatever happens, he will not get the oats from the first level. Cerealguy is sure that there is such a scenario, when the rat gets at least some number of the oats. Help the Fat Rat and the Cerealguy. Determine, which one is right.", "input_spec": "The first line contains a single integer n (1 ≤ n ≤ 50) — the number of rows with scales. The next line contains n space-separated integers ai (1 ≤ ai ≤ 106) — the masses of the oats in kilograms. The next n lines contain descriptions of the scales: the i-th line contains (n - i + 1) space-separated integers wi, k (1 ≤ wi, k ≤ 106) — the weight capacity parameters for the scales that stand on the i-th row, in kilograms.", "output_spec": "Print \"Fat Rat\" if the Fat Rat is right, otherwise print \"Cerealguy\".", "sample_inputs": ["1\n1\n2", "2\n2 2\n1 2\n4", "2\n2 2\n1 2\n5"], "sample_outputs": ["Fat Rat", "Cerealguy", "Fat Rat"], "notes": "NoteNotes to the examples:   The first example: the scale with weight capacity 2 gets 1. That means that the lower scale don't break.  The second sample: all scales in the top row obviously break. Then the oats fall on the lower row. Their total mass is 4,and that's exactly the weight that the lower scale can \"nearly endure\". So, as 4  ≥  4, the scale breaks."}, "src_uid": "0a77937c01ac69490f8b478eae77de1d"}
{"nl": {"description": "Bear Limak prepares problems for a programming competition. Of course, it would be unprofessional to mention the sponsor name in the statement. Limak takes it seriously and he is going to change some words. To make it still possible to read, he will try to modify each word as little as possible.Limak has a string s that consists of uppercase English letters. In one move he can swap two adjacent letters of the string. For example, he can transform a string \"ABBC\" into \"BABC\" or \"ABCB\" in one move.Limak wants to obtain a string without a substring \"VK\" (i.e. there should be no letter 'V' immediately followed by letter 'K'). It can be easily proved that it's possible for any initial string s.What is the minimum possible number of moves Limak can do?", "input_spec": "The first line of the input contains an integer n (1 ≤ n ≤ 75) — the length of the string. The second line contains a string s, consisting of uppercase English letters. The length of the string is equal to n.", "output_spec": "Print one integer, denoting the minimum possible number of moves Limak can do, in order to obtain a string without a substring \"VK\".", "sample_inputs": ["4\nVKVK", "5\nBVVKV", "7\nVVKEVKK", "20\nVKVKVVVKVOVKVQKKKVVK", "5\nLIMAK"], "sample_outputs": ["3", "2", "3", "8", "0"], "notes": "NoteIn the first sample, the initial string is \"VKVK\". The minimum possible number of moves is 3. One optimal sequence of moves is: Swap two last letters. The string becomes \"VKKV\". Swap first two letters. The string becomes \"KVKV\". Swap the second and the third letter. The string becomes \"KKVV\". Indeed, this string doesn't have a substring \"VK\".In the second sample, there are two optimal sequences of moves. One is \"BVVKV\"  →  \"VBVKV\"  →  \"VVBKV\". The other is \"BVVKV\"  →  \"BVKVV\"  →  \"BKVVV\".In the fifth sample, no swaps are necessary."}, "src_uid": "08444f9ab1718270b5ade46852b155d7"}
{"nl": {"description": "Olesya loves numbers consisting of n digits, and Rodion only likes numbers that are divisible by t. Find some number that satisfies both of them.Your task is: given the n and t print an integer strictly larger than zero consisting of n digits that is divisible by t. If such number doesn't exist, print  - 1.", "input_spec": "The single line contains two numbers, n and t (1 ≤ n ≤ 100, 2 ≤ t ≤ 10) — the length of the number and the number it should be divisible by.", "output_spec": "Print one such positive number without leading zeroes, — the answer to the problem, or  - 1, if such number doesn't exist. If there are multiple possible answers, you are allowed to print any of them.", "sample_inputs": ["3 2"], "sample_outputs": ["712"], "notes": null}, "src_uid": "77ffc1e38c32087f98ab5b3cb11cd2ed"}
{"nl": {"description": "A famous Berland's painter Kalevitch likes to shock the public. One of his last obsessions is chess. For more than a thousand years people have been playing this old game on uninteresting, monotonous boards. Kalevitch decided to put an end to this tradition and to introduce a new attitude to chessboards.As before, the chessboard is a square-checkered board with the squares arranged in a 8 × 8 grid, each square is painted black or white. Kalevitch suggests that chessboards should be painted in the following manner: there should be chosen a horizontal or a vertical line of 8 squares (i.e. a row or a column), and painted black. Initially the whole chessboard is white, and it can be painted in the above described way one or more times. It is allowed to paint a square many times, but after the first time it does not change its colour any more and remains black. Kalevitch paints chessboards neatly, and it is impossible to judge by an individual square if it was painted with a vertical or a horizontal stroke.Kalevitch hopes that such chessboards will gain popularity, and he will be commissioned to paint chessboards, which will help him ensure a comfortable old age. The clients will inform him what chessboard they want to have, and the painter will paint a white chessboard meeting the client's requirements.It goes without saying that in such business one should economize on everything — for each commission he wants to know the minimum amount of strokes that he has to paint to fulfill the client's needs. You are asked to help Kalevitch with this task.", "input_spec": "The input file contains 8 lines, each of the lines contains 8 characters. The given matrix describes the client's requirements, W character stands for a white square, and B character — for a square painted black. It is guaranteed that client's requirments can be fulfilled with a sequence of allowed strokes (vertical/column or horizontal/row).", "output_spec": "Output the only number — the minimum amount of rows and columns that Kalevitch has to paint on the white chessboard to meet the client's requirements.", "sample_inputs": ["WWWBWWBW\nBBBBBBBB\nWWWBWWBW\nWWWBWWBW\nWWWBWWBW\nWWWBWWBW\nWWWBWWBW\nWWWBWWBW", "WWWWWWWW\nBBBBBBBB\nWWWWWWWW\nWWWWWWWW\nWWWWWWWW\nWWWWWWWW\nWWWWWWWW\nWWWWWWWW"], "sample_outputs": ["3", "1"], "notes": null}, "src_uid": "8b6ae2190413b23f47e2958a7d4e7bc0"}
{"nl": {"description": "You have r red, g green and b blue balloons. To decorate a single table for the banquet you need exactly three balloons. Three balloons attached to some table shouldn't have the same color. What maximum number t of tables can be decorated if we know number of balloons of each color?Your task is to write a program that for given values r, g and b will find the maximum number t of tables, that can be decorated in the required manner.", "input_spec": "The single line contains three integers r, g and b (0 ≤ r, g, b ≤ 2·109) — the number of red, green and blue baloons respectively. The numbers are separated by exactly one space.", "output_spec": "Print a single integer t — the maximum number of tables that can be decorated in the required manner.", "sample_inputs": ["5 4 3", "1 1 1", "2 3 3"], "sample_outputs": ["4", "1", "2"], "notes": "NoteIn the first sample you can decorate the tables with the following balloon sets: \"rgg\", \"gbb\", \"brr\", \"rrg\", where \"r\", \"g\" and \"b\" represent the red, green and blue balls, respectively."}, "src_uid": "bae7cbcde19114451b8712d6361d2b01"}
{"nl": {"description": "Vasilisa the Wise from the Kingdom of Far Far Away got a magic box with a secret as a present from her friend Hellawisa the Wise from the Kingdom of A Little Closer. However, Vasilisa the Wise does not know what the box's secret is, since she cannot open it again. She hopes that you will help her one more time with that.The box's lock looks as follows: it contains 4 identical deepenings for gems as a 2 × 2 square, and some integer numbers are written at the lock's edge near the deepenings. The example of a lock is given on the picture below.  The box is accompanied with 9 gems. Their shapes match the deepenings' shapes and each gem contains one number from 1 to 9 (each number is written on exactly one gem). The box will only open after it is decorated with gems correctly: that is, each deepening in the lock should be filled with exactly one gem. Also, the sums of numbers in the square's rows, columns and two diagonals of the square should match the numbers written at the lock's edge. For example, the above lock will open if we fill the deepenings with gems with numbers as is shown on the picture below.  Now Vasilisa the Wise wants to define, given the numbers on the box's lock, which gems she should put in the deepenings to open the box. Help Vasilisa to solve this challenging task.", "input_spec": "The input contains numbers written on the edges of the lock of the box. The first line contains space-separated integers r1 and r2 that define the required sums of numbers in the rows of the square. The second line contains space-separated integers c1 and c2 that define the required sums of numbers in the columns of the square. The third line contains space-separated integers d1 and d2 that define the required sums of numbers on the main and on the side diagonals of the square (1 ≤ r1, r2, c1, c2, d1, d2 ≤ 20). Correspondence between the above 6 variables and places where they are written is shown on the picture below. For more clarifications please look at the second sample test that demonstrates the example given in the problem statement.   ", "output_spec": "Print the scheme of decorating the box with stones: two lines containing two space-separated integers from 1 to 9. The numbers should be pairwise different. If there is no solution for the given lock, then print the single number \"-1\" (without the quotes). If there are several solutions, output any.", "sample_inputs": ["3 7\n4 6\n5 5", "11 10\n13 8\n5 16", "1 2\n3 4\n5 6", "10 10\n10 10\n10 10"], "sample_outputs": ["1 2\n3 4", "4 7\n9 1", "-1", "-1"], "notes": "NotePay attention to the last test from the statement: it is impossible to open the box because for that Vasilisa the Wise would need 4 identical gems containing number \"5\". However, Vasilisa only has one gem with each number from 1 to 9."}, "src_uid": "6821f502f5b6ec95c505e5dd8f3cd5d3"}
{"nl": {"description": "Mahmoud and Ehab play a game called the even-odd game. Ehab chooses his favorite integer n and then they take turns, starting from Mahmoud. In each player's turn, he has to choose an integer a and subtract it from n such that:  1 ≤ a ≤ n.  If it's Mahmoud's turn, a has to be even, but if it's Ehab's turn, a has to be odd. If the current player can't choose any number satisfying the conditions, he loses. Can you determine the winner if they both play optimally?", "input_spec": "The only line contains an integer n (1 ≤ n ≤ 109), the number at the beginning of the game.", "output_spec": "Output \"Mahmoud\" (without quotes) if Mahmoud wins and \"Ehab\" (without quotes) otherwise.", "sample_inputs": ["1", "2"], "sample_outputs": ["Ehab", "Mahmoud"], "notes": "NoteIn the first sample, Mahmoud can't choose any integer a initially because there is no positive even integer less than or equal to 1 so Ehab wins.In the second sample, Mahmoud has to choose a = 2 and subtract it from n. It's Ehab's turn and n = 0. There is no positive odd integer less than or equal to 0 so Mahmoud wins."}, "src_uid": "5e74750f44142624e6da41d4b35beb9a"}
{"nl": {"description": "A boy Valera registered on site Codeforces as Valera, and wrote his first Codeforces Round #300. He boasted to a friend Arkady about winning as much as x points for his first contest. But Arkady did not believe his friend's words and decided to check whether Valera could have shown such a result.He knows that the contest number 300 was unusual because there were only two problems. The contest lasted for t minutes, the minutes are numbered starting from zero. The first problem had the initial cost of a points, and every minute its cost reduced by da points. The second problem had the initial cost of b points, and every minute this cost reduced by db points. Thus, as soon as the zero minute of the contest is over, the first problem will cost a - da points, and the second problem will cost b - db points. It is guaranteed that at any moment of the contest each problem has a non-negative cost.Arkady asks you to find out whether Valera could have got exactly x points for this contest. You should assume that Valera could have solved any number of the offered problems. You should also assume that for each problem Valera made no more than one attempt, besides, he could have submitted both problems at the same minute of the contest, starting with minute 0 and ending with minute number t - 1. Please note that Valera can't submit a solution exactly t minutes after the start of the contest or later.", "input_spec": "The single line of the input contains six integers x, t, a, b, da, db (0 ≤ x ≤ 600; 1 ≤ t, a, b, da, db ≤ 300) — Valera's result, the contest's duration, the initial cost of the first problem, the initial cost of the second problem, the number of points that the first and the second problem lose per minute, correspondingly. It is guaranteed that at each minute of the contest each problem has a non-negative cost, that is, a - i·da ≥ 0 and b - i·db ≥ 0 for all 0 ≤ i ≤ t - 1.", "output_spec": "If Valera could have earned exactly x points at a contest, print \"YES\", otherwise print \"NO\" (without the quotes).", "sample_inputs": ["30 5 20 20 3 5", "10 4 100 5 5 1"], "sample_outputs": ["YES", "NO"], "notes": "NoteIn the first sample Valera could have acted like this: he could have submitted the first problem at minute 0 and the second problem — at minute 2. Then the first problem brings him 20 points and the second problem brings him 10 points, that in total gives the required 30 points."}, "src_uid": "f98168cdd72369303b82b5a7ac45c3af"}
{"nl": {"description": "You're given a row with $$$n$$$ chairs. We call a seating of people \"maximal\" if the two following conditions hold:  There are no neighbors adjacent to anyone seated.  It's impossible to seat one more person without violating the first rule. The seating is given as a string consisting of zeros and ones ($$$0$$$ means that the corresponding seat is empty, $$$1$$$ — occupied). The goal is to determine whether this seating is \"maximal\".Note that the first and last seats are not adjacent (if $$$n \\ne 2$$$).", "input_spec": "The first line contains a single integer $$$n$$$ ($$$1 \\leq n \\leq 1000$$$) — the number of chairs. The next line contains a string of $$$n$$$ characters, each of them is either zero or one, describing the seating.", "output_spec": "Output \"Yes\" (without quotation marks) if the seating is \"maximal\". Otherwise print \"No\". You are allowed to print letters in whatever case you'd like (uppercase or lowercase).", "sample_inputs": ["3\n101", "4\n1011", "5\n10001"], "sample_outputs": ["Yes", "No", "No"], "notes": "NoteIn sample case one the given seating is maximal.In sample case two the person at chair three has a neighbour to the right.In sample case three it is possible to seat yet another person into chair three."}, "src_uid": "c14d255785b1f668d04b0bf6dcadf32d"}
{"nl": {"description": "You are given a tetrahedron. Let's mark its vertices with letters A, B, C and D correspondingly.  An ant is standing in the vertex D of the tetrahedron. The ant is quite active and he wouldn't stay idle. At each moment of time he makes a step from one vertex to another one along some edge of the tetrahedron. The ant just can't stand on one place.You do not have to do much to solve the problem: your task is to count the number of ways in which the ant can go from the initial vertex D to itself in exactly n steps. In other words, you are asked to find out the number of different cyclic paths with the length of n from vertex D to itself. As the number can be quite large, you should print it modulo 1000000007 (109 + 7). ", "input_spec": "The first line contains the only integer n (1 ≤ n ≤ 107) — the required length of the cyclic path.", "output_spec": "Print the only integer — the required number of ways modulo 1000000007 (109 + 7).", "sample_inputs": ["2", "4"], "sample_outputs": ["3", "21"], "notes": "NoteThe required paths in the first sample are:   D - A - D  D - B - D  D - C - D "}, "src_uid": "77627cc366a22e38da412c3231ac91a8"}
{"nl": {"description": "Top-model Izabella participates in the competition. She wants to impress judges and show her mathematical skills.Her problem is following: for given string, consisting of only 0 and 1, tell if it's possible to remove some digits in such a way, that remaining number is a representation of some positive integer, divisible by 64, in the binary numerical system.", "input_spec": "In the only line given a non-empty binary string s with length up to 100.", "output_spec": "Print «yes» (without quotes) if it's possible to remove digits required way and «no» otherwise.", "sample_inputs": ["100010001", "100"], "sample_outputs": ["yes", "no"], "notes": "NoteIn the first test case, you can get string 1 000 000 after removing two ones which is a representation of number 64 in the binary numerical system.You can read more about binary numeral system representation here: https://en.wikipedia.org/wiki/Binary_system"}, "src_uid": "88364b8d71f2ce2b90bdfaa729eb92ca"}
{"nl": {"description": "The finalists of the \"Russian Code Cup\" competition in 2214 will be the participants who win in one of the elimination rounds.The elimination rounds are divided into main and additional. Each of the main elimination rounds consists of c problems, the winners of the round are the first n people in the rating list. Each of the additional elimination rounds consists of d problems. The winner of the additional round is one person. Besides, k winners of the past finals are invited to the finals without elimination.As a result of all elimination rounds at least n·m people should go to the finals. You need to organize elimination rounds in such a way, that at least n·m people go to the finals, and the total amount of used problems in all rounds is as small as possible.", "input_spec": "The first line contains two integers c and d (1 ≤ c, d ≤ 100) — the number of problems in the main and additional rounds, correspondingly. The second line contains two integers n and m (1 ≤ n, m ≤ 100). Finally, the third line contains an integer k (1 ≤ k ≤ 100) — the number of the pre-chosen winners. ", "output_spec": "In the first line, print a single integer — the minimum number of problems the jury needs to prepare.", "sample_inputs": ["1 10\n7 2\n1", "2 2\n2 1\n2"], "sample_outputs": ["2", "0"], "notes": null}, "src_uid": "c6ec932b852e0e8c30c822a226ef7bcb"}
{"nl": {"description": "You are given n k-digit integers. You have to rearrange the digits in the integers so that the difference between the largest and the smallest number was minimum. Digits should be rearranged by the same rule in all integers.", "input_spec": "The first line contains integers n and k — the number and digit capacity of numbers correspondingly (1 ≤ n, k ≤ 8). Next n lines contain k-digit positive integers. Leading zeroes are allowed both in the initial integers and the integers resulting from the rearranging of digits.", "output_spec": "Print a single number: the minimally possible difference between the largest and the smallest number after the digits are rearranged in all integers by the same rule.", "sample_inputs": ["6 4\n5237\n2753\n7523\n5723\n5327\n2537", "3 3\n010\n909\n012", "7 5\n50808\n36603\n37198\n44911\n29994\n42543\n50156"], "sample_outputs": ["2700", "3", "20522"], "notes": "NoteIn the first sample, if we rearrange the digits in numbers as (3,1,4,2), then the 2-nd and the 4-th numbers will equal 5237 and 2537 correspondingly (they will be maximum and minimum for such order of digits).In the second sample, if we swap the second digits and the first ones, we get integers 100, 99 and 102."}, "src_uid": "08f85cd4ffbd135f0b630235209273a4"}
{"nl": {"description": "In the spirit of the holidays, Saitama has given Genos two grid paths of length n (a weird gift even by Saitama's standards). A grid path is an ordered sequence of neighbouring squares in an infinite grid. Two squares are neighbouring if they share a side.One example of a grid path is (0, 0) → (0, 1) → (0, 2) → (1, 2) → (1, 1) → (0, 1) → ( - 1, 1). Note that squares in this sequence might be repeated, i.e. path has self intersections.Movement within a grid path is restricted to adjacent squares within the sequence. That is, from the i-th square, one can only move to the (i - 1)-th or (i + 1)-th squares of this path. Note that there is only a single valid move from the first and last squares of a grid path. Also note, that even if there is some j-th square of the path that coincides with the i-th square, only moves to (i - 1)-th and (i + 1)-th squares are available. For example, from the second square in the above sequence, one can only move to either the first or third squares.To ensure that movement is not ambiguous, the two grid paths will not have an alternating sequence of three squares. For example, a contiguous subsequence (0, 0) → (0, 1) → (0, 0) cannot occur in a valid grid path.One marble is placed on the first square of each grid path. Genos wants to get both marbles to the last square of each grid path. However, there is a catch. Whenever he moves one marble, the other marble will copy its movement if possible. For instance, if one marble moves east, then the other marble will try and move east as well. By try, we mean if moving east is a valid move, then the marble will move east.Moving north increases the second coordinate by 1, while moving south decreases it by 1. Similarly, moving east increases first coordinate by 1, while moving west decreases it.Given these two valid grid paths, Genos wants to know if it is possible to move both marbles to the ends of their respective paths. That is, if it is possible to move the marbles such that both marbles rest on the last square of their respective paths.", "input_spec": "The first line of the input contains a single integer n (2 ≤ n ≤ 1 000 000) — the length of the paths. The second line of the input contains a string consisting of n - 1 characters (each of which is either 'N', 'E', 'S', or 'W') — the first grid path. The characters can be thought of as the sequence of moves needed to traverse the grid path. For example, the example path in the problem statement can be expressed by the string \"NNESWW\". The third line of the input contains a string of n - 1 characters (each of which is either 'N', 'E', 'S', or 'W') — the second grid path.", "output_spec": "Print \"YES\" (without quotes) if it is possible for both marbles to be at the end position at the same time. Print \"NO\" (without quotes) otherwise. In both cases, the answer is case-insensitive.", "sample_inputs": ["7\nNNESWW\nSWSWSW", "3\nNN\nSS"], "sample_outputs": ["YES", "NO"], "notes": "NoteIn the first sample, the first grid path is the one described in the statement. Moreover, the following sequence of moves will get both marbles to the end: NNESWWSWSW.In the second sample, no sequence of moves can get both marbles to the end."}, "src_uid": "85f43628bec7e9b709273c34b894df6b"}
{"nl": {"description": "Jon fought bravely to rescue the wildlings who were attacked by the white-walkers at Hardhome. On his arrival, Sam tells him that he wants to go to Oldtown to train at the Citadel to become a maester, so he can return and take the deceased Aemon's place as maester of Castle Black. Jon agrees to Sam's proposal and Sam sets off his journey to the Citadel. However becoming a trainee at the Citadel is not a cakewalk and hence the maesters at the Citadel gave Sam a problem to test his eligibility. Initially Sam has a list with a single element n. Then he has to perform certain operations on this list. In each operation Sam must remove any element x, such that x > 1, from the list and insert at the same position , ,  sequentially. He must continue with these operations until all the elements in the list are either 0 or 1.Now the masters want the total number of 1s in the range l to r (1-indexed). Sam wants to become a maester but unfortunately he cannot solve this problem. Can you help Sam to pass the eligibility test?", "input_spec": "The first line contains three integers n, l, r (0 ≤ n < 250, 0 ≤ r - l ≤ 105, r ≥ 1, l ≥ 1) – initial element and the range l to r. It is guaranteed that r is not greater than the length of the final list.", "output_spec": "Output the total number of 1s in the range l to r in the final sequence.", "sample_inputs": ["7 2 5", "10 3 10"], "sample_outputs": ["4", "5"], "notes": "NoteConsider first example:Elements on positions from 2-nd to 5-th in list is [1, 1, 1, 1]. The number of ones is 4.For the second example:Elements on positions from 3-rd to 10-th in list is [1, 1, 1, 0, 1, 0, 1, 0]. The number of ones is 5."}, "src_uid": "3ac61b1f8deee7911b1055c243f5eb6a"}
{"nl": {"description": "HQ9+ is a joke programming language which has only four one-character instructions: \"H\" prints \"Hello, World!\", \"Q\" prints the source code of the program itself, \"9\" prints the lyrics of \"99 Bottles of Beer\" song,  \"+\" increments the value stored in the internal accumulator.Instructions \"H\" and \"Q\" are case-sensitive and must be uppercase. The characters of the program which are not instructions are ignored.You are given a program written in HQ9+. You have to figure out whether executing this program will produce any output.", "input_spec": "The input will consist of a single line p which will give a program in HQ9+. String p will contain between 1 and 100 characters, inclusive. ASCII-code of each character of p will be between 33 (exclamation mark) and 126 (tilde), inclusive.", "output_spec": "Output \"YES\", if executing the program will produce any output, and \"NO\" otherwise.", "sample_inputs": ["Hi!", "Codeforces"], "sample_outputs": ["YES", "NO"], "notes": "NoteIn the first case the program contains only one instruction — \"H\", which prints \"Hello, World!\".In the second case none of the program characters are language instructions."}, "src_uid": "1baf894c1c7d5aeea01129c7900d3c12"}
{"nl": {"description": "You have a rectangular board of size $$$n\\times m$$$ ($$$n$$$ rows, $$$m$$$ columns). The $$$n$$$ rows are numbered from $$$1$$$ to $$$n$$$ from top to bottom, and the $$$m$$$ columns are numbered from $$$1$$$ to $$$m$$$ from left to right. The cell at the intersection of row $$$i$$$ and column $$$j$$$ contains the number $$$i^j$$$ ($$$i$$$ raised to the power of $$$j$$$). For example, if $$$n=3$$$ and $$$m=3$$$ the board is as follows:  Find the number of distinct integers written on the board.", "input_spec": "The only line contains two integers $$$n$$$ and $$$m$$$ ($$$1\\le n,m\\le 10^6$$$) — the number of rows and columns of the board.", "output_spec": "Print one integer, the number of distinct integers on the board.", "sample_inputs": ["3 3", "2 4", "4 2"], "sample_outputs": ["7", "5", "6"], "notes": "NoteThe statement shows the board for the first test case. In this case there are $$$7$$$ distinct integers: $$$1$$$, $$$2$$$, $$$3$$$, $$$4$$$, $$$8$$$, $$$9$$$, and $$$27$$$.In the second test case, the board is as follows:  There are $$$5$$$ distinct numbers: $$$1$$$, $$$2$$$, $$$4$$$, $$$8$$$ and $$$16$$$.In the third test case, the board is as follows:  There are $$$6$$$ distinct numbers: $$$1$$$, $$$2$$$, $$$3$$$, $$$4$$$, $$$9$$$ and $$$16$$$."}, "src_uid": "6ca310cb0b6fc4e62e63a731cd55aead"}
{"nl": {"description": "Any resemblance to any real championship and sport is accidental.The Berland National team takes part in the local Football championship which now has a group stage. Let's describe the formal rules of the local championship:   the team that kicked most balls in the enemy's goal area wins the game;  the victory gives 3 point to the team, the draw gives 1 point and the defeat gives 0 points;  a group consists of four teams, the teams are ranked by the results of six games: each team plays exactly once with each other team;  the teams that get places 1 and 2 in the group stage results, go to the next stage of the championship. In the group stage the team's place is defined by the total number of scored points: the more points, the higher the place is. If two or more teams have the same number of points, then the following criteria are used (the criteria are listed in the order of falling priority, starting from the most important one):   the difference between the total number of scored goals and the total number of missed goals in the championship: the team with a higher value gets a higher place;  the total number of scored goals in the championship: the team with a higher value gets a higher place;  the lexicographical order of the name of the teams' countries: the country with the lexicographically smaller name gets a higher place. The Berland team plays in the group where the results of 5 out of 6 games are already known. To be exact, there is the last game left. There the Berand national team plays with some other team. The coach asks you to find such score X:Y (where X is the number of goals Berland scored and Y is the number of goals the opponent scored in the game), that fulfills the following conditions:   X > Y, that is, Berland is going to win this game;  after the game Berland gets the 1st or the 2nd place in the group;  if there are multiple variants, you should choose such score X:Y, where value X - Y is minimum;  if it is still impossible to come up with one score, you should choose the score where value Y (the number of goals Berland misses) is minimum. ", "input_spec": "The input has five lines. Each line describes a game as \"team1 team2 goals1:goals2\" (without the quotes), what means that team team1 played a game with team team2, besides, team1 scored goals1 goals and team2 scored goals2 goals. The names of teams team1 and team2 are non-empty strings, consisting of uppercase English letters, with length of no more than 20 characters; goals1, goals2 are integers from 0 to 9.  The Berland team is called \"BERLAND\". It is guaranteed that the Berland team and one more team played exactly 2 games and the the other teams played exactly 3 games.", "output_spec": "Print the required score in the last game as X:Y, where X is the number of goals Berland scored and Y is the number of goals the opponent scored. If the Berland team does not get the first or the second place in the group, whatever this game's score is, then print on a single line \"IMPOSSIBLE\" (without the quotes). Note, that the result score can be very huge, 10:0 for example.", "sample_inputs": ["AERLAND DERLAND 2:1\nDERLAND CERLAND 0:3\nCERLAND AERLAND 0:1\nAERLAND BERLAND 2:0\nDERLAND BERLAND 4:0", "AERLAND DERLAND 2:2\nDERLAND CERLAND 2:3\nCERLAND AERLAND 1:3\nAERLAND BERLAND 2:1\nDERLAND BERLAND 4:1"], "sample_outputs": ["6:0", "IMPOSSIBLE"], "notes": "NoteIn the first sample \"BERLAND\" plays the last game with team \"CERLAND\". If Berland wins with score 6:0, the results' table looks like that in the end:   AERLAND (points: 9, the difference between scored and missed goals: 4, scored goals: 5)  BERLAND (points: 3, the difference between scored and missed goals: 0, scored goals: 6)  DERLAND (points: 3, the difference between scored and missed goals: 0, scored goals: 5)  CERLAND (points: 3, the difference between scored and missed goals: -4, scored goals: 3) In the second sample teams \"AERLAND\" and \"DERLAND\" have already won 7 and 4 points, respectively. The Berland team wins only 3 points, which is not enough to advance to the next championship stage."}, "src_uid": "5033d51c67b7ae0b1a2d9fd292fdced1"}
