{"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": "Greg has a pad. The pad's screen is an n × m rectangle, each cell can be either black or white. We'll consider the pad rows to be numbered with integers from 1 to n from top to bottom. Similarly, the pad's columns are numbered with integers from 1 to m from left to right.Greg thinks that the pad's screen displays a cave if the following conditions hold:  There is a segment [l, r] (1 ≤ l ≤ r ≤ n), such that each of the rows l, l + 1, ..., r has exactly two black cells and all other rows have only white cells.  There is a row number t (l ≤ t ≤ r), such that for all pairs of rows with numbers i and j (l ≤ i ≤ j ≤ t) the set of columns between the black cells in row i (with the columns where is these black cells) is the subset of the set of columns between the black cells in row j (with the columns where is these black cells). Similarly, for all pairs of rows with numbers i and j (t ≤ i ≤ j ≤ r) the set of columns between the black cells in row j (with the columns where is these black cells) is the subset of the set of columns between the black cells in row i (with the columns where is these black cells). Greg wondered, how many ways there are to paint a cave on his pad. Two ways can be considered distinct if there is a cell that has distinct colors on the two pictures.Help Greg.", "input_spec": "The first line contains two integers n, m — the pad's screen size (1 ≤ n, m ≤ 2000).", "output_spec": "In the single line print the remainder after dividing the answer to the problem by 1000000007 (109 + 7).", "sample_inputs": ["1 1", "4 4", "3 5"], "sample_outputs": ["0", "485", "451"], "notes": null}, "src_uid": "9ca1ad2fa16ca81e9ab5eba220b162c1"}
{"nl": {"description": "Student Andrey has been skipping physical education lessons for the whole term, and now he must somehow get a passing grade on this subject. Obviously, it is impossible to do this by legal means, but Andrey doesn't give up. Having obtained an empty certificate from a local hospital, he is going to use his knowledge of local doctor's handwriting to make a counterfeit certificate of illness. However, after writing most of the certificate, Andrey suddenly discovered that doctor's signature is impossible to forge. Or is it?For simplicity, the signature is represented as an $$$n\\times m$$$ grid, where every cell is either filled with ink or empty. Andrey's pen can fill a $$$3\\times3$$$ square without its central cell if it is completely contained inside the grid, as shown below. xxxx.xxxx Determine whether is it possible to forge the signature on an empty $$$n\\times m$$$ grid.", "input_spec": "The first line of input contains two integers $$$n$$$ and $$$m$$$ ($$$3 \\le n, m \\le 1000$$$). Then $$$n$$$ lines follow, each contains $$$m$$$ characters. Each of the characters is either '.', representing an empty cell, or '#', representing an ink filled cell.", "output_spec": "If Andrey can forge the signature, output \"YES\". Otherwise output \"NO\". You can print each letter in any case (upper or lower).", "sample_inputs": ["3 3\n###\n#.#\n###", "3 3\n###\n###\n###", "4 3\n###\n###\n###\n###", "5 7\n.......\n.#####.\n.#.#.#.\n.#####.\n......."], "sample_outputs": ["YES", "NO", "YES", "YES"], "notes": "NoteIn the first sample Andrey can paint the border of the square with the center in $$$(2, 2)$$$.In the second sample the signature is impossible to forge.In the third sample Andrey can paint the borders of the squares with the centers in $$$(2, 2)$$$ and $$$(3, 2)$$$:   we have a clear paper: ............  use the pen with center at $$$(2, 2)$$$. ####.####...  use the pen with center at $$$(3, 2)$$$. ############ In the fourth sample Andrey can paint the borders of the squares with the centers in $$$(3, 3)$$$ and $$$(3, 5)$$$."}, "src_uid": "49e5eabe8d69b3d27a251cccc001ab25"}
{"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": "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": "Karen is getting ready for a new school day!  It is currently hh:mm, given in a 24-hour format. As you know, Karen loves palindromes, and she believes that it is good luck to wake up when the time is a palindrome.What is the minimum number of minutes she should sleep, such that, when she wakes up, the time is a palindrome?Remember that a palindrome is a string that reads the same forwards and backwards. For instance, 05:39 is not a palindrome, because 05:39 backwards is 93:50. On the other hand, 05:50 is a palindrome, because 05:50 backwards is 05:50.", "input_spec": "The first and only line of input contains a single string in the format hh:mm (00 ≤  hh  ≤ 23, 00 ≤  mm  ≤ 59).", "output_spec": "Output a single integer on a line by itself, the minimum number of minutes she should sleep, such that, when she wakes up, the time is a palindrome.", "sample_inputs": ["05:39", "13:31", "23:59"], "sample_outputs": ["11", "0", "1"], "notes": "NoteIn the first test case, the minimum number of minutes Karen should sleep for is 11. She can wake up at 05:50, when the time is a palindrome.In the second test case, Karen can wake up immediately, as the current time, 13:31, is already a palindrome.In the third test case, the minimum number of minutes Karen should sleep for is 1 minute. She can wake up at 00:00, when the time is a palindrome."}, "src_uid": "3ad3b8b700f6f34b3a53fdb63af351a5"}
{"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": "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": "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": "Students in a class are making towers of blocks. Each student makes a (non-zero) tower by stacking pieces lengthwise on top of each other. n of the students use pieces made of two blocks and m of the students use pieces made of three blocks.The students don’t want to use too many blocks, but they also want to be unique, so no two students’ towers may contain the same number of blocks. Find the minimum height necessary for the tallest of the students' towers.", "input_spec": "The first line of the input contains two space-separated integers n and m (0 ≤ n, m ≤ 1 000 000, n + m > 0) — the number of students using two-block pieces and the number of students using three-block pieces, respectively.", "output_spec": "Print a single integer, denoting the minimum possible height of the tallest tower.", "sample_inputs": ["1 3", "3 2", "5 0"], "sample_outputs": ["9", "8", "10"], "notes": "NoteIn the first case, the student using two-block pieces can make a tower of height 4, and the students using three-block pieces can make towers of height 3, 6, and 9 blocks. The tallest tower has a height of 9 blocks.In the second case, the students can make towers of heights 2, 4, and 8 with two-block pieces and towers of heights 3 and 6 with three-block pieces, for a maximum height of 8 blocks."}, "src_uid": "23f2c8cac07403899199abdcfd947a5a"}
{"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": "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": "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": "You are given a bracket sequence $$$s$$$ (not necessarily a regular one). A bracket sequence is a string containing only characters '(' and ')'.A regular bracket sequence is a bracket sequence that can be transformed into a correct arithmetic expression by inserting characters '1' and '+' between the original characters of the sequence. For example, bracket sequences \"()()\" and \"(())\" are regular (the resulting expressions are: \"(1)+(1)\" and \"((1+1)+1)\"), and \")(\", \"(\" and \")\" are not.Your problem is to calculate the number of regular bracket sequences of length $$$2n$$$ containing the given bracket sequence $$$s$$$ as a substring (consecutive sequence of characters) modulo $$$10^9+7$$$ ($$$1000000007$$$).", "input_spec": "The first line of the input contains one integer $$$n$$$ ($$$1 \\le n \\le 100$$$) — the half-length of the resulting regular bracket sequences (the resulting sequences must have length equal to $$$2n$$$). The second line of the input contains one string $$$s$$$ ($$$1 \\le |s| \\le 200$$$) — the string $$$s$$$ that should be a substring in each of the resulting regular bracket sequences ($$$|s|$$$ is the length of $$$s$$$).", "output_spec": "Print only one integer — the number of regular bracket sequences containing the given bracket sequence $$$s$$$ as a substring. Since this number can be huge, print it modulo $$$10^9+7$$$ ($$$1000000007$$$).", "sample_inputs": ["5\n()))()", "3\n(()", "2\n((("], "sample_outputs": ["5", "4", "0"], "notes": "NoteAll regular bracket sequences satisfying the conditions above for the first example:   \"(((()))())\";  \"((()()))()\";  \"((()))()()\";  \"(()(()))()\";  \"()((()))()\". All regular bracket sequences satisfying the conditions above for the second example:   \"((()))\";  \"(()())\";  \"(())()\";  \"()(())\". And there is no regular bracket sequences of length $$$4$$$ containing \"(((\" as a substring in the third example."}, "src_uid": "590a49a7af0eb83376ed911ed488d7e5"}
{"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": "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": "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": "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": "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": "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": "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": "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": "Iahub isn't well prepared on geometry problems, but he heard that this year there will be a lot of geometry problems on the IOI selection camp. Scared, Iahub locked himself in the basement and started thinking of new problems of this kind. One of them is the following.Iahub wants to draw n distinct points and m segments on the OX axis. He can draw each point with either red or blue. The drawing is good if and only if the following requirement is met: for each segment [li, ri] consider all the red points belong to it (ri points), and all the blue points belong to it (bi points); each segment i should satisfy the inequality |ri - bi| ≤ 1.Iahub thinks that point x belongs to segment [l, r], if inequality l ≤ x ≤ r holds.Iahub gives to you all coordinates of points and segments. Please, help him to find any good drawing.", "input_spec": "The first line of input contains two integers: n (1 ≤ n ≤ 100) and m (1 ≤ m ≤ 100). The next line contains n space-separated integers x1, x2, ..., xn (0 ≤ xi ≤ 100) — the coordinates of the points. The following m lines contain the descriptions of the m segments. Each line contains two integers li and ri (0 ≤ li ≤ ri ≤ 100) — the borders of the i-th segment. It's guaranteed that all the points are distinct.", "output_spec": "If there is no good drawing for a given test, output a single integer -1. Otherwise output n integers, each integer must be 0 or 1. The i-th number denotes the color of the i-th point (0 is red, and 1 is blue). If there are multiple good drawings you can output any of them.", "sample_inputs": ["3 3\n3 7 14\n1 5\n6 10\n11 15", "3 4\n1 2 3\n1 2\n2 3\n5 6\n2 2"], "sample_outputs": ["0 0 0", "1 0 1"], "notes": null}, "src_uid": "692698d4b49ad446984f3a7a631f961d"}
{"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": "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": "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": "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": "«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": "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": "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": "Berland.Taxi is a new taxi company with k cars which started operating in the capital of Berland just recently. The capital has n houses on a straight line numbered from 1 (leftmost) to n (rightmost), and the distance between any two neighboring houses is the same.You have to help the company schedule all the taxi rides which come throughout the day according to the following rules:   All cars are available for picking up passengers. Initially the j-th car is located next to the house with the number xj at time 0.  All cars have the same speed. It takes exactly 1 minute for any car to travel between neighboring houses i and i + 1.  The i-th request for taxi ride comes at the time ti, asking for a passenger to be picked up at the house ai and dropped off at the house bi. All requests for taxi rides are given in the increasing order of ti. All ti are distinct. When a request for taxi ride is received at time ti, Berland.Taxi operator assigns a car to it as follows:   Out of cars which are currently available, operator assigns the car which is the closest to the pick up spot ai. Needless to say, if a car is already on a ride with a passenger, it won't be available for any rides until that passenger is dropped off at the corresponding destination.  If there are several such cars, operator will pick one of them which has been waiting the most since it became available.  If there are several such cars, operator will pick one of them which has the lowest number. After a car gets assigned to the taxi ride request:   The driver immediately starts driving from current position to the house ai.  Once the car reaches house ai, the passenger is immediately picked up and the driver starts driving to house bi.  Once house bi is reached, the passenger gets dropped off and the car becomes available for new rides staying next to the house bi.  It is allowed for multiple cars to be located next to the same house at the same point in time, while waiting for ride requests or just passing by. If there are no available cars at time ti when a request for taxi ride comes, then:   The i-th passenger will have to wait for a car to become available.  When a car becomes available, operator will immediately assign it to this taxi ride request.  If multiple cars become available at once while the passenger is waiting, operator will pick a car out of them according to the rules described above. Operator processes taxi ride requests one by one. So if multiple passengers are waiting for the cars to become available, operator will not move on to processing the (i + 1)-th ride request until the car gets assigned to the i-th ride request.Your task is to write a program that will process the given list of m taxi ride requests. For each request you have to find out which car will get assigned to it, and how long the passenger will have to wait for a car to arrive. Note, if there is already car located at the house ai, then the corresponding wait time will be 0.", "input_spec": "The first line of input contains integers n, k and m (2 ≤ n ≤ 2·105, 1 ≤ k, m ≤ 2·105) — number of houses, number of cars, and number of taxi ride requests. The second line contains integers x1, x2, ..., xk (1 ≤ xi ≤ n) — initial positions of cars. xi is a house number at which the i-th car is located initially. It's allowed for more than one car to be located next to the same house. The following m lines contain information about ride requests. Each ride request is represented by integers tj, aj and bj (1 ≤ tj ≤ 1012, 1 ≤ aj, bj ≤ n, aj ≠ bj), where tj is time in minutes when a request is made, aj is a house where passenger needs to be picked up, and bj is a house where passenger needs to be dropped off. All taxi ride requests are given in the increasing order of tj. All tj are distinct.", "output_spec": "Print m lines: the j-th line should contain two integer numbers, the answer for the j-th ride request — car number assigned by the operator and passenger wait time.", "sample_inputs": ["10 1 2\n3\n5 2 8\n9 10 3", "5 2 1\n1 5\n10 3 5", "5 2 2\n1 5\n10 3 5\n20 4 1"], "sample_outputs": ["1 1\n1 5", "1 2", "1 2\n2 1"], "notes": "NoteIn the first sample test, a request comes in at time 5 and the car needs to get from house 3 to house 2 to pick up the passenger. Therefore wait time will be 1 and the ride will be completed at time 5 + 1 + 6 = 12. The second request comes in at time 9, so the passenger will have to wait for the car to become available at time 12, and then the car needs another 2 minutes to get from house 8 to house 10. So the total wait time is 3 + 2 = 5. In the second sample test, cars 1 and 2 are located at the same distance from the first passenger and have the same \"wait time since it became available\". Car 1 wins a tiebreaker according to the rules because it has the lowest number. It will come to house 3 at time 3, so the wait time will be 2."}, "src_uid": "cbfed699fd3d4eacfe36e1c064a4448c"}
{"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": "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": "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": "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": "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": "You are given a permutation $$$a_1, a_2, \\dots, a_n$$$ of numbers from $$$1$$$ to $$$n$$$. Also, you have $$$n$$$ sets $$$S_1,S_2,\\dots, S_n$$$, where $$$S_i=\\{a_i\\}$$$. Lastly, you have a variable $$$cnt$$$, representing the current number of sets. Initially, $$$cnt = n$$$.We define two kinds of functions on sets:$$$f(S)=\\min\\limits_{u\\in S} u$$$;$$$g(S)=\\max\\limits_{u\\in S} u$$$.You can obtain a new set by merging two sets $$$A$$$ and $$$B$$$, if they satisfy $$$g(A)<f(B)$$$ (Notice that the old sets do not disappear).Formally, you can perform the following sequence of operations:$$$cnt\\gets cnt+1$$$;$$$S_{cnt}=S_u\\cup S_v$$$, you are free to choose $$$u$$$ and $$$v$$$ for which $$$1\\le u, v < cnt$$$ and which satisfy $$$g(S_u)<f(S_v)$$$.You are required to obtain some specific sets.There are $$$q$$$ requirements, each of which contains two integers $$$l_i$$$,$$$r_i$$$, which means that there must exist a set $$$S_{k_i}$$$ ($$$k_i$$$ is the ID of the set, you should determine it) which equals $$$\\{a_u\\mid l_i\\leq u\\leq r_i\\}$$$, which is, the set consisting of all $$$a_i$$$ with indices between $$$l_i$$$ and $$$r_i$$$.In the end you must ensure that $$$cnt\\leq 2.2\\times 10^6$$$. Note that you don't have to minimize $$$cnt$$$. It is guaranteed that a solution under given constraints exists.", "input_spec": "The first line contains two integers $$$n,q$$$ $$$(1\\leq n \\leq 2^{12},1 \\leq q \\leq 2^{16})$$$  — the length of the permutation and the number of needed sets correspondently. The next line consists of $$$n$$$ integers $$$a_1,a_2,\\cdots, a_n$$$ ($$$1\\leq a_i\\leq n$$$, $$$a_i$$$ are pairwise distinct)  — given permutation. $$$i$$$-th of the next $$$q$$$ lines contains two integers $$$l_i,r_i$$$ $$$(1\\leq l_i\\leq r_i\\leq n)$$$, describing a requirement of the $$$i$$$-th set.", "output_spec": "It is guaranteed that a solution under given constraints exists. The first line should contain one integer $$$cnt_E$$$ $$$(n\\leq cnt_E\\leq 2.2\\times 10^6)$$$, representing the number of sets after all operations. $$$cnt_E-n$$$ lines must follow, each line should contain two integers $$$u$$$, $$$v$$$ ($$$1\\leq u, v\\leq cnt'$$$, where $$$cnt'$$$ is the value of $$$cnt$$$ before this operation), meaning that you choose $$$S_u$$$, $$$S_v$$$ and perform a merging operation. In an operation, $$$g(S_u)<f(S_v)$$$ must be satisfied. The last line should contain $$$q$$$ integers $$$k_1,k_2,\\cdots,k_q$$$ $$$(1\\leq k_i\\leq cnt_E)$$$, representing that set $$$S_{k_i}$$$ is the $$$i$$$th required set. Please notice the large amount of output.", "sample_inputs": ["3 2\n1 3 2\n2 3\n1 3", "2 4\n2 1\n1 2\n1 2\n1 2\n1 1"], "sample_outputs": ["6\n3 2\n1 3\n5 2\n4 6", "5\n2 1\n2 1\n2 1\n5 3 3 1"], "notes": "NoteIn the first sample:We have $$$S_1=\\{1\\},S_2=\\{3\\},S_3=\\{2\\}$$$ initially.In the first operation, because $$$g(S_3)=2<f(S_2)=3$$$, we can merge $$$S_3,S_2$$$ into $$$S_4=\\{2,3\\}$$$.In the second operation, because $$$g(S_1)=1<f(S_3)=2$$$, we can merge $$$S_1,S_3$$$ into $$$S_5=\\{1,2\\}$$$.In the third operation, because $$$g(S_5)=2<f(S_2)=3$$$, we can merge $$$S_5,S_2$$$ into $$$S_6=\\{1,2,3\\}$$$.For the first requirement, $$$S_4=\\{2,3\\}=\\{a_2,a_3\\}$$$, satisfies it, thus $$$k_1=4$$$.For the second requirement, $$$S_6=\\{1,2,3\\}=\\{a_1,a_2,a_3\\}$$$, satisfies it, thus $$$k_2=6$$$Notice that unused sets, identical sets, outputting the same set multiple times, and using sets that are present initially are all allowed."}, "src_uid": "60cf596ad4853ebf3bbf9a96ef5d8791"}
{"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": "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": "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": "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": "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": "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": "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": "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": "Dima loves representing an odd number as the sum of multiple primes, and Lisa loves it when there are at most three primes. Help them to represent the given number as the sum of at most than three primes.More formally, you are given an odd numer n. Find a set of numbers pi (1 ≤ i ≤ k), such that 1 ≤ k ≤ 3 pi is a prime The numbers pi do not necessarily have to be distinct. It is guaranteed that at least one possible solution exists.", "input_spec": "The single line contains an odd number n (3 ≤ n < 109).", "output_spec": "In the first line print k (1 ≤ k ≤ 3), showing how many numbers are in the representation you found. In the second line print numbers pi in any order. If there are multiple possible solutions, you can print any of them.", "sample_inputs": ["27"], "sample_outputs": ["3\n5 11 11"], "notes": "NoteA prime is an integer strictly larger than one that is divisible only by one and by itself."}, "src_uid": "f2aaa149ce81bf332d0b5d80b2a13bc3"}
{"nl": {"description": "Today's morning was exceptionally snowy. Meshanya decided to go outside and noticed a huge snowball rolling down the mountain! Luckily, there are two stones on that mountain.Initially, snowball is at height $$$h$$$ and it has weight $$$w$$$. Each second the following sequence of events happens: snowball's weights increases by $$$i$$$, where $$$i$$$ — is the current height of snowball, then snowball hits the stone (if it's present at the current height), then snowball moves one meter down. If the snowball reaches height zero, it stops.There are exactly two stones on the mountain. First stone has weight $$$u_1$$$ and is located at height $$$d_1$$$, the second one — $$$u_2$$$ and $$$d_2$$$ respectively. When the snowball hits either of two stones, it loses weight equal to the weight of that stone. If after this snowball has negative weight, then its weight becomes zero, but the snowball continues moving as before.  Find the weight of the snowball when it stops moving, that is, it reaches height 0.", "input_spec": "First line contains two integers $$$w$$$ and $$$h$$$ — initial weight and height of the snowball ($$$0 \\le w \\le 100$$$; $$$1 \\le h \\le 100$$$). Second line contains two integers $$$u_1$$$ and $$$d_1$$$ — weight and height of the first stone ($$$0 \\le u_1 \\le 100$$$; $$$1 \\le d_1 \\le h$$$). Third line contains two integers $$$u_2$$$ and $$$d_2$$$ — weight and heigth of the second stone ($$$0 \\le u_2 \\le 100$$$; $$$1 \\le d_2 \\le h$$$; $$$d_1 \\ne d_2$$$). Notice that stones always have different heights.", "output_spec": "Output a single integer — final weight of the snowball after it reaches height 0.", "sample_inputs": ["4 3\n1 1\n1 2", "4 3\n9 2\n0 1"], "sample_outputs": ["8", "1"], "notes": "NoteIn the first example, initially a snowball of weight 4 is located at a height of 3, there are two stones of weight 1, at a height of 1 and 2, respectively. The following events occur sequentially:   The weight of the snowball increases by 3 (current height), becomes equal to 7.  The snowball moves one meter down, the current height becomes equal to 2.  The weight of the snowball increases by 2 (current height), becomes equal to 9.  The snowball hits the stone, its weight decreases by 1 (the weight of the stone), becomes equal to 8.  The snowball moves one meter down, the current height becomes equal to 1.  The weight of the snowball increases by 1 (current height), becomes equal to 9.  The snowball hits the stone, its weight decreases by 1 (the weight of the stone), becomes equal to 8.  The snowball moves one meter down, the current height becomes equal to 0. Thus, at the end the weight of the snowball is equal to 8."}, "src_uid": "084a12eb3a708b43b880734f3ee51374"}
{"nl": {"description": "When preparing a tournament, Codeforces coordinators try treir best to make the first problem as easy as possible. This time the coordinator had chosen some problem and asked $$$n$$$ people about their opinions. Each person answered whether this problem is easy or hard.If at least one of these $$$n$$$ people has answered that the problem is hard, the coordinator decides to change the problem. For the given responses, check if the problem is easy enough.", "input_spec": "The first line contains a single integer $$$n$$$ ($$$1 \\le n \\le 100$$$) — the number of people who were asked to give their opinions. The second line contains $$$n$$$ integers, each integer is either $$$0$$$ or $$$1$$$. If $$$i$$$-th integer is $$$0$$$, then $$$i$$$-th person thinks that the problem is easy; if it is $$$1$$$, then $$$i$$$-th person thinks that the problem is hard.", "output_spec": "Print one word: \"EASY\" if the problem is easy according to all responses, or \"HARD\" if there is at least one person who thinks the problem is hard.  You may print every letter in any register: \"EASY\", \"easy\", \"EaSY\" and \"eAsY\" all will be processed correctly.", "sample_inputs": ["3\n0 0 1", "1\n0"], "sample_outputs": ["HARD", "EASY"], "notes": "NoteIn the first example the third person says it's a hard problem, so it should be replaced.In the second example the problem easy for the only person, so it doesn't have to be replaced."}, "src_uid": "060406cd57739d929f54b4518a7ba83e"}
{"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": "You are given a positive integer n. Let's build a graph on vertices 1, 2, ..., n in such a way that there is an edge between vertices u and v if and only if . Let d(u, v) be the shortest distance between u and v, or 0 if there is no path between them. Compute the sum of values d(u, v) over all 1 ≤ u < v ≤ n.The gcd (greatest common divisor) of two positive integers is the maximum positive integer that divides both of the integers.", "input_spec": "Single integer n (1 ≤ n ≤ 107).", "output_spec": "Print the sum of d(u, v) over all 1 ≤ u < v ≤ n.", "sample_inputs": ["6", "10"], "sample_outputs": ["8", "44"], "notes": "NoteAll shortest paths in the first example:              There are no paths between other pairs of vertices.The total distance is 2 + 1 + 1 + 2 + 1 + 1 = 8."}, "src_uid": "bb1bd5d8bab7d79e514281230d484996"}
{"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": "Welcome to Codeforces Stock Exchange! We're pretty limited now as we currently allow trading on one stock, Codeforces Ltd. We hope you'll still be able to make profit from the market!In the morning, there are $$$n$$$ opportunities to buy shares. The $$$i$$$-th of them allows to buy as many shares as you want, each at the price of $$$s_i$$$ bourles.In the evening, there are $$$m$$$ opportunities to sell shares. The $$$i$$$-th of them allows to sell as many shares as you want, each at the price of $$$b_i$$$ bourles. You can't sell more shares than you have.It's morning now and you possess $$$r$$$ bourles and no shares.What is the maximum number of bourles you can hold after the evening?", "input_spec": "The first line of the input contains three integers $$$n, m, r$$$ ($$$1 \\leq n \\leq 30$$$, $$$1 \\leq m \\leq 30$$$, $$$1 \\leq r \\leq 1000$$$) — the number of ways to buy the shares on the market, the number of ways to sell the shares on the market, and the number of bourles you hold now. The next line contains $$$n$$$ integers $$$s_1, s_2, \\dots, s_n$$$ ($$$1 \\leq s_i \\leq 1000$$$); $$$s_i$$$ indicates the opportunity to buy shares at the price of $$$s_i$$$ bourles. The following line contains $$$m$$$ integers $$$b_1, b_2, \\dots, b_m$$$ ($$$1 \\leq b_i \\leq 1000$$$); $$$b_i$$$ indicates the opportunity to sell shares at the price of $$$b_i$$$ bourles.", "output_spec": "Output a single integer — the maximum number of bourles you can hold after the evening.", "sample_inputs": ["3 4 11\n4 2 5\n4 4 5 4", "2 2 50\n5 7\n4 2"], "sample_outputs": ["26", "50"], "notes": "NoteIn the first example test, you have $$$11$$$ bourles in the morning. It's optimal to buy $$$5$$$ shares of a stock at the price of $$$2$$$ bourles in the morning, and then to sell all of them at the price of $$$5$$$ bourles in the evening. It's easy to verify that you'll have $$$26$$$ bourles after the evening.In the second example test, it's optimal not to take any action."}, "src_uid": "42f25d492bddc12d3d89d39315d63cb9"}
{"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": "Let's introduce a number system which is based on a roman digits. There are digits I, V, X, L which correspond to the numbers $$$1$$$, $$$5$$$, $$$10$$$ and $$$50$$$ respectively. The use of other roman digits is not allowed.Numbers in this system are written as a sequence of one or more digits. We define the value of the sequence simply as the sum of digits in it.For example, the number XXXV evaluates to $$$35$$$ and the number IXI — to $$$12$$$.Pay attention to the difference to the traditional roman system — in our system any sequence of digits is valid, moreover the order of digits doesn't matter, for example IX means $$$11$$$, not $$$9$$$.One can notice that this system is ambiguous, and some numbers can be written in many different ways. Your goal is to determine how many distinct integers can be represented by exactly $$$n$$$ roman digits I, V, X, L.", "input_spec": "The only line of the input file contains a single integer $$$n$$$ ($$$1 \\le n \\le 10^9$$$) — the number of roman digits to use.", "output_spec": "Output a single integer — the number of distinct integers which can be represented using $$$n$$$ roman digits exactly.", "sample_inputs": ["1", "2", "10"], "sample_outputs": ["4", "10", "244"], "notes": "NoteIn the first sample there are exactly $$$4$$$ integers which can be represented — I, V, X and L.In the second sample it is possible to represent integers $$$2$$$ (II), $$$6$$$ (VI), $$$10$$$ (VV), $$$11$$$ (XI), $$$15$$$ (XV), $$$20$$$ (XX), $$$51$$$ (IL), $$$55$$$ (VL), $$$60$$$ (XL) and $$$100$$$ (LL)."}, "src_uid": "75ec99318736a8a1b62a8d51efd95355"}
