{"nl": {"description": "Given a positive integer n, find k integers (not necessary distinct) such that all these integers are strictly greater than 1, and their product is equal to n.", "input_spec": "The first line contains two integers n and k (2\u2009\u2264\u2009n\u2009\u2264\u2009100000, 1\u2009\u2264\u2009k\u2009\u2264\u200920).", "output_spec": "If it's impossible to find the representation of n as a product of k numbers, print -1. Otherwise, print k integers in any order. Their product must be equal to n. If there are multiple answers, print any of them.", "sample_inputs": ["100000 2", "100000 20", "1024 5"], "sample_outputs": ["2 50000", "-1", "2 64 2 2 2"], "notes": null}, "src_uid": "bd0bc809d52e0a17da07ccfd450a4d79"}
{"nl": {"description": "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,\u2009j) such that i\u2009<\u2009j and pi\u2009>\u2009pj.", "input_spec": "The first line of the input contains two integers n and k (1\u2009\u2264\u2009n,\u2009k\u2009\u2264\u2009100\u2009000)\u00a0\u2014 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": "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\u00b7k 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,\u2009n,\u2009w (1\u2009\u2009\u2264\u2009\u2009k,\u2009w\u2009\u2009\u2264\u2009\u20091000, 0\u2009\u2264\u2009n\u2009\u2264\u2009109), the cost of the first banana, initial number of dollars the soldier has and number of bananas he wants. ", "output_spec": "Output one integer \u2014 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": "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 \u2014 left, s \u2014 straight, r \u2014 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 \u2014 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": "User ainta has a stack of n red and blue balls. He can apply a certain operation which changes the colors of the balls inside the stack.  While the top ball inside the stack is red, pop the ball from the top of the stack.  Then replace the blue ball on the top with a red ball.  And finally push some blue balls to the stack until the stack has total of n balls inside.  \u00a0If there are no blue balls inside the stack, ainta can't apply this operation. Given the initial state of the stack, ainta wants to know the maximum number of operations he can repeatedly apply.", "input_spec": "The first line contains an integer n (1\u2009\u2264\u2009n\u2009\u2264\u200950) \u2014 the number of balls inside the stack. The second line contains a string s (|s|\u2009=\u2009n) describing the initial state of the stack. The i-th character of the string s denotes the color of the i-th ball (we'll number the balls from top to bottom of the stack). If the character is \"R\", the color is red. If the character is \"B\", the color is blue.", "output_spec": "Print the maximum number of operations ainta can repeatedly apply. Please, do not write the %lld specifier to read or write 64-bit integers in \u0421++. It is preferred to use the cin, cout streams or the %I64d specifier.", "sample_inputs": ["3\nRBR", "4\nRBBR", "5\nRBBRR"], "sample_outputs": ["2", "6", "6"], "notes": "NoteThe first example is depicted below.The explanation how user ainta applies the first operation. He pops out one red ball, changes the color of the ball in the middle from blue to red, and pushes one blue ball.  The explanation how user ainta applies the second operation. He will not pop out red balls, he simply changes the color of the ball on the top from blue to red.  From now on, ainta can't apply any operation because there are no blue balls inside the stack. ainta applied two operations, so the answer is 2.The second example is depicted below. The blue arrow denotes a single operation.  "}, "src_uid": "d86a1b5bf9fe9a985f7b030fedd29d58"}
{"nl": {"description": "Bizon the Champion is called the Champion for a reason. Bizon the Champion has recently got a present \u2014 a new glass cupboard with n shelves and he decided to put all his presents there. All the presents can be divided into two types: medals and cups. Bizon the Champion has a1 first prize cups, a2 second prize cups and a3 third prize cups. Besides, he has b1 first prize medals, b2 second prize medals and b3 third prize medals. Naturally, the rewards in the cupboard must look good, that's why Bizon the Champion decided to follow the rules:  any shelf cannot contain both cups and medals at the same time;  no shelf can contain more than five cups;  no shelf can have more than ten medals. Help Bizon the Champion find out if we can put all the rewards so that all the conditions are fulfilled.", "input_spec": "The first line contains integers a1, a2 and a3 (0\u2009\u2264\u2009a1,\u2009a2,\u2009a3\u2009\u2264\u2009100). The second line contains integers b1, b2 and b3 (0\u2009\u2264\u2009b1,\u2009b2,\u2009b3\u2009\u2264\u2009100). The third line contains integer n (1\u2009\u2264\u2009n\u2009\u2264\u2009100). The numbers in the lines are separated by single spaces.", "output_spec": "Print \"YES\" (without the quotes) if all the rewards can be put on the shelves in the described manner. Otherwise, print \"NO\" (without the quotes).", "sample_inputs": ["1 1 1\n1 1 1\n4", "1 1 3\n2 3 4\n2", "1 0 0\n1 0 0\n1"], "sample_outputs": ["YES", "YES", "NO"], "notes": null}, "src_uid": "fe6301816dea7d9cea1c3a06a7d1ea7e"}
{"nl": {"description": " \u2014 Thanks a lot for today.\u2014 I experienced so many great things.\u2014 You gave me memories like dreams... But I have to leave now...\u2014 One last request, can you...\u2014 Help me solve a Codeforces problem?\u2014 ......\u2014 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\u2009\u2264\u2009k\u2009\u2264\u2009105,\u20091\u2009\u2264\u2009p\u2009\u2264\u2009109).", "output_spec": "Output single integer\u00a0\u2014 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": "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\" \u2014 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\" \u2014 Zoma recieves no commands, doesn't move at all and ends up at position $$$0$$$ as well;  \"LRLR\" \u2014 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 $$$n$$$ $$$(1 \\le n \\le 10^5)$$$ \u2014 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 \u2014 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": "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": "Special Agent Smart Beaver works in a secret research department of ABBYY. He's been working there for a long time and is satisfied with his job, as it allows him to eat out in the best restaurants and order the most expensive and exotic wood types there. The content special agent has got an important task: to get the latest research by British scientists on the English Language. These developments are encoded and stored in a large safe. The Beaver's teeth are strong enough, so the authorities assured that upon arriving at the place the beaver won't have any problems with opening the safe.And he finishes his aspen sprig and leaves for this important task. Of course, the Beaver arrived at the location without any problems, but alas. He can't open the safe with his strong and big teeth. At this point, the Smart Beaver get a call from the headquarters and learns that opening the safe with the teeth is not necessary, as a reliable source has sent the following information: the safe code consists of digits and has no leading zeroes. There also is a special hint, which can be used to open the safe. The hint is string s with the following structure:  if si = \"?\", then the digit that goes i-th in the safe code can be anything (between 0 to 9, inclusively);  if si is a digit (between 0 to 9, inclusively), then it means that there is digit si on position i in code;  if the string contains letters from \"A\" to \"J\", then all positions with the same letters must contain the same digits and the positions with distinct letters must contain distinct digits.  The length of the safe code coincides with the length of the hint. For example, hint \"?JGJ9\" has such matching safe code variants: \"51919\", \"55959\", \"12329\", \"93539\" and so on, and has wrong variants such as: \"56669\", \"00111\", \"03539\" and \"13666\".After receiving such information, the authorities change the plan and ask the special agents to work quietly and gently and not to try to open the safe by mechanical means, and try to find the password using the given hint.At a special agent school the Smart Beaver was the fastest in his platoon finding codes for such safes, but now he is not in that shape: the years take their toll ... Help him to determine the number of possible variants of the code to the safe, matching the given hint. After receiving this information, and knowing his own speed of entering codes, the Smart Beaver will be able to determine whether he will have time for tonight's show \"Beavers are on the trail\" on his favorite TV channel, or he should work for a sleepless night...", "input_spec": "The first line contains string s \u2014 the hint to the safe code. String s consists of the following characters: ?, 0-9, A-J. It is guaranteed that the first character of string s doesn't equal to character 0. The input limits for scoring 30 points are (subproblem A1):    1\u2009\u2264\u2009|s|\u2009\u2264\u20095.  The input limits for scoring 100 points are (subproblems A1+A2):    1\u2009\u2264\u2009|s|\u2009\u2264\u2009105.  Here |s| means the length of string s.", "output_spec": "Print the number of codes that match the given hint.", "sample_inputs": ["AJ", "1?AA"], "sample_outputs": ["81", "100"], "notes": null}, "src_uid": "d3c10d1b1a17ad018359e2dab80d2b82"}
{"nl": {"description": "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:   \">\" \u2009\u2192\u2009 1000,  \"<\" \u2009\u2192\u2009 1001,  \"+\" \u2009\u2192\u2009 1010,  \"-\" \u2009\u2192\u2009 1011,  \".\" \u2009\u2192\u2009 1100,  \",\" \u2009\u2192\u2009 1101,  \"[\" \u2009\u2192\u2009 1110,  \"]\" \u2009\u2192\u2009 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 \u2014 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\u2009+\u20093).", "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\u2009+\u20093).", "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": "Sheldon, Leonard, Penny, Rajesh and Howard are in the queue for a \"Double Cola\" drink vending machine; there are no other people in the queue. The first one in the queue (Sheldon) buys a can, drinks it and doubles! The resulting two Sheldons go to the end of the queue. Then the next in the queue (Leonard) buys a can, drinks it and gets to the end of the queue as two Leonards, and so on. This process continues ad infinitum.For example, Penny drinks the third can of cola and the queue will look like this: Rajesh, Howard, Sheldon, Sheldon, Leonard, Leonard, Penny, Penny.Write a program that will print the name of a man who will drink the n-th can.Note that in the very beginning the queue looks like that: Sheldon, Leonard, Penny, Rajesh, Howard. The first person is Sheldon.", "input_spec": "The input data consist of a single integer n (1\u2009\u2264\u2009n\u2009\u2264\u2009109). It is guaranteed that the pretests check the spelling of all the five names, that is, that they contain all the five possible answers.", "output_spec": "Print the single line \u2014 the name of the person who drinks the n-th can of cola. The cans are numbered starting from 1. Please note that you should spell the names like this: \"Sheldon\", \"Leonard\", \"Penny\", \"Rajesh\", \"Howard\" (without the quotes). In that order precisely the friends are in the queue initially.", "sample_inputs": ["1", "6", "1802"], "sample_outputs": ["Sheldon", "Sheldon", "Penny"], "notes": null}, "src_uid": "023b169765e81d896cdc1184e5a82b22"}
{"nl": {"description": "Limak is a grizzly bear who desires power and adoration. He wants to win in upcoming elections and rule over the Bearland.There are n candidates, including Limak. We know how many citizens are going to vote for each candidate. Now i-th candidate would get ai votes. Limak is candidate number 1. To win in elections, he must get strictly more votes than any other candidate.Victory is more important than everything else so Limak decided to cheat. He will steal votes from his opponents by bribing some citizens. To bribe a citizen, Limak must give him or her one candy - citizens are bears and bears like candies. Limak doesn't have many candies and wonders - how many citizens does he have to bribe?", "input_spec": "The first line contains single integer n (2\u2009\u2264\u2009n\u2009\u2264\u2009100) - number of candidates. The second line contains n space-separated integers a1,\u2009a2,\u2009...,\u2009an (1\u2009\u2264\u2009ai\u2009\u2264\u20091000) - number of votes for each candidate. Limak is candidate number 1. Note that after bribing number of votes for some candidate might be zero or might be greater than 1000.", "output_spec": "Print the minimum number of citizens Limak must bribe to have strictly more votes than any other candidate.", "sample_inputs": ["5\n5 1 11 2 8", "4\n1 8 8 8", "2\n7 6"], "sample_outputs": ["4", "6", "0"], "notes": "NoteIn the first sample Limak has 5 votes. One of the ways to achieve victory is to bribe 4 citizens who want to vote for the third candidate. Then numbers of votes would be 9,\u20091,\u20097,\u20092,\u20098 (Limak would have 9 votes). Alternatively, Limak could steal only 3 votes from the third candidate and 1 vote from the second candidate to get situation 9,\u20090,\u20098,\u20092,\u20098.In the second sample Limak will steal 2 votes from each candidate. Situation will be 7,\u20096,\u20096,\u20096.In the third sample Limak is a winner without bribing any citizen."}, "src_uid": "aa8fabf7c817dfd3d585b96a07bb7f58"}
{"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\u2009<\u2009b) 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\u2009\u2264\u2009n\u2009\u2264\u20091018)\u00a0\u2014 the number of rubles Kolya has at the beginning. Then follow three lines containing integers a, b and c (1\u2009\u2264\u2009a\u2009\u2264\u20091018, 1\u2009\u2264\u2009c\u2009<\u2009b\u2009\u2264\u20091018)\u00a0\u2014 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\u00a0\u2014 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": "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:   $$$p_i$$$\u00a0\u2014 the power of the laser;  $$$t_i$$$\u00a0\u2014 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.\u2009e. $$$(P - s)$$$ gets subtracted from its durability), where $$$P$$$ is the total power of the lasers that Monocarp shoots (i.\u2009e. $$$p_i$$$ 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 $$$t_1$$$ ($$$2 \\le p_1 \\le 5000$$$; $$$1 \\le t_1 \\le 10^{12}$$$)\u00a0\u2014 the power and the reload time of the first laser. The second line contains two integers $$$p_2$$$ and $$$t_2$$$ ($$$2 \\le p_2 \\le 5000$$$; $$$1 \\le t_2 \\le 10^{12}$$$)\u00a0\u2014 the power and the reload time of the second laser. The third line contains two integers $$$h$$$ and $$$s$$$ ($$$1 \\le h \\le 5000$$$; $$$1 \\le s < \\min(p_1, p_2)$$$)\u00a0\u2014 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\u00a0\u2014 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": "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\u2009\u2264\u2009a,\u2009b,\u2009c\u2009\u2264\u200910).", "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": "Vasya has got many devices that work on electricity. He's got n supply-line filters to plug the devices, the i-th supply-line filter has ai sockets.Overall Vasya has got m devices and k electrical sockets in his flat, he can plug the devices or supply-line filters directly. Of course, he can plug the supply-line filter to any other supply-line filter. The device (or the supply-line filter) is considered plugged to electricity if it is either plugged to one of k electrical sockets, or if it is plugged to some supply-line filter that is in turn plugged to electricity. What minimum number of supply-line filters from the given set will Vasya need to plug all the devices he has to electricity? Note that all devices and supply-line filters take one socket for plugging and that he can use one socket to plug either one device or one supply-line filter.", "input_spec": "The first line contains three integers n, m, k (1\u2009\u2264\u2009n,\u2009m,\u2009k\u2009\u2264\u200950) \u2014 the number of supply-line filters, the number of devices and the number of sockets that he can plug to directly, correspondingly. The second line contains n space-separated integers a1,\u2009a2,\u2009...,\u2009an (1\u2009\u2264\u2009ai\u2009\u2264\u200950) \u2014 number ai stands for the number of sockets on the i-th supply-line filter.", "output_spec": "Print a single number \u2014 the minimum number of supply-line filters that is needed to plug all the devices to electricity. If it is impossible to plug all the devices even using all the supply-line filters, print -1.", "sample_inputs": ["3 5 3\n3 1 2", "4 7 2\n3 3 2 4", "5 5 1\n1 3 1 2 1"], "sample_outputs": ["1", "2", "-1"], "notes": "NoteIn the first test case he can plug the first supply-line filter directly to electricity. After he plug it, he get 5 (3 on the supply-line filter and 2 remaining sockets for direct plugging) available sockets to plug. Thus, one filter is enough to plug 5 devices.One of the optimal ways in the second test sample is to plug the second supply-line filter directly and plug the fourth supply-line filter to one of the sockets in the second supply-line filter. Thus, he gets exactly 7 sockets, available to plug: one to plug to the electricity directly, 2 on the second supply-line filter, 4 on the fourth supply-line filter. There's no way he can plug 7 devices if he use one supply-line filter."}, "src_uid": "b32ab27503ee3c4196d6f0d0f133d13c"}
{"nl": {"description": "You are given a permutation p of numbers 1,\u20092,\u2009...,\u2009n. 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\u2009\u2264\u2009m\u2009\u2264\u2009cntn), 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\u2009\u2264\u2009n\u2009\u2264\u20098 will hold.  In subproblem B2 (4 points), the constraint 1\u2009\u2264\u2009n\u2009\u2264\u200950 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,\u20091) comes second in lexicographical order."}, "src_uid": "a8da7cbd9ddaec8e0468c6cce884e7a2"}
{"nl": {"description": "A new delivery of clothing has arrived today to the clothing store. This delivery consists of $$$a$$$ ties, $$$b$$$ scarves, $$$c$$$ vests and $$$d$$$ jackets.The store does not sell single clothing items \u2014 instead, it sells suits of two types:  a suit of the first type consists of one tie and one jacket;  a suit of the second type consists of one scarf, one vest and one jacket. Each suit of the first type costs $$$e$$$ coins, and each suit of the second type costs $$$f$$$ coins.Calculate the maximum possible cost of a set of suits that can be composed from the delivered clothing items. Note that one item cannot be used in more than one suit (though some items may be left unused).", "input_spec": "The first line contains one integer $$$a$$$ $$$(1 \\le a \\le 100\\,000)$$$ \u2014 the number of ties. The second line contains one integer $$$b$$$ $$$(1 \\le b \\le 100\\,000)$$$ \u2014 the number of scarves. The third line contains one integer $$$c$$$ $$$(1 \\le c \\le 100\\,000)$$$ \u2014 the number of vests. The fourth line contains one integer $$$d$$$ $$$(1 \\le d \\le 100\\,000)$$$ \u2014 the number of jackets. The fifth line contains one integer $$$e$$$ $$$(1 \\le e \\le 1\\,000)$$$ \u2014 the cost of one suit of the first type. The sixth line contains one integer $$$f$$$ $$$(1 \\le f \\le 1\\,000)$$$ \u2014 the cost of one suit of the second type.", "output_spec": "Print one integer \u2014 the maximum total cost of some set of suits that can be composed from the delivered items. ", "sample_inputs": ["4\n5\n6\n3\n1\n2", "12\n11\n13\n20\n4\n6", "17\n14\n5\n21\n15\n17"], "sample_outputs": ["6", "102", "325"], "notes": "NoteIt is possible to compose three suits of the second type in the first example, and their total cost will be $$$6$$$. Since all jackets will be used, it's impossible to add anything to this set.The best course of action in the second example is to compose nine suits of the first type and eleven suits of the second type. The total cost is $$$9 \\cdot 4 + 11 \\cdot 6 = 102$$$."}, "src_uid": "84d9e7e9c9541d997e6573edb421ae0a"}
{"nl": {"description": "Absent-minded Masha got set of n cubes for her birthday.At each of 6 faces of each cube, there is exactly one digit from 0 to 9. Masha became interested what is the largest natural x such she can make using her new cubes all integers from 1 to x.To make a number Masha can rotate her cubes and put them in a row. After that, she looks at upper faces of cubes from left to right and reads the number.The number can't contain leading zeros. It's not required to use all cubes to build a number.Pay attention: Masha can't make digit 6 from digit 9 and vice-versa using cube rotations.", "input_spec": "In first line integer n is given (1\u2009\u2264\u2009n\u2009\u2264\u20093)\u00a0\u2014 the number of cubes, Masha got for her birthday. Each of next n lines contains 6 integers aij (0\u2009\u2264\u2009aij\u2009\u2264\u20099)\u00a0\u2014 number on j-th face of i-th cube.", "output_spec": "Print single integer\u00a0\u2014 maximum number x such Masha can make any integers from 1 to x using her cubes or 0 if Masha can't make even 1.", "sample_inputs": ["3\n0 1 2 3 4 5\n6 7 8 9 0 1\n2 3 4 5 6 7", "3\n0 1 3 5 6 8\n1 2 4 5 7 8\n2 3 4 6 7 9"], "sample_outputs": ["87", "98"], "notes": "NoteIn the first test case, Masha can build all numbers from 1 to 87, but she can't make 88 because there are no two cubes with digit 8."}, "src_uid": "20aa53bffdfd47b4e853091ee6b11a4b"}
{"nl": {"description": "Capitalization is writing a word with its first letter as a capital letter. Your task is to capitalize the given word.Note, that during capitalization all the letters except the first one remains unchanged.", "input_spec": "A single line contains a non-empty word. This word consists of lowercase and uppercase English letters. The length of the word will not exceed 103.", "output_spec": "Output the given word after capitalization.", "sample_inputs": ["ApPLe", "konjac"], "sample_outputs": ["ApPLe", "Konjac"], "notes": null}, "src_uid": "29e0fc0c5c0e136ac8e58011c91397e4"}
{"nl": {"description": "InputThe only line of the input contains a 7-digit hexadecimal number. The first \"digit\" of the number is letter A, the rest of the \"digits\" are decimal digits 0-9.OutputOutput a single integer.ExamplesInput\nA278832\nOutput\n0\nInput\nA089956\nOutput\n0\nInput\nA089957\nOutput\n1\nInput\nA144045\nOutput\n1\n", "input_spec": "The only line of the input contains a 7-digit hexadecimal number. The first \"digit\" of the number is letter A, the rest of the \"digits\" are decimal digits 0-9.", "output_spec": "Output a single integer.", "sample_inputs": ["A278832", "A089956", "A089957", "A144045"], "sample_outputs": ["0", "0", "1", "1"], "notes": null}, "src_uid": "e52bc741bb72bb8e79cf392b2d15354f"}
{"nl": {"description": "Dwarfs have planted a very interesting plant, which is a triangle directed \"upwards\". This plant has an amusing feature. After one year a triangle plant directed \"upwards\" divides into four triangle plants: three of them will point \"upwards\" and one will point \"downwards\". After another year, each triangle plant divides into four triangle plants: three of them will be directed in the same direction as the parent plant, and one of them will be directed in the opposite direction. Then each year the process repeats. The figure below illustrates this process.  Help the dwarfs find out how many triangle plants that point \"upwards\" will be in n years.", "input_spec": "The first line contains a single integer n (0\u2009\u2264\u2009n\u2009\u2264\u20091018) \u2014 the number of full years when the plant grew. Please do not use the %lld specifier to read or write 64-bit integers in \u0421++. It is preferred to use cin, cout streams or the %I64d specifier.", "output_spec": "Print a single integer \u2014 the remainder of dividing the number of plants that will point \"upwards\" in n years by 1000000007 (109\u2009+\u20097).", "sample_inputs": ["1", "2"], "sample_outputs": ["3", "10"], "notes": "NoteThe first test sample corresponds to the second triangle on the figure in the statement. The second test sample corresponds to the third one."}, "src_uid": "782b819eb0bfc86d6f96f15ac09d5085"}
{"nl": {"description": "Petr wants to make a calendar for current month. For this purpose he draws a table in which columns correspond to weeks (a week is seven consequent days from Monday to Sunday), rows correspond to weekdays, and cells contain dates. For example, a calendar for January 2017 should look like on the picture:  Petr wants to know how many columns his table should have given the month and the weekday of the first date of that month? Assume that the year is non-leap.", "input_spec": "The only line contain two integers m and d (1\u2009\u2264\u2009m\u2009\u2264\u200912, 1\u2009\u2264\u2009d\u2009\u2264\u20097)\u00a0\u2014 the number of month (January is the first month, December is the twelfth) and the weekday of the first date of this month (1 is Monday, 7 is Sunday).", "output_spec": "Print single integer: the number of columns the table should have.", "sample_inputs": ["1 7", "1 1", "11 6"], "sample_outputs": ["6", "5", "5"], "notes": "NoteThe first example corresponds to the January 2017 shown on the picture in the statements.In the second example 1-st January is Monday, so the whole month fits into 5 columns.In the third example 1-st November is Saturday and 5 columns is enough."}, "src_uid": "5b969b6f564df6f71e23d4adfb2ded74"}