{"nl": {"description": "The Smart Beaver from ABBYY came up with another splendid problem for the ABBYY Cup participants! This time the Beaver invites the contest participants to check out a problem on sorting documents by their subjects. Let's describe the problem:You've got some training set of documents. For each document you know its subject. The subject in this problem is an integer from 1 to 3. Each of these numbers has a physical meaning. For instance, all documents with subject 3 are about trade.You can download the training set of documents at the following link: http://download4.abbyy.com/a2/X2RZ2ZWXBG5VYWAL61H76ZQM/train.zip. The archive contains three directories with names \"1\", \"2\", \"3\". Directory named \"1\" contains documents on the 1-st subject, directory \"2\" contains documents on the 2-nd subject, and directory \"3\" contains documents on the 3-rd subject. Each document corresponds to exactly one file from some directory.All documents have the following format: the first line contains the document identifier, the second line contains the name of the document, all subsequent lines contain the text of the document. The document identifier is used to make installing the problem more convenient and has no useful information for the participants.You need to write a program that should indicate the subject for a given document. It is guaranteed that all documents given as input to your program correspond to one of the three subjects of the training set.", "input_spec": "The first line contains integer id (0 ≤ id ≤ 106) — the document identifier. The second line contains the name of the document. The third and the subsequent lines contain the text of the document. It is guaranteed that the size of any given document will not exceed 10 kilobytes. The tests for this problem are divided into 10 groups. Documents of groups 1 and 2 are taken from the training set, but their identifiers will not match the identifiers specified in the training set. Groups from the 3-rd to the 10-th are roughly sorted by the author in ascending order of difficulty (these groups contain documents which aren't present in the training set).", "output_spec": "Print an integer from 1 to 3, inclusive — the number of the subject the given document corresponds to.", "sample_inputs": [], "sample_outputs": [], "notes": null}, "src_uid": "d163975cdad000ce89ee251ef9129779"}
{"nl": {"description": "There are $$$n$$$ benches in the Berland Central park. It is known that $$$a_i$$$ people are currently sitting on the $$$i$$$-th bench. Another $$$m$$$ people are coming to the park and each of them is going to have a seat on some bench out of $$$n$$$ available.Let $$$k$$$ be the maximum number of people sitting on one bench after additional $$$m$$$ people came to the park. Calculate the minimum possible $$$k$$$ and the maximum possible $$$k$$$.Nobody leaves the taken seat during the whole process.", "input_spec": "The first line contains a single integer $$$n$$$ $$$(1 \\le n \\le 100)$$$ — the number of benches in the park. The second line contains a single integer $$$m$$$ $$$(1 \\le m \\le 10\\,000)$$$ — the number of people additionally coming to the park. Each of the next $$$n$$$ lines contains a single integer $$$a_i$$$ $$$(1 \\le a_i \\le 100)$$$ — the initial number of people on the $$$i$$$-th bench.", "output_spec": "Print the minimum possible $$$k$$$ and the maximum possible $$$k$$$, where $$$k$$$ is the maximum number of people sitting on one bench after additional $$$m$$$ people came to the park.", "sample_inputs": ["4\n6\n1\n1\n1\n1", "1\n10\n5", "3\n6\n1\n6\n5", "3\n7\n1\n6\n5"], "sample_outputs": ["3 7", "15 15", "6 12", "7 13"], "notes": "NoteIn the first example, each of four benches is occupied by a single person. The minimum $$$k$$$ is $$$3$$$. For example, it is possible to achieve if two newcomers occupy the first bench, one occupies the second bench, one occupies the third bench, and two remaining — the fourth bench. The maximum $$$k$$$ is $$$7$$$. That requires all six new people to occupy the same bench.The second example has its minimum $$$k$$$ equal to $$$15$$$ and maximum $$$k$$$ equal to $$$15$$$, as there is just a single bench in the park and all $$$10$$$ people will occupy it."}, "src_uid": "78f696bd954c9f0f9bb502e515d85a8d"}
{"nl": {"description": "We'll call string s[a, b] = sasa + 1... sb (1 ≤ a ≤ b ≤ |s|) a substring of string s = s1s2... s|s|, where |s| is the length of string s.The trace of a non-empty string t is a set of characters that the string consists of. For example, the trace of string \"aab\" equals {'a', 'b'}.Let's consider an arbitrary string s and the set of its substrings with trace equal to C. We will denote the number of substrings from this set that are maximal by inclusion by r(C, s). Substring s[a, b] of length n = b - a + 1 belonging to some set is called maximal by inclusion, if there is no substring s[x, y] in this set with length greater than n, such that 1 ≤ x ≤ a ≤ b ≤ y ≤ |s|. Two substrings of string s are considered different even if they are equal but they are located at different positions of s.Polycarpus got a challenging practical task on a stringology exam. He must do the following: given string s and non-empty sets of characters C1, C2, ..., Cm, find r(Ci, s) for each set Ci. Help Polycarpus to solve the problem as he really doesn't want to be expelled from the university and go to the army!", "input_spec": "The first line contains a non-empty string s (1 ≤ |s| ≤ 106). The second line contains a single integer m (1 ≤ m ≤ 104). Next m lines contain descriptions of sets Ci. The i-th line contains string ci such that its trace equals Ci. It is guaranteed that all characters of each string ci are different. Note that Ci are not necessarily different. All given strings consist of lowercase English letters.", "output_spec": "Print m integers — the i-th integer must equal r(Ci, s).", "sample_inputs": ["aaaaa\n2\na\na", "abacaba\n3\nac\nba\na"], "sample_outputs": ["1\n1", "1\n2\n4"], "notes": null}, "src_uid": "9bafcd579d38d5c3f073839ccb1c6ed3"}
{"nl": {"description": "Vova, the Ultimate Thule new shaman, wants to build a pipeline. As there are exactly n houses in Ultimate Thule, Vova wants the city to have exactly n pipes, each such pipe should be connected to the water supply. A pipe can be connected to the water supply if there's water flowing out of it. Initially Vova has only one pipe with flowing water. Besides, Vova has several splitters.A splitter is a construction that consists of one input (it can be connected to a water pipe) and x output pipes. When a splitter is connected to a water pipe, water flows from each output pipe. You can assume that the output pipes are ordinary pipes. For example, you can connect water supply to such pipe if there's water flowing out from it. At most one splitter can be connected to any water pipe.  The figure shows a 4-output splitter Vova has one splitter of each kind: with 2, 3, 4, ..., k outputs. Help Vova use the minimum number of splitters to build the required pipeline or otherwise state that it's impossible.Vova needs the pipeline to have exactly n pipes with flowing out water. Note that some of those pipes can be the output pipes of the splitters.", "input_spec": "The first line contains two space-separated integers n and k (1 ≤ n ≤ 1018, 2 ≤ k ≤ 109). Please, do not use the %lld specifier to read or write 64-bit integers in С++. It is preferred to use the cin, cout streams or the %I64d specifier.", "output_spec": "Print a single integer — the minimum number of splitters needed to build the pipeline. If it is impossible to build a pipeline with the given splitters, print -1.", "sample_inputs": ["4 3", "5 5", "8 4"], "sample_outputs": ["2", "1", "-1"], "notes": null}, "src_uid": "83bcfe32db302fbae18e8a95d89cf411"}
{"nl": {"description": "Every year, hundreds of people come to summer camps, they learn new algorithms and solve hard problems.This is your first year at summer camp, and you are asked to solve the following problem. All integers starting with 1 are written in one line. The prefix of these line is \"123456789101112131415...\". Your task is to print the n-th digit of this string (digits are numbered starting with 1.", "input_spec": "The only line of the input contains a single integer n (1 ≤ n ≤ 1000) — the position of the digit you need to print.", "output_spec": "Print the n-th digit of the line.", "sample_inputs": ["3", "11"], "sample_outputs": ["3", "0"], "notes": "NoteIn the first sample the digit at position 3 is '3', as both integers 1 and 2 consist on one digit.In the second sample, the digit at position 11 is '0', it belongs to the integer 10."}, "src_uid": "2d46e34839261eda822f0c23c6e19121"}
{"nl": {"description": "Permutation p is an ordered set of integers p1,  p2,  ...,  pn, consisting of n distinct positive integers, each of them doesn't exceed n. We'll denote the i-th element of permutation p as pi. We'll call number n the size or the length of permutation p1,  p2,  ...,  pn.We'll call position i (1 ≤ i ≤ n) in permutation p1, p2, ..., pn good, if |p[i] - i| = 1. Count the number of permutations of size n with exactly k good positions. Print the answer modulo 1000000007 (109 + 7).", "input_spec": "The single line contains two space-separated integers n and k (1 ≤ n ≤ 1000, 0 ≤ k ≤ n).", "output_spec": "Print the number of permutations of length n with exactly k good positions modulo 1000000007 (109 + 7).", "sample_inputs": ["1 0", "2 1", "3 2", "4 1", "7 4"], "sample_outputs": ["1", "0", "4", "6", "328"], "notes": "NoteThe only permutation of size 1 has 0 good positions.Permutation (1, 2) has 0 good positions, and permutation (2, 1) has 2 positions.Permutations of size 3: (1, 2, 3) — 0 positions  — 2 positions  — 2 positions  — 2 positions  — 2 positions (3, 2, 1) — 0 positions"}, "src_uid": "1243e98fe2ebd6e6d1de851984b96079"}
{"nl": {"description": "Girl Lena likes it when everything is in order, and looks for order everywhere. Once she was getting ready for the University and noticed that the room was in a mess — all the objects from her handbag were thrown about the room. Of course, she wanted to put them back into her handbag. The problem is that the girl cannot carry more than two objects at a time, and cannot move the handbag. Also, if he has taken an object, she cannot put it anywhere except her handbag — her inherent sense of order does not let her do so.You are given the coordinates of the handbag and the coordinates of the objects in some Сartesian coordinate system. It is known that the girl covers the distance between any two objects in the time equal to the squared length of the segment between the points of the objects. It is also known that initially the coordinates of the girl and the handbag are the same. You are asked to find such an order of actions, that the girl can put all the objects back into her handbag in a minimum time period.", "input_spec": "The first line of the input file contains the handbag's coordinates xs, ys. The second line contains number n (1 ≤ n ≤ 24) — the amount of objects the girl has. The following n lines contain the objects' coordinates. All the coordinates do not exceed 100 in absolute value. All the given positions are different. All the numbers are integer.", "output_spec": "In the first line output the only number — the minimum time the girl needs to put the objects into her handbag.  In the second line output the possible optimum way for Lena. Each object in the input is described by its index number (from 1 to n), the handbag's point is described by number 0. The path should start and end in the handbag's point. If there are several optimal paths, print any of them. ", "sample_inputs": ["0 0\n2\n1 1\n-1 1", "1 1\n3\n4 3\n3 4\n0 0"], "sample_outputs": ["8\n0 1 2 0", "32\n0 1 2 0 3 0"], "notes": null}, "src_uid": "2ecbac20dc5f4060bc873553946281bc"}
{"nl": {"description": "You are given names of two days of the week.Please, determine whether it is possible that during some non-leap year the first day of some month was equal to the first day of the week you are given, while the first day of the next month was equal to the second day of the week you are given. Both months should belong to one year.In this problem, we consider the Gregorian calendar to be used. The number of months in this calendar is equal to 12. The number of days in months during any non-leap year is: 31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31.Names of the days of the week are given with lowercase English letters: \"monday\", \"tuesday\", \"wednesday\", \"thursday\", \"friday\", \"saturday\", \"sunday\".", "input_spec": "The input consists of two lines, each of them containing the name of exactly one day of the week. It's guaranteed that each string in the input is from the set \"monday\", \"tuesday\", \"wednesday\", \"thursday\", \"friday\", \"saturday\", \"sunday\".", "output_spec": "Print \"YES\" (without quotes) if such situation is possible during some non-leap year. Otherwise, print \"NO\" (without quotes).", "sample_inputs": ["monday\ntuesday", "sunday\nsunday", "saturday\ntuesday"], "sample_outputs": ["NO", "YES", "YES"], "notes": "NoteIn the second sample, one can consider February 1 and March 1 of year 2015. Both these days were Sundays.In the third sample, one can consider July 1 and August 1 of year 2017. First of these two days is Saturday, while the second one is Tuesday."}, "src_uid": "2a75f68a7374b90b80bb362c6ead9a35"}
{"nl": {"description": "  It's the end of July – the time when a festive evening is held at Jelly Castle! Guests from all over the kingdom gather here to discuss new trends in the world of confectionery. Yet some of the things discussed here are not supposed to be disclosed to the general public: the information can cause discord in the kingdom of Sweetland in case it turns out to reach the wrong hands. So it's a necessity to not let any uninvited guests in.There are 26 entrances in Jelly Castle, enumerated with uppercase English letters from A to Z. Because of security measures, each guest is known to be assigned an entrance he should enter the castle through. The door of each entrance is opened right before the first guest's arrival and closed right after the arrival of the last guest that should enter the castle through this entrance. No two guests can enter the castle simultaneously.For an entrance to be protected from possible intrusion, a candy guard should be assigned to it. There are k such guards in the castle, so if there are more than k opened doors, one of them is going to be left unguarded! Notice that a guard can't leave his post until the door he is assigned to is closed.Slastyona had a suspicion that there could be uninvited guests at the evening. She knows the order in which the invited guests entered the castle, and wants you to help her check whether there was a moment when more than k doors were opened.", "input_spec": "Two integers are given in the first string: the number of guests n and the number of guards k (1 ≤ n ≤ 106, 1 ≤ k ≤ 26). In the second string, n uppercase English letters s1s2... sn are given, where si is the entrance used by the i-th guest.", "output_spec": "Output «YES» if at least one door was unguarded during some time, and «NO» otherwise. You can output each letter in arbitrary case (upper or lower).", "sample_inputs": ["5 1\nAABBB", "5 1\nABABB"], "sample_outputs": ["NO", "YES"], "notes": "NoteIn the first sample case, the door A is opened right before the first guest's arrival and closed when the second guest enters the castle. The door B is opened right before the arrival of the third guest, and closed after the fifth one arrives. One guard can handle both doors, as the first one is closed before the second one is opened.In the second sample case, the door B is opened before the second guest's arrival, but the only guard can't leave the door A unattended, as there is still one more guest that should enter the castle through this door. "}, "src_uid": "216323563f5b2dd63edc30cb9b4849a5"}
{"nl": {"description": "One day a bear lived on the Oxy axis. He was afraid of the dark, so he couldn't move at night along the plane points that aren't lit. One day the bear wanted to have a night walk from his house at point (l, 0) to his friend's house at point (r, 0), along the segment of length (r - l). Of course, if he wants to make this walk, he needs each point of the segment to be lit. That's why the bear called his friend (and yes, in the middle of the night) asking for a very delicate favor.The Oxy axis contains n floodlights. Floodlight i is at point (xi, yi) and can light any angle of the plane as large as ai degree with vertex at point (xi, yi). The bear asked his friend to turn the floodlights so that he (the bear) could go as far away from his house as possible during the walking along the segment. His kind friend agreed to fulfill his request. And while he is at it, the bear wonders: what is the furthest he can go away from his house? Hep him and find this distance.Consider that the plane has no obstacles and no other light sources besides the floodlights. The bear's friend cannot turn the floodlights during the bear's walk. Assume that after all the floodlights are turned in the correct direction, the bear goes for a walk and his friend goes to bed.", "input_spec": "The first line contains three space-separated integers n, l, r (1 ≤ n ≤ 20;  - 105 ≤ l ≤ r ≤ 105). The i-th of the next n lines contain three space-separated integers xi, yi, ai ( - 1000 ≤ xi ≤ 1000; 1 ≤ yi ≤ 1000; 1 ≤ ai ≤ 90) — the floodlights' description.  Note that two floodlights can be at the same point of the plane.", "output_spec": "Print a single real number — the answer to the problem. The answer will be considered correct if its relative or absolute error doesn't exceed 10 - 6.", "sample_inputs": ["2 3 5\n3 1 45\n5 1 45", "1 0 1\n1 1 30", "1 0 1\n1 1 45", "1 0 2\n0 2 90"], "sample_outputs": ["2.000000000", "0.732050808", "1.000000000", "2.000000000"], "notes": "NoteIn the first sample, one of the possible solutions is:   In the second sample, a single solution is:   In the third sample, a single solution is:   "}, "src_uid": "4fad1233e08bef09e5aa7e2dc6167d6a"}
{"nl": {"description": "You have a fraction . You need to find the first occurrence of digit c into decimal notation of the fraction after decimal point.", "input_spec": "The first contains three single positive integers a, b, c (1 ≤ a < b ≤ 105, 0 ≤ c ≤ 9).", "output_spec": "Print position of the first occurrence of digit c into the fraction. Positions are numbered from 1 after decimal point. It there is no such position, print -1.", "sample_inputs": ["1 2 0", "2 3 7"], "sample_outputs": ["2", "-1"], "notes": "NoteThe fraction in the first example has the following decimal notation: . The first zero stands on second position.The fraction in the second example has the following decimal notation: . There is no digit 7 in decimal notation of the fraction. "}, "src_uid": "0bc7bf67b96e2898cfd8d129ad486910"}
{"nl": {"description": "Dr. Evil kidnapped Mahmoud and Ehab in the evil land because of their performance in the Evil Olympiad in Informatics (EOI). He decided to give them some problems to let them go.Dr. Evil is interested in sets, He has a set of n integers. Dr. Evil calls a set of integers evil if the MEX of it is exactly x. the MEX of a set of integers is the minimum non-negative integer that doesn't exist in it. For example, the MEX of the set {0, 2, 4} is 1 and the MEX of the set {1, 2, 3} is 0 .Dr. Evil is going to make his set evil. To do this he can perform some operations. During each operation he can add some non-negative integer to his set or erase some element from it. What is the minimal number of operations Dr. Evil has to perform to make his set evil?", "input_spec": "The first line contains two integers n and x (1 ≤ n ≤ 100, 0 ≤ x ≤ 100) — the size of the set Dr. Evil owns, and the desired MEX. The second line contains n distinct non-negative integers not exceeding 100 that represent the set.", "output_spec": "The only line should contain one integer — the minimal number of operations Dr. Evil should perform.", "sample_inputs": ["5 3\n0 4 5 6 7", "1 0\n0", "5 0\n1 2 3 4 5"], "sample_outputs": ["2", "1", "0"], "notes": "NoteFor the first test case Dr. Evil should add 1 and 2 to the set performing 2 operations.For the second test case Dr. Evil should erase 0 from the set. After that, the set becomes empty, so the MEX of it is 0.In the third test case the set is already evil."}, "src_uid": "21f579ba807face432a7664091581cd8"}
{"nl": {"description": "There are $$$n$$$ students in a school class, the rating of the $$$i$$$-th student on Codehorses is $$$a_i$$$. You have to form a team consisting of $$$k$$$ students ($$$1 \\le k \\le n$$$) such that the ratings of all team members are distinct.If it is impossible to form a suitable team, print \"NO\" (without quotes). Otherwise print \"YES\", and then print $$$k$$$ distinct numbers which should be the indices of students in the team you form. If there are multiple answers, print any of them.", "input_spec": "The first line contains two integers $$$n$$$ and $$$k$$$ ($$$1 \\le k \\le n \\le 100$$$) — the number of students and the size of the team you have to form. The second line contains $$$n$$$ integers $$$a_1, a_2, \\dots, a_n$$$ ($$$1 \\le a_i \\le 100$$$), where $$$a_i$$$ is the rating of $$$i$$$-th student.", "output_spec": "If it is impossible to form a suitable team, print \"NO\" (without quotes). Otherwise print \"YES\", and then print $$$k$$$ distinct integers from $$$1$$$ to $$$n$$$ which should be the indices of students in the team you form. All the ratings of the students in the team should be distinct. You may print the indices in any order. If there are multiple answers, print any of them. Assume that the students are numbered from $$$1$$$ to $$$n$$$.", "sample_inputs": ["5 3\n15 13 15 15 12", "5 4\n15 13 15 15 12", "4 4\n20 10 40 30"], "sample_outputs": ["YES\n1 2 5", "NO", "YES\n1 2 3 4"], "notes": "NoteAll possible answers for the first example:   {1 2 5}  {2 3 5}  {2 4 5} Note that the order does not matter."}, "src_uid": "5de6574d57ab04ca195143e08d28d0ad"}
{"nl": {"description": "Let's define a split of $$$n$$$ as a nonincreasing sequence of positive integers, the sum of which is $$$n$$$. For example, the following sequences are splits of $$$8$$$: $$$[4, 4]$$$, $$$[3, 3, 2]$$$, $$$[2, 2, 1, 1, 1, 1]$$$, $$$[5, 2, 1]$$$.The following sequences aren't splits of $$$8$$$: $$$[1, 7]$$$, $$$[5, 4]$$$, $$$[11, -3]$$$, $$$[1, 1, 4, 1, 1]$$$.The weight of a split is the number of elements in the split that are equal to the first element. For example, the weight of the split $$$[1, 1, 1, 1, 1]$$$ is $$$5$$$, the weight of the split $$$[5, 5, 3, 3, 3]$$$ is $$$2$$$ and the weight of the split $$$[9]$$$ equals $$$1$$$.For a given $$$n$$$, find out the number of different weights of its splits.", "input_spec": "The first line contains one integer $$$n$$$ ($$$1 \\leq n \\leq 10^9$$$).", "output_spec": "Output one integer — the answer to the problem.", "sample_inputs": ["7", "8", "9"], "sample_outputs": ["4", "5", "5"], "notes": "NoteIn the first sample, there are following possible weights of splits of $$$7$$$:Weight 1: [$$$\\textbf 7$$$] Weight 2: [$$$\\textbf 3$$$, $$$\\textbf 3$$$, 1] Weight 3: [$$$\\textbf 2$$$, $$$\\textbf 2$$$, $$$\\textbf 2$$$, 1] Weight 7: [$$$\\textbf 1$$$, $$$\\textbf 1$$$, $$$\\textbf 1$$$, $$$\\textbf 1$$$, $$$\\textbf 1$$$, $$$\\textbf 1$$$, $$$\\textbf 1$$$]"}, "src_uid": "5551742f6ab39fdac3930d866f439e3e"}
{"nl": {"description": "Students Vasya and Petya are studying at the BSU (Byteland State University). At one of the breaks they decided to order a pizza. In this problem pizza is a circle of some radius. The pizza was delivered already cut into n pieces. The i-th piece is a sector of angle equal to ai. Vasya and Petya want to divide all pieces of pizza into two continuous sectors in such way that the difference between angles of these sectors is minimal. Sector angle is sum of angles of all pieces in it. Pay attention, that one of sectors can be empty.", "input_spec": "The first line contains one integer n (1 ≤ n ≤ 360)  — the number of pieces into which the delivered pizza was cut. The second line contains n integers ai (1 ≤ ai ≤ 360)  — the angles of the sectors into which the pizza was cut. The sum of all ai is 360.", "output_spec": "Print one integer  — the minimal difference between angles of sectors that will go to Vasya and Petya.", "sample_inputs": ["4\n90 90 90 90", "3\n100 100 160", "1\n360", "4\n170 30 150 10"], "sample_outputs": ["0", "40", "360", "0"], "notes": "NoteIn first sample Vasya can take 1 and 2 pieces, Petya can take 3 and 4 pieces. Then the answer is |(90 + 90) - (90 + 90)| = 0.In third sample there is only one piece of pizza that can be taken by only one from Vasya and Petya. So the answer is |360 - 0| = 360.In fourth sample Vasya can take 1 and 4 pieces, then Petya will take 2 and 3 pieces. So the answer is |(170 + 10) - (30 + 150)| = 0.Picture explaning fourth sample:Both red and green sectors consist of two adjacent pieces of pizza. So Vasya can take green sector, then Petya will take red sector."}, "src_uid": "1b6a6aff81911865356ec7cbf6883e82"}
{"nl": {"description": "Andrey thinks he is truly a successful developer, but in reality he didn't know about the binary search algorithm until recently. After reading some literature Andrey understood that this algorithm allows to quickly find a certain number $$$x$$$ in an array. For an array $$$a$$$ indexed from zero, and an integer $$$x$$$ the pseudocode of the algorithm is as follows:  Note that the elements of the array are indexed from zero, and the division is done in integers (rounding down).Andrey read that the algorithm only works if the array is sorted. However, he found this statement untrue, because there certainly exist unsorted arrays for which the algorithm find $$$x$$$!Andrey wants to write a letter to the book authors, but before doing that he must consider the permutations of size $$$n$$$ such that the algorithm finds $$$x$$$ in them. A permutation of size $$$n$$$ is an array consisting of $$$n$$$ distinct integers between $$$1$$$ and $$$n$$$ in arbitrary order.Help Andrey and find the number of permutations of size $$$n$$$ which contain $$$x$$$ at position $$$pos$$$ and for which the given implementation of the binary search algorithm finds $$$x$$$ (returns true). As the result may be extremely large, print the remainder of its division by $$$10^9+7$$$.", "input_spec": "The only line of input contains integers $$$n$$$, $$$x$$$ and $$$pos$$$ ($$$1 \\le x \\le n \\le 1000$$$, $$$0 \\le pos \\le n - 1$$$) — the required length of the permutation, the number to search, and the required position of that number, respectively.", "output_spec": "Print a single number — the remainder of the division of the number of valid permutations by $$$10^9+7$$$.", "sample_inputs": ["4 1 2", "123 42 24"], "sample_outputs": ["6", "824071958"], "notes": "NoteAll possible permutations in the first test case: $$$(2, 3, 1, 4)$$$, $$$(2, 4, 1, 3)$$$, $$$(3, 2, 1, 4)$$$, $$$(3, 4, 1, 2)$$$, $$$(4, 2, 1, 3)$$$, $$$(4, 3, 1, 2)$$$."}, "src_uid": "24e2f10463f440affccc2755f4462d8a"}
{"nl": {"description": "The girl Taylor has a beautiful calendar for the year y. In the calendar all days are given with their days of week: Monday, Tuesday, Wednesday, Thursday, Friday, Saturday and Sunday.The calendar is so beautiful that she wants to know what is the next year after y when the calendar will be exactly the same. Help Taylor to find that year.Note that leap years has 366 days. The year is leap if it is divisible by 400 or it is divisible by 4, but not by 100 (https://en.wikipedia.org/wiki/Leap_year).", "input_spec": "The only line contains integer y (1000 ≤ y < 100'000) — the year of the calendar.", "output_spec": "Print the only integer y' — the next year after y when the calendar will be the same. Note that you should find the first year after y with the same calendar.", "sample_inputs": ["2016", "2000", "50501"], "sample_outputs": ["2044", "2028", "50507"], "notes": "NoteToday is Monday, the 13th of June, 2016."}, "src_uid": "565bbd09f79eb7bfe2f2da46647af0f2"}