{"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 an integer sequence $$$1, 2, \\dots, n$$$. You have to divide it into two sets $$$A$$$ and $$$B$$$ in such a way that each element belongs to exactly one set and $$$|sum(A) - sum(B)|$$$ is minimum possible.The value $$$|x|$$$ is the absolute value of $$$x$$$ and $$$sum(S)$$$ is the sum of elements of the set $$$S$$$.", "input_spec": "The first line of the input contains one integer $$$n$$$ ($$$1 \\le n \\le 2 \\cdot 10^9$$$).", "output_spec": "Print one integer — the minimum possible value of $$$|sum(A) - sum(B)|$$$ if you divide the initial sequence $$$1, 2, \\dots, n$$$ into two sets $$$A$$$ and $$$B$$$.", "sample_inputs": ["3", "5", "6"], "sample_outputs": ["0", "1", "1"], "notes": "NoteSome (not all) possible answers to examples:In the first example you can divide the initial sequence into sets $$$A = \\{1, 2\\}$$$ and $$$B = \\{3\\}$$$ so the answer is $$$0$$$.In the second example you can divide the initial sequence into sets $$$A = \\{1, 3, 4\\}$$$ and $$$B = \\{2, 5\\}$$$ so the answer is $$$1$$$.In the third example you can divide the initial sequence into sets $$$A = \\{1, 4, 5\\}$$$ and $$$B = \\{2, 3, 6\\}$$$ so the answer is $$$1$$$."}, "src_uid": "fa163c5b619d3892e33e1fb9c22043a9"}
{"nl": {"description": "Monocarp is playing a video game. In the game, he controls a spaceship and has to destroy an enemy spaceship.Monocarp has two lasers installed on his spaceship. Both lasers $$$1$$$ and $$$2$$$ have two values:   $$$p_i$$$ — the power of the laser;  $$$t_i$$$ — the reload time of the laser. When a laser is fully charged, Monocarp can either shoot it or wait for the other laser to charge and shoot both of them at the same time.An enemy spaceship has $$$h$$$ durability and $$$s$$$ shield capacity. When Monocarp shoots an enemy spaceship, it receives $$$(P - s)$$$ damage (i. e. $$$(P - s)$$$ gets subtracted from its durability), where $$$P$$$ is the total power of the lasers that Monocarp shoots (i. e. $$$p_i$$$ if he only shoots laser $$$i$$$ and $$$p_1 + p_2$$$ if he shoots both lasers at the same time). An enemy spaceship is considered destroyed when its durability becomes $$$0$$$ or lower.Initially, both lasers are zero charged.What's the lowest amount of time it can take Monocarp to destroy an enemy spaceship?", "input_spec": "The first line contains two integers $$$p_1$$$ and $$$t_1$$$ ($$$2 \\le p_1 \\le 5000$$$; $$$1 \\le t_1 \\le 10^{12}$$$) — the power and the reload time of the first laser. The second line contains two integers $$$p_2$$$ and $$$t_2$$$ ($$$2 \\le p_2 \\le 5000$$$; $$$1 \\le t_2 \\le 10^{12}$$$) — the power and the reload time of the second laser. The third line contains two integers $$$h$$$ and $$$s$$$ ($$$1 \\le h \\le 5000$$$; $$$1 \\le s < \\min(p_1, p_2)$$$) — the durability and the shield capacity of an enemy spaceship. Note that the last constraint implies that Monocarp will always be able to destroy an enemy spaceship.", "output_spec": "Print a single integer — the lowest amount of time it can take Monocarp to destroy an enemy spaceship.", "sample_inputs": ["5 10\n4 9\n16 1", "10 1\n5000 100000\n25 9"], "sample_outputs": ["20", "25"], "notes": "NoteIn the first example, Monocarp waits for both lasers to charge, then shoots both lasers at $$$10$$$, they deal $$$(5 + 4 - 1) = 8$$$ damage. Then he waits again and shoots lasers at $$$20$$$, dealing $$$8$$$ more damage.In the second example, Monocarp doesn't wait for the second laser to charge. He just shoots the first laser $$$25$$$ times, dealing $$$(10 - 9) = 1$$$ damage each time."}, "src_uid": "ca9d48e48e69b931236907a9ac262433"}
{"nl": {"description": "Vasya has n pairs of socks. In the morning of each day Vasya has to put on a pair of socks before he goes to school. When he comes home in the evening, Vasya takes off the used socks and throws them away. Every m-th day (at days with numbers m, 2m, 3m, ...) mom buys a pair of socks to Vasya. She does it late in the evening, so that Vasya cannot put on a new pair of socks before the next day. How many consecutive days pass until Vasya runs out of socks?", "input_spec": "The single line contains two integers n and m (1 ≤ n ≤ 100; 2 ≤ m ≤ 100), separated by a space.", "output_spec": "Print a single integer — the answer to the problem.", "sample_inputs": ["2 2", "9 3"], "sample_outputs": ["3", "13"], "notes": "NoteIn the first sample Vasya spends the first two days wearing the socks that he had initially. Then on day three he puts on the socks that were bought on day two.In the second sample Vasya spends the first nine days wearing the socks that he had initially. Then he spends three days wearing the socks that were bought on the third, sixth and ninth days. Than he spends another day wearing the socks that were bought on the twelfth day."}, "src_uid": "42b25b7335ec01794fbb1d4086aa9dd0"}
{"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": "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": "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": "Kyoya Ootori is selling photobooks of the Ouran High School Host Club. He has 26 photos, labeled \"a\" to \"z\", and he has compiled them into a photo booklet with some photos in some order (possibly with some photos being duplicated). A photo booklet can be described as a string of lowercase letters, consisting of the photos in the booklet in order. He now wants to sell some \"special edition\" photobooks, each with one extra photo inserted anywhere in the book. He wants to make as many distinct photobooks as possible, so he can make more money. He asks Haruhi, how many distinct photobooks can he make by inserting one extra photo into the photobook he already has?Please help Haruhi solve this problem.", "input_spec": "The first line of input will be a single string s (1 ≤ |s| ≤ 20). String s consists only of lowercase English letters. ", "output_spec": "Output a single integer equal to the number of distinct photobooks Kyoya Ootori can make.", "sample_inputs": ["a", "hi"], "sample_outputs": ["51", "76"], "notes": "NoteIn the first case, we can make 'ab','ac',...,'az','ba','ca',...,'za', and 'aa', producing a total of 51 distinct photo booklets. "}, "src_uid": "556684d96d78264ad07c0cdd3b784bc9"}
{"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": " — 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": "Masha lives in a multi-storey building, where floors are numbered with positive integers. Two floors are called adjacent if their numbers differ by one. Masha decided to visit Egor. Masha lives on the floor $$$x$$$, Egor on the floor $$$y$$$ (not on the same floor with Masha).The house has a staircase and an elevator. If Masha uses the stairs, it takes $$$t_1$$$ seconds for her to walk between adjacent floors (in each direction). The elevator passes between adjacent floors (in each way) in $$$t_2$$$ seconds. The elevator moves with doors closed. The elevator spends $$$t_3$$$ seconds to open or close the doors. We can assume that time is not spent on any action except moving between adjacent floors and waiting for the doors to open or close. If Masha uses the elevator, it immediately goes directly to the desired floor.Coming out of the apartment on her floor, Masha noticed that the elevator is now on the floor $$$z$$$ and has closed doors. Now she has to choose whether to use the stairs or use the elevator. If the time that Masha needs to get to the Egor's floor by the stairs is strictly less than the time it will take her using the elevator, then she will use the stairs, otherwise she will choose the elevator.Help Mary to understand whether to use the elevator or the stairs.", "input_spec": "The only line contains six integers $$$x$$$, $$$y$$$, $$$z$$$, $$$t_1$$$, $$$t_2$$$, $$$t_3$$$ ($$$1 \\leq x, y, z, t_1, t_2, t_3 \\leq 1000$$$) — the floor Masha is at, the floor Masha wants to get to, the floor the elevator is located on, the time it takes Masha to pass between two floors by stairs, the time it takes the elevator to pass between two floors and the time it takes for the elevator to close or open the doors. It is guaranteed that $$$x \\ne y$$$.", "output_spec": "If the time it will take to use the elevator is not greater than the time it will take to use the stairs, print «YES» (without quotes), otherwise print «NO> (without quotes). You can print each letter in any case (upper or lower).", "sample_inputs": ["5 1 4 4 2 1", "1 6 6 2 1 1", "4 1 7 4 1 2"], "sample_outputs": ["YES", "NO", "YES"], "notes": "NoteIn the first example:If Masha goes by the stairs, the time she spends is $$$4 \\cdot 4 = 16$$$, because she has to go $$$4$$$ times between adjacent floors and each time she spends $$$4$$$ seconds. If she chooses the elevator, she will have to wait $$$2$$$ seconds while the elevator leaves the $$$4$$$-th floor and goes to the $$$5$$$-th. After that the doors will be opening for another $$$1$$$ second. Then Masha will enter the elevator, and she will have to wait for $$$1$$$ second for the doors closing. Next, the elevator will spend $$$4 \\cdot 2 = 8$$$ seconds going from the $$$5$$$-th floor to the $$$1$$$-st, because the elevator has to pass $$$4$$$ times between adjacent floors and spends $$$2$$$ seconds each time. And finally, it will take another $$$1$$$ second before the doors are open and Masha can come out. Thus, all the way by elevator will take $$$2 + 1 + 1 + 8 + 1 = 13$$$ seconds, which is less than $$$16$$$ seconds, so Masha has to choose the elevator.In the second example, it is more profitable for Masha to use the stairs, because it will take $$$13$$$ seconds to use the elevator, that is more than the $$$10$$$ seconds it will takes to go by foot.In the third example, the time it takes to use the elevator is equal to the time it takes to walk up by the stairs, and is equal to $$$12$$$ seconds. That means Masha will take the elevator."}, "src_uid": "05cffd59b28b9e026ca3203718b2e6ca"}
{"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": "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": "Calendars in widespread use today include the Gregorian calendar, which is the de facto international standard, and is used almost everywhere in the world for civil purposes. The Gregorian reform modified the Julian calendar's scheme of leap years as follows: Every year that is exactly divisible by four is a leap year, except for years that are exactly divisible by 100; the centurial years that are exactly divisible by 400 are still leap years. For example, the year 1900 is not a leap year; the year 2000 is a leap year.   In this problem, you have been given two dates and your task is to calculate how many days are between them. Note, that leap years have unusual number of days in February.Look at the sample to understand what borders are included in the aswer.", "input_spec": "The first two lines contain two dates, each date is in the format yyyy:mm:dd (1900 ≤ yyyy ≤ 2038 and yyyy:mm:dd is a legal date).", "output_spec": "Print a single integer — the answer to the problem.", "sample_inputs": ["1900:01:01\n2038:12:31", "1996:03:09\n1991:11:12"], "sample_outputs": ["50768", "1579"], "notes": null}, "src_uid": "bdf99d78dc291758fa09ec133fff1e9c"}
{"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": "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 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": "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": "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": "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": "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": "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": "It is known that passages in Singer house are complex and intertwined. Let's define a Singer k-house as a graph built by the following process: take complete binary tree of height k and add edges from each vertex to all its successors, if they are not yet present.  Singer 4-house Count the number of non-empty paths in Singer k-house which do not pass the same vertex twice. Two paths are distinct if the sets or the orders of visited vertices are different. Since the answer can be large, output it modulo 109 + 7.", "input_spec": "The only line contains single integer k (1 ≤ k ≤ 400).", "output_spec": "Print single integer — the answer for the task modulo 109 + 7.", "sample_inputs": ["2", "3", "20"], "sample_outputs": ["9", "245", "550384565"], "notes": "NoteThere are 9 paths in the first example (the vertices are numbered on the picture below): 1, 2, 3, 1-2, 2-1, 1-3, 3-1, 2-1-3, 3-1-2.  Singer 2-house "}, "src_uid": "fda761834f7b5800f540178ac1c79fca"}
{"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": "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": "After playing Neo in the legendary \"Matrix\" trilogy, Keanu Reeves started doubting himself: maybe we really live in virtual reality? To find if this is true, he needs to solve the following problem.Let's call a string consisting of only zeroes and ones good if it contains different numbers of zeroes and ones. For example, 1, 101, 0000 are good, while 01, 1001, and 111000 are not good.We are given a string $$$s$$$ of length $$$n$$$ consisting of only zeroes and ones. We need to cut $$$s$$$ into minimal possible number of substrings $$$s_1, s_2, \\ldots, s_k$$$ such that all of them are good. More formally, we have to find minimal by number of strings sequence of good strings $$$s_1, s_2, \\ldots, s_k$$$ such that their concatenation (joining) equals $$$s$$$, i.e. $$$s_1 + s_2 + \\dots + s_k = s$$$.For example, cuttings 110010 into 110 and 010 or into 11 and 0010 are valid, as 110, 010, 11, 0010 are all good, and we can't cut 110010 to the smaller number of substrings as 110010 isn't good itself. At the same time, cutting of 110010 into 1100 and 10 isn't valid as both strings aren't good. Also, cutting of 110010 into 1, 1, 0010 isn't valid, as it isn't minimal, even though all $$$3$$$ strings are good.Can you help Keanu? We can show that the solution always exists. If there are multiple optimal answers, print any.", "input_spec": "The first line of the input contains a single integer $$$n$$$ ($$$1\\le n \\le 100$$$) — the length of the string $$$s$$$. The second line contains the string $$$s$$$ of length $$$n$$$ consisting only from zeros and ones.", "output_spec": "In the first line, output a single integer $$$k$$$ ($$$1\\le k$$$) — a minimal number of strings you have cut $$$s$$$ into. In the second line, output $$$k$$$ strings $$$s_1, s_2, \\ldots, s_k$$$ separated with spaces. The length of each string has to be positive. Their concatenation has to be equal to $$$s$$$ and all of them have to be good. If there are multiple answers, print any.", "sample_inputs": ["1\n1", "2\n10", "6\n100011"], "sample_outputs": ["1\n1", "2\n1 0", "2\n100 011"], "notes": "NoteIn the first example, the string 1 wasn't cut at all. As it is good, the condition is satisfied.In the second example, 1 and 0 both are good. As 10 isn't good, the answer is indeed minimal.In the third example, 100 and 011 both are good. As 100011 isn't good, the answer is indeed minimal."}, "src_uid": "4ebed264d40a449602a26ceef2e849d1"}
{"nl": {"description": "Arpa is researching the Mexican wave.There are n spectators in the stadium, labeled from 1 to n. They start the Mexican wave at time 0.   At time 1, the first spectator stands.  At time 2, the second spectator stands.  ...  At time k, the k-th spectator stands.  At time k + 1, the (k + 1)-th spectator stands and the first spectator sits.  At time k + 2, the (k + 2)-th spectator stands and the second spectator sits.  ...  At time n, the n-th spectator stands and the (n - k)-th spectator sits.  At time n + 1, the (n + 1 - k)-th spectator sits.  ...  At time n + k, the n-th spectator sits. Arpa wants to know how many spectators are standing at time t.", "input_spec": "The first line contains three integers n, k, t (1 ≤ n ≤ 109, 1 ≤ k ≤ n, 1 ≤ t < n + k).", "output_spec": "Print single integer: how many spectators are standing at time t.", "sample_inputs": ["10 5 3", "10 5 7", "10 5 12"], "sample_outputs": ["3", "5", "3"], "notes": "NoteIn the following a sitting spectator is represented as -, a standing spectator is represented as ^.  At t = 0  ----------  number of standing spectators = 0.  At t = 1  ^---------  number of standing spectators = 1.  At t = 2  ^^--------  number of standing spectators = 2.  At t = 3  ^^^-------  number of standing spectators = 3.  At t = 4  ^^^^------  number of standing spectators = 4.  At t = 5  ^^^^^-----  number of standing spectators = 5.  At t = 6  -^^^^^----  number of standing spectators = 5.  At t = 7  --^^^^^---  number of standing spectators = 5.  At t = 8  ---^^^^^--  number of standing spectators = 5.  At t = 9  ----^^^^^-  number of standing spectators = 5.  At t = 10 -----^^^^^  number of standing spectators = 5.  At t = 11 ------^^^^  number of standing spectators = 4.  At t = 12 -------^^^  number of standing spectators = 3.  At t = 13 --------^^  number of standing spectators = 2.  At t = 14 ---------^  number of standing spectators = 1.  At t = 15 ----------  number of standing spectators = 0. "}, "src_uid": "7e614526109a2052bfe7934381e7f6c2"}
{"nl": {"description": "You are given $$$n$$$ pairwise non-collinear two-dimensional vectors. You can make shapes in the two-dimensional plane with these vectors in the following fashion: Start at the origin $$$(0, 0)$$$. Choose a vector and add the segment of the vector to the current point. For example, if your current point is at $$$(x, y)$$$ and you choose the vector $$$(u, v)$$$, draw a segment from your current point to the point at $$$(x + u, y + v)$$$ and set your current point to $$$(x + u, y + v)$$$. Repeat step 2 until you reach the origin again.You can reuse a vector as many times as you want.Count the number of different, non-degenerate (with an area greater than $$$0$$$) and convex shapes made from applying the steps, such that the shape can be contained within a $$$m \\times m$$$ square, and the vectors building the shape are in counter-clockwise fashion. Since this number can be too large, you should calculate it by modulo $$$998244353$$$.Two shapes are considered the same if there exists some parallel translation of the first shape to another.A shape can be contained within a $$$m \\times m$$$ square if there exists some parallel translation of this shape so that every point $$$(u, v)$$$ inside or on the border of the shape satisfies $$$0 \\leq u, v \\leq m$$$.", "input_spec": "The first line contains two integers $$$n$$$ and $$$m$$$  — the number of vectors and the size of the square ($$$1 \\leq n \\leq 5$$$, $$$1 \\leq m \\leq 10^9$$$). Each of the next $$$n$$$ lines contains two integers $$$x_i$$$ and $$$y_i$$$  — the $$$x$$$-coordinate and $$$y$$$-coordinate of the $$$i$$$-th vector ($$$|x_i|, |y_i| \\leq 4$$$, $$$(x_i, y_i) \\neq (0, 0)$$$). It is guaranteed, that no two vectors are parallel, so for any two indices $$$i$$$ and $$$j$$$ such that $$$1 \\leq i < j \\leq n$$$, there is no real value $$$k$$$ such that $$$x_i \\cdot k = x_j$$$ and $$$y_i \\cdot k = y_j$$$.", "output_spec": "Output a single integer  — the number of satisfiable shapes by modulo $$$998244353$$$.", "sample_inputs": ["3 3\n-1 0\n1 1\n0 -1", "3 3\n-1 0\n2 2\n0 -1", "3 1776966\n-1 0\n3 3\n0 -2", "4 15\n-4 -4\n-1 1\n-1 -4\n4 3", "5 10\n3 -4\n4 -3\n1 -3\n2 -3\n-3 -4", "5 1000000000\n-2 4\n2 -3\n0 -4\n2 4\n-1 -3"], "sample_outputs": ["3", "1", "296161", "1", "0", "9248783"], "notes": "NoteThe shapes for the first sample are:  The only shape for the second sample is:  The only shape for the fourth sample is:  "}, "src_uid": "fba104bc43111a6f2692216a4edea2bc"}
{"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": "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": "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": "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": "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 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": "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": "Today is the final contest of INOI (Iranian National Olympiad in Informatics). The contest room is a row with $$$n$$$ computers. All computers are numbered with integers from $$$1$$$ to $$$n$$$ from left to right. There are $$$m$$$ participants, numbered with integers from $$$1$$$ to $$$m$$$.We have an array $$$a$$$ of length $$$m$$$ where $$$a_{i}$$$ ($$$1 \\leq a_i \\leq n$$$) is the computer behind which the $$$i$$$-th participant wants to sit.Also, we have another array $$$b$$$ of length $$$m$$$ consisting of characters 'L' and 'R'. $$$b_i$$$ is the side from which the $$$i$$$-th participant enters the room. 'L' means the participant enters from the left of computer $$$1$$$ and goes from left to right, and 'R' means the participant enters from the right of computer $$$n$$$ and goes from right to left.The participants in the order from $$$1$$$ to $$$m$$$ enter the room one by one. The $$$i$$$-th of them enters the contest room in the direction $$$b_i$$$ and goes to sit behind the $$$a_i$$$-th computer. If it is occupied he keeps walking in his direction until he reaches the first unoccupied computer. After that, he sits behind it. If he doesn't find any computer he gets upset and gives up on the contest.The madness of the $$$i$$$-th participant is the distance between his assigned computer ($$$a_i$$$) and the computer he ends up sitting behind. The distance between computers $$$i$$$ and $$$j$$$ is equal to $$$|i - j|$$$.The values in the array $$$a$$$ can be equal. There exist $$$n^m \\cdot 2^m$$$ possible pairs of arrays $$$(a, b)$$$.Consider all pairs of arrays $$$(a, b)$$$ such that no person becomes upset. For each of them let's calculate the sum of participants madnesses. Find the sum of all these values.You will be given some prime modulo $$$p$$$. Find this sum by modulo $$$p$$$.", "input_spec": "The only line contains three integers $$$n$$$, $$$m$$$, $$$p$$$ ($$$1 \\leq m \\leq n \\leq 500, 10^8 \\leq p \\leq 10 ^ 9 + 9$$$). It is guaranteed, that the number $$$p$$$ is prime.", "output_spec": "Print only one integer — the required sum by modulo $$$p$$$.", "sample_inputs": ["3 1 1000000007", "2 2 1000000009", "3 2 998244353", "20 10 1000000009"], "sample_outputs": ["0", "4", "8", "352081045"], "notes": "NoteIn the first test, there are three possible arrays $$$a$$$: $$$\\{1\\}$$$, $$$\\{2\\}$$$, and $$$ \\{3\\}$$$ and two possible arrays $$$b$$$: $$$\\{\\mathtt{L}\\}$$$ and $$$\\{\\mathtt{R}\\}$$$. For all six pairs of arrays $$$(a, b)$$$, the only participant will sit behind the computer $$$a_1$$$, so his madness will be $$$0$$$. So the total sum of madnesses will be $$$0$$$.In the second test, all possible pairs of arrays $$$(a, b)$$$, such that no person becomes upset are:  $$$(\\{1, 1\\}, \\{\\mathtt{L}, \\mathtt{L}\\})$$$, the sum of madnesses is $$$1$$$;  $$$(\\{1, 1\\}, \\{\\mathtt{R}, \\mathtt{L}\\})$$$, the sum of madnesses is $$$1$$$;  $$$(\\{2, 2\\}, \\{\\mathtt{R}, \\mathtt{R}\\})$$$, the sum of madnesses is $$$1$$$;  $$$(\\{2, 2\\}, \\{\\mathtt{L}, \\mathtt{R}\\})$$$, the sum of madnesses is $$$1$$$;  all possible pairs of $$$a \\in \\{\\{1, 2\\}, \\{2, 1\\}\\}$$$ and $$$b \\in \\{\\{\\mathtt{L}, \\mathtt{L}\\}, \\{\\mathtt{R}, \\mathtt{L}\\}, \\{\\mathtt{L}, \\mathtt{R}\\}, \\{\\mathtt{R}, \\mathtt{R}\\}\\}$$$, the sum of madnesses is $$$0$$$. So, the answer is $$$1 + 1 + 1 + 1 + 0 \\ldots = 4$$$."}, "src_uid": "9812de5f2d272511a63ead8765b23190"}
{"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": "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": "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": "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": "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": "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 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": "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": "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": "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": "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": "The preferred way to generate user login in Polygon is to concatenate a prefix of the user's first name and a prefix of their last name, in that order. Each prefix must be non-empty, and any of the prefixes can be the full name. Typically there are multiple possible logins for each person.You are given the first and the last name of a user. Return the alphabetically earliest login they can get (regardless of other potential Polygon users).As a reminder, a prefix of a string s is its substring which occurs at the beginning of s: \"a\", \"ab\", \"abc\" etc. are prefixes of string \"{abcdef}\" but \"b\" and 'bc\" are not. A string a is alphabetically earlier than a string b, if a is a prefix of b, or a and b coincide up to some position, and then a has a letter that is alphabetically earlier than the corresponding letter in b: \"a\" and \"ab\" are alphabetically earlier than \"ac\" but \"b\" and \"ba\" are alphabetically later than \"ac\".", "input_spec": "The input consists of a single line containing two space-separated strings: the first and the last names. Each character of each string is a lowercase English letter. The length of each string is between 1 and 10, inclusive. ", "output_spec": "Output a single string — alphabetically earliest possible login formed from these names. The output should be given in lowercase as well.", "sample_inputs": ["harry potter", "tom riddle"], "sample_outputs": ["hap", "tomr"], "notes": null}, "src_uid": "aed892f2bda10b6aee10dcb834a63709"}
{"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": "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": "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": "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": "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": "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": "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": "  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": "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 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": "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": "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": "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": "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": "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": "One day Vasya was sitting on a not so interesting Maths lesson and making an origami from a rectangular a mm  ×  b mm sheet of paper (a > b). Usually the first step in making an origami is making a square piece of paper from the rectangular sheet by folding the sheet along the bisector of the right angle, and cutting the excess part.  After making a paper ship from the square piece, Vasya looked on the remaining (a - b) mm  ×  b mm strip of paper. He got the idea to use this strip of paper in the same way to make an origami, and then use the remainder (if it exists) and so on. At the moment when he is left with a square piece of paper, he will make the last ship from it and stop.Can you determine how many ships Vasya will make during the lesson?", "input_spec": "The first line of the input contains two integers a, b (1 ≤ b < a ≤ 1012) — the sizes of the original sheet of paper.", "output_spec": "Print a single integer — the number of ships that Vasya will make.", "sample_inputs": ["2 1", "10 7", "1000000000000 1"], "sample_outputs": ["2", "6", "1000000000000"], "notes": "NotePictures to the first and second sample test.  "}, "src_uid": "ce698a0eb3f5b82de58feb177ce43b83"}