{"nl": {"description": "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\u2009\u2264\u2009i\u2009\u2264\u2009min(|x|,\u2009|y|)), that xi\u2009<\u2009yi and for any j (1\u2009\u2264\u2009j\u2009<\u2009i) xj\u2009=\u2009yj. 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": "Girl Lena likes it when everything is in order, and looks for order everywhere. Once she was getting ready for the University and noticed that the room was in a mess \u2014 all the objects from her handbag were thrown about the room. Of course, she wanted to put them back into her handbag. The problem is that the girl cannot carry more than two objects at a time, and cannot move the handbag. Also, if he has taken an object, she cannot put it anywhere except her handbag \u2014 her inherent sense of order does not let her do so.You are given the coordinates of the handbag and the coordinates of the objects in some \u0421artesian coordinate system. It is known that the girl covers the distance between any two objects in the time equal to the squared length of the segment between the points of the objects. It is also known that initially the coordinates of the girl and the handbag are the same. You are asked to find such an order of actions, that the girl can put all the objects back into her handbag in a minimum time period.", "input_spec": "The first line of the input file contains the handbag's coordinates xs,\u2009ys. The second line contains number n (1\u2009\u2264\u2009n\u2009\u2264\u200924) \u2014 the amount of objects the girl has. The following n lines contain the objects' coordinates. All the coordinates do not exceed 100 in absolute value. All the given positions are different. All the numbers are integer.", "output_spec": "In the first line output the only number \u2014 the minimum time the girl needs to put the objects into her handbag.  In the second line output the possible optimum way for Lena. Each object in the input is described by its index number (from 1 to n), the handbag's point is described by number 0. The path should start and end in the handbag's point. If there are several optimal paths, print any of them. ", "sample_inputs": ["0 0\n2\n1 1\n-1 1", "1 1\n3\n4 3\n3 4\n0 0"], "sample_outputs": ["8\n0 1 2 0", "32\n0 1 2 0 3 0"], "notes": null}, "src_uid": "2ecbac20dc5f4060bc873553946281bc"}
{"nl": {"description": "You won't find this sequence on OEIS.", "input_spec": "One integer $$$r$$$ ($$$-45 \\le r \\le 2999$$$).", "output_spec": "One integer.", "sample_inputs": ["2999"], "sample_outputs": ["3000"], "notes": null}, "src_uid": "22725effa6dc68b9c2a499d148e613c2"}
{"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\u00a0\u2014 it's guaranteed that pi\u2009<\u2009pi\u2009+\u20091 and ti\u2009<\u2009ti\u2009+\u20091.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,\u2009 pi\u2009-\u2009c\u00b7x) points.Limak is going to solve problems in order 1,\u20092,\u2009...,\u2009n (sorted increasingly by pi). Radewoosh is going to solve them in order n,\u2009n\u2009-\u20091,\u2009...,\u20091 (sorted decreasingly by pi). Your task is to predict the outcome\u00a0\u2014 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\u2009\u2264\u2009n\u2009\u2264\u200950,\u20091\u2009\u2264\u2009c\u2009\u2264\u20091000)\u00a0\u2014 the number of problems and the constant representing the speed of loosing points. The second line contains n integers p1,\u2009p2,\u2009...,\u2009pn (1\u2009\u2264\u2009pi\u2009\u2264\u20091000,\u2009pi\u2009<\u2009pi\u2009+\u20091)\u00a0\u2014 initial scores. The third line contains n integers t1,\u2009t2,\u2009...,\u2009tn (1\u2009\u2264\u2009ti\u2009\u2264\u20091000,\u2009ti\u2009<\u2009ti\u2009+\u20091) 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\u2009-\u2009c\u00b710\u2009=\u200950\u2009-\u20092\u00b710\u2009=\u200930 points.  Limak spends 15 minutes on the 2-nd problem so he submits it 10\u2009+\u200915\u2009=\u200925 minutes after the start of the contest. For the 2-nd problem he gets 85\u2009-\u20092\u00b725\u2009=\u200935 points.  He spends 25 minutes on the 3-rd problem so he submits it 10\u2009+\u200915\u2009+\u200925\u2009=\u200950 minutes after the start. For this problem he gets 250\u2009-\u20092\u00b750\u2009=\u2009150 points. So, Limak got 30\u2009+\u200935\u2009+\u2009150\u2009=\u2009215 points.Radewoosh solves problem in the reversed order:  Radewoosh solves 3-rd problem after 25 minutes so he gets 250\u2009-\u20092\u00b725\u2009=\u2009200 points.  He spends 15 minutes on the 2-nd problem so he submits it 25\u2009+\u200915\u2009=\u200940 minutes after the start. He gets 85\u2009-\u20092\u00b740\u2009=\u20095 points for this problem.  He spends 10 minutes on the 1-st problem so he submits it 25\u2009+\u200915\u2009+\u200910\u2009=\u200950 minutes after the start. He gets max(0,\u200950\u2009-\u20092\u00b750)\u2009=\u2009max(0,\u2009\u2009-\u200950)\u2009=\u20090 points. Radewoosh got 200\u2009+\u20095\u2009+\u20090\u2009=\u2009205 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\u2009-\u20096\u00b725\u2009=\u2009100 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\u2009+\u20092\u2009=\u20094."}, "src_uid": "8c704de75ab85f9e2c04a926143c8b4a"}
{"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 $$$t$$$ ($$$1 \\le t \\le 5$$$)\u2014 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 \u2014 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": "Consider a playoff tournament where $$$2^n$$$ athletes compete. The athletes are numbered from $$$1$$$ to $$$2^n$$$.The tournament is held in $$$n$$$ stages. In each stage, the athletes are split into pairs in such a way that each athlete belongs exactly to one pair. In each pair, the athletes compete against each other, and exactly one of them wins. The winner of each pair advances to the next stage, the athlete who was defeated gets eliminated from the tournament.The pairs are formed as follows:  in the first stage, athlete $$$1$$$ competes against athlete $$$2$$$; $$$3$$$ competes against $$$4$$$; $$$5$$$ competes against $$$6$$$, and so on;  in the second stage, the winner of the match \"$$$1$$$\u2013$$$2$$$\" competes against the winner of the match \"$$$3$$$\u2013$$$4$$$\"; the winner of the match \"$$$5$$$\u2013$$$6$$$\" competes against the winner of the match \"$$$7$$$\u2013$$$8$$$\", and so on;  the next stages are held according to the same rules. When athletes $$$x$$$ and $$$y$$$ compete, the winner is decided as follows:  if $$$x+y$$$ is odd, the athlete with the lower index wins (i.\u2009e. if $$$x < y$$$, then $$$x$$$ wins, otherwise $$$y$$$ wins);  if $$$x+y$$$ is even, the athlete with the higher index wins. The following picture describes the way the tournament with $$$n = 3$$$ goes.  Your task is the following one: given the integer $$$n$$$, determine the index of the athlete who wins the tournament.", "input_spec": "The first line contains one integer $$$t$$$ ($$$1 \\le t \\le 30$$$) \u2014 the number of test cases. Each test case consists of one line containing one integer $$$n$$$ ($$$1 \\le n \\le 30$$$).", "output_spec": "For each test case, print one integer \u2014 the index of the winner of the tournament.", "sample_inputs": ["2\n3\n1"], "sample_outputs": ["7\n1"], "notes": "NoteThe case $$$n = 3$$$ is shown in the picture from the statement.If $$$n = 1$$$, then there's only one match between athletes $$$1$$$ and $$$2$$$. Since $$$1 + 2 = 3$$$ is an odd number, the athlete with the lower index wins. So, the athlete $$$1$$$ is the winner."}, "src_uid": "d5e66e34601cad6d78c3f02898fa09f4"}
{"nl": {"description": "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": " 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\u00a0\u2014 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": "Alena has successfully passed the entrance exams to the university and is now looking forward to start studying.One two-hour lesson at the Russian university is traditionally called a pair, it lasts for two academic hours (an academic hour is equal to 45 minutes).The University works in such a way that every day it holds exactly n lessons. Depending on the schedule of a particular group of students, on a given day, some pairs may actually contain classes, but some may be empty (such pairs are called breaks).The official website of the university has already published the schedule for tomorrow for Alena's group. Thus, for each of the n pairs she knows if there will be a class at that time or not.Alena's House is far from the university, so if there are breaks, she doesn't always go home. Alena has time to go home only if the break consists of at least two free pairs in a row, otherwise she waits for the next pair at the university.Of course, Alena does not want to be sleepy during pairs, so she will sleep as long as possible, and will only come to the first pair that is presented in her schedule. Similarly, if there are no more pairs, then Alena immediately goes home.Alena appreciates the time spent at home, so she always goes home when it is possible, and returns to the university only at the beginning of the next pair. Help Alena determine for how many pairs she will stay at the university. Note that during some pairs Alena may be at the university waiting for the upcoming pair.", "input_spec": "The first line of the input contains a positive integer n (1\u2009\u2264\u2009n\u2009\u2264\u2009100) \u2014 the number of lessons at the university.  The second line contains n numbers ai (0\u2009\u2264\u2009ai\u2009\u2264\u20091). Number ai equals 0, if Alena doesn't have the i-th pairs, otherwise it is equal to 1. Numbers a1,\u2009a2,\u2009...,\u2009an are separated by spaces.", "output_spec": "Print a single number \u2014 the number of pairs during which Alena stays at the university.", "sample_inputs": ["5\n0 1 0 1 1", "7\n1 0 1 0 0 1 0", "1\n0"], "sample_outputs": ["4", "4", "0"], "notes": "NoteIn the first sample Alena stays at the university from the second to the fifth pair, inclusive, during the third pair she will be it the university waiting for the next pair. In the last sample Alena doesn't have a single pair, so she spends all the time at home."}, "src_uid": "2896aadda9e7a317d33315f91d1ca64d"}
{"nl": {"description": "Let quasi-palindromic number be such number that adding some leading zeros (possible none) to it produces a palindromic string. String t is called a palindrome, if it reads the same from left to right and from right to left.For example, numbers 131 and 2010200 are quasi-palindromic, they can be transformed to strings \"131\" and \"002010200\", respectively, which are palindromes.You are given some integer number x. Check if it's a quasi-palindromic number.", "input_spec": "The first line contains one integer number x (1\u2009\u2264\u2009x\u2009\u2264\u2009109). This number is given without any leading zeroes.", "output_spec": "Print \"YES\" if number x is quasi-palindromic. Otherwise, print \"NO\" (without quotes).", "sample_inputs": ["131", "320", "2010200"], "sample_outputs": ["YES", "NO", "YES"], "notes": null}, "src_uid": "d82278932881e3aa997086c909f29051"}
{"nl": {"description": "Vasya has n days of vacations! So he decided to improve his IT skills and do sport. Vasya knows the following information about each of this n days: whether that gym opened and whether a contest was carried out in the Internet on that day. For the i-th day there are four options:  on this day the gym is closed and the contest is not carried out;  on this day the gym is closed and the contest is carried out;  on this day the gym is open and the contest is not carried out;  on this day the gym is open and the contest is carried out. On each of days Vasya can either have a rest or write the contest (if it is carried out on this day), or do sport (if the gym is open on this day).Find the minimum number of days on which Vasya will have a rest (it means, he will not do sport and write the contest at the same time). The only limitation that Vasya has \u2014 he does not want to do the same activity on two consecutive days: it means, he will not do sport on two consecutive days, and write the contest on two consecutive days.", "input_spec": "The first line contains a positive integer n (1\u2009\u2264\u2009n\u2009\u2264\u2009100) \u2014 the number of days of Vasya's vacations. The second line contains the sequence of integers a1,\u2009a2,\u2009...,\u2009an (0\u2009\u2264\u2009ai\u2009\u2264\u20093) separated by space, where:    ai equals 0, if on the i-th day of vacations the gym is closed and the contest is not carried out;  ai equals 1, if on the i-th day of vacations the gym is closed, but the contest is carried out;  ai equals 2, if on the i-th day of vacations the gym is open and the contest is not carried out;  ai equals 3, if on the i-th day of vacations the gym is open and the contest is carried out.", "output_spec": "Print the minimum possible number of days on which Vasya will have a rest. Remember that Vasya refuses:   to do sport on any two consecutive days,  to write the contest on any two consecutive days. ", "sample_inputs": ["4\n1 3 2 0", "7\n1 3 3 2 1 2 3", "2\n2 2"], "sample_outputs": ["2", "0", "1"], "notes": "NoteIn the first test Vasya can write the contest on the day number 1 and do sport on the day number 3. Thus, he will have a rest for only 2 days.In the second test Vasya should write contests on days number 1, 3, 5 and 7, in other days do sport. Thus, he will not have a rest for a single day.In the third test Vasya can do sport either on a day number 1 or number 2. He can not do sport in two days, because it will be contrary to the his limitation. Thus, he will have a rest for only one day."}, "src_uid": "08f1ba79ced688958695a7cfcfdda035"}
{"nl": {"description": "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\u2009\u2264\u2009n\u2009\u2264\u2009100)\u00a0\u2014 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": "You can't possibly imagine how cold our friends are this winter in Nvodsk! Two of them play the following game to warm up: initially a piece of paper has an integer q. During a move a player should write any integer number that is a non-trivial divisor of the last written number. Then he should run this number of circles around the hotel. Let us remind you that a number's divisor is called non-trivial if it is different from one and from the divided number itself. The first person who can't make a move wins as he continues to lie in his warm bed under three blankets while the other one keeps running. Determine which player wins considering that both players play optimally. If the first player wins, print any winning first move.", "input_spec": "The first line contains the only integer q (1\u2009\u2264\u2009q\u2009\u2264\u20091013). Please do not use the %lld specificator to read or write 64-bit integers in \u0421++. It is preferred to use the cin, cout streams or the %I64d specificator.", "output_spec": "In the first line print the number of the winning player (1 or 2). If the first player wins then the second line should contain another integer \u2014 his first move (if the first player can't even make the first move, print 0). If there are multiple solutions, print any of them.", "sample_inputs": ["6", "30", "1"], "sample_outputs": ["2", "1\n6", "1\n0"], "notes": "NoteNumber 6 has only two non-trivial divisors: 2 and 3. It is impossible to make a move after the numbers 2 and 3 are written, so both of them are winning, thus, number 6 is the losing number. A player can make a move and write number 6 after number 30; 6, as we know, is a losing number. Thus, this move will bring us the victory."}, "src_uid": "f0a138b9f6ad979c5ca32437e05d6f43"}
{"nl": {"description": "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\u2009\u2264\u2009n\u2009\u2264\u2009109) \u2014 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 \u2014 300. In the third \u2014 5000."}, "src_uid": "a3e15c0632e240a0ef6fe43a5ab3cc3e"}
{"nl": {"description": "Recently you have received two positive integer numbers $$$x$$$ and $$$y$$$. You forgot them, but you remembered a shuffled list containing all divisors of $$$x$$$ (including $$$1$$$ and $$$x$$$) and all divisors of $$$y$$$ (including $$$1$$$ and $$$y$$$). If $$$d$$$ is a divisor of both numbers $$$x$$$ and $$$y$$$ at the same time, there are two occurrences of $$$d$$$ in the list.For example, if $$$x=4$$$ and $$$y=6$$$ then the given list can be any permutation of the list $$$[1, 2, 4, 1, 2, 3, 6]$$$. Some of the possible lists are: $$$[1, 1, 2, 4, 6, 3, 2]$$$, $$$[4, 6, 1, 1, 2, 3, 2]$$$ or $$$[1, 6, 3, 2, 4, 1, 2]$$$.Your problem is to restore suitable positive integer numbers $$$x$$$ and $$$y$$$ that would yield the same list of divisors (possibly in different order).It is guaranteed that the answer exists, i.e. the given list of divisors corresponds to some positive integers $$$x$$$ and $$$y$$$.", "input_spec": "The first line contains one integer $$$n$$$ ($$$2 \\le n \\le 128$$$) \u2014 the number of divisors of $$$x$$$ and $$$y$$$. The second line of the input contains $$$n$$$ integers $$$d_1, d_2, \\dots, d_n$$$ ($$$1 \\le d_i \\le 10^4$$$), where $$$d_i$$$ is either divisor of $$$x$$$ or divisor of $$$y$$$. If a number is divisor of both numbers $$$x$$$ and $$$y$$$ then there are two copies of this number in the list.", "output_spec": "Print two positive integer numbers $$$x$$$ and $$$y$$$ \u2014 such numbers that merged list of their divisors is the permutation of the given list of integers. It is guaranteed that the answer exists.", "sample_inputs": ["10\n10 2 8 1 2 4 1 20 4 5"], "sample_outputs": ["20 8"], "notes": null}, "src_uid": "868407df0a93085057d06367aecaf9be"}
{"nl": {"description": "Mr. Chanek has an integer represented by a string $$$s$$$. Zero or more digits have been erased and are denoted by the character _. There are also zero or more digits marked by the character X, meaning they're the same digit.Mr. Chanek wants to count the number of possible integer $$$s$$$, where $$$s$$$ is divisible by $$$25$$$. Of course, $$$s$$$ must not contain any leading zero. He can replace the character _ with any digit. He can also replace the character X with any digit, but it must be the same for every character X.As a note, a leading zero is any 0 digit that comes before the first nonzero digit in a number string in positional notation. For example, 0025 has two leading zeroes. An exception is the integer zero, (0 has no leading zero, but 0000 has three leading zeroes).", "input_spec": "One line containing the string $$$s$$$ ($$$1 \\leq |s| \\leq 8$$$). The string $$$s$$$ consists of the characters 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, _, and X.", "output_spec": "Output an integer denoting the number of possible integer $$$s$$$.", "sample_inputs": ["25", "_00", "_XX", "0", "0_25"], "sample_outputs": ["1", "9", "9", "1", "0"], "notes": "NoteIn the first example, the only possible $$$s$$$ is $$$25$$$.In the second and third example, $$$s \\in \\{100, 200,300,400,500,600,700,800,900\\}$$$.In the fifth example, all possible $$$s$$$ will have at least one leading zero."}, "src_uid": "4a905f419550a6c839992b40f1617af3"}
{"nl": {"description": "On her way to programming school tiger Dasha faced her first test \u2014 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 \u2014 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\u2009\u2264\u2009l\u2009\u2264\u2009r), for which values that Dasha has found are correct.", "input_spec": "In the only line you are given two integers a, b (0\u2009\u2264\u2009a,\u2009b\u2009\u2264\u2009100) \u2014 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\u00a0\u2014 2 and 4, and three odd: 1, 3 and 5."}, "src_uid": "ec5e3b3f5ee6a13eaf01b9a9a66ff037"}
{"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\u2009\u2264\u2009n\u2009\u2264\u20092h, 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,\u2009n (1\u2009\u2264\u2009h\u2009\u2264\u200950, 1\u2009\u2264\u2009n\u2009\u2264\u20092h).", "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\u2009+\u20091 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": "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,\u2009a2,\u2009...,\u2009an 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\u2009-\u20091\u00a0\u00a0\u00a0\u00a0loop integer variable j from i to n\u2009-\u20091\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0if (aj\u2009>\u2009aj\u2009+\u20091), then swap the values of elements aj and aj\u2009+\u20091But 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\u2009\u2264\u2009n\u2009\u2264\u200950) \u2014 the size of the sorted array.", "output_spec": "Print n space-separated integers a1,\u2009a2,\u2009...,\u2009an (1\u2009\u2264\u2009ai\u2009\u2264\u2009100) \u2014 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": "The start of the new academic year brought about the problem of accommodation students into dormitories. One of such dormitories has a a\u2009\u00d7\u2009b square meter wonder room. The caretaker wants to accommodate exactly n students there. But the law says that there must be at least 6 square meters per student in a room (that is, the room for n students must have the area of at least 6n square meters). The caretaker can enlarge any (possibly both) side of the room by an arbitrary positive integer of meters. Help him change the room so as all n students could live in it and the total area of the room was as small as possible.", "input_spec": "The first line contains three space-separated integers n, a and b (1\u2009\u2264\u2009n,\u2009a,\u2009b\u2009\u2264\u2009109) \u2014 the number of students and the sizes of the room.", "output_spec": "Print three integers s, a1 and b1 (a\u2009\u2264\u2009a1;\u00a0b\u2009\u2264\u2009b1) \u2014 the final area of the room and its sizes. If there are multiple optimal solutions, print any of them.", "sample_inputs": ["3 3 5", "2 4 4"], "sample_outputs": ["18\n3 6", "16\n4 4"], "notes": null}, "src_uid": "6a2a584d36008151d18e5080aea5029c"}
{"nl": {"description": "Chouti was doing a competitive programming competition. However, after having all the problems accepted, he got bored and decided to invent some small games.He came up with the following game. The player has a positive integer $$$n$$$. Initially the value of $$$n$$$ equals to $$$v$$$ and the player is able to do the following operation as many times as the player want (possibly zero): choose a positive integer $$$x$$$ that $$$x<n$$$ and $$$x$$$ is not a divisor of $$$n$$$, then subtract $$$x$$$ from $$$n$$$. The goal of the player is to minimize the value of $$$n$$$ in the end.Soon, Chouti found the game trivial. Can you also beat the game?", "input_spec": "The input contains only one integer in the first line: $$$v$$$ ($$$1 \\le v \\le 10^9$$$), the initial value of $$$n$$$.", "output_spec": "Output a single integer, the minimum value of $$$n$$$ the player can get.", "sample_inputs": ["8", "1"], "sample_outputs": ["1", "1"], "notes": "NoteIn the first example, the player can choose $$$x=3$$$ in the first turn, then $$$n$$$ becomes $$$5$$$. He can then choose $$$x=4$$$ in the second turn to get $$$n=1$$$ as the result. There are other ways to get this minimum. However, for example, he cannot choose $$$x=2$$$ in the first turn because $$$2$$$ is a divisor of $$$8$$$.In the second example, since $$$n=1$$$ initially, the player can do nothing."}, "src_uid": "c30b372a9cc0df4948dca48ef4c5d80d"}
{"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\u2009-\u2009j|.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\u2009\u2264\u2009a\u2009\u2264\u2009n\u2009\u2264\u2009100)\u00a0\u2014 the number of cities and the index of city where Limak lives. The second line contains n integers t1,\u2009t2,\u2009...,\u2009tn (0\u2009\u2264\u2009ti\u2009\u2264\u20091). 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\u00a0\u2014 Limak is sure that this criminal is exactly in the third city.  There is one criminal at distance 1 from the third city\u00a0\u2014 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\u00a0\u2014 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": "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\u2009\u2264\u2009n\u2009\u2264\u200955) \u2014 the maximum length of a number that a door-plate can hold.", "output_spec": "Output one integer \u2014 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": "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\u00a0\u2014 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\u2009\u2264\u2009h\u2009\u2264\u200912, 0\u2009\u2264\u2009m,\u2009s\u2009\u2264\u200959, 1\u2009\u2264\u2009t1,\u2009t2\u2009\u2264\u200912, t1\u2009\u2260\u2009t2). 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": "A number is called quasibinary if its decimal representation contains only digits 0 or 1. For example, numbers 0, 1, 101, 110011\u00a0\u2014 are quasibinary and numbers 2, 12, 900 are not.You are given a positive integer n. Represent it as a sum of minimum number of quasibinary numbers.", "input_spec": "The first line contains a single integer n (1\u2009\u2264\u2009n\u2009\u2264\u2009106).", "output_spec": "In the first line print a single integer k\u00a0\u2014 the minimum number of numbers in the representation of number n as a sum of quasibinary numbers. In the second line print k numbers \u2014 the elements of the sum. All these numbers should be quasibinary according to the definition above, their sum should equal n. Do not have to print the leading zeroes in the numbers. The order of numbers doesn't matter. If there are multiple possible representations, you are allowed to print any of them.", "sample_inputs": ["9", "32"], "sample_outputs": ["9\n1 1 1 1 1 1 1 1 1", "3\n10 11 11"], "notes": null}, "src_uid": "033068c5e16d25f09039e29c88474275"}