{"nl": {"description": "Running with barriers on the circle track is very popular in the country where Dasha lives, so no wonder that on her way to classes she saw the following situation:The track is the circle with length L, in distinct points of which there are n barriers. Athlete always run the track in counterclockwise direction if you look on him from above. All barriers are located at integer distance from each other along the track. Her friends the parrot Kefa and the leopard Sasha participated in competitions and each of them ran one lap. Each of the friends started from some integral point on the track. Both friends wrote the distance from their start along the track to each of the n barriers. Thus, each of them wrote n integers in the ascending order, each of them was between 0 and L - 1, inclusively.    Consider an example. Let L = 8, blue points are barriers, and green points are Kefa's start (A) and Sasha's start (B). Then Kefa writes down the sequence [2, 4, 6], and Sasha writes down [1, 5, 7]. There are several tracks in the country, all of them have same length and same number of barriers, but the positions of the barriers can differ among different tracks. Now Dasha is interested if it is possible that Kefa and Sasha ran the same track or they participated on different tracks. Write the program which will check that Kefa's and Sasha's tracks coincide (it means that one can be obtained from the other by changing the start position). Note that they always run the track in one direction — counterclockwise, if you look on a track from above. ", "input_spec": "The first line contains two integers n and L (1 ≤ n ≤ 50, n ≤ L ≤ 100) — the number of barriers on a track and its length.  The second line contains n distinct integers in the ascending order — the distance from Kefa's start to each barrier in the order of its appearance. All integers are in the range from 0 to L - 1 inclusively. The second line contains n distinct integers in the ascending order — the distance from Sasha's start to each barrier in the order of its overcoming. All integers are in the range from 0 to L - 1 inclusively.", "output_spec": "Print \"YES\" (without quotes), if Kefa and Sasha ran the coinciding tracks (it means that the position of all barriers coincides, if they start running from the same points on the track). Otherwise print \"NO\" (without quotes).", "sample_inputs": ["3 8\n2 4 6\n1 5 7", "4 9\n2 3 5 8\n0 1 3 6", "2 4\n1 3\n1 2"], "sample_outputs": ["YES", "YES", "NO"], "notes": "NoteThe first test is analyzed in the statement."}, "src_uid": "3d931684ca11fe6141c6461e85d91d63"}
{"nl": {"description": "Life is not easy for the perfectly common variable named Vasya. Wherever it goes, it is either assigned a value, or simply ignored, or is being used!Vasya's life goes in states of a program. In each state, Vasya can either be used (for example, to calculate the value of another variable), or be assigned a value, or ignored. Between some states are directed (oriented) transitions.A path is a sequence of states v1, v2, ..., vx, where for any 1 ≤ i < x exists a transition from vi to vi + 1.Vasya's value in state v is interesting to the world, if exists path p1, p2, ..., pk such, that pi = v for some i (1 ≤ i ≤ k), in state p1 Vasya gets assigned a value, in state pk Vasya is used and there is no state pi (except for p1) where Vasya gets assigned a value.Help Vasya, find the states in which Vasya's value is interesting to the world.", "input_spec": "The first line contains two space-separated integers n and m (1 ≤ n, m ≤ 105) — the numbers of states and transitions, correspondingly. The second line contains space-separated n integers f1, f2, ..., fn (0 ≤ fi ≤ 2), fi described actions performed upon Vasya in state i: 0 represents ignoring, 1 — assigning a value, 2 — using. Next m lines contain space-separated pairs of integers ai, bi (1 ≤ ai, bi ≤ n, ai ≠ bi), each pair represents the transition from the state number ai to the state number bi. Between two states can be any number of transitions.", "output_spec": "Print n integers r1, r2, ..., rn, separated by spaces or new lines. Number ri should equal 1, if Vasya's value in state i is interesting to the world and otherwise, it should equal 0. The states are numbered from 1 to n in the order, in which they are described in the input.", "sample_inputs": ["4 3\n1 0 0 2\n1 2\n2 3\n3 4", "3 1\n1 0 2\n1 3", "3 1\n2 0 1\n1 3"], "sample_outputs": ["1\n1\n1\n1", "1\n0\n1", "0\n0\n0"], "notes": "NoteIn the first sample the program states can be used to make the only path in which the value of Vasya interests the world, 1  2  3  4; it includes all the states, so in all of them Vasya's value is interesting to the world.The second sample the only path in which Vasya's value is interesting to the world is , — 1  3; state 2 is not included there.In the third sample we cannot make from the states any path in which the value of Vasya would be interesting to the world, so the value of Vasya is never interesting to the world."}, "src_uid": "87d869a0fd4a510c5e7e310886b86a57"}
{"nl": {"description": "Two participants are each given a pair of distinct numbers from 1 to 9 such that there's exactly one number that is present in both pairs. They want to figure out the number that matches by using a communication channel you have access to without revealing it to you.Both participants communicated to each other a set of pairs of numbers, that includes the pair given to them. Each pair in the communicated sets comprises two different numbers.Determine if you can with certainty deduce the common number, or if you can determine with certainty that both participants know the number but you do not.", "input_spec": "The first line contains two integers $$$n$$$ and $$$m$$$ ($$$1 \\le n, m \\le 12$$$) — the number of pairs the first participant communicated to the second and vice versa. The second line contains $$$n$$$ pairs of integers, each between $$$1$$$ and $$$9$$$, — pairs of numbers communicated from first participant to the second. The third line contains $$$m$$$ pairs of integers, each between $$$1$$$ and $$$9$$$, — pairs of numbers communicated from the second participant to the first. All pairs within each set are distinct (in particular, if there is a pair $$$(1,2)$$$, there will be no pair $$$(2,1)$$$ within the same set), and no pair contains the same number twice. It is guaranteed that the two sets do not contradict the statements, in other words, there is pair from the first set and a pair from the second set that share exactly one number.", "output_spec": "If you can deduce the shared number with certainty, print that number. If you can with certainty deduce that both participants know the shared number, but you do not know it, print $$$0$$$. Otherwise print $$$-1$$$.", "sample_inputs": ["2 2\n1 2 3 4\n1 5 3 4", "2 2\n1 2 3 4\n1 5 6 4", "2 3\n1 2 4 5\n1 2 1 3 2 3"], "sample_outputs": ["1", "0", "-1"], "notes": "NoteIn the first example the first participant communicated pairs $$$(1,2)$$$ and $$$(3,4)$$$, and the second communicated $$$(1,5)$$$, $$$(3,4)$$$. Since we know that the actual pairs they received share exactly one number, it can't be that they both have $$$(3,4)$$$. Thus, the first participant has $$$(1,2)$$$ and the second has $$$(1,5)$$$, and at this point you already know the shared number is $$$1$$$.In the second example either the first participant has $$$(1,2)$$$ and the second has $$$(1,5)$$$, or the first has $$$(3,4)$$$ and the second has $$$(6,4)$$$. In the first case both of them know the shared number is $$$1$$$, in the second case both of them know the shared number is $$$4$$$. You don't have enough information to tell $$$1$$$ and $$$4$$$ apart.In the third case if the first participant was given $$$(1,2)$$$, they don't know what the shared number is, since from their perspective the second participant might have been given either $$$(1,3)$$$, in which case the shared number is $$$1$$$, or $$$(2,3)$$$, in which case the shared number is $$$2$$$. While the second participant does know the number with certainty, neither you nor the first participant do, so the output is $$$-1$$$."}, "src_uid": "cb4de190ae26127df6eeb7a1a1db8a6d"}
{"nl": {"description": "Today Tavas got his test result as an integer score and he wants to share it with his girlfriend, Nafas.His phone operating system is Tavdroid, and its keyboard doesn't have any digits! He wants to share his score with Nafas via text, so he has no choice but to send this number using words.  He ate coffee mix without water again, so right now he's really messed up and can't think.Your task is to help him by telling him what to type.", "input_spec": "The first and only line of input contains an integer s (0 ≤ s ≤ 99), Tavas's score. ", "output_spec": "In the first and only line of output, print a single string consisting only from English lowercase letters and hyphens ('-'). Do not use spaces.", "sample_inputs": ["6", "99", "20"], "sample_outputs": ["six", "ninety-nine", "twenty"], "notes": "NoteYou can find all you need to know about English numerals in http://en.wikipedia.org/wiki/English_numerals ."}, "src_uid": "a49ca177b2f1f9d5341462a38a25d8b7"}
{"nl": {"description": "This problem's actual name, \"Lexicographically Largest Palindromic Subsequence\" is too long to fit into the page headline.You are given string s consisting of lowercase English letters only. Find its lexicographically largest palindromic subsequence.We'll call a non-empty string s[p1p2... pk] = sp1sp2... spk (1  ≤  p1 < p2 < ... < pk  ≤  |s|) a subsequence of string s = s1s2... s|s|, where |s| is the length of string s. For example, strings \"abcb\", \"b\" and \"abacaba\" are subsequences of string \"abacaba\".String x = x1x2... x|x| is lexicographically larger than string y = y1y2... y|y| if either |x| > |y| and x1 = y1, x2 = y2, ..., x|y| = y|y|, or there exists such number r (r < |x|, r < |y|) that x1 = y1, x2 = y2, ..., xr = yr and xr  +  1 > yr  +  1. Characters in the strings are compared according to their ASCII codes. For example, string \"ranger\" is lexicographically larger than string \"racecar\" and string \"poster\" is lexicographically larger than string \"post\".String s = s1s2... s|s| is a palindrome if it matches string rev(s) = s|s|s|s| - 1... s1. In other words, a string is a palindrome if it reads the same way from left to right and from right to left. For example, palindromic strings are \"racecar\", \"refer\" and \"z\".", "input_spec": "The only input line contains a non-empty string s consisting of lowercase English letters only. Its length does not exceed 10.", "output_spec": "Print the lexicographically largest palindromic subsequence of string s.", "sample_inputs": ["radar", "bowwowwow", "codeforces", "mississipp"], "sample_outputs": ["rr", "wwwww", "s", "ssss"], "notes": "NoteAmong all distinct subsequences of string \"radar\" the following ones are palindromes: \"a\", \"d\", \"r\", \"aa\", \"rr\", \"ada\", \"rar\", \"rdr\", \"raar\" and \"radar\". The lexicographically largest of them is \"rr\"."}, "src_uid": "9a40e9b122962a1f83b74ddee6246a40"}
{"nl": {"description": "Igor K. always used to trust his favorite Kashpirovsky Antivirus. That is why he didn't hesitate to download the link one of his groupmates sent him via QIP Infinium. The link was said to contain \"some real funny stuff about swine influenza\". The antivirus had no objections and Igor K. run the flash application he had downloaded. Immediately his QIP Infinium said: \"invalid login/password\".Igor K. entered the ISQ from his additional account and looked at the info of his main one. His name and surname changed to \"H1N1\" and \"Infected\" correspondingly, and the \"Additional Information\" field contained a strange-looking binary code 80 characters in length, consisting of zeroes and ones. \"I've been hacked\" — thought Igor K. and run the Internet Exploiter browser to quickly type his favourite search engine's address.Soon he learned that it really was a virus that changed ISQ users' passwords. Fortunately, he soon found out that the binary code was actually the encrypted password where each group of 10 characters stood for one decimal digit. Accordingly, the original password consisted of 8 decimal digits.Help Igor K. restore his ISQ account by the encrypted password and encryption specification.", "input_spec": "The input data contains 11 lines. The first line represents the binary code 80 characters in length. That is the code written in Igor K.'s ISQ account's info. Next 10 lines contain pairwise distinct binary codes 10 characters in length, corresponding to numbers 0, 1, ..., 9.", "output_spec": "Print one line containing 8 characters — The password to Igor K.'s ISQ account. It is guaranteed that the solution exists.", "sample_inputs": ["01001100100101100000010110001001011001000101100110010110100001011010100101101100\n0100110000\n0100110010\n0101100000\n0101100010\n0101100100\n0101100110\n0101101000\n0101101010\n0101101100\n0101101110", "10101101111001000010100100011010101101110010110111011000100011011110010110001000\n1001000010\n1101111001\n1001000110\n1010110111\n0010110111\n1101001101\n1011000001\n1110010101\n1011011000\n0110001000"], "sample_outputs": ["12345678", "30234919"], "notes": null}, "src_uid": "0f4f7ca388dd1b2192436c67f9ac74d9"}
{"nl": {"description": "This morning, Roman woke up and opened the browser with $$$n$$$ opened tabs numbered from $$$1$$$ to $$$n$$$. There are two kinds of tabs: those with the information required for the test and those with social network sites. Roman decided that there are too many tabs open so he wants to close some of them.He decided to accomplish this by closing every $$$k$$$-th ($$$2 \\leq k \\leq n - 1$$$) tab. Only then he will decide whether he wants to study for the test or to chat on the social networks. Formally, Roman will choose one tab (let its number be $$$b$$$) and then close all tabs with numbers $$$c = b + i \\cdot k$$$ that satisfy the following condition: $$$1 \\leq c \\leq n$$$ and $$$i$$$ is an integer (it may be positive, negative or zero).For example, if $$$k = 3$$$, $$$n = 14$$$ and Roman chooses $$$b = 8$$$, then he will close tabs with numbers $$$2$$$, $$$5$$$, $$$8$$$, $$$11$$$ and $$$14$$$.After closing the tabs Roman will calculate the amount of remaining tabs with the information for the test (let's denote it $$$e$$$) and the amount of remaining social network tabs ($$$s$$$). Help Roman to calculate the maximal absolute value of the difference of those values $$$|e - s|$$$ so that it would be easy to decide what to do next.", "input_spec": "The first line contains two integers $$$n$$$ and $$$k$$$ ($$$2 \\leq k < n \\leq 100$$$) — the amount of tabs opened currently and the distance between the tabs closed. The second line consists of $$$n$$$ integers, each of them equal either to $$$1$$$ or to $$$-1$$$. The $$$i$$$-th integer denotes the type of the $$$i$$$-th tab: if it is equal to $$$1$$$, this tab contains information for the test, and if it is equal to $$$-1$$$, it's a social network tab.", "output_spec": "Output a single integer — the maximum absolute difference between the amounts of remaining tabs of different types $$$|e - s|$$$.", "sample_inputs": ["4 2\n1 1 -1 1", "14 3\n-1 1 -1 -1 1 -1 -1 1 -1 -1 1 -1 -1 1"], "sample_outputs": ["2", "9"], "notes": "NoteIn the first example we can choose $$$b = 1$$$ or $$$b = 3$$$. We will delete then one tab of each type and the remaining tabs are then all contain test information. Thus, $$$e = 2$$$ and $$$s = 0$$$ and $$$|e - s| = 2$$$.In the second example, on the contrary, we can leave opened only tabs that have social networks opened in them."}, "src_uid": "6119258322e06fa6146e592c63313df3"}
{"nl": {"description": "Anton likes to listen to fairy tales, especially when Danik, Anton's best friend, tells them. Right now Danik tells Anton a fairy tale:\"Once upon a time, there lived an emperor. He was very rich and had much grain. One day he ordered to build a huge barn to put there all his grain. Best builders were building that barn for three days and three nights. But they overlooked and there remained a little hole in the barn, from which every day sparrows came through. Here flew a sparrow, took a grain and flew away...\"More formally, the following takes place in the fairy tale. At the beginning of the first day the barn with the capacity of n grains was full. Then, every day (starting with the first day) the following happens:  m grains are brought to the barn. If m grains doesn't fit to the barn, the barn becomes full and the grains that doesn't fit are brought back (in this problem we can assume that the grains that doesn't fit to the barn are not taken into account).  Sparrows come and eat grain. In the i-th day i sparrows come, that is on the first day one sparrow come, on the second day two sparrows come and so on. Every sparrow eats one grain. If the barn is empty, a sparrow eats nothing. Anton is tired of listening how Danik describes every sparrow that eats grain from the barn. Anton doesn't know when the fairy tale ends, so he asked you to determine, by the end of which day the barn will become empty for the first time. Help Anton and write a program that will determine the number of that day!", "input_spec": "The only line of the input contains two integers n and m (1 ≤ n, m ≤ 1018) — the capacity of the barn and the number of grains that are brought every day.", "output_spec": "Output one integer — the number of the day when the barn will become empty for the first time. Days are numbered starting with one.", "sample_inputs": ["5 2", "8 1"], "sample_outputs": ["4", "5"], "notes": "NoteIn the first sample the capacity of the barn is five grains and two grains are brought every day. The following happens:  At the beginning of the first day grain is brought to the barn. It's full, so nothing happens.  At the end of the first day one sparrow comes and eats one grain, so 5 - 1 = 4 grains remain.  At the beginning of the second day two grains are brought. The barn becomes full and one grain doesn't fit to it.  At the end of the second day two sparrows come. 5 - 2 = 3 grains remain.  At the beginning of the third day two grains are brought. The barn becomes full again.  At the end of the third day three sparrows come and eat grain. 5 - 3 = 2 grains remain.  At the beginning of the fourth day grain is brought again. 2 + 2 = 4 grains remain.  At the end of the fourth day four sparrows come and eat grain. 4 - 4 = 0 grains remain. The barn is empty. So the answer is 4, because by the end of the fourth day the barn becomes empty."}, "src_uid": "3b585ea852ffc41034ef6804b6aebbd8"}
{"nl": {"description": "Petya has an array $$$a$$$ consisting of $$$n$$$ integers. He wants to remove duplicate (equal) elements.Petya wants to leave only the rightmost entry (occurrence) for each element of the array. The relative order of the remaining unique elements should not be changed.", "input_spec": "The first line contains a single integer $$$n$$$ ($$$1 \\le n \\le 50$$$) — the number of elements in Petya's array. The following line contains a sequence $$$a_1, a_2, \\dots, a_n$$$ ($$$1 \\le a_i \\le 1\\,000$$$) — the Petya's array.", "output_spec": "In the first line print integer $$$x$$$ — the number of elements which will be left in Petya's array after he removed the duplicates. In the second line print $$$x$$$ integers separated with a space — Petya's array after he removed the duplicates. For each unique element only the rightmost entry should be left.", "sample_inputs": ["6\n1 5 5 1 6 1", "5\n2 4 2 4 4", "5\n6 6 6 6 6"], "sample_outputs": ["3\n5 6 1", "2\n2 4", "1\n6"], "notes": "NoteIn the first example you should remove two integers $$$1$$$, which are in the positions $$$1$$$ and $$$4$$$. Also you should remove the integer $$$5$$$, which is in the position $$$2$$$.In the second example you should remove integer $$$2$$$, which is in the position $$$1$$$, and two integers $$$4$$$, which are in the positions $$$2$$$ and $$$4$$$.In the third example you should remove four integers $$$6$$$, which are in the positions $$$1$$$, $$$2$$$, $$$3$$$ and $$$4$$$."}, "src_uid": "1b9d3dfcc2353eac20b84c75c27fab5a"}
{"nl": {"description": "A prime number is a number which has exactly two distinct divisors: one and itself. For example, numbers 2, 7, 3 are prime, and 1, 6, 4 are not.The next prime number after x is the smallest prime number greater than x. For example, the next prime number after 2 is 3, and the next prime number after 3 is 5. Note that there is exactly one next prime number after each number. So 5 is not the next prime number for 2.One cold April morning Panoramix predicted that soon Kakofonix will break free from his straitjacket, and this will be a black day for the residents of the Gallic countryside.Panoramix's prophecy tells that if some day Asterix and Obelix beat exactly x Roman soldiers, where x is a prime number, and next day they beat exactly y Roman soldiers, where y is the next prime number after x, then it's time to wait for Armageddon, for nothing can shut Kakofonix up while he sings his infernal song.Yesterday the Gauls beat n Roman soldiers and it turned out that the number n was prime! Today their victims were a troop of m Romans (m > n). Determine whether the Gauls should wait for the black day after today's victory of Asterix and Obelix?", "input_spec": "The first and only input line contains two positive integers — n and m (2 ≤ n < m ≤ 50). It is guaranteed that n is prime. Pretests contain all the cases with restrictions 2 ≤ n < m ≤ 4.", "output_spec": "Print YES, if m is the next prime number after n, or NO otherwise.", "sample_inputs": ["3 5", "7 11", "7 9"], "sample_outputs": ["YES", "YES", "NO"], "notes": null}, "src_uid": "9d52ff51d747bb59aa463b6358258865"}
{"nl": {"description": "Qwerty the Ranger took up a government job and arrived on planet Mars. He should stay in the secret lab and conduct some experiments on bacteria that have funny and abnormal properties. The job isn't difficult, but the salary is high.At the beginning of the first experiment there is a single bacterium in the test tube. Every second each bacterium in the test tube divides itself into k bacteria. After that some abnormal effects create b more bacteria in the test tube. Thus, if at the beginning of some second the test tube had x bacteria, then at the end of the second it will have kx + b bacteria.The experiment showed that after n seconds there were exactly z bacteria and the experiment ended at this point.For the second experiment Qwerty is going to sterilize the test tube and put there t bacteria. He hasn't started the experiment yet but he already wonders, how many seconds he will need to grow at least z bacteria. The ranger thinks that the bacteria will divide by the same rule as in the first experiment. Help Qwerty and find the minimum number of seconds needed to get a tube with at least z bacteria in the second experiment.", "input_spec": "The first line contains four space-separated integers k, b, n and t (1 ≤ k, b, n, t ≤ 106) — the parameters of bacterial growth, the time Qwerty needed to grow z bacteria in the first experiment and the initial number of bacteria in the second experiment, correspondingly.", "output_spec": "Print a single number — the minimum number of seconds Qwerty needs to grow at least z bacteria in the tube.", "sample_inputs": ["3 1 3 5", "1 4 4 7", "2 2 4 100"], "sample_outputs": ["2", "3", "0"], "notes": null}, "src_uid": "e2357a1f54757bce77dce625772e4f18"}
{"nl": {"description": "Alice has a string consisting of characters 'A', 'B' and 'C'. Bob can use the following transitions on any substring of our string in any order any number of times:   A  BC  B  AC  C  AB  AAA  empty string Note that a substring is one or more consecutive characters. For given queries, determine whether it is possible to obtain the target string from source.", "input_spec": "The first line contains a string S (1 ≤ |S| ≤ 105). The second line contains a string T (1 ≤ |T| ≤ 105), each of these strings consists only of uppercase English letters 'A', 'B' and 'C'. The third line contains the number of queries Q (1 ≤ Q ≤ 105). The following Q lines describe queries. The i-th of these lines contains four space separated integers ai, bi, ci, di. These represent the i-th query: is it possible to create T[ci..di] from S[ai..bi] by applying the above transitions finite amount of times? Here, U[x..y] is a substring of U that begins at index x (indexed from 1) and ends at index y. In particular, U[1..|U|] is the whole string U. It is guaranteed that 1 ≤ a ≤ b ≤ |S| and 1 ≤ c ≤ d ≤ |T|.", "output_spec": "Print a string of Q characters, where the i-th character is '1' if the answer to the i-th query is positive, and '0' otherwise.", "sample_inputs": ["AABCCBAAB\nABCB\n5\n1 3 1 2\n2 2 2 4\n7 9 1 1\n3 4 2 3\n4 5 1 3"], "sample_outputs": ["10011"], "notes": "NoteIn the first query we can achieve the result, for instance, by using transitions .The third query asks for changing AAB to A — but in this case we are not able to get rid of the character 'B'."}, "src_uid": "98e3182f047a7e7b10be7f207b219267"}
{"nl": {"description": "Can you imagine our life if we removed all zeros from it? For sure we will have many problems.In this problem we will have a simple example if we removed all zeros from our life, it's the addition operation. Let's assume you are given this equation a + b = c, where a and b are positive integers, and c is the sum of a and b. Now let's remove all zeros from this equation. Will the equation remain correct after removing all zeros?For example if the equation is 101 + 102 = 203, if we removed all zeros it will be 11 + 12 = 23 which is still a correct equation.But if the equation is 105 + 106 = 211, if we removed all zeros it will be 15 + 16 = 211 which is not a correct equation.", "input_spec": "The input will consist of two lines, the first line will contain the integer a, and the second line will contain the integer b which are in the equation as described above (1 ≤ a, b ≤ 109). There won't be any leading zeros in both. The value of c should be calculated as c = a + b.", "output_spec": "The output will be just one line, you should print \"YES\" if the equation will remain correct after removing all zeros, and print \"NO\" otherwise.", "sample_inputs": ["101\n102", "105\n106"], "sample_outputs": ["YES", "NO"], "notes": null}, "src_uid": "ac6971f4feea0662d82da8e0862031ad"}
{"nl": {"description": "Bizon the Champion isn't just a bison. He also is a favorite of the \"Bizons\" team.At a competition the \"Bizons\" got the following problem: \"You are given two distinct words (strings of English letters), s and t. You need to transform word s into word t\". The task looked simple to the guys because they know the suffix data structures well. Bizon Senior loves suffix automaton. By applying it once to a string, he can remove from this string any single character. Bizon Middle knows suffix array well. By applying it once to a string, he can swap any two characters of this string. The guys do not know anything about the suffix tree, but it can help them do much more. Bizon the Champion wonders whether the \"Bizons\" can solve the problem. Perhaps, the solution do not require both data structures. Find out whether the guys can solve the problem and if they can, how do they do it? Can they solve it either only with use of suffix automaton or only with use of suffix array or they need both structures? Note that any structure may be used an unlimited number of times, the structures may be used in any order.", "input_spec": "The first line contains a non-empty word s. The second line contains a non-empty word t. Words s and t are different. Each word consists only of lowercase English letters. Each word contains at most 100 letters.", "output_spec": "In the single line print the answer to the problem. Print \"need tree\" (without the quotes) if word s cannot be transformed into word t even with use of both suffix array and suffix automaton. Print \"automaton\" (without the quotes) if you need only the suffix automaton to solve the problem. Print \"array\" (without the quotes) if you need only the suffix array to solve the problem. Print \"both\" (without the quotes), if you need both data structures to solve the problem. It's guaranteed that if you can solve the problem only with use of suffix array, then it is impossible to solve it only with use of suffix automaton. This is also true for suffix automaton.", "sample_inputs": ["automaton\ntomat", "array\narary", "both\nhot", "need\ntree"], "sample_outputs": ["automaton", "array", "both", "need tree"], "notes": "NoteIn the third sample you can act like that: first transform \"both\" into \"oth\" by removing the first character using the suffix automaton and then make two swaps of the string using the suffix array and get \"hot\"."}, "src_uid": "edb9d51e009a59a340d7d589bb335c14"}
{"nl": {"description": "Gaius Julius Caesar, a famous general, loved to line up his soldiers. Overall the army had n1 footmen and n2 horsemen. Caesar thought that an arrangement is not beautiful if somewhere in the line there are strictly more that k1 footmen standing successively one after another, or there are strictly more than k2 horsemen standing successively one after another. Find the number of beautiful arrangements of the soldiers. Note that all n1 + n2 warriors should be present at each arrangement. All footmen are considered indistinguishable among themselves. Similarly, all horsemen are considered indistinguishable among themselves.", "input_spec": "The only line contains four space-separated integers n1, n2, k1, k2 (1 ≤ n1, n2 ≤ 100, 1 ≤ k1, k2 ≤ 10) which represent how many footmen and horsemen there are and the largest acceptable number of footmen and horsemen standing in succession, correspondingly.", "output_spec": "Print the number of beautiful arrangements of the army modulo 100000000 (108). That is, print the number of such ways to line up the soldiers, that no more than k1 footmen stand successively, and no more than k2 horsemen stand successively.", "sample_inputs": ["2 1 1 10", "2 3 1 2", "2 4 1 1"], "sample_outputs": ["1", "5", "0"], "notes": "NoteLet's mark a footman as 1, and a horseman as 2.In the first sample the only beautiful line-up is: 121In the second sample 5 beautiful line-ups exist: 12122, 12212, 21212, 21221, 22121"}, "src_uid": "63aabef26fe008e4c6fc9336eb038289"}