{"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": "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": "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": "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": "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": "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": "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": "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": "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": "Kicker (table football) is a board game based on football, in which players control the footballers' figures mounted on rods by using bars to get the ball into the opponent's goal. When playing two on two, one player of each team controls the goalkeeper and the full-backs (plays defence), the other player controls the half-backs and forwards (plays attack).Two teams of company Q decided to battle each other. Let's enumerate players from both teams by integers from 1 to 4. The first and second player play in the first team, the third and the fourth one play in the second team. For each of the four players we know their game skills in defence and attack. The defence skill of the i-th player is ai, the attack skill is bi.Before the game, the teams determine how they will play. First the players of the first team decide who will play in the attack, and who will play in the defence. Then the second team players do the same, based on the choice of their opponents.We will define a team's defence as the defence skill of player of the team who plays defence. Similarly, a team's attack is the attack skill of the player of the team who plays attack. We assume that one team is guaranteed to beat the other one, if its defence is strictly greater than the opponent's attack and its attack is strictly greater than the opponent's defence.The teams of company Q know each other's strengths and therefore arrange their teams optimally. Identify the team that is guaranteed to win (if both teams act optimally) or tell that there is no such team.", "input_spec": "The input contain the players' description in four lines. The i-th line contains two space-separated integers ai and bi (1 ≤ ai, bi ≤ 100) — the defence and the attack skill of the i-th player, correspondingly.", "output_spec": "If the first team can win, print phrase \"Team 1\" (without the quotes), if the second team can win, print phrase \"Team 2\" (without the quotes). If no of the teams can definitely win, print \"Draw\" (without the quotes).", "sample_inputs": ["1 100\n100 1\n99 99\n99 99", "1 1\n2 2\n3 3\n2 2", "3 3\n2 2\n1 1\n2 2"], "sample_outputs": ["Team 1", "Team 2", "Draw"], "notes": "NoteLet consider the first test sample. The first team can definitely win if it will choose the following arrangement: the first player plays attack, the second player plays defence.Consider the second sample. The order of the choosing roles for players makes sense in this sample. As the members of the first team choose first, the members of the second team can beat them (because they know the exact defence value and attack value of the first team)."}, "src_uid": "1a70ed6f58028a7c7a86e73c28ff245f"}
{"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": "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": "You are given an array a consisting of n integers, and additionally an integer m. You have to choose some sequence of indices b1, b2, ..., bk (1 ≤ b1 < b2 < ... < bk ≤ n) in such a way that the value of  is maximized. Chosen sequence can be empty.Print the maximum possible value of .", "input_spec": "The first line contains two integers n and m (1 ≤ n ≤ 35, 1 ≤ m ≤ 109). The second line contains n integers a1, a2, ..., an (1 ≤ ai ≤ 109).", "output_spec": "Print the maximum possible value of .", "sample_inputs": ["4 4\n5 2 4 1", "3 20\n199 41 299"], "sample_outputs": ["3", "19"], "notes": "NoteIn the first example you can choose a sequence b = {1, 2}, so the sum  is equal to 7 (and that's 3 after taking it modulo 4).In the second example you can choose a sequence b = {3}."}, "src_uid": "d3a8a3e69a55936ee33aedd66e5b7f4a"}
{"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": "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": "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": "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": "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": "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": "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": "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": "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": "Where do odds begin, and where do they end? Where does hope emerge, and will they ever break?Given an integer sequence a1, a2, ..., an of length n. Decide whether it is possible to divide it into an odd number of non-empty subsegments, the each of which has an odd length and begins and ends with odd numbers.A subsegment is a contiguous slice of the whole sequence. For example, {3, 4, 5} and {1} are subsegments of sequence {1, 2, 3, 4, 5, 6}, while {1, 2, 4} and {7} are not.", "input_spec": "The first line of input contains a non-negative integer n (1 ≤ n ≤ 100) — the length of the sequence. The second line contains n space-separated non-negative integers a1, a2, ..., an (0 ≤ ai ≤ 100) — the elements of the sequence.", "output_spec": "Output \"Yes\" if it's possible to fulfill the requirements, and \"No\" otherwise. You can output each letter in any case (upper or lower).", "sample_inputs": ["3\n1 3 5", "5\n1 0 1 5 1", "3\n4 3 1", "4\n3 9 9 3"], "sample_outputs": ["Yes", "Yes", "No", "No"], "notes": "NoteIn the first example, divide the sequence into 1 subsegment: {1, 3, 5} and the requirements will be met.In the second example, divide the sequence into 3 subsegments: {1, 0, 1}, {5}, {1}.In the third example, one of the subsegments must start with 4 which is an even number, thus the requirements cannot be met.In the fourth example, the sequence can be divided into 2 subsegments: {3, 9, 9}, {3}, but this is not a valid solution because 2 is an even number."}, "src_uid": "2b8c2deb5d7e49e8e3ededabfd4427db"}
{"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": "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": "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": "$$$k$$$ 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": "A tree is a connected graph without cycles.Two trees, consisting of n vertices each, are called isomorphic if there exists a permutation p: {1, ..., n} → {1, ..., n} such that the edge (u, v) is present in the first tree if and only if the edge (pu, pv) is present in the second tree.Vertex of the tree is called internal if its degree is greater than or equal to two.Count the number of different non-isomorphic trees, consisting of n vertices, such that the degree of each internal vertex is exactly d. Print the answer over the given prime modulo mod.", "input_spec": "The single line of the input contains three integers n, d and mod (1 ≤ n ≤ 1000, 2 ≤ d ≤ 10, 108 ≤ mod ≤ 109)  — the number of vertices in the tree, the degree of internal vertices and the prime modulo.", "output_spec": "Print the number of trees over the modulo mod.", "sample_inputs": ["5 2 433416647", "10 3 409693891", "65 4 177545087"], "sample_outputs": ["1", "2", "910726"], "notes": null}, "src_uid": "bdd0fc1d6dbab5eeb5aea135fdfffc9d"}
{"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": "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": "Little girl Tanya is learning how to decrease a number by one, but she does it wrong with a number consisting of two or more digits. Tanya subtracts one from a number by the following algorithm:  if the last digit of the number is non-zero, she decreases the number by one;  if the last digit of the number is zero, she divides the number by 10 (i.e. removes the last digit). You are given an integer number $$$n$$$. Tanya will subtract one from it $$$k$$$ times. Your task is to print the result after all $$$k$$$ subtractions.It is guaranteed that the result will be positive integer number.", "input_spec": "The first line of the input contains two integer numbers $$$n$$$ and $$$k$$$ ($$$2 \\le n \\le 10^9$$$, $$$1 \\le k \\le 50$$$) — the number from which Tanya will subtract and the number of subtractions correspondingly.", "output_spec": "Print one integer number — the result of the decreasing $$$n$$$ by one $$$k$$$ times. It is guaranteed that the result will be positive integer number. ", "sample_inputs": ["512 4", "1000000000 9"], "sample_outputs": ["50", "1"], "notes": "NoteThe first example corresponds to the following sequence: $$$512 \\rightarrow 511 \\rightarrow 510 \\rightarrow 51 \\rightarrow 50$$$."}, "src_uid": "064162604284ce252b88050b4174ba55"}
{"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": "You have an initially empty cauldron, and you want to brew a potion in it. The potion consists of two ingredients: magic essence and water. The potion you want to brew should contain exactly $$$k\\ \\%$$$ magic essence and $$$(100 - k)\\ \\%$$$ water.In one step, you can pour either one liter of magic essence or one liter of water into the cauldron. What is the minimum number of steps to brew a potion? You don't care about the total volume of the potion, only about the ratio between magic essence and water in it.A small reminder: if you pour $$$e$$$ liters of essence and $$$w$$$ liters of water ($$$e + w > 0$$$) into the cauldron, then it contains $$$\\frac{e}{e + w} \\cdot 100\\ \\%$$$ (without rounding) magic essence and $$$\\frac{w}{e + w} \\cdot 100\\ \\%$$$ water.", "input_spec": "The first line contains the single $$$t$$$ ($$$1 \\le t \\le 100$$$) — the number of test cases. The first and only line of each test case contains a single integer $$$k$$$ ($$$1 \\le k \\le 100$$$) — the percentage of essence in a good potion.", "output_spec": "For each test case, print the minimum number of steps to brew a good potion. It can be proved that it's always possible to achieve it in a finite number of steps.", "sample_inputs": ["3\n3\n100\n25"], "sample_outputs": ["100\n1\n4"], "notes": "NoteIn the first test case, you should pour $$$3$$$ liters of magic essence and $$$97$$$ liters of water into the cauldron to get a potion with $$$3\\ \\%$$$ of magic essence.In the second test case, you can pour only $$$1$$$ liter of essence to get a potion with $$$100\\ \\%$$$ of magic essence.In the third test case, you can pour $$$1$$$ liter of magic essence and $$$3$$$ liters of water."}, "src_uid": "19a2bcb727510c729efe442a13c2ff7c"}
{"nl": {"description": "You are given a square board, consisting of $$$n$$$ rows and $$$n$$$ columns. Each tile in it should be colored either white or black.Let's call some coloring beautiful if each pair of adjacent rows are either the same or different in every position. The same condition should be held for the columns as well.Let's call some coloring suitable if it is beautiful and there is no rectangle of the single color, consisting of at least $$$k$$$ tiles.Your task is to count the number of suitable colorings of the board of the given size.Since the answer can be very large, print it modulo $$$998244353$$$.", "input_spec": "A single line contains two integers $$$n$$$ and $$$k$$$ ($$$1 \\le n \\le 500$$$, $$$1 \\le k \\le n^2$$$) — the number of rows and columns of the board and the maximum number of tiles inside the rectangle of the single color, respectively.", "output_spec": "Print a single integer — the number of suitable colorings of the board of the given size modulo $$$998244353$$$.", "sample_inputs": ["1 1", "2 3", "49 1808"], "sample_outputs": ["0", "6", "359087121"], "notes": "NoteBoard of size $$$1 \\times 1$$$ is either a single black tile or a single white tile. Both of them include a rectangle of a single color, consisting of $$$1$$$ tile.Here are the beautiful colorings of a board of size $$$2 \\times 2$$$ that don't include rectangles of a single color, consisting of at least $$$3$$$ tiles:  The rest of beautiful colorings of a board of size $$$2 \\times 2$$$ are the following:  "}, "src_uid": "77177b1a2faf0ba4ca1f4d77632b635b"}
{"nl": {"description": "A never-ending, fast-changing and dream-like world unfolds, as the secret door opens.A world is an unordered graph G, in whose vertex set V(G) there are two special vertices s(G) and t(G). An initial world has vertex set {s(G), t(G)} and an edge between them.A total of n changes took place in an initial world. In each change, a new vertex w is added into V(G), an existing edge (u, v) is chosen, and two edges (u, w) and (v, w) are added into E(G). Note that it's possible that some edges are chosen in more than one change.It's known that the capacity of the minimum s-t cut of the resulting graph is m, that is, at least m edges need to be removed in order to make s(G) and t(G) disconnected.Count the number of non-similar worlds that can be built under the constraints, modulo 109 + 7. We define two worlds similar, if they are isomorphic and there is isomorphism in which the s and t vertices are not relabelled. Formally, two worlds G and H are considered similar, if there is a bijection between their vertex sets , such that:   f(s(G)) = s(H);  f(t(G)) = t(H);  Two vertices u and v of G are adjacent in G if and only if f(u) and f(v) are adjacent in H. ", "input_spec": "The first and only line of input contains two space-separated integers n, m (1 ≤ n, m ≤ 50) — the number of operations performed and the minimum cut, respectively.", "output_spec": "Output one integer — the number of non-similar worlds that can be built, modulo 109 + 7.", "sample_inputs": ["3 2", "4 4", "7 3", "31 8"], "sample_outputs": ["6", "3", "1196", "64921457"], "notes": "NoteIn the first example, the following 6 worlds are pairwise non-similar and satisfy the constraints, with s(G) marked in green, t(G) marked in blue, and one of their minimum cuts in light blue.  In the second example, the following 3 worlds satisfy the constraints.  "}, "src_uid": "aca6148effff8b893c961b1ee465e4e4"}
{"nl": {"description": "There is a field of size $$$2 \\times 2$$$. Each cell of this field can either contain grass or be empty. The value $$$a_{i, j}$$$ is $$$1$$$ if the cell $$$(i, j)$$$ contains grass, or $$$0$$$ otherwise.In one move, you can choose one row and one column and cut all the grass in this row and this column. In other words, you choose the row $$$x$$$ and the column $$$y$$$, then you cut the grass in all cells $$$a_{x, i}$$$ and all cells $$$a_{i, y}$$$ for all $$$i$$$ from $$$1$$$ to $$$2$$$. After you cut the grass from a cell, it becomes empty (i. e. its value is replaced by $$$0$$$).Your task is to find the minimum number of moves required to cut the grass in all non-empty cells of the field (i. e. make all $$$a_{i, j}$$$ zeros).You have to answer $$$t$$$ independent test cases.", "input_spec": "The first line of the input contains one integer $$$t$$$ ($$$1 \\le t \\le 16$$$) — the number of test cases. Then $$$t$$$ test cases follow. The test case consists of two lines, each of these lines contains two integers. The $$$j$$$-th integer in the $$$i$$$-th row is $$$a_{i, j}$$$. If $$$a_{i, j} = 0$$$ then the cell $$$(i, j)$$$ is empty, and if $$$a_{i, j} = 1$$$ the cell $$$(i, j)$$$ contains grass.", "output_spec": "For each test case, print one integer — the minimum number of moves required to cut the grass in all non-empty cells of the field (i. e. make all $$$a_{i, j}$$$ zeros) in the corresponding test case.", "sample_inputs": ["3\n\n0 0\n\n0 0\n\n1 0\n\n0 1\n\n1 1\n\n1 1"], "sample_outputs": ["0\n1\n2"], "notes": null}, "src_uid": "7336b8becd2438f0439240ee8f9610ec"}
{"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": "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": "Masha has three sticks of length $$$a$$$, $$$b$$$ and $$$c$$$ centimeters respectively. In one minute Masha can pick one arbitrary stick and increase its length by one centimeter. She is not allowed to break sticks.What is the minimum number of minutes she needs to spend increasing the stick's length in order to be able to assemble a triangle of positive area. Sticks should be used as triangle's sides (one stick for one side) and their endpoints should be located at triangle's vertices.", "input_spec": "The only line contains tree integers $$$a$$$, $$$b$$$ and $$$c$$$ ($$$1 \\leq a, b, c \\leq 100$$$) — the lengths of sticks Masha possesses.", "output_spec": "Print a single integer — the minimum number of minutes that Masha needs to spend in order to be able to make the triangle of positive area from her sticks.", "sample_inputs": ["3 4 5", "2 5 3", "100 10 10"], "sample_outputs": ["0", "1", "81"], "notes": "NoteIn the first example, Masha can make a triangle from the sticks without increasing the length of any of them.In the second example, Masha can't make a triangle of positive area from the sticks she has at the beginning, but she can spend one minute to increase the length $$$2$$$ centimeter stick by one and after that form a triangle with sides $$$3$$$, $$$3$$$ and $$$5$$$ centimeters.In the third example, Masha can take $$$33$$$ minutes to increase one of the $$$10$$$ centimeters sticks by $$$33$$$ centimeters, and after that take $$$48$$$ minutes to increase another $$$10$$$ centimeters stick by $$$48$$$ centimeters. This way she can form a triangle with lengths $$$43$$$, $$$58$$$ and $$$100$$$ centimeters in $$$81$$$ minutes. One can show that it is impossible to get a valid triangle faster."}, "src_uid": "3dc56bc08606a39dd9ca40a43c452f09"}
{"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": "There are n shovels in Polycarp's shop. The i-th shovel costs i burles, that is, the first shovel costs 1 burle, the second shovel costs 2 burles, the third shovel costs 3 burles, and so on. Polycarps wants to sell shovels in pairs.Visitors are more likely to buy a pair of shovels if their total cost ends with several 9s. Because of this, Polycarp wants to choose a pair of shovels to sell in such a way that the sum of their costs ends with maximum possible number of nines. For example, if he chooses shovels with costs 12345 and 37454, their total cost is 49799, it ends with two nines.You are to compute the number of pairs of shovels such that their total cost ends with maximum possible number of nines. Two pairs are considered different if there is a shovel presented in one pair, but not in the other.", "input_spec": "The first line contains a single integer n (2 ≤ n ≤ 109) — the number of shovels in Polycarp's shop.", "output_spec": "Print the number of pairs of shovels such that their total cost ends with maximum possible number of nines.  Note that it is possible that the largest number of 9s at the end is 0, then you should count all such ways. It is guaranteed that for every n ≤ 109 the answer doesn't exceed 2·109.", "sample_inputs": ["7", "14", "50"], "sample_outputs": ["3", "9", "1"], "notes": "NoteIn the first example the maximum possible number of nines at the end is one. Polycarp cah choose the following pairs of shovels for that purpose:  2 and 7;  3 and 6;  4 and 5. In the second example the maximum number of nines at the end of total cost of two shovels is one. The following pairs of shovels suit Polycarp:  1 and 8;  2 and 7;  3 and 6;  4 and 5;  5 and 14;  6 and 13;  7 and 12;  8 and 11;  9 and 10. In the third example it is necessary to choose shovels 49 and 50, because the sum of their cost is 99, that means that the total number of nines is equal to two, which is maximum possible for n = 50."}, "src_uid": "c20744c44269ae0779c5f549afd2e3f2"}
{"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": "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": "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": "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": "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": "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": "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": "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": "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": "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": "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": "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": "Let's call a string good if and only if it consists of only two types of letters — 'a' and 'b' and every two consecutive letters are distinct. For example \"baba\" and \"aba\" are good strings and \"abb\" is a bad string.You have $$$a$$$ strings \"a\", $$$b$$$ strings \"b\" and $$$c$$$ strings \"ab\". You want to choose some subset of these strings and concatenate them in any arbitrarily order.What is the length of the longest good string you can obtain this way?", "input_spec": "The first line contains three positive integers $$$a$$$, $$$b$$$, $$$c$$$ ($$$1 \\leq a, b, c \\leq 10^9$$$) — the number of strings \"a\", \"b\" and \"ab\" respectively.", "output_spec": "Print a single number — the maximum possible length of the good string you can obtain.", "sample_inputs": ["1 1 1", "2 1 2", "3 5 2", "2 2 1", "1000000000 1000000000 1000000000"], "sample_outputs": ["4", "7", "11", "6", "4000000000"], "notes": "NoteIn the first example the optimal string is \"baba\".In the second example the optimal string is \"abababa\".In the third example the optimal string is \"bababababab\".In the fourth example the optimal string is \"ababab\"."}, "src_uid": "609f131325c13213aedcf8d55fc3ed77"}
{"nl": {"description": "Vasya has a pile, that consists of some number of stones. $$$n$$$ times he either took one stone from the pile or added one stone to the pile. The pile was non-empty before each operation of taking one stone from the pile.You are given $$$n$$$ operations which Vasya has made. Find the minimal possible number of stones that can be in the pile after making these operations.", "input_spec": "The first line contains one positive integer $$$n$$$ — the number of operations, that have been made by Vasya ($$$1 \\leq n \\leq 100$$$). The next line contains the string $$$s$$$, consisting of $$$n$$$ symbols, equal to \"-\" (without quotes) or \"+\" (without quotes). If Vasya took the stone on $$$i$$$-th operation, $$$s_i$$$ is equal to \"-\" (without quotes), if added, $$$s_i$$$ is equal to \"+\" (without quotes).", "output_spec": "Print one integer — the minimal possible number of stones that can be in the pile after these $$$n$$$ operations.", "sample_inputs": ["3\n---", "4\n++++", "2\n-+", "5\n++-++"], "sample_outputs": ["0", "4", "1", "3"], "notes": "NoteIn the first test, if Vasya had $$$3$$$ stones in the pile at the beginning, after making operations the number of stones will be equal to $$$0$$$. It is impossible to have less number of piles, so the answer is $$$0$$$. Please notice, that the number of stones at the beginning can't be less, than $$$3$$$, because in this case, Vasya won't be able to take a stone on some operation (the pile will be empty).In the second test, if Vasya had $$$0$$$ stones in the pile at the beginning, after making operations the number of stones will be equal to $$$4$$$. It is impossible to have less number of piles because after making $$$4$$$ operations the number of stones in the pile increases on $$$4$$$ stones. So, the answer is $$$4$$$.In the third test, if Vasya had $$$1$$$ stone in the pile at the beginning, after making operations the number of stones will be equal to $$$1$$$. It can be proved, that it is impossible to have less number of stones after making the operations.In the fourth test, if Vasya had $$$0$$$ stones in the pile at the beginning, after making operations the number of stones will be equal to $$$3$$$."}, "src_uid": "a593016e4992f695be7c7cd3c920d1ed"}
{"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": "Nowadays, most of the internet advertisements are not statically linked to a web page. Instead, what will be shown to the person opening a web page is determined within 100 milliseconds after the web page is opened. Usually, multiple companies compete for each ad slot on the web page in an auction. Each of them receives a request with details about the user, web page and ad slot and they have to respond within those 100 milliseconds with a bid they would pay for putting an advertisement on that ad slot. The company that suggests the highest bid wins the auction and gets to place its advertisement. If there are several companies tied for the highest bid, the winner gets picked at random.However, the company that won the auction does not have to pay the exact amount of its bid. In most of the cases, a second-price auction is used. This means that the amount paid by the company is equal to the maximum of all the other bids placed for this ad slot.Let's consider one such bidding. There are n companies competing for placing an ad. The i-th of these companies will bid an integer number of microdollars equiprobably randomly chosen from the range between Li and Ri, inclusive. In the other words, the value of the i-th company bid can be any integer from the range [Li, Ri] with the same probability. Determine the expected value that the winner will have to pay in a second-price auction.", "input_spec": "The first line of input contains an integer number n (2 ≤ n ≤ 5). n lines follow, the i-th of them containing two numbers Li and Ri (1 ≤ Li ≤ Ri ≤ 10000) describing the i-th company's bid preferences. This problem doesn't have subproblems. You will get 8 points for the correct submission.", "output_spec": "Output the answer with absolute or relative error no more than 1e - 9.", "sample_inputs": ["3\n4 7\n8 10\n5 5", "3\n2 5\n3 4\n1 6"], "sample_outputs": ["5.7500000000", "3.5000000000"], "notes": "NoteConsider the first example. The first company bids a random integer number of microdollars in range [4, 7]; the second company bids between 8 and 10, and the third company bids 5 microdollars. The second company will win regardless of the exact value it bids, however the price it will pay depends on the value of first company's bid. With probability 0.5 the first company will bid at most 5 microdollars, and the second-highest price of the whole auction will be 5. With probability 0.25 it will bid 6 microdollars, and with probability 0.25 it will bid 7 microdollars. Thus, the expected value the second company will have to pay is 0.5·5 + 0.25·6 + 0.25·7 = 5.75."}, "src_uid": "5258ce738eb268b9750cfef309d265ef"}
{"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": "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": "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": "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": "Even if the world is full of counterfeits, I still regard it as wonderful.Pile up herbs and incense, and arise again from the flames and ashes of its predecessor — as is known to many, the phoenix does it like this.The phoenix has a rather long lifespan, and reincarnates itself once every a! years. Here a! denotes the factorial of integer a, that is, a! = 1 × 2 × ... × a. Specifically, 0! = 1.Koyomi doesn't care much about this, but before he gets into another mess with oddities, he is interested in the number of times the phoenix will reincarnate in a timespan of b! years, that is, . Note that when b ≥ a this value is always integer.As the answer can be quite large, it would be enough for Koyomi just to know the last digit of the answer in decimal representation. And you're here to provide Koyomi with this knowledge.", "input_spec": "The first and only line of input contains two space-separated integers a and b (0 ≤ a ≤ b ≤ 1018).", "output_spec": "Output one line containing a single decimal digit — the last digit of the value that interests Koyomi.", "sample_inputs": ["2 4", "0 10", "107 109"], "sample_outputs": ["2", "0", "2"], "notes": "NoteIn the first example, the last digit of  is 2;In the second example, the last digit of  is 0;In the third example, the last digit of  is 2."}, "src_uid": "2ed5a7a6176ed9b0bda1de21aad13d60"}
{"nl": {"description": "Mad scientist Mike is busy carrying out experiments in chemistry. Today he will attempt to join three atoms into one molecule.A molecule consists of atoms, with some pairs of atoms connected by atomic bonds. Each atom has a valence number — the number of bonds the atom must form with other atoms. An atom can form one or multiple bonds with any other atom, but it cannot form a bond with itself. The number of bonds of an atom in the molecule must be equal to its valence number.  Mike knows valence numbers of the three atoms. Find a molecule that can be built from these atoms according to the stated rules, or determine that it is impossible.", "input_spec": "The single line of the input contains three space-separated integers a, b and c (1 ≤ a, b, c ≤ 106) — the valence numbers of the given atoms.", "output_spec": "If such a molecule can be built, print three space-separated integers — the number of bonds between the 1-st and the 2-nd, the 2-nd and the 3-rd, the 3-rd and the 1-st atoms, correspondingly. If there are multiple solutions, output any of them. If there is no solution, print \"Impossible\" (without the quotes).", "sample_inputs": ["1 1 2", "3 4 5", "4 1 1"], "sample_outputs": ["0 1 1", "1 3 2", "Impossible"], "notes": "NoteThe first sample corresponds to the first figure. There are no bonds between atoms 1 and 2 in this case.The second sample corresponds to the second figure. There is one or more bonds between each pair of atoms.The third sample corresponds to the third figure. There is no solution, because an atom cannot form bonds with itself.The configuration in the fourth figure is impossible as each atom must have at least one atomic bond."}, "src_uid": "b3b986fddc3770fed64b878fa42ab1bc"}
{"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": "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": "Consider an array $$$a$$$ of length $$$n$$$ with elements numbered from $$$1$$$ to $$$n$$$. It is possible to remove the $$$i$$$-th element of $$$a$$$ if $$$gcd(a_i, i) = 1$$$, where $$$gcd$$$ denotes the greatest common divisor. After an element is removed, the elements to the right are shifted to the left by one position.An array $$$b$$$ with $$$n$$$ integers such that $$$1 \\le b_i \\le n - i + 1$$$ is a removal sequence for the array $$$a$$$ if it is possible to remove all elements of $$$a$$$, if you remove the $$$b_1$$$-th element, then the $$$b_2$$$-th, ..., then the $$$b_n$$$-th element. For example, let $$$a = [42, 314]$$$:  $$$[1, 1]$$$ is a removal sequence: when you remove the $$$1$$$-st element of the array, the condition $$$gcd(42, 1) = 1$$$ holds, and the array becomes $$$[314]$$$; when you remove the $$$1$$$-st element again, the condition $$$gcd(314, 1) = 1$$$ holds, and the array becomes empty.  $$$[2, 1]$$$ is not a removal sequence: when you try to remove the $$$2$$$-nd element, the condition $$$gcd(314, 2) = 1$$$ is false. An array is ambiguous if it has at least two removal sequences. For example, the array $$$[1, 2, 5]$$$ is ambiguous: it has removal sequences $$$[3, 1, 1]$$$ and $$$[1, 2, 1]$$$. The array $$$[42, 314]$$$ is not ambiguous: the only removal sequence it has is $$$[1, 1]$$$.You are given two integers $$$n$$$ and $$$m$$$. You have to calculate the number of ambiguous arrays $$$a$$$ such that the length of $$$a$$$ is from $$$1$$$ to $$$n$$$ and each $$$a_i$$$ is an integer from $$$1$$$ to $$$m$$$.", "input_spec": "The only line of the input contains two integers $$$n$$$ and $$$m$$$ ($$$2 \\le n \\le 3 \\cdot 10^5$$$; $$$1 \\le m \\le 10^{12}$$$).", "output_spec": "Print one integer — the number of ambiguous arrays $$$a$$$ such that the length of $$$a$$$ is from $$$1$$$ to $$$n$$$ and each $$$a_i$$$ is an integer from $$$1$$$ to $$$m$$$. Since the answer can be very large, print it modulo $$$998244353$$$.", "sample_inputs": ["2 3", "4 2", "4 6", "1337 424242424242"], "sample_outputs": ["6", "26", "1494", "119112628"], "notes": null}, "src_uid": "0fdd91ed33431848614075ebe9d2ee68"}