{"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 \u2014 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": "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,\u2009x2,\u2009...,\u2009xn and y1,\u2009y2,\u2009...,\u2009yn 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,\u2009j) (1\u2009\u2264\u2009i,\u2009j\u2009\u2264\u2009n) 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\u2009\u2264\u2009n\u2009\u2264\u20092\u2009000) \u2014 the length of both sequences. The second line contains n space-separated integers x1,\u2009x2,\u2009...,\u2009xn (1\u2009\u2264\u2009xi\u2009\u2264\u20092\u00b7106) \u2014 the integers finally chosen by Koyomi. The third line contains n space-separated integers y1,\u2009y2,\u2009...,\u2009yn (1\u2009\u2264\u2009yi\u2009\u2264\u20092\u00b7106) \u2014 the integers finally chosen by Karen. Input guarantees that the given 2n integers are pairwise distinct, that is, no pair (i,\u2009j) (1\u2009\u2264\u2009i,\u2009j\u2009\u2264\u2009n) exists such that one of the following holds: xi\u2009=\u2009yj; i\u2009\u2260\u2009j and xi\u2009=\u2009xj; i\u2009\u2260\u2009j and yi\u2009=\u2009yj.", "output_spec": "Output one line \u2014 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,\u20091), (1,\u20092), (2,\u20091), (2,\u20093), (3,\u20092) and (3,\u20093). 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": "Vasya studies music. He has learned lots of interesting stuff. For example, he knows that there are 12 notes: C, C#, D, D#, E, F, F#, G, G#, A, B, H. He also knows that the notes are repeated cyclically: after H goes C again, and before C stands H. We will consider the C note in the row's beginning and the C note after the H similar and we will identify them with each other. The distance between the notes along the musical scale is measured in tones: between two consecutive notes there's exactly one semitone, that is, 0.5 tone. The distance is taken from the lowest tone to the uppest one, that is, the distance between C and E is 4 semitones and between E and C is 8 semitonesVasya also knows what a chord is. A chord is an unordered set of no less than three notes. However, for now Vasya only works with triads, that is with the chords that consist of exactly three notes. He can already distinguish between two types of triads \u2014 major and minor.Let's define a major triad. Let the triad consist of notes X, Y and Z. If we can order the notes so as the distance along the musical scale between X and Y equals 4 semitones and the distance between Y and Z is 3 semitones, then the triad is major. The distance between X and Z, accordingly, equals 7 semitones.A minor triad is different in that the distance between X and Y should be 3 semitones and between Y and Z \u2014 4 semitones.For example, the triad \"C E G\" is major: between C and E are 4 semitones, and between E and G are 3 semitones. And the triplet \"C# B F\" is minor, because if we order the notes as \"B C# F\", than between B and C# will be 3 semitones, and between C# and F \u2014 4 semitones.Help Vasya classify the triad the teacher has given to him.", "input_spec": "The only line contains 3 space-separated notes in the above-given notation.", "output_spec": "Print \"major\" if the chord is major, \"minor\" if it is minor, and \"strange\" if the teacher gave Vasya some weird chord which is neither major nor minor. Vasya promises you that the answer will always be unambiguous. That is, there are no chords that are both major and minor simultaneously.", "sample_inputs": ["C E G", "C# B F", "A B H"], "sample_outputs": ["major", "minor", "strange"], "notes": null}, "src_uid": "6aa83c2f6e095848bc63aba7d013aa58"}
{"nl": {"description": "There are well-known formulas: , , . Also mathematicians found similar formulas for higher degrees.Find the value of the sum  modulo 109\u2009+\u20097 (so you should find the remainder after dividing the answer by the value 109\u2009+\u20097).", "input_spec": "The only line contains two integers n,\u2009k (1\u2009\u2264\u2009n\u2009\u2264\u2009109,\u20090\u2009\u2264\u2009k\u2009\u2264\u2009106).", "output_spec": "Print the only integer a \u2014 the remainder after dividing the value of the sum by the value 109\u2009+\u20097.", "sample_inputs": ["4 1", "4 2", "4 3", "4 0"], "sample_outputs": ["10", "30", "100", "4"], "notes": null}, "src_uid": "6f6fc42a367cdce60d76fd1914e73f0c"}
{"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,\u20090) and (x2,\u20090) 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\u2009\u2264\u2009n\u2009\u2264\u2009103). The second line contains n distinct integers x1,\u2009x2,\u2009...,\u2009xn (\u2009-\u2009106\u2009\u2264\u2009xi\u2009\u2264\u2009106) \u2014 the i-th point has coordinates (xi,\u20090). 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": "There are n cards (n is even) in the deck. Each card has a positive integer written on it. n\u2009/\u20092 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\u2009\u2264\u2009n\u2009\u2264\u2009100)\u00a0\u2014 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,\u2009a2,\u2009...,\u2009an (1\u2009\u2264\u2009ai\u2009\u2264\u2009100), where ai is equal to the number written on the i-th card.", "output_spec": "Print n\u2009/\u20092 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": "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 \u2014 $$$(x_2, y_2)$$$.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 \u2014 $$$(x_4, y_4)$$$. Coordinates of the bottom left corner of the second black sheet are $$$(x_5, y_5)$$$, and the top right \u2014 $$$(x_6, y_6)$$$.     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 $$$x_1, y_1, x_2, y_2$$$ $$$(0 \\le x_1 < x_2 \\le 10^{6}, 0 \\le y_1 < y_2 \\le 10^{6})$$$ \u2014 coordinates of the bottom left and the top right corners of the white sheet. The second line of the input contains four integers $$$x_3, y_3, x_4, y_4$$$ $$$(0 \\le x_3 < x_4 \\le 10^{6}, 0 \\le y_3 < y_4 \\le 10^{6})$$$ \u2014 coordinates of the bottom left and the top right corners of the first black sheet. The third line of the input contains four integers $$$x_5, y_5, x_6, y_6$$$ $$$(0 \\le x_5 < x_6 \\le 10^{6}, 0 \\le y_5 < y_6 \\le 10^{6})$$$ \u2014 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": "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\u00b780\u2009=\u200930000. 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\u2009\u2264\u2009n\u2009\u2264\u2009109, 0\u2009\u2264\u2009k\u2009\u2264\u20098).", "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": "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\u2009\u2264\u2009m\u2009\u2264\u2009100,\u20090\u2009\u2264\u2009s\u2009\u2264\u2009900) \u2014 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 \u2014 first the minimum possible number, then \u2014 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": "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 \u2014 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": "The circle line of the Roflanpolis subway has $$$n$$$ stations.There are two parallel routes in the subway. The first one visits stations in order $$$1 \\to 2 \\to \\ldots \\to n \\to 1 \\to 2 \\to \\ldots$$$ (so the next stop after station $$$x$$$ is equal to $$$(x+1)$$$ if $$$x < n$$$ and $$$1$$$ otherwise). The second route visits stations in order $$$n \\to (n-1) \\to \\ldots \\to 1 \\to n \\to (n-1) \\to \\ldots$$$ (so the next stop after station $$$x$$$ is equal to $$$(x-1)$$$ if $$$x>1$$$ and $$$n$$$ otherwise). All trains depart their stations simultaneously, and it takes exactly $$$1$$$ minute to arrive at the next station.Two toads live in this city, their names are Daniel and Vlad.Daniel is currently in a train of the first route at station $$$a$$$ and will exit the subway when his train reaches station $$$x$$$.Coincidentally, Vlad is currently in a train of the second route at station $$$b$$$ and he will exit the subway when his train reaches station $$$y$$$.Surprisingly, all numbers $$$a,x,b,y$$$ are distinct.Toad Ilya asks you to check if Daniel and Vlad will ever be at the same station at the same time during their journey. In other words, check if there is a moment when their trains stop at the same station. Note that this includes the moments when Daniel or Vlad enter or leave the subway.", "input_spec": "The first line contains five space-separated integers $$$n$$$, $$$a$$$, $$$x$$$, $$$b$$$, $$$y$$$ ($$$4 \\leq n \\leq 100$$$, $$$1 \\leq a, x, b, y \\leq n$$$, all numbers among $$$a$$$, $$$x$$$, $$$b$$$, $$$y$$$ are distinct)\u00a0\u2014 the number of stations in Roflanpolis, Daniel's start station, Daniel's finish station, Vlad's start station and Vlad's finish station, respectively.", "output_spec": "Output \"YES\" if there is a time moment when Vlad and Daniel are at the same station, and \"NO\" otherwise. You can print each letter in any case (upper or lower).", "sample_inputs": ["5 1 4 3 2", "10 2 1 9 10"], "sample_outputs": ["YES", "NO"], "notes": "NoteIn the first example, Daniel and Vlad start at the stations $$$(1, 3)$$$. One minute later they are at stations $$$(2, 2)$$$. They are at the same station at this moment. Note that Vlad leaves the subway right after that.Consider the second example, let's look at the stations Vlad and Daniel are at. They are:   initially $$$(2, 9)$$$,  after $$$1$$$ minute $$$(3, 8)$$$,  after $$$2$$$ minutes $$$(4, 7)$$$,  after $$$3$$$ minutes $$$(5, 6)$$$,  after $$$4$$$ minutes $$$(6, 5)$$$,  after $$$5$$$ minutes $$$(7, 4)$$$,  after $$$6$$$ minutes $$$(8, 3)$$$,  after $$$7$$$ minutes $$$(9, 2)$$$,  after $$$8$$$ minutes $$$(10, 1)$$$,  after $$$9$$$ minutes $$$(1, 10)$$$. After that, they both leave the subway because they are at their finish stations, so there is no moment when they both are at the same station."}, "src_uid": "5b889751f82c9f32f223cdee0c0095e4"}
{"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": "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\u2009\u2264\u2009n\u2009\u2264\u20094)\u00a0\u2014 the number of vertices that were not erased by Wilbur's friend. Each of the following n lines contains two integers xi and yi (\u2009-\u20091000\u2009\u2264\u2009xi,\u2009yi\u2009\u2264\u20091000)\u00a0\u2014the 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 \u2009-\u20091. ", "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": "A little girl loves problems on bitwise operations very much. Here's one of them.You are given two integers l and r. Let's consider the values of  for all pairs of integers a and b (l\u2009\u2264\u2009a\u2009\u2264\u2009b\u2009\u2264\u2009r). Your task is to find the maximum value among all considered ones.Expression  means applying bitwise excluding or operation to integers x and y. The given operation exists in all modern programming languages, for example, in languages C++ and Java it is represented as \"^\", in Pascal \u2014 as \"xor\".", "input_spec": "The single line contains space-separated integers l and r (1\u2009\u2264\u2009l\u2009\u2264\u2009r\u2009\u2264\u20091018). Please, do not use the %lld specifier to read or write 64-bit integers in C++. It is preferred to use the cin, cout streams or the %I64d specifier.", "output_spec": "In a single line print a single integer \u2014 the maximum value of  for all pairs of integers a, b (l\u2009\u2264\u2009a\u2009\u2264\u2009b\u2009\u2264\u2009r).", "sample_inputs": ["1 2", "8 16", "1 1"], "sample_outputs": ["3", "31", "0"], "notes": null}, "src_uid": "d90e99d539b16590c17328d79a5921e0"}
{"nl": {"description": "Heidi the Cow is aghast: cracks in the northern Wall? Zombies gathering outside, forming groups, preparing their assault? This must not happen! Quickly, she fetches her HC2 (Handbook of Crazy Constructions) and looks for the right chapter:How to build a wall:  Take a set of bricks.  Select one of the possible wall designs. Computing the number of possible designs is left as an exercise to the reader.  Place bricks on top of each other, according to the chosen design. This seems easy enough. But Heidi is a Coding Cow, not a Constructing Cow. Her mind keeps coming back to point 2b. Despite the imminent danger of a zombie onslaught, she wonders just how many possible walls she could build with up to n bricks.A wall is a set of wall segments as defined in the easy version. How many different walls can be constructed such that the wall consists of at least 1 and at most n bricks? Two walls are different if there exist a column c and a row r such that one wall has a brick in this spot, and the other does not.Along with n, you will be given C, the width of the wall (as defined in the easy version). Return the number of different walls modulo 106\u2009+\u20093.", "input_spec": "The first line contains two space-separated integers n and C, 1\u2009\u2264\u2009n\u2009\u2264\u2009500000, 1\u2009\u2264\u2009C\u2009\u2264\u2009200000.", "output_spec": "Print the number of different walls that Heidi could build, modulo 106\u2009+\u20093.", "sample_inputs": ["5 1", "2 2", "3 2", "11 5", "37 63"], "sample_outputs": ["5", "5", "9", "4367", "230574"], "notes": "NoteThe number 106\u2009+\u20093 is prime.In the second sample case, the five walls are:             B        BB., .B, BB, B., and .BIn the third sample case, the nine walls are the five as in the second sample case and in addition the following four: B    BB    B  B        BB., .B, BB, and BB"}, "src_uid": "e63c70a9c96a94bce99618f2e695f83a"}
{"nl": {"description": "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,\u20092,\u2009...,\u2009z. 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\u00a0\u2014 n, m and z (1\u2009\u2264\u2009n,\u2009m,\u2009z\u2009\u2264\u2009104).", "output_spec": "Print single integer\u00a0\u2014 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\u00a0\u2014 only the artist which comes on the sixth minute. "}, "src_uid": "e7ad55ce26fc8610639323af1de36c2d"}
{"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 $$$a_4$$$ ($$$1 \\leq a_i \\leq 100$$$) \u2014 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": "In order to make the \"Sea Battle\" game more interesting, Boris decided to add a new ship type to it. The ship consists of two rectangles. The first rectangle has a width of $$$w_1$$$ and a height of $$$h_1$$$, while the second rectangle has a width of $$$w_2$$$ and a height of $$$h_2$$$, where $$$w_1 \\ge w_2$$$. In this game, exactly one ship is used, made up of two rectangles. There are no other ships on the field.The rectangles are placed on field in the following way:  the second rectangle is on top the first rectangle;  they are aligned to the left, i.e. their left sides are on the same line;  the rectangles are adjacent to each other without a gap. See the pictures in the notes: the first rectangle is colored red, the second rectangle is colored blue.Formally, let's introduce a coordinate system. Then, the leftmost bottom cell of the first rectangle has coordinates $$$(1, 1)$$$, the rightmost top cell of the first rectangle has coordinates $$$(w_1, h_1)$$$, the leftmost bottom cell of the second rectangle has coordinates $$$(1, h_1 + 1)$$$ and the rightmost top cell of the second rectangle has coordinates $$$(w_2, h_1 + h_2)$$$.After the ship is completely destroyed, all cells neighboring by side or a corner with the ship are marked. Of course, only cells, which don't belong to the ship are marked. On the pictures in the notes such cells are colored green.Find out how many cells should be marked after the ship is destroyed. The field of the game is infinite in any direction.", "input_spec": "Four lines contain integers $$$w_1, h_1, w_2$$$ and $$$h_2$$$ ($$$1 \\leq w_1, h_1, w_2, h_2 \\leq 10^8$$$, $$$w_1 \\ge w_2$$$)\u00a0\u2014 the width of the first rectangle, the height of the first rectangle, the width of the second rectangle and the height of the second rectangle. You can't rotate the rectangles.", "output_spec": "Print exactly one integer\u00a0\u2014 the number of cells, which should be marked after the ship is destroyed.", "sample_inputs": ["2 1 2 1", "2 2 1 2"], "sample_outputs": ["12", "16"], "notes": "NoteIn the first example the field looks as follows (the first rectangle is red, the second rectangle is blue, green shows the marked squares):  In the second example the field looks as:  "}, "src_uid": "b5d44e0041053c996938aadd1b3865f6"}
{"nl": {"description": "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 ($$$1 \\leq n,m \\leq 10^9$$$)\u00a0\u2014 the number of kinds of presents and the number of boxes that Alice has.", "output_spec": "Print one integer \u00a0\u2014 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": "Tattah is asleep if and only if Tattah is attending a lecture. This is a well-known formula among Tattah's colleagues.On a Wednesday afternoon, Tattah was attending Professor HH's lecture. At 12:21, right before falling asleep, he was staring at the digital watch around Saher's wrist. He noticed that the digits on the clock were the same when read from both directions i.e. a palindrome.In his sleep, he started dreaming about such rare moments of the day when the time displayed on a digital clock is a palindrome. As soon as he woke up, he felt destined to write a program that finds the next such moment.However, he still hasn't mastered the skill of programming while sleeping, so your task is to help him.", "input_spec": "The first and only line of the input starts with a string with the format \"HH:MM\" where \"HH\" is from \"00\" to \"23\" and \"MM\" is from \"00\" to \"59\". Both \"HH\" and \"MM\" have exactly two digits.", "output_spec": "Print the palindromic time of day that comes soonest after the time given in the input. If the input time is palindromic, output the soonest palindromic time after the input time.", "sample_inputs": ["12:21", "23:59"], "sample_outputs": ["13:31", "00:00"], "notes": null}, "src_uid": "158eae916daa3e0162d4eac0426fa87f"}
{"nl": {"description": "Alice has a lovely piece of cloth. It has the shape of a square with a side of length $$$a$$$ centimeters. Bob also wants such piece of cloth. He would prefer a square with a side of length $$$b$$$ centimeters (where $$$b < a$$$). Alice wanted to make Bob happy, so she cut the needed square out of the corner of her piece and gave it to Bob. Now she is left with an ugly L shaped cloth (see pictures below).Alice would like to know whether the area of her cloth expressed in square centimeters is prime. Could you help her to determine it?", "input_spec": "The first line contains a number $$$t$$$\u00a0($$$1 \\leq t \\leq 5$$$)\u00a0\u2014 the number of test cases. Each of the next $$$t$$$ lines describes the $$$i$$$-th test case. It contains two integers $$$a$$$ and $$$b~(1 \\leq b < a \\leq 10^{11})$$$\u00a0\u2014 the side length of Alice's square and the side length of the square that Bob wants.", "output_spec": "Print $$$t$$$ lines, where the $$$i$$$-th line is the answer to the $$$i$$$-th test case. Print \"YES\" (without quotes) if the area of the remaining piece of cloth is prime, otherwise print \"NO\". You can print each letter in an arbitrary case (upper or lower).", "sample_inputs": ["4\n6 5\n16 13\n61690850361 24777622630\n34 33"], "sample_outputs": ["YES\nNO\nNO\nYES"], "notes": "NoteThe figure below depicts the first test case. The blue part corresponds to the piece which belongs to Bob, and the red part is the piece that Alice keeps for herself. The area of the red part is $$$6^2 - 5^2 = 36 - 25 = 11$$$, which is prime, so the answer is \"YES\".  In the second case, the area is $$$16^2 - 13^2 = 87$$$, which is divisible by $$$3$$$.  In the third case, the area of the remaining piece is $$$61690850361^2 - 24777622630^2 = 3191830435068605713421$$$. This number is not prime because $$$3191830435068605713421 = 36913227731 \\cdot 86468472991 $$$.In the last case, the area is $$$34^2 - 33^2 = 67$$$."}, "src_uid": "5a052e4e6c64333d94c83df890b1183c"}
{"nl": {"description": "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\u2009\u2264\u2009a1,\u2009a2\u2009\u2264\u2009100), 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": "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\u2009\u2264\u2009n\u2009\u2264\u2009200)\u00a0\u2014 the total number of cards. The next line contains a string s of length n \u2014 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\u00a0\u2014 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": "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\u2009-\u2009t. 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\u2009\u2264\u2009x\u2009\u2264\u20091018) \u2014 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": "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,\u20092m,\u20093m,\u2009...) 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\u2009\u2264\u2009n\u2009\u2264\u2009100;\u00a02\u2009\u2264\u2009m\u2009\u2264\u2009100), separated by a space.", "output_spec": "Print a single integer \u2014 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": "Today an outstanding event is going to happen in the forest\u00a0\u2014 hedgehog Filya will come to his old fried Sonya!Sonya is an owl and she sleeps during the day and stay awake from minute l1 to minute r1 inclusive. Also, during the minute k she prinks and is unavailable for Filya.Filya works a lot and he plans to visit Sonya from minute l2 to minute r2 inclusive.Calculate the number of minutes they will be able to spend together.", "input_spec": "The only line of the input contains integers l1, r1, l2, r2 and k (1\u2009\u2264\u2009l1,\u2009r1,\u2009l2,\u2009r2,\u2009k\u2009\u2264\u20091018, l1\u2009\u2264\u2009r1, l2\u2009\u2264\u2009r2), providing the segments of time for Sonya and Filya and the moment of time when Sonya prinks.", "output_spec": "Print one integer\u00a0\u2014 the number of minutes Sonya and Filya will be able to spend together.", "sample_inputs": ["1 10 9 20 1", "1 100 50 200 75"], "sample_outputs": ["2", "50"], "notes": "NoteIn the first sample, they will be together during minutes 9 and 10.In the second sample, they will be together from minute 50 to minute 74 and from minute 76 to minute 100."}, "src_uid": "9a74b3b0e9f3a351f2136842e9565a82"}
{"nl": {"description": "This problem's actual name, \"Lexicographically Largest Palindromic Subsequence\" is too long to fit into the page headline.You are given string s consisting of lowercase English letters only. Find its lexicographically largest palindromic subsequence.We'll call a non-empty string s[p1p2... pk] = sp1sp2... spk (1 \u2009\u2264\u2009 p1\u2009<\u2009p2\u2009<\u2009...\u2009<\u2009pk \u2009\u2264\u2009 |s|) a subsequence of string s = s1s2... s|s|, where |s| is the length of string s. For example, strings \"abcb\", \"b\" and \"abacaba\" are subsequences of string \"abacaba\".String x = x1x2... x|x| is lexicographically larger than string y = y1y2... y|y| if either |x| > |y| and x1\u2009=\u2009y1, x2\u2009=\u2009y2, ...,\u2009x|y|\u2009=\u2009y|y|, or there exists such number r (r\u2009<\u2009|x|, r\u2009<\u2009|y|) that x1\u2009=\u2009y1, x2\u2009=\u2009y2, ..., xr\u2009=\u2009yr and xr\u2009\u2009+\u2009\u20091\u2009>\u2009yr\u2009\u2009+\u2009\u20091. Characters in the strings are compared according to their ASCII codes. For example, string \"ranger\" is lexicographically larger than string \"racecar\" and string \"poster\" is lexicographically larger than string \"post\".String s = s1s2... s|s| is a palindrome if it matches string rev(s) = s|s|s|s|\u2009-\u20091... s1. In other words, a string is a palindrome if it reads the same way from left to right and from right to left. For example, palindromic strings are \"racecar\", \"refer\" and \"z\".", "input_spec": "The only input line contains a non-empty string s consisting of lowercase English letters only. Its length does not exceed 10.", "output_spec": "Print the lexicographically largest palindromic subsequence of string s.", "sample_inputs": ["radar", "bowwowwow", "codeforces", "mississipp"], "sample_outputs": ["rr", "wwwww", "s", "ssss"], "notes": "NoteAmong all distinct subsequences of string \"radar\" the following ones are palindromes: \"a\", \"d\", \"r\", \"aa\", \"rr\", \"ada\", \"rar\", \"rdr\", \"raar\" and \"radar\". The lexicographically largest of them is \"rr\"."}, "src_uid": "9a40e9b122962a1f83b74ddee6246a40"}
{"nl": {"description": "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\u2009\u2264\u2009n,\u2009m\u2009\u2264\u2009100). The next line contains n integers: a1,\u2009a2,\u2009...,\u2009an (1\u2009\u2264\u2009ai\u2009\u2264\u2009m).", "output_spec": "Print a single integer \u2014 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": "You are given a rectangular board of M\u2009\u00d7\u2009N squares. Also you are given an unlimited number of standard domino pieces of 2\u2009\u00d7\u20091 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 \u2014 board sizes in squares (1\u2009\u2264\u2009M\u2009\u2264\u2009N\u2009\u2264\u200916).", "output_spec": "Output one number \u2014 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": "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 $$$n$$$ ($$$1 \\leq n \\leq 100$$$)\u00a0\u2014 order of a rhombus whose numbers of cells should be computed.", "output_spec": "Print exactly one integer\u00a0\u2014 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": "Jzzhu has a big rectangular chocolate bar that consists of n\u2009\u00d7\u2009m 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\u2009\u00d7\u20096 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,\u2009m,\u2009k (1\u2009\u2264\u2009n,\u2009m\u2009\u2264\u2009109;\u00a01\u2009\u2264\u2009k\u2009\u2264\u20092\u00b7109).", "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\u2009\u00d7\u20093 chocolate 4 times."}, "src_uid": "bb453bbe60769bcaea6a824c72120f73"}
{"nl": {"description": "The king is left alone on the chessboard. In spite of this loneliness, he doesn't lose heart, because he has business of national importance. For example, he has to pay an official visit to square t. As the king is not in habit of wasting his time, he wants to get from his current position s to square t in the least number of moves. Help him to do this.  In one move the king can get to the square that has a common side or a common vertex with the square the king is currently in (generally there are 8 different squares he can move to).", "input_spec": "The first line contains the chessboard coordinates of square s, the second line \u2014 of square t. Chessboard coordinates consist of two characters, the first one is a lowercase Latin letter (from a to h), the second one is a digit from 1 to 8.", "output_spec": "In the first line print n \u2014 minimum number of the king's moves. Then in n lines print the moves themselves. Each move is described with one of the 8: L, R, U, D, LU, LD, RU or RD.  L, R, U, D stand respectively for moves left, right, up and down (according to the picture), and 2-letter combinations stand for diagonal moves. If the answer is not unique, print any of them. ", "sample_inputs": ["a8\nh1"], "sample_outputs": ["7\nRD\nRD\nRD\nRD\nRD\nRD\nRD"], "notes": null}, "src_uid": "d25d454702b7755297a7a8e1f6f36ab9"}
{"nl": {"description": "Way to go! Heidi now knows how many brains there must be for her to get one. But throwing herself in the midst of a clutch of hungry zombies is quite a risky endeavor. Hence Heidi wonders: what is the smallest number of brains that must be in the chest for her to get out at all (possibly empty-handed, but alive)?The brain dinner night will evolve just as in the previous subtask: the same crowd is present, the N\u2009-\u20091 zombies have the exact same mindset as before and Heidi is to make the first proposal, which must be accepted by at least half of the attendees for her to survive.", "input_spec": "The only line of input contains one integer: N, the number of attendees (1\u2009\u2264\u2009N\u2009\u2264\u2009109).", "output_spec": "Output one integer: the smallest number of brains in the chest which allows Heidi to merely survive.", "sample_inputs": ["1", "3", "99"], "sample_outputs": ["0", "1", "49"], "notes": null}, "src_uid": "422abdf2f705c069e540d4f5c09a4948"}