{"nl": {"description": "Recall that the permutation is an array consisting of $$$n$$$ distinct integers from $$$1$$$ to $$$n$$$ in arbitrary order. For example, $$$[2,3,1,5,4]$$$ is a permutation, but $$$[1,2,2]$$$ is not a permutation ($$$2$$$ appears twice in the array) and $$$[1,3,4]$$$ is also not a permutation ($$$n=3$$$ but there is $$$4$$$ in the array).A sequence $$$a$$$ is a subsegment of a sequence $$$b$$$ if $$$a$$$ can be obtained from $$$b$$$ by deletion of several (possibly, zero or all) elements from the beginning and several (possibly, zero or all) elements from the end. We will denote the subsegments as $$$[l, r]$$$, where $$$l, r$$$ are two integers with $$$1 \\le l \\le r \\le n$$$. This indicates the subsegment where $$$l-1$$$ elements from the beginning and $$$n-r$$$ elements from the end are deleted from the sequence.For a permutation $$$p_1, p_2, \\ldots, p_n$$$, we define a framed segment as a subsegment $$$[l,r]$$$ where $$$\\max\\{p_l, p_{l+1}, \\dots, p_r\\} - \\min\\{p_l, p_{l+1}, \\dots, p_r\\} = r - l$$$. For example, for the permutation $$$(6, 7, 1, 8, 5, 3, 2, 4)$$$ some of its framed segments are: $$$[1, 2], [5, 8], [6, 7], [3, 3], [8, 8]$$$. In particular, a subsegment $$$[i,i]$$$ is always a framed segments for any $$$i$$$ between $$$1$$$ and $$$n$$$, inclusive.We define the happiness of a permutation $$$p$$$ as the number of pairs $$$(l, r)$$$ such that $$$1 \\le l \\le r \\le n$$$, and $$$[l, r]$$$ is a framed segment. For example, the permutation $$$[3, 1, 2]$$$ has happiness $$$5$$$: all segments except $$$[1, 2]$$$ are framed segments.Given integers $$$n$$$ and $$$m$$$, Jongwon wants to compute the sum of happiness for all permutations of length $$$n$$$, modulo the prime number $$$m$$$. Note that there exist $$$n!$$$ (factorial of $$$n$$$) different permutations of length $$$n$$$.", "input_spec": "The only line contains two integers $$$n$$$ and $$$m$$$ ($$$1 \\le n \\le 250\\,000$$$, $$$10^8 \\le m \\le 10^9$$$, $$$m$$$ is prime).", "output_spec": "Print $$$r$$$ ($$$0 \\le r < m$$$), the sum of happiness for all permutations of length $$$n$$$, modulo a prime number $$$m$$$.", "sample_inputs": ["1 993244853", "2 993244853", "3 993244853", "2019 993244853", "2020 437122297"], "sample_outputs": ["1", "6", "32", "923958830", "265955509"], "notes": "NoteFor sample input $$$n=3$$$, let's consider all permutations of length $$$3$$$:  $$$[1, 2, 3]$$$, all subsegments are framed segment. Happiness is $$$6$$$.  $$$[1, 3, 2]$$$, all subsegments except $$$[1, 2]$$$ are framed segment. Happiness is $$$5$$$.  $$$[2, 1, 3]$$$, all subsegments except $$$[2, 3]$$$ are framed segment. Happiness is $$$5$$$.  $$$[2, 3, 1]$$$, all subsegments except $$$[2, 3]$$$ are framed segment. Happiness is $$$5$$$.  $$$[3, 1, 2]$$$, all subsegments except $$$[1, 2]$$$ are framed segment. Happiness is $$$5$$$.  $$$[3, 2, 1]$$$, all subsegments are framed segment. Happiness is $$$6$$$. Thus, the sum of happiness is $$$6+5+5+5+5+6 = 32$$$."}, "src_uid": "020d5dae7157d937c3f58554c9b155f9"}
{"nl": {"description": "Little Artem got n stones on his birthday and now wants to give some of them to Masha. He knows that Masha cares more about the fact of receiving the present, rather than the value of that present, so he wants to give her stones as many times as possible. However, Masha remembers the last present she received, so Artem can't give her the same number of stones twice in a row. For example, he can give her 3 stones, then 1 stone, then again 3 stones, but he can't give her 3 stones and then again 3 stones right after that.How many times can Artem give presents to Masha?", "input_spec": "The only line of the input contains a single integer n (1 ≤ n ≤ 109) — number of stones Artem received on his birthday.", "output_spec": "Print the maximum possible number of times Artem can give presents to Masha.", "sample_inputs": ["1", "2", "3", "4"], "sample_outputs": ["1", "1", "2", "3"], "notes": "NoteIn the first sample, Artem can only give 1 stone to Masha.In the second sample, Atrem can give Masha 1 or 2 stones, though he can't give her 1 stone two times.In the third sample, Atrem can first give Masha 2 stones, a then 1 more stone.In the fourth sample, Atrem can first give Masha 1 stone, then 2 stones, and finally 1 stone again."}, "src_uid": "a993069e35b35ae158d35d6fe166aaef"}
{"nl": {"description": "Vasya works as a DJ in the best Berland nightclub, and he often uses dubstep music in his performance. Recently, he has decided to take a couple of old songs and make dubstep remixes from them.Let's assume that a song consists of some number of words. To make the dubstep remix of this song, Vasya inserts a certain number of words \"WUB\" before the first word of the song (the number may be zero), after the last word (the number may be zero), and between words (at least one between any pair of neighbouring words), and then the boy glues together all the words, including \"WUB\", in one string and plays the song at the club.For example, a song with words \"I AM X\" can transform into a dubstep remix as \"WUBWUBIWUBAMWUBWUBX\" and cannot transform into \"WUBWUBIAMWUBX\".Recently, Petya has heard Vasya's new dubstep track, but since he isn't into modern music, he decided to find out what was the initial song that Vasya remixed. Help Petya restore the original song.", "input_spec": "The input consists of a single non-empty string, consisting only of uppercase English letters, the string's length doesn't exceed 200 characters. It is guaranteed that before Vasya remixed the song, no word contained substring \"WUB\" in it; Vasya didn't change the word order. It is also guaranteed that initially the song had at least one word.", "output_spec": "Print the words of the initial song that Vasya used to make a dubsteb remix. Separate the words with a space.", "sample_inputs": ["WUBWUBABCWUB", "WUBWEWUBAREWUBWUBTHEWUBCHAMPIONSWUBMYWUBFRIENDWUB"], "sample_outputs": ["ABC", "WE ARE THE CHAMPIONS MY FRIEND"], "notes": "NoteIn the first sample: \"WUBWUBABCWUB\" = \"WUB\" + \"WUB\" + \"ABC\" + \"WUB\". That means that the song originally consisted of a single word \"ABC\", and all words \"WUB\" were added by Vasya.In the second sample Vasya added a single word \"WUB\" between all neighbouring words, in the beginning and in the end, except for words \"ARE\" and \"THE\" — between them Vasya added two \"WUB\"."}, "src_uid": "edede580da1395fe459a480f6a0a548d"}
{"nl": {"description": "You are given a positive integer $$$n$$$.Let $$$S(x)$$$ be sum of digits in base 10 representation of $$$x$$$, for example, $$$S(123) = 1 + 2 + 3 = 6$$$, $$$S(0) = 0$$$.Your task is to find two integers $$$a, b$$$, such that $$$0 \\leq a, b \\leq n$$$, $$$a + b = n$$$ and $$$S(a) + S(b)$$$ is the largest possible among all such pairs.", "input_spec": "The only line of input contains an integer $$$n$$$ $$$(1 \\leq n \\leq 10^{12})$$$.", "output_spec": "Print largest $$$S(a) + S(b)$$$ among all pairs of integers $$$a, b$$$, such that $$$0 \\leq a, b \\leq n$$$ and $$$a + b = n$$$.", "sample_inputs": ["35", "10000000000"], "sample_outputs": ["17", "91"], "notes": "NoteIn the first example, you can choose, for example, $$$a = 17$$$ and $$$b = 18$$$, so that $$$S(17) + S(18) = 1 + 7 + 1 + 8 = 17$$$. It can be shown that it is impossible to get a larger answer.In the second test example, you can choose, for example, $$$a = 5000000001$$$ and $$$b = 4999999999$$$, with $$$S(5000000001) + S(4999999999) = 91$$$. It can be shown that it is impossible to get a larger answer."}, "src_uid": "5c61b4a4728070b9de49d72831cd2329"}
{"nl": {"description": "Tattah's youngest brother, Tuftuf, is new to programming.Since his older brother is such a good programmer, his biggest dream is to outshine him. Tuftuf is a student at the German University in Cairo (GUC) where he learns to write programs in Gava.Today, Tuftuf was introduced to Gava's unsigned integer datatypes. Gava has n unsigned integer datatypes of sizes (in bits) a1, a2, ... an. The i-th datatype have size ai bits, so it can represent every integer between 0 and 2ai - 1 inclusive. Tuftuf is thinking of learning a better programming language. If there exists an integer x, such that x fits in some type i (in ai bits) and x·x does not fit in some other type j (in aj bits) where ai < aj, then Tuftuf will stop using Gava.Your task is to determine Tuftuf's destiny.", "input_spec": "The first line contains integer n (2 ≤ n ≤ 105) — the number of Gava's unsigned integer datatypes' sizes. The second line contains a single-space-separated list of n integers (1 ≤ ai ≤ 109) — sizes of datatypes in bits. Some datatypes may have equal sizes.", "output_spec": "Print \"YES\" if Tuftuf will stop using Gava, and \"NO\" otherwise.", "sample_inputs": ["3\n64 16 32", "4\n4 2 1 3"], "sample_outputs": ["NO", "YES"], "notes": "NoteIn the second example, x = 7 (1112) fits in 3 bits, but x2 = 49 (1100012) does not fit in 4 bits."}, "src_uid": "ab003ab094931fc105384df9d144131e"}
{"nl": {"description": "A girl named Xenia has a cupboard that looks like an arc from ahead. The arc is made of a semicircle with radius r (the cupboard's top) and two walls of height h (the cupboard's sides). The cupboard's depth is r, that is, it looks like a rectangle with base r and height h + r from the sides. The figure below shows what the cupboard looks like (the front view is on the left, the side view is on the right).  Xenia got lots of balloons for her birthday. The girl hates the mess, so she wants to store the balloons in the cupboard. Luckily, each balloon is a sphere with radius . Help Xenia calculate the maximum number of balloons she can put in her cupboard. You can say that a balloon is in the cupboard if you can't see any part of the balloon on the left or right view. The balloons in the cupboard can touch each other. It is not allowed to squeeze the balloons or deform them in any way. You can assume that the cupboard's walls are negligibly thin.", "input_spec": "The single line contains two integers r, h (1 ≤ r, h ≤ 107).", "output_spec": "Print a single integer — the maximum number of balloons Xenia can put in the cupboard.", "sample_inputs": ["1 1", "1 2", "2 1"], "sample_outputs": ["3", "5", "2"], "notes": null}, "src_uid": "ae883bf16842c181ea4bd123dee12ef9"}
{"nl": {"description": "Kolya loves putting gnomes at the circle table and giving them coins, and Tanya loves studying triplets of gnomes, sitting in the vertexes of an equilateral triangle.More formally, there are 3n gnomes sitting in a circle. Each gnome can have from 1 to 3 coins. Let's number the places in the order they occur in the circle by numbers from 0 to 3n - 1, let the gnome sitting on the i-th place have ai coins. If there is an integer i (0 ≤ i < n) such that ai + ai + n + ai + 2n ≠ 6, then Tanya is satisfied. Count the number of ways to choose ai so that Tanya is satisfied. As there can be many ways of distributing coins, print the remainder of this number modulo 109 + 7. Two ways, a and b, are considered distinct if there is index i (0 ≤ i < 3n), such that ai ≠ bi (that is, some gnome got different number of coins in these two ways).", "input_spec": "A single line contains number n (1 ≤ n ≤ 105) — the number of the gnomes divided by three.", "output_spec": "Print a single number — the remainder of the number of variants of distributing coins that satisfy Tanya modulo 109 + 7.", "sample_inputs": ["1", "2"], "sample_outputs": ["20", "680"], "notes": "Note20 ways for n = 1 (gnome with index 0 sits on the top of the triangle, gnome 1 on the right vertex, gnome 2 on the left vertex):   "}, "src_uid": "eae87ec16c284f324d86b7e65fda093c"}
{"nl": {"description": "Some time ago Leonid have known about idempotent functions. Idempotent function defined on a set {1, 2, ..., n} is such function , that for any  the formula g(g(x)) = g(x) holds.Let's denote as f(k)(x) the function f applied k times to the value x. More formally, f(1)(x) = f(x), f(k)(x) = f(f(k - 1)(x)) for each k > 1.You are given some function . Your task is to find minimum positive integer k such that function f(k)(x) is idempotent.", "input_spec": "In the first line of the input there is a single integer n (1 ≤ n ≤ 200) — the size of function f domain. In the second line follow f(1), f(2), ..., f(n) (1 ≤ f(i) ≤ n for each 1 ≤ i ≤ n), the values of a function.", "output_spec": "Output minimum k such that function f(k)(x) is idempotent.", "sample_inputs": ["4\n1 2 2 4", "3\n2 3 3", "3\n2 3 1"], "sample_outputs": ["1", "2", "3"], "notes": "NoteIn the first sample test function f(x) = f(1)(x) is already idempotent since f(f(1)) = f(1) = 1, f(f(2)) = f(2) = 2, f(f(3)) = f(3) = 2, f(f(4)) = f(4) = 4.In the second sample test:   function f(x) = f(1)(x) isn't idempotent because f(f(1)) = 3 but f(1) = 2;  function f(x) = f(2)(x) is idempotent since for any x it is true that f(2)(x) = 3, so it is also true that f(2)(f(2)(x)) = 3. In the third sample test:   function f(x) = f(1)(x) isn't idempotent because f(f(1)) = 3 but f(1) = 2;  function f(f(x)) = f(2)(x) isn't idempotent because f(2)(f(2)(1)) = 2 but f(2)(1) = 3;  function f(f(f(x))) = f(3)(x) is idempotent since it is identity function: f(3)(x) = x for any  meaning that the formula f(3)(f(3)(x)) = f(3)(x) also holds. "}, "src_uid": "1daa784c0eb1cde514e4319da07c8d00"}
{"nl": {"description": "The tram in Berland goes along a straight line from the point 0 to the point s and back, passing 1 meter per t1 seconds in both directions. It means that the tram is always in the state of uniform rectilinear motion, instantly turning around at points x = 0 and x = s.Igor is at the point x1. He should reach the point x2. Igor passes 1 meter per t2 seconds. Your task is to determine the minimum time Igor needs to get from the point x1 to the point x2, if it is known where the tram is and in what direction it goes at the moment Igor comes to the point x1.Igor can enter the tram unlimited number of times at any moment when his and the tram's positions coincide. It is not obligatory that points in which Igor enter and exit the tram are integers. Assume that any boarding and unboarding happens instantly. Igor can move arbitrary along the line (but not faster than 1 meter per t2 seconds). He can also stand at some point for some time.", "input_spec": "The first line contains three integers s, x1 and x2 (2 ≤ s ≤ 1000, 0 ≤ x1, x2 ≤ s, x1 ≠ x2) — the maximum coordinate of the point to which the tram goes, the point Igor is at, and the point he should come to. The second line contains two integers t1 and t2 (1 ≤ t1, t2 ≤ 1000) — the time in seconds in which the tram passes 1 meter and the time in seconds in which Igor passes 1 meter. The third line contains two integers p and d (1 ≤ p ≤ s - 1, d is either 1 or ) — the position of the tram in the moment Igor came to the point x1 and the direction of the tram at this moment. If , the tram goes in the direction from the point s to the point 0. If d = 1, the tram goes in the direction from the point 0 to the point s.", "output_spec": "Print the minimum time in seconds which Igor needs to get from the point x1 to the point x2.", "sample_inputs": ["4 2 4\n3 4\n1 1", "5 4 0\n1 2\n3 1"], "sample_outputs": ["8", "7"], "notes": "NoteIn the first example it is profitable for Igor to go by foot and not to wait the tram. Thus, he has to pass 2 meters and it takes 8 seconds in total, because he passes 1 meter per 4 seconds. In the second example Igor can, for example, go towards the point x2 and get to the point 1 in 6 seconds (because he has to pass 3 meters, but he passes 1 meters per 2 seconds). At that moment the tram will be at the point 1, so Igor can enter the tram and pass 1 meter in 1 second. Thus, Igor will reach the point x2 in 7 seconds in total."}, "src_uid": "fb3aca6eba3a952e9d5736c5d8566821"}
{"nl": {"description": "The king is left alone on the chessboard. In spite of this loneliness, he doesn't lose heart, because he has business of national importance. For example, he has to pay an official visit to square t. As the king is not in habit of wasting his time, he wants to get from his current position s to square t in the least number of moves. Help him to do this.  In one move the king can get to the square that has a common side or a common vertex with the square the king is currently in (generally there are 8 different squares he can move to).", "input_spec": "The first line contains the chessboard coordinates of square s, the second line — of square t. Chessboard coordinates consist of two characters, the first one is a lowercase Latin letter (from a to h), the second one is a digit from 1 to 8.", "output_spec": "In the first line print n — minimum number of the king's moves. Then in n lines print the moves themselves. Each move is described with one of the 8: L, R, U, D, LU, LD, RU or RD.  L, R, U, D stand respectively for moves left, right, up and down (according to the picture), and 2-letter combinations stand for diagonal moves. If the answer is not unique, print any of them. ", "sample_inputs": ["a8\nh1"], "sample_outputs": ["7\nRD\nRD\nRD\nRD\nRD\nRD\nRD"], "notes": null}, "src_uid": "d25d454702b7755297a7a8e1f6f36ab9"}
{"nl": {"description": "You may have heard of the pie rule before. It states that if two people wish to fairly share a slice of pie, one person should cut the slice in half, and the other person should choose who gets which slice. Alice and Bob have many slices of pie, and rather than cutting the slices in half, each individual slice will be eaten by just one person.The way Alice and Bob decide who eats each slice is as follows. First, the order in which the pies are to be handed out is decided. There is a special token called the \"decider\" token, initially held by Bob. Until all the pie is handed out, whoever has the decider token will give the next slice of pie to one of the participants, and the decider token to the other participant. They continue until no slices of pie are left.All of the slices are of excellent quality, so each participant obviously wants to maximize the total amount of pie they get to eat. Assuming both players make their decisions optimally, how much pie will each participant receive?", "input_spec": "Input will begin with an integer N (1 ≤ N ≤ 50), the number of slices of pie.  Following this is a line with N integers indicating the sizes of the slices (each between 1 and 100000, inclusive), in the order in which they must be handed out.", "output_spec": "Print two integers. First, the sum of the sizes of slices eaten by Alice, then the sum of the sizes of the slices eaten by Bob, assuming both players make their decisions optimally.", "sample_inputs": ["3\n141 592 653", "5\n10 21 10 21 10"], "sample_outputs": ["653 733", "31 41"], "notes": "NoteIn the first example, Bob takes the size 141 slice for himself and gives the decider token to Alice. Then Alice gives the size 592 slice to Bob and keeps the decider token for herself, so that she can then give the size 653 slice to herself."}, "src_uid": "414540223db9d4cfcec6a973179a0216"}
{"nl": {"description": "There are $$$n$$$ computers in a row, all originally off, and Phoenix wants to turn all of them on. He will manually turn on computers one at a time. At any point, if computer $$$i-1$$$ and computer $$$i+1$$$ are both on, computer $$$i$$$ $$$(2 \\le i \\le n-1)$$$ will turn on automatically if it is not already on. Note that Phoenix cannot manually turn on a computer that already turned on automatically.If we only consider the sequence of computers that Phoenix turns on manually, how many ways can he turn on all the computers? Two sequences are distinct if either the set of computers turned on manually is distinct, or the order of computers turned on manually is distinct. Since this number may be large, please print it modulo $$$M$$$.", "input_spec": "The first line contains two integers $$$n$$$ and $$$M$$$ ($$$3 \\le n \\le 400$$$; $$$10^8 \\le M \\le 10^9$$$) — the number of computers and the modulo. It is guaranteed that $$$M$$$ is prime.", "output_spec": "Print one integer — the number of ways to turn on the computers modulo $$$M$$$.", "sample_inputs": ["3 100000007", "4 100000007", "400 234567899"], "sample_outputs": ["6", "20", "20914007"], "notes": "NoteIn the first example, these are the $$$6$$$ orders in which Phoenix can turn on all computers:   $$$[1,3]$$$. Turn on computer $$$1$$$, then $$$3$$$. Note that computer $$$2$$$ turns on automatically after computer $$$3$$$ is turned on manually, but we only consider the sequence of computers that are turned on manually.  $$$[3,1]$$$. Turn on computer $$$3$$$, then $$$1$$$.  $$$[1,2,3]$$$. Turn on computer $$$1$$$, $$$2$$$, then $$$3$$$.  $$$[2,1,3]$$$  $$$[2,3,1]$$$  $$$[3,2,1]$$$ "}, "src_uid": "4f0e0d1deef0761a46b64de3eb98e774"}
{"nl": {"description": "Recently you have received two positive integer numbers $$$x$$$ and $$$y$$$. You forgot them, but you remembered a shuffled list containing all divisors of $$$x$$$ (including $$$1$$$ and $$$x$$$) and all divisors of $$$y$$$ (including $$$1$$$ and $$$y$$$). If $$$d$$$ is a divisor of both numbers $$$x$$$ and $$$y$$$ at the same time, there are two occurrences of $$$d$$$ in the list.For example, if $$$x=4$$$ and $$$y=6$$$ then the given list can be any permutation of the list $$$[1, 2, 4, 1, 2, 3, 6]$$$. Some of the possible lists are: $$$[1, 1, 2, 4, 6, 3, 2]$$$, $$$[4, 6, 1, 1, 2, 3, 2]$$$ or $$$[1, 6, 3, 2, 4, 1, 2]$$$.Your problem is to restore suitable positive integer numbers $$$x$$$ and $$$y$$$ that would yield the same list of divisors (possibly in different order).It is guaranteed that the answer exists, i.e. the given list of divisors corresponds to some positive integers $$$x$$$ and $$$y$$$.", "input_spec": "The first line contains one integer $$$n$$$ ($$$2 \\le n \\le 128$$$) — the number of divisors of $$$x$$$ and $$$y$$$. The second line of the input contains $$$n$$$ integers $$$d_1, d_2, \\dots, d_n$$$ ($$$1 \\le d_i \\le 10^4$$$), where $$$d_i$$$ is either divisor of $$$x$$$ or divisor of $$$y$$$. If a number is divisor of both numbers $$$x$$$ and $$$y$$$ then there are two copies of this number in the list.", "output_spec": "Print two positive integer numbers $$$x$$$ and $$$y$$$ — such numbers that merged list of their divisors is the permutation of the given list of integers. It is guaranteed that the answer exists.", "sample_inputs": ["10\n10 2 8 1 2 4 1 20 4 5"], "sample_outputs": ["20 8"], "notes": null}, "src_uid": "868407df0a93085057d06367aecaf9be"}
{"nl": {"description": "Vasya plays the Plane of Tanks. The tanks in this game keep trying to finish each other off. But your \"Pedalny\" is not like that... He just needs to drive in a straight line from point A to point B on the plane. Unfortunately, on the same plane are n enemy tanks. We shall regard all the tanks as points. At the initial moment of time Pedalny is at the point A. Enemy tanks would be happy to destroy it immediately, but initially their turrets are tuned in other directions. Specifically, for each tank we know the initial rotation of the turret ai (the angle in radians relative to the OX axis in the counterclockwise direction) and the maximum speed of rotation of the turret wi (radians per second). If at any point of time a tank turret will be aimed precisely at the tank Pedalny, then the enemy fires and it never misses. Pedalny can endure no more than k shots. Gun reloading takes very much time, so we can assume that every enemy will produce no more than one shot. Your task is to determine what minimum speed of v Pedalny must have to get to the point B. It is believed that Pedalny is able to instantly develop the speed of v, and the first k shots at him do not reduce the speed and do not change the coordinates of the tank.", "input_spec": "The first line contains 4 numbers – the coordinates of points A and B (in meters), the points do not coincide. On the second line number n is given (1 ≤ n ≤ 104). It is the number of enemy tanks. Each of the following n lines contain the coordinates of a corresponding tank xi, yi and its parameters ai and wi (0 ≤ ai ≤ 2π, 0 ≤ wi ≤ 100). Numbers ai and wi contain at most 5 digits after the decimal point. All coordinates are integers and their absolute values do not exceed 105. Enemy tanks can rotate a turret in the clockwise as well as in the counterclockwise direction at the angular speed of not more than wi. It is guaranteed that each of the enemy tanks will need at least 0.1 seconds to aim at any point of the segment AB and each of the enemy tanks is posistioned no closer than 0.1 meters to line AB. On the last line is given the number k (0 ≤ k ≤ n).", "output_spec": "Print a single number with absolute or relative error no more than 10 - 4 — the minimum required speed of Pedalny in meters per second.", "sample_inputs": ["0 0 10 0\n1\n5 -5 4.71238 1\n0", "0 0 10 0\n1\n5 -5 4.71238 1\n1"], "sample_outputs": ["4.2441", "0.0000"], "notes": null}, "src_uid": "38c14ab8b9c5107c2a2f70a35f166d8b"}
{"nl": {"description": "Once upon a time in the Kingdom of Far Far Away lived Sam the Farmer. Sam had a cow named Dawn and he was deeply attached to her. Sam would spend the whole summer stocking hay to feed Dawn in winter. Sam scythed hay and put it into haystack. As Sam was a bright farmer, he tried to make the process of storing hay simpler and more convenient to use. He collected the hay into cubical hay blocks of the same size. Then he stored the blocks in his barn. After a summer spent in hard toil Sam stored A·B·C hay blocks and stored them in a barn as a rectangular parallelepiped A layers high. Each layer had B rows and each row had C blocks.At the end of the autumn Sam came into the barn to admire one more time the hay he'd been stacking during this hard summer. Unfortunately, Sam was horrified to see that the hay blocks had been carelessly scattered around the barn. The place was a complete mess. As it turned out, thieves had sneaked into the barn. They completely dissembled and took away a layer of blocks from the parallelepiped's front, back, top and sides. As a result, the barn only had a parallelepiped containing (A - 1) × (B - 2) × (C - 2) hay blocks. To hide the evidence of the crime, the thieves had dissembled the parallelepiped into single 1 × 1 × 1 blocks and scattered them around the barn. After the theft Sam counted n hay blocks in the barn but he forgot numbers A, B и C.Given number n, find the minimally possible and maximally possible number of stolen hay blocks.", "input_spec": "The only line contains integer n from the problem's statement (1 ≤ n ≤ 109).", "output_spec": "Print space-separated minimum and maximum number of hay blocks that could have been stolen by the thieves. Note that the answer to the problem can be large enough, so you must use the 64-bit integer type for calculations. Please, do not use the %lld specificator to read or write 64-bit integers in С++. It is preferred to use cin, cout streams or the %I64d specificator.", "sample_inputs": ["4", "7", "12"], "sample_outputs": ["28 41", "47 65", "48 105"], "notes": "NoteLet's consider the first sample test. If initially Sam has a parallelepiped consisting of 32 = 2 × 4 × 4 hay blocks in his barn, then after the theft the barn has 4 = (2 - 1) × (4 - 2) × (4 - 2) hay blocks left. Thus, the thieves could have stolen 32 - 4 = 28 hay blocks. If Sam initially had a parallelepiped consisting of 45 = 5 × 3 × 3 hay blocks in his barn, then after the theft the barn has 4 = (5 - 1) × (3 - 2) × (3 - 2) hay blocks left. Thus, the thieves could have stolen 45 - 4 = 41 hay blocks. No other variants of the blocks' initial arrangement (that leave Sam with exactly 4 blocks after the theft) can permit the thieves to steal less than 28 or more than 41 blocks."}, "src_uid": "2468eead8acc5b8f5ddc51bfa2bd4fb7"}
{"nl": {"description": "Memory is now interested in the de-evolution of objects, specifically triangles. He starts with an equilateral triangle of side length x, and he wishes to perform operations to obtain an equilateral triangle of side length y.In a single second, he can modify the length of a single side of the current triangle such that it remains a non-degenerate triangle (triangle of positive area). At any moment of time, the length of each side should be integer.What is the minimum number of seconds required for Memory to obtain the equilateral triangle of side length y?", "input_spec": "The first and only line contains two integers x and y (3 ≤ y < x ≤ 100 000) — the starting and ending equilateral triangle side lengths respectively.", "output_spec": "Print a single integer — the minimum number of seconds required for Memory to obtain the equilateral triangle of side length y if he starts with the equilateral triangle of side length x.", "sample_inputs": ["6 3", "8 5", "22 4"], "sample_outputs": ["4", "3", "6"], "notes": "NoteIn the first sample test, Memory starts with an equilateral triangle of side length 6 and wants one of side length 3. Denote a triangle with sides a, b, and c as (a, b, c). Then, Memory can do .In the second sample test, Memory can do .In the third sample test, Memory can do: ."}, "src_uid": "8edf64f5838b19f9a8b19a14977f5615"}