{"nl": {"description": "Catherine has a deck of n cards, each of which is either red, green, or blue. As long as there are at least two cards left, she can do one of two actions:   take any two (not necessarily adjacent) cards with different colors and exchange them for a new card of the third color;  take any two (not necessarily adjacent) cards with the same color and exchange them for a new card with that color. She repeats this process until there is only one card left. What are the possible colors for the final card?", "input_spec": "The first line of the input contains a single integer n (1 ≤ n ≤ 200) — the total number of cards. The next line contains a string s of length n — the colors of the cards. s contains only the characters 'B', 'G', and 'R', representing blue, green, and red, respectively.", "output_spec": "Print a single string of up to three characters — the possible colors of the final card (using the same symbols as the input) in alphabetical order.", "sample_inputs": ["2\nRB", "3\nGRG", "5\nBBBBB"], "sample_outputs": ["G", "BR", "B"], "notes": "NoteIn the first sample, Catherine has one red card and one blue card, which she must exchange for a green card.In the second sample, Catherine has two green cards and one red card. She has two options: she can exchange the two green cards for a green card, then exchange the new green card and the red card for a blue card. Alternatively, she can exchange a green and a red card for a blue card, then exchange the blue card and remaining green card for a red card.In the third sample, Catherine only has blue cards, so she can only exchange them for more blue cards."}, "src_uid": "4cedd3b70d793bc8ed4a93fc5a827f8f"}
{"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": "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": "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": "One rainy gloomy evening when all modules hid in the nearby cafes to drink hot energetic cocktails, the Hexadecimal virus decided to fly over the Mainframe to look for a Great Idea. And she has found one!Why not make her own Codeforces, with blackjack and other really cool stuff? Many people will surely be willing to visit this splendid shrine of high culture.In Mainframe a standard pack of 52 cards is used to play blackjack. The pack contains cards of 13 values: 2, 3, 4, 5, 6, 7, 8, 9, 10, jacks, queens, kings and aces. Each value also exists in one of four suits: hearts, diamonds, clubs and spades. Also, each card earns some value in points assigned to it: cards with value from two to ten earn from 2 to 10 points, correspondingly. An ace can either earn 1 or 11, whatever the player wishes. The picture cards (king, queen and jack) earn 10 points. The number of points a card earns does not depend on the suit. The rules of the game are very simple. The player gets two cards, if the sum of points of those cards equals n, then the player wins, otherwise the player loses.The player has already got the first card, it's the queen of spades. To evaluate chances for victory, you should determine how many ways there are to get the second card so that the sum of points exactly equals n.", "input_spec": "The only line contains n (1 ≤ n ≤ 25) — the required sum of points.", "output_spec": "Print the numbers of ways to get the second card in the required way if the first card is the queen of spades.", "sample_inputs": ["12", "20", "10"], "sample_outputs": ["4", "15", "0"], "notes": "NoteIn the first sample only four two's of different suits can earn the required sum of points.In the second sample we can use all tens, jacks, queens and kings; overall it's 15 cards, as the queen of spades (as any other card) is only present once in the pack of cards and it's already in use.In the third sample there is no card, that would add a zero to the current ten points."}, "src_uid": "5802f52caff6015f21b80872274ab16c"}
{"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": "Petr stands in line of n people, but he doesn't know exactly which position he occupies. He can say that there are no less than a people standing in front of him and no more than b people standing behind him. Find the number of different positions Petr can occupy.", "input_spec": "The only line contains three integers n, a and b (0 ≤ a, b < n ≤ 100).", "output_spec": "Print the single number — the number of the sought positions.", "sample_inputs": ["3 1 1", "5 2 3"], "sample_outputs": ["2", "3"], "notes": "NoteThe possible positions in the first sample are: 2 and 3 (if we number the positions starting with 1).In the second sample they are 3, 4 and 5."}, "src_uid": "51a072916bff600922a77da0c4582180"}
{"nl": {"description": "Polycarp has just invented a new binary protocol for data transmission. He is encoding positive integer decimal number to binary string using following algorithm:  Each digit is represented with number of '1' characters equal to the value of that digit (for 0 it is zero ones).  Digits are written one by one in order corresponding to number and separated by single '0' character. Though Polycarp learnt how to encode the numbers, he has no idea how to decode them back. Help him calculate the decoded number.", "input_spec": "The first line contains one integer number n (1 ≤ n ≤ 89) — length of the string s. The second line contains string s — sequence of '0' and '1' characters, number in its encoded format. It is guaranteed that the number corresponding to the string is positive and doesn't exceed 109. The string always starts with '1'.", "output_spec": "Print the decoded number.", "sample_inputs": ["3\n111", "9\n110011101"], "sample_outputs": ["3", "2031"], "notes": null}, "src_uid": "a4b3da4cb9b6a7ed0a33a862e940cafa"}
{"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": "Princess Twilight went to Celestia and Luna's old castle to research the chest from the Elements of Harmony.  A sequence of positive integers bi is harmony if and only if for every two elements of the sequence their greatest common divisor equals 1. According to an ancient book, the key of the chest is a harmony sequence bi which minimizes the following expression:You are given sequence ai, help Princess Twilight to find the key.", "input_spec": "The first line contains an integer n (1 ≤ n ≤ 100) — the number of elements of the sequences a and b. The next line contains n integers a1, a2, ..., an (1 ≤ ai ≤ 30).", "output_spec": "Output the key — sequence bi that minimizes the sum described above. If there are multiple optimal sequences, you can output any of them.", "sample_inputs": ["5\n1 1 1 1 1", "5\n1 6 4 2 8"], "sample_outputs": ["1 1 1 1 1", "1 5 3 1 8"], "notes": null}, "src_uid": "f26c74f27bbc723efd69c38ad0e523c6"}
{"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": "Vadim is really keen on travelling. Recently he heard about kayaking activity near his town and became very excited about it, so he joined a party of kayakers.Now the party is ready to start its journey, but firstly they have to choose kayaks. There are 2·n people in the group (including Vadim), and they have exactly n - 1 tandem kayaks (each of which, obviously, can carry two people) and 2 single kayaks. i-th person's weight is wi, and weight is an important matter in kayaking — if the difference between the weights of two people that sit in the same tandem kayak is too large, then it can crash. And, of course, people want to distribute their seats in kayaks in order to minimize the chances that kayaks will crash.Formally, the instability of a single kayak is always 0, and the instability of a tandem kayak is the absolute difference between weights of the people that are in this kayak. Instability of the whole journey is the total instability of all kayaks.Help the party to determine minimum possible total instability! ", "input_spec": "The first line contains one number n (2 ≤ n ≤ 50). The second line contains 2·n integer numbers w1, w2, ..., w2n, where wi is weight of person i (1 ≤ wi ≤ 1000).", "output_spec": "Print minimum possible total instability.", "sample_inputs": ["2\n1 2 3 4", "4\n1 3 4 6 3 4 100 200"], "sample_outputs": ["1", "5"], "notes": null}, "src_uid": "76659c0b7134416452585c391daadb16"}
{"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": "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": "Natasha is going to fly to Mars. She needs to build a rocket, which consists of several stages in some order. Each of the stages is defined by a lowercase Latin letter. This way, the rocket can be described by the string — concatenation of letters, which correspond to the stages.There are $$$n$$$ stages available. The rocket must contain exactly $$$k$$$ of them. Stages in the rocket should be ordered by their weight. So, after the stage with some letter can go only stage with a letter, which is at least two positions after in the alphabet (skipping one letter in between, or even more). For example, after letter 'c' can't go letters 'a', 'b', 'c' and 'd', but can go letters 'e', 'f', ..., 'z'.For the rocket to fly as far as possible, its weight should be minimal. The weight of the rocket is equal to the sum of the weights of its stages. The weight of the stage is the number of its letter in the alphabet. For example, the stage 'a 'weighs one ton,' b 'weighs two tons, and' z' — $$$26$$$ tons.Build the rocket with the minimal weight or determine, that it is impossible to build a rocket at all. Each stage can be used at most once.", "input_spec": "The first line of input contains two integers — $$$n$$$ and $$$k$$$ ($$$1 \\le k \\le n \\le 50$$$) – the number of available stages and the number of stages to use in the rocket. The second line contains string $$$s$$$, which consists of exactly $$$n$$$ lowercase Latin letters. Each letter defines a new stage, which can be used to build the rocket. Each stage can be used at most once.", "output_spec": "Print a single integer — the minimal total weight of the rocket or -1, if it is impossible to build the rocket at all.", "sample_inputs": ["5 3\nxyabd", "7 4\nproblem", "2 2\nab", "12 1\nabaabbaaabbb"], "sample_outputs": ["29", "34", "-1", "1"], "notes": "NoteIn the first example, the following rockets satisfy the condition: \"adx\" (weight is $$$1+4+24=29$$$); \"ady\" (weight is $$$1+4+25=30$$$); \"bdx\" (weight is $$$2+4+24=30$$$); \"bdy\" (weight is $$$2+4+25=31$$$).Rocket \"adx\" has the minimal weight, so the answer is $$$29$$$.In the second example, target rocket is \"belo\". Its weight is $$$2+5+12+15=34$$$.In the third example, $$$n=k=2$$$, so the rocket must have both stages: 'a' and 'b'. This rocket doesn't satisfy the condition, because these letters are adjacent in the alphabet. Answer is -1."}, "src_uid": "56b13d313afef9dc6c6ba2758b5ea313"}
{"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": "Bishwock is a chess figure that consists of three squares resembling an \"L-bar\". This figure can be rotated by 90, 180 and 270 degrees so it can have four possible states: XX   XX   .X   X.X.   .X   XX   XX Bishwocks don't attack any squares and can even occupy on the adjacent squares as long as they don't occupy the same square. Vasya has a board with $$$2\\times n$$$ squares onto which he wants to put some bishwocks. To his dismay, several squares on this board are already occupied by pawns and Vasya can't put bishwocks there. However, pawns also don't attack bishwocks and they can occupy adjacent squares peacefully.Knowing the positions of pawns on the board, help Vasya to determine the maximum amount of bishwocks he can put onto the board so that they wouldn't occupy the same squares and wouldn't occupy squares with pawns.", "input_spec": "The input contains two nonempty strings that describe Vasya's board. Those strings contain only symbols \"0\" (zero) that denote the empty squares and symbols \"X\" (uppercase English letter) that denote the squares occupied by pawns. Strings are nonempty and are of the same length that does not exceed $$$100$$$.", "output_spec": "Output a single integer — the maximum amount of bishwocks that can be placed onto the given board.", "sample_inputs": ["00\n00", "00X00X0XXX0\n0XXX0X00X00", "0X0X0\n0X0X0", "0XXX0\n00000"], "sample_outputs": ["1", "4", "0", "2"], "notes": null}, "src_uid": "e6b3e787919e96fc893a034eae233fc6"}
{"nl": {"description": "Unary is a minimalistic Brainfuck dialect in which programs are written using only one token. Brainfuck programs use 8 commands: \"+\", \"-\", \"[\", \"]\", \"<\", \">\", \".\" and \",\" (their meaning is not important for the purposes of this problem). Unary programs are created from Brainfuck programs using the following algorithm. First, replace each command with a corresponding binary code, using the following conversion table:   \">\"  →  1000,  \"<\"  →  1001,  \"+\"  →  1010,  \"-\"  →  1011,  \".\"  →  1100,  \",\"  →  1101,  \"[\"  →  1110,  \"]\"  →  1111. Next, concatenate the resulting binary codes into one binary number in the same order as in the program. Finally, write this number using unary numeral system — this is the Unary program equivalent to the original Brainfuck one.You are given a Brainfuck program. Your task is to calculate the size of the equivalent Unary program, and print it modulo 1000003 (106 + 3).", "input_spec": "The input will consist of a single line p which gives a Brainfuck program. String p will contain between 1 and 100 characters, inclusive. Each character of p will be \"+\", \"-\", \"[\", \"]\", \"<\", \">\", \".\" or \",\".", "output_spec": "Output the size of the equivalent Unary program modulo 1000003 (106 + 3).", "sample_inputs": [",.", "++++[>,.<-]"], "sample_outputs": ["220", "61425"], "notes": "NoteTo write a number n in unary numeral system, one simply has to write 1 n times. For example, 5 written in unary system will be 11111.In the first example replacing Brainfuck commands with binary code will give us 1101 1100. After we concatenate the codes, we'll get 11011100 in binary system, or 220 in decimal. That's exactly the number of tokens in the equivalent Unary program."}, "src_uid": "04fc8dfb856056f35d296402ad1b2da1"}
{"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": "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": "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": "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": "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": "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": "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": "You are given a sequence of integers $$$a_1, a_2, \\dots, a_n$$$. You need to paint elements in colors, so that:   If we consider any color, all elements of this color must be divisible by the minimal element of this color.  The number of used colors must be minimized. For example, it's fine to paint elements $$$[40, 10, 60]$$$ in a single color, because they are all divisible by $$$10$$$. You can use any color an arbitrary amount of times (in particular, it is allowed to use a color only once). The elements painted in one color do not need to be consecutive.For example, if $$$a=[6, 2, 3, 4, 12]$$$ then two colors are required: let's paint $$$6$$$, $$$3$$$ and $$$12$$$ in the first color ($$$6$$$, $$$3$$$ and $$$12$$$ are divisible by $$$3$$$) and paint $$$2$$$ and $$$4$$$ in the second color ($$$2$$$ and $$$4$$$ are divisible by $$$2$$$). For example, if $$$a=[10, 7, 15]$$$ then $$$3$$$ colors are required (we can simply paint each element in an unique color).", "input_spec": "The first line contains an integer $$$n$$$ ($$$1 \\le n \\le 100$$$), where $$$n$$$ is the length of the given sequence. The second line contains $$$n$$$ integers $$$a_1, a_2, \\dots, a_n$$$ ($$$1 \\le a_i \\le 100$$$). These numbers can contain duplicates.", "output_spec": "Print the minimal number of colors to paint all the given numbers in a valid way.", "sample_inputs": ["6\n10 2 3 5 4 2", "4\n100 100 100 100", "8\n7 6 5 4 3 2 2 3"], "sample_outputs": ["3", "1", "4"], "notes": "NoteIn the first example, one possible way to paint the elements in $$$3$$$ colors is:  paint in the first color the elements: $$$a_1=10$$$ and $$$a_4=5$$$,  paint in the second color the element $$$a_3=3$$$,  paint in the third color the elements: $$$a_2=2$$$, $$$a_5=4$$$ and $$$a_6=2$$$. In the second example, you can use one color to paint all the elements.In the third example, one possible way to paint the elements in $$$4$$$ colors is:  paint in the first color the elements: $$$a_4=4$$$, $$$a_6=2$$$ and $$$a_7=2$$$,  paint in the second color the elements: $$$a_2=6$$$, $$$a_5=3$$$ and $$$a_8=3$$$,  paint in the third color the element $$$a_3=5$$$,  paint in the fourth color the element $$$a_1=7$$$. "}, "src_uid": "63d9b7416aa96129c57d20ec6145e0cd"}
{"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": "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 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": "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": "Kostya likes Codeforces contests very much. However, he is very disappointed that his solutions are frequently hacked. That's why he decided to obfuscate (intentionally make less readable) his code before upcoming contest.To obfuscate the code, Kostya first looks at the first variable name used in his program and replaces all its occurrences with a single symbol a, then he looks at the second variable name that has not been replaced yet, and replaces all its occurrences with b, and so on. Kostya is well-mannered, so he doesn't use any one-letter names before obfuscation. Moreover, there are at most 26 unique identifiers in his programs.You are given a list of identifiers of some program with removed spaces and line breaks. Check if this program can be a result of Kostya's obfuscation.", "input_spec": "In the only line of input there is a string S of lowercase English letters (1 ≤ |S| ≤ 500) — the identifiers of a program with removed whitespace characters.", "output_spec": "If this program can be a result of Kostya's obfuscation, print \"YES\" (without quotes), otherwise print \"NO\".", "sample_inputs": ["abacaba", "jinotega"], "sample_outputs": ["YES", "NO"], "notes": "NoteIn the first sample case, one possible list of identifiers would be \"number string number character number string number\". Here how Kostya would obfuscate the program: replace all occurences of number with a, the result would be \"a string a character a string a\", replace all occurences of string with b, the result would be \"a b a character a b a\", replace all occurences of character with c, the result would be \"a b a c a b a\", all identifiers have been replaced, thus the obfuscation is finished."}, "src_uid": "c4551f66a781b174f95865fa254ca972"}
{"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": "There are three doors in front of you, numbered from $$$1$$$ to $$$3$$$ from left to right. Each door has a lock on it, which can only be opened with a key with the same number on it as the number on the door.There are three keys — one for each door. Two of them are hidden behind the doors, so that there is no more than one key behind each door. So two doors have one key behind them, one door doesn't have a key behind it. To obtain a key hidden behind a door, you should first unlock that door. The remaining key is in your hands.Can you open all the doors?", "input_spec": "The first line contains a single integer $$$t$$$ ($$$1 \\le t \\le 18$$$) — the number of testcases. The first line of each testcase contains a single integer $$$x$$$ ($$$1 \\le x \\le 3$$$) — the number on the key in your hands. The second line contains three integers $$$a, b$$$ and $$$c$$$ ($$$0 \\le a, b, c \\le 3$$$) — the number on the key behind each of the doors. If there is no key behind the door, the number is equal to $$$0$$$. Values $$$1, 2$$$ and $$$3$$$ appear exactly once among $$$x, a, b$$$ and $$$c$$$.", "output_spec": "For each testcase, print \"YES\" if you can open all the doors. Otherwise, print \"NO\".", "sample_inputs": ["4\n\n3\n\n0 1 2\n\n1\n\n0 3 2\n\n2\n\n3 1 0\n\n2\n\n1 3 0"], "sample_outputs": ["YES\nNO\nYES\nNO"], "notes": null}, "src_uid": "5cd113a30bbbb93d8620a483d4da0349"}
{"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": "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": "One tradition of welcoming the New Year is launching fireworks into the sky. Usually a launched firework flies vertically upward for some period of time, then explodes, splitting into several parts flying in different directions. Sometimes those parts also explode after some period of time, splitting into even more parts, and so on.Limak, who lives in an infinite grid, has a single firework. The behaviour of the firework is described with a recursion depth n and a duration for each level of recursion t1, t2, ..., tn. Once Limak launches the firework in some cell, the firework starts moving upward. After covering t1 cells (including the starting cell), it explodes and splits into two parts, each moving in the direction changed by 45 degrees (see the pictures below for clarification). So, one part moves in the top-left direction, while the other one moves in the top-right direction. Each part explodes again after covering t2 cells, splitting into two parts moving in directions again changed by 45 degrees. The process continues till the n-th level of recursion, when all 2n - 1 existing parts explode and disappear without creating new parts. After a few levels of recursion, it's possible that some parts will be at the same place and at the same time — it is allowed and such parts do not crash.Before launching the firework, Limak must make sure that nobody stands in cells which will be visited at least once by the firework. Can you count the number of those cells?", "input_spec": "The first line of the input contains a single integer n (1 ≤ n ≤ 30) — the total depth of the recursion. The second line contains n integers t1, t2, ..., tn (1 ≤ ti ≤ 5). On the i-th level each of 2i - 1 parts will cover ti cells before exploding.", "output_spec": "Print one integer, denoting the number of cells which will be visited at least once by any part of the firework.", "sample_inputs": ["4\n4 2 2 3", "6\n1 1 1 1 1 3", "1\n3"], "sample_outputs": ["39", "85", "3"], "notes": "NoteFor the first sample, the drawings below show the situation after each level of recursion. Limak launched the firework from the bottom-most red cell. It covered t1 = 4 cells (marked red), exploded and divided into two parts (their further movement is marked green). All explosions are marked with an 'X' character. On the last drawing, there are 4 red, 4 green, 8 orange and 23 pink cells. So, the total number of visited cells is 4 + 4 + 8 + 23 = 39.  For the second sample, the drawings below show the situation after levels 4, 5 and 6. The middle drawing shows directions of all parts that will move in the next level.  "}, "src_uid": "a96bc7f93fe9d9d4b78018b49bbc68d9"}
{"nl": {"description": "Mr. Funt now lives in a country with a very specific tax laws. The total income of mr. Funt during this year is equal to n (n ≥ 2) burles and the amount of tax he has to pay is calculated as the maximum divisor of n (not equal to n, of course). For example, if n = 6 then Funt has to pay 3 burles, while for n = 25 he needs to pay 5 and if n = 2 he pays only 1 burle.As mr. Funt is a very opportunistic person he wants to cheat a bit. In particular, he wants to split the initial n in several parts n1 + n2 + ... + nk = n (here k is arbitrary, even k = 1 is allowed) and pay the taxes for each part separately. He can't make some part equal to 1 because it will reveal him. So, the condition ni ≥ 2 should hold for all i from 1 to k.Ostap Bender wonders, how many money Funt has to pay (i.e. minimal) if he chooses and optimal way to split n in parts.", "input_spec": "The first line of the input contains a single integer n (2 ≤ n ≤ 2·109) — the total year income of mr. Funt.", "output_spec": "Print one integer — minimum possible number of burles that mr. Funt has to pay as a tax.", "sample_inputs": ["4", "27"], "sample_outputs": ["2", "3"], "notes": null}, "src_uid": "684ce84149d6a5f4776ecd1ea6cb455b"}
{"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": "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": "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": "Nastya received a gift on New Year — a magic wardrobe. It is magic because in the end of each month the number of dresses in it doubles (i.e. the number of dresses becomes twice as large as it is in the beginning of the month).Unfortunately, right after the doubling the wardrobe eats one of the dresses (if any) with the 50% probability. It happens every month except the last one in the year. Nastya owns x dresses now, so she became interested in the expected number of dresses she will have in one year. Nastya lives in Byteland, so the year lasts for k + 1 months.Nastya is really busy, so she wants you to solve this problem. You are the programmer, after all. Also, you should find the answer modulo 109 + 7, because it is easy to see that it is always integer.", "input_spec": "The only line contains two integers x and k (0 ≤ x, k ≤ 1018), where x is the initial number of dresses and k + 1 is the number of months in a year in Byteland.", "output_spec": "In the only line print a single integer — the expected number of dresses Nastya will own one year later modulo 109 + 7.", "sample_inputs": ["2 0", "2 1", "3 2"], "sample_outputs": ["4", "7", "21"], "notes": "NoteIn the first example a year consists on only one month, so the wardrobe does not eat dresses at all.In the second example after the first month there are 3 dresses with 50% probability and 4 dresses with 50% probability. Thus, in the end of the year there are 6 dresses with 50% probability and 8 dresses with 50% probability. This way the answer for this test is (6 + 8) / 2 = 7."}, "src_uid": "e0e017e8c8872fc1957242ace739464d"}
{"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": "Copying large hexadecimal (base 16) strings by hand can be error prone, but that doesn't stop people from doing it. You've discovered a bug in the code that was likely caused by someone making a mistake when copying such a string. You suspect that whoever copied the string did not change any of the digits in the string, nor the length of the string, but may have permuted the digits arbitrarily. For example, if the original string was 0abc they may have changed it to a0cb or 0bca, but not abc or 0abb.Unfortunately you don't have access to the original string nor the copied string, but you do know the length of the strings and their numerical absolute difference. You will be given this difference as a hexadecimal string S, which has been zero-extended to be equal in length to the original and copied strings. Determine the smallest possible numerical value of the original string.", "input_spec": "Input will contain a hexadecimal string S consisting only of digits 0 to 9 and lowercase English letters from a to f, with length at most 14. At least one of the characters is non-zero.", "output_spec": "If it is not possible, print \"NO\" (without quotes). Otherwise, print the lowercase hexadecimal string corresponding to the smallest possible numerical value, including any necessary leading zeros for the length to be correct.", "sample_inputs": ["f1e", "0f1e", "12d2c"], "sample_outputs": ["NO", "00f1", "00314"], "notes": "NoteThe numerical value of a hexadecimal string is computed by multiplying each digit by successive powers of 16, starting with the rightmost digit, which is multiplied by 160. Hexadecimal digits representing values greater than 9 are represented by letters: a = 10, b = 11, c = 12, d = 13, e = 14, f = 15.For example, the numerical value of 0f1e is 0·163 + 15·162 + 1·161 + 14·160 = 3870, the numerical value of 00f1 is 0·163 + 0·162 + 15·161 + 1·160 = 241, and the numerical value of 100f is 1·163 + 0·162 + 0·161 + 15·160 = 4111. Since 3870 + 241 = 4111 and 00f1 is a permutation of 100f, 00f1 is a valid answer to the second test case."}, "src_uid": "7fab93f1307159262fcc6044ecba6284"}
{"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": "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": "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": "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": "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": "There are n cards (n is even) in the deck. Each card has a positive integer written on it. n / 2 people will play new card game. At the beginning of the game each player gets two cards, each card is given to exactly one player. Find the way to distribute cards such that the sum of values written of the cards will be equal for each player. It is guaranteed that it is always possible.", "input_spec": "The first line of the input contains integer n (2 ≤ n ≤ 100) — the number of cards in the deck. It is guaranteed that n is even. The second line contains the sequence of n positive integers a1, a2, ..., an (1 ≤ ai ≤ 100), where ai is equal to the number written on the i-th card.", "output_spec": "Print n / 2 pairs of integers, the i-th pair denote the cards that should be given to the i-th player. Each card should be given to exactly one player. Cards are numbered in the order they appear in the input. It is guaranteed that solution exists. If there are several correct answers, you are allowed to print any of them.", "sample_inputs": ["6\n1 5 7 4 4 3", "4\n10 10 10 10"], "sample_outputs": ["1 3\n6 2\n4 5", "1 2\n3 4"], "notes": "NoteIn the first sample, cards are distributed in such a way that each player has the sum of numbers written on his cards equal to 8. In the second sample, all values ai are equal. Thus, any distribution is acceptable."}, "src_uid": "6e5011801ceff9d76e33e0908b695132"}