{"nl": {"description": "Imp is in a magic forest, where xorangles grow (wut?)  A xorangle of order n is such a non-degenerate triangle, that lengths of its sides are integers not exceeding n, and the xor-sum of the lengths is equal to zero. Imp has to count the number of distinct xorangles of order n to get out of the forest. Formally, for a given integer n you have to find the number of such triples (a,\u2009b,\u2009c), that:  1\u2009\u2264\u2009a\u2009\u2264\u2009b\u2009\u2264\u2009c\u2009\u2264\u2009n;  , where  denotes the bitwise xor of integers x and y.  (a,\u2009b,\u2009c) form a non-degenerate (with strictly positive area) triangle. ", "input_spec": "The only line contains a single integer n (1\u2009\u2264\u2009n\u2009\u2264\u20092500).", "output_spec": "Print the number of xorangles of order n.", "sample_inputs": ["6", "10"], "sample_outputs": ["1", "2"], "notes": "NoteThe only xorangle in the first sample is (3,\u20095,\u20096)."}, "src_uid": "838f2e75fdff0f13f002c0dfff0b2e8d"}
{"nl": {"description": "One day a highly important task was commissioned to Vasya \u2014 writing a program in a night. The program consists of n lines of code. Vasya is already exhausted, so he works like that: first he writes v lines of code, drinks a cup of tea, then he writes as much as  lines, drinks another cup of tea, then he writes  lines and so on: , , , ...The expression  is regarded as the integral part from dividing number a by number b.The moment the current value  equals 0, Vasya immediately falls asleep and he wakes up only in the morning, when the program should already be finished.Vasya is wondering, what minimum allowable value v can take to let him write not less than n lines of code before he falls asleep.", "input_spec": "The input consists of two integers n and k, separated by spaces \u2014 the size of the program in lines and the productivity reduction coefficient, 1\u2009\u2264\u2009n\u2009\u2264\u2009109, 2\u2009\u2264\u2009k\u2009\u2264\u200910.", "output_spec": "Print the only integer \u2014 the minimum value of v that lets Vasya write the program in one night.", "sample_inputs": ["7 2", "59 9"], "sample_outputs": ["4", "54"], "notes": "NoteIn the first sample the answer is v\u2009=\u20094. Vasya writes the code in the following portions: first 4 lines, then 2, then 1, and then Vasya falls asleep. Thus, he manages to write 4\u2009+\u20092\u2009+\u20091\u2009=\u20097 lines in a night and complete the task.In the second sample the answer is v\u2009=\u200954. Vasya writes the code in the following portions: 54, 6. The total sum is 54\u2009+\u20096\u2009=\u200960, that's even more than n\u2009=\u200959."}, "src_uid": "41dfc86d341082dd96e089ac5433dc04"}
{"nl": {"description": "Throughout Igor K.'s life he has had many situations worthy of attention. We remember the story with the virus, the story of his mathematical career and of course, his famous programming achievements. However, one does not always adopt new hobbies, one can quit something as well.This time Igor K. got disappointed in one of his hobbies: editing and voicing videos. Moreover, he got disappointed in it so much, that he decided to destroy his secret archive for good. Igor K. use Pindows XR operation system which represents files and folders by small icons. At that, m icons can fit in a horizontal row in any window.Igor K.'s computer contains n folders in the D: disk's root catalog. The folders are numbered from 1 to n in the order from the left to the right and from top to bottom (see the images). At that the folders with secret videos have numbers from a to b inclusive. Igor K. wants to delete them forever, at that making as few frame selections as possible, and then pressing Shift+Delete exactly once. What is the minimum number of times Igor K. will have to select the folder in order to select folders from a to b and only them? Let us note that if some selected folder is selected repeatedly, then it is deselected. Each selection possesses the shape of some rectangle with sides parallel to the screen's borders.", "input_spec": "The only line contains four integers n, m, a, b (1\u2009\u2264\u2009n,\u2009m\u2009\u2264\u2009109, 1\u2009\u2264\u2009a\u2009\u2264\u2009b\u2009\u2264\u2009n). They are the number of folders in Igor K.'s computer, the width of a window and the numbers of the first and the last folders that need to be deleted.", "output_spec": "Print a single number: the least possible number of times Igor K. will have to select the folders using frames to select only the folders with numbers from a to b.", "sample_inputs": ["11 4 3 9", "20 5 2 20"], "sample_outputs": ["3", "2"], "notes": "NoteThe images below illustrate statement tests.The first test:In this test we can select folders 3 and 4 with out first selection, folders 5, 6, 7, 8 with our second selection and folder 9 with our third, last selection.The second test:In this test we can first select all folders in the first row (2, 3, 4, 5), then \u2014 all other ones."}, "src_uid": "f256235c0b2815aae85a6f9435c69dac"}
{"nl": {"description": "Jabber ID on the national Berland service \u00abBabber\u00bb has a form <username>@<hostname>[/resource], where   <username> \u2014 is a sequence of Latin letters (lowercase or uppercase), digits or underscores characters \u00ab_\u00bb, the length of <username> is between 1 and 16, inclusive.  <hostname> \u2014 is a sequence of word separated by periods (characters \u00ab.\u00bb), 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> \u2014 is a sequence of Latin letters (lowercase or uppercase), digits or underscores characters \u00ab_\u00bb, the length of <resource> is between 1 and 16, inclusive. The content of square brackets is optional \u2014 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": "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\u2009>\u20091, 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\u2009\u2264\u2009n\u2009<\u2009250, 0\u2009\u2264\u2009r\u2009-\u2009l\u2009\u2264\u2009105, r\u2009\u2265\u20091, l\u2009\u2265\u20091) \u2013 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,\u20091,\u20091,\u20091]. The number of ones is 4.For the second example:Elements on positions from 3-rd to 10-th in list is [1,\u20091,\u20091,\u20090,\u20091,\u20090,\u20091,\u20090]. The number of ones is 5."}, "src_uid": "3ac61b1f8deee7911b1055c243f5eb6a"}
{"nl": {"description": "Luba has to do n chores today. i-th chore takes ai units of time to complete. It is guaranteed that for every  the condition ai\u2009\u2265\u2009ai\u2009-\u20091 is met, so the sequence is sorted.Also Luba can work really hard on some chores. She can choose not more than k any chores and do each of them in x units of time instead of ai ().Luba is very responsible, so she has to do all n chores, and now she wants to know the minimum time she needs to do everything. Luba cannot do two chores simultaneously.", "input_spec": "The first line contains three integers n,\u2009k,\u2009x\u00a0(1\u2009\u2264\u2009k\u2009\u2264\u2009n\u2009\u2264\u2009100,\u20091\u2009\u2264\u2009x\u2009\u2264\u200999) \u2014 the number of chores Luba has to do, the number of chores she can do in x units of time, and the number x itself. The second line contains n integer numbers ai\u00a0(2\u2009\u2264\u2009ai\u2009\u2264\u2009100) \u2014 the time Luba has to spend to do i-th chore. It is guaranteed that , and for each  ai\u2009\u2265\u2009ai\u2009-\u20091.", "output_spec": "Print one number \u2014 minimum time Luba needs to do all n chores.", "sample_inputs": ["4 2 2\n3 6 7 10", "5 2 1\n100 100 100 100 100"], "sample_outputs": ["13", "302"], "notes": "NoteIn the first example the best option would be to do the third and the fourth chore, spending x\u2009=\u20092 time on each instead of a3 and a4, respectively. Then the answer is 3\u2009+\u20096\u2009+\u20092\u2009+\u20092\u2009=\u200913.In the second example Luba can choose any two chores to spend x time on them instead of ai. So the answer is 100\u00b73\u2009+\u20092\u00b71\u2009=\u2009302."}, "src_uid": "92a233f8d9c73d9f33e4e6116b7d0a96"}
{"nl": {"description": " When the curtains are opened, a canvas unfolds outside. Kanno marvels at all the blonde colours along the riverside\u00a0\u2014 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 ($$$\\lvert s \\rvert \\leq 100$$$)\u00a0\u2014 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": "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 $$$t$$$ ($$$1 \\le t \\le 20$$$) \u2014 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 \u2014 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": "JATC and his friend Giraffe are currently in their room, solving some problems. Giraffe has written on the board an array $$$a_1$$$, $$$a_2$$$, ..., $$$a_n$$$ of integers, such that $$$1 \\le a_1 < a_2 < \\ldots < a_n \\le 10^3$$$, and then went to the bathroom.JATC decided to prank his friend by erasing some consecutive elements in the array. Since he doesn't want for the prank to go too far, he will only erase in a way, such that Giraffe can still restore the array using the information from the remaining elements. Because Giraffe has created the array, he's also aware that it's an increasing array and all the elements are integers in the range $$$[1, 10^3]$$$.JATC wonders what is the greatest number of elements he can erase?", "input_spec": "The first line of the input contains a single integer $$$n$$$ ($$$1 \\le n \\le 100$$$)\u00a0\u2014 the number of elements in the array. The second line of the input contains $$$n$$$ integers $$$a_i$$$ ($$$1 \\le a_1<a_2<\\dots<a_n \\le 10^3$$$)\u00a0\u2014 the array written by Giraffe.", "output_spec": "Print a single integer\u00a0\u2014 the maximum number of consecutive elements in the array that JATC can erase. If it is impossible to erase even a single element, print $$$0$$$.", "sample_inputs": ["6\n1 3 4 5 6 9", "3\n998 999 1000", "5\n1 2 3 4 5"], "sample_outputs": ["2", "2", "4"], "notes": "NoteIn the first example, JATC can erase the third and fourth elements, leaving the array $$$[1, 3, \\_, \\_, 6, 9]$$$. As you can see, there is only one way to fill in the blanks.In the second example, JATC can erase the second and the third elements. The array will become $$$[998, \\_, \\_]$$$. Because all the elements are less than or equal to $$$1000$$$, the array is still can be restored. Note, that he can't erase the first $$$2$$$ elements.In the third example, JATC can erase the first $$$4$$$ elements. Since all the elements are greater than or equal to $$$1$$$, Giraffe can still restore the array. Note, that he can't erase the last $$$4$$$ elements."}, "src_uid": "858b5e75e21c4cba6d08f3f66be0c198"}
{"nl": {"description": "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\u2009=\u20091 and b\u2009=\u20093 then at first the calculator will print 2 segments, then \u2014 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,\u2009b (1\u2009\u2264\u2009a\u2009\u2264\u2009b\u2009\u2264\u2009106) \u2014 the first and the last number typed by Max.", "output_spec": "Print the only integer a \u2014 the total number of printed segments.", "sample_inputs": ["1 3", "10 15"], "sample_outputs": ["12", "39"], "notes": null}, "src_uid": "1193de6f80a9feee8522a404d16425b9"}
{"nl": {"description": "Two bears are playing tic-tac-toe via mail. It's boring for them to play usual tic-tac-toe game, so they are a playing modified version of this game. Here are its rules.The game is played on the following field.  Players are making moves by turns. At first move a player can put his chip in any cell of any small field. For following moves, there are some restrictions: if during last move the opposite player put his chip to cell with coordinates (xl,\u2009yl) in some small field, the next move should be done in one of the cells of the small field with coordinates (xl,\u2009yl). For example, if in the first move a player puts his chip to lower left cell of central field, then the second player on his next move should put his chip into some cell of lower left field (pay attention to the first test case). If there are no free cells in the required field, the player can put his chip to any empty cell on any field.You are given current state of the game and coordinates of cell in which the last move was done. You should find all cells in which the current player can put his chip.A hare works as a postman in the forest, he likes to foul bears. Sometimes he changes the game field a bit, so the current state of the game could be unreachable. However, after his changes the cell where the last move was done is not empty. You don't need to find if the state is unreachable or not, just output possible next moves according to the rules.", "input_spec": "First 11 lines contains descriptions of table with 9 rows and 9 columns which are divided into 9 small fields by spaces and empty lines. Each small field is described by 9 characters without spaces and empty lines. character \"x\" (ASCII-code 120) means that the cell is occupied with chip of the first player, character \"o\" (ASCII-code 111) denotes a field occupied with chip of the second player, character \".\" (ASCII-code 46) describes empty cell. The line after the table contains two integers x and y (1\u2009\u2264\u2009x,\u2009y\u2009\u2264\u20099). They describe coordinates of the cell in table where the last move was done. Rows in the table are numbered from up to down and columns are numbered from left to right. It's guaranteed that cell where the last move was done is filled with \"x\" or \"o\". Also, it's guaranteed that there is at least one empty cell. It's not guaranteed that current state of game is reachable.", "output_spec": "Output the field in same format with characters \"!\" (ASCII-code 33) on positions where the current player can put his chip. All other cells should not be modified.", "sample_inputs": ["... ... ...\n... ... ...\n... ... ...\n\n... ... ...\n... ... ...\n... x.. ...\n\n... ... ...\n... ... ...\n... ... ...\n6 4", "xoo x.. x..\nooo ... ...\nooo ... ...\n\nx.. x.. x..\n... ... ...\n... ... ...\n\nx.. x.. x..\n... ... ...\n... ... ...\n7 4", "o.. ... ...\n... ... ...\n... ... ...\n\n... xxx ...\n... xox ...\n... ooo ...\n\n... ... ...\n... ... ...\n... ... ...\n5 5"], "sample_outputs": ["... ... ... \n... ... ... \n... ... ... \n\n... ... ... \n... ... ... \n... x.. ... \n\n!!! ... ... \n!!! ... ... \n!!! ... ...", "xoo x!! x!! \nooo !!! !!! \nooo !!! !!! \n\nx!! x!! x!! \n!!! !!! !!! \n!!! !!! !!! \n\nx!! x!! x!! \n!!! !!! !!! \n!!! !!! !!!", "o!! !!! !!! \n!!! !!! !!! \n!!! !!! !!! \n\n!!! xxx !!! \n!!! xox !!! \n!!! ooo !!! \n\n!!! !!! !!! \n!!! !!! !!! \n!!! !!! !!!"], "notes": "NoteIn the first test case the first player made a move to lower left cell of central field, so the second player can put a chip only to cells of lower left field.In the second test case the last move was done to upper left cell of lower central field, however all cells in upper left field are occupied, so the second player can put his chip to any empty cell.In the third test case the last move was done to central cell of central field, so current player can put his chip to any cell of central field, which is already occupied, so he can move anywhere. Pay attention that this state of the game is unreachable."}, "src_uid": "8f0fad22f629332868c39969492264d3"}
{"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\u00b7i 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\u2009\u2264\u2009n\u2009\u2264\u200910, 1\u2009\u2264\u2009k\u2009\u2264\u2009240)\u00a0\u2014 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\u2009+\u200910\u2009=\u200915 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\u2009+\u200910\u2009+\u200915\u2009+\u200920\u2009=\u200950 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": "There are literally dozens of snooker competitions held each year, and team Jinotega tries to attend them all (for some reason they prefer name \"snookah\")! When a competition takes place somewhere far from their hometown, Ivan, Artsem and Konstantin take a flight to the contest and back.Jinotega's best friends, team Base have found a list of their itinerary receipts with information about departure and arrival airports. Now they wonder, where is Jinotega now: at home or at some competition far away? They know that:   this list contains all Jinotega's flights in this year (in arbitrary order),  Jinotega has only flown from his hometown to a snooker contest and back,  after each competition Jinotega flies back home (though they may attend a competition in one place several times),  and finally, at the beginning of the year Jinotega was at home. Please help them to determine Jinotega's location!", "input_spec": "In the first line of input there is a single integer n: the number of Jinotega's flights (1\u2009\u2264\u2009n\u2009\u2264\u2009100). In the second line there is a string of 3 capital Latin letters: the name of Jinotega's home airport. In the next n lines there is flight information, one flight per line, in form \"XXX->YYY\", where \"XXX\" is the name of departure airport \"YYY\" is the name of arrival airport. Exactly one of these airports is Jinotega's home airport. It is guaranteed that flights information is consistent with the knowledge of Jinotega's friends, which is described in the main part of the statement.", "output_spec": "If Jinotega is now at home, print \"home\" (without quotes), otherwise print \"contest\".", "sample_inputs": ["4\nSVO\nSVO->CDG\nLHR->SVO\nSVO->LHR\nCDG->SVO", "3\nSVO\nSVO->HKT\nHKT->SVO\nSVO->RAP"], "sample_outputs": ["home", "contest"], "notes": "NoteIn the first sample Jinotega might first fly from SVO to CDG and back, and then from SVO to LHR and back, so now they should be at home. In the second sample Jinotega must now be at RAP because a flight from RAP back to SVO is not on the list."}, "src_uid": "51d1c79a52d3d4f80c98052b6ec77222"}
{"nl": {"description": "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:  $$$s_i$$$ \u2014 the day, when questions for the $$$i$$$-th exam will be published,  $$$d_i$$$ \u2014 the day of the $$$i$$$-th exam ($$$s_i < d_i$$$),  $$$c_i$$$ \u2014 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 $$$m$$$ $$$(2 \\le n \\le 100, 1 \\le m \\le n)$$$ \u2014 the number of days and the number of exams. Each of the following $$$m$$$ lines contains three integers $$$s_i$$$, $$$d_i$$$, $$$c_i$$$ $$$(1 \\le s_i < d_i \\le n, 1 \\le c_i \\le n)$$$ \u2014 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": "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\u2009\u2264\u2009n\u2009\u2264\u2009107, 1\u2009\u2264\u2009x,\u2009y\u2009\u2264\u2009109) \u2014 the number of letters 'a' in the input file and the parameters from the problem statement.", "output_spec": "Print the only integer t \u2014 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": "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\u2009+\u20097). ", "input_spec": "The first line contains the only integer n (1\u2009\u2264\u2009n\u2009\u2264\u2009107) \u2014 the required length of the cyclic path.", "output_spec": "Print the only integer \u2014 the required number of ways modulo 1000000007 (109\u2009+\u20097).", "sample_inputs": ["2", "4"], "sample_outputs": ["3", "21"], "notes": "NoteThe required paths in the first sample are:   D\u2009-\u2009A\u2009-\u2009D  D\u2009-\u2009B\u2009-\u2009D  D\u2009-\u2009C\u2009-\u2009D "}, "src_uid": "77627cc366a22e38da412c3231ac91a8"}
{"nl": {"description": "Ivan has a robot which is situated on an infinite grid. Initially the robot is standing in the starting cell (0,\u20090). The robot can process commands. There are four types of commands it can perform:  U \u2014 move from the cell (x,\u2009y) to (x,\u2009y\u2009+\u20091);  D \u2014 move from (x,\u2009y) to (x,\u2009y\u2009-\u20091);  L \u2014 move from (x,\u2009y) to (x\u2009-\u20091,\u2009y);  R \u2014 move from (x,\u2009y) to (x\u2009+\u20091,\u2009y). Ivan entered a sequence of n commands, and the robot processed it. After this sequence the robot ended up in the starting cell (0,\u20090), 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 \u2014 the length of sequence of commands entered by Ivan (1\u2009\u2264\u2009n\u2009\u2264\u2009100). The second line contains the sequence itself \u2014 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": "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)\u2009<\u2009val(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\u2009\u2264\u2009n\u2009\u2264\u2009100) \u2014 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 \u2014 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": "Ralph has a magic field which is divided into n\u2009\u00d7\u2009m blocks. That is to say, there are n rows and m columns on the field. Ralph can put an integer in each block. However, the magic field doesn't always work properly. It works only if the product of integers in each row and each column equals to k, where k is either 1 or -1.Now Ralph wants you to figure out the number of ways to put numbers in each block in such a way that the magic field works properly. Two ways are considered different if and only if there exists at least one block where the numbers in the first way and in the second way are different. You are asked to output the answer modulo 1000000007\u2009=\u2009109\u2009+\u20097.Note that there is no range of the numbers to put in the blocks, but we can prove that the answer is not infinity.", "input_spec": "The only line contains three integers n, m and k (1\u2009\u2264\u2009n,\u2009m\u2009\u2264\u20091018, k is either 1 or -1).", "output_spec": "Print a single number denoting the answer modulo 1000000007.", "sample_inputs": ["1 1 -1", "1 3 1", "3 3 -1"], "sample_outputs": ["1", "1", "16"], "notes": "NoteIn the first example the only way is to put -1 into the only block.In the second example the only way is to put 1 into every block."}, "src_uid": "6b9eff690fae14725885cbc891ff7243"}
{"nl": {"description": "The football season has just ended in Berland. According to the rules of Berland football, each match is played between two teams. The result of each match is either a draw, or a victory of one of the playing teams. If a team wins the match, it gets $$$w$$$ points, and the opposing team gets $$$0$$$ points. If the game results in a draw, both teams get $$$d$$$ points.The manager of the Berland capital team wants to summarize the results of the season, but, unfortunately, all information about the results of each match is lost. The manager only knows that the team has played $$$n$$$ games and got $$$p$$$ points for them.You have to determine three integers $$$x$$$, $$$y$$$ and $$$z$$$ \u2014 the number of wins, draws and loses of the team. If there are multiple answers, print any of them. If there is no suitable triple $$$(x, y, z)$$$, report about it.", "input_spec": "The first line contains four integers $$$n$$$, $$$p$$$, $$$w$$$ and $$$d$$$ $$$(1 \\le n \\le 10^{12}, 0 \\le p \\le 10^{17}, 1 \\le d < w \\le 10^{5})$$$ \u2014 the number of games, the number of points the team got, the number of points awarded for winning a match, and the number of points awarded for a draw, respectively. Note that $$$w > d$$$, so the number of points awarded for winning is strictly greater than the number of points awarded for draw.", "output_spec": "If there is no answer, print $$$-1$$$. Otherwise print three non-negative integers $$$x$$$, $$$y$$$ and $$$z$$$ \u2014 the number of wins, draws and losses of the team. If there are multiple possible triples $$$(x, y, z)$$$, print any of them. The numbers should meet the following conditions:    $$$x \\cdot w + y \\cdot d = p$$$,  $$$x + y + z = n$$$. ", "sample_inputs": ["30 60 3 1", "10 51 5 4", "20 0 15 5"], "sample_outputs": ["17 9 4", "-1", "0 0 20"], "notes": "NoteOne of the possible answers in the first example \u2014 $$$17$$$ wins, $$$9$$$ draws and $$$4$$$ losses. Then the team got $$$17 \\cdot 3 + 9 \\cdot 1 = 60$$$ points in $$$17 + 9 + 4 = 30$$$ games.In the second example the maximum possible score is $$$10 \\cdot 5 = 50$$$. Since $$$p = 51$$$, there is no answer.In the third example the team got $$$0$$$ points, so all $$$20$$$ games were lost."}, "src_uid": "503116e144d19eb953954d99c5526a7d"}
{"nl": {"description": "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": "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\u2009\u2264\u2009n\u2009<\u20091018) and m (1\u2009\u2264\u2009m\u2009\u2264\u2009100).", "output_spec": "In a single line print a single integer \u2014 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": "A flea is sitting at one of the n hassocks, arranged in a circle, at the moment. After minute number k the flea jumps through k\u2009-\u20091 hasso\u0441ks (clockwise). For example, after the first minute the flea jumps to the neighboring hassock. You should answer: will the flea visit all the hassocks or not. We assume that flea has infinitely much time for this jumping.", "input_spec": "The only line contains single integer: 1\u2009\u2264\u2009n\u2009\u2264\u20091000 \u2014 number of hassocks.", "output_spec": "Output \"YES\" if all the hassocks will be visited and \"NO\" otherwise.", "sample_inputs": ["1", "3"], "sample_outputs": ["YES", "NO"], "notes": null}, "src_uid": "4bd174a997707ed3a368bd0f2424590f"}
{"nl": {"description": "Vasya works as a watchman in the gallery. Unfortunately, one of the most expensive paintings was stolen while he was on duty. He doesn't want to be fired, so he has to quickly restore the painting. He remembers some facts about it.  The painting is a square 3\u2009\u00d7\u20093, each cell contains a single integer from 1 to n, and different cells may contain either different or equal integers.  The sum of integers in each of four squares 2\u2009\u00d7\u20092 is equal to the sum of integers in the top left square 2\u2009\u00d7\u20092.  Four elements a, b, c and d are known and are located as shown on the picture below. Help Vasya find out the number of distinct squares the satisfy all the conditions above. Note, that this number may be equal to 0, meaning Vasya remembers something wrong.Two squares are considered to be different, if there exists a cell that contains two different integers in different squares.", "input_spec": "The first line of the input contains five integers n, a, b, c and d (1\u2009\u2264\u2009n\u2009\u2264\u2009100\u2009000, 1\u2009\u2264\u2009a,\u2009b,\u2009c,\u2009d\u2009\u2264\u2009n)\u00a0\u2014 maximum possible value of an integer in the cell and four integers that Vasya remembers.", "output_spec": "Print one integer\u00a0\u2014 the number of distinct valid squares.", "sample_inputs": ["2 1 1 1 2", "3 3 1 2 3"], "sample_outputs": ["2", "6"], "notes": "NoteBelow are all the possible paintings for the first sample.  In the second sample, only paintings displayed below satisfy all the rules.      "}, "src_uid": "b732869015baf3dee5094c51a309e32c"}