{"nl": {"description": "This problem consists of three subproblems: for solving subproblem C1 you will receive 4 points, for solving subproblem C2 you will receive 4 points, and for solving subproblem C3 you will receive 8 points.Manao decided to pursue a fighter's career. He decided to begin with an ongoing tournament. Before Manao joined, there were n contestants in the tournament, numbered from 1 to n. Each of them had already obtained some amount of tournament points, namely the i-th fighter had pi points.Manao is going to engage in a single fight against each contestant. Each of Manao's fights ends in either a win or a loss. A win grants Manao one point, and a loss grants Manao's opponent one point. For each i, Manao estimated the amount of effort ei he needs to invest to win against the i-th contestant. Losing a fight costs no effort.After Manao finishes all of his fights, the ranklist will be determined, with 1 being the best rank and n + 1 being the worst. The contestants will be ranked in descending order of their tournament points. The contestants with the same number of points as Manao will be ranked better than him if they won the match against him and worse otherwise. The exact mechanism of breaking ties for other fighters is not relevant here.Manao's objective is to have rank k or better. Determine the minimum total amount of effort he needs to invest in order to fulfill this goal, if it is possible.", "input_spec": "The first line contains a pair of integers n and k (1 ≤ k ≤ n + 1). The i-th of the following n lines contains two integers separated by a single space — pi and ei (0 ≤ pi, ei ≤ 200000). The problem consists of three subproblems. The subproblems have different constraints on the input. You will get some score for the correct submission of the subproblem. The description of the subproblems follows.   In subproblem C1 (4 points), the constraint 1 ≤ n ≤ 15 will hold.  In subproblem C2 (4 points), the constraint 1 ≤ n ≤ 100 will hold.  In subproblem C3 (8 points), the constraint 1 ≤ n ≤ 200000 will hold. ", "output_spec": "Print a single number in a single line — the minimum amount of effort Manao needs to use to rank in the top k. If no amount of effort can earn Manao such a rank, output number -1.", "sample_inputs": ["3 2\n1 1\n1 4\n2 2", "2 1\n3 2\n4 0", "5 2\n2 10\n2 10\n1 1\n3 1\n3 1"], "sample_outputs": ["3", "-1", "12"], "notes": "NoteConsider the first test case. At the time when Manao joins the tournament, there are three fighters. The first of them has 1 tournament point and the victory against him requires 1 unit of effort. The second contestant also has 1 tournament point, but Manao needs 4 units of effort to defeat him. The third contestant has 2 points and victory against him costs Manao 2 units of effort. Manao's goal is top be in top 2. The optimal decision is to win against fighters 1 and 3, after which Manao, fighter 2, and fighter 3 will all have 2 points. Manao will rank better than fighter 3 and worse than fighter 2, thus finishing in second place.Consider the second test case. Even if Manao wins against both opponents, he will still rank third."}, "src_uid": "19a098cef100fc3652c59abf7c373814"}
{"nl": {"description": "For a given positive integer n denote its k-rounding as the minimum positive integer x, such that x ends with k or more zeros in base 10 and is divisible by n.For example, 4-rounding of 375 is 375·80 = 30000. 30000 is the minimum integer such that it ends with 4 or more zeros and is divisible by 375.Write a program that will perform the k-rounding of n.", "input_spec": "The only line contains two integers n and k (1 ≤ n ≤ 109, 0 ≤ k ≤ 8).", "output_spec": "Print the k-rounding of n.", "sample_inputs": ["375 4", "10000 1", "38101 0", "123456789 8"], "sample_outputs": ["30000", "10000", "38101", "12345678900000000"], "notes": null}, "src_uid": "73566d4d9f20f7bbf71bc06bc9a4e9f3"}
{"nl": {"description": "Limak is a grizzly bear who desires power and adoration. He wants to win in upcoming elections and rule over the Bearland.There are n candidates, including Limak. We know how many citizens are going to vote for each candidate. Now i-th candidate would get ai votes. Limak is candidate number 1. To win in elections, he must get strictly more votes than any other candidate.Victory is more important than everything else so Limak decided to cheat. He will steal votes from his opponents by bribing some citizens. To bribe a citizen, Limak must give him or her one candy - citizens are bears and bears like candies. Limak doesn't have many candies and wonders - how many citizens does he have to bribe?", "input_spec": "The first line contains single integer n (2 ≤ n ≤ 100) - number of candidates. The second line contains n space-separated integers a1, a2, ..., an (1 ≤ ai ≤ 1000) - number of votes for each candidate. Limak is candidate number 1. Note that after bribing number of votes for some candidate might be zero or might be greater than 1000.", "output_spec": "Print the minimum number of citizens Limak must bribe to have strictly more votes than any other candidate.", "sample_inputs": ["5\n5 1 11 2 8", "4\n1 8 8 8", "2\n7 6"], "sample_outputs": ["4", "6", "0"], "notes": "NoteIn the first sample Limak has 5 votes. One of the ways to achieve victory is to bribe 4 citizens who want to vote for the third candidate. Then numbers of votes would be 9, 1, 7, 2, 8 (Limak would have 9 votes). Alternatively, Limak could steal only 3 votes from the third candidate and 1 vote from the second candidate to get situation 9, 0, 8, 2, 8.In the second sample Limak will steal 2 votes from each candidate. Situation will be 7, 6, 6, 6.In the third sample Limak is a winner without bribing any citizen."}, "src_uid": "aa8fabf7c817dfd3d585b96a07bb7f58"}
{"nl": {"description": "A and B are preparing themselves for programming contests.An important part of preparing for a competition is sharing programming knowledge from the experienced members to those who are just beginning to deal with the contests. Therefore, during the next team training A decided to make teams so that newbies are solving problems together with experienced participants.A believes that the optimal team of three people should consist of one experienced participant and two newbies. Thus, each experienced participant can share the experience with a large number of people.However, B believes that the optimal team should have two experienced members plus one newbie. Thus, each newbie can gain more knowledge and experience.As a result, A and B have decided that all the teams during the training session should belong to one of the two types described above. Furthermore, they agree that the total number of teams should be as much as possible.There are n experienced members and m newbies on the training session. Can you calculate what maximum number of teams can be formed?", "input_spec": "The first line contains two integers n and m (0 ≤ n, m ≤ 5·105) — the number of experienced participants and newbies that are present at the training session. ", "output_spec": "Print the maximum number of teams that can be formed.", "sample_inputs": ["2 6", "4 5"], "sample_outputs": ["2", "3"], "notes": "NoteLet's represent the experienced players as XP and newbies as NB.In the first test the teams look as follows: (XP, NB, NB), (XP, NB, NB).In the second test sample the teams look as follows: (XP, NB, NB), (XP, NB, NB), (XP, XP, NB)."}, "src_uid": "0718c6afe52cd232a5e942052527f31b"}
{"nl": {"description": "Given 2 integers $$$u$$$ and $$$v$$$, find the shortest array such that bitwise-xor of its elements is $$$u$$$, and the sum of its elements is $$$v$$$.", "input_spec": "The only line contains 2 integers $$$u$$$ and $$$v$$$ $$$(0 \\le u,v \\le 10^{18})$$$.", "output_spec": "If there's no array that satisfies the condition, print \"-1\". Otherwise: The first line should contain one integer, $$$n$$$, representing the length of the desired array. The next line should contain $$$n$$$ positive integers, the array itself. If there are multiple possible answers, print any.", "sample_inputs": ["2 4", "1 3", "8 5", "0 0"], "sample_outputs": ["2\n3 1", "3\n1 1 1", "-1", "0"], "notes": "NoteIn the first sample, $$$3\\oplus 1 = 2$$$ and $$$3 + 1 = 4$$$. There is no valid array of smaller length.Notice that in the fourth sample the array is empty."}, "src_uid": "490f23ced6c43f9e12f1bcbecbb14904"}
{"nl": {"description": "A new airplane SuperPuperJet has an infinite number of rows, numbered with positive integers starting with 1 from cockpit to tail. There are six seats in each row, denoted with letters from 'a' to 'f'. Seats 'a', 'b' and 'c' are located to the left of an aisle (if one looks in the direction of the cockpit), while seats 'd', 'e' and 'f' are located to the right. Seats 'a' and 'f' are located near the windows, while seats 'c' and 'd' are located near the aisle.    It's lunch time and two flight attendants have just started to serve food. They move from the first rows to the tail, always maintaining a distance of two rows from each other because of the food trolley. Thus, at the beginning the first attendant serves row 1 while the second attendant serves row 3. When both rows are done they move one row forward: the first attendant serves row 2 while the second attendant serves row 4. Then they move three rows forward and the first attendant serves row 5 while the second attendant serves row 7. Then they move one row forward again and so on.Flight attendants work with the same speed: it takes exactly 1 second to serve one passenger and 1 second to move one row forward. Each attendant first serves the passengers on the seats to the right of the aisle and then serves passengers on the seats to the left of the aisle (if one looks in the direction of the cockpit). Moreover, they always serve passengers in order from the window to the aisle. Thus, the first passenger to receive food in each row is located in seat 'f', and the last one — in seat 'c'. Assume that all seats are occupied.Vasya has seat s in row n and wants to know how many seconds will pass before he gets his lunch.", "input_spec": "The only line of input contains a description of Vasya's seat in the format ns, where n (1 ≤ n ≤ 1018) is the index of the row and s is the seat in this row, denoted as letter from 'a' to 'f'. The index of the row and the seat are not separated by a space.", "output_spec": "Print one integer — the number of seconds Vasya has to wait until he gets his lunch.", "sample_inputs": ["1f", "2d", "4a", "5e"], "sample_outputs": ["1", "10", "11", "18"], "notes": "NoteIn the first sample, the first flight attendant serves Vasya first, so Vasya gets his lunch after 1 second.In the second sample, the flight attendants will spend 6 seconds to serve everyone in the rows 1 and 3, then they will move one row forward in 1 second. As they first serve seats located to the right of the aisle in order from window to aisle, Vasya has to wait 3 more seconds. The total is 6 + 1 + 3 = 10."}, "src_uid": "069d0cb9b7c798a81007fb5b63fa0f45"}
{"nl": {"description": "Only T milliseconds left before the start of well-known online programming contest Codehorses Round 2017.Polycarp needs to download B++ compiler to take part in the contest. The size of the file is f bytes.Polycarp's internet tariff allows to download data at the rate of one byte per t0 milliseconds. This tariff is already prepaid, and its use does not incur any expense for Polycarp. In addition, the Internet service provider offers two additional packages:  download a1 bytes at the rate of one byte per t1 milliseconds, paying p1 burles for the package;  download a2 bytes at the rate of one byte per t2 milliseconds, paying p2 burles for the package. Polycarp can buy any package many times. When buying a package, its price (p1 or p2) is prepaid before usage. Once a package is bought it replaces the regular tariff until package data limit is completely used. After a package is consumed Polycarp can immediately buy a new package or switch to the regular tariff without loosing any time. While a package is in use Polycarp can't buy another package or switch back to the regular internet tariff.Find the minimum amount of money Polycarp has to spend to download an f bytes file no more than in T milliseconds.Note that because of technical reasons Polycarp can download only integer number of bytes using regular tariff and both packages. I.e. in each of three downloading modes the number of downloaded bytes will be integer. It means that Polycarp can't download a byte partially using the regular tariff or/and both packages.", "input_spec": "The first line contains three integer numbers f, T and t0 (1 ≤ f, T, t0 ≤ 107) — size of the file to download (in bytes), maximal time to download the file (in milliseconds) and number of milliseconds to download one byte using the regular internet tariff. The second line contains a description of the first additional package. The line contains three integer numbers a1, t1 and p1 (1 ≤ a1, t1, p1 ≤ 107), where a1 is maximal sizes of downloaded data (in bytes), t1 is time to download one byte (in milliseconds), p1 is price of the package (in burles). The third line contains a description of the second additional package. The line contains three integer numbers a2, t2 and p2 (1 ≤ a2, t2, p2 ≤ 107), where a2 is maximal sizes of downloaded data (in bytes), t2 is time to download one byte (in milliseconds), p2 is price of the package (in burles). Polycarp can buy any package many times. Once package is bought it replaces the regular tariff until package data limit is completely used. While a package is in use Polycarp can't buy another package or switch back to the regular internet tariff.", "output_spec": "Print the minimum amount of money that Polycarp needs to pay to download B++ compiler no more than in T milliseconds. If there is no solution, print the only integer -1.", "sample_inputs": ["120 964 20\n26 8 8\n13 10 4", "10 200 20\n1 1 1\n2 2 3", "8 81 11\n4 10 16\n3 10 12", "8 79 11\n4 10 16\n3 10 12"], "sample_outputs": ["40", "0", "28", "-1"], "notes": "NoteIn the first example Polycarp has to buy the first additional package 5 times and do not buy the second additional package. He downloads 120 bytes (of total 26·5 = 130 bytes) in 120·8 = 960 milliseconds (960 ≤ 964). He spends 8·5 = 40 burles on it.In the second example Polycarp has enough time to download 10 bytes. It takes 10·20 = 200 milliseconds which equals to upper constraint on download time.In the third example Polycarp has to buy one first additional package and one second additional package.In the fourth example Polycarp has no way to download the file on time."}, "src_uid": "f5f85e75af5b0f25f1f436a21e12fad1"}
{"nl": {"description": "Recently Anton found a box with digits in his room. There are k2 digits 2, k3 digits 3, k5 digits 5 and k6 digits 6.Anton's favorite integers are 32 and 256. He decided to compose this integers from digits he has. He wants to make the sum of these integers as large as possible. Help him solve this task!Each digit can be used no more than once, i.e. the composed integers should contain no more than k2 digits 2, k3 digits 3 and so on. Of course, unused digits are not counted in the sum.", "input_spec": "The only line of the input contains four integers k2, k3, k5 and k6 — the number of digits 2, 3, 5 and 6 respectively (0 ≤ k2, k3, k5, k6 ≤ 5·106).", "output_spec": "Print one integer — maximum possible sum of Anton's favorite integers that can be composed using digits from the box.", "sample_inputs": ["5 1 3 4", "1 1 1 1"], "sample_outputs": ["800", "256"], "notes": "NoteIn the first sample, there are five digits 2, one digit 3, three digits 5 and four digits 6. Anton can compose three integers 256 and one integer 32 to achieve the value 256 + 256 + 256 + 32 = 800. Note, that there is one unused integer 2 and one unused integer 6. They are not counted in the answer.In the second sample, the optimal answer is to create on integer 256, thus the answer is 256."}, "src_uid": "082b31cc156a7ba1e0a982f07ecc207e"}
{"nl": {"description": "The city park of IT City contains n east to west paths and n north to south paths. Each east to west path crosses each north to south path, so there are n2 intersections.The city funded purchase of five benches. To make it seems that there are many benches it was decided to place them on as many paths as possible. Obviously this requirement is satisfied by the following scheme: each bench is placed on a cross of paths and each path contains not more than one bench.Help the park administration count the number of ways to place the benches.", "input_spec": "The only line of the input contains one integer n (5 ≤ n ≤ 100) — the number of east to west paths and north to south paths.", "output_spec": "Output one integer — the number of ways to place the benches.", "sample_inputs": ["5"], "sample_outputs": ["120"], "notes": null}, "src_uid": "92db14325cd8aee06b502c12d2e3dd81"}
{"nl": {"description": "You are given an alphabet consisting of n letters, your task is to make a string of the maximum possible length so that the following conditions are satisfied:   the i-th letter occurs in the string no more than ai times;  the number of occurrences of each letter in the string must be distinct for all the letters that occurred in the string at least once. ", "input_spec": "The first line of the input contains a single integer n (2  ≤  n  ≤  26) — the number of letters in the alphabet. The next line contains n integers ai (1 ≤ ai ≤ 109) — i-th of these integers gives the limitation on the number of occurrences of the i-th character in the string.", "output_spec": "Print a single integer — the maximum length of the string that meets all the requirements.", "sample_inputs": ["3\n2 5 5", "3\n1 1 2"], "sample_outputs": ["11", "3"], "notes": "NoteFor convenience let's consider an alphabet consisting of three letters: \"a\", \"b\", \"c\". In the first sample, some of the optimal strings are: \"cccaabbccbb\", \"aabcbcbcbcb\". In the second sample some of the optimal strings are: \"acc\", \"cbc\"."}, "src_uid": "3c4b2d1c9440515bc3002eddd2b89f6f"}
{"nl": {"description": "A flea is sitting at one of the n hassocks, arranged in a circle, at the moment. After minute number k the flea jumps through k - 1 hassoсks (clockwise). For example, after the first minute the flea jumps to the neighboring hassock. You should answer: will the flea visit all the hassocks or not. We assume that flea has infinitely much time for this jumping.", "input_spec": "The only line contains single integer: 1 ≤ n ≤ 1000 — number of hassocks.", "output_spec": "Output \"YES\" if all the hassocks will be visited and \"NO\" otherwise.", "sample_inputs": ["1", "3"], "sample_outputs": ["YES", "NO"], "notes": null}, "src_uid": "4bd174a997707ed3a368bd0f2424590f"}
{"nl": {"description": "Pasha has a positive integer a without leading zeroes. Today he decided that the number is too small and he should make it larger. Unfortunately, the only operation Pasha can do is to swap two adjacent decimal digits of the integer.Help Pasha count the maximum number he can get if he has the time to make at most k swaps.", "input_spec": "The single line contains two integers a and k (1 ≤ a ≤ 1018; 0 ≤ k ≤ 100).", "output_spec": "Print the maximum number that Pasha can get if he makes at most k swaps.", "sample_inputs": ["1990 1", "300 0", "1034 2", "9090000078001234 6"], "sample_outputs": ["9190", "300", "3104", "9907000008001234"], "notes": null}, "src_uid": "e56f6c343167745821f0b18dcf0d0cde"}
{"nl": {"description": "Given the number n, find the smallest positive integer which has exactly n divisors. It is guaranteed that for the given n the answer will not exceed 1018.", "input_spec": "The first line of the input contains integer n (1 ≤ n ≤ 1000).", "output_spec": "Output the smallest positive integer with exactly n divisors.", "sample_inputs": ["4", "6"], "sample_outputs": ["6", "12"], "notes": null}, "src_uid": "62db589bad3b7023418107de05b7a8ee"}
{"nl": {"description": "The king Copa often has been reported about the Codeforces site, which is rapidly getting more and more popular among the brightest minds of the humanity, who are using it for training and competing. Recently Copa understood that to conquer the world he needs to organize the world Codeforces tournament. He hopes that after it the brightest minds will become his subordinates, and the toughest part of conquering the world will be completed.The final round of the Codeforces World Finals 20YY is scheduled for DD.MM.YY, where DD is the day of the round, MM is the month and YY are the last two digits of the year. Bob is lucky to be the first finalist form Berland. But there is one problem: according to the rules of the competition, all participants must be at least 18 years old at the moment of the finals. Bob was born on BD.BM.BY. This date is recorded in his passport, the copy of which he has already mailed to the organizers. But Bob learned that in different countries the way, in which the dates are written, differs. For example, in the US the month is written first, then the day and finally the year. Bob wonders if it is possible to rearrange the numbers in his date of birth so that he will be at least 18 years old on the day DD.MM.YY. He can always tell that in his motherland dates are written differently. Help him.According to another strange rule, eligible participant must be born in the same century as the date of the finals. If the day of the finals is participant's 18-th birthday, he is allowed to participate. As we are considering only the years from 2001 to 2099 for the year of the finals, use the following rule: the year is leap if it's number is divisible by four.", "input_spec": "The first line contains the date DD.MM.YY, the second line contains the date BD.BM.BY. It is guaranteed that both dates are correct, and YY and BY are always in [01;99]. It could be that by passport Bob was born after the finals. In this case, he can still change the order of numbers in date.", "output_spec": "If it is possible to rearrange the numbers in the date of birth so that Bob will be at least 18 years old on the DD.MM.YY, output YES. In the other case, output NO.  Each number contains exactly two digits and stands for day, month or year in a date. Note that it is permitted to rearrange only numbers, not digits.", "sample_inputs": ["01.01.98\n01.01.80", "20.10.20\n10.02.30", "28.02.74\n28.02.64"], "sample_outputs": ["YES", "NO", "NO"], "notes": null}, "src_uid": "5418c98fe362909f7b28f95225837d33"}
{"nl": {"description": "Imagine you have an infinite 2D plane with Cartesian coordinate system. Some of the integral points are blocked, and others are not. Two integral points A and B on the plane are 4-connected if and only if:  the Euclidean distance between A and B is one unit and neither A nor B is blocked;  or there is some integral point C, such that A is 4-connected with C, and C is 4-connected with B. Let's assume that the plane doesn't contain blocked points. Consider all the integral points of the plane whose Euclidean distance from the origin is no more than n, we'll name these points special. Chubby Yang wants to get the following property: no special point is 4-connected to some non-special point. To get the property she can pick some integral points of the plane and make them blocked. What is the minimum number of points she needs to pick?", "input_spec": "The first line contains an integer n (0 ≤ n ≤ 4·107).", "output_spec": "Print a single integer — the minimum number of points that should be blocked.", "sample_inputs": ["1", "2", "3"], "sample_outputs": ["4", "8", "16"], "notes": null}, "src_uid": "d87ce09acb8401e910ca6ef3529566f4"}
{"nl": {"description": "On the way to Rio de Janeiro Ostap kills time playing with a grasshopper he took with him in a special box. Ostap builds a line of length n such that some cells of this line are empty and some contain obstacles. Then, he places his grasshopper to one of the empty cells and a small insect in another empty cell. The grasshopper wants to eat the insect.Ostap knows that grasshopper is able to jump to any empty cell that is exactly k cells away from the current (to the left or to the right). Note that it doesn't matter whether intermediate cells are empty or not as the grasshopper makes a jump over them. For example, if k = 1 the grasshopper can jump to a neighboring cell only, and if k = 2 the grasshopper can jump over a single cell.Your goal is to determine whether there is a sequence of jumps such that grasshopper will get from his initial position to the cell with an insect.", "input_spec": "The first line of the input contains two integers n and k (2 ≤ n ≤ 100, 1 ≤ k ≤ n - 1) — the number of cells in the line and the length of one grasshopper's jump. The second line contains a string of length n consisting of characters '.', '#', 'G' and 'T'. Character '.' means that the corresponding cell is empty, character '#' means that the corresponding cell contains an obstacle and grasshopper can't jump there. Character 'G' means that the grasshopper starts at this position and, finally, 'T' means that the target insect is located at this cell. It's guaranteed that characters 'G' and 'T' appear in this line exactly once.", "output_spec": "If there exists a sequence of jumps (each jump of length k), such that the grasshopper can get from his initial position to the cell with the insect, print \"YES\" (without quotes) in the only line of the input. Otherwise, print \"NO\" (without quotes).", "sample_inputs": ["5 2\n#G#T#", "6 1\nT....G", "7 3\nT..#..G", "6 2\n..GT.."], "sample_outputs": ["YES", "YES", "NO", "NO"], "notes": "NoteIn the first sample, the grasshopper can make one jump to the right in order to get from cell 2 to cell 4.In the second sample, the grasshopper is only able to jump to neighboring cells but the way to the insect is free — he can get there by jumping left 5 times.In the third sample, the grasshopper can't make a single jump.In the fourth sample, the grasshopper can only jump to the cells with odd indices, thus he won't be able to reach the insect."}, "src_uid": "189a9b5ce669bdb04b9d371d74a5dd41"}
{"nl": {"description": "User ainta is making a web site. This time he is going to make a navigation of the pages. In his site, there are n pages numbered by integers from 1 to n. Assume that somebody is on the p-th page now. The navigation will look like this: << p - k p - k + 1 ... p - 1 (p) p + 1 ... p + k - 1 p + k >> When someone clicks the button \"<<\" he is redirected to page 1, and when someone clicks the button \">>\" he is redirected to page n. Of course if someone clicks on a number, he is redirected to the corresponding page.There are some conditions in the navigation:  If page 1 is in the navigation, the button \"<<\" must not be printed.  If page n is in the navigation, the button \">>\" must not be printed.  If the page number is smaller than 1 or greater than n, it must not be printed.   You can see some examples of the navigations. Make a program that prints the navigation.", "input_spec": "The first and the only line contains three integers n, p, k (3 ≤ n ≤ 100; 1 ≤ p ≤ n; 1 ≤ k ≤ n)", "output_spec": "Print the proper navigation. Follow the format of the output from the test samples.", "sample_inputs": ["17 5 2", "6 5 2", "6 1 2", "6 2 2", "9 6 3", "10 6 3", "8 5 4"], "sample_outputs": ["<< 3 4 (5) 6 7 >>", "<< 3 4 (5) 6", "(1) 2 3 >>", "1 (2) 3 4 >>", "<< 3 4 5 (6) 7 8 9", "<< 3 4 5 (6) 7 8 9 >>", "1 2 3 4 (5) 6 7 8"], "notes": null}, "src_uid": "526e2cce272e42a3220e33149b1c9c84"}
{"nl": {"description": "We'll define S(n) for positive integer n as follows: the number of the n's digits in the decimal base. For example, S(893) = 3, S(114514) = 6.You want to make a consecutive integer sequence starting from number m (m, m + 1, ...). But you need to pay S(n)·k to add the number n to the sequence.You can spend a cost up to w, and you want to make the sequence as long as possible. Write a program that tells sequence's maximum length.", "input_spec": "The first line contains three integers w (1 ≤ w ≤ 1016), m (1 ≤ m ≤ 1016), k (1 ≤ k ≤ 109). Please, do not write the %lld specifier to read or write 64-bit integers in C++. It is preferred to use the cin, cout streams or the %I64d specifier.", "output_spec": "The first line should contain a single integer — the answer to the problem.", "sample_inputs": ["9 1 1", "77 7 7", "114 5 14", "1 1 2"], "sample_outputs": ["9", "7", "6", "0"], "notes": null}, "src_uid": "8ef8a09e33d38a2d7f023316bc38b6ea"}
{"nl": {"description": "Petya loves football very much. One day, as he was watching a football match, he was writing the players' current positions on a piece of paper. To simplify the situation he depicted it as a string consisting of zeroes and ones. A zero corresponds to players of one team; a one corresponds to players of another team. If there are at least 7 players of some team standing one after another, then the situation is considered dangerous. For example, the situation 00100110111111101 is dangerous and 11110111011101 is not. You are given the current situation. Determine whether it is dangerous or not.", "input_spec": "The first input line contains a non-empty string consisting of characters \"0\" and \"1\", which represents players. The length of the string does not exceed 100 characters. There's at least one player from each team present on the field.", "output_spec": "Print \"YES\" if the situation is dangerous. Otherwise, print \"NO\".", "sample_inputs": ["001001", "1000000001"], "sample_outputs": ["NO", "YES"], "notes": null}, "src_uid": "ed9a763362abc6ed40356731f1036b38"}
{"nl": {"description": "Each evening after the dinner the SIS's students gather together to play the game of Sport Mafia. For the tournament, Alya puts candies into the box, which will serve as a prize for a winner. To do that, she performs $$$n$$$ actions. The first action performed is to put a single candy into the box. For each of the remaining moves she can choose from two options:  the first option, in case the box contains at least one candy, is to take exactly one candy out and eat it. This way the number of candies in the box decreased by $$$1$$$;  the second option is to put candies in the box. In this case, Alya will put $$$1$$$ more candy, than she put in the previous time. Thus, if the box is empty, then it can only use the second option.For example, one possible sequence of Alya's actions look as follows:  put one candy into the box;  put two candies into the box;  eat one candy from the box;  eat one candy from the box;  put three candies into the box;  eat one candy from the box;  put four candies into the box;  eat one candy from the box;  put five candies into the box; This way she will perform $$$9$$$ actions, the number of candies at the end will be $$$11$$$, while Alya will eat $$$4$$$ candies in total.You know the total number of actions $$$n$$$ and the number of candies at the end $$$k$$$. You need to find the total number of sweets Alya ate. That is the number of moves of the first option. It's guaranteed, that for the given $$$n$$$ and $$$k$$$ the answer always exists.Please note, that during an action of the first option, Alya takes out and eats exactly one candy.", "input_spec": "The first line contains two integers $$$n$$$ and $$$k$$$ ($$$1 \\le n \\le 10^9$$$; $$$0 \\le k \\le 10^9$$$) — the total number of moves and the number of candies in the box at the end.  It's guaranteed, that for the given $$$n$$$ and $$$k$$$ the answer exists.", "output_spec": "Print a single integer — the number of candies, which Alya ate. Please note, that in this problem there aren't multiple possible answers — the answer is unique for any input data. ", "sample_inputs": ["1 1", "9 11", "5 0", "3 2"], "sample_outputs": ["0", "4", "3", "1"], "notes": "NoteIn the first example, Alya has made one move only. According to the statement, the first move is always putting one candy in the box. Hence Alya ate $$$0$$$ candies.In the second example the possible sequence of Alya's actions looks as follows:   put $$$1$$$ candy,  put $$$2$$$ candies,  eat a candy,  eat a candy,  put $$$3$$$ candies,  eat a candy,  put $$$4$$$ candies,  eat a candy,  put $$$5$$$ candies.  This way, she will make exactly $$$n=9$$$ actions and in the end the box will contain $$$1+2-1-1+3-1+4-1+5=11$$$ candies. The answer is $$$4$$$, since she ate $$$4$$$ candies in total."}, "src_uid": "17b5ec1c6263ef63c668c2b903db1d77"}