{"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": "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": "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": "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": "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": "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": "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": "You are given two integer numbers, $$$n$$$ and $$$x$$$. You may perform several operations with the integer $$$x$$$.Each operation you perform is the following one: choose any digit $$$y$$$ that occurs in the decimal representation of $$$x$$$ at least once, and replace $$$x$$$ by $$$x \\cdot y$$$.You want to make the length of decimal representation of $$$x$$$ (without leading zeroes) equal to $$$n$$$. What is the minimum number of operations required to do that?", "input_spec": "The only line of the input contains two integers $$$n$$$ and $$$x$$$ ($$$2 \\le n \\le 19$$$; $$$1 \\le x < 10^{n-1}$$$).", "output_spec": "Print one integer — the minimum number of operations required to make the length of decimal representation of $$$x$$$ (without leading zeroes) equal to $$$n$$$, or $$$-1$$$ if it is impossible.", "sample_inputs": ["2 1", "3 2", "13 42"], "sample_outputs": ["-1", "4", "12"], "notes": "NoteIn the second example, the following sequence of operations achieves the goal:  multiply $$$x$$$ by $$$2$$$, so $$$x = 2 \\cdot 2 = 4$$$;  multiply $$$x$$$ by $$$4$$$, so $$$x = 4 \\cdot 4 = 16$$$;  multiply $$$x$$$ by $$$6$$$, so $$$x = 16 \\cdot 6 = 96$$$;  multiply $$$x$$$ by $$$9$$$, so $$$x = 96 \\cdot 9 = 864$$$. "}, "src_uid": "cedcc3cee864bf8684148df93804d029"}
{"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": "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": "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 $$$m$$$ ($$$2 \\le n \\le 4 \\cdot 10^6$$$; $$$10^8 < m < 10^9$$$; $$$m$$$ 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", "787788 100000007"], "sample_outputs": ["5", "25", "793019428", "94810539"], "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": "77443424be253352aaf2b6c89bdd4671"}
{"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": "On the planet Mars a year lasts exactly n days (there are no leap years on Mars). But Martians have the same weeks as earthlings — 5 work days and then 2 days off. Your task is to determine the minimum possible and the maximum possible number of days off per year on Mars.", "input_spec": "The first line of the input contains a positive integer n (1 ≤ n ≤ 1 000 000) — the number of days in a year on Mars.", "output_spec": "Print two integers — the minimum possible and the maximum possible number of days off per year on Mars.", "sample_inputs": ["14", "2"], "sample_outputs": ["4 4", "0 2"], "notes": "NoteIn the first sample there are 14 days in a year on Mars, and therefore independently of the day a year starts with there will be exactly 4 days off .In the second sample there are only 2 days in a year on Mars, and they can both be either work days or days off."}, "src_uid": "8152daefb04dfa3e1a53f0a501544c35"}
{"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": "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": "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": "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": "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": "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": "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": "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": "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": "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": "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": "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": "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": "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": "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": "This is an easier version of the problem. In this version, $$$n \\le 500$$$.Vasya is an experienced developer of programming competitions' problems. As all great minds at some time, Vasya faced a creative crisis. To improve the situation, Petya gifted him a string consisting of opening and closing brackets only. Petya believes, that the beauty of the bracket string is a number of its cyclical shifts, which form a correct bracket sequence.To digress from his problems, Vasya decided to select two positions of the string (not necessarily distinct) and swap characters located at this positions with each other. Vasya will apply this operation exactly once. He is curious what is the maximum possible beauty he can achieve this way. Please help him.We remind that bracket sequence $$$s$$$ is called correct if:   $$$s$$$ is empty;  $$$s$$$ is equal to \"($$$t$$$)\", where $$$t$$$ is correct bracket sequence;  $$$s$$$ is equal to $$$t_1 t_2$$$, i.e. concatenation of $$$t_1$$$ and $$$t_2$$$, where $$$t_1$$$ and $$$t_2$$$ are correct bracket sequences. For example, \"(()())\", \"()\" are correct, while \")(\" and \"())\" are not.The cyclical shift of the string $$$s$$$ of length $$$n$$$ by $$$k$$$ ($$$0 \\leq k < n$$$) is a string formed by a concatenation of the last $$$k$$$ symbols of the string $$$s$$$ with the first $$$n - k$$$ symbols of string $$$s$$$. For example, the cyclical shift of string \"(())()\" by $$$2$$$ equals \"()(())\".Cyclical shifts $$$i$$$ and $$$j$$$ are considered different, if $$$i \\ne j$$$.", "input_spec": "The first line contains an integer $$$n$$$ ($$$1 \\le n \\le 500$$$), the length of the string. The second line contains a string, consisting of exactly $$$n$$$ characters, where each of the characters is either \"(\" or \")\".", "output_spec": "The first line should contain a single integer — the largest beauty of the string, which can be achieved by swapping some two characters. The second line should contain integers $$$l$$$ and $$$r$$$ ($$$1 \\leq l, r \\leq n$$$) — the indices of two characters, which should be swapped in order to maximize the string's beauty. In case there are several possible swaps, print any of them.", "sample_inputs": ["10\n()()())(()", "12\n)(()(()())()", "6\n)))(()"], "sample_outputs": ["5\n8 7", "4\n5 10", "0\n1 1"], "notes": "NoteIn the first example, we can swap $$$7$$$-th and $$$8$$$-th character, obtaining a string \"()()()()()\". The cyclical shifts by $$$0, 2, 4, 6, 8$$$ of this string form a correct bracket sequence.In the second example, after swapping $$$5$$$-th and $$$10$$$-th character, we obtain a string \")(())()()(()\". The cyclical shifts by $$$11, 7, 5, 3$$$ of this string form a correct bracket sequence.In the third example, swap of any two brackets results in $$$0$$$ cyclical shifts being correct bracket sequences. "}, "src_uid": "2d10668fcc2d8e90e102b043f5e0578d"}
{"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": "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": "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": "Recall that a binary search tree is a rooted binary tree, whose nodes each store a key and each have at most two distinguished subtrees, left and right. The key in each node must be greater than any key stored in the left subtree, and less than any key stored in the right subtree.The depth of a vertex is the number of edges on the simple path from the vertex to the root. In particular, the depth of the root is $$$0$$$.Let's call a binary search tree perfectly balanced if there doesn't exist a binary search tree with the same number of vertices that has a strictly smaller sum of depths of its vertices.Let's call a binary search tree with integer keys striped if both of the following conditions are satisfied for every vertex $$$v$$$:   If $$$v$$$ has a left subtree whose root is $$$u$$$, then the parity of the key of $$$v$$$ is different from the parity of the key of $$$u$$$.  If $$$v$$$ has a right subtree whose root is $$$w$$$, then the parity of the key of $$$v$$$ is the same as the parity of the key of $$$w$$$. You are given a single integer $$$n$$$. Find the number of perfectly balanced striped binary search trees with $$$n$$$ vertices that have distinct integer keys between $$$1$$$ and $$$n$$$, inclusive. Output this number modulo $$$998\\,244\\,353$$$.", "input_spec": "The only line contains a single integer $$$n$$$ ($$$1 \\le n \\le 10^6$$$), denoting the required number of vertices.", "output_spec": "Output the number of perfectly balanced striped binary search trees with $$$n$$$ vertices and distinct integer keys between $$$1$$$ and $$$n$$$, inclusive, modulo $$$998\\,244\\,353$$$.", "sample_inputs": ["4", "3"], "sample_outputs": ["1", "0"], "notes": "NoteIn the first example, this is the only tree that satisfies the conditions: In the second example, here are various trees that don't satisfy some condition: "}, "src_uid": "821409c1b9bdcd18c4dcf35dc5116501"}
{"nl": {"description": "Misha and Vanya have played several table tennis sets. Each set consists of several serves, each serve is won by one of the players, he receives one point and the loser receives nothing. Once one of the players scores exactly k points, the score is reset and a new set begins.Across all the sets Misha scored a points in total, and Vanya scored b points. Given this information, determine the maximum number of sets they could have played, or that the situation is impossible.Note that the game consisted of several complete sets.", "input_spec": "The first line contains three space-separated integers k, a and b (1 ≤ k ≤ 109, 0 ≤ a, b ≤ 109, a + b > 0).", "output_spec": "If the situation is impossible, print a single number -1. Otherwise, print the maximum possible number of sets.", "sample_inputs": ["11 11 5", "11 2 3"], "sample_outputs": ["1", "-1"], "notes": "NoteNote that the rules of the game in this problem differ from the real table tennis game, for example, the rule of \"balance\" (the winning player has to be at least two points ahead to win a set) has no power within the present problem."}, "src_uid": "6e3b8193d1ca1a1d449dc7a4ad45b8f2"}
{"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": "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": "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": "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": "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": "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": "Today is Wednesday, the third day of the week. What's more interesting is that tomorrow is the last day of the year 2015.Limak is a little polar bear. He enjoyed this year a lot. Now, he is so eager to the coming year 2016.Limak wants to prove how responsible a bear he is. He is going to regularly save candies for the entire year 2016! He considers various saving plans. He can save one candy either on some fixed day of the week or on some fixed day of the month.Limak chose one particular plan. He isn't sure how many candies he will save in the 2016 with his plan. Please, calculate it and tell him.", "input_spec": "The only line of the input is in one of the following two formats:    \"x of week\" where x (1 ≤ x ≤ 7) denotes the day of the week. The 1-st day is Monday and the 7-th one is Sunday.  \"x of month\" where x (1 ≤ x ≤ 31) denotes the day of the month. ", "output_spec": "Print one integer — the number of candies Limak will save in the year 2016.", "sample_inputs": ["4 of week", "30 of month"], "sample_outputs": ["52", "11"], "notes": "NotePolar bears use the Gregorian calendar. It is the most common calendar and you likely use it too. You can read about it on Wikipedia if you want to – https://en.wikipedia.org/wiki/Gregorian_calendar. The week starts with Monday.In the first sample Limak wants to save one candy on each Thursday (the 4-th day of the week). There are 52 Thursdays in the 2016. Thus, he will save 52 candies in total.In the second sample Limak wants to save one candy on the 30-th day of each month. There is the 30-th day in exactly 11 months in the 2016 — all months but February. It means that Limak will save 11 candies in total."}, "src_uid": "9b8543c1ae3666e6c163d268fdbeef6b"}
{"nl": {"description": "Vasya lives in a round building, whose entrances are numbered sequentially by integers from 1 to n. Entrance n and entrance 1 are adjacent.Today Vasya got bored and decided to take a walk in the yard. Vasya lives in entrance a and he decided that during his walk he will move around the house b entrances in the direction of increasing numbers (in this order entrance n should be followed by entrance 1). The negative value of b corresponds to moving |b| entrances in the order of decreasing numbers (in this order entrance 1 is followed by entrance n). If b = 0, then Vasya prefers to walk beside his entrance.    Illustration for n = 6, a = 2, b =  - 5. Help Vasya to determine the number of the entrance, near which he will be at the end of his walk.", "input_spec": "The single line of the input contains three space-separated integers n, a and b (1 ≤ n ≤ 100, 1 ≤ a ≤ n,  - 100 ≤ b ≤ 100) — the number of entrances at Vasya's place, the number of his entrance and the length of his walk, respectively.", "output_spec": "Print a single integer k (1 ≤ k ≤ n) — the number of the entrance where Vasya will be at the end of his walk.", "sample_inputs": ["6 2 -5", "5 1 3", "3 2 7"], "sample_outputs": ["3", "4", "3"], "notes": "NoteThe first example is illustrated by the picture in the statements."}, "src_uid": "cd0e90042a6aca647465f1d51e6dffc4"}
{"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": "Kolya is developing an economy simulator game. His most favourite part of the development process is in-game testing. Once he was entertained by the testing so much, that he found out his game-coin score become equal to 0.Kolya remembers that at the beginning of the game his game-coin score was equal to n and that he have bought only some houses (for 1 234 567 game-coins each), cars (for 123 456 game-coins each) and computers (for 1 234 game-coins each).Kolya is now interested, whether he could have spent all of his initial n game-coins buying only houses, cars and computers or there is a bug in the game. Formally, is there a triple of non-negative integers a, b and c such that a × 1 234 567 + b × 123 456 + c × 1 234 = n?Please help Kolya answer this question.", "input_spec": "The first line of the input contains a single integer n (1 ≤ n ≤ 109) — Kolya's initial game-coin score.", "output_spec": "Print \"YES\" (without quotes) if it's possible that Kolya spent all of his initial n coins buying only houses, cars and computers. Otherwise print \"NO\" (without quotes).", "sample_inputs": ["1359257", "17851817"], "sample_outputs": ["YES", "NO"], "notes": "NoteIn the first sample, one of the possible solutions is to buy one house, one car and one computer, spending 1 234 567 + 123 456 + 1234 = 1 359 257 game-coins in total."}, "src_uid": "72d7e422a865cc1f85108500bdf2adf2"}
{"nl": {"description": "A magic number is a number formed by concatenation of numbers 1, 14 and 144. We can use each of these numbers any number of times. Therefore 14144, 141414 and 1411 are magic numbers but 1444, 514 and 414 are not.You're given a number. Determine if it is a magic number or not.", "input_spec": "The first line of input contains an integer n, (1 ≤ n ≤ 109). This number doesn't contain leading zeros.", "output_spec": "Print \"YES\" if n is a magic number or print \"NO\" if it's not.", "sample_inputs": ["114114", "1111", "441231"], "sample_outputs": ["YES", "YES", "NO"], "notes": null}, "src_uid": "3153cfddae27fbd817caaf2cb7a6a4b5"}
{"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": "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": "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": "You are given a tree (a connected non-oriented graph without cycles) with vertices numbered from 1 to n, and the length of the i-th edge is wi. In the vertex s there is a policeman, in the vertices x1, x2, ..., xm (xj ≠ s) m criminals are located.The policeman can walk along the edges with speed 1, the criminals can move with arbitrary large speed. If a criminal at some moment is at the same point as the policeman, he instantly gets caught by the policeman. Determine the time needed for the policeman to catch all criminals, assuming everybody behaves optimally (i.e. the criminals maximize that time, the policeman minimizes that time). Everybody knows positions of everybody else at any moment of time.", "input_spec": "The first line contains single integer n (1 ≤ n ≤ 50) — the number of vertices in the tree. The next n - 1 lines contain three integers each: ui, vi, wi (1 ≤ ui, vi ≤ n, 1 ≤ wi ≤ 50) denoting edges and their lengths. It is guaranteed that the given graph is a tree. The next line contains single integer s (1 ≤ s ≤ n) — the number of vertex where the policeman starts. The next line contains single integer m (1 ≤ m ≤ 50) — the number of criminals. The next line contains m integers x1, x2, ..., xm (1 ≤ xj ≤ n, xj ≠ s) — the number of vertices where the criminals are located. xj are not necessarily distinct.", "output_spec": "If the policeman can't catch criminals, print single line \"Terrorists win\" (without quotes). Otherwise, print single integer — the time needed to catch all criminals.", "sample_inputs": ["4\n1 2 2\n1 3 1\n1 4 1\n2\n4\n3 1 4 1", "6\n1 2 3\n2 3 5\n3 4 1\n3 5 4\n2 6 3\n2\n3\n1 3 5"], "sample_outputs": ["8", "21"], "notes": "NoteIn the first example one of the optimal scenarios is the following. The criminal number 2 moves to vertex 3, the criminal 4 — to vertex 4. The policeman goes to vertex 4 and catches two criminals. After that the criminal number 1 moves to the vertex 2. The policeman goes to vertex 3 and catches criminal 2, then goes to the vertex 2 and catches the remaining criminal."}, "src_uid": "34b926f903c2412fe76f912ccb8a00dd"}
{"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": "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": "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": "Today, Osama gave Fadi an integer $$$X$$$, and Fadi was wondering about the minimum possible value of $$$max(a, b)$$$ such that $$$LCM(a, b)$$$ equals $$$X$$$. Both $$$a$$$ and $$$b$$$ should be positive integers.$$$LCM(a, b)$$$ is the smallest positive integer that is divisible by both $$$a$$$ and $$$b$$$. For example, $$$LCM(6, 8) = 24$$$, $$$LCM(4, 12) = 12$$$, $$$LCM(2, 3) = 6$$$.Of course, Fadi immediately knew the answer. Can you be just like Fadi and find any such pair?", "input_spec": "The first and only line contains an integer $$$X$$$ ($$$1 \\le X \\le 10^{12}$$$).", "output_spec": "Print two positive integers, $$$a$$$ and $$$b$$$, such that the value of $$$max(a, b)$$$ is minimum possible and $$$LCM(a, b)$$$ equals $$$X$$$. If there are several possible such pairs, you can print any.", "sample_inputs": ["2", "6", "4", "1"], "sample_outputs": ["1 2", "2 3", "1 4", "1 1"], "notes": null}, "src_uid": "e504a04cefef3da093573f9df711bcea"}
{"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": "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": "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": "The only difference between easy and hard versions is the length of the string.You are given a string $$$s$$$ and a string $$$t$$$, both consisting only of lowercase Latin letters. It is guaranteed that $$$t$$$ can be obtained from $$$s$$$ by removing some (possibly, zero) number of characters (not necessary contiguous) from $$$s$$$ without changing order of remaining characters (in other words, it is guaranteed that $$$t$$$ is a subsequence of $$$s$$$).For example, the strings \"test\", \"tst\", \"tt\", \"et\" and \"\" are subsequences of the string \"test\". But the strings \"tset\", \"se\", \"contest\" are not subsequences of the string \"test\".You want to remove some substring (contiguous subsequence) from $$$s$$$ of maximum possible length such that after removing this substring $$$t$$$ will remain a subsequence of $$$s$$$.If you want to remove the substring $$$s[l;r]$$$ then the string $$$s$$$ will be transformed to $$$s_1 s_2 \\dots s_{l-1} s_{r+1} s_{r+2} \\dots s_{|s|-1} s_{|s|}$$$ (where $$$|s|$$$ is the length of $$$s$$$).Your task is to find the maximum possible length of the substring you can remove so that $$$t$$$ is still a subsequence of $$$s$$$.", "input_spec": "The first line of the input contains one string $$$s$$$ consisting of at least $$$1$$$ and at most $$$200$$$ lowercase Latin letters. The second line of the input contains one string $$$t$$$ consisting of at least $$$1$$$ and at most $$$200$$$ lowercase Latin letters. It is guaranteed that $$$t$$$ is a subsequence of $$$s$$$.", "output_spec": "Print one integer — the maximum possible length of the substring you can remove so that $$$t$$$ is still a subsequence of $$$s$$$.", "sample_inputs": ["bbaba\nbb", "baaba\nab", "abcde\nabcde", "asdfasdf\nfasd"], "sample_outputs": ["3", "2", "0", "3"], "notes": null}, "src_uid": "0fd33e1bdfd6c91feb3bf00a2461603f"}
{"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": "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": "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": "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": "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": "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": "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": "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": "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": "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": "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": "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": "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": "It is a balmy spring afternoon, and Farmer John's n cows are ruminating about link-cut cacti in their stalls. The cows, labeled 1 through n, are arranged so that the i-th cow occupies the i-th stall from the left. However, Elsie, after realizing that she will forever live in the shadows beyond Bessie's limelight, has formed the Mischievous Mess Makers and is plotting to disrupt this beautiful pastoral rhythm. While Farmer John takes his k minute long nap, Elsie and the Mess Makers plan to repeatedly choose two distinct stalls and swap the cows occupying those stalls, making no more than one swap each minute.Being the meticulous pranksters that they are, the Mischievous Mess Makers would like to know the maximum messiness attainable in the k minutes that they have. We denote as pi the label of the cow in the i-th stall. The messiness of an arrangement of cows is defined as the number of pairs (i, j) such that i < j and pi > pj.", "input_spec": "The first line of the input contains two integers n and k (1 ≤ n, k ≤ 100 000) — the number of cows and the length of Farmer John's nap, respectively.", "output_spec": "Output a single integer, the maximum messiness that the Mischievous Mess Makers can achieve by performing no more than k swaps. ", "sample_inputs": ["5 2", "1 10"], "sample_outputs": ["10", "0"], "notes": "NoteIn the first sample, the Mischievous Mess Makers can swap the cows in the stalls 1 and 5 during the first minute, then the cows in stalls 2 and 4 during the second minute. This reverses the arrangement of cows, giving us a total messiness of 10.In the second sample, there is only one cow, so the maximum possible messiness is 0."}, "src_uid": "ea36ca0a3c336424d5b7e1b4c56947b0"}
{"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": "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": "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": "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": "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": "Gerald is very particular to eight point sets. He thinks that any decent eight point set must consist of all pairwise intersections of three distinct integer vertical straight lines and three distinct integer horizontal straight lines, except for the average of these nine points. In other words, there must be three integers x1, x2, x3 and three more integers y1, y2, y3, such that x1 < x2 < x3, y1 < y2 < y3 and the eight point set consists of all points (xi, yj) (1 ≤ i, j ≤ 3), except for point (x2, y2).You have a set of eight points. Find out if Gerald can use this set?", "input_spec": "The input consists of eight lines, the i-th line contains two space-separated integers xi and yi (0 ≤ xi, yi ≤ 106). You do not have any other conditions for these points.", "output_spec": "In a single line print word \"respectable\", if the given set of points corresponds to Gerald's decency rules, and \"ugly\" otherwise.", "sample_inputs": ["0 0\n0 1\n0 2\n1 0\n1 2\n2 0\n2 1\n2 2", "0 0\n1 0\n2 0\n3 0\n4 0\n5 0\n6 0\n7 0", "1 1\n1 2\n1 3\n2 1\n2 2\n2 3\n3 1\n3 2"], "sample_outputs": ["respectable", "ugly", "ugly"], "notes": null}, "src_uid": "f3c96123334534056f26b96f90886807"}
{"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": "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": "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": "All bus tickets in Berland have their numbers. A number consists of $$$n$$$ digits ($$$n$$$ is even). Only $$$k$$$ decimal digits $$$d_1, d_2, \\dots, d_k$$$ can be used to form ticket numbers. If $$$0$$$ is among these digits, then numbers may have leading zeroes. For example, if $$$n = 4$$$ and only digits $$$0$$$ and $$$4$$$ can be used, then $$$0000$$$, $$$4004$$$, $$$4440$$$ are valid ticket numbers, and $$$0002$$$, $$$00$$$, $$$44443$$$ are not.A ticket is lucky if the sum of first $$$n / 2$$$ digits is equal to the sum of remaining $$$n / 2$$$ digits. Calculate the number of different lucky tickets in Berland. Since the answer may be big, print it modulo $$$998244353$$$.", "input_spec": "The first line contains two integers $$$n$$$ and $$$k$$$ $$$(2 \\le n \\le 2 \\cdot 10^5, 1 \\le k \\le 10)$$$ — the number of digits in each ticket number, and the number of different decimal digits that may be used. $$$n$$$ is even. The second line contains a sequence of pairwise distinct integers $$$d_1, d_2, \\dots, d_k$$$ $$$(0 \\le d_i \\le 9)$$$ — the digits that may be used in ticket numbers. The digits are given in arbitrary order.", "output_spec": "Print the number of lucky ticket numbers, taken modulo $$$998244353$$$.", "sample_inputs": ["4 2\n1 8", "20 1\n6", "10 5\n6 1 4 0 3", "1000 7\n5 4 0 1 8 3 2"], "sample_outputs": ["6", "1", "569725", "460571165"], "notes": "NoteIn the first example there are $$$6$$$ lucky ticket numbers: $$$1111$$$, $$$1818$$$, $$$1881$$$, $$$8118$$$, $$$8181$$$ and $$$8888$$$.There is only one ticket number in the second example, it consists of $$$20$$$ digits $$$6$$$. This ticket number is lucky, so the answer is $$$1$$$."}, "src_uid": "279f1f7d250a4be6406c6c7bfc818bbf"}
{"nl": {"description": "A divisor tree is a rooted tree that meets the following conditions:   Each vertex of the tree contains a positive integer number.  The numbers written in the leaves of the tree are prime numbers.  For any inner vertex, the number within it is equal to the product of the numbers written in its children. Manao has n distinct integers a1, a2, ..., an. He tries to build a divisor tree which contains each of these numbers. That is, for each ai, there should be at least one vertex in the tree which contains ai. Manao loves compact style, but his trees are too large. Help Manao determine the minimum possible number of vertices in the divisor tree sought.", "input_spec": "The first line contains a single integer n (1 ≤ n ≤ 8). The second line contains n distinct space-separated integers ai (2 ≤ ai ≤ 1012).", "output_spec": "Print a single integer — the minimum number of vertices in the divisor tree that contains each of the numbers ai.", "sample_inputs": ["2\n6 10", "4\n6 72 8 4", "1\n7"], "sample_outputs": ["7", "12", "1"], "notes": "NoteSample 1. The smallest divisor tree looks this way: Sample 2. In this case you can build the following divisor tree: Sample 3. Note that the tree can consist of a single vertex."}, "src_uid": "52b8b6c68518d5129272b8c56e5b7662"}