{"nl": {"description": "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\u2009\u2264\u2009l,\u2009r,\u2009a\u2009\u2264\u2009100) \u2014 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\u00a0\u2014 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": "Imagine that you are in a building that has exactly n floors. You can move between the floors in a lift. Let's number the floors from bottom to top with integers from 1 to n. Now you're on the floor number a. You are very bored, so you want to take the lift. Floor number b has a secret lab, the entry is forbidden. However, you already are in the mood and decide to make k consecutive trips in the lift.Let us suppose that at the moment you are on the floor number x (initially, you were on floor a). For another trip between floors you choose some floor with number y (y\u2009\u2260\u2009x) and the lift travels to this floor. As you cannot visit floor b with the secret lab, you decided that the distance from the current floor x to the chosen y must be strictly less than the distance from the current floor x to floor b with the secret lab. Formally, it means that the following inequation must fulfill: |x\u2009-\u2009y|\u2009<\u2009|x\u2009-\u2009b|. After the lift successfully transports you to floor y, you write down number y in your notepad.Your task is to find the number of distinct number sequences that you could have written in the notebook as the result of k trips in the lift. As the sought number of trips can be rather large, find the remainder after dividing the number by 1000000007 (109\u2009+\u20097).", "input_spec": "The first line of the input contains four space-separated integers n, a, b, k (2\u2009\u2264\u2009n\u2009\u2264\u20095000, 1\u2009\u2264\u2009k\u2009\u2264\u20095000, 1\u2009\u2264\u2009a,\u2009b\u2009\u2264\u2009n, a\u2009\u2260\u2009b).", "output_spec": "Print a single integer \u2014 the remainder after dividing the sought number of sequences by 1000000007 (109\u2009+\u20097).", "sample_inputs": ["5 2 4 1", "5 2 4 2", "5 3 4 1"], "sample_outputs": ["2", "2", "0"], "notes": "NoteTwo sequences p1,\u2009p2,\u2009...,\u2009pk and q1,\u2009q2,\u2009...,\u2009qk are distinct, if there is such integer j (1\u2009\u2264\u2009j\u2009\u2264\u2009k), that pj\u2009\u2260\u2009qj.Notes to the samples:  In the first sample after the first trip you are either on floor 1, or on floor 3, because |1\u2009-\u20092|\u2009<\u2009|2\u2009-\u20094| and |3\u2009-\u20092|\u2009<\u2009|2\u2009-\u20094|.  In the second sample there are two possible sequences: (1,\u20092); (1,\u20093). You cannot choose floor 3 for the first trip because in this case no floor can be the floor for the second trip.  In the third sample there are no sought sequences, because you cannot choose the floor for the first trip. "}, "src_uid": "142b06ed43b3473513995de995e19fc3"}
{"nl": {"description": "There is a card game called \"Durak\", which means \"Fool\" in Russian. The game is quite popular in the countries that used to form USSR. The problem does not state all the game's rules explicitly \u2014 you can find them later yourselves if you want.To play durak you need a pack of 36 cards. Each card has a suit (\"S\", \"H\", \"D\" and \"C\") and a rank (in the increasing order \"6\", \"7\", \"8\", \"9\", \"T\", \"J\", \"Q\", \"K\" and \"A\"). At the beginning of the game one suit is arbitrarily chosen as trump. The players move like that: one player puts one or several of his cards on the table and the other one should beat each of them with his cards.A card beats another one if both cards have similar suits and the first card has a higher rank then the second one. Besides, a trump card can beat any non-trump card whatever the cards\u2019 ranks are. In all other cases you can not beat the second card with the first one.You are given the trump suit and two different cards. Determine whether the first one beats the second one or not.", "input_spec": "The first line contains the tramp suit. It is \"S\", \"H\", \"D\" or \"C\". The second line contains the description of the two different cards. Each card is described by one word consisting of two symbols. The first symbol stands for the rank (\"6\", \"7\", \"8\", \"9\", \"T\", \"J\", \"Q\", \"K\" and \"A\"), and the second one stands for the suit (\"S\", \"H\", \"D\" and \"C\").", "output_spec": "Print \"YES\" (without the quotes) if the first cards beats the second one. Otherwise, print \"NO\" (also without the quotes).", "sample_inputs": ["H\nQH 9S", "S\n8D 6D", "C\n7H AS"], "sample_outputs": ["YES", "YES", "NO"], "notes": null}, "src_uid": "da13bd5a335c7f81c5a963b030655c26"}
{"nl": {"description": "InputThe only line of the input is a string of 7 characters. The first character is letter A, followed by 6 digits. The input is guaranteed to be valid (for certain definition of \"valid\").OutputOutput a single integer.ExamplesInputA221033Output21InputA223635Output22InputA232726Output23", "input_spec": "The only line of the input is a string of 7 characters. The first character is letter A, followed by 6 digits. The input is guaranteed to be valid (for certain definition of \"valid\").", "output_spec": "Output a single integer.", "sample_inputs": ["A221033", "A223635", "A232726"], "sample_outputs": ["21", "22", "23"], "notes": null}, "src_uid": "47287f8bc61fec72d729638d5e0e67f5"}
{"nl": {"description": "Everybody knows of spaghetti sort. You decided to implement an analog sorting algorithm yourself, but as you survey your pantry you realize you're out of spaghetti! The only type of pasta you have is ravioli, but you are not going to let this stop you...You come up with the following algorithm. For each number in the array ai, build a stack of ai ravioli. The image shows the stack for ai\u2009=\u20094.  Arrange the stacks in one row in the order in which the corresponding numbers appear in the input array. Find the tallest one (if there are several stacks of maximal height, use the leftmost one). Remove it and add its height to the end of the output array. Shift the stacks in the row so that there is no gap between them. Repeat the procedure until all stacks have been removed.At first you are very happy with your algorithm, but as you try it on more inputs you realize that it doesn't always produce the right sorted array. Turns out when two stacks of ravioli are next to each other (at any step of the process) and differ in height by two or more, the top ravioli of the taller stack slides down on top of the lower stack.Given an input array, figure out whether the described algorithm will sort it correctly.", "input_spec": "The first line of input contains a single number n (1\u2009\u2264\u2009n\u2009\u2264\u200910) \u2014 the size of the array. The second line of input contains n space-separated integers ai (1\u2009\u2264\u2009ai\u2009\u2264\u2009100) \u2014 the elements of the array.", "output_spec": "Output \"YES\" if the array can be sorted using the described procedure and \"NO\" if it can not.", "sample_inputs": ["3\n1 2 3", "3\n3 1 2"], "sample_outputs": ["YES", "NO"], "notes": "NoteIn the second example the array will change even before the tallest stack is chosen for the first time: ravioli from stack of height 3 will slide on the stack of height 1, and the algorithm will output an array {2,\u20092,\u20092}."}, "src_uid": "704d0ae50bccaa8bc49319812ae0be45"}
{"nl": {"description": "Sereja owns a restaurant for n people. The restaurant hall has a coat rack with n hooks. Each restaurant visitor can use a hook to hang his clothes on it. Using the i-th hook costs ai rubles. Only one person can hang clothes on one hook.Tonight Sereja expects m guests in the restaurant. Naturally, each guest wants to hang his clothes on an available hook with minimum price (if there are multiple such hooks, he chooses any of them). However if the moment a guest arrives the rack has no available hooks, Sereja must pay a d ruble fine to the guest. Help Sereja find out the profit in rubles (possibly negative) that he will get tonight. You can assume that before the guests arrive, all hooks on the rack are available, all guests come at different time, nobody besides the m guests is visiting Sereja's restaurant tonight.", "input_spec": "The first line contains two integers n and d (1\u2009\u2264\u2009n,\u2009d\u2009\u2264\u2009100). The next line contains integers a1, a2, ..., an (1\u2009\u2264\u2009ai\u2009\u2264\u2009100). The third line contains integer m (1\u2009\u2264\u2009m\u2009\u2264\u2009100).", "output_spec": "In a single line print a single integer \u2014 the answer to the problem.", "sample_inputs": ["2 1\n2 1\n2", "2 1\n2 1\n10"], "sample_outputs": ["3", "-5"], "notes": "NoteIn the first test both hooks will be used, so Sereja gets 1\u2009+\u20092\u2009=\u20093 rubles.In the second test both hooks will be used but Sereja pays a fine 8 times, so the answer is 3\u2009-\u20098\u2009=\u2009\u2009-\u20095."}, "src_uid": "5c21e2dd658825580522af525142397d"}
{"nl": {"description": "Limak is a little polar bear. Polar bears hate long strings and thus they like to compress them. You should also know that Limak is so young that he knows only first six letters of the English alphabet: 'a', 'b', 'c', 'd', 'e' and 'f'.You are given a set of q possible operations. Limak can perform them in any order, any operation may be applied any number of times. The i-th operation is described by a string ai of length two and a string bi of length one. No two of q possible operations have the same string ai.When Limak has a string s he can perform the i-th operation on s if the first two letters of s match a two-letter string ai. Performing the i-th operation removes first two letters of s and inserts there a string bi. See the notes section for further clarification.You may note that performing an operation decreases the length of a string s exactly by 1. Also, for some sets of operations there may be a string that cannot be compressed any further, because the first two letters don't match any ai.Limak wants to start with a string of length n and perform n\u2009-\u20091 operations to finally get a one-letter string \"a\". In how many ways can he choose the starting string to be able to get \"a\"? Remember that Limak can use only letters he knows.", "input_spec": "The first line contains two integers n and q (2\u2009\u2264\u2009n\u2009\u2264\u20096, 1\u2009\u2264\u2009q\u2009\u2264\u200936)\u00a0\u2014 the length of the initial string and the number of available operations. The next q lines describe the possible operations. The i-th of them contains two strings ai and bi (|ai|\u2009=\u20092,\u2009|bi|\u2009=\u20091). It's guaranteed that ai\u2009\u2260\u2009aj for i\u2009\u2260\u2009j and that all ai and bi consist of only first six lowercase English letters.", "output_spec": "Print the number of strings of length n that Limak will be able to transform to string \"a\" by applying only operations given in the input.", "sample_inputs": ["3 5\nab a\ncc c\nca a\nee c\nff d", "2 8\naf e\ndc d\ncc f\nbc b\nda b\neb a\nbb b\nff c", "6 2\nbb a\nba a"], "sample_outputs": ["4", "1", "0"], "notes": "NoteIn the first sample, we count initial strings of length 3 from which Limak can get a required string \"a\". There are 4 such strings: \"abb\", \"cab\", \"cca\", \"eea\". The first one Limak can compress using operation 1 two times (changing \"ab\" to a single \"a\"). The first operation would change \"abb\" to \"ab\" and the second operation would change \"ab\" to \"a\".Other three strings may be compressed as follows:   \"cab\"  \"ab\"  \"a\"  \"cca\"  \"ca\"  \"a\"  \"eea\"  \"ca\"  \"a\" In the second sample, the only correct initial string is \"eb\" because it can be immediately compressed to \"a\"."}, "src_uid": "c42abec29bfd17de3f43385fa6bea534"}
{"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\u2009\u2264\u2009hh\u2009<\u200924,\u20090\u2009\u2264\u2009mm\u2009<\u200960). 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\u2009\u2264\u2009a\u2009\u2264\u2009104) \u2014 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": "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 $$$k$$$ ($$$1 \\le k \\le 10000$$$) \u2014 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": "Little Lesha loves listening to music via his smartphone. But the smartphone doesn't have much memory, so Lesha listens to his favorite songs in a well-known social network InTalk.Unfortunately, internet is not that fast in the city of Ekaterinozavodsk and the song takes a lot of time to download. But Lesha is quite impatient. The song's duration is T seconds. Lesha downloads the first S seconds of the song and plays it. When the playback reaches the point that has not yet been downloaded, Lesha immediately plays the song from the start (the loaded part of the song stays in his phone, and the download is continued from the same place), and it happens until the song is downloaded completely and Lesha listens to it to the end. For q seconds of real time the Internet allows you to download q\u2009-\u20091 seconds of the track.Tell Lesha, for how many times he will start the song, including the very first start.", "input_spec": "The single line contains three integers T,\u2009S,\u2009q (2\u2009\u2264\u2009q\u2009\u2264\u2009104, 1\u2009\u2264\u2009S\u2009<\u2009T\u2009\u2264\u2009105).", "output_spec": "Print a single integer\u00a0\u2014 the number of times the song will be restarted.", "sample_inputs": ["5 2 2", "5 4 7", "6 2 3"], "sample_outputs": ["2", "1", "1"], "notes": "NoteIn the first test, the song is played twice faster than it is downloaded, which means that during four first seconds Lesha reaches the moment that has not been downloaded, and starts the song again. After another two seconds, the song is downloaded completely, and thus, Lesha starts the song twice.In the second test, the song is almost downloaded, and Lesha will start it only once.In the third sample test the download finishes and Lesha finishes listening at the same moment. Note that song isn't restarted in this case."}, "src_uid": "0d01bf286fb2c7950ce5d5fa59a17dd9"}
{"nl": {"description": "Barney is standing in a bar and starring at a pretty girl. He wants to shoot her with his heart arrow but he needs to know the distance between him and the girl to make his shot accurate.  Barney asked the bar tender Carl about this distance value, but Carl was so busy talking to the customers so he wrote the distance value (it's a real number) on a napkin. The problem is that he wrote it in scientific notation. The scientific notation of some real number x is the notation of form AeB, where A is a real number and B is an integer and x\u2009=\u2009A\u2009\u00d7\u200910B is true. In our case A is between 0 and 9 and B is non-negative.Barney doesn't know anything about scientific notation (as well as anything scientific at all). So he asked you to tell him the distance value in usual decimal representation with minimal number of digits after the decimal point (and no decimal point if it is an integer). See the output format for better understanding.", "input_spec": "The first and only line of input contains a single string of form a.deb where a, d and b are integers and e is usual character 'e' (0\u2009\u2264\u2009a\u2009\u2264\u20099,\u20090\u2009\u2264\u2009d\u2009<\u200910100,\u20090\u2009\u2264\u2009b\u2009\u2264\u2009100)\u00a0\u2014 the scientific notation of the desired distance value. a and b contain no leading zeros and d contains no trailing zeros (but may be equal to 0). Also, b can not be non-zero if a is zero.", "output_spec": "Print the only real number x (the desired distance value) in the only line in its decimal notation.  Thus if x is an integer, print it's integer value without decimal part and decimal point and without leading zeroes.  Otherwise print x in a form of p.q such that p is an integer that have no leading zeroes (but may be equal to zero), and q is an integer that have no trailing zeroes (and may not be equal to zero).", "sample_inputs": ["8.549e2", "8.549e3", "0.33e0"], "sample_outputs": ["854.9", "8549", "0.33"], "notes": null}, "src_uid": "a79358099f08f3ec50c013d47d910eef"}
{"nl": {"description": "Sometimes one has to spell email addresses over the phone. Then one usually pronounces a dot as dot, an at sign as at. As a result, we get something like vasyaatgmaildotcom. Your task is to transform it into a proper email address (vasya@gmail.com). It is known that a proper email address contains only such symbols as . @ and lower-case Latin letters, doesn't start with and doesn't end with a dot. Also, a proper email address doesn't start with and doesn't end with an at sign. Moreover, an email address contains exactly one such symbol as @, yet may contain any number (possible, zero) of dots. You have to carry out a series of replacements so that the length of the result was as short as possible and it was a proper email address. If the lengths are equal, you should print the lexicographically minimal result. Overall, two variants of replacement are possible: dot can be replaced by a dot, at can be replaced by an at. ", "input_spec": "The first line contains the email address description. It is guaranteed that that is a proper email address with all the dots replaced by dot an the at signs replaced by at. The line is not empty and its length does not exceed 100 symbols.", "output_spec": "Print the shortest email address, from which the given line could be made by the described above replacements. If there are several solutions to that problem, print the lexicographically minimal one (the lexicographical comparison of the lines are implemented with an operator < in modern programming languages). In the ASCII table the symbols go in this order: . @ ab...z", "sample_inputs": ["vasyaatgmaildotcom", "dotdotdotatdotdotat", "aatt"], "sample_outputs": ["vasya@gmail.com", "dot..@..at", "a@t"], "notes": null}, "src_uid": "a11c9679d8e2dca51be17d466202df6e"}
{"nl": {"description": "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 $$$n$$$ ($$$2 \\le n \\le 100$$$) \u2014 the number of figures. The second line contains $$$n$$$ integer numbers $$$a_1, a_2, \\dots, a_n$$$ ($$$1 \\le a_i \\le 3$$$, $$$a_i \\ne a_{i + 1}$$$) \u2014 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": "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\u2009\u2264\u2009a\u2009\u2264\u20091000;\u00a02\u2009\u2264\u2009b\u2009\u2264\u20091000).", "output_spec": "Print a single integer \u2014 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 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\u2009=\u20090, then Vasya prefers to walk beside his entrance.    Illustration for n\u2009=\u20096, a\u2009=\u20092, b\u2009=\u2009\u2009-\u20095. 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\u2009\u2264\u2009n\u2009\u2264\u2009100,\u20091\u2009\u2264\u2009a\u2009\u2264\u2009n,\u2009\u2009-\u2009100\u2009\u2264\u2009b\u2009\u2264\u2009100)\u00a0\u2014 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\u2009\u2264\u2009k\u2009\u2264\u2009n)\u00a0\u2014 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": "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\u2009+\u20099).", "input_spec": "The single line contains three space-separated integers n, m and k (2\u2009\u2264\u2009k\u2009\u2264\u2009n\u2009\u2264\u2009109;\u00a00\u2009\u2264\u2009m\u2009\u2264\u2009n).", "output_spec": "Print a single integer \u2014 the remainder from division of Manao's minimum possible score in the quiz by 1000000009 (109\u2009+\u20099).", "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\u00a0mod\u00a01000000009, even though 2000000020\u00a0mod\u00a01000000009 is a smaller number."}, "src_uid": "9cc1aecd70ed54400821c290e2c8018e"}
{"nl": {"description": "Furik loves writing all sorts of problems, especially such that he can't solve himself. You've got one of his problems, the one Furik gave to Rubik. And Rubik asks you to solve it.There is integer n and array a, consisting of ten integers, indexed by numbers from 0 to 9. Your task is to count the number of positive integers with the following properties:  the number's length does not exceed n;  the number doesn't have leading zeroes;  digit i (0\u2009\u2264\u2009i\u2009\u2264\u20099) occurs in the number at least a[i] times. ", "input_spec": "The first line contains integer n (1\u2009\u2264\u2009n\u2009\u2264\u2009100). The next line contains 10 integers a[0], a[1], ..., a[9] (0\u2009\u2264\u2009a[i]\u2009\u2264\u2009100) \u2014 elements of array a. The numbers are separated by spaces.", "output_spec": "On a single line print the remainder of dividing the answer to the problem by 1000000007 (109\u2009+\u20097).", "sample_inputs": ["1\n0 0 0 0 0 0 0 0 0 1", "2\n1 1 0 0 0 0 0 0 0 0", "3\n1 1 0 0 0 0 0 0 0 0"], "sample_outputs": ["1", "1", "36"], "notes": "NoteIn the first sample number 9 meets the requirements.In the second sample number 10 meets the requirements.In the third sample numbers 10, 110, 210, 120, 103 meet the requirements. There are other suitable numbers, 36 in total."}, "src_uid": "c1b5169a5c3b1bd4a2f1df1069ee7755"}
{"nl": {"description": "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\u2019t want to use too many blocks, but they also want to be unique, so no two students\u2019 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\u2009\u2264\u2009n,\u2009m\u2009\u2264\u20091\u2009000\u2009000, n\u2009+\u2009m\u2009>\u20090)\u00a0\u2014 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": "Vasya came up with his own weather forecasting method. He knows the information about the average air temperature for each of the last n days. Assume that the average air temperature for each day is integral.Vasya believes that if the average temperatures over the last n days form an arithmetic progression, where the first term equals to the average temperature on the first day, the second term equals to the average temperature on the second day and so on, then the average temperature of the next (n\u2009+\u20091)-th day will be equal to the next term of the arithmetic progression. Otherwise, according to Vasya's method, the temperature of the (n\u2009+\u20091)-th day will be equal to the temperature of the n-th day.Your task is to help Vasya predict the average temperature for tomorrow, i. e. for the (n\u2009+\u20091)-th day.", "input_spec": "The first line contains a single integer n (2\u2009\u2264\u2009n\u2009\u2264\u2009100) \u2014 the number of days for which the average air temperature is known. The second line contains a sequence of integers t1,\u2009t2,\u2009...,\u2009tn (\u2009-\u20091000\u2009\u2264\u2009ti\u2009\u2264\u20091000)\u00a0\u2014 where ti is the average temperature in the i-th day.", "output_spec": "Print the average air temperature in the (n\u2009+\u20091)-th day, which Vasya predicts according to his method. Note that the absolute value of the predicted temperature can exceed 1000.", "sample_inputs": ["5\n10 5 0 -5 -10", "4\n1 1 1 1", "3\n5 1 -5", "2\n900 1000"], "sample_outputs": ["-15", "1", "-5", "1100"], "notes": "NoteIn the first example the sequence of the average temperatures is an arithmetic progression where the first term is 10 and each following terms decreases by 5. So the predicted average temperature for the sixth day is \u2009-\u200910\u2009-\u20095\u2009=\u2009\u2009-\u200915.In the second example the sequence of the average temperatures is an arithmetic progression where the first term is 1 and each following terms equals to the previous one. So the predicted average temperature in the fifth day is 1.In the third example the average temperatures do not form an arithmetic progression, so the average temperature of the fourth day equals to the temperature of the third day and equals to \u2009-\u20095.In the fourth example the sequence of the average temperatures is an arithmetic progression where the first term is 900 and each the following terms increase by 100. So predicted average temperature in the third day is 1000\u2009+\u2009100\u2009=\u20091100."}, "src_uid": "d04fa4322a1b300bdf4a56f09681b17f"}
{"nl": {"description": "You've got a 5\u2009\u00d7\u20095 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\u2009+\u20091 for some integer i (1\u2009\u2264\u2009i\u2009<\u20095).  Swap two neighboring matrix columns, that is, columns with indexes j and j\u2009+\u20091 for some integer j (1\u2009\u2264\u2009j\u2009<\u20095). 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 \u2014 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": "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\u2009\u2264\u2009r,\u2009g,\u2009b\u2009\u2264\u2009100). It is guaranteed that r\u2009+\u2009g\u2009+\u2009b\u2009>\u20090, it means that the group consists of at least one student. ", "output_spec": "Print a single number \u2014 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": "A frog lives on the axis Ox and needs to reach home which is in the point n. She starts from the point 1. The frog can jump to the right at a distance not more than d. So, after she jumped from the point x she can reach the point x\u2009+\u2009a, where a is an integer from 1 to d.For each point from 1 to n is known if there is a lily flower in it. The frog can jump only in points with a lilies. Guaranteed that there are lilies in the points 1 and n.Determine the minimal number of jumps that the frog needs to reach home which is in the point n from the point 1. Consider that initially the frog is in the point 1. If the frog can not reach home, print -1.", "input_spec": "The first line contains two integers n and d (2\u2009\u2264\u2009n\u2009\u2264\u2009100, 1\u2009\u2264\u2009d\u2009\u2264\u2009n\u2009-\u20091) \u2014 the point, which the frog wants to reach, and the maximal length of the frog jump. The second line contains a string s of length n, consisting of zeros and ones. If a character of the string s equals to zero, then in the corresponding point there is no lily flower. In the other case, in the corresponding point there is a lily flower. Guaranteed that the first and the last characters of the string s equal to one.", "output_spec": "If the frog can not reach the home, print -1. In the other case, print the minimal number of jumps that the frog needs to reach the home which is in the point n from the point 1.", "sample_inputs": ["8 4\n10010101", "4 2\n1001", "8 4\n11100101", "12 3\n101111100101"], "sample_outputs": ["2", "-1", "3", "4"], "notes": "NoteIn the first example the from can reach home in two jumps: the first jump from the point 1 to the point 4 (the length of the jump is three), and the second jump from the point 4 to the point 8 (the length of the jump is four).In the second example the frog can not reach home, because to make it she need to jump on a distance three, but the maximum length of her jump equals to two."}, "src_uid": "c08d2ecdfc66cd07fbbd461b1f069c9e"}