{"nl": {"description": "The Little Elephant loves chess very much. One day the Little Elephant and his friend decided to play chess. They've got the chess pieces but the board is a problem. They've got an 8 × 8 checkered board, each square is painted either black or white. The Little Elephant and his friend know that a proper chessboard doesn't have any side-adjacent cells with the same color and the upper left cell is white. To play chess, they want to make the board they have a proper chessboard. For that the friends can choose any row of the board and cyclically shift the cells of the chosen row, that is, put the last (rightmost) square on the first place in the row and shift the others one position to the right. You can run the described operation multiple times (or not run it at all).For example, if the first line of the board looks like that \"BBBBBBWW\" (the white cells of the line are marked with character \"W\", the black cells are marked with character \"B\"), then after one cyclic shift it will look like that \"WBBBBBBW\".Help the Little Elephant and his friend to find out whether they can use any number of the described operations to turn the board they have into a proper chessboard.", "input_spec": "The input consists of exactly eight lines. Each line contains exactly eight characters \"W\" or \"B\" without any spaces: the j-th character in the i-th line stands for the color of the j-th cell of the i-th row of the elephants' board. Character \"W\" stands for the white color, character \"B\" stands for the black color. Consider the rows of the board numbered from 1 to 8 from top to bottom, and the columns — from 1 to 8 from left to right. The given board can initially be a proper chessboard.", "output_spec": "In a single line print \"YES\" (without the quotes), if we can make the board a proper chessboard and \"NO\" (without the quotes) otherwise.", "sample_inputs": ["WBWBWBWB\nBWBWBWBW\nBWBWBWBW\nBWBWBWBW\nWBWBWBWB\nWBWBWBWB\nBWBWBWBW\nWBWBWBWB", "WBWBWBWB\nWBWBWBWB\nBBWBWWWB\nBWBWBWBW\nBWBWBWBW\nBWBWBWWW\nBWBWBWBW\nBWBWBWBW"], "sample_outputs": ["YES", "NO"], "notes": "NoteIn the first sample you should shift the following lines one position to the right: the 3-rd, the 6-th, the 7-th and the 8-th.In the second sample there is no way you can achieve the goal."}, "src_uid": "ca65e023be092b2ce25599f52acc1a67"}
{"nl": {"description": "This problem consists of two subproblems: for solving subproblem E1 you will receive 11 points, and for solving subproblem E2 you will receive 13 points.A tree is an undirected connected graph containing no cycles. The distance between two nodes in an unweighted tree is the minimum number of edges that have to be traversed to get from one node to another.You are given 3 trees that have to be united into a single tree by adding two edges between these trees. Each of these edges can connect any pair of nodes from two trees. After the trees are connected, the distances between all unordered pairs of nodes in the united tree should be computed. What is the maximum possible value of the sum of these distances?", "input_spec": "The first line contains three space-separated integers n1, n2, n3 — the number of vertices in the first, second, and third trees, respectively. The following n1 - 1 lines describe the first tree. Each of these lines describes an edge in the first tree and contains a pair of integers separated by a single space — the numeric labels of vertices connected by the edge. The following n2 - 1 lines describe the second tree in the same fashion, and the n3 - 1 lines after that similarly describe the third tree. The vertices in each tree are numbered with consecutive integers starting with 1. The problem consists of two subproblems. The subproblems have different constraints on the input. You will get some score for the correct submission of the subproblem. The description of the subproblems follows.   In subproblem E1 (11 points), the number of vertices in each tree will be between 1 and 1000, inclusive.  In subproblem E2 (13 points), the number of vertices in each tree will be between 1 and 100000, inclusive. ", "output_spec": "Print a single integer number — the maximum possible sum of distances between all pairs of nodes in the united tree.", "sample_inputs": ["2 2 3\n1 2\n1 2\n1 2\n2 3", "5 1 4\n1 2\n2 5\n3 4\n4 2\n1 2\n1 3\n1 4"], "sample_outputs": ["56", "151"], "notes": "NoteConsider the first test case. There are two trees composed of two nodes, and one tree with three nodes. The maximum possible answer is obtained if the trees are connected in a single chain of 7 vertices.In the second test case, a possible choice of new edges to obtain the maximum answer is the following:   Connect node 3 from the first tree to node 1 from the second tree;  Connect node 2 from the third tree to node 1 from the second tree. "}, "src_uid": "2f299b0083b89d8b8ec8b26b65d201f2"}
{"nl": {"description": "Vasya plays The Elder Trolls IV: Oblivon. Oh, those creators of computer games! What they do not come up with! Absolutely unique monsters have been added to the The Elder Trolls IV: Oblivon. One of these monsters is Unkillable Slug. Why it is \"Unkillable\"? Firstly, because it can be killed with cutting weapon only, so lovers of two-handed amber hammers should find suitable knife themselves. Secondly, it is necessary to make so many cutting strokes to Unkillable Slug. Extremely many. Too many! Vasya has already promoted his character to 80-th level and in order to gain level 81 he was asked to kill Unkillable Slug. The monster has a very interesting shape. It looks like a rectangular parallelepiped with size x × y × z, consisting of undestructable cells 1 × 1 × 1. At one stroke Vasya can cut the Slug along an imaginary grid, i.e. cut with a plane parallel to one of the parallelepiped side. Monster dies when amount of parts it is divided reaches some critical value.All parts of monster do not fall after each cut, they remains exactly on its places. I. e. Vasya can cut several parts with one cut.Vasya wants to know what the maximum number of pieces he can cut the Unkillable Slug into striking him at most k times.Vasya's character uses absolutely thin sword with infinite length.", "input_spec": "The first line of input contains four integer numbers x, y, z, k (1 ≤ x, y, z ≤ 106, 0 ≤ k ≤ 109).", "output_spec": "Output the only number — the answer for the problem. Please, do not use %lld specificator to read or write 64-bit integers in C++. It is preffered to use cout (also you may use %I64d).", "sample_inputs": ["2 2 2 3", "2 2 2 1"], "sample_outputs": ["8", "2"], "notes": "NoteIn the first sample Vasya make 3 pairwise perpendicular cuts. He cuts monster on two parts with the first cut, then he divides each part on two with the second cut, and finally he divides each of the 4 parts on two."}, "src_uid": "8787c5d46d7247d93d806264a8957639"}
{"nl": {"description": "A triangular number is the number of dots in an equilateral triangle uniformly filled with dots. For example, three dots can be arranged in a triangle; thus three is a triangular number. The n-th triangular number is the number of dots in a triangle with n dots on a side. . You can learn more about these numbers from Wikipedia (http://en.wikipedia.org/wiki/Triangular_number).Your task is to find out if a given integer is a triangular number.", "input_spec": "The first line contains the single number n (1 ≤ n ≤ 500) — the given integer.", "output_spec": "If the given integer is a triangular number output YES, otherwise output NO.", "sample_inputs": ["1", "2", "3"], "sample_outputs": ["YES", "NO", "YES"], "notes": null}, "src_uid": "587d4775dbd6a41fc9e4b81f71da7301"}
{"nl": {"description": "One industrial factory is reforming working plan. The director suggested to set a mythical detail production norm. If at the beginning of the day there were x details in the factory storage, then by the end of the day the factory has to produce  (remainder after dividing x by m) more details. Unfortunately, no customer has ever bought any mythical detail, so all the details produced stay on the factory. The board of directors are worried that the production by the given plan may eventually stop (that means that there will be а moment when the current number of details on the factory is divisible by m). Given the number of details a on the first day and number m check if the production stops at some moment.", "input_spec": "The first line contains two integers a and m (1 ≤ a, m ≤ 105).", "output_spec": "Print \"Yes\" (without quotes) if the production will eventually stop, otherwise print \"No\".", "sample_inputs": ["1 5", "3 6"], "sample_outputs": ["No", "Yes"], "notes": null}, "src_uid": "f726133018e2149ec57e113860ec498a"}
{"nl": {"description": "Sheldon, Leonard, Penny, Rajesh and Howard are in the queue for a \"Double Cola\" drink vending machine; there are no other people in the queue. The first one in the queue (Sheldon) buys a can, drinks it and doubles! The resulting two Sheldons go to the end of the queue. Then the next in the queue (Leonard) buys a can, drinks it and gets to the end of the queue as two Leonards, and so on. This process continues ad infinitum.For example, Penny drinks the third can of cola and the queue will look like this: Rajesh, Howard, Sheldon, Sheldon, Leonard, Leonard, Penny, Penny.Write a program that will print the name of a man who will drink the n-th can.Note that in the very beginning the queue looks like that: Sheldon, Leonard, Penny, Rajesh, Howard. The first person is Sheldon.", "input_spec": "The input data consist of a single integer n (1 ≤ n ≤ 109). It is guaranteed that the pretests check the spelling of all the five names, that is, that they contain all the five possible answers.", "output_spec": "Print the single line — the name of the person who drinks the n-th can of cola. The cans are numbered starting from 1. Please note that you should spell the names like this: \"Sheldon\", \"Leonard\", \"Penny\", \"Rajesh\", \"Howard\" (without the quotes). In that order precisely the friends are in the queue initially.", "sample_inputs": ["1", "6", "1802"], "sample_outputs": ["Sheldon", "Sheldon", "Penny"], "notes": null}, "src_uid": "023b169765e81d896cdc1184e5a82b22"}
{"nl": {"description": "Having learned (not without some help from the Codeforces participants) to play the card game from the previous round optimally, Shrek and Donkey (as you may remember, they too live now in the Kingdom of Far Far Away) have decided to quit the boring card games and play with toy soldiers.The rules of the game are as follows: there is a battlefield, its size equals n × m squares, some squares contain the toy soldiers (the green ones belong to Shrek and the red ones belong to Donkey). Besides, each of the n lines of the area contains not more than two soldiers. During a move a players should select not less than 1 and not more than k soldiers belonging to him and make them either attack or retreat.An attack is moving all of the selected soldiers along the lines on which they stand in the direction of an enemy soldier, if he is in this line. If this line doesn't have an enemy soldier, then the selected soldier on this line can move in any direction during the player's move. Each selected soldier has to move at least by one cell. Different soldiers can move by a different number of cells. During the attack the soldiers are not allowed to cross the cells where other soldiers stand (or stood immediately before the attack). It is also not allowed to go beyond the battlefield or finish the attack in the cells, where other soldiers stand (or stood immediately before attack).A retreat is moving all of the selected soldiers along the lines on which they stand in the direction from an enemy soldier, if he is in this line. The other rules repeat the rules of the attack.For example, let's suppose that the original battlefield had the form (here symbols \"G\" mark Shrek's green soldiers and symbols \"R\" mark Donkey's red ones):  -G-R--R-G-  Let's suppose that k = 2 and Shrek moves first. If he decides to attack, then after his move the battlefield can look like that:  --GR-     --GR-     -G-R--RG--     -R-G-     -RG--  If in the previous example Shrek decides to retreat, then after his move the battlefield can look like that:  G--R-     G--R-     -G-R--R--G     -R-G-     -R--G  On the other hand, the followings fields cannot result from Shrek's correct move:  G--R-     ---RG     --GR--RG--     -R-G-     GR---  Shrek starts the game. To make a move means to attack or to retreat by the rules. A player who cannot make a move loses and his opponent is the winner. Determine the winner of the given toy soldier game if Shrek and Donkey continue to be under the yellow pills from the last rounds' problem. Thus, they always play optimally (that is, they try to win if it is possible, or finish the game in a draw, by ensuring that it lasts forever, if they cannot win).", "input_spec": "The first line contains space-separated integers n, m and k (1 ≤ n, m, k ≤ 100). Then n lines contain m characters each. These characters belong to the set {\"-\", \"G\", \"R\"}, denoting, respectively, a battlefield's free cell, a cell occupied by Shrek's soldiers and a cell occupied by Donkey's soldiers. It is guaranteed that each line contains no more than two soldiers.", "output_spec": "Print \"First\" (without the quotes) if Shrek wins in the given Toy Soldier game. If Donkey wins, print \"Second\" (without the quotes). If the game continues forever, print \"Draw\" (also without the quotes).", "sample_inputs": ["2 3 1\nR-G\nRG-", "3 3 2\nG-R\nR-G\nG-R", "2 3 1\n-R-\n-G-", "2 5 2\n-G-R-\n-R-G-"], "sample_outputs": ["First", "Second", "Draw", "First"], "notes": null}, "src_uid": "69062f7c9b834e925ab23ebc2da96b52"}
{"nl": {"description": "You have two friends. You want to present each of them several positive integers. You want to present cnt1 numbers to the first friend and cnt2 numbers to the second friend. Moreover, you want all presented numbers to be distinct, that also means that no number should be presented to both friends.In addition, the first friend does not like the numbers that are divisible without remainder by prime number x. The second one does not like the numbers that are divisible without remainder by prime number y. Of course, you're not going to present your friends numbers they don't like.Your task is to find such minimum number v, that you can form presents using numbers from a set 1, 2, ..., v. Of course you may choose not to present some numbers at all.A positive integer number greater than 1 is called prime if it has no positive divisors other than 1 and itself.", "input_spec": "The only line contains four positive integers cnt1, cnt2, x, y (1 ≤ cnt1, cnt2 < 109; cnt1 + cnt2 ≤ 109; 2 ≤ x < y ≤ 3·104) — the numbers that are described in the statement. It is guaranteed that numbers x, y are prime.", "output_spec": "Print a single integer — the answer to the problem.", "sample_inputs": ["3 1 2 3", "1 3 2 3"], "sample_outputs": ["5", "4"], "notes": "NoteIn the first sample you give the set of numbers {1, 3, 5} to the first friend and the set of numbers {2} to the second friend. Note that if you give set {1, 3, 5} to the first friend, then we cannot give any of the numbers 1, 3, 5 to the second friend. In the second sample you give the set of numbers {3} to the first friend, and the set of numbers {1, 2, 4} to the second friend. Thus, the answer to the problem is 4."}, "src_uid": "ff3c39b759a049580a6e96c66c904fdc"}
{"nl": {"description": "There are $$$n$$$ heroes fighting in the arena. Initially, the $$$i$$$-th hero has $$$a_i$$$ health points.The fight in the arena takes place in several rounds. At the beginning of each round, each alive hero deals $$$1$$$ damage to all other heroes. Hits of all heroes occur simultaneously. Heroes whose health is less than $$$1$$$ at the end of the round are considered killed.If exactly $$$1$$$ hero remains alive after a certain round, then he is declared the winner. Otherwise, there is no winner.Your task is to calculate the number of ways to choose the initial health points for each hero $$$a_i$$$, where $$$1 \\le a_i \\le x$$$, so that there is no winner of the fight. The number of ways can be very large, so print it modulo $$$998244353$$$. Two ways are considered different if at least one hero has a different amount of health. For example, $$$[1, 2, 1]$$$ and $$$[2, 1, 1]$$$ are different.", "input_spec": "The only line contains two integers $$$n$$$ and $$$x$$$ ($$$2 \\le n \\le 500; 1 \\le x \\le 500$$$).", "output_spec": "Print one integer — the number of ways to choose the initial health points for each hero $$$a_i$$$, where $$$1 \\le a_i \\le x$$$, so that there is no winner of the fight, taken modulo $$$998244353$$$. ", "sample_inputs": ["2 5", "3 3", "5 4", "13 37"], "sample_outputs": ["5", "15", "1024", "976890680"], "notes": null}, "src_uid": "1908d1c8c6b122a4c6633a7af094f17f"}
{"nl": {"description": "Bad news came to Mike's village, some thieves stole a bunch of chocolates from the local factory! Horrible! Aside from loving sweet things, thieves from this area are known to be very greedy. So after a thief takes his number of chocolates for himself, the next thief will take exactly k times more than the previous one. The value of k (k > 1) is a secret integer known only to them. It is also known that each thief's bag can carry at most n chocolates (if they intend to take more, the deal is cancelled) and that there were exactly four thieves involved. Sadly, only the thieves know the value of n, but rumours say that the numbers of ways they could have taken the chocolates (for a fixed n, but not fixed k) is m. Two ways are considered different if one of the thieves (they should be numbered in the order they take chocolates) took different number of chocolates in them.Mike want to track the thieves down, so he wants to know what their bags are and value of n will help him in that. Please find the smallest possible value of n or tell him that the rumors are false and there is no such n.", "input_spec": "The single line of input contains the integer m (1 ≤ m ≤ 1015) — the number of ways the thieves might steal the chocolates, as rumours say.", "output_spec": "Print the only integer n — the maximum amount of chocolates that thieves' bags can carry. If there are more than one n satisfying the rumors, print the smallest one. If there is no such n for a false-rumoured m, print  - 1.", "sample_inputs": ["1", "8", "10"], "sample_outputs": ["8", "54", "-1"], "notes": "NoteIn the first sample case the smallest n that leads to exactly one way of stealing chocolates is n = 8, whereas the amounts of stealed chocolates are (1, 2, 4, 8) (the number of chocolates stolen by each of the thieves).In the second sample case the smallest n that leads to exactly 8 ways is n = 54 with the possibilities: (1, 2, 4, 8),  (1, 3, 9, 27),  (2, 4, 8, 16),  (2, 6, 18, 54),  (3, 6, 12, 24),  (4, 8, 16, 32),  (5, 10, 20, 40),  (6, 12, 24, 48).There is no n leading to exactly 10 ways of stealing chocolates in the third sample case."}, "src_uid": "602deaad5c66e264997249457d555129"}
{"nl": {"description": "In some game by Playrix it takes t minutes for an oven to bake k carrot cakes, all cakes are ready at the same moment t minutes after they started baking. Arkady needs at least n cakes to complete a task, but he currently don't have any. However, he has infinitely many ingredients and one oven. Moreover, Arkady can build one more similar oven to make the process faster, it would take d minutes to build the oven. While the new oven is being built, only old one can bake cakes, after the new oven is built, both ovens bake simultaneously. Arkady can't build more than one oven.Determine if it is reasonable to build the second oven, i.e. will it decrease the minimum time needed to get n cakes or not. If the time needed with the second oven is the same as with one oven, then it is unreasonable.", "input_spec": "The only line contains four integers n, t, k, d (1 ≤ n, t, k, d ≤ 1 000) — the number of cakes needed, the time needed for one oven to bake k cakes, the number of cakes baked at the same time, the time needed to build the second oven. ", "output_spec": "If it is reasonable to build the second oven, print \"YES\". Otherwise print \"NO\".", "sample_inputs": ["8 6 4 5", "8 6 4 6", "10 3 11 4", "4 2 1 4"], "sample_outputs": ["YES", "NO", "NO", "YES"], "notes": "NoteIn the first example it is possible to get 8 cakes in 12 minutes using one oven. The second oven can be built in 5 minutes, so after 6 minutes the first oven bakes 4 cakes, the second oven bakes 4 more ovens after 11 minutes. Thus, it is reasonable to build the second oven. In the second example it doesn't matter whether we build the second oven or not, thus it takes 12 minutes to bake 8 cakes in both cases. Thus, it is unreasonable to build the second oven.In the third example the first oven bakes 11 cakes in 3 minutes, that is more than needed 10. It is unreasonable to build the second oven, because its building takes more time that baking the needed number of cakes using the only oven."}, "src_uid": "32c866d3d394e269724b4930df5e4407"}
{"nl": {"description": "It seems like the year of 2013 came only yesterday. Do you know a curious fact? The year of 2013 is the first year after the old 1987 with only distinct digits.Now you are suggested to solve the following problem: given a year number, find the minimum year number which is strictly larger than the given one and has only distinct digits.", "input_spec": "The single line contains integer y (1000 ≤ y ≤ 9000) — the year number.", "output_spec": "Print a single integer — the minimum year number that is strictly larger than y and all it's digits are distinct. It is guaranteed that the answer exists.", "sample_inputs": ["1987", "2013"], "sample_outputs": ["2013", "2014"], "notes": null}, "src_uid": "d62dabfbec52675b7ed7b582ad133acd"}
{"nl": {"description": "Shrek and the Donkey (as you can guess, they also live in the far away kingdom) decided to play a card game called YAGame. The rules are very simple: initially Shrek holds m cards and the Donkey holds n cards (the players do not see each other's cards), and one more card lies on the table face down so that both players cannot see it as well. Thus, at the beginning of the game there are overall m + n + 1 cards. Besides, the players know which cards the pack of cards consists of and their own cards (but they do not know which card lies on the table and which ones the other player has). The players move in turn and Shrek starts. During a move a player can: Try to guess which card is lying on the table. If he guesses correctly, the game ends and he wins. If his guess is wrong, the game also ends but this time the other player wins. Name any card from the pack. If the other player has such card, he must show it and put it aside (so that this card is no longer used in the game). If the other player doesn't have such card, he says about that. Recently Donkey started taking some yellow pills and winning over Shrek. Now Shrek wants to evaluate his chances to win if he too starts taking the pills.Help Shrek assuming the pills are good in quality and that both players using them start playing in the optimal manner.", "input_spec": "The first line contains space-separated integers m and n (0 ≤ m, n ≤ 1000).", "output_spec": "Print space-separated probabilities that Shrek wins and Donkey wins correspondingly; the absolute error should not exceed 10 - 9.", "sample_inputs": ["0 3", "1 0", "1 1"], "sample_outputs": ["0.25 0.75", "1 0", "0.5 0.5"], "notes": null}, "src_uid": "f51586ab88399c04ffb7eaa658d294dd"}
{"nl": {"description": "One day Vasya the Hipster decided to count how many socks he had. It turned out that he had a red socks and b blue socks.According to the latest fashion, hipsters should wear the socks of different colors: a red one on the left foot, a blue one on the right foot.Every day Vasya puts on new socks in the morning and throws them away before going to bed as he doesn't want to wash them.Vasya wonders, what is the maximum number of days when he can dress fashionable and wear different socks, and after that, for how many days he can then wear the same socks until he either runs out of socks or cannot make a single pair from the socks he's got.Can you help him?", "input_spec": "The single line of the input contains two positive integers a and b (1 ≤ a, b ≤ 100) — the number of red and blue socks that Vasya's got.", "output_spec": "Print two space-separated integers — the maximum number of days when Vasya can wear different socks and the number of days when he can wear the same socks until he either runs out of socks or cannot make a single pair from the socks he's got. Keep in mind that at the end of the day Vasya throws away the socks that he's been wearing on that day.", "sample_inputs": ["3 1", "2 3", "7 3"], "sample_outputs": ["1 1", "2 0", "3 2"], "notes": "NoteIn the first sample Vasya can first put on one pair of different socks, after that he has two red socks left to wear on the second day."}, "src_uid": "775766790e91e539c1cfaa5030e5b955"}
{"nl": {"description": "In order to make the \"Sea Battle\" game more interesting, Boris decided to add a new ship type to it. The ship consists of two rectangles. The first rectangle has a width of $$$w_1$$$ and a height of $$$h_1$$$, while the second rectangle has a width of $$$w_2$$$ and a height of $$$h_2$$$, where $$$w_1 \\ge w_2$$$. In this game, exactly one ship is used, made up of two rectangles. There are no other ships on the field.The rectangles are placed on field in the following way:  the second rectangle is on top the first rectangle;  they are aligned to the left, i.e. their left sides are on the same line;  the rectangles are adjacent to each other without a gap. See the pictures in the notes: the first rectangle is colored red, the second rectangle is colored blue.Formally, let's introduce a coordinate system. Then, the leftmost bottom cell of the first rectangle has coordinates $$$(1, 1)$$$, the rightmost top cell of the first rectangle has coordinates $$$(w_1, h_1)$$$, the leftmost bottom cell of the second rectangle has coordinates $$$(1, h_1 + 1)$$$ and the rightmost top cell of the second rectangle has coordinates $$$(w_2, h_1 + h_2)$$$.After the ship is completely destroyed, all cells neighboring by side or a corner with the ship are marked. Of course, only cells, which don't belong to the ship are marked. On the pictures in the notes such cells are colored green.Find out how many cells should be marked after the ship is destroyed. The field of the game is infinite in any direction.", "input_spec": "Four lines contain integers $$$w_1, h_1, w_2$$$ and $$$h_2$$$ ($$$1 \\leq w_1, h_1, w_2, h_2 \\leq 10^8$$$, $$$w_1 \\ge w_2$$$) — the width of the first rectangle, the height of the first rectangle, the width of the second rectangle and the height of the second rectangle. You can't rotate the rectangles.", "output_spec": "Print exactly one integer — the number of cells, which should be marked after the ship is destroyed.", "sample_inputs": ["2 1 2 1", "2 2 1 2"], "sample_outputs": ["12", "16"], "notes": "NoteIn the first example the field looks as follows (the first rectangle is red, the second rectangle is blue, green shows the marked squares):  In the second example the field looks as:  "}, "src_uid": "b5d44e0041053c996938aadd1b3865f6"}
{"nl": {"description": "Greatest common divisor GCD(a, b) of two positive integers a and b is equal to the biggest integer d such that both integers a and b are divisible by d. There are many efficient algorithms to find greatest common divisor GCD(a, b), for example, Euclid algorithm. Formally, find the biggest integer d, such that all integers a, a + 1, a + 2, ..., b are divisible by d. To make the problem even more complicated we allow a and b to be up to googol, 10100 — such number do not fit even in 64-bit integer type!", "input_spec": "The only line of the input contains two integers a and b (1 ≤ a ≤ b ≤ 10100).", "output_spec": "Output one integer — greatest common divisor of all integers from a to b inclusive.", "sample_inputs": ["1 2", "61803398874989484820458683436563811772030917980576 61803398874989484820458683436563811772030917980576"], "sample_outputs": ["1", "61803398874989484820458683436563811772030917980576"], "notes": null}, "src_uid": "9c5b6d8a20414d160069010b2965b896"}