{"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": "The Floral Clock has been standing by the side of Mirror Lake for years. Though unable to keep time, it reminds people of the passage of time and the good old days.On the rim of the Floral Clock are 2n flowers, numbered from 1 to 2n clockwise, each of which has a colour among all n possible ones. For each colour, there are exactly two flowers with it, the distance between which either is less than or equal to 2, or equals n. Additionally, if flowers u and v are of the same colour, then flowers opposite to u and opposite to v should be of the same colour as well — symmetry is beautiful!Formally, the distance between two flowers is 1 plus the number of flowers on the minor arc (or semicircle) between them. Below is a possible arrangement with n = 6 that cover all possibilities.  The beauty of an arrangement is defined to be the product of the lengths of flower segments separated by all opposite flowers of the same colour. In other words, in order to compute the beauty, we remove from the circle all flowers that have the same colour as flowers opposite to them. Then, the beauty is the product of lengths of all remaining segments. Note that we include segments of length 0 in this product. If there are no flowers that have the same colour as flower opposite to them, the beauty equals 0. For instance, the beauty of the above arrangement equals 1 × 3 × 1 × 3 = 9 — the segments are {2}, {4, 5, 6}, {8} and {10, 11, 12}.While keeping the constraints satisfied, there may be lots of different arrangements. Find out the sum of beauty over all possible arrangements, modulo 998 244 353. Two arrangements are considered different, if a pair (u, v) (1 ≤ u, v ≤ 2n) exists such that flowers u and v are of the same colour in one of them, but not in the other.", "input_spec": "The first and only line of input contains a lonely positive integer n (3 ≤ n ≤ 50 000) — the number of colours present on the Floral Clock.", "output_spec": "Output one integer — the sum of beauty over all possible arrangements of flowers, modulo 998 244 353.", "sample_inputs": ["3", "4", "7", "15"], "sample_outputs": ["24", "4", "1316", "3436404"], "notes": "NoteWith n = 3, the following six arrangements each have a beauty of 2 × 2 = 4.  While many others, such as the left one in the figure below, have a beauty of 0. The right one is invalid, since it's asymmetric.  "}, "src_uid": "24fd5cd218f65d4ffb7c5b97b725293e"}
{"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": "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": "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": "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"}
{"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": "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 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": "Dreamoon is standing at the position 0 on a number line. Drazil is sending a list of commands through Wi-Fi to Dreamoon's smartphone and Dreamoon follows them.Each command is one of the following two types:   Go 1 unit towards the positive direction, denoted as '+'  Go 1 unit towards the negative direction, denoted as '-' But the Wi-Fi condition is so poor that Dreamoon's smartphone reports some of the commands can't be recognized and Dreamoon knows that some of them might even be wrong though successfully recognized. Dreamoon decides to follow every recognized command and toss a fair coin to decide those unrecognized ones (that means, he moves to the 1 unit to the negative or positive direction with the same probability 0.5). You are given an original list of commands sent by Drazil and list received by Dreamoon. What is the probability that Dreamoon ends in the position originally supposed to be final by Drazil's commands?", "input_spec": "The first line contains a string s1 — the commands Drazil sends to Dreamoon, this string consists of only the characters in the set {'+', '-'}.  The second line contains a string s2 — the commands Dreamoon's smartphone recognizes, this string consists of only the characters in the set {'+', '-', '?'}. '?' denotes an unrecognized command. Lengths of two strings are equal and do not exceed 10.", "output_spec": "Output a single real number corresponding to the probability. The answer will be considered correct if its relative or absolute error doesn't exceed 10 - 9.", "sample_inputs": ["++-+-\n+-+-+", "+-+-\n+-??", "+++\n??-"], "sample_outputs": ["1.000000000000", "0.500000000000", "0.000000000000"], "notes": "NoteFor the first sample, both s1 and s2 will lead Dreamoon to finish at the same position  + 1. For the second sample, s1 will lead Dreamoon to finish at position 0, while there are four possibilites for s2: {\"+-++\", \"+-+-\", \"+--+\", \"+---\"} with ending position {+2, 0, 0, -2} respectively. So there are 2 correct cases out of 4, so the probability of finishing at the correct position is 0.5. For the third sample, s2 could only lead us to finish at positions {+1, -1, -3}, so the probability to finish at the correct position  + 3 is 0."}, "src_uid": "f7f68a15cfd33f641132fac265bc5299"}
{"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": "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": "Kavi has $$$2n$$$ points lying on the $$$OX$$$ axis, $$$i$$$-th of which is located at $$$x = i$$$.Kavi considers all ways to split these $$$2n$$$ points into $$$n$$$ pairs. Among those, he is interested in good pairings, which are defined as follows:Consider $$$n$$$ segments with ends at the points in correspondent pairs. The pairing is called good, if for every $$$2$$$ different segments $$$A$$$ and $$$B$$$ among those, at least one of the following holds:  One of the segments $$$A$$$ and $$$B$$$ lies completely inside the other.  $$$A$$$ and $$$B$$$ have the same length. Consider the following example:  $$$A$$$ is a good pairing since the red segment lies completely inside the blue segment.$$$B$$$ is a good pairing since the red and the blue segment have the same length.$$$C$$$ is not a good pairing since none of the red or blue segments lies inside the other, neither do they have the same size.Kavi is interested in the number of good pairings, so he wants you to find it for him. As the result can be large, find this number modulo $$$998244353$$$.Two pairings are called different, if some two points are in one pair in some pairing and in different pairs in another.", "input_spec": "The single line of the input contains a single integer $$$n$$$ $$$(1\\le n \\le 10^6)$$$.", "output_spec": "Print the number of good pairings modulo $$$998244353$$$.", "sample_inputs": ["1", "2", "3", "100"], "sample_outputs": ["1", "3", "6", "688750769"], "notes": "NoteThe good pairings for the second example are:   In the third example, the good pairings are:   "}, "src_uid": "09be46206a151c237dc9912df7e0f057"}
{"nl": {"description": "Alas, finding one's true love is not easy. Masha has been unsuccessful in that yet. Her friend Dasha told Masha about a way to determine the phone number of one's Prince Charming through arithmancy. The phone number is divined like that. First one needs to write down one's own phone numbers. For example, let's suppose that Masha's phone number is 12345. After that one should write her favorite digit from 0 to 9 under the first digit of her number. That will be the first digit of the needed number. For example, Masha's favorite digit is 9. The second digit is determined as a half sum of the second digit of Masha's number and the already written down first digit from her beloved one's number. In this case the arithmetic average equals to (2 + 9) / 2 = 5.5. Masha can round the number up or down, depending on her wishes. For example, she chooses the digit 5. Having written down the resulting digit under the second digit of her number, Masha moves to finding the third digit in the same way, i.e. finding the half sum the the third digit of her number and the second digit of the new number. The result is (5 + 3) / 2 = 4. In this case the answer is unique. Thus, every i-th digit is determined as an arithmetic average of the i-th digit of Masha's number and the i - 1-th digit of her true love's number. If needed, the digit can be rounded up or down. For example, Masha can get: 12345 95444 Unfortunately, when Masha tried dialing the number, she got disappointed: as it turned out, the number was unavailable or outside the coverage area. But Masha won't give up. Perhaps, she rounded to a wrong digit or chose the first digit badly. That's why she keeps finding more and more new numbers and calling them. Count the number of numbers Masha calls. Masha calls all the possible numbers that can be found by the described means of arithmancy, except for, perhaps, her own one.", "input_spec": "The first line contains nonempty sequence consisting of digits from 0 to 9 — Masha's phone number. The sequence length does not exceed 50.", "output_spec": "Output the single number — the number of phone numbers Masha will dial.", "sample_inputs": ["12345", "09"], "sample_outputs": ["48", "15"], "notes": null}, "src_uid": "2dd8bb6e8182278d037aa3a59ca3517b"}
{"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": "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": "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": "Arkadiy has lots square photos with size a × a. He wants to put some of them on a rectangular wall with size h × w. The photos which Arkadiy will put on the wall must form a rectangular grid and the distances between neighboring vertically and horizontally photos and also the distances between outside rows and columns of photos to the nearest bound of the wall must be equal to x, where x is some non-negative real number. Look on the picture below for better understanding of the statement.  Arkadiy haven't chosen yet how many photos he would put on the wall, however, he want to put at least one photo. Your task is to determine the minimum value of x which can be obtained after putting photos, or report that there is no way to put positive number of photos and satisfy all the constraints. Suppose that Arkadiy has enough photos to make any valid arrangement according to the constraints.Note that Arkadiy wants to put at least one photo on the wall. The photos should not overlap, should completely lie inside the wall bounds and should have sides parallel to the wall sides.", "input_spec": "The first line contains three integers a, h and w (1 ≤ a, h, w ≤ 109) — the size of photos and the height and the width of the wall.", "output_spec": "Print one non-negative real number — the minimum value of x which can be obtained after putting the photos on the wall. The absolute or the relative error of the answer must not exceed 10 - 6. Print -1 if there is no way to put positive number of photos and satisfy the constraints.", "sample_inputs": ["2 18 13", "4 4 4", "3 4 3"], "sample_outputs": ["0.5", "0", "-1"], "notes": "NoteIn the first example Arkadiy can put 7 rows of photos with 5 photos in each row, so the minimum value of x equals to 0.5.In the second example Arkadiy can put only 1 photo which will take the whole wall, so the minimum value of x equals to 0.In the third example there is no way to put positive number of photos and satisfy the constraints described in the statement, so the answer is -1."}, "src_uid": "7fbefd3eb1aad6865adcfac394f0a7e6"}
{"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": "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": "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": "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": "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": "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": "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": "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": "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": "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": "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": "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": "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": "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": "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": "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": "You are given an integer number $$$n$$$. The following algorithm is applied to it:  if $$$n = 0$$$, then end algorithm;  find the smallest prime divisor $$$d$$$ of $$$n$$$;  subtract $$$d$$$ from $$$n$$$ and go to step $$$1$$$. Determine the number of subtrations the algorithm will make.", "input_spec": "The only line contains a single integer $$$n$$$ ($$$2 \\le n \\le 10^{10}$$$).", "output_spec": "Print a single integer — the number of subtractions the algorithm will make.", "sample_inputs": ["5", "4"], "sample_outputs": ["1", "2"], "notes": "NoteIn the first example $$$5$$$ is the smallest prime divisor, thus it gets subtracted right away to make a $$$0$$$.In the second example $$$2$$$ is the smallest prime divisor at both steps."}, "src_uid": "a1e80ddd97026835a84f91bac8eb21e6"}
{"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": "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": "Calculate the number of ways to place $$$n$$$ rooks on $$$n \\times n$$$ chessboard so that both following conditions are met:  each empty cell is under attack;  exactly $$$k$$$ pairs of rooks attack each other. An empty cell is under attack if there is at least one rook in the same row or at least one rook in the same column. Two rooks attack each other if they share the same row or column, and there are no other rooks between them. For example, there are only two pairs of rooks that attack each other in the following picture:  One of the ways to place the rooks for $$$n = 3$$$ and $$$k = 2$$$ Two ways to place the rooks are considered different if there exists at least one cell which is empty in one of the ways but contains a rook in another way.The answer might be large, so print it modulo $$$998244353$$$.", "input_spec": "The only line of the input contains two integers $$$n$$$ and $$$k$$$ ($$$1 \\le n \\le 200000$$$; $$$0 \\le k \\le \\frac{n(n - 1)}{2}$$$).", "output_spec": "Print one integer — the number of ways to place the rooks, taken modulo $$$998244353$$$.", "sample_inputs": ["3 2", "3 3", "4 0", "1337 42"], "sample_outputs": ["6", "0", "24", "807905441"], "notes": null}, "src_uid": "6c1a9aaa7bdd7de97220b8c6d35740cc"}
{"nl": {"description": "Polycarp likes squares and cubes of positive integers. Here is the beginning of the sequence of numbers he likes: $$$1$$$, $$$4$$$, $$$8$$$, $$$9$$$, ....For a given number $$$n$$$, count the number of integers from $$$1$$$ to $$$n$$$ that Polycarp likes. In other words, find the number of such $$$x$$$ that $$$x$$$ is a square of a positive integer number or a cube of a positive integer number (or both a square and a cube simultaneously).", "input_spec": "The first line contains an integer $$$t$$$ ($$$1 \\le t \\le 20$$$) — the number of test cases. Then $$$t$$$ lines contain the test cases, one per line. Each of the lines contains one integer $$$n$$$ ($$$1 \\le n \\le 10^9$$$).", "output_spec": "For each test case, print the answer you are looking for — the number of integers from $$$1$$$ to $$$n$$$ that Polycarp likes.", "sample_inputs": ["6\n10\n1\n25\n1000000000\n999999999\n500000000"], "sample_outputs": ["4\n1\n6\n32591\n32590\n23125"], "notes": null}, "src_uid": "015afbefe1514a0e18fcb9286c7b6624"}
{"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": "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": "Valera has got n domino pieces in a row. Each piece consists of two halves — the upper one and the lower one. Each of the halves contains a number from 1 to 6. Valera loves even integers very much, so he wants the sum of the numbers on the upper halves and the sum of the numbers on the lower halves to be even.To do that, Valera can rotate the dominoes by 180 degrees. After the rotation the upper and the lower halves swap places. This action takes one second. Help Valera find out the minimum time he must spend rotating dominoes to make his wish come true.", "input_spec": "The first line contains integer n (1 ≤ n ≤ 100), denoting the number of dominoes Valera has. Next n lines contain two space-separated integers xi, yi (1 ≤ xi, yi ≤ 6). Number xi is initially written on the upper half of the i-th domino, yi is initially written on the lower half.", "output_spec": "Print a single number — the minimum required number of seconds. If Valera can't do the task in any time, print  - 1.", "sample_inputs": ["2\n4 2\n6 4", "1\n2 3", "3\n1 4\n2 3\n4 4"], "sample_outputs": ["0", "-1", "1"], "notes": "NoteIn the first test case the sum of the numbers on the upper halves equals 10 and the sum of the numbers on the lower halves equals 6. Both numbers are even, so Valera doesn't required to do anything.In the second sample Valera has only one piece of domino. It is written 3 on the one of its halves, therefore one of the sums will always be odd.In the third case Valera can rotate the first piece, and after that the sum on the upper halves will be equal to 10, and the sum on the lower halves will be equal to 8."}, "src_uid": "f9bc04aed2b84c7dd288749ac264bb43"}
{"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": "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": "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": "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": "Apart from having lots of holidays throughout the year, residents of Berland also have whole lucky years. Year is considered lucky if it has no more than 1 non-zero digit in its number. So years 100, 40000, 5 are lucky and 12, 3001 and 12345 are not.You are given current year in Berland. Your task is to find how long will residents of Berland wait till the next lucky year.", "input_spec": "The first line contains integer number n (1 ≤ n ≤ 109) — current year in Berland.", "output_spec": "Output amount of years from the current year to the next lucky one.", "sample_inputs": ["4", "201", "4000"], "sample_outputs": ["1", "99", "1000"], "notes": "NoteIn the first example next lucky year is 5. In the second one — 300. In the third — 5000."}, "src_uid": "a3e15c0632e240a0ef6fe43a5ab3cc3e"}
{"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": "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": "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": "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": "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": "In this problem we assume the Earth to be a completely round ball and its surface a perfect sphere. The length of the equator and any meridian is considered to be exactly 40 000 kilometers. Thus, travelling from North Pole to South Pole or vice versa takes exactly 20 000 kilometers.Limak, a polar bear, lives on the North Pole. Close to the New Year, he helps somebody with delivering packages all around the world. Instead of coordinates of places to visit, Limak got a description how he should move, assuming that he starts from the North Pole. The description consists of n parts. In the i-th part of his journey, Limak should move ti kilometers in the direction represented by a string diri that is one of: \"North\", \"South\", \"West\", \"East\".Limak isn’t sure whether the description is valid. You must help him to check the following conditions:  If at any moment of time (before any of the instructions or while performing one of them) Limak is on the North Pole, he can move only to the South.  If at any moment of time (before any of the instructions or while performing one of them) Limak is on the South Pole, he can move only to the North.  The journey must end on the North Pole. Check if the above conditions are satisfied and print \"YES\" or \"NO\" on a single line.", "input_spec": "The first line of the input contains a single integer n (1 ≤ n ≤ 50). The i-th of next n lines contains an integer ti and a string diri (1 ≤ ti ≤ 106, ) — the length and the direction of the i-th part of the journey, according to the description Limak got.", "output_spec": "Print \"YES\" if the description satisfies the three conditions, otherwise print \"NO\", both without the quotes.", "sample_inputs": ["5\n7500 South\n10000 East\n3500 North\n4444 West\n4000 North", "2\n15000 South\n4000 East", "5\n20000 South\n1000 North\n1000000 West\n9000 North\n10000 North", "3\n20000 South\n10 East\n20000 North", "2\n1000 North\n1000 South", "4\n50 South\n50 North\n15000 South\n15000 North"], "sample_outputs": ["YES", "NO", "YES", "NO", "NO", "YES"], "notes": "NoteDrawings below show how Limak's journey would look like in first two samples. In the second sample the answer is \"NO\" because he doesn't end on the North Pole.  "}, "src_uid": "11ac96a9daa97ae1900f123be921e517"}
{"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": "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": "There is a grid with $$$n$$$ rows and $$$m$$$ columns. Every cell of the grid should be colored either blue or yellow.A coloring of the grid is called stupid if every row has exactly one segment of blue cells and every column has exactly one segment of yellow cells.In other words, every row must have at least one blue cell, and all blue cells in a row must be consecutive. Similarly, every column must have at least one yellow cell, and all yellow cells in a column must be consecutive.  An example of a stupid coloring.   Examples of clever colorings. The first coloring is missing a blue cell in the second row, and the second coloring has two yellow segments in the second column. How many stupid colorings of the grid are there? Two colorings are considered different if there is some cell that is colored differently.", "input_spec": "The only line contains two integers $$$n$$$, $$$m$$$ ($$$1\\le n, m\\le 2021$$$).", "output_spec": "Output a single integer — the number of stupid colorings modulo $$$998244353$$$.", "sample_inputs": ["2 2", "4 3", "2020 2021"], "sample_outputs": ["2", "294", "50657649"], "notes": "NoteIn the first test case, these are the only two stupid $$$2\\times 2$$$ colorings.  "}, "src_uid": "1738dc65af1fffa445cb0c3074c6bedb"}
{"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": "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": " 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": "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": "Grigoriy, like the hero of one famous comedy film, found a job as a night security guard at the museum. At first night he received embosser and was to take stock of the whole exposition.Embosser is a special devise that allows to \"print\" the text of a plastic tape. Text is printed sequentially, character by character. The device consists of a wheel with a lowercase English letters written in a circle, static pointer to the current letter and a button that print the chosen letter. At one move it's allowed to rotate the alphabetic wheel one step clockwise or counterclockwise. Initially, static pointer points to letter 'a'. Other letters are located as shown on the picture:  After Grigoriy add new item to the base he has to print its name on the plastic tape and attach it to the corresponding exhibit. It's not required to return the wheel to its initial position with pointer on the letter 'a'.Our hero is afraid that some exhibits may become alive and start to attack him, so he wants to print the names as fast as possible. Help him, for the given string find the minimum number of rotations of the wheel required to print it.", "input_spec": "The only line of input contains the name of some exhibit — the non-empty string consisting of no more than 100 characters. It's guaranteed that the string consists of only lowercase English letters.", "output_spec": "Print one integer — the minimum number of rotations of the wheel, required to print the name given in the input.", "sample_inputs": ["zeus", "map", "ares"], "sample_outputs": ["18", "35", "34"], "notes": "Note   To print the string from the first sample it would be optimal to perform the following sequence of rotations:   from 'a' to 'z' (1 rotation counterclockwise),  from 'z' to 'e' (5 clockwise rotations),  from 'e' to 'u' (10 rotations counterclockwise),  from 'u' to 's' (2 counterclockwise rotations).  In total, 1 + 5 + 10 + 2 = 18 rotations are required."}, "src_uid": "ecc890b3bdb9456441a2a265c60722dd"}
{"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": "Vasya plays Robot Bicorn Attack.The game consists of three rounds. For each one a non-negative integer amount of points is given. The result of the game is the sum of obtained points. Vasya has already played three rounds and wrote obtained points one by one (without leading zeros) into the string s. Vasya decided to brag about his achievement to the friends. However, he has forgotten how many points he got for each round. The only thing he remembers is the string s.Help Vasya to find out what is the maximum amount of points he could get. Take into account that Vasya played Robot Bicorn Attack for the first time, so he could not get more than 1000000 (106) points for one round.", "input_spec": "The only line of input contains non-empty string s obtained by Vasya. The string consists of digits only. The string length does not exceed 30 characters.", "output_spec": "Print the only number — the maximum amount of points Vasya could get. If Vasya is wrong and the string could not be obtained according to the rules then output number -1.", "sample_inputs": ["1234", "9000", "0009"], "sample_outputs": ["37", "90", "-1"], "notes": "NoteIn the first example the string must be split into numbers 1, 2 and 34.In the second example the string must be split into numbers 90, 0 and 0. In the third example the string is incorrect, because after splitting the string into 3 numbers number 00 or 09 will be obtained, but numbers cannot have leading zeroes."}, "src_uid": "bf4e72636bd1998ad3d034ad72e63097"}
{"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": "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": "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": "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": "After passing a test, Vasya got himself a box of $$$n$$$ candies. He decided to eat an equal amount of candies each morning until there are no more candies. However, Petya also noticed the box and decided to get some candies for himself.This means the process of eating candies is the following: in the beginning Vasya chooses a single integer $$$k$$$, same for all days. After that, in the morning he eats $$$k$$$ candies from the box (if there are less than $$$k$$$ candies in the box, he eats them all), then in the evening Petya eats $$$10\\%$$$ of the candies remaining in the box. If there are still candies left in the box, the process repeats — next day Vasya eats $$$k$$$ candies again, and Petya — $$$10\\%$$$ of the candies left in a box, and so on.If the amount of candies in the box is not divisible by $$$10$$$, Petya rounds the amount he takes from the box down. For example, if there were $$$97$$$ candies in the box, Petya would eat only $$$9$$$ of them. In particular, if there are less than $$$10$$$ candies in a box, Petya won't eat any at all.Your task is to find out the minimal amount of $$$k$$$ that can be chosen by Vasya so that he would eat at least half of the $$$n$$$ candies he initially got. Note that the number $$$k$$$ must be integer.", "input_spec": "The first line contains a single integer $$$n$$$ ($$$1 \\leq n \\leq 10^{18}$$$) — the initial amount of candies in the box.", "output_spec": "Output a single integer — the minimal amount of $$$k$$$ that would allow Vasya to eat at least half of candies he got.", "sample_inputs": ["68"], "sample_outputs": ["3"], "notes": "NoteIn the sample, the amount of candies, with $$$k=3$$$, would change in the following way (Vasya eats first):$$$68 \\to 65 \\to 59 \\to 56 \\to 51 \\to 48 \\to 44 \\to 41 \\\\ \\to 37 \\to 34 \\to 31 \\to 28 \\to 26 \\to 23 \\to 21 \\to 18 \\to 17 \\to 14 \\\\ \\to 13 \\to 10 \\to 9 \\to 6 \\to 6 \\to 3 \\to 3 \\to 0$$$.In total, Vasya would eat $$$39$$$ candies, while Petya — $$$29$$$."}, "src_uid": "db1a50da538fa82038f8db6104d2ab93"}
{"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": "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": "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": "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": "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": "Ksenia has her winter exams. Today she is learning combinatorics. Here's one of the problems she needs to learn to solve.How many distinct trees are there consisting of n vertices, each with the following properties:  the tree is marked, that is, the vertices of the tree are numbered from 1 to n;  each vertex of the tree is connected with at most three other vertices, and at the same moment the vertex with number 1 is connected with at most two other vertices;  the size of the tree's maximum matching equals k. Two trees are considered distinct if there are such two vertices u and v, that in one tree they are connected by an edge and in the other tree they are not.Help Ksenia solve the problem for the given n and k. As the answer to the problem can be very huge you should output it modulo 1000000007 (109 + 7).", "input_spec": "The first line contains two integers n, k (1 ≤ n, k ≤ 50).", "output_spec": "Print a single integer — the answer to the problem modulo 1000000007 (109 + 7).", "sample_inputs": ["1 1", "2 1", "3 1", "4 2"], "sample_outputs": ["0", "1", "3", "12"], "notes": "NoteIf you aren't familiar with matchings, please, read the following link: http://en.wikipedia.org/wiki/Matching_(graph_theory)."}, "src_uid": "f98b740183281943eafd90328854746b"}
{"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": "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": "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": "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": "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": "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": "While swimming at the beach, Mike has accidentally dropped his cellphone into the water. There was no worry as he bought a cheap replacement phone with an old-fashioned keyboard. The keyboard has only ten digital equal-sized keys, located in the following way:  Together with his old phone, he lost all his contacts and now he can only remember the way his fingers moved when he put some number in. One can formally consider finger movements as a sequence of vectors connecting centers of keys pressed consecutively to put in a number. For example, the finger movements for number \"586\" are the same as finger movements for number \"253\":    Mike has already put in a number by his \"finger memory\" and started calling it, so he is now worrying, can he be sure that he is calling the correct number? In other words, is there any other number, that has the same finger movements?", "input_spec": "The first line of the input contains the only integer n (1 ≤ n ≤ 9) — the number of digits in the phone number that Mike put in. The second line contains the string consisting of n digits (characters from '0' to '9') representing the number that Mike put in.", "output_spec": "If there is no other phone number with the same finger movements and Mike can be sure he is calling the correct number, print \"YES\" (without quotes) in the only line. Otherwise print \"NO\" (without quotes) in the first line.", "sample_inputs": ["3\n586", "2\n09", "9\n123456789", "3\n911"], "sample_outputs": ["NO", "NO", "YES", "YES"], "notes": "NoteYou can find the picture clarifying the first sample case in the statement above."}, "src_uid": "d0f5174bb0bcca5a486db327b492bf33"}