{"nl": {"description": "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,\u20092,\u20093,\u2009...,\u2009k. 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\u2009+\u20097). ", "input_spec": "A single line contains three space-separated integers: n, k and d (1\u2009\u2264\u2009n,\u2009k\u2009\u2264\u2009100; 1\u2009\u2264\u2009d\u2009\u2264\u2009k).", "output_spec": "Print a single integer \u2014 the answer to the problem modulo 1000000007 (109\u2009+\u20097). ", "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": "The king's birthday dinner was attended by $$$k$$$ guests. The dinner was quite a success: every person has eaten several dishes (though the number of dishes was the same for every person) and every dish was served alongside with a new set of kitchen utensils.All types of utensils in the kingdom are numbered from $$$1$$$ to $$$100$$$. It is known that every set of utensils is the same and consist of different types of utensils, although every particular type may appear in the set at most once. For example, a valid set of utensils can be composed of one fork, one spoon and one knife.After the dinner was over and the guests were dismissed, the king wondered what minimum possible number of utensils could be stolen. Unfortunately, the king has forgotten how many dishes have been served for every guest but he knows the list of all the utensils left after the dinner. Your task is to find the minimum possible number of stolen utensils.", "input_spec": "The first line contains two integer numbers $$$n$$$ and $$$k$$$ ($$$1 \\le n \\le 100, 1 \\le k \\le 100$$$) \u00a0\u2014 the number of kitchen utensils remaining after the dinner and the number of guests correspondingly. The next line contains $$$n$$$ integers $$$a_1, a_2, \\ldots, a_n$$$ ($$$1 \\le a_i \\le 100$$$) \u00a0\u2014 the types of the utensils remaining. Equal values stand for identical utensils while different values stand for different utensils.", "output_spec": "Output a single value \u2014 the minimum number of utensils that could be stolen by the guests.", "sample_inputs": ["5 2\n1 2 2 1 3", "10 3\n1 3 3 1 3 5 5 5 5 100"], "sample_outputs": ["1", "14"], "notes": "NoteIn the first example it is clear that at least one utensil of type $$$3$$$ has been stolen, since there are two guests and only one such utensil. But it is also possible that every person received only one dish and there were only six utensils in total, when every person got a set $$$(1, 2, 3)$$$ of utensils. Therefore, the answer is $$$1$$$.One can show that in the second example at least $$$2$$$ dishes should have been served for every guest, so the number of utensils should be at least $$$24$$$: every set contains $$$4$$$ utensils and every one of the $$$3$$$ guests gets two such sets. Therefore, at least $$$14$$$ objects have been stolen. Please note that utensils of some types (for example, of types $$$2$$$ and $$$4$$$ in this example) may be not present in the set served for dishes."}, "src_uid": "c03ff0bc6a8c4ce5372194e8ea18527f"}
{"nl": {"description": "The Little Elephant loves numbers. He has a positive integer x. The Little Elephant wants to find the number of positive integers d, such that d is the divisor of x, and x and d have at least one common (the same) digit in their decimal representations. Help the Little Elephant to find the described number.", "input_spec": "A single line contains a single integer x (1\u2009\u2264\u2009x\u2009\u2264\u2009109).", "output_spec": "In a single line print an integer \u2014 the answer to the problem.", "sample_inputs": ["1", "10"], "sample_outputs": ["1", "2"], "notes": null}, "src_uid": "ada94770281765f54ab264b4a1ef766e"}
{"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\u00a0\u2014 201510\u2009=\u2009111110111112. 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\u2009\u2264\u2009a\u2009\u2264\u2009b\u2009\u2264\u20091018)\u00a0\u2014 the first year and the last year in Limak's interval respectively.", "output_spec": "Print one integer\u00a0\u2013 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\u2009=\u20091012, 610\u2009=\u20091102, 710\u2009=\u20091112, 810\u2009=\u200910002, 910\u2009=\u200910012 and 1010\u2009=\u200910102. Two of them (1012 and 1102) have the described property."}, "src_uid": "581f61b1f50313bf4c75833cefd4d022"}
{"nl": {"description": "A simple recommendation system would recommend a user things liked by a certain number of their friends. In this problem you will implement part of such a system.You are given user's friends' opinions about a list of items. You are also given a threshold T \u2014 the minimal number of \"likes\" necessary for an item to be recommended to the user.Output the number of items in the list liked by at least T of user's friends.", "input_spec": "The first line of the input will contain three space-separated integers: the number of friends F (1\u2009\u2264\u2009F\u2009\u2264\u200910), the number of items I (1\u2009\u2264\u2009I\u2009\u2264\u200910) and the threshold T (1\u2009\u2264\u2009T\u2009\u2264\u2009F). The following F lines of input contain user's friends' opinions. j-th character of i-th line is 'Y' if i-th friend likes j-th item, and 'N' otherwise.", "output_spec": "Output an integer \u2014 the number of items liked by at least T of user's friends.", "sample_inputs": ["3 3 2\nYYY\nNNN\nYNY", "4 4 1\nNNNY\nNNYN\nNYNN\nYNNN"], "sample_outputs": ["2", "4"], "notes": null}, "src_uid": "4c978130187e8ae6ca013d3f781b064e"}
{"nl": {"description": "Kitahara Haruki has bought n apples for Touma Kazusa and Ogiso Setsuna. Now he wants to divide all the apples between the friends.Each apple weights 100 grams or 200 grams. Of course Kitahara Haruki doesn't want to offend any of his friend. Therefore the total weight of the apples given to Touma Kazusa must be equal to the total weight of the apples given to Ogiso Setsuna.But unfortunately Kitahara Haruki doesn't have a knife right now, so he cannot split any apple into some parts. Please, tell him: is it possible to divide all the apples in a fair way between his friends?", "input_spec": "The first line contains an integer n (1\u2009\u2264\u2009n\u2009\u2264\u2009100) \u2014 the number of apples. The second line contains n integers w1,\u2009w2,\u2009...,\u2009wn (wi\u2009=\u2009100 or wi\u2009=\u2009200), where wi is the weight of the i-th apple.", "output_spec": "In a single line print \"YES\" (without the quotes) if it is possible to divide all the apples between his friends. Otherwise print \"NO\" (without the quotes).", "sample_inputs": ["3\n100 200 100", "4\n100 100 100 200"], "sample_outputs": ["YES", "NO"], "notes": "NoteIn the first test sample Kitahara Haruki can give the first and the last apple to Ogiso Setsuna and the middle apple to Touma Kazusa."}, "src_uid": "9679acef82356004e47b1118f8fc836a"}
{"nl": {"description": "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\u2009\u2264\u2009a\u2009\u2264\u2009n.  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\u2009\u2264\u2009n\u2009\u2264\u2009109), 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\u2009=\u20092 and subtract it from n. It's Ehab's turn and n\u2009=\u20090. There is no positive odd integer less than or equal to 0 so Mahmoud wins."}, "src_uid": "5e74750f44142624e6da41d4b35beb9a"}
{"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 $$$n$$$ ($$$2 \\le n \\le 100$$$)\u00a0\u2014 the length of the array $$$a$$$. The second line contains $$$n$$$ integers $$$a_1$$$, $$$a_2$$$, $$$\\ldots$$$, $$$a_{n}$$$ ($$$1 \\le a_i \\le 2000$$$)\u00a0\u2014 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": "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\u2009\u2264\u2009n\u2009\u2264\u2009109).", "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": "Little Artem got n stones on his birthday and now wants to give some of them to Masha. He knows that Masha cares more about the fact of receiving the present, rather than the value of that present, so he wants to give her stones as many times as possible. However, Masha remembers the last present she received, so Artem can't give her the same number of stones twice in a row. For example, he can give her 3 stones, then 1 stone, then again 3 stones, but he can't give her 3 stones and then again 3 stones right after that.How many times can Artem give presents to Masha?", "input_spec": "The only line of the input contains a single integer n (1\u2009\u2264\u2009n\u2009\u2264\u2009109)\u00a0\u2014 number of stones Artem received on his birthday.", "output_spec": "Print the maximum possible number of times Artem can give presents to Masha.", "sample_inputs": ["1", "2", "3", "4"], "sample_outputs": ["1", "1", "2", "3"], "notes": "NoteIn the first sample, Artem can only give 1 stone to Masha.In the second sample, Atrem can give Masha 1 or 2 stones, though he can't give her 1 stone two times.In the third sample, Atrem can first give Masha 2 stones, a then 1 more stone.In the fourth sample, Atrem can first give Masha 1 stone, then 2 stones, and finally 1 stone again."}, "src_uid": "a993069e35b35ae158d35d6fe166aaef"}
{"nl": {"description": "Pasha has a positive integer a without leading zeroes. Today he decided that the number is too small and he should make it larger. Unfortunately, the only operation Pasha can do is to swap two adjacent decimal digits of the integer.Help Pasha count the maximum number he can get if he has the time to make at most k swaps.", "input_spec": "The single line contains two integers a and k (1\u2009\u2264\u2009a\u2009\u2264\u20091018;\u00a00\u2009\u2264\u2009k\u2009\u2264\u2009100).", "output_spec": "Print the maximum number that Pasha can get if he makes at most k swaps.", "sample_inputs": ["1990 1", "300 0", "1034 2", "9090000078001234 6"], "sample_outputs": ["9190", "300", "3104", "9907000008001234"], "notes": null}, "src_uid": "e56f6c343167745821f0b18dcf0d0cde"}
{"nl": {"description": "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 $$$D$$$ ($$$1 \\leq A \\leq B \\leq C \\leq D \\leq 5 \\cdot 10^5$$$)\u00a0\u2014 Yuri's favourite numbers.", "output_spec": "Print the number of non-degenerate triangles with integer sides $$$x$$$, $$$y$$$, and $$$z$$$ such that the inequality $$$A \\leq x \\leq B \\leq y \\leq C \\leq z \\leq D$$$ holds.", "sample_inputs": ["1 2 3 4", "1 2 2 5", "500000 500000 500000 500000"], "sample_outputs": ["4", "3", "1"], "notes": "NoteIn the first example Yuri can make up triangles with sides $$$(1, 3, 3)$$$, $$$(2, 2, 3)$$$, $$$(2, 3, 3)$$$ and $$$(2, 3, 4)$$$.In the second example Yuri can make up triangles with sides $$$(1, 2, 2)$$$, $$$(2, 2, 2)$$$ and $$$(2, 2, 3)$$$.In the third example Yuri can make up only one equilateral triangle with sides equal to $$$5 \\cdot 10^5$$$."}, "src_uid": "4f92791b9ec658829f667fcea1faee01"}
{"nl": {"description": "Let\u2019s define a grid to be a set of tiles with 2 rows and 13 columns. Each tile has an English letter written in it. The letters don't have to be unique: there might be two or more tiles with the same letter written on them. Here is an example of a grid: ABCDEFGHIJKLMNOPQRSTUVWXYZ We say that two tiles are adjacent if they share a side or a corner. In the example grid above, the tile with the letter 'A' is adjacent only to the tiles with letters 'B', 'N', and 'O'. A tile is not adjacent to itself.A sequence of tiles is called a path if each tile in the sequence is adjacent to the tile which follows it (except for the last tile in the sequence, which of course has no successor). In this example, \"ABC\" is a path, and so is \"KXWIHIJK\". \"MAB\" is not a path because 'M' is not adjacent to 'A'. A single tile can be used more than once by a path (though the tile cannot occupy two consecutive places in the path because no tile is adjacent to itself).You\u2019re given a string s which consists of 27 upper-case English letters. Each English letter occurs at least once in s. Find a grid that contains a path whose tiles, viewed in the order that the path visits them, form the string s. If there\u2019s no solution, print \"Impossible\" (without the quotes).", "input_spec": "The only line of the input contains the string s, consisting of 27 upper-case English letters. Each English letter occurs at least once in s.", "output_spec": "Output two lines, each consisting of 13 upper-case English characters, representing the rows of the grid. If there are multiple solutions, print any of them. If there is no solution print \"Impossible\".", "sample_inputs": ["ABCDEFGHIJKLMNOPQRSGTUVWXYZ", "BUVTYZFQSNRIWOXXGJLKACPEMDH"], "sample_outputs": ["YXWVUTGHIJKLM\nZABCDEFSRQPON", "Impossible"], "notes": null}, "src_uid": "56c5ea443dec7a732802b16aed5b934d"}
{"nl": {"description": "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": "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)\u00a0\u2014 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": "\u0420\u0430\u0441\u0441\u043c\u043e\u0442\u0440\u0438\u043c \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u0439 \u043a\u043e\u0434 \u0441\u043e\u0440\u0442\u0438\u0440\u043e\u0432\u043a\u0438 \u0441\u043b\u0438\u044f\u043d\u0438\u0435\u043c \u043d\u0430 \u044f\u0437\u044b\u043a\u0435 Python: def sort(a):  n = len(a)  b = [0 for i in range(n)]  log = []  def mergeSort(l, r):    if r - l <= 1:      return    m = (l + r) >> 1    mergeSort(l, m)    mergeSort(m, r)    i, j, k = l, m, l    while i < m and j < r:      if a[i] < a[j]:        log.append('0')        b[k] = a[i]        i += 1      else:        log.append('1')        b[k] = a[j]        j += 1      k += 1    while i < m:      b[k] = a[i]      i += 1      k += 1    while j < r:      b[k] = a[j]      j += 1      k += 1    for p in range(l, r):      a[p] = b[p]  mergeSort(0, n)  return \"\".join(log)\u041a\u0430\u043a \u043c\u043e\u0436\u043d\u043e \u0437\u0430\u043c\u0435\u0442\u0438\u0442\u044c, \u044d\u0442\u043e\u0442 \u043a\u043e\u0434 \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u0435\u0442 \u043b\u043e\u0433\u0438\u0440\u043e\u0432\u0430\u043d\u0438\u0435\u00a0\u2014 \u0432\u0430\u0436\u043d\u0435\u0439\u0448\u0438\u0439 \u0438\u043d\u0441\u0442\u0440\u0443\u043c\u0435\u043d\u0442 \u0440\u0430\u0437\u0440\u0430\u0431\u043e\u0442\u043a\u0438.\u0421\u0442\u0430\u0440\u0448\u0438\u0439 \u0440\u0430\u0437\u0440\u0430\u0431\u043e\u0442\u0447\u0438\u043a \u0412\u041a\u043e\u043d\u0442\u0430\u043a\u0442\u0435 \u0412\u0430\u0441\u044f \u0441\u0433\u0435\u043d\u0435\u0440\u0438\u0440\u043e\u0432\u0430\u043b \u043f\u0435\u0440\u0435\u0441\u0442\u0430\u043d\u043e\u0432\u043a\u0443 $$$a$$$ (\u043c\u0430\u0441\u0441\u0438\u0432 \u0438\u0437 $$$n$$$ \u0440\u0430\u0437\u043b\u0438\u0447\u043d\u044b\u0445 \u0446\u0435\u043b\u044b\u0445 \u0447\u0438\u0441\u0435\u043b \u043e\u0442 $$$1$$$ \u0434\u043e $$$n$$$), \u0434\u0430\u043b \u0435\u0451 \u043d\u0430 \u0432\u0445\u043e\u0434 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 sort \u0438 \u043f\u043e\u043b\u0443\u0447\u0438\u043b \u043d\u0430 \u0432\u044b\u0445\u043e\u0434\u0435 \u0441\u0442\u0440\u043e\u043a\u0443 $$$s$$$. \u041d\u0430 \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u0439 \u0434\u0435\u043d\u044c \u0441\u0442\u0440\u043e\u043a\u0443 $$$s$$$ \u0412\u0430\u0441\u044f \u043d\u0430\u0448\u0451\u043b, \u0430 \u043f\u0435\u0440\u0435\u0441\u0442\u0430\u043d\u043e\u0432\u043a\u0430 $$$a$$$ \u043f\u043e\u0442\u0435\u0440\u044f\u043b\u0430\u0441\u044c. \u0412\u0430\u0441\u044f \u0445\u043e\u0447\u0435\u0442 \u0432\u043e\u0441\u0441\u0442\u0430\u043d\u043e\u0432\u0438\u0442\u044c \u043b\u044e\u0431\u0443\u044e \u043f\u0435\u0440\u0435\u0441\u0442\u0430\u043d\u043e\u0432\u043a\u0443 $$$a$$$ \u0442\u0430\u043a\u0443\u044e, \u0447\u0442\u043e \u0432\u044b\u0437\u043e\u0432 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 sort \u043e\u0442 \u043d\u0435\u0451 \u0434\u0430\u0441\u0442 \u0442\u0443 \u0436\u0435 \u0441\u0442\u0440\u043e\u043a\u0443 $$$s$$$. \u041f\u043e\u043c\u043e\u0433\u0438\u0442\u0435 \u0435\u043c\u0443!", "input_spec": "\u0412\u0432\u043e\u0434 \u0441\u043e\u0434\u0435\u0440\u0436\u0438\u0442 \u043d\u0435\u043f\u0443\u0441\u0442\u0443\u044e \u0441\u0442\u0440\u043e\u043a\u0443 $$$s$$$, \u0441\u043e\u0441\u0442\u043e\u044f\u0449\u0443\u044e \u0438\u0437 \u0441\u0438\u043c\u0432\u043e\u043b\u043e\u0432 0 \u0438 1.  \u0412 \u044d\u0442\u043e\u0439 \u0432\u0435\u0440\u0441\u0438\u0438 \u0437\u0430\u0434\u0430\u0447\u0438 \u0434\u043b\u044f \u043b\u044e\u0431\u043e\u0433\u043e \u0442\u0435\u0441\u0442\u0430 \u0441\u0443\u0449\u0435\u0441\u0442\u0432\u0443\u0435\u0442 \u043f\u0435\u0440\u0435\u0441\u0442\u0430\u043d\u043e\u0432\u043a\u0430 \u0434\u043b\u0438\u043d\u044b $$$16$$$, \u0443\u0434\u043e\u0432\u043b\u0435\u0442\u0432\u043e\u0440\u044f\u044e\u0449\u0430\u044f \u0443\u0441\u043b\u043e\u0432\u0438\u044e. \u0422\u0435\u043c \u043d\u0435 \u043c\u0435\u043d\u0435\u0435, \u0432\u0430\u0448 \u043e\u0442\u0432\u0435\u0442 \u043c\u043e\u0436\u0435\u0442 \u0438\u043c\u0435\u0442\u044c \u043b\u044e\u0431\u0443\u044e \u0434\u043b\u0438\u043d\u0443, \u0432 \u0442\u043e\u043c \u0447\u0438\u0441\u043b\u0435 \u043e\u0442\u043b\u0438\u0447\u043d\u0443\u044e \u043e\u0442 $$$16$$$.", "output_spec": "\u0412 \u043f\u0435\u0440\u0432\u043e\u0439 \u0441\u0442\u0440\u043e\u043a\u0435 \u0432\u044b\u0432\u0435\u0434\u0438\u0442\u0435 \u0446\u0435\u043b\u043e\u0435 \u0447\u0438\u0441\u043b\u043e $$$n$$$\u00a0\u2014 \u0434\u043b\u0438\u043d\u0443 \u043f\u0435\u0440\u0435\u0441\u0442\u0430\u043d\u043e\u0432\u043a\u0438. \u0412\u043e \u0432\u0442\u043e\u0440\u043e\u0439 \u0441\u0442\u0440\u043e\u043a\u0435 \u0432\u044b\u0432\u0435\u0434\u0438\u0442\u0435 $$$n$$$ \u0440\u0430\u0437\u043b\u0438\u0447\u043d\u044b\u0445 \u0446\u0435\u043b\u044b\u0445 \u0447\u0438\u0441\u0435\u043b $$$a_0, a_1, \\ldots, a_{n-1}$$$ ($$$1 \\le a_i \\le n$$$)\u00a0\u2014 \u044d\u043b\u0435\u043c\u0435\u043d\u0442\u044b \u043f\u0435\u0440\u0435\u0441\u0442\u0430\u043d\u043e\u0432\u043a\u0438. \u0415\u0441\u043b\u0438 \u0441\u0443\u0449\u0435\u0441\u0442\u0432\u0443\u0435\u0442 \u043d\u0435\u0441\u043a\u043e\u043b\u044c\u043a\u043e \u0432\u0430\u0440\u0438\u0430\u043d\u0442\u043e\u0432 \u043e\u0442\u0432\u0435\u0442\u0430, \u0432\u044b\u0432\u0435\u0434\u0438\u0442\u0435 \u043b\u044e\u0431\u043e\u0439 \u0438\u0437 \u043d\u0438\u0445.", "sample_inputs": ["00000000000000000000000000000000", "11111111111111111111111111111111", "101011010001100100011011001111011000011110010"], "sample_outputs": ["16\n1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16", "16\n16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1", "16\n13 6 1 7 12 5 4 15 14 16 10 11 3 8 9 2"], "notes": null}, "src_uid": "b2ee84d23d73947fa84faaaebfde85c8"}
{"nl": {"description": "Valera the horse lives on a plane. The Cartesian coordinate system is defined on this plane. Also an infinite spiral is painted on the plane. The spiral consists of segments: [(0,\u20090),\u2009(1,\u20090)], [(1,\u20090),\u2009(1,\u20091)], [(1,\u20091),\u2009(\u2009-\u20091,\u20091)], [(\u2009-\u20091,\u20091),\u2009(\u2009-\u20091,\u2009\u2009-\u20091)], [(\u2009-\u20091,\u2009\u2009-\u20091),\u2009(2,\u2009\u2009-\u20091)], [(2,\u2009\u2009-\u20091),\u2009(2,\u20092)] and so on. Thus, this infinite spiral passes through each integer point of the plane.Valera the horse lives on the plane at coordinates (0,\u20090). He wants to walk along the spiral to point (x,\u2009y). Valera the horse has four legs, so he finds turning very difficult. Count how many times he will have to turn if he goes along a spiral from point (0,\u20090) to point (x,\u2009y).", "input_spec": "The first line contains two space-separated integers x and y (|x|,\u2009|y|\u2009\u2264\u2009100).", "output_spec": "Print a single integer, showing how many times Valera has to turn.", "sample_inputs": ["0 0", "1 0", "0 1", "-1 -1"], "sample_outputs": ["0", "0", "2", "3"], "notes": null}, "src_uid": "2fb2a129e01efc03cfc3ad91dac88382"}
{"nl": {"description": "The girl Taylor has a beautiful calendar for the year y. In the calendar all days are given with their days of week: Monday, Tuesday, Wednesday, Thursday, Friday, Saturday and Sunday.The calendar is so beautiful that she wants to know what is the next year after y when the calendar will be exactly the same. Help Taylor to find that year.Note that leap years has 366 days. The year is leap if it is divisible by 400 or it is divisible by 4, but not by 100 (https://en.wikipedia.org/wiki/Leap_year).", "input_spec": "The only line contains integer y (1000\u2009\u2264\u2009y\u2009<\u2009100'000) \u2014 the year of the calendar.", "output_spec": "Print the only integer y' \u2014 the next year after y when the calendar will be the same. Note that you should find the first year after y with the same calendar.", "sample_inputs": ["2016", "2000", "50501"], "sample_outputs": ["2044", "2028", "50507"], "notes": "NoteToday is Monday, the 13th of June, 2016."}, "src_uid": "565bbd09f79eb7bfe2f2da46647af0f2"}
{"nl": {"description": "One day Vasya was sitting on a not so interesting Maths lesson and making an origami from a rectangular a mm \u2009\u00d7\u2009 b mm sheet of paper (a\u2009>\u2009b). 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\u2009-\u2009b) mm \u2009\u00d7\u2009 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\u2009\u2264\u2009b\u2009<\u2009a\u2009\u2264\u20091012) \u2014 the sizes of the original sheet of paper.", "output_spec": "Print a single integer \u2014 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": "Dr. Evil kidnapped Mahmoud and Ehab in the evil land because of their performance in the Evil Olympiad in Informatics (EOI). He decided to give them some problems to let them go.Dr. Evil is interested in sets, He has a set of n integers. Dr. Evil calls a set of integers evil if the MEX of it is exactly x. the MEX of a set of integers is the minimum non-negative integer that doesn't exist in it. For example, the MEX of the set {0,\u20092,\u20094} is 1 and the MEX of the set {1,\u20092,\u20093} is 0 .Dr. Evil is going to make his set evil. To do this he can perform some operations. During each operation he can add some non-negative integer to his set or erase some element from it. What is the minimal number of operations Dr. Evil has to perform to make his set evil?", "input_spec": "The first line contains two integers n and x (1\u2009\u2264\u2009n\u2009\u2264\u2009100, 0\u2009\u2264\u2009x\u2009\u2264\u2009100)\u00a0\u2014 the size of the set Dr. Evil owns, and the desired MEX. The second line contains n distinct non-negative integers not exceeding 100 that represent the set.", "output_spec": "The only line should contain one integer\u00a0\u2014 the minimal number of operations Dr. Evil should perform.", "sample_inputs": ["5 3\n0 4 5 6 7", "1 0\n0", "5 0\n1 2 3 4 5"], "sample_outputs": ["2", "1", "0"], "notes": "NoteFor the first test case Dr. Evil should add 1 and 2 to the set performing 2 operations.For the second test case Dr. Evil should erase 0 from the set. After that, the set becomes empty, so the MEX of it is 0.In the third test case the set is already evil."}, "src_uid": "21f579ba807face432a7664091581cd8"}
{"nl": {"description": "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\u2009\u2265\u20092) 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\u2009=\u20096 then Funt has to pay 3 burles, while for n\u2009=\u200925 he needs to pay 5 and if n\u2009=\u20092 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\u2009+\u2009n2\u2009+\u2009...\u2009+\u2009nk\u2009=\u2009n (here k is arbitrary, even k\u2009=\u20091 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\u2009\u2265\u20092 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\u2009\u2264\u2009n\u2009\u2264\u20092\u00b7109)\u00a0\u2014 the total year income of mr. Funt.", "output_spec": "Print one integer\u00a0\u2014 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": "Gaius Julius Caesar, a famous general, loved to line up his soldiers. Overall the army had n1 footmen and n2 horsemen. Caesar thought that an arrangement is not beautiful if somewhere in the line there are strictly more that k1 footmen standing successively one after another, or there are strictly more than k2 horsemen standing successively one after another. Find the number of beautiful arrangements of the soldiers. Note that all n1\u2009+\u2009n2 warriors should be present at each arrangement. All footmen are considered indistinguishable among themselves. Similarly, all horsemen are considered indistinguishable among themselves.", "input_spec": "The only line contains four space-separated integers n1, n2, k1, k2 (1\u2009\u2264\u2009n1,\u2009n2\u2009\u2264\u2009100,\u20091\u2009\u2264\u2009k1,\u2009k2\u2009\u2264\u200910) which represent how many footmen and horsemen there are and the largest acceptable number of footmen and horsemen standing in succession, correspondingly.", "output_spec": "Print the number of beautiful arrangements of the army modulo 100000000 (108). That is, print the number of such ways to line up the soldiers, that no more than k1 footmen stand successively, and no more than k2 horsemen stand successively.", "sample_inputs": ["2 1 1 10", "2 3 1 2", "2 4 1 1"], "sample_outputs": ["1", "5", "0"], "notes": "NoteLet's mark a footman as 1, and a horseman as 2.In the first sample the only beautiful line-up is: 121In the second sample 5 beautiful line-ups exist: 12122, 12212, 21212, 21221, 22121"}, "src_uid": "63aabef26fe008e4c6fc9336eb038289"}