{"nl": {"description": "There is a card game called \"Durak\", which means \"Fool\" in Russian. The game is quite popular in the countries that used to form USSR. The problem does not state all the game's rules explicitly — you can find them later yourselves if you want.To play durak you need a pack of 36 cards. Each card has a suit (\"S\", \"H\", \"D\" and \"C\") and a rank (in the increasing order \"6\", \"7\", \"8\", \"9\", \"T\", \"J\", \"Q\", \"K\" and \"A\"). At the beginning of the game one suit is arbitrarily chosen as trump. The players move like that: one player puts one or several of his cards on the table and the other one should beat each of them with his cards.A card beats another one if both cards have similar suits and the first card has a higher rank then the second one. Besides, a trump card can beat any non-trump card whatever the cards’ ranks are. In all other cases you can not beat the second card with the first one.You are given the trump suit and two different cards. Determine whether the first one beats the second one or not.", "input_spec": "The first line contains the tramp suit. It is \"S\", \"H\", \"D\" or \"C\". The second line contains the description of the two different cards. Each card is described by one word consisting of two symbols. The first symbol stands for the rank (\"6\", \"7\", \"8\", \"9\", \"T\", \"J\", \"Q\", \"K\" and \"A\"), and the second one stands for the suit (\"S\", \"H\", \"D\" and \"C\").", "output_spec": "Print \"YES\" (without the quotes) if the first cards beats the second one. Otherwise, print \"NO\" (also without the quotes).", "sample_inputs": ["H\nQH 9S", "S\n8D 6D", "C\n7H AS"], "sample_outputs": ["YES", "YES", "NO"], "notes": null}, "src_uid": "da13bd5a335c7f81c5a963b030655c26"}
{"nl": {"description": "The on-board computer on Polycarp's car measured that the car speed at the beginning of some section of the path equals v1 meters per second, and in the end it is v2 meters per second. We know that this section of the route took exactly t seconds to pass.Assuming that at each of the seconds the speed is constant, and between seconds the speed can change at most by d meters per second in absolute value (i.e., the difference in the speed of any two adjacent seconds does not exceed d in absolute value), find the maximum possible length of the path section in meters.", "input_spec": "The first line contains two integers v1 and v2 (1 ≤ v1, v2 ≤ 100) — the speeds in meters per second at the beginning of the segment and at the end of the segment, respectively. The second line contains two integers t (2 ≤ t ≤ 100) — the time when the car moves along the segment in seconds, d (0 ≤ d ≤ 10) — the maximum value of the speed change between adjacent seconds. It is guaranteed that there is a way to complete the segment so that:   the speed in the first second equals v1,  the speed in the last second equals v2,  the absolute value of difference of speeds between any two adjacent seconds doesn't exceed d. ", "output_spec": "Print the maximum possible length of the path segment in meters. ", "sample_inputs": ["5 6\n4 2", "10 10\n10 0"], "sample_outputs": ["26", "100"], "notes": "NoteIn the first sample the sequence of speeds of Polycarpus' car can look as follows: 5, 7, 8, 6. Thus, the total path is 5 + 7 + 8 + 6 = 26 meters.In the second sample, as d = 0, the car covers the whole segment at constant speed v = 10. In t = 10 seconds it covers the distance of 100 meters."}, "src_uid": "9246aa2f506fcbcb47ad24793d09f2cf"}
{"nl": {"description": "Sergey is testing a next-generation processor. Instead of bytes the processor works with memory cells consisting of n bits. These bits are numbered from 1 to n. An integer is stored in the cell in the following way: the least significant bit is stored in the first bit of the cell, the next significant bit is stored in the second bit, and so on; the most significant bit is stored in the n-th bit.Now Sergey wants to test the following instruction: \"add 1 to the value of the cell\". As a result of the instruction, the integer that is written in the cell must be increased by one; if some of the most significant bits of the resulting number do not fit into the cell, they must be discarded.Sergey wrote certain values ​​of the bits in the cell and is going to add one to its value. How many bits of the cell will change after the operation?", "input_spec": "The first line contains a single integer n (1 ≤ n ≤ 100) — the number of bits in the cell. The second line contains a string consisting of n characters — the initial state of the cell. The first character denotes the state of the first bit of the cell. The second character denotes the second least significant bit and so on. The last character denotes the state of the most significant bit.", "output_spec": "Print a single integer — the number of bits in the cell which change their state after we add 1 to the cell.", "sample_inputs": ["4\n1100", "4\n1111"], "sample_outputs": ["3", "4"], "notes": "NoteIn the first sample the cell ends up with value 0010, in the second sample — with 0000."}, "src_uid": "54cb2e987f2cc06c02c7638ea879a1ab"}
{"nl": {"description": "A word or a sentence in some language is called a pangram if all the characters of the alphabet of this language appear in it at least once. Pangrams are often used to demonstrate fonts in printing or test the output devices.You are given a string consisting of lowercase and uppercase Latin letters. Check whether this string is a pangram. We say that the string contains a letter of the Latin alphabet if this letter occurs in the string in uppercase or lowercase.", "input_spec": "The first line contains a single integer n (1 ≤ n ≤ 100) — the number of characters in the string. The second line contains the string. The string consists only of uppercase and lowercase Latin letters.", "output_spec": "Output \"YES\", if the string is a pangram and \"NO\" otherwise.", "sample_inputs": ["12\ntoosmallword", "35\nTheQuickBrownFoxJumpsOverTheLazyDog"], "sample_outputs": ["NO", "YES"], "notes": null}, "src_uid": "f13eba0a0fb86e20495d218fc4ad532d"}
{"nl": {"description": "Polar bears Menshykov and Uslada from the zoo of St. Petersburg and elephant Horace from the zoo of Kiev decided to build a house of cards. For that they've already found a hefty deck of n playing cards. Let's describe the house they want to make:   The house consists of some non-zero number of floors.  Each floor consists of a non-zero number of rooms and the ceiling. A room is two cards that are leaned towards each other. The rooms are made in a row, each two adjoining rooms share a ceiling made by another card.  Each floor besides for the lowest one should contain less rooms than the floor below. Please note that the house may end by the floor with more than one room, and in this case they also must be covered by the ceiling. Also, the number of rooms on the adjoining floors doesn't have to differ by one, the difference may be more. While bears are practicing to put cards, Horace tries to figure out how many floors their house should consist of. The height of the house is the number of floors in it. It is possible that you can make a lot of different houses of different heights out of n cards. It seems that the elephant cannot solve this problem and he asks you to count the number of the distinct heights of the houses that they can make using exactly n cards.", "input_spec": "The single line contains integer n (1 ≤ n ≤ 1012) — the number of cards.", "output_spec": "Print the number of distinct heights that the houses made of exactly n cards can have.", "sample_inputs": ["13", "6"], "sample_outputs": ["1", "0"], "notes": "NoteIn the first sample you can build only these two houses (remember, you must use all the cards):  Thus, 13 cards are enough only for two floor houses, so the answer is 1.The six cards in the second sample are not enough to build any house."}, "src_uid": "ab4f9cb3bb0df6389a4128e9ff1207de"}
{"nl": {"description": "Flatland is inhabited by pixels of three colors: red, green and blue. We know that if two pixels of different colors meet in a violent fight, only one of them survives the fight (that is, the total number of pixels decreases by one). Besides, if pixels of colors x and y (x ≠ y) meet in a violent fight, then the pixel that survives the fight immediately changes its color to z (z ≠ x; z ≠ y). Pixels of the same color are friends, so they don't fight.The King of Flatland knows that his land will be peaceful and prosperous when the pixels are of the same color. For each of the three colors you know the number of pixels of this color that inhabit Flatland. Help the king and determine whether fights can bring peace and prosperity to the country and if it is possible, find the minimum number of fights needed to make the land peaceful and prosperous. ", "input_spec": "The first line contains three space-separated integers a, b and c (0 ≤ a, b, c ≤ 231; a + b + c > 0) — the number of red, green and blue pixels, correspondingly.", "output_spec": "Print a single number — the minimum number of pixel fights before the country becomes peaceful and prosperous. If making the country peaceful and prosperous is impossible, print -1.", "sample_inputs": ["1 1 1", "3 1 0"], "sample_outputs": ["1", "3"], "notes": "NoteIn the first test sample the country needs only one fight to achieve peace and prosperity. Besides, it can be any fight whatsoever. For example, let's assume that the green and the blue pixels fight, then the surviving pixel will be red. As a result, after the fight there are two red pixels. There won't be other pixels.In the second sample the following sequence of fights is possible: red and blue, green and red, red and blue. As a result, after all fights there is one green pixel left."}, "src_uid": "b8008caf788336775cb8ebb76478b04c"}
{"nl": {"description": "Iahub is training for the IOI. What is a better way to train than playing a Zuma-like game? There are n balls put in a row. Each ball is colored in one of k colors. Initially the row doesn't contain three or more contiguous balls with the same color. Iahub has a single ball of color x. He can insert his ball at any position in the row (probably, between two other balls). If at any moment there are three or more contiguous balls of the same color in the row, they are destroyed immediately. This rule is applied multiple times, until there are no more sets of 3 or more contiguous balls of the same color. For example, if Iahub has the row of balls [black, black, white, white, black, black] and a white ball, he can insert the ball between two white balls. Thus three white balls are destroyed, and then four black balls become contiguous, so all four balls are destroyed. The row will not contain any ball in the end, so Iahub can destroy all 6 balls.Iahub wants to destroy as many balls as possible. You are given the description of the row of balls, and the color of Iahub's ball. Help Iahub train for the IOI by telling him the maximum number of balls from the row he can destroy.", "input_spec": "The first line of input contains three integers: n (1 ≤ n ≤ 100), k (1 ≤ k ≤ 100) and x (1 ≤ x ≤ k). The next line contains n space-separated integers c1, c2, ..., cn (1 ≤ ci ≤ k). Number ci means that the i-th ball in the row has color ci. It is guaranteed that the initial row of balls will never contain three or more contiguous balls of the same color. ", "output_spec": "Print a single integer — the maximum number of balls Iahub can destroy.", "sample_inputs": ["6 2 2\n1 1 2 2 1 1", "1 1 1\n1"], "sample_outputs": ["6", "0"], "notes": null}, "src_uid": "d73d9610e3800817a3109314b1e6f88c"}
{"nl": {"description": "You want to arrange n integers a1, a2, ..., an in some order in a row. Let's define the value of an arrangement as the sum of differences between all pairs of adjacent integers.More formally, let's denote some arrangement as a sequence of integers x1, x2, ..., xn, where sequence x is a permutation of sequence a. The value of such an arrangement is (x1 - x2) + (x2 - x3) + ... + (xn - 1 - xn).Find the largest possible value of an arrangement. Then, output the lexicographically smallest sequence x that corresponds to an arrangement of the largest possible value.", "input_spec": "The first line of the input contains integer n (2 ≤ n ≤ 100). The second line contains n space-separated integers a1, a2, ..., an (|ai| ≤ 1000).", "output_spec": "Print the required sequence x1, x2, ..., xn. Sequence x should be the lexicographically smallest permutation of a that corresponds to an arrangement of the largest possible value.", "sample_inputs": ["5\n100 -100 50 0 -50"], "sample_outputs": ["100 -50 0 50 -100"], "notes": "NoteIn the sample test case, the value of the output arrangement is (100 - ( - 50)) + (( - 50) - 0) + (0 - 50) + (50 - ( - 100)) = 200. No other arrangement has a larger value, and among all arrangements with the value of 200, the output arrangement is the lexicographically smallest one.Sequence x1, x2, ... , xp is lexicographically smaller than sequence y1, y2, ... , yp if there exists an integer r (0 ≤ r < p) such that x1 = y1, x2 = y2, ... , xr = yr and xr + 1 < yr + 1."}, "src_uid": "4408eba2c5c0693e6b70bdcbe2dda2f4"}
{"nl": {"description": "Once upon a time there were several little pigs and several wolves on a two-dimensional grid of size n × m. Each cell in this grid was either empty, containing one little pig, or containing one wolf.A little pig and a wolf are adjacent if the cells that they are located at share a side. The little pigs are afraid of wolves, so there will be at most one wolf adjacent to each little pig. But each wolf may be adjacent to any number of little pigs.They have been living peacefully for several years. But today the wolves got hungry. One by one, each wolf will choose one of the little pigs adjacent to it (if any), and eats the poor little pig. This process is not repeated. That is, each wolf will get to eat at most one little pig. Once a little pig gets eaten, it disappears and cannot be eaten by any other wolf.What is the maximum number of little pigs that may be eaten by the wolves?", "input_spec": "The first line contains integers n and m (1 ≤ n, m ≤ 10) which denotes the number of rows and columns in our two-dimensional grid, respectively. Then follow n lines containing m characters each — that is the grid description. \".\" means that this cell is empty. \"P\" means that this cell contains a little pig. \"W\" means that this cell contains a wolf.  It is guaranteed that there will be at most one wolf adjacent to any little pig.", "output_spec": "Print a single number — the maximal number of little pigs that may be eaten by the wolves.", "sample_inputs": ["2 3\nPPW\nW.P", "3 3\nP.W\n.P.\nW.P"], "sample_outputs": ["2", "0"], "notes": "NoteIn the first example, one possible scenario in which two little pigs get eaten by the wolves is as follows.   "}, "src_uid": "969b24ed98d916184821b2b2f8fd3aac"}
{"nl": {"description": "Maxim wants to buy an apartment in a new house at Line Avenue of Metropolis. The house has n apartments that are numbered from 1 to n and are arranged in a row. Two apartments are adjacent if their indices differ by 1. Some of the apartments can already be inhabited, others are available for sale.Maxim often visits his neighbors, so apartment is good for him if it is available for sale and there is at least one already inhabited apartment adjacent to it. Maxim knows that there are exactly k already inhabited apartments, but he doesn't know their indices yet.Find out what could be the minimum possible and the maximum possible number of apartments that are good for Maxim.", "input_spec": "The only line of the input contains two integers: n and k (1 ≤ n ≤ 109, 0 ≤ k ≤ n).", "output_spec": "Print the minimum possible and the maximum possible number of apartments good for Maxim.", "sample_inputs": ["6 3"], "sample_outputs": ["1 3"], "notes": "NoteIn the sample test, the number of good apartments could be minimum possible if, for example, apartments with indices 1, 2 and 3 were inhabited. In this case only apartment 4 is good. The maximum possible number could be, for example, if apartments with indices 1, 3 and 5 were inhabited. In this case all other apartments: 2, 4 and 6 are good."}, "src_uid": "bdccf34b5a5ae13238c89a60814b9f86"}
{"nl": {"description": "There are r red and g green blocks for construction of the red-green tower. Red-green tower can be built following next rules:  Red-green tower is consisting of some number of levels;  Let the red-green tower consist of n levels, then the first level of this tower should consist of n blocks, second level — of n - 1 blocks, the third one — of n - 2 blocks, and so on — the last level of such tower should consist of the one block. In other words, each successive level should contain one block less than the previous one;  Each level of the red-green tower should contain blocks of the same color.  Let h be the maximum possible number of levels of red-green tower, that can be built out of r red and g green blocks meeting the rules above. The task is to determine how many different red-green towers having h levels can be built out of the available blocks.Two red-green towers are considered different if there exists some level, that consists of red blocks in the one tower and consists of green blocks in the other tower.You are to write a program that will find the number of different red-green towers of height h modulo 109 + 7.", "input_spec": "The only line of input contains two integers r and g, separated by a single space — the number of available red and green blocks respectively (0 ≤ r, g ≤ 2·105, r + g ≥ 1).", "output_spec": "Output the only integer — the number of different possible red-green towers of height h modulo 109 + 7.", "sample_inputs": ["4 6", "9 7", "1 1"], "sample_outputs": ["2", "6", "2"], "notes": "NoteThe image in the problem statement shows all possible red-green towers for the first sample."}, "src_uid": "34b6286350e3531c1fbda6b0c184addc"}
{"nl": {"description": "Mary has just graduated from one well-known University and is now attending celebration party. Students like to dream of a beautiful life, so they used champagne glasses to construct a small pyramid. The height of the pyramid is n. The top level consists of only 1 glass, that stands on 2 glasses on the second level (counting from the top), then 3 glasses on the third level and so on.The bottom level consists of n glasses.Vlad has seen in the movies many times how the champagne beautifully flows from top levels to bottom ones, filling all the glasses simultaneously. So he took a bottle and started to pour it in the glass located at the top of the pyramid.Each second, Vlad pours to the top glass the amount of champagne equal to the size of exactly one glass. If the glass is already full, but there is some champagne flowing in it, then it pours over the edge of the glass and is equally distributed over two glasses standing under. If the overflowed glass is at the bottom level, then the champagne pours on the table. For the purpose of this problem we consider that champagne is distributed among pyramid glasses immediately. Vlad is interested in the number of completely full glasses if he stops pouring champagne in t seconds.Pictures below illustrate the pyramid consisting of three levels.   ", "input_spec": "The only line of the input contains two integers n and t (1 ≤ n ≤ 10, 0 ≤ t ≤ 10 000) — the height of the pyramid and the number of seconds Vlad will be pouring champagne from the bottle.", "output_spec": "Print the single integer — the number of completely full glasses after t seconds.", "sample_inputs": ["3 5", "4 8"], "sample_outputs": ["4", "6"], "notes": "NoteIn the first sample, the glasses full after 5 seconds are: the top glass, both glasses on the second level and the middle glass at the bottom level. Left and right glasses of the bottom level will be half-empty."}, "src_uid": "b2b49b7f6e3279d435766085958fb69d"}
{"nl": {"description": "Small, but very brave, mouse Brain was not accepted to summer school of young villains. He was upset and decided to postpone his plans of taking over the world, but to become a photographer instead.As you may know, the coolest photos are on the film (because you can specify the hashtag #film for such).Brain took a lot of colourful pictures on colored and black-and-white film. Then he developed and translated it into a digital form. But now, color and black-and-white photos are in one folder, and to sort them, one needs to spend more than one hour!As soon as Brain is a photographer not programmer now, he asks you to help him determine for a single photo whether it is colored or black-and-white.Photo can be represented as a matrix sized n × m, and each element of the matrix stores a symbol indicating corresponding pixel color. There are only 6 colors:   'C' (cyan) 'M' (magenta) 'Y' (yellow) 'W' (white) 'G' (grey) 'B' (black) The photo is considered black-and-white if it has only white, black and grey pixels in it. If there are any of cyan, magenta or yellow pixels in the photo then it is considered colored.", "input_spec": "The first line of the input contains two integers n and m (1 ≤ n, m ≤ 100) — the number of photo pixel matrix rows and columns respectively. Then n lines describing matrix rows follow. Each of them contains m space-separated characters describing colors of pixels in a row. Each character in the line is one of the 'C', 'M', 'Y', 'W', 'G' or 'B'.", "output_spec": "Print the \"#Black&White\" (without quotes), if the photo is black-and-white and \"#Color\" (without quotes), if it is colored, in the only line.", "sample_inputs": ["2 2\nC M\nY Y", "3 2\nW W\nW W\nB B", "1 1\nW"], "sample_outputs": ["#Color", "#Black&White", "#Black&White"], "notes": null}, "src_uid": "19c311c02380f9a73cd477e4fde27454"}
{"nl": {"description": "Pak Chanek plans to build a garage. He wants the garage to consist of a square and a right triangle that are arranged like the following illustration.  Define $$$a$$$ and $$$b$$$ as the lengths of two of the sides in the right triangle as shown in the illustration. An integer $$$x$$$ is suitable if and only if we can construct a garage with assigning positive integer values for the lengths $$$a$$$ and $$$b$$$ ($$$a<b$$$) so that the area of the square at the bottom is exactly $$$x$$$. As a good friend of Pak Chanek, you are asked to help him find the $$$N$$$-th smallest suitable number.", "input_spec": "The only line contains a single integer $$$N$$$ ($$$1 \\leq N \\leq 10^9$$$).", "output_spec": "An integer that represents the $$$N$$$-th smallest suitable number.", "sample_inputs": ["3"], "sample_outputs": ["7"], "notes": "NoteThe $$$3$$$-rd smallest suitable number is $$$7$$$. A square area of $$$7$$$ can be obtained by assigning $$$a=3$$$ and $$$b=4$$$."}, "src_uid": "d0a8604b78ba19ab769fd1ec90a72e4e"}
{"nl": {"description": "Allen has a LOT of money. He has $$$n$$$ dollars in the bank. For security reasons, he wants to withdraw it in cash (we will not disclose the reasons here). The denominations for dollar bills are $$$1$$$, $$$5$$$, $$$10$$$, $$$20$$$, $$$100$$$. What is the minimum number of bills Allen could receive after withdrawing his entire balance?", "input_spec": "The first and only line of input contains a single integer $$$n$$$ ($$$1 \\le n \\le 10^9$$$).", "output_spec": "Output the minimum number of bills that Allen could receive.", "sample_inputs": ["125", "43", "1000000000"], "sample_outputs": ["3", "5", "10000000"], "notes": "NoteIn the first sample case, Allen can withdraw this with a $$$100$$$ dollar bill, a $$$20$$$ dollar bill, and a $$$5$$$ dollar bill. There is no way for Allen to receive $$$125$$$ dollars in one or two bills.In the second sample case, Allen can withdraw two $$$20$$$ dollar bills and three $$$1$$$ dollar bills.In the third sample case, Allen can withdraw $$$100000000$$$ (ten million!) $$$100$$$ dollar bills."}, "src_uid": "8e81ad7110552c20297f08ad3e5f8ddc"}
{"nl": {"description": "Attention: we lost all the test cases for this problem, so instead of solving the problem, we need you to generate test cases. We're going to give you the answer, and you need to print a test case that produces the given answer. The original problem is in the following paragraph.People don't use cash as often as they used to. Having a credit card solves some of the hassles of cash, such as having to receive change when you can't form the exact amount of money needed to purchase an item. Typically cashiers will give you as few coins as possible in change, but they don't have to. For example, if your change is 30 cents, a cashier could give you a 5 cent piece and a 25 cent piece, or they could give you three 10 cent pieces, or ten 1 cent pieces, two 5 cent pieces, and one 10 cent piece. Altogether there are 18 different ways to make 30 cents using only 1 cent pieces, 5 cent pieces, 10 cent pieces, and 25 cent pieces. Two ways are considered different if they contain a different number of at least one type of coin. Given the denominations of the coins and an amount of change to be made, how many different ways are there to make change?As we mentioned before, we lost all the test cases for this problem, so we're actually going to give you the number of ways, and want you to produce a test case for which the number of ways is the given number. There could be many ways to achieve this (we guarantee there's always at least one), so you can print any, as long as it meets the constraints described below.", "input_spec": "Input will consist of a single integer A (1 ≤ A ≤ 105), the desired number of ways.", "output_spec": "In the first line print integers N and M (1 ≤ N ≤ 106, 1 ≤ M ≤ 10), the amount of change to be made, and the number of denominations, respectively. Then print M integers D1, D2, ..., DM (1 ≤ Di ≤ 106), the denominations of the coins. All denominations must be distinct: for any i ≠ j we must have Di ≠ Dj. If there are multiple tests, print any of them. You can print denominations in atbitrary order.", "sample_inputs": ["18", "3", "314"], "sample_outputs": ["30 4\n1 5 10 25", "20 2\n5 2", "183 4\n6 5 2 139"], "notes": null}, "src_uid": "5c000b4c82a8ecef764f53fda8cee541"}
{"nl": {"description": "Vasya likes to solve equations. Today he wants to solve $$$(x~\\mathrm{div}~k) \\cdot (x \\bmod k) = n$$$, where $$$\\mathrm{div}$$$ and $$$\\mathrm{mod}$$$ stand for integer division and modulo operations (refer to the Notes below for exact definition). In this equation, $$$k$$$ and $$$n$$$ are positive integer parameters, and $$$x$$$ is a positive integer unknown. If there are several solutions, Vasya wants to find the smallest possible $$$x$$$. Can you help him?", "input_spec": "The first line contains two integers $$$n$$$ and $$$k$$$ ($$$1 \\leq n \\leq 10^6$$$, $$$2 \\leq k \\leq 1000$$$).", "output_spec": "Print a single integer $$$x$$$ — the smallest positive integer solution to $$$(x~\\mathrm{div}~k) \\cdot (x \\bmod k) = n$$$. It is guaranteed that this equation has at least one positive integer solution.", "sample_inputs": ["6 3", "1 2", "4 6"], "sample_outputs": ["11", "3", "10"], "notes": "NoteThe result of integer division $$$a~\\mathrm{div}~b$$$ is equal to the largest integer $$$c$$$ such that $$$b \\cdot c \\leq a$$$. $$$a$$$ modulo $$$b$$$ (shortened $$$a \\bmod b$$$) is the only integer $$$c$$$ such that $$$0 \\leq c < b$$$, and $$$a - c$$$ is divisible by $$$b$$$.In the first sample, $$$11~\\mathrm{div}~3 = 3$$$ and $$$11 \\bmod 3 = 2$$$. Since $$$3 \\cdot 2 = 6$$$, then $$$x = 11$$$ is a solution to $$$(x~\\mathrm{div}~3) \\cdot (x \\bmod 3) = 6$$$. One can see that $$$19$$$ is the only other positive integer solution, hence $$$11$$$ is the smallest one."}, "src_uid": "ed0ebc1e484fcaea875355b5b7944c57"}
{"nl": {"description": "You are given three sticks with positive integer lengths of a, b, and c centimeters. You can increase length of some of them by some positive integer number of centimeters (different sticks can be increased by a different length), but in total by at most l centimeters. In particular, it is allowed not to increase the length of any stick.Determine the number of ways to increase the lengths of some sticks so that you can form from them a non-degenerate (that is, having a positive area) triangle. Two ways are considered different, if the length of some stick is increased by different number of centimeters in them.", "input_spec": "The single line contains 4 integers a, b, c, l (1 ≤ a, b, c ≤ 3·105, 0 ≤ l ≤ 3·105).", "output_spec": "Print a single integer — the number of ways to increase the sizes of the sticks by the total of at most l centimeters, so that you can make a non-degenerate triangle from it.", "sample_inputs": ["1 1 1 2", "1 2 3 1", "10 2 1 7"], "sample_outputs": ["4", "2", "0"], "notes": "NoteIn the first sample test you can either not increase any stick or increase any two sticks by 1 centimeter.In the second sample test you can increase either the first or the second stick by one centimeter. Note that the triangle made from the initial sticks is degenerate and thus, doesn't meet the conditions."}, "src_uid": "185ff90a8b0ae0e2b75605f772589410"}
{"nl": {"description": "Special Agent Smart Beaver works in a secret research department of ABBYY. He's been working there for a long time and is satisfied with his job, as it allows him to eat out in the best restaurants and order the most expensive and exotic wood types there. The content special agent has got an important task: to get the latest research by British scientists on the English Language. These developments are encoded and stored in a large safe. The Beaver's teeth are strong enough, so the authorities assured that upon arriving at the place the beaver won't have any problems with opening the safe.And he finishes his aspen sprig and leaves for this important task. Of course, the Beaver arrived at the location without any problems, but alas. He can't open the safe with his strong and big teeth. At this point, the Smart Beaver get a call from the headquarters and learns that opening the safe with the teeth is not necessary, as a reliable source has sent the following information: the safe code consists of digits and has no leading zeroes. There also is a special hint, which can be used to open the safe. The hint is string s with the following structure:  if si = \"?\", then the digit that goes i-th in the safe code can be anything (between 0 to 9, inclusively);  if si is a digit (between 0 to 9, inclusively), then it means that there is digit si on position i in code;  if the string contains letters from \"A\" to \"J\", then all positions with the same letters must contain the same digits and the positions with distinct letters must contain distinct digits.  The length of the safe code coincides with the length of the hint. For example, hint \"?JGJ9\" has such matching safe code variants: \"51919\", \"55959\", \"12329\", \"93539\" and so on, and has wrong variants such as: \"56669\", \"00111\", \"03539\" and \"13666\".After receiving such information, the authorities change the plan and ask the special agents to work quietly and gently and not to try to open the safe by mechanical means, and try to find the password using the given hint.At a special agent school the Smart Beaver was the fastest in his platoon finding codes for such safes, but now he is not in that shape: the years take their toll ... Help him to determine the number of possible variants of the code to the safe, matching the given hint. After receiving this information, and knowing his own speed of entering codes, the Smart Beaver will be able to determine whether he will have time for tonight's show \"Beavers are on the trail\" on his favorite TV channel, or he should work for a sleepless night...", "input_spec": "The first line contains string s — the hint to the safe code. String s consists of the following characters: ?, 0-9, A-J. It is guaranteed that the first character of string s doesn't equal to character 0. The input limits for scoring 30 points are (subproblem A1):    1 ≤ |s| ≤ 5.  The input limits for scoring 100 points are (subproblems A1+A2):    1 ≤ |s| ≤ 105.  Here |s| means the length of string s.", "output_spec": "Print the number of codes that match the given hint.", "sample_inputs": ["AJ", "1?AA"], "sample_outputs": ["81", "100"], "notes": null}, "src_uid": "d3c10d1b1a17ad018359e2dab80d2b82"}