{"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": "During the winter holidays, the demand for Christmas balls is exceptionally high. Since it's already 2018, the advances in alchemy allow easy and efficient ball creation by utilizing magic crystals.Grisha needs to obtain some yellow, green and blue balls. It's known that to produce a yellow ball one needs two yellow crystals, green — one yellow and one blue, and for a blue ball, three blue crystals are enough.Right now there are A yellow and B blue crystals in Grisha's disposal. Find out how many additional crystals he should acquire in order to produce the required number of balls.", "input_spec": "The first line features two integers A and B (0 ≤ A, B ≤ 109), denoting the number of yellow and blue crystals respectively at Grisha's disposal. The next line contains three integers x, y and z (0 ≤ x, y, z ≤ 109) — the respective amounts of yellow, green and blue balls to be obtained.", "output_spec": "Print a single integer — the minimum number of crystals that Grisha should acquire in addition.", "sample_inputs": ["4 3\n2 1 1", "3 9\n1 1 3", "12345678 87654321\n43043751 1000000000 53798715"], "sample_outputs": ["2", "1", "2147483648"], "notes": "NoteIn the first sample case, Grisha needs five yellow and four blue crystals to create two yellow balls, one green ball, and one blue ball. To do that, Grisha needs to obtain two additional crystals: one yellow and one blue."}, "src_uid": "35202a4601a03d25e18dda1539c5beba"}
{"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": "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": "As Kevin is in BigMan's house, suddenly a trap sends him onto a grid with $$$n$$$ rows and $$$m$$$ columns.BigMan's trap is configured by two arrays: an array $$$a_1,a_2,\\ldots,a_n$$$ and an array $$$b_1,b_2,\\ldots,b_m$$$.In the $$$i$$$-th row there is a heater which heats the row by $$$a_i$$$ degrees, and in the $$$j$$$-th column there is a heater which heats the column by $$$b_j$$$ degrees, so that the temperature of cell $$$(i,j)$$$ is $$$a_i+b_j$$$.Fortunately, Kevin has a suit with one parameter $$$x$$$ and two modes:  heat resistance. In this mode suit can stand all temperatures greater or equal to $$$x$$$, but freezes as soon as reaches a cell with temperature less than $$$x$$$.  cold resistance. In this mode suit can stand all temperatures less than $$$x$$$, but will burn as soon as reaches a cell with temperature at least $$$x$$$.Once Kevin lands on a cell the suit automatically turns to cold resistance mode if the cell has temperature less than $$$x$$$, or to heat resistance mode otherwise, and cannot change after that.We say that two cells are adjacent if they share an edge.Let a path be a sequence $$$c_1,c_2,\\ldots,c_k$$$ of cells such that $$$c_i$$$ and $$$c_{i+1}$$$ are adjacent for $$$1 \\leq i \\leq k-1$$$.We say that two cells are connected if there is a path between the two cells consisting only of cells that Kevin can step on.A connected component is a maximal set of pairwise connected cells.We say that a connected component is good if Kevin can escape the grid starting from it  — when it contains at least one border cell of the grid, and that it's bad otherwise.To evaluate the situation, Kevin gives a score of $$$1$$$ to each good component and a score of $$$2$$$ for each bad component.The final score will be the difference between the total score of components with temperatures bigger than or equal to $$$x$$$ and the score of components with temperatures smaller than $$$x$$$.There are $$$q$$$ possible values of $$$x$$$ that Kevin can use, and for each of them Kevin wants to know the final score.Help Kevin defeat BigMan!", "input_spec": "The first line contains three integers $$$n$$$,$$$m$$$,$$$q$$$ ($$$1 \\leq n,m,q \\leq 10^5$$$)  – the number of rows, columns, and the number of possible values for $$$x$$$ respectively. The second line contains $$$n$$$ integers $$$a_1, a_2, \\dots, a_n$$$ ($$$1 \\leq a_i \\leq 10^5$$$). The third line contains $$$m$$$ integers $$$b_1, b_2, \\dots, b_m$$$ ($$$1 \\leq b_i \\leq 10^5$$$). Each of the next $$$q$$$ lines contains one integer $$$x$$$ ($$$1 \\leq x \\leq 2 \\cdot 10^5$$$).", "output_spec": "Output $$$q$$$ lines, in the $$$i$$$-th line output the answer for the $$$i$$$-th possible value of $$$x$$$ from the input.", "sample_inputs": ["5 5 1\n1 3 2 3 1\n1 3 2 3 1\n5", "3 3 2\n1 2 2\n2 1 2\n3\n4"], "sample_outputs": ["-1", "0\n1"], "notes": "NoteIn the first example, the score for components with temperature smaller than $$$5$$$ is $$$1+2$$$, and the score for components with temperature at least $$$5$$$ is $$$2$$$. Thus, the final score is $$$2-3=-1$$$."}, "src_uid": "25a6428f57022c12dfabdabbcc69c5a4"}
{"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": "Vanya got n cubes. He decided to build a pyramid from them. Vanya wants to build the pyramid as follows: the top level of the pyramid must consist of 1 cube, the second level must consist of 1 + 2 = 3 cubes, the third level must have 1 + 2 + 3 = 6 cubes, and so on. Thus, the i-th level of the pyramid must have 1 + 2 + ... + (i - 1) + i cubes.Vanya wants to know what is the maximum height of the pyramid that he can make using the given cubes.", "input_spec": "The first line contains integer n (1 ≤ n ≤ 104) — the number of cubes given to Vanya.", "output_spec": "Print the maximum possible height of the pyramid in the single line.", "sample_inputs": ["1", "25"], "sample_outputs": ["1", "4"], "notes": "NoteIllustration to the second sample:   "}, "src_uid": "873a12edffc57a127fdfb1c65d43bdb0"}
{"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": "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": "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": "— 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": "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": "A necklace can be described as a string of links ('-') and pearls ('o'), with the last link or pearl connected to the first one.  You can remove a link or a pearl and insert it between two other existing links or pearls (or between a link and a pearl) on the necklace. This process can be repeated as many times as you like, but you can't throw away any parts.Can you make the number of links between every two adjacent pearls equal? Two pearls are considered to be adjacent if there is no other pearl between them.Note that the final necklace should remain as one circular part of the same length as the initial necklace.", "input_spec": "The only line of input contains a string $$$s$$$ ($$$3 \\leq |s| \\leq 100$$$), representing the necklace, where a dash '-' represents a link and the lowercase English letter 'o' represents a pearl.", "output_spec": "Print \"YES\" if the links and pearls can be rejoined such that the number of links between adjacent pearls is equal. Otherwise print \"NO\". You can print each letter in any case (upper or lower).", "sample_inputs": ["-o-o--", "-o---", "-o---o-", "ooo"], "sample_outputs": ["YES", "YES", "NO", "YES"], "notes": null}, "src_uid": "6e006ae3df3bcd24755358a5f584ec03"}
{"nl": {"description": "Ivan has a robot which is situated on an infinite grid. Initially the robot is standing in the starting cell (0, 0). The robot can process commands. There are four types of commands it can perform:  U — move from the cell (x, y) to (x, y + 1);  D — move from (x, y) to (x, y - 1);  L — move from (x, y) to (x - 1, y);  R — move from (x, y) to (x + 1, y). Ivan entered a sequence of n commands, and the robot processed it. After this sequence the robot ended up in the starting cell (0, 0), but Ivan doubts that the sequence is such that after performing it correctly the robot ends up in the same cell. He thinks that some commands were ignored by robot. To acknowledge whether the robot is severely bugged, he needs to calculate the maximum possible number of commands that were performed correctly. Help Ivan to do the calculations!", "input_spec": "The first line contains one number n — the length of sequence of commands entered by Ivan (1 ≤ n ≤ 100). The second line contains the sequence itself — a string consisting of n characters. Each character can be U, D, L or R.", "output_spec": "Print the maximum possible number of commands from the sequence the robot could perform to end up in the starting cell.", "sample_inputs": ["4\nLDUR", "5\nRRRUU", "6\nLLRRRR"], "sample_outputs": ["4", "0", "4"], "notes": null}, "src_uid": "b9fa2bb8001bd064ede531a5281cfd8a"}
{"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": "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": "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": "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": "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": "A sweet little monster Om Nom loves candies very much. One day he found himself in a rather tricky situation that required him to think a bit in order to enjoy candies the most. Would you succeed with the same task if you were on his place?  One day, when he came to his friend Evan, Om Nom didn't find him at home but he found two bags with candies. The first was full of blue candies and the second bag was full of red candies. Om Nom knows that each red candy weighs Wr grams and each blue candy weighs Wb grams. Eating a single red candy gives Om Nom Hr joy units and eating a single blue candy gives Om Nom Hb joy units.Candies are the most important thing in the world, but on the other hand overeating is not good. Om Nom knows if he eats more than C grams of candies, he will get sick. Om Nom thinks that it isn't proper to leave candy leftovers, so he can only eat a whole candy. Om Nom is a great mathematician and he quickly determined how many candies of what type he should eat in order to get the maximum number of joy units. Can you repeat his achievement? You can assume that each bag contains more candies that Om Nom can eat.", "input_spec": "The single line contains five integers C, Hr, Hb, Wr, Wb (1 ≤ C, Hr, Hb, Wr, Wb ≤ 109).", "output_spec": "Print a single integer — the maximum number of joy units that Om Nom can get.", "sample_inputs": ["10 3 5 2 3"], "sample_outputs": ["16"], "notes": "NoteIn the sample test Om Nom can eat two candies of each type and thus get 16 joy units."}, "src_uid": "eb052ca12ca293479992680581452399"}
{"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": "East or west, home is best. That's why family reunion, the indispensable necessity of Lunar New Year celebration, is put in such a position.After the reunion dinner, Little Tommy plays a game with the family. Here is a concise introduction to this game:   There is a sequence of n non-negative integers p1, p2, ..., pn in the beginning. It is ruled that each integer in this sequence should be non-negative at any time.  You can select two consecutive positive integers in this sequence, pi and pi + 1 (1 ≤ i < n), and then decrease them by their minimum (i. e. min(pi, pi + 1)), the cost of this operation is equal to min(pi, pi + 1). We call such operation as a descension.  The game immediately ends when there are no two consecutive positive integers. Your task is to end the game so that the total cost of your operations is as small as possible. Obviously, every game ends after at most n - 1 descensions. Please share your solution of this game with the lowest cost.", "input_spec": "The first line contains one integer n (1 ≤ n ≤ 3·105). The second line contains n space-separated integers p1, p2, ..., pn (0 ≤ pi ≤ 109, i = 1, 2, ..., n).", "output_spec": "In the first line print one integer as the number of descensions m (0 ≤ m ≤ n - 1). In the next m lines print the descensions chronologically. More precisely, in each line of the next m lines print one integer i (1 ≤ i < n) representing a descension would operate on pi and pi + 1 such that all the descensions could be utilized from top to bottom. If there are many possible solutions to reach the minimal cost, print any of them.", "sample_inputs": ["4\n2 1 3 1", "5\n2 2 1 3 1"], "sample_outputs": ["2\n1\n3", "3\n2\n1\n4"], "notes": "NoteIn the first sample, one possible best solution is , of which the cost is 1 + 1 = 2.In the second sample, one possible best solution is , of which the cost is 1 + 1 + 1 = 3."}, "src_uid": "8ed6af24a3d9f249fe6ba68efbe787e4"}
{"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": "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": "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": "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": "Let's call a string a phone number if it has length 11 and fits the pattern \"8xxxxxxxxxx\", where each \"x\" is replaced by a digit.For example, \"80123456789\" and \"80000000000\" are phone numbers, while \"8012345678\" and \"79000000000\" are not.You have $$$n$$$ cards with digits, and you want to use them to make as many phone numbers as possible. Each card must be used in at most one phone number, and you don't have to use all cards. The phone numbers do not necessarily have to be distinct.", "input_spec": "The first line contains an integer $$$n$$$ — the number of cards with digits that you have ($$$1 \\leq n \\leq 100$$$). The second line contains a string of $$$n$$$ digits (characters \"0\", \"1\", ..., \"9\") $$$s_1, s_2, \\ldots, s_n$$$. The string will not contain any other characters, such as leading or trailing spaces.", "output_spec": "If at least one phone number can be made from these cards, output the maximum number of phone numbers that can be made. Otherwise, output 0.", "sample_inputs": ["11\n00000000008", "22\n0011223344556677889988", "11\n31415926535"], "sample_outputs": ["1", "2", "0"], "notes": "NoteIn the first example, one phone number, \"8000000000\", can be made from these cards.In the second example, you can make two phone numbers from the cards, for example, \"80123456789\" and \"80123456789\".In the third example you can't make any phone number from the given cards."}, "src_uid": "259d01b81bef5536b969247ff2c2d776"}
{"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": "Ksenia has ordinary pan scales and several weights of an equal mass. Ksenia has already put some weights on the scales, while other weights are untouched. Ksenia is now wondering whether it is possible to put all the remaining weights on the scales so that the scales were in equilibrium. The scales is in equilibrium if the total sum of weights on the left pan is equal to the total sum of weights on the right pan.", "input_spec": "The first line has a non-empty sequence of characters describing the scales. In this sequence, an uppercase English letter indicates a weight, and the symbol \"|\" indicates the delimiter (the character occurs in the sequence exactly once). All weights that are recorded in the sequence before the delimiter are initially on the left pan of the scale. All weights that are recorded in the sequence after the delimiter are initially on the right pan of the scale.  The second line contains a non-empty sequence containing uppercase English letters. Each letter indicates a weight which is not used yet.  It is guaranteed that all the English letters in the input data are different. It is guaranteed that the input does not contain any extra characters.", "output_spec": "If you cannot put all the weights on the scales so that the scales were in equilibrium, print string \"Impossible\". Otherwise, print the description of the resulting scales, copy the format of the input. If there are multiple answers, print any of them.", "sample_inputs": ["AC|T\nL", "|ABC\nXYZ", "W|T\nF", "ABC|\nD"], "sample_outputs": ["AC|TL", "XYZ|ABC", "Impossible", "Impossible"], "notes": null}, "src_uid": "917f173b8523ddd38925238e5d2089b9"}
{"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": "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": "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": "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": "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 Chris is bored during his physics lessons (too easy), so he has built a toy box to keep himself occupied. The box is special, since it has the ability to change gravity.There are n columns of toy cubes in the box arranged in a line. The i-th column contains ai cubes. At first, the gravity in the box is pulling the cubes downwards. When Chris switches the gravity, it begins to pull all the cubes to the right side of the box. The figure shows the initial and final configurations of the cubes in the box: the cubes that have changed their position are highlighted with orange.  Given the initial configuration of the toy cubes in the box, find the amounts of cubes in each of the n columns after the gravity switch!", "input_spec": "The first line of input contains an integer n (1 ≤ n ≤ 100), the number of the columns in the box. The next line contains n space-separated integer numbers. The i-th number ai (1 ≤ ai ≤ 100) denotes the number of cubes in the i-th column.", "output_spec": "Output n integer numbers separated by spaces, where the i-th number is the amount of cubes in the i-th column after the gravity switch.", "sample_inputs": ["4\n3 2 1 2", "3\n2 3 8"], "sample_outputs": ["1 2 2 3", "2 3 8"], "notes": "NoteThe first example case is shown on the figure. The top cube of the first column falls to the top of the last column; the top cube of the second column falls to the top of the third column; the middle cube of the first column falls to the top of the second column.In the second example case the gravity switch does not change the heights of the columns."}, "src_uid": "ae20712265d4adf293e75d016b4b82d8"}
{"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": "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": "Fedya loves problems involving data structures. Especially ones about different queries on subsegments. Fedya had a nice array $$$a_1, a_2, \\ldots a_n$$$ and a beautiful data structure. This data structure, given $$$l$$$ and $$$r$$$, $$$1 \\le l \\le r \\le n$$$, could find the greatest integer $$$d$$$, such that $$$d$$$ divides each of $$$a_l$$$, $$$a_{l+1}$$$, ..., $$$a_{r}$$$. Fedya really likes this data structure, so he applied it to every non-empty contiguous subarray of array $$$a$$$, put all answers into the array and sorted it. He called this array $$$b$$$. It's easy to see that array $$$b$$$ contains $$$n(n+1)/2$$$ elements.After that, Fedya implemented another cool data structure, that allowed him to find sum $$$b_l + b_{l+1} + \\ldots + b_r$$$ for given $$$l$$$ and $$$r$$$, $$$1 \\le l \\le r \\le n(n+1)/2$$$. Surely, Fedya applied this data structure to every contiguous subarray of array $$$b$$$, called the result $$$c$$$ and sorted it. Help Fedya find the lower median of array $$$c$$$.Recall that for a sorted array of length $$$k$$$ the lower median is an element at position $$$\\lfloor \\frac{k + 1}{2} \\rfloor$$$, if elements of the array are enumerated starting from $$$1$$$. For example, the lower median of array $$$(1, 1, 2, 3, 6)$$$ is $$$2$$$, and the lower median of $$$(0, 17, 23, 96)$$$ is $$$17$$$.", "input_spec": "First line contains a single integer $$$n$$$ — number of elements in array $$$a$$$ ($$$1 \\le n \\le 50\\,000$$$).  Second line contains $$$n$$$ integers $$$a_1, a_2, \\ldots, a_n$$$ — elements of the array ($$$1 \\le a_i \\le 100\\,000$$$).", "output_spec": "Print a single integer — the lower median of array $$$c$$$.", "sample_inputs": ["2\n6 3", "2\n8 8", "5\n19 16 2 12 15"], "sample_outputs": ["6", "8", "12"], "notes": "NoteIn the first sample array $$$b$$$ is equal to $$${3, 3, 6}$$$, then array $$$c$$$ is equal to $$${3, 3, 6, 6, 9, 12}$$$, so the lower median is $$$6$$$.In the second sample $$$b$$$ is $$${8, 8, 8}$$$, $$$c$$$ is $$${8, 8, 8, 16, 16, 24}$$$, so the lower median is $$$8$$$."}, "src_uid": "7516cc0a6d76569a761cf795cfb22d50"}
{"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": "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": "A permutation p of size n is an array such that every integer from 1 to n occurs exactly once in this array.Let's call a permutation an almost identity permutation iff there exist at least n - k indices i (1 ≤ i ≤ n) such that pi = i.Your task is to count the number of almost identity permutations for given numbers n and k.", "input_spec": "The first line contains two integers n and k (4 ≤ n ≤ 1000, 1 ≤ k ≤ 4).", "output_spec": "Print the number of almost identity permutations for given n and k.", "sample_inputs": ["4 1", "4 2", "5 3", "5 4"], "sample_outputs": ["1", "7", "31", "76"], "notes": null}, "src_uid": "96d839dc2d038f8ae95fc47c217b2e2f"}
{"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": "Roman is a young mathematician, very famous in Uzhland. Unfortunately, Sereja doesn't think so. To make Sereja change his mind, Roman is ready to solve any mathematical problem. After some thought, Sereja asked Roma to find, how many numbers are close to number n, modulo m.Number x is considered close to number n modulo m, if:  it can be obtained by rearranging the digits of number n,  it doesn't have any leading zeroes,  the remainder after dividing number x by m equals 0. Roman is a good mathematician, but the number of such numbers is too huge for him. So he asks you to help him. ", "input_spec": "The first line contains two integers: n (1 ≤ n < 1018) and m (1 ≤ m ≤ 100).", "output_spec": "In a single line print a single integer — the number of numbers close to number n modulo m.", "sample_inputs": ["104 2", "223 4", "7067678 8"], "sample_outputs": ["3", "1", "47"], "notes": "NoteIn the first sample the required numbers are: 104, 140, 410.In the second sample the required number is 232."}, "src_uid": "5eb90c23ffa3794fdddc5670c0373829"}
{"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": "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": "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": "It's Piegirl's birthday soon, and Pieguy has decided to buy her a bouquet of flowers and a basket of chocolates.The flower shop has F different types of flowers available. The i-th type of flower always has exactly pi petals. Pieguy has decided to buy a bouquet consisting of exactly N flowers. He may buy the same type of flower multiple times. The N flowers are then arranged into a bouquet. The position of the flowers within a bouquet matters. You can think of a bouquet as an ordered list of flower types.The chocolate shop sells chocolates in boxes. There are B different types of boxes available. The i-th type of box contains ci pieces of chocolate. Pieguy can buy any number of boxes, and can buy the same type of box multiple times. He will then place these boxes into a basket. The position of the boxes within the basket matters. You can think of the basket as an ordered list of box types.Pieguy knows that Piegirl likes to pluck a petal from a flower before eating each piece of chocolate. He would like to ensure that she eats the last piece of chocolate from the last box just after plucking the last petal from the last flower. That is, the total number of petals on all the flowers in the bouquet should equal the total number of pieces of chocolate in all the boxes in the basket.How many different bouquet+basket combinations can Pieguy buy? The answer may be very large, so compute it modulo 1000000007 = 109 + 7.", "input_spec": "The first line of input will contain integers F, B, and N (1 ≤ F ≤ 10, 1 ≤ B ≤ 100, 1 ≤ N ≤ 1018), the number of types of flowers, the number of types of boxes, and the number of flowers that must go into the bouquet, respectively. The second line of input will contain F integers p1, p2, ..., pF (1 ≤ pi ≤ 109), the numbers of petals on each of the flower types. The third line of input will contain B integers c1, c2, ..., cB (1 ≤ ci ≤ 250), the number of pieces of chocolate in each of the box types.", "output_spec": "Print the number of bouquet+basket combinations Pieguy can buy, modulo 1000000007 = 109 + 7.", "sample_inputs": ["2 3 3\n3 5\n10 3 7", "6 5 10\n9 3 3 4 9 9\n9 9 1 6 4"], "sample_outputs": ["17", "31415926"], "notes": "NoteIn the first example, there is 1 way to make a bouquet with 9 petals (3 + 3 + 3), and 1 way to make a basket with 9 pieces of chocolate (3 + 3 + 3), for 1 possible combination. There are 3 ways to make a bouquet with 13 petals (3 + 5 + 5, 5 + 3 + 5, 5 + 5 + 3), and 5 ways to make a basket with 13 pieces of chocolate (3 + 10, 10 + 3, 3 + 3 + 7, 3 + 7 + 3, 7 + 3 + 3), for 15 more combinations. Finally there is 1 way to make a bouquet with 15 petals (5 + 5 + 5) and 1 way to make a basket with 15 pieces of chocolate (3 + 3 + 3 + 3 + 3), for 1 more combination.Note that it is possible for multiple types of flowers to have the same number of petals. Such types are still considered different. Similarly different types of boxes may contain the same number of pieces of chocolate, but are still considered different."}, "src_uid": "c3a4c109080f49b88be5fb13157d1af0"}
{"nl": {"description": "Petya is preparing for IQ test and he has noticed that there many problems like: you are given a sequence, find the next number. Now Petya can solve only problems with arithmetic or geometric progressions.Arithmetic progression is a sequence a1, a1 + d, a1 + 2d, ..., a1 + (n - 1)d, where a1 and d are any numbers.Geometric progression is a sequence b1, b2 = b1q, ..., bn = bn - 1q, where b1 ≠ 0, q ≠ 0, q ≠ 1. Help Petya and write a program to determine if the given sequence is arithmetic or geometric. Also it should found the next number. If the sequence is neither arithmetic nor geometric, print 42 (he thinks it is impossible to find better answer). You should also print 42 if the next element of progression is not integer. So answer is always integer.", "input_spec": "The first line contains exactly four integer numbers between 1 and 1000, inclusively.", "output_spec": "Print the required number. If the given sequence is arithmetic progression, print the next progression element. Similarly, if the given sequence is geometric progression, print the next progression element. Print 42 if the given sequence is not an arithmetic or geometric progression.", "sample_inputs": ["836 624 412 200", "1 334 667 1000"], "sample_outputs": ["-12", "1333"], "notes": "NoteThis problem contains very weak pretests!"}, "src_uid": "68a9508d49fec672f9c61766d6051047"}
{"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": "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": "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": "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": "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": "Polycarp has a cat and his cat is a real gourmet! Dependent on a day of the week he eats certain type of food:  on Mondays, Thursdays and Sundays he eats fish food;  on Tuesdays and Saturdays he eats rabbit stew;  on other days of week he eats chicken stake. Polycarp plans to go on a trip and already packed his backpack. His backpack contains:  $$$a$$$ daily rations of fish food;  $$$b$$$ daily rations of rabbit stew;  $$$c$$$ daily rations of chicken stakes. Polycarp has to choose such day of the week to start his trip that his cat can eat without additional food purchases as long as possible. Print the maximum number of days the cat can eat in a trip without additional food purchases, if Polycarp chooses the day of the week to start his trip optimally.", "input_spec": "The first line of the input contains three positive integers $$$a$$$, $$$b$$$ and $$$c$$$ ($$$1 \\le a, b, c \\le 7\\cdot10^8$$$) — the number of daily rations of fish food, rabbit stew and chicken stakes in Polycarps backpack correspondingly.", "output_spec": "Print the maximum number of days the cat can eat in a trip without additional food purchases, if Polycarp chooses the day of the week to start his trip optimally.", "sample_inputs": ["2 1 1", "3 2 2", "1 100 1", "30 20 10"], "sample_outputs": ["4", "7", "3", "39"], "notes": "NoteIn the first example the best day for start of the trip is Sunday. In this case, during Sunday and Monday the cat will eat fish food, during Tuesday — rabbit stew and during Wednesday — chicken stake. So, after four days of the trip all food will be eaten.In the second example Polycarp can start his trip in any day of the week. In any case there are food supplies only for one week in Polycarps backpack.In the third example Polycarp can start his trip in any day, excluding Wednesday, Saturday and Sunday. In this case, the cat will eat three different dishes in three days. Nevertheless that after three days of a trip there will be $$$99$$$ portions of rabbit stew in a backpack, can cannot eat anything in fourth day of a trip."}, "src_uid": "e17df52cc0615585e4f8f2d31d2daafb"}