{"nl": {"description": "In one very old text file there was written Great Wisdom. This Wisdom was so Great that nobody could decipher it, even Phong \u2014 the oldest among the inhabitants of Mainframe. But still he managed to get some information from there. For example, he managed to learn that User launches games for pleasure \u2014 and then terrible Game Cubes fall down on the city, bringing death to those modules, who cannot win the game...For sure, as guard Bob appeared in Mainframe many modules stopped fearing Game Cubes. Because Bob (as he is alive yet) has never been defeated by User, and he always meddles with Game Cubes, because he is programmed to this.However, unpleasant situations can happen, when a Game Cube falls down on Lost Angles. Because there lives a nasty virus \u2014 Hexadecimal, who is... mmm... very strange. And she likes to play very much. So, willy-nilly, Bob has to play with her first, and then with User.This time Hexadecimal invented the following entertainment: Bob has to leap over binary search trees with n nodes. We should remind you that a binary search tree is a binary tree, each node has a distinct key, for each node the following is true: the left sub-tree of a node contains only nodes with keys less than the node's key, the right sub-tree of a node contains only nodes with keys greater than the node's key. All the keys are different positive integer numbers from 1 to n. Each node of such a tree can have up to two children, or have no children at all (in the case when a node is a leaf).In Hexadecimal's game all the trees are different, but the height of each is not lower than h. In this problem \u00abheight\u00bb stands for the maximum amount of nodes on the way from the root to the remotest leaf, the root node and the leaf itself included. When Bob leaps over a tree, it disappears. Bob gets the access to a Cube, when there are no trees left. He knows how many trees he will have to leap over in the worst case. And you?", "input_spec": "The input data contains two space-separated positive integer numbers n and h (n\u2009\u2264\u200935, h\u2009\u2264\u2009n).", "output_spec": "Output one number \u2014 the answer to the problem. It is guaranteed that it does not exceed 9\u00b71018.", "sample_inputs": ["3 2", "3 3"], "sample_outputs": ["5", "4"], "notes": null}, "src_uid": "faf12a603d0c27f8be6bf6b02531a931"}
{"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\u2009\u2264\u2009n\u2009\u2264\u2009109) \u2014 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\u2009\u2264\u2009109 the answer doesn't exceed 2\u00b7109.", "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\u2009=\u200950."}, "src_uid": "c20744c44269ae0779c5f549afd2e3f2"}
{"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\u2009\u2264\u2009n\u2009\u2264\u2009100, 0\u2009\u2264\u2009k\u2009\u2264\u2009n) \u2014 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 \u2014 the episode number 3 and the episode number 4. The answer is \"YES\", because k\u2009=\u20092.In the second test k\u2009=\u20091, 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 \u2014 number 5 and number 6), even if he has watched the episodes from the first to the fourth, inclusive."}, "src_uid": "5bd578d3da5837c259b222336a194d12"}
{"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": "Bessie the cow and her best friend Elsie each received a sliding puzzle on Pi Day. Their puzzles consist of a 2\u2009\u00d7\u20092 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\u2009\u00d7\u20092 grid describing the initial configuration of Bessie's puzzle. The next two lines contain a 2\u2009\u00d7\u20092 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": "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 $$$n$$$ ($$$1 \\le n \\le 100$$$) \u2014 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": "Polycarp is crazy about round numbers. He especially likes the numbers divisible by 10k.In the given number of n Polycarp wants to remove the least number of digits to get a number that is divisible by 10k. For example, if k\u2009=\u20093, in the number 30020 it is enough to delete a single digit (2). In this case, the result is 3000 that is divisible by 103\u2009=\u20091000.Write a program that prints the minimum number of digits to be deleted from the given integer number n, so that the result is divisible by 10k. The result should not start with the unnecessary leading zero (i.e., zero can start only the number 0, which is required to be written as exactly one digit).It is guaranteed that the answer exists.", "input_spec": "The only line of the input contains two integer numbers n and k (0\u2009\u2264\u2009n\u2009\u2264\u20092\u2009000\u2009000\u2009000, 1\u2009\u2264\u2009k\u2009\u2264\u20099). It is guaranteed that the answer exists. All numbers in the input are written in traditional notation of integers, that is, without any extra leading zeros.", "output_spec": "Print w \u2014 the required minimal number of digits to erase. After removing the appropriate w digits from the number n, the result should have a value that is divisible by 10k. The result can start with digit 0 in the single case (the result is zero and written by exactly the only digit 0).", "sample_inputs": ["30020 3", "100 9", "10203049 2"], "sample_outputs": ["1", "2", "3"], "notes": "NoteIn the example 2 you can remove two digits: 1 and any 0. The result is number 0 which is divisible by any number."}, "src_uid": "7a8890417aa48c2b93b559ca118853f9"}
{"nl": {"description": "The weather is fine today and hence it's high time to climb the nearby pine and enjoy the landscape.The pine's trunk includes several branches, located one above another and numbered from 2 to y. Some of them (more precise, from 2 to p) are occupied by tiny vile grasshoppers which you're at war with. These grasshoppers are known for their awesome jumping skills: the grasshopper at branch x can jump to branches .Keeping this in mind, you wisely decided to choose such a branch that none of the grasshoppers could interrupt you. At the same time you wanna settle as high as possible since the view from up there is simply breathtaking.In other words, your goal is to find the highest branch that cannot be reached by any of the grasshoppers or report that it's impossible.", "input_spec": "The only line contains two integers p and y (2\u2009\u2264\u2009p\u2009\u2264\u2009y\u2009\u2264\u2009109).", "output_spec": "Output the number of the highest suitable branch. If there are none, print -1 instead.", "sample_inputs": ["3 6", "3 4"], "sample_outputs": ["5", "-1"], "notes": "NoteIn the first sample case grasshopper from branch 2 reaches branches 2, 4 and 6 while branch 3 is initially settled by another grasshopper. Therefore the answer is 5.It immediately follows that there are no valid branches in second sample case."}, "src_uid": "b533203f488fa4caf105f3f46dd5844d"}
{"nl": {"description": "You are given a sequence $$$a_1, a_2, \\dots, a_n$$$ consisting of $$$n$$$ integers.You can choose any non-negative integer $$$D$$$ (i.e. $$$D \\ge 0$$$), and for each $$$a_i$$$ you can:  add $$$D$$$ (only once), i.\u2009e. perform $$$a_i := a_i + D$$$, or  subtract $$$D$$$ (only once), i.\u2009e. perform $$$a_i := a_i - D$$$, or  leave the value of $$$a_i$$$ unchanged. It is possible that after an operation the value $$$a_i$$$ becomes negative.Your goal is to choose such minimum non-negative integer $$$D$$$ and perform changes in such a way, that all $$$a_i$$$ are equal (i.e. $$$a_1=a_2=\\dots=a_n$$$).Print the required $$$D$$$ or, if it is impossible to choose such value $$$D$$$, print -1.For example, for array $$$[2, 8]$$$ the value $$$D=3$$$ is minimum possible because you can obtain the array $$$[5, 5]$$$ if you will add $$$D$$$ to $$$2$$$ and subtract $$$D$$$ from $$$8$$$. And for array $$$[1, 4, 7, 7]$$$ the value $$$D=3$$$ is also minimum possible. You can add it to $$$1$$$ and subtract it from $$$7$$$ and obtain the array $$$[4, 4, 4, 4]$$$.", "input_spec": "The first line of the input contains one integer $$$n$$$ ($$$1 \\le n \\le 100$$$) \u2014 the number of elements in $$$a$$$. The second line of the input contains $$$n$$$ integers $$$a_1, a_2, \\dots, a_n$$$ ($$$1 \\le a_i \\le 100$$$) \u2014 the sequence $$$a$$$.", "output_spec": "Print one integer \u2014 the minimum non-negative integer value $$$D$$$ such that if you add this value to some $$$a_i$$$, subtract this value from some $$$a_i$$$ and leave some $$$a_i$$$ without changes, all obtained values become equal. If it is impossible to choose such value $$$D$$$, print -1.", "sample_inputs": ["6\n1 4 4 7 4 1", "5\n2 2 5 2 5", "4\n1 3 3 7", "2\n2 8"], "sample_outputs": ["3", "3", "-1", "3"], "notes": null}, "src_uid": "d486a88939c132848a7efdf257b9b066"}
{"nl": {"description": "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\u2009-\u20091 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\u2009+\u20091.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\u2009\u2264\u2009n\u2009\u2264\u2009100\u2009000).", "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": "\u00abOne dragon. Two dragon. Three dragon\u00bb, \u2014 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,\u2009l,\u2009m,\u2009n and d, each number in a separate line (1\u2009\u2264\u2009k,\u2009l,\u2009m,\u2009n\u2009\u2264\u200910, 1\u2009\u2264\u2009d\u2009\u2264\u2009105).", "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": "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": "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:\u20092:\u20094. 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\u00a0\u2014 lemons, apples and pears\u00a0\u2014 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\u2009\u2264\u2009a\u2009\u2264\u20091000)\u00a0\u2014 the number of lemons Nikolay has.  The second line contains the positive integer b (1\u2009\u2264\u2009b\u2009\u2264\u20091000)\u00a0\u2014 the number of apples Nikolay has.  The third line contains the positive integer c (1\u2009\u2264\u2009c\u2009\u2264\u20091000)\u00a0\u2014 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\u2009+\u20092\u2009+\u20094\u2009=\u20097.In the second example Nikolay can use 3 lemons, 6 apples and 12 pears, so the answer is 3\u2009+\u20096\u2009+\u200912\u2009=\u200921.In the third example Nikolay don't have enough pears to cook any compote, so the answer is 0. "}, "src_uid": "82a4a60eac90765fb62f2a77d2305c01"}
{"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 $$$t$$$ ($$$1 \\le t \\le 100$$$) \u2014 the number of queries. Each of the next $$$t$$$ lines contains one integer each. The $$$i$$$-th line contains one integer $$$x_i$$$ ($$$2 \\le x_i \\le 100$$$) \u2014 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 industrial factory is reforming working plan. The director suggested to set a mythical detail production norm. If at the beginning of the day there were x details in the factory storage, then by the end of the day the factory has to produce  (remainder after dividing x by m) more details. Unfortunately, no customer has ever bought any mythical detail, so all the details produced stay on the factory. The board of directors are worried that the production by the given plan may eventually stop (that means that there will be \u0430 moment when the current number of details on the factory is divisible by m). Given the number of details a on the first day and number m check if the production stops at some moment.", "input_spec": "The first line contains two integers a and m (1\u2009\u2264\u2009a,\u2009m\u2009\u2264\u2009105).", "output_spec": "Print \"Yes\" (without quotes) if the production will eventually stop, otherwise print \"No\".", "sample_inputs": ["1 5", "3 6"], "sample_outputs": ["No", "Yes"], "notes": null}, "src_uid": "f726133018e2149ec57e113860ec498a"}
{"nl": {"description": "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\u2009\u2264\u2009n\u2009\u2264\u2009200; 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 \u2014 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": "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\u2009\u2264\u2009n\u2009\u2264\u2009100)\u00a0\u2014 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": "You have n problems. You have estimated the difficulty of the i-th one as integer ci. Now you want to prepare a problemset for a contest, using some of the problems you've made.A problemset for the contest must consist of at least two problems. You think that the total difficulty of the problems of the contest must be at least l and at most r. Also, you think that the difference between difficulties of the easiest and the hardest of the chosen problems must be at least x.Find the number of ways to choose a problemset for the contest.", "input_spec": "The first line contains four integers n, l, r, x (1\u2009\u2264\u2009n\u2009\u2264\u200915, 1\u2009\u2264\u2009l\u2009\u2264\u2009r\u2009\u2264\u2009109, 1\u2009\u2264\u2009x\u2009\u2264\u2009106) \u2014 the number of problems you have, the minimum and maximum value of total difficulty of the problemset and the minimum difference in difficulty between the hardest problem in the pack and the easiest one, respectively. The second line contains n integers c1,\u2009c2,\u2009...,\u2009cn (1\u2009\u2264\u2009ci\u2009\u2264\u2009106) \u2014 the difficulty of each problem.", "output_spec": "Print the number of ways to choose a suitable problemset for the contest. ", "sample_inputs": ["3 5 6 1\n1 2 3", "4 40 50 10\n10 20 30 25", "5 25 35 10\n10 10 20 10 20"], "sample_outputs": ["2", "2", "6"], "notes": "NoteIn the first example two sets are suitable, one consisting of the second and third problem, another one consisting of all three problems.In the second example, two sets of problems are suitable \u2014 the set of problems with difficulties 10 and 30 as well as the set of problems with difficulties 20 and 30.In the third example any set consisting of one problem of difficulty 10 and one problem of difficulty 20 is suitable."}, "src_uid": "0d43104a0de924cdcf8e4aced5aa825d"}
{"nl": {"description": "It is the easy version of the problem. The difference is that in this version, there are no nodes with already chosen colors.Theofanis is starving, and he wants to eat his favorite food, sheftalia. However, he should first finish his homework. Can you help him with this problem?You have a perfect binary tree of $$$2^k - 1$$$ nodes\u00a0\u2014 a binary tree where all vertices $$$i$$$ from $$$1$$$ to $$$2^{k - 1} - 1$$$ have exactly two children: vertices $$$2i$$$ and $$$2i + 1$$$. Vertices from $$$2^{k - 1}$$$ to $$$2^k - 1$$$ don't have any children. You want to color its vertices with the $$$6$$$ Rubik's cube colors (White, Green, Red, Blue, Orange and Yellow).Let's call a coloring good when all edges connect nodes with colors that are neighboring sides in the Rubik's cube.  A picture of Rubik's cube and its 2D map. More formally:   a white node can not be neighboring with white and yellow nodes;  a yellow node can not be neighboring with white and yellow nodes;  a green node can not be neighboring with green and blue nodes;  a blue node can not be neighboring with green and blue nodes;  a red node can not be neighboring with red and orange nodes;  an orange node can not be neighboring with red and orange nodes; You want to calculate the number of the good colorings of the binary tree. Two colorings are considered different if at least one node is colored with a different color.The answer may be too large, so output the answer modulo $$$10^9+7$$$.", "input_spec": "The first and only line contains the integers $$$k$$$ ($$$1 \\le k \\le 60$$$)\u00a0\u2014 the number of levels in the perfect binary tree you need to color.", "output_spec": "Print one integer\u00a0\u2014 the number of the different colorings modulo $$$10^9+7$$$.", "sample_inputs": ["3", "14"], "sample_outputs": ["24576", "934234"], "notes": "NoteIn the picture below, you can see one of the correct colorings of the first example.  "}, "src_uid": "5144b9b281ea4087d8334d91c3c8bda4"}
{"nl": {"description": "You are given a positive integer $$$n$$$.Let $$$S(x)$$$ be sum of digits in base 10 representation of $$$x$$$, for example, $$$S(123) = 1 + 2 + 3 = 6$$$, $$$S(0) = 0$$$.Your task is to find two integers $$$a, b$$$, such that $$$0 \\leq a, b \\leq n$$$, $$$a + b = n$$$ and $$$S(a) + S(b)$$$ is the largest possible among all such pairs.", "input_spec": "The only line of input contains an integer $$$n$$$ $$$(1 \\leq n \\leq 10^{12})$$$.", "output_spec": "Print largest $$$S(a) + S(b)$$$ among all pairs of integers $$$a, b$$$, such that $$$0 \\leq a, b \\leq n$$$ and $$$a + b = n$$$.", "sample_inputs": ["35", "10000000000"], "sample_outputs": ["17", "91"], "notes": "NoteIn the first example, you can choose, for example, $$$a = 17$$$ and $$$b = 18$$$, so that $$$S(17) + S(18) = 1 + 7 + 1 + 8 = 17$$$. It can be shown that it is impossible to get a larger answer.In the second test example, you can choose, for example, $$$a = 5000000001$$$ and $$$b = 4999999999$$$, with $$$S(5000000001) + S(4999999999) = 91$$$. It can be shown that it is impossible to get a larger answer."}, "src_uid": "5c61b4a4728070b9de49d72831cd2329"}
{"nl": {"description": "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 '/'\u00a0\u2014 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": "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] \u2014 it contains no koutsu or shuntsu, so it includes no mentsu;  [4s, 3m, 3p, 4s, 5p, 4s, 5p] \u2014 it contains a koutsu, [4s, 4s, 4s], but no shuntsu, so it includes a mentsu;  [5p, 5s, 9m, 4p, 1s, 7p, 7m, 6p] \u2014 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\u00a0\u2014 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\u00a0\u2014 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\u00a0\u2014 1p or 4p. The resulting tiles will be [3p, 9m, 2p, 1p] or [3p, 9m, 2p, 4p]."}, "src_uid": "7e42cebc670e76ace967e01021f752d3"}
{"nl": {"description": "Iahub got bored, so he invented a game to be played on paper. He writes n integers a1,\u2009a2,\u2009...,\u2009an. Each of those integers can be either 0 or 1. He's allowed to do exactly one move: he chooses two indices i and j (1\u2009\u2264\u2009i\u2009\u2264\u2009j\u2009\u2264\u2009n) and flips all values ak for which their positions are in range [i,\u2009j] (that is i\u2009\u2264\u2009k\u2009\u2264\u2009j). Flip the value of x means to apply operation x\u2009=\u20091 - x.The goal of the game is that after exactly one move to obtain the maximum number of ones. Write a program to solve the little game of Iahub.", "input_spec": "The first line of the input contains an integer n (1\u2009\u2264\u2009n\u2009\u2264\u2009100). In the second line of the input there are n integers: a1,\u2009a2,\u2009...,\u2009an. It is guaranteed that each of those n values is either 0 or 1.", "output_spec": "Print an integer \u2014 the maximal number of 1s that can be obtained after exactly one move. ", "sample_inputs": ["5\n1 0 0 1 0", "4\n1 0 0 1"], "sample_outputs": ["4", "4"], "notes": "NoteIn the first case, flip the segment from 2 to 5 (i\u2009=\u20092,\u2009j\u2009=\u20095). That flip changes the sequence, it becomes: [1 1 1 0 1]. So, it contains four ones. There is no way to make the whole sequence equal to [1 1 1 1 1].In the second case, flipping only the second and the third element (i\u2009=\u20092,\u2009j\u2009=\u20093) will turn all numbers into 1."}, "src_uid": "9b543e07e805fe1dd8fa869d5d7c8b99"}
{"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\u2009\u2264\u2009a,\u2009b\u2009\u2264\u20096)\u00a0\u2014 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\u2009-\u2009x|\u2009<\u2009|b\u2009-\u2009x|."}, "src_uid": "504b8aae3a3abedf873a3b8b127c5dd8"}
{"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 \u2014 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": "\u2014 This is not playing but duty as allies of justice, Nii-chan!\u2014 Not allies but justice itself, Onii-chan!With hands joined, go everywhere at a speed faster than our thoughts! This time, the Fire Sisters\u00a0\u2014 Karen and Tsukihi\u00a0\u2014 is heading for somewhere they've never reached\u00a0\u2014 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\u2009244\u2009353. 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\u2009\u2264\u2009a,\u2009b,\u2009c\u2009\u2264\u20095\u2009000)\u00a0\u2014 the number of islands in the red, blue and purple clusters, respectively.", "output_spec": "Output one line containing an integer\u00a0\u2014 the number of different ways to build bridges, modulo 998\u2009244\u2009353.", "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\u2009=\u20098.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": "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 $$$M$$$ ($$$3 \\le n \\le 400$$$; $$$10^8 \\le M \\le 10^9$$$)\u00a0\u2014 the number of computers and the modulo. It is guaranteed that $$$M$$$ is prime.", "output_spec": "Print one integer\u00a0\u2014 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 have two variables a and b. Consider the following sequence of actions performed with these variables: If a\u2009=\u20090 or b\u2009=\u20090, end the process. Otherwise, go to step 2; If a\u2009\u2265\u20092\u00b7b, then set the value of a to a\u2009-\u20092\u00b7b, and repeat step 1. Otherwise, go to step 3; If b\u2009\u2265\u20092\u00b7a, then set the value of b to b\u2009-\u20092\u00b7a, and repeat step 1. Otherwise, end the process.Initially the values of a and b are positive integers, and so the process will be finite.You have to determine the values of a and b after the process ends.", "input_spec": "The only line of the input contains two integers n and m (1\u2009\u2264\u2009n,\u2009m\u2009\u2264\u20091018). n is the initial value of variable a, and m is the initial value of variable b.", "output_spec": "Print two integers \u2014 the values of a and b after the end of the process.", "sample_inputs": ["12 5", "31 12"], "sample_outputs": ["0 1", "7 12"], "notes": "NoteExplanations to the samples: a\u2009=\u200912, b\u2009=\u20095  a\u2009=\u20092, b\u2009=\u20095  a\u2009=\u20092, b\u2009=\u20091  a\u2009=\u20090, b\u2009=\u20091; a\u2009=\u200931, b\u2009=\u200912  a\u2009=\u20097, b\u2009=\u200912."}, "src_uid": "1f505e430eb930ea2b495ab531274114"}
{"nl": {"description": "Jamie loves sleeping. One day, he decides that he needs to wake up at exactly hh:\u2009mm. However, he hates waking up, so he wants to make waking up less painful by setting the alarm at a lucky time. He will then press the snooze button every x minutes until hh:\u2009mm is reached, and only then he will wake up. He wants to know what is the smallest number of times he needs to press the snooze button.A time is considered lucky if it contains a digit '7'. For example, 13:\u200907 and 17:\u200927 are lucky, while 00:\u200948 and 21:\u200934 are not lucky.Note that it is not necessary that the time set for the alarm and the wake-up time are on the same day. It is guaranteed that there is a lucky time Jamie can set so that he can wake at hh:\u2009mm.Formally, find the smallest possible non-negative integer y such that the time representation of the time x\u00b7y minutes before hh:\u2009mm contains the digit '7'.Jamie uses 24-hours clock, so after 23:\u200959 comes 00:\u200900.", "input_spec": "The first line contains a single integer x (1\u2009\u2264\u2009x\u2009\u2264\u200960). The second line contains two two-digit integers, hh and mm (00\u2009\u2264\u2009hh\u2009\u2264\u200923,\u200900\u2009\u2264\u2009mm\u2009\u2264\u200959).", "output_spec": "Print the minimum number of times he needs to press the button.", "sample_inputs": ["3\n11 23", "5\n01 07"], "sample_outputs": ["2", "0"], "notes": "NoteIn the first sample, Jamie needs to wake up at 11:23. So, he can set his alarm at 11:17. He would press the snooze button when the alarm rings at 11:17 and at 11:20.In the second sample, Jamie can set his alarm at exactly at 01:07 which is lucky."}, "src_uid": "5ecd569e02e0164a5da9ff549fca3ceb"}
{"nl": {"description": "A group of $$$n$$$ dancers rehearses a performance for the closing ceremony. The dancers are arranged in a row, they've studied their dancing moves and can't change positions. For some of them, a white dancing suit is already bought, for some of them \u2014 a black one, and for the rest the suit will be bought in the future.On the day when the suits were to be bought, the director was told that the participants of the olympiad will be happy if the colors of the suits on the scene will form a palindrome. A palindrome is a sequence that is the same when read from left to right and when read from right to left. The director liked the idea, and she wants to buy suits so that the color of the leftmost dancer's suit is the same as the color of the rightmost dancer's suit, the 2nd left is the same as 2nd right, and so on.The director knows how many burls it costs to buy a white suit, and how many burls to buy a black suit. You need to find out whether it is possible to buy suits to form a palindrome, and if it's possible, what's the minimal cost of doing so. Remember that dancers can not change positions, and due to bureaucratic reasons it is not allowed to buy new suits for the dancers who already have suits, even if it reduces the overall spending.", "input_spec": "The first line contains three integers $$$n$$$, $$$a$$$, and $$$b$$$ ($$$1 \\leq n \\leq 20$$$, $$$1 \\leq a, b \\leq 100$$$)\u00a0\u2014 the number of dancers, the cost of a white suit, and the cost of a black suit. The next line contains $$$n$$$ numbers $$$c_i$$$, $$$i$$$-th of which denotes the color of the suit of the $$$i$$$-th dancer. Number $$$0$$$ denotes the white color, $$$1$$$\u00a0\u2014 the black color, and $$$2$$$ denotes that a suit for this dancer is still to be bought.", "output_spec": "If it is not possible to form a palindrome without swapping dancers and buying new suits for those who have one, then output -1. Otherwise, output the minimal price to get the desired visual effect.", "sample_inputs": ["5 100 1\n0 1 2 1 2", "3 10 12\n1 2 0", "3 12 1\n0 1 0"], "sample_outputs": ["101", "-1", "0"], "notes": "NoteIn the first sample, the cheapest way to obtain palindromic colors is to buy a black suit for the third from left dancer and a white suit for the rightmost dancer.In the second sample, the leftmost dancer's suit already differs from the rightmost dancer's suit so there is no way to obtain the desired coloring.In the third sample, all suits are already bought and their colors form a palindrome."}, "src_uid": "af07223819aeb5bd6ded4340c472b2b6"}