{"nl": {"description": "Little Petya likes numbers a lot. He found that number 123 in base 16 consists of two digits: the first is 7 and the second is 11. So the sum of digits of 123 in base 16 is equal to 18.Now he wonders what is an average value of sum of digits of the number A written in all bases from 2 to A - 1.Note that all computations should be done in base 10. You should find the result as an irreducible fraction, written in base 10.", "input_spec": "Input contains one integer number A (3 ≤ A ≤ 1000).", "output_spec": "Output should contain required average value in format «X/Y», where X is the numerator and Y is the denominator.", "sample_inputs": ["5", "3"], "sample_outputs": ["7/3", "2/1"], "notes": "NoteIn the first sample number 5 written in all bases from 2 to 4 looks so: 101, 12, 11. Sums of digits are 2, 3 and 2, respectively."}, "src_uid": "1366732dddecba26db232d6ca8f35fdc"}
{"nl": {"description": "Imp is watching a documentary about cave painting.  Some numbers, carved in chaotic order, immediately attracted his attention. Imp rapidly proposed a guess that they are the remainders of division of a number n by all integers i from 1 to k. Unfortunately, there are too many integers to analyze for Imp.Imp wants you to check whether all these remainders are distinct. Formally, he wants to check, if all , 1 ≤ i ≤ k, are distinct, i. e. there is no such pair (i, j) that:   1 ≤ i < j ≤ k,  , where  is the remainder of division x by y. ", "input_spec": "The only line contains two integers n, k (1 ≤ n, k ≤ 1018).", "output_spec": "Print \"Yes\", if all the remainders are distinct, and \"No\" otherwise. You can print each letter in arbitrary case (lower or upper).", "sample_inputs": ["4 4", "5 3"], "sample_outputs": ["No", "Yes"], "notes": "NoteIn the first sample remainders modulo 1 and 4 coincide."}, "src_uid": "5271c707c9c72ef021a0baf762bf3eb2"}
{"nl": {"description": "Kolya Gerasimov loves kefir very much. He lives in year 1984 and knows all the details of buying this delicious drink. One day, as you probably know, he found himself in year 2084, and buying kefir there is much more complicated.Kolya is hungry, so he went to the nearest milk shop. In 2084 you may buy kefir in a plastic liter bottle, that costs a rubles, or in glass liter bottle, that costs b rubles. Also, you may return empty glass bottle and get c (c < b) rubles back, but you cannot return plastic bottles.Kolya has n rubles and he is really hungry, so he wants to drink as much kefir as possible. There were no plastic bottles in his 1984, so Kolya doesn't know how to act optimally and asks for your help.", "input_spec": "First line of the input contains a single integer n (1 ≤ n ≤ 1018) — the number of rubles Kolya has at the beginning. Then follow three lines containing integers a, b and c (1 ≤ a ≤ 1018, 1 ≤ c < b ≤ 1018) — the cost of one plastic liter bottle, the cost of one glass liter bottle and the money one can get back by returning an empty glass bottle, respectively.", "output_spec": "Print the only integer — maximum number of liters of kefir, that Kolya can drink.", "sample_inputs": ["10\n11\n9\n8", "10\n5\n6\n1"], "sample_outputs": ["2", "2"], "notes": "NoteIn the first sample, Kolya can buy one glass bottle, then return it and buy one more glass bottle. Thus he will drink 2 liters of kefir.In the second sample, Kolya can buy two plastic bottle and get two liters of kefir, or he can buy one liter glass bottle, then return it and buy one plastic bottle. In both cases he will drink two liters of kefir."}, "src_uid": "0ee9abec69230eab25de51aef0984f8f"}
{"nl": {"description": "There are three friend living on the straight line Ox in Lineland. The first friend lives at the point x1, the second friend lives at the point x2, and the third friend lives at the point x3. They plan to celebrate the New Year together, so they need to meet at one point. What is the minimum total distance they have to travel in order to meet at some point and celebrate the New Year?It's guaranteed that the optimal answer is always integer.", "input_spec": "The first line of the input contains three distinct integers x1, x2 and x3 (1 ≤ x1, x2, x3 ≤ 100) — the coordinates of the houses of the first, the second and the third friends respectively. ", "output_spec": "Print one integer — the minimum total distance the friends need to travel in order to meet together.", "sample_inputs": ["7 1 4", "30 20 10"], "sample_outputs": ["6", "20"], "notes": "NoteIn the first sample, friends should meet at the point 4. Thus, the first friend has to travel the distance of 3 (from the point 7 to the point 4), the second friend also has to travel the distance of 3 (from the point 1 to the point 4), while the third friend should not go anywhere because he lives at the point 4."}, "src_uid": "7bffa6e8d2d21bbb3b7f4aec109b3319"}
{"nl": {"description": "The Smart Beaver from ABBYY was offered a job of a screenwriter for the ongoing TV series. In particular, he needs to automate the hard decision: which main characters will get married by the end of the series.There are n single men and n single women among the main characters. An opinion poll showed that viewers like several couples, and a marriage of any of them will make the audience happy. The Smart Beaver formalized this fact as k triples of numbers (h, w, r), where h is the index of the man, w is the index of the woman, and r is the measure of the audience's delight in case of the marriage of this couple. The same poll showed that the marriage of any other couple will leave the audience indifferent, so the screenwriters decided not to include any such marriages in the plot.The script allows you to arrange several marriages between the heroes or not to arrange marriages at all. A subset of some of the k marriages is considered acceptable if each man and each woman is involved in at most one marriage of the subset (the series won't allow any divorces). The value of the acceptable set of marriages is the total delight the spectators will get from the marriages included in this set.Obviously, there is a finite number of acceptable sets, and they all describe some variants of the script. The screenwriters do not want to choose a set with maximum value — it would make the plot too predictable. So the Smart Beaver offers the following option: sort all the acceptable sets in increasing order of value and choose the t-th set from the sorted list. Thus, t = 1 corresponds to a plot without marriages, t = 2 — to a single marriage resulting in minimal delight for the audience, and so on.Help the Beaver to implement the algorithm for selecting the desired set.", "input_spec": "The first input line contains integers n, k and t (1 ≤ k ≤ min(100, n2), 1 ≤ t ≤ 2·105), separated by single spaces. Next k lines contain triples of integers (h, w, r) (1 ≤ h, w ≤ n; 1 ≤ r ≤ 1000), separated by single spaces, which describe the possible marriages. It is guaranteed that the input data is correct: t doesn't exceed the total number of acceptable sets, and each pair (h, w) is present in at most one triple. The input limitations for getting 30 points are:    1 ≤ n ≤ 5  The input limitations for getting 100 points are:    1 ≤ n ≤ 20 ", "output_spec": "Print a single number — the value of the t-th acceptable variant.", "sample_inputs": ["2 4 3\n1 1 1\n1 2 2\n2 1 3\n2 2 7", "2 4 7\n1 1 1\n1 2 2\n2 1 3\n2 2 7"], "sample_outputs": ["2", "8"], "notes": "NoteThe figure shows 7 acceptable sets of marriages that exist in the first sample.   "}, "src_uid": "7348b5644f232bf377a4834eded42e4b"}
{"nl": {"description": "Alice and Bob decided to eat some fruit. In the kitchen they found a large bag of oranges and apples. Alice immediately took an orange for herself, Bob took an apple. To make the process of sharing the remaining fruit more fun, the friends decided to play a game. They put multiple cards and on each one they wrote a letter, either 'A', or the letter 'B'. Then they began to remove the cards one by one from left to right, every time they removed a card with the letter 'A', Alice gave Bob all the fruits she had at that moment and took out of the bag as many apples and as many oranges as she had before. Thus the number of oranges and apples Alice had, did not change. If the card had written letter 'B', then Bob did the same, that is, he gave Alice all the fruit that he had, and took from the bag the same set of fruit. After the last card way removed, all the fruit in the bag were over.You know how many oranges and apples was in the bag at first. Your task is to find any sequence of cards that Alice and Bob could have played with.", "input_spec": "The first line of the input contains two integers, x, y (1 ≤ x, y ≤ 1018, xy > 1) — the number of oranges and apples that were initially in the bag.", "output_spec": "Print any sequence of cards that would meet the problem conditions as a compressed string of characters 'A' and 'B. That means that you need to replace the segments of identical consecutive characters by the number of repetitions of the characters and the actual character. For example, string AAABAABBB should be replaced by string 3A1B2A3B, but cannot be replaced by 2A1A1B2A3B or by 3AB2A3B. See the samples for clarifications of the output format. The string that you print should consist of at most 106 characters. It is guaranteed that if the answer exists, its compressed representation exists, consisting of at most 106 characters. If there are several possible answers, you are allowed to print any of them. If the sequence of cards that meet the problem statement does not not exist, print a single word Impossible.", "sample_inputs": ["1 4", "2 2", "3 2"], "sample_outputs": ["3B", "Impossible", "1A1B"], "notes": "NoteIn the first sample, if the row contained three cards with letter 'B', then Bob should give one apple to Alice three times. So, in the end of the game Alice has one orange and three apples, and Bob has one apple, in total it is one orange and four apples.In second sample, there is no answer since one card is not enough for game to finish, and two cards will produce at least three apples or three oranges.In the third sample, cards contain letters 'AB', so after removing the first card Bob has one orange and one apple, and after removal of second card Alice has two oranges and one apple. So, in total it is three oranges and two apples."}, "src_uid": "6a9ec3b23bd462353d985e0c0f2f7671"}
{"nl": {"description": "Sereja showed an interesting game to his friends. The game goes like that. Initially, there is a table with an empty cup and n water mugs on it. Then all players take turns to move. During a move, a player takes a non-empty mug of water and pours all water from it into the cup. If the cup overfills, then we assume that this player lost.As soon as Sereja's friends heard of the game, they wanted to play it. Sereja, on the other hand, wanted to find out whether his friends can play the game in such a way that there are no losers. You are given the volumes of all mugs and the cup. Also, you know that Sereja has (n - 1) friends. Determine if Sereja's friends can play the game so that nobody loses.", "input_spec": "The first line contains integers n and s (2 ≤ n ≤ 100; 1 ≤ s ≤ 1000) — the number of mugs and the volume of the cup. The next line contains n integers a1, a2, ..., an (1 ≤ ai ≤ 10). Number ai means the volume of the i-th mug.", "output_spec": "In a single line, print \"YES\" (without the quotes) if his friends can play in the described manner, and \"NO\" (without the quotes) otherwise.", "sample_inputs": ["3 4\n1 1 1", "3 4\n3 1 3", "3 4\n4 4 4"], "sample_outputs": ["YES", "YES", "NO"], "notes": null}, "src_uid": "496baae594b32c5ffda35b896ebde629"}
{"nl": {"description": "Two beavers, Timur and Marsel, play the following game.There are n logs, each of exactly m meters in length. The beavers move in turns. For each move a beaver chooses a log and gnaws it into some number (more than one) of equal parts, the length of each one is expressed by an integer and is no less than k meters. Each resulting part is also a log which can be gnawed in future by any beaver. The beaver that can't make a move loses. Thus, the other beaver wins.Timur makes the first move. The players play in the optimal way. Determine the winner.", "input_spec": "The first line contains three integers n, m, k (1 ≤ n, m, k ≤ 109).", "output_spec": "Print \"Timur\", if Timur wins, or \"Marsel\", if Marsel wins. You should print everything without the quotes. ", "sample_inputs": ["1 15 4", "4 9 5"], "sample_outputs": ["Timur", "Marsel"], "notes": "NoteIn the first sample the beavers only have one log, of 15 meters in length. Timur moves first. The only move he can do is to split the log into 3 parts each 5 meters in length. Then Marsel moves but he can't split any of the resulting logs, as k = 4. Thus, the winner is Timur.In the second example the beavers have 4 logs 9 meters in length. Timur can't split any of them, so that the resulting parts possessed the length of not less than 5 meters, that's why he loses instantly."}, "src_uid": "4a3767011ddac874efa021fff7c94432"}
{"nl": {"description": "Polycarp has $$$n$$$ coins, the value of the $$$i$$$-th coin is $$$a_i$$$. Polycarp wants to distribute all the coins between his pockets, but he cannot put two coins with the same value into the same pocket.For example, if Polycarp has got six coins represented as an array $$$a = [1, 2, 4, 3, 3, 2]$$$, he can distribute the coins into two pockets as follows: $$$[1, 2, 3], [2, 3, 4]$$$.Polycarp wants to distribute all the coins with the minimum number of used pockets. Help him to do that.", "input_spec": "The first line of the input contains one integer $$$n$$$ ($$$1 \\le n \\le 100$$$) — the number of coins. The second line of the input contains $$$n$$$ integers $$$a_1, a_2, \\dots, a_n$$$ ($$$1 \\le a_i \\le 100$$$) — values of coins.", "output_spec": "Print only one integer — the minimum number of pockets Polycarp needs to distribute all the coins so no two coins with the same value are put into the same pocket.", "sample_inputs": ["6\n1 2 4 3 3 2", "1\n100"], "sample_outputs": ["2", "1"], "notes": null}, "src_uid": "f30329023e84b4c50b1b118dc98ae73c"}
{"nl": {"description": "Polycarp is crazy about round numbers. He especially likes the numbers divisible by 10k.In the given number of n Polycarp wants to remove the least number of digits to get a number that is divisible by 10k. For example, if k = 3, in the number 30020 it is enough to delete a single digit (2). In this case, the result is 3000 that is divisible by 103 = 1000.Write a program that prints the minimum number of digits to be deleted from the given integer number n, so that the result is divisible by 10k. The result should not start with the unnecessary leading zero (i.e., zero can start only the number 0, which is required to be written as exactly one digit).It is guaranteed that the answer exists.", "input_spec": "The only line of the input contains two integer numbers n and k (0 ≤ n ≤ 2 000 000 000, 1 ≤ k ≤ 9). It is guaranteed that the answer exists. All numbers in the input are written in traditional notation of integers, that is, without any extra leading zeros.", "output_spec": "Print w — the required minimal number of digits to erase. After removing the appropriate w digits from the number n, the result should have a value that is divisible by 10k. The result can start with digit 0 in the single case (the result is zero and written by exactly the only digit 0).", "sample_inputs": ["30020 3", "100 9", "10203049 2"], "sample_outputs": ["1", "2", "3"], "notes": "NoteIn the example 2 you can remove two digits: 1 and any 0. The result is number 0 which is divisible by any number."}, "src_uid": "7a8890417aa48c2b93b559ca118853f9"}
{"nl": {"description": "A string $$$s$$$ of length $$$n$$$ can be encrypted by the following algorithm:  iterate over all divisors of $$$n$$$ in decreasing order (i.e. from $$$n$$$ to $$$1$$$),  for each divisor $$$d$$$, reverse the substring $$$s[1 \\dots d]$$$ (i.e. the substring which starts at position $$$1$$$ and ends at position $$$d$$$). For example, the above algorithm applied to the string $$$s$$$=\"codeforces\" leads to the following changes: \"codeforces\" $$$\\to$$$ \"secrofedoc\" $$$\\to$$$ \"orcesfedoc\" $$$\\to$$$ \"rocesfedoc\" $$$\\to$$$ \"rocesfedoc\" (obviously, the last reverse operation doesn't change the string because $$$d=1$$$).You are given the encrypted string $$$t$$$. Your task is to decrypt this string, i.e., to find a string $$$s$$$ such that the above algorithm results in string $$$t$$$. It can be proven that this string $$$s$$$ always exists and is unique.", "input_spec": "The first line of input consists of a single integer $$$n$$$ ($$$1 \\le n \\le 100$$$) — the length of the string $$$t$$$. The second line of input consists of the string $$$t$$$. The length of $$$t$$$ is $$$n$$$, and it consists only of lowercase Latin letters.", "output_spec": "Print a string $$$s$$$ such that the above algorithm results in $$$t$$$.", "sample_inputs": ["10\nrocesfedoc", "16\nplmaetwoxesisiht", "1\nz"], "sample_outputs": ["codeforces", "thisisexampletwo", "z"], "notes": "NoteThe first example is described in the problem statement."}, "src_uid": "1b0b2ee44c63cb0634cb63f2ad65cdd3"}
{"nl": {"description": "Alice and Bob are decorating a Christmas Tree. Alice wants only $$$3$$$ types of ornaments to be used on the Christmas Tree: yellow, blue and red. They have $$$y$$$ yellow ornaments, $$$b$$$ blue ornaments and $$$r$$$ red ornaments.In Bob's opinion, a Christmas Tree will be beautiful if:  the number of blue ornaments used is greater by exactly $$$1$$$ than the number of yellow ornaments, and  the number of red ornaments used is greater by exactly $$$1$$$ than the number of blue ornaments. That is, if they have $$$8$$$ yellow ornaments, $$$13$$$ blue ornaments and $$$9$$$ red ornaments, we can choose $$$4$$$ yellow, $$$5$$$ blue and $$$6$$$ red ornaments ($$$5=4+1$$$ and $$$6=5+1$$$).Alice wants to choose as many ornaments as possible, but she also wants the Christmas Tree to be beautiful according to Bob's opinion.In the example two paragraphs above, we would choose $$$7$$$ yellow, $$$8$$$ blue and $$$9$$$ red ornaments. If we do it, we will use $$$7+8+9=24$$$ ornaments. That is the maximum number.Since Alice and Bob are busy with preparing food to the New Year's Eve, they are asking you to find out the maximum number of ornaments that can be used in their beautiful Christmas Tree! It is guaranteed that it is possible to choose at least $$$6$$$ ($$$1+2+3=6$$$) ornaments.", "input_spec": "The only line contains three integers $$$y$$$, $$$b$$$, $$$r$$$ ($$$1 \\leq y \\leq 100$$$, $$$2 \\leq b \\leq 100$$$, $$$3 \\leq r \\leq 100$$$) — the number of yellow, blue and red ornaments.  It is guaranteed that it is possible to choose at least $$$6$$$ ($$$1+2+3=6$$$) ornaments.", "output_spec": "Print one number — the maximum number of ornaments that can be used. ", "sample_inputs": ["8 13 9", "13 3 6"], "sample_outputs": ["24", "9"], "notes": "NoteIn the first example, the answer is $$$7+8+9=24$$$.In the second example, the answer is $$$2+3+4=9$$$."}, "src_uid": "03ac8efe10de17590e1ae151a7bae1a5"}
{"nl": {"description": "A string is called bracket sequence if it does not contain any characters other than \"(\" and \")\". A bracket sequence is called regular if it it is possible to obtain correct arithmetic expression by inserting characters \"+\" and \"1\" into this sequence. For example, \"\", \"(())\" and \"()()\" are regular bracket sequences; \"))\" and \")((\" are bracket sequences (but not regular ones), and \"(a)\" and \"(1)+(1)\" are not bracket sequences at all.You have a number of strings; each string is a bracket sequence of length $$$2$$$. So, overall you have $$$cnt_1$$$ strings \"((\", $$$cnt_2$$$ strings \"()\", $$$cnt_3$$$ strings \")(\" and $$$cnt_4$$$ strings \"))\". You want to write all these strings in some order, one after another; after that, you will get a long bracket sequence of length $$$2(cnt_1 + cnt_2 + cnt_3 + cnt_4)$$$. You wonder: is it possible to choose some order of the strings you have such that you will get a regular bracket sequence? Note that you may not remove any characters or strings, and you may not add anything either.", "input_spec": "The input consists of four lines, $$$i$$$-th of them contains one integer $$$cnt_i$$$ ($$$0 \\le cnt_i \\le 10^9$$$).", "output_spec": "Print one integer: $$$1$$$ if it is possible to form a regular bracket sequence by choosing the correct order of the given strings, $$$0$$$ otherwise.", "sample_inputs": ["3\n1\n4\n3", "0\n0\n0\n0", "1\n2\n3\n4"], "sample_outputs": ["1", "1", "0"], "notes": "NoteIn the first example it is possible to construct a string \"(())()(()((()()()())))\", which is a regular bracket sequence.In the second example it is possible to construct a string \"\", which is a regular bracket sequence."}, "src_uid": "b99578086043537297d374dc01eeb6f8"}
{"nl": {"description": "Dreamoon wants to climb up a stair of n steps. He can climb 1 or 2 steps at each move. Dreamoon wants the number of moves to be a multiple of an integer m. What is the minimal number of moves making him climb to the top of the stairs that satisfies his condition?", "input_spec": "The single line contains two space separated integers n, m (0 < n ≤ 10000, 1 < m ≤ 10).", "output_spec": "Print a single integer — the minimal number of moves being a multiple of m. If there is no way he can climb satisfying condition print  - 1 instead.", "sample_inputs": ["10 2", "3 5"], "sample_outputs": ["6", "-1"], "notes": "NoteFor the first sample, Dreamoon could climb in 6 moves with following sequence of steps: {2, 2, 2, 2, 1, 1}.For the second sample, there are only three valid sequence of steps {2, 1}, {1, 2}, {1, 1, 1} with 2, 2, and 3 steps respectively. All these numbers are not multiples of 5."}, "src_uid": "0fa526ebc0b4fa3a5866c7c5b3a4656f"}
{"nl": {"description": "Mishka is decorating the Christmas tree. He has got three garlands, and all of them will be put on the tree. After that Mishka will switch these garlands on.When a garland is switched on, it periodically changes its state — sometimes it is lit, sometimes not. Formally, if i-th garland is switched on during x-th second, then it is lit only during seconds x, x + ki, x + 2ki, x + 3ki and so on.Mishka wants to switch on the garlands in such a way that during each second after switching the garlands on there would be at least one lit garland. Formally, Mishka wants to choose three integers x1, x2 and x3 (not necessarily distinct) so that he will switch on the first garland during x1-th second, the second one — during x2-th second, and the third one — during x3-th second, respectively, and during each second starting from max(x1, x2, x3) at least one garland will be lit.Help Mishka by telling him if it is possible to do this!", "input_spec": "The first line contains three integers k1, k2 and k3 (1 ≤ ki ≤ 1500) — time intervals of the garlands.", "output_spec": "If Mishka can choose moments of time to switch on the garlands in such a way that each second after switching the garlands on at least one garland will be lit, print YES. Otherwise, print NO.", "sample_inputs": ["2 2 3", "4 2 3"], "sample_outputs": ["YES", "NO"], "notes": "NoteIn the first example Mishka can choose x1 = 1, x2 = 2, x3 = 1. The first garland will be lit during seconds 1, 3, 5, 7, ..., the second — 2, 4, 6, 8, ..., which already cover all the seconds after the 2-nd one. It doesn't even matter what x3 is chosen. Our choice will lead third to be lit during seconds 1, 4, 7, 10, ..., though.In the second example there is no way to choose such moments of time, there always be some seconds when no garland is lit."}, "src_uid": "df48af9f5e68cb6efc1214f7138accf9"}
{"nl": {"description": "Captain Bill the Hummingbird and his crew recieved an interesting challenge offer. Some stranger gave them a map, potion of teleportation and said that only this potion might help them to reach the treasure. Bottle with potion has two values x and y written on it. These values define four moves which can be performed using the potion:         Map shows that the position of Captain Bill the Hummingbird is (x1, y1) and the position of the treasure is (x2, y2).You task is to tell Captain Bill the Hummingbird whether he should accept this challenge or decline. If it is possible for Captain to reach the treasure using the potion then output \"YES\", otherwise \"NO\" (without quotes).The potion can be used infinite amount of times.", "input_spec": "The first line contains four integer numbers x1, y1, x2, y2 ( - 105 ≤ x1, y1, x2, y2 ≤ 105) — positions of Captain Bill the Hummingbird and treasure respectively. The second line contains two integer numbers x, y (1 ≤ x, y ≤ 105) — values on the potion bottle.", "output_spec": "Print \"YES\" if it is possible for Captain to reach the treasure using the potion, otherwise print \"NO\" (without quotes).", "sample_inputs": ["0 0 0 6\n2 3", "1 1 3 6\n1 5"], "sample_outputs": ["YES", "NO"], "notes": "NoteIn the first example there exists such sequence of moves:   — the first type of move   — the third type of move "}, "src_uid": "1c80040104e06c9f24abfcfe654a851f"}
{"nl": {"description": "On the math lesson a teacher asked each pupil to come up with his own lucky numbers. As a fan of number theory Peter chose prime numbers. Bob was more original. He said that number t is his lucky number, if it can be represented as: t = a2 + b2,  where a, b are arbitrary positive integers.Now, the boys decided to find out how many days of the interval [l, r] (l ≤ r) are suitable for pair programming. They decided that the day i (l ≤ i ≤ r) is suitable for pair programming if and only if the number i is lucky for Peter and lucky for Bob at the same time. Help the boys to find the number of such days.", "input_spec": "The first line of the input contains integer numbers l, r (1 ≤ l, r ≤ 3·108).", "output_spec": "In the only line print the number of days on the segment [l, r], which are lucky for Peter and Bob at the same time.", "sample_inputs": ["3 5", "6 66"], "sample_outputs": ["1", "7"], "notes": null}, "src_uid": "55a83526c10126ac3a6e6e5154b120d0"}
{"nl": {"description": "A bus moves along the coordinate line Ox from the point x = 0 to the point x = a. After starting from the point x = 0, it reaches the point x = a, immediately turns back and then moves to the point x = 0. After returning to the point x = 0 it immediately goes back to the point x = a and so on. Thus, the bus moves from x = 0 to x = a and back. Moving from the point x = 0 to x = a or from the point x = a to x = 0 is called a bus journey. In total, the bus must make k journeys.The petrol tank of the bus can hold b liters of gasoline. To pass a single unit of distance the bus needs to spend exactly one liter of gasoline. The bus starts its first journey with a full petrol tank.There is a gas station in point x = f. This point is between points x = 0 and x = a. There are no other gas stations on the bus route. While passing by a gas station in either direction the bus can stop and completely refuel its tank. Thus, after stopping to refuel the tank will contain b liters of gasoline.What is the minimum number of times the bus needs to refuel at the point x = f to make k journeys? The first journey starts in the point x = 0.", "input_spec": "The first line contains four integers a, b, f, k (0 < f < a ≤ 106, 1 ≤ b ≤ 109, 1 ≤ k ≤ 104) — the endpoint of the first bus journey, the capacity of the fuel tank of the bus, the point where the gas station is located, and the required number of journeys.", "output_spec": "Print the minimum number of times the bus needs to refuel to make k journeys. If it is impossible for the bus to make k journeys, print -1.", "sample_inputs": ["6 9 2 4", "6 10 2 4", "6 5 4 3"], "sample_outputs": ["4", "2", "-1"], "notes": "NoteIn the first example the bus needs to refuel during each journey.In the second example the bus can pass 10 units of distance without refueling. So the bus makes the whole first journey, passes 4 units of the distance of the second journey and arrives at the point with the gas station. Then it can refuel its tank, finish the second journey and pass 2 units of distance from the third journey. In this case, it will again arrive at the point with the gas station. Further, he can refill the tank up to 10 liters to finish the third journey and ride all the way of the fourth journey. At the end of the journey the tank will be empty. In the third example the bus can not make all 3 journeys because if it refuels during the second journey, the tanks will contain only 5 liters of gasoline, but the bus needs to pass 8 units of distance until next refueling."}, "src_uid": "283aff24320c6518e8518d4b045e1eca"}