{"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": "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": "Polycarp is going to participate in the contest. It starts at $$$h_1:m_1$$$ and ends at $$$h_2:m_2$$$. It is guaranteed that the contest lasts an even number of minutes (i.e. $$$m_1 \\% 2 = m_2 \\% 2$$$, where $$$x \\% y$$$ is $$$x$$$ modulo $$$y$$$). It is also guaranteed that the entire contest is held during a single day. And finally it is guaranteed that the contest lasts at least two minutes.Polycarp wants to know the time of the midpoint of the contest. For example, if the contest lasts from $$$10:00$$$ to $$$11:00$$$ then the answer is $$$10:30$$$, if the contest lasts from $$$11:10$$$ to $$$11:12$$$ then the answer is $$$11:11$$$.", "input_spec": "The first line of the input contains two integers $$$h_1$$$ and $$$m_1$$$ in the format hh:mm. The second line of the input contains two integers $$$h_2$$$ and $$$m_2$$$ in the same format (hh:mm). It is guaranteed that $$$0 \\le h_1, h_2 \\le 23$$$ and $$$0 \\le m_1, m_2 \\le 59$$$. It is guaranteed that the contest lasts an even number of minutes (i.e. $$$m_1 \\% 2 = m_2 \\% 2$$$, where $$$x \\% y$$$ is $$$x$$$ modulo $$$y$$$). It is also guaranteed that the entire contest is held during a single day. And finally it is guaranteed that the contest lasts at least two minutes.", "output_spec": "Print two integers $$$h_3$$$ and $$$m_3$$$ ($$$0 \\le h_3 \\le 23, 0 \\le m_3 \\le 59$$$) corresponding to the midpoint of the contest in the format hh:mm. Print each number as exactly two digits (prepend a number with leading zero if needed), separate them with ':'.", "sample_inputs": ["10:00\n11:00", "11:10\n11:12", "01:02\n03:02"], "sample_outputs": ["10:30", "11:11", "02:02"], "notes": null}, "src_uid": "f7a32a8325ce97c4c50ce3a5c282ec50"}
{"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": "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": "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": "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": "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": "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": "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": "Little penguin Polo loves his home village. The village has n houses, indexed by integers from 1 to n. Each house has a plaque containing an integer, the i-th house has a plaque containing integer pi (1 ≤ pi ≤ n).Little penguin Polo loves walking around this village. The walk looks like that. First he stands by a house number x. Then he goes to the house whose number is written on the plaque of house x (that is, to house px), then he goes to the house whose number is written on the plaque of house px (that is, to house ppx), and so on.We know that:  When the penguin starts walking from any house indexed from 1 to k, inclusive, he can walk to house number 1.  When the penguin starts walking from any house indexed from k + 1 to n, inclusive, he definitely cannot walk to house number 1.  When the penguin starts walking from house number 1, he can get back to house number 1 after some non-zero number of walks from a house to a house. You need to find the number of ways you may write the numbers on the houses' plaques so as to fulfill the three above described conditions. Print the remainder after dividing this number by 1000000007 (109 + 7).", "input_spec": "The single line contains two space-separated integers n and k (1 ≤ n ≤ 1000, 1 ≤ k ≤ min(8, n)) — the number of the houses and the number k from the statement.", "output_spec": "In a single line print a single integer — the answer to the problem modulo 1000000007 (109 + 7).", "sample_inputs": ["5 2", "7 4"], "sample_outputs": ["54", "1728"], "notes": null}, "src_uid": "cc838bc14408f14f984a349fea9e9694"}
{"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": "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": "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": "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": "When Petya went to school, he got interested in large numbers and what they were called in ancient times. For instance, he learned that the Russian word \"tma\" (which now means \"too much to be counted\") used to stand for a thousand and \"tma tmyschaya\" (which literally means \"the tma of tmas\") used to stand for a million.Petya wanted to modernize the words we use for numbers and invented a word petricium that represents number k. Moreover, petricium la petricium stands for number k2, petricium la petricium la petricium stands for k3 and so on. All numbers of this form are called petriciumus cifera, and the number's importance is the number of articles la in its title.Petya's invention brought on a challenge that needed to be solved quickly: does some number l belong to the set petriciumus cifera? As Petya is a very busy schoolboy he needs to automate the process, he asked you to solve it.", "input_spec": "The first input line contains integer number k, the second line contains integer number l (2 ≤ k, l ≤ 231 - 1).", "output_spec": "You should print in the first line of the output \"YES\", if the number belongs to the set petriciumus cifera and otherwise print \"NO\". If the number belongs to the set, then print on the seconds line the only number — the importance of number l.", "sample_inputs": ["5\n25", "3\n8"], "sample_outputs": ["YES\n1", "NO"], "notes": null}, "src_uid": "8ce89b754aa4080e7c3b2c3b10f4be46"}
{"nl": {"description": "This is an interactive problem. In the interaction section below you will find the information about flushing the output.The New Year tree of height h is a perfect binary tree with vertices numbered 1 through 2h - 1 in some order. In this problem we assume that h is at least 2. The drawing below shows one example New Year tree of height 3:  Polar bears love decorating the New Year tree and Limak is no exception. To decorate the tree, he must first find its root, i.e. a vertex with exactly two neighbours (assuming that h ≥ 2). It won't be easy because Limak is a little bear and he doesn't even see the whole tree. Can you help him?There are t testcases. In each testcase, you should first read h from the input. Then you can ask at most 16 questions of format \"? x\" (without quotes), where x is an integer between 1 and 2h - 1, inclusive. As a reply you will get the list of neighbours of vertex x (more details in the \"Interaction\" section below). For example, for a tree on the drawing above after asking \"? 1\" you would get a response with 3 neighbours: 4, 5 and 7. Your goal is to find the index of the root y and print it in the format \"! y\". You will be able to read h for a next testcase only after printing the answer in a previous testcase and flushing the output.Each tree is fixed from the beginning and it doesn't change during your questions.", "input_spec": "The first line of the input contains a single integer t (1 ≤ t ≤ 500) — the number of testcases. At the beginning of each testcase you should read from the input a single integer h (2 ≤ h ≤ 7) — the height of the tree. You can't read the value of h in a next testcase until you answer a previous testcase.", "output_spec": null, "sample_inputs": ["1\n3\n3\n4 5 7\n2\n1 2\n1\n2", "2\n2\n1\n3\n2\n1 2\n2\n1 2\n4\n3\n3 12 13"], "sample_outputs": ["? 1\n? 5\n? 6\n! 5", "? 1\n? 3\n? 3\n! 3\n? 6\n! 1"], "notes": "NoteIn the first sample, a tree corresponds to the drawing from the statement.In the second sample, there are two two testcases. A tree in the first testcase has height 2 and thus 3 vertices. A tree in the second testcase has height 4 and thus 15 vertices. You can see both trees on the drawing below.  "}, "src_uid": "5c0db518fa326b1e405479313216426a"}
{"nl": {"description": "THE SxPLAY & KIVΛ - 漂流 KIVΛ & Nikki Simmons - PerspectivesWith a new body, our idol Aroma White (or should we call her Kaori Minamiya?) begins to uncover her lost past through the OS space.The space can be considered a 2D plane, with an infinite number of data nodes, indexed from $$$0$$$, with their coordinates defined as follows:  The coordinates of the $$$0$$$-th node is $$$(x_0, y_0)$$$  For $$$i > 0$$$, the coordinates of $$$i$$$-th node is $$$(a_x \\cdot x_{i-1} + b_x, a_y \\cdot y_{i-1} + b_y)$$$ Initially Aroma stands at the point $$$(x_s, y_s)$$$. She can stay in OS space for at most $$$t$$$ seconds, because after this time she has to warp back to the real world. She doesn't need to return to the entry point $$$(x_s, y_s)$$$ to warp home.While within the OS space, Aroma can do the following actions:  From the point $$$(x, y)$$$, Aroma can move to one of the following points: $$$(x-1, y)$$$, $$$(x+1, y)$$$, $$$(x, y-1)$$$ or $$$(x, y+1)$$$. This action requires $$$1$$$ second.  If there is a data node at where Aroma is staying, she can collect it. We can assume this action costs $$$0$$$ seconds. Of course, each data node can be collected at most once. Aroma wants to collect as many data as possible before warping back. Can you help her in calculating the maximum number of data nodes she could collect within $$$t$$$ seconds?", "input_spec": "The first line contains integers $$$x_0$$$, $$$y_0$$$, $$$a_x$$$, $$$a_y$$$, $$$b_x$$$, $$$b_y$$$ ($$$1 \\leq x_0, y_0 \\leq 10^{16}$$$, $$$2 \\leq a_x, a_y \\leq 100$$$, $$$0 \\leq b_x, b_y \\leq 10^{16}$$$), which define the coordinates of the data nodes. The second line contains integers $$$x_s$$$, $$$y_s$$$, $$$t$$$ ($$$1 \\leq x_s, y_s, t \\leq 10^{16}$$$) – the initial Aroma's coordinates and the amount of time available.", "output_spec": "Print a single integer — the maximum number of data nodes Aroma can collect within $$$t$$$ seconds.", "sample_inputs": ["1 1 2 3 1 0\n2 4 20", "1 1 2 3 1 0\n15 27 26", "1 1 2 3 1 0\n2 2 1"], "sample_outputs": ["3", "2", "0"], "notes": "NoteIn all three examples, the coordinates of the first $$$5$$$ data nodes are $$$(1, 1)$$$, $$$(3, 3)$$$, $$$(7, 9)$$$, $$$(15, 27)$$$ and $$$(31, 81)$$$ (remember that nodes are numbered from $$$0$$$).In the first example, the optimal route to collect $$$3$$$ nodes is as follows:   Go to the coordinates $$$(3, 3)$$$ and collect the $$$1$$$-st node. This takes $$$|3 - 2| + |3 - 4| = 2$$$ seconds.  Go to the coordinates $$$(1, 1)$$$ and collect the $$$0$$$-th node. This takes $$$|1 - 3| + |1 - 3| = 4$$$ seconds.  Go to the coordinates $$$(7, 9)$$$ and collect the $$$2$$$-nd node. This takes $$$|7 - 1| + |9 - 1| = 14$$$ seconds. In the second example, the optimal route to collect $$$2$$$ nodes is as follows:   Collect the $$$3$$$-rd node. This requires no seconds.  Go to the coordinates $$$(7, 9)$$$ and collect the $$$2$$$-th node. This takes $$$|15 - 7| + |27 - 9| = 26$$$ seconds. In the third example, Aroma can't collect any nodes. She should have taken proper rest instead of rushing into the OS space like that."}, "src_uid": "d8a7ae2959b3781a8a4566a2f75a4e28"}
{"nl": {"description": "Your search for Heidi is over – you finally found her at a library, dressed up as a human. In fact, she has spent so much time there that she now runs the place! Her job is to buy books and keep them at the library so that people can borrow and read them. There are n different books, numbered 1 through n.We will look at the library's operation during n consecutive days. Heidi knows in advance that on the i-th day (1 ≤ i ≤ n) precisely one person will come to the library, request to borrow the book ai, read it in a few hours, and return the book later on the same day.Heidi desperately wants to please all her guests, so she will make sure to always have the book ai available in the library on the i-th day. During the night before the i-th day, she has the option of going to the bookstore (which operates at nights to avoid competition with the library) and buying any book for the price of 1 CHF. Of course, if she already has a book at the library, she does not need to buy it again. Initially, the library contains no books.There is a problem, though. The capacity of the library is k – this means that at any time, there can be at most k books at the library. If buying a new book would cause Heidi to have more than k books, she must first get rid of some book that she already has, in order to make room for the new book. If she later needs a book that she got rid of, she will need to buy that book again.You are given k and the sequence of requests for books a1, a2, ..., an. What is the minimum cost (in CHF) of buying new books to satisfy all the requests?", "input_spec": "The first line of input will contain two integers n and k (1 ≤ n, k ≤ 80). The second line will contain n integers a1, a2, ..., an (1 ≤ ai ≤ n) – the sequence of book requests.", "output_spec": "On a single line print the minimum cost of buying books at the store so as to satisfy all requests.", "sample_inputs": ["4 80\n1 2 2 1", "4 1\n1 2 2 1", "4 2\n1 2 3 1"], "sample_outputs": ["2", "3", "3"], "notes": "NoteIn the first test case, Heidi is able to keep all books forever. Therefore, she only needs to buy the book 1 before the first day and the book 2 before the second day.In the second test case, she can only keep one book at a time. Therefore she will need to buy new books on the first, second and fourth day.In the third test case, before buying book 3 on the third day, she must decide which of the books 1 and 2 she should get rid of. Of course, she should keep the book 1, which will be requested on the fourth day."}, "src_uid": "956228e31679caa9952b216e010f9773"}
{"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": "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": "Let's write all the positive integer numbers one after another from $$$1$$$ without any delimiters (i.e. as a single string). It will be the infinite sequence starting with 123456789101112131415161718192021222324252627282930313233343536...Your task is to print the $$$k$$$-th digit of this sequence.", "input_spec": "The first and only line contains integer $$$k$$$ ($$$1 \\le k \\le 10000$$$) — the position to process ($$$1$$$-based index).", "output_spec": "Print the $$$k$$$-th digit of the resulting infinite sequence.", "sample_inputs": ["7", "21"], "sample_outputs": ["7", "5"], "notes": null}, "src_uid": "1503d761dd4e129fb7c423da390544ff"}
{"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": "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": "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": "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": "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": "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 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": "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": "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": "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": "Polycarp has interviewed Oleg and has written the interview down without punctuation marks and spaces to save time. Thus, the interview is now a string s consisting of n lowercase English letters.There is a filler word ogo in Oleg's speech. All words that can be obtained from ogo by adding go several times to the end of it are also considered to be fillers. For example, the words ogo, ogogo, ogogogo are fillers, but the words go, og, ogog, ogogog and oggo are not fillers.The fillers have maximal size, for example, for ogogoo speech we can't consider ogo a filler and goo as a normal phrase. We should consider ogogo as a filler here.To print the interview, Polycarp has to replace each of the fillers with three asterisks. Note that a filler word is replaced with exactly three asterisks regardless of its length.Polycarp has dealt with this problem in no time. Can you do the same? The clock is ticking!", "input_spec": "The first line contains a positive integer n (1 ≤ n ≤ 100) — the length of the interview. The second line contains the string s of length n, consisting of lowercase English letters.", "output_spec": "Print the interview text after the replacement of each of the fillers with \"***\". It is allowed for the substring \"***\" to have several consecutive occurences.", "sample_inputs": ["7\naogogob", "13\nogogmgogogogo", "9\nogoogoogo"], "sample_outputs": ["a***b", "***gmg***", "*********"], "notes": "NoteThe first sample contains one filler word ogogo, so the interview for printing is \"a***b\".The second sample contains two fillers ogo and ogogogo. Thus, the interview is transformed to \"***gmg***\"."}, "src_uid": "619665bed79ecf77b083251fe6fe7eb3"}
{"nl": {"description": "zscoder has a deck of $$$n+m$$$ custom-made cards, which consists of $$$n$$$ cards labelled from $$$1$$$ to $$$n$$$ and $$$m$$$ jokers. Since zscoder is lonely, he wants to play a game with himself using those cards. Initially, the deck is shuffled uniformly randomly and placed on the table. zscoder has a set $$$S$$$ which is initially empty. Every second, zscoder draws the top card from the deck.   If the card has a number $$$x$$$ written on it, zscoder removes the card and adds $$$x$$$ to the set $$$S$$$.  If the card drawn is a joker, zscoder places all the cards back into the deck and reshuffles (uniformly randomly) the $$$n+m$$$ cards to form a new deck (hence the new deck now contains all cards from $$$1$$$ to $$$n$$$ and the $$$m$$$ jokers). Then, if $$$S$$$ currently contains all the elements from $$$1$$$ to $$$n$$$, the game ends. Shuffling the deck doesn't take time at all. What is the expected number of seconds before the game ends? We can show that the answer can be written in the form $$$\\frac{P}{Q}$$$ where $$$P, Q$$$ are relatively prime integers and $$$Q \\neq 0 \\bmod 998244353$$$. Output the value of $$$(P \\cdot Q^{-1})$$$ modulo $$$998244353$$$.", "input_spec": "The only line of the input contains two integers $$$n$$$ and $$$m$$$ ($$$1 \\le n, m \\le 2 \\cdot 10^{6}$$$).", "output_spec": "Output a single integer, the value of $$$(P \\cdot Q^{-1})$$$ modulo $$$998244353$$$.", "sample_inputs": ["2 1", "3 2", "14 9"], "sample_outputs": ["5", "332748127", "969862773"], "notes": "NoteFor the first sample, it can be proven that the expected time before the game ends is $$$5$$$ seconds.For the second sample, it can be proven that the expected time before the game ends is $$$\\frac{28}{3}$$$ seconds."}, "src_uid": "9f2b59df7bef2aeee0ce71facd2b1613"}
{"nl": {"description": "Amr doesn't like Maths as he finds it really boring, so he usually sleeps in Maths lectures. But one day the teacher suspected that Amr is sleeping and asked him a question to make sure he wasn't.First he gave Amr two positive integers n and k. Then he asked Amr, how many integer numbers x > 0 exist such that:  Decimal representation of x (without leading zeroes) consists of exactly n digits;  There exists some integer y > 0 such that:   ;  decimal representation of y is a suffix of decimal representation of x.  As the answer to this question may be pretty huge the teacher asked Amr to output only its remainder modulo a number m.Can you help Amr escape this embarrassing situation?", "input_spec": "Input consists of three integers n, k, m (1 ≤ n ≤ 1000, 1 ≤ k ≤ 100, 1 ≤ m ≤ 109).", "output_spec": "Print the required number modulo m.", "sample_inputs": ["1 2 1000", "2 2 1000", "5 3 1103"], "sample_outputs": ["4", "45", "590"], "notes": "NoteA suffix of a string S is a non-empty string that can be obtained by removing some number (possibly, zero) of first characters from S."}, "src_uid": "656bf8df1e79499aa2ab2c28712851f0"}
{"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": "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": "Friends are going to play console. They have two joysticks and only one charger for them. Initially first joystick is charged at a1 percent and second one is charged at a2 percent. You can connect charger to a joystick only at the beginning of each minute. In one minute joystick either discharges by 2 percent (if not connected to a charger) or charges by 1 percent (if connected to a charger).Game continues while both joysticks have a positive charge. Hence, if at the beginning of minute some joystick is charged by 1 percent, it has to be connected to a charger, otherwise the game stops. If some joystick completely discharges (its charge turns to 0), the game also stops.Determine the maximum number of minutes that game can last. It is prohibited to pause the game, i. e. at each moment both joysticks should be enabled. It is allowed for joystick to be charged by more than 100 percent.", "input_spec": "The first line of the input contains two positive integers a1 and a2 (1 ≤ a1, a2 ≤ 100), the initial charge level of first and second joystick respectively.", "output_spec": "Output the only integer, the maximum number of minutes that the game can last. Game continues until some joystick is discharged.", "sample_inputs": ["3 5", "4 4"], "sample_outputs": ["6", "5"], "notes": "NoteIn the first sample game lasts for 6 minute by using the following algorithm:  at the beginning of the first minute connect first joystick to the charger, by the end of this minute first joystick is at 4%, second is at 3%;  continue the game without changing charger, by the end of the second minute the first joystick is at 5%, second is at 1%;  at the beginning of the third minute connect second joystick to the charger, after this minute the first joystick is at 3%, the second one is at 2%;  continue the game without changing charger, by the end of the fourth minute first joystick is at 1%, second one is at 3%;  at the beginning of the fifth minute connect first joystick to the charger, after this minute the first joystick is at 2%, the second one is at 1%;  at the beginning of the sixth minute connect second joystick to the charger, after this minute the first joystick is at 0%, the second one is at 2%. After that the first joystick is completely discharged and the game is stopped."}, "src_uid": "ba0f9f5f0ad4786b9274c829be587961"}
{"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": "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": "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": "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": "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": "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": "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": "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": "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": "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 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": "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": "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": "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": "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": "On one of the planets of Solar system, in Atmosphere University, many students are fans of bingo game.It is well known that one month on this planet consists of $$$n^2$$$ days, so calendars, represented as square matrix $$$n$$$ by $$$n$$$ are extremely popular.Weather conditions are even more unusual. Due to the unique composition of the atmosphere, when interacting with sunlight, every day sky takes one of three colors: blue, green or red.To play the bingo, you need to observe the sky for one month — after each day, its cell is painted with the color of the sky in that day, that is, blue, green or red.At the end of the month, students examine the calendar. If at least one row or column contains only cells of one color, that month is called lucky.Let's call two colorings of calendar different, if at least one cell has different colors in them. It is easy to see that there are $$$3^{n \\cdot n}$$$ different colorings. How much of them are lucky? Since this number can be quite large, print it modulo $$$998244353$$$.", "input_spec": "The first and only line of input contains a single integer $$$n$$$ ($$$1 \\le n \\le 1000\\,000$$$) — the number of rows and columns in the calendar.", "output_spec": "Print one number — number of lucky colorings of the calendar modulo $$$998244353$$$", "sample_inputs": ["1", "2", "3"], "sample_outputs": ["3", "63", "9933"], "notes": "NoteIn the first sample any coloring is lucky, since the only column contains cells of only one color.In the second sample, there are a lot of lucky colorings, in particular, the following colorings are lucky:  While these colorings are not lucky:  "}, "src_uid": "6e4b0ee2e1406041a961582ead299a3a"}
{"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": "Your task is to calculate the number of arrays such that:  each array contains $$$n$$$ elements;  each element is an integer from $$$1$$$ to $$$m$$$;  for each array, there is exactly one pair of equal elements;  for each array $$$a$$$, there exists an index $$$i$$$ such that the array is strictly ascending before the $$$i$$$-th element and strictly descending after it (formally, it means that $$$a_j < a_{j + 1}$$$, if $$$j < i$$$, and $$$a_j > a_{j + 1}$$$, if $$$j \\ge i$$$). ", "input_spec": "The first line contains two integers $$$n$$$ and $$$m$$$ ($$$2 \\le n \\le m \\le 2 \\cdot 10^5$$$).", "output_spec": "Print one integer — the number of arrays that meet all of the aforementioned conditions, taken modulo $$$998244353$$$.", "sample_inputs": ["3 4", "3 5", "42 1337", "100000 200000"], "sample_outputs": ["6", "10", "806066790", "707899035"], "notes": "NoteThe arrays in the first example are:  $$$[1, 2, 1]$$$;  $$$[1, 3, 1]$$$;  $$$[1, 4, 1]$$$;  $$$[2, 3, 2]$$$;  $$$[2, 4, 2]$$$;  $$$[3, 4, 3]$$$. "}, "src_uid": "28d6fc8973a3e0076a21c2ea490dfdba"}
{"nl": {"description": "A chip was placed on a field with coordinate system onto point (0, 0).Every second the chip moves randomly. If the chip is currently at a point (x, y), after a second it moves to the point (x - 1, y) with probability p1, to the point (x, y - 1) with probability p2, to the point (x + 1, y) with probability p3 and to the point (x, y + 1) with probability p4. It's guaranteed that p1 + p2 + p3 + p4 = 1. The moves are independent.Find out the expected time after which chip will move away from origin at a distance greater than R (i.e.  will be satisfied).", "input_spec": "First line contains five integers R, a1, a2, a3 and a4 (0 ≤ R ≤ 50, 1 ≤ a1, a2, a3, a4 ≤ 1000). Probabilities pi can be calculated using formula .", "output_spec": "It can be shown that answer for this problem is always a rational number of form , where . Print P·Q - 1 modulo 109 + 7. ", "sample_inputs": ["0 1 1 1 1", "1 1 1 1 1", "1 1 2 1 2"], "sample_outputs": ["1", "666666674", "538461545"], "notes": "NoteIn the first example initially the chip is located at a distance 0 from origin. In one second chip will move to distance 1 is some direction, so distance to origin will become 1.Answers to the second and the third tests:  and ."}, "src_uid": "bd6bcb5bffd039de93f217b02f5eae17"}
{"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": "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": "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": "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": "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": "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": "Bessie the cow and her best friend Elsie each received a sliding puzzle on Pi Day. Their puzzles consist of a 2 × 2 grid and three tiles labeled 'A', 'B', and 'C'. The three tiles sit on top of the grid, leaving one grid cell empty. To make a move, Bessie or Elsie can slide a tile adjacent to the empty cell into the empty cell as shown below:  In order to determine if they are truly Best Friends For Life (BFFLs), Bessie and Elsie would like to know if there exists a sequence of moves that takes their puzzles to the same configuration (moves can be performed in both puzzles). Two puzzles are considered to be in the same configuration if each tile is on top of the same grid cell in both puzzles. Since the tiles are labeled with letters, rotations and reflections are not allowed.", "input_spec": "The first two lines of the input consist of a 2 × 2 grid describing the initial configuration of Bessie's puzzle. The next two lines contain a 2 × 2 grid describing the initial configuration of Elsie's puzzle. The positions of the tiles are labeled 'A', 'B', and 'C', while the empty cell is labeled 'X'. It's guaranteed that both puzzles contain exactly one tile with each letter and exactly one empty position.", "output_spec": "Output \"YES\"(without quotes) if the puzzles can reach the same configuration (and Bessie and Elsie are truly BFFLs). Otherwise, print \"NO\" (without quotes).", "sample_inputs": ["AB\nXC\nXB\nAC", "AB\nXC\nAC\nBX"], "sample_outputs": ["YES", "NO"], "notes": "NoteThe solution to the first sample is described by the image. All Bessie needs to do is slide her 'A' tile down.In the second sample, the two puzzles can never be in the same configuration. Perhaps Bessie and Elsie are not meant to be friends after all..."}, "src_uid": "46f051f58d626587a5ec449c27407771"}
{"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": "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": "You are a lover of bacteria. You want to raise some bacteria in a box. Initially, the box is empty. Each morning, you can put any number of bacteria into the box. And each night, every bacterium in the box will split into two bacteria. You hope to see exactly x bacteria in the box at some moment. What is the minimum number of bacteria you need to put into the box across those days?", "input_spec": "The only line containing one integer x (1 ≤ x ≤ 109).", "output_spec": "The only line containing one integer: the answer.", "sample_inputs": ["5", "8"], "sample_outputs": ["2", "1"], "notes": "NoteFor the first sample, we can add one bacterium in the box in the first day morning and at the third morning there will be 4 bacteria in the box. Now we put one more resulting 5 in the box. We added 2 bacteria in the process so the answer is 2.For the second sample, we can put one in the first morning and in the 4-th morning there will be 8 in the box. So the answer is 1."}, "src_uid": "03e4482d53a059134676f431be4c16d2"}
{"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": "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": "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"}