{"nl": {"description": "Stepan has a very big positive integer.Let's consider all cyclic shifts of Stepan's integer (if we look at his integer like at a string) which are also integers (i.e. they do not have leading zeros). Let's call such shifts as good shifts. For example, for the integer 10203 the good shifts are the integer itself 10203 and integers 20310 and 31020.Stepan wants to know the minimum remainder of the division by the given number m among all good shifts. Your task is to determine the minimum remainder of the division by m.", "input_spec": "The first line contains the integer which Stepan has. The length of Stepan's integer is between 2 and 200\u2009000 digits, inclusive. It is guaranteed that Stepan's integer does not contain leading zeros. The second line contains the integer m (2\u2009\u2264\u2009m\u2009\u2264\u2009108) \u2014 the number by which Stepan divides good shifts of his integer.", "output_spec": "Print the minimum remainder which Stepan can get if he divides all good shifts of his integer by the given number m.", "sample_inputs": ["521\n3", "1001\n5", "5678901234567890123456789\n10000"], "sample_outputs": ["2", "0", "123"], "notes": "NoteIn the first example all good shifts of the integer 521 (good shifts are equal to 521, 215 and 152) has same remainder 2 when dividing by 3.In the second example there are only two good shifts: the Stepan's integer itself and the shift by one position to the right. The integer itself is 1001 and the remainder after dividing it by 5 equals 1. The shift by one position to the right equals to 1100 and the remainder after dividing it by 5 equals 0, which is the minimum possible remainder."}, "src_uid": "d13c7b5b5fc5c433cc8f374ddb16ef79"}
{"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": "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": "InputThe input contains a single integer a (0\u2009\u2264\u2009a\u2009\u2264\u200935).OutputOutput a single integer.ExamplesInput3Output8Input10Output1024", "input_spec": "The input contains a single integer a (0\u2009\u2264\u2009a\u2009\u2264\u200935).", "output_spec": "Output a single integer.", "sample_inputs": ["3", "10"], "sample_outputs": ["8", "1024"], "notes": null}, "src_uid": "76f6ebfaeea789952c931d65c6a5fdff"}
{"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) \u2009\u2192\u2009 (x, y+1);  'D': go down, (x, y) \u2009\u2192\u2009 (x, y-1);  'L': go left, (x, y) \u2009\u2192\u2009 (x-1, y);  'R': go right, (x, y) \u2009\u2192\u2009 (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,\u2009b).", "input_spec": "The first line contains two integers a and b, (\u2009-\u2009109\u2009\u2264\u2009a,\u2009b\u2009\u2264\u2009109). The second line contains a string s (1\u2009\u2264\u2009|s|\u2009\u2264\u2009100, s only contains characters 'U', 'D', 'L', 'R') \u2014 the command.", "output_spec": "Print \"Yes\" if the robot will be located at (a,\u2009b), 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) \u2009\u2192\u2009 (1, 0) \u2009\u2192\u2009 (1, 1) \u2009\u2192\u2009 (2, 1) \u2009\u2192\u2009 (2, 2) \u2009\u2192\u2009 ...So it can reach (2, 2) but not (1, 2)."}, "src_uid": "5d6212e28c7942e9ff4d096938b782bf"}
{"nl": {"description": "You're given a row with $$$n$$$ chairs. We call a seating of people \"maximal\" if the two following conditions hold:  There are no neighbors adjacent to anyone seated.  It's impossible to seat one more person without violating the first rule. The seating is given as a string consisting of zeros and ones ($$$0$$$ means that the corresponding seat is empty, $$$1$$$ \u2014 occupied). The goal is to determine whether this seating is \"maximal\".Note that the first and last seats are not adjacent (if $$$n \\ne 2$$$).", "input_spec": "The first line contains a single integer $$$n$$$ ($$$1 \\leq n \\leq 1000$$$)\u00a0\u2014 the number of chairs. The next line contains a string of $$$n$$$ characters, each of them is either zero or one, describing the seating.", "output_spec": "Output \"Yes\" (without quotation marks) if the seating is \"maximal\". Otherwise print \"No\". You are allowed to print letters in whatever case you'd like (uppercase or lowercase).", "sample_inputs": ["3\n101", "4\n1011", "5\n10001"], "sample_outputs": ["Yes", "No", "No"], "notes": "NoteIn sample case one the given seating is maximal.In sample case two the person at chair three has a neighbour to the right.In sample case three it is possible to seat yet another person into chair three."}, "src_uid": "c14d255785b1f668d04b0bf6dcadf32d"}
{"nl": {"description": "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 $$$c$$$ ($$$1 \\leq a, b, c \\leq 100$$$)\u00a0\u2014 the lengths of sticks Masha possesses.", "output_spec": "Print a single integer\u00a0\u2014 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": "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\u2009\u2264\u2009n\u2009\u2264\u2009100)\u00a0\u2014 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\u00a0\u2014 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": "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\u2009\u2264\u2009n\u2009\u2264\u20091017). Please, do not use the %lld specifier to read or write 64 bit integers in \u0421++. 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": "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\u2009\u2264\u2009n\u2009\u2264\u20091018). Please do not use the %lld specificator to read or write 64-bit numbers in \u0421++. 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": "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\u2009\u2264\u2009s\u2009\u2264\u200999), 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": "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,\u2009y) to (x\u2009-\u20091,\u2009y) or (x,\u2009y\u2009-\u20091). Vasiliy can move his pawn from (x,\u2009y) to one of cells: (x\u2009-\u20091,\u2009y),\u2009(x\u2009-\u20091,\u2009y\u2009-\u20091) and (x,\u2009y\u2009-\u20091). Both players are also allowed to skip move. There are some additional restrictions \u2014 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,\u20090). 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,\u2009yp,\u2009xv,\u2009yv (0\u2009\u2264\u2009xp,\u2009yp,\u2009xv,\u2009yv\u2009\u2264\u2009105) \u2014 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,\u20090).", "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,\u20091) and will move to (1,\u20091) in the first turn. No matter what his opponent is doing, in the second turn Polycarp can move to (1,\u20090) and finally to (0,\u20090) in the third turn."}, "src_uid": "2637d57f7809ff8f922549c617709074"}
{"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\u2009\u2264\u2009v1,\u2009v2\u2009\u2264\u2009100) \u2014 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\u2009\u2264\u2009t\u2009\u2264\u2009100) \u2014 the time when the car moves along the segment in seconds, d (0\u2009\u2264\u2009d\u2009\u2264\u200910) \u2014 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\u2009+\u20097\u2009+\u20098\u2009+\u20096\u2009=\u200926 meters.In the second sample, as d\u2009=\u20090, the car covers the whole segment at constant speed v\u2009=\u200910. In t\u2009=\u200910 seconds it covers the distance of 100 meters."}, "src_uid": "9246aa2f506fcbcb47ad24793d09f2cf"}
{"nl": {"description": "One day a bear lived on the Oxy axis. He was afraid of the dark, so he couldn't move at night along the plane points that aren't lit. One day the bear wanted to have a night walk from his house at point (l,\u20090) to his friend's house at point (r,\u20090), along the segment of length (r\u2009-\u2009l). Of course, if he wants to make this walk, he needs each point of the segment to be lit. That's why the bear called his friend (and yes, in the middle of the night) asking for a very delicate favor.The Oxy axis contains n floodlights. Floodlight i is at point (xi,\u2009yi) and can light any angle of the plane as large as ai degree with vertex at point (xi,\u2009yi). The bear asked his friend to turn the floodlights so that he (the bear) could go as far away from his house as possible during the walking along the segment. His kind friend agreed to fulfill his request. And while he is at it, the bear wonders: what is the furthest he can go away from his house? Hep him and find this distance.Consider that the plane has no obstacles and no other light sources besides the floodlights. The bear's friend cannot turn the floodlights during the bear's walk. Assume that after all the floodlights are turned in the correct direction, the bear goes for a walk and his friend goes to bed.", "input_spec": "The first line contains three space-separated integers n, l, r (1\u2009\u2264\u2009n\u2009\u2264\u200920;\u00a0\u2009-\u2009105\u2009\u2264\u2009l\u2009\u2264\u2009r\u2009\u2264\u2009105). The i-th of the next n lines contain three space-separated integers xi, yi, ai (\u2009-\u20091000\u2009\u2264\u2009xi\u2009\u2264\u20091000;\u00a01\u2009\u2264\u2009yi\u2009\u2264\u20091000;\u00a01\u2009\u2264\u2009ai\u2009\u2264\u200990) \u2014 the floodlights' description.  Note that two floodlights can be at the same point of the plane.", "output_spec": "Print a single real number \u2014 the answer to the problem. The answer will be considered correct if its relative or absolute error doesn't exceed 10\u2009-\u20096.", "sample_inputs": ["2 3 5\n3 1 45\n5 1 45", "1 0 1\n1 1 30", "1 0 1\n1 1 45", "1 0 2\n0 2 90"], "sample_outputs": ["2.000000000", "0.732050808", "1.000000000", "2.000000000"], "notes": "NoteIn the first sample, one of the possible solutions is:   In the second sample, a single solution is:   In the third sample, a single solution is:   "}, "src_uid": "4fad1233e08bef09e5aa7e2dc6167d6a"}
{"nl": {"description": "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\u2009\u2264\u2009|s|\u2009\u2264\u2009100), consisting of lowercase English letters. Here, |s| denotes the length of the string. The second line contains string t (|t|\u2009=\u2009|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\u2009=\u2009s1s2... sn is said to be lexicographically smaller than t\u2009=\u2009t1t2... tn, if there exists such i, that s1\u2009=\u2009t1,\u2009s2\u2009=\u2009t2,\u2009... si\u2009-\u20091\u2009=\u2009ti\u2009-\u20091,\u2009si\u2009<\u2009ti."}, "src_uid": "47618510d2a17b1cc1e6a688201d51a3"}
{"nl": {"description": "Devu is a renowned classical singer. He is invited to many big functions/festivals. Recently he was invited to \"All World Classical Singing Festival\". Other than Devu, comedian Churu was also invited.Devu has provided organizers a list of the songs and required time for singing them. He will sing n songs, ith song will take ti minutes exactly. The Comedian, Churu will crack jokes. All his jokes are of 5 minutes exactly.People have mainly come to listen Devu. But you know that he needs rest of 10 minutes after each song. On the other hand, Churu being a very active person, doesn't need any rest.You as one of the organizers should make an optimal s\u0441hedule for the event. For some reasons you must follow the conditions:  The duration of the event must be no more than d minutes;  Devu must complete all his songs;  With satisfying the two previous conditions the number of jokes cracked by Churu should be as many as possible. If it is not possible to find a way to conduct all the songs of the Devu, output -1. Otherwise find out maximum number of jokes that Churu can crack in the grand event.", "input_spec": "The first line contains two space separated integers n, d (1\u2009\u2264\u2009n\u2009\u2264\u2009100;\u00a01\u2009\u2264\u2009d\u2009\u2264\u200910000). The second line contains n space-separated integers: t1,\u2009t2,\u2009...,\u2009tn (1\u2009\u2264\u2009ti\u2009\u2264\u2009100).", "output_spec": "If there is no way to conduct all the songs of Devu, output -1. Otherwise output the maximum number of jokes that Churu can crack in the grand event.", "sample_inputs": ["3 30\n2 2 1", "3 20\n2 1 1"], "sample_outputs": ["5", "-1"], "notes": "NoteConsider the first example. The duration of the event is 30 minutes. There could be maximum 5 jokes in the following way:  First Churu cracks a joke in 5 minutes.  Then Devu performs the first song for 2 minutes.  Then Churu cracks 2 jokes in 10 minutes.  Now Devu performs second song for 2 minutes.  Then Churu cracks 2 jokes in 10 minutes.  Now finally Devu will perform his last song in 1 minutes.  Total time spent is 5\u2009+\u20092\u2009+\u200910\u2009+\u20092\u2009+\u200910\u2009+\u20091\u2009=\u200930 minutes.Consider the second example. There is no way of organizing Devu's all songs. Hence the answer is -1. "}, "src_uid": "b16f5f5c4eeed2a3700506003e8ea8ea"}
{"nl": {"description": "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\u00a0\u2014 \"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 $$$n$$$ ($$$4 \\leq n \\leq 50$$$)\u00a0\u2014 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\"\u00a0\u2014 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\"\u00a0\u2014 with the letter \"A\" for three operations. You will get the string \"ZACTG\", in which there is a genome."}, "src_uid": "ee4f88abe4c9fa776abd15c5f3a94543"}
{"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\u2009\u2264\u2009k,\u2009l\u2009\u2264\u2009231\u2009-\u20091).", "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 \u2014 the importance of number l.", "sample_inputs": ["5\n25", "3\n8"], "sample_outputs": ["YES\n1", "NO"], "notes": null}, "src_uid": "8ce89b754aa4080e7c3b2c3b10f4be46"}
{"nl": {"description": "At first, let's define function $$$f(x)$$$ as follows: $$$$$$ \\begin{matrix} f(x) & = & \\left\\{ \\begin{matrix} \\frac{x}{2} & \\mbox{if } x \\text{ is even} \\\\ x - 1 & \\mbox{otherwise } \\end{matrix} \\right. \\end{matrix} $$$$$$We can see that if we choose some value $$$v$$$ and will apply function $$$f$$$ to it, then apply $$$f$$$ to $$$f(v)$$$, and so on, we'll eventually get $$$1$$$. Let's write down all values we get in this process in a list and denote this list as $$$path(v)$$$. For example, $$$path(1) = [1]$$$, $$$path(15) = [15, 14, 7, 6, 3, 2, 1]$$$, $$$path(32) = [32, 16, 8, 4, 2, 1]$$$.Let's write all lists $$$path(x)$$$ for every $$$x$$$ from $$$1$$$ to $$$n$$$. The question is next: what is the maximum value $$$y$$$ such that $$$y$$$ is contained in at least $$$k$$$ different lists $$$path(x)$$$?Formally speaking, you need to find maximum $$$y$$$ such that $$$\\left| \\{ x ~|~ 1 \\le x \\le n, y \\in path(x) \\} \\right| \\ge k$$$.", "input_spec": "The first line contains two integers $$$n$$$ and $$$k$$$ ($$$1 \\le k \\le n \\le 10^{18}$$$).", "output_spec": "Print the only integer \u2014 the maximum value that is contained in at least $$$k$$$ paths.", "sample_inputs": ["11 3", "11 6", "20 20", "14 5", "1000000 100"], "sample_outputs": ["5", "4", "1", "6", "31248"], "notes": "NoteIn the first example, the answer is $$$5$$$, since $$$5$$$ occurs in $$$path(5)$$$, $$$path(10)$$$ and $$$path(11)$$$.In the second example, the answer is $$$4$$$, since $$$4$$$ occurs in $$$path(4)$$$, $$$path(5)$$$, $$$path(8)$$$, $$$path(9)$$$, $$$path(10)$$$ and $$$path(11)$$$.In the third example $$$n = k$$$, so the answer is $$$1$$$, since $$$1$$$ is the only number occuring in all paths for integers from $$$1$$$ to $$$20$$$."}, "src_uid": "783c4b3179c558369f94f4a16ac562d4"}
{"nl": {"description": "You can not just take the file and send it. When Polycarp trying to send a file in the social network \"Codehorses\", he encountered an unexpected problem. If the name of the file contains three or more \"x\" (lowercase Latin letters \"x\") in a row, the system considers that the file content does not correspond to the social network topic. In this case, the file is not sent and an error message is displayed.Determine the minimum number of characters to remove from the file name so after that the name does not contain \"xxx\" as a substring. Print 0 if the file name does not initially contain a forbidden substring \"xxx\".You can delete characters in arbitrary positions (not necessarily consecutive). If you delete a character, then the length of a string is reduced by $$$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)$$$ \u2014 the length of the file name. The second line contains a string of length $$$n$$$ consisting of lowercase Latin letters only \u2014 the file name.", "output_spec": "Print the minimum number of characters to remove from the file name so after that the name does not contain \"xxx\" as a substring. If initially the file name dost not contain a forbidden substring \"xxx\", print 0.", "sample_inputs": ["6\nxxxiii", "5\nxxoxx", "10\nxxxxxxxxxx"], "sample_outputs": ["1", "0", "8"], "notes": "NoteIn the first example Polycarp tried to send a file with name contains number $$$33$$$, written in Roman numerals. But he can not just send the file, because it name contains three letters \"x\" in a row. To send the file he needs to remove any one of this letters."}, "src_uid": "8de14db41d0acee116bd5d8079cb2b02"}
{"nl": {"description": " In every generation there is a Chosen One. She alone will stand against the vampires, the demons, and the forces of darkness. She is the Slayer. \u2014 Joss Whedon ", "input_spec": "A string $$$s$$$ ($$$3 \\le |s| \\le 7$$$) consisting of lowercase English letters.", "output_spec": "A single string. If there is no answer, print \"none\" (without the quotes).", "sample_inputs": ["tourist"], "sample_outputs": ["ooggqjx"], "notes": null}, "src_uid": "56ec50526a3843fe3784d395850f45ae"}
{"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\u2009\u2264\u2009m\u2009\u2264\u2009100). The second line contains m integers c1, c2, ..., cm, separated by single spaces (0\u2009\u2264\u2009ci\u2009\u2264\u2009100). The third line contains two space-separated integers x and y (1\u2009\u2264\u2009x\u2009\u2264\u2009y\u2009\u2264\u200910000). 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 \u2014 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": "Do you remember a kind cartoon \"Beauty and the Beast\"? No, no, there was no firing from machine guns or radiation mutants time-travels!There was a beauty named Belle. Once she had violated the Beast's order and visited the West Wing. After that she was banished from the castle... Everybody was upset. The beautiful Belle was upset, so was the Beast, so was Lumiere the candlestick. But the worst thing was that Cogsworth was upset. Cogsworth is not a human, but is the mantel clock, which was often used as an alarm clock.Due to Cogsworth's frustration all the inhabitants of the castle were in trouble: now they could not determine when it was time to drink morning tea, and when it was time for an evening stroll. Fortunately, deep in the basement are lying digital clock showing the time in the format HH:MM. Now the residents of the castle face a difficult task. They should turn Cogsworth's hour and minute mustache hands in such a way, that Cogsworth began to show the correct time. Moreover they need to find turn angles in degrees for each mustache hands. The initial time showed by Cogsworth is 12:00.You can only rotate the hands forward, that is, as is shown in the picture:   As since there are many ways too select such angles because of full rotations, choose the smallest angles in the right (non-negative) direction.Note that Cogsworth's hour and minute mustache hands move evenly and continuously. Hands are moving independently, so when turning one hand the other hand remains standing still.", "input_spec": "The only line of input contains current time according to the digital clock, formatted as HH:MM (00\u2009\u2264\u2009HH\u2009\u2264\u200923, 00\u2009\u2264\u2009MM\u2009\u2264\u200959). The mantel clock initially shows 12:00. Pretests contain times of the beginning of some morning TV programs of the Channel One Russia.", "output_spec": "Print two numbers x and y \u2014 the angles of turning the hour and minute hands, respectively (0\u2009\u2264\u2009x,\u2009y\u2009<\u2009360). The absolute or relative error in the answer should not exceed 10\u2009-\u20099.", "sample_inputs": ["12:00", "04:30", "08:17"], "sample_outputs": ["0 0", "135 180", "248.5 102"], "notes": "NoteA note to the second example: the hour hand will be positioned exactly in the middle, between 4 and 5."}, "src_uid": "175dc0bdb5c9513feb49be6644d0d150"}
{"nl": {"description": "Pak Chanek plans to build a garage. He wants the garage to consist of a square and a right triangle that are arranged like the following illustration.  Define $$$a$$$ and $$$b$$$ as the lengths of two of the sides in the right triangle as shown in the illustration. An integer $$$x$$$ is suitable if and only if we can construct a garage with assigning positive integer values for the lengths $$$a$$$ and $$$b$$$ ($$$a<b$$$) so that the area of the square at the bottom is exactly $$$x$$$. As a good friend of Pak Chanek, you are asked to help him find the $$$N$$$-th smallest suitable number.", "input_spec": "The only line contains a single integer $$$N$$$ ($$$1 \\leq N \\leq 10^9$$$).", "output_spec": "An integer that represents the $$$N$$$-th smallest suitable number.", "sample_inputs": ["3"], "sample_outputs": ["7"], "notes": "NoteThe $$$3$$$-rd smallest suitable number is $$$7$$$. A square area of $$$7$$$ can be obtained by assigning $$$a=3$$$ and $$$b=4$$$."}, "src_uid": "d0a8604b78ba19ab769fd1ec90a72e4e"}
{"nl": {"description": "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\u2009=\u200901123 tor 12123\u2009=\u200910213\u2009=\u20093410.Petya wrote numbers a and c on a piece of paper. Help him find such number b, that a tor b\u2009=\u2009c. If there are several such numbers, print the smallest one.", "input_spec": "The first line contains two integers a and c (0\u2009\u2264\u2009a,\u2009c\u2009\u2264\u2009109). Both numbers are written in decimal notation.", "output_spec": "Print the single integer b, such that a tor b\u2009=\u2009c. 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": "Alice and Bob begin their day with a quick game. They first choose a starting number X0\u2009\u2265\u20093 and try to reach one million by the process described below. Alice goes first and then they take alternating turns. In the i-th turn, the player whose turn it is selects a prime number smaller than the current number, and announces the smallest multiple of this prime number that is not smaller than the current number.Formally, he or she selects a prime p\u2009<\u2009Xi\u2009-\u20091 and then finds the minimum Xi\u2009\u2265\u2009Xi\u2009-\u20091 such that p divides Xi. Note that if the selected prime p already divides Xi\u2009-\u20091, then the number does not change.Eve has witnessed the state of the game after two turns. Given X2, help her determine what is the smallest possible starting number X0. Note that the players don't necessarily play optimally. You should consider all possible game evolutions.", "input_spec": "The input contains a single integer X2 (4\u2009\u2264\u2009X2\u2009\u2264\u2009106). It is guaranteed that the integer X2 is composite, that is, is not prime.", "output_spec": "Output a single integer\u00a0\u2014 the minimum possible X0.", "sample_inputs": ["14", "20", "8192"], "sample_outputs": ["6", "15", "8191"], "notes": "NoteIn the first test, the smallest possible starting number is X0\u2009=\u20096. One possible course of the game is as follows:   Alice picks prime 5 and announces X1\u2009=\u200910  Bob picks prime 7 and announces X2\u2009=\u200914. In the second case, let X0\u2009=\u200915.   Alice picks prime 2 and announces X1\u2009=\u200916  Bob picks prime 5 and announces X2\u2009=\u200920. "}, "src_uid": "43ff6a223c68551eff793ba170110438"}
{"nl": {"description": "Galois is one of the strongest chess players of Byteforces. He has even invented a new variant of chess, which he named \u00abPawnChess\u00bb.This new game is played on a board consisting of 8 rows and 8 columns. At the beginning of every game some black and white pawns are placed on the board. The number of black pawns placed is not necessarily equal to the number of white pawns placed.   Lets enumerate rows and columns with integers from 1 to 8. Rows are numbered from top to bottom, while columns are numbered from left to right. Now we denote as (r,\u2009c) the cell located at the row r and at the column c.There are always two players A and B playing the game. Player A plays with white pawns, while player B plays with black ones. The goal of player A is to put any of his pawns to the row 1, while player B tries to put any of his pawns to the row 8. As soon as any of the players completes his goal the game finishes immediately and the succeeded player is declared a winner.Player A moves first and then they alternate turns. On his move player A must choose exactly one white pawn and move it one step upward and player B (at his turn) must choose exactly one black pawn and move it one step down. Any move is possible only if the targeted cell is empty. It's guaranteed that for any scenario of the game there will always be at least one move available for any of the players.Moving upward means that the pawn located in (r,\u2009c) will go to the cell (r\u2009-\u20091,\u2009c), while moving down means the pawn located in (r,\u2009c) will go to the cell (r\u2009+\u20091,\u2009c). Again, the corresponding cell must be empty, i.e. not occupied by any other pawn of any color.Given the initial disposition of the board, determine who wins the game if both players play optimally. Note that there will always be a winner due to the restriction that for any game scenario both players will have some moves available.", "input_spec": "The input consists of the board description given in eight lines, each line contains eight characters. Character 'B' is used to denote a black pawn, and character 'W' represents a white pawn. Empty cell is marked with '.'.  It's guaranteed that there will not be white pawns on the first row neither black pawns on the last row.", "output_spec": "Print 'A' if player A wins the game on the given board, and 'B' if player B will claim the victory. Again, it's guaranteed that there will always be a winner on the given board.", "sample_inputs": ["........\n........\n.B....B.\n....W...\n........\n..W.....\n........\n........", "..B.....\n..W.....\n......B.\n........\n.....W..\n......B.\n........\n........"], "sample_outputs": ["A", "B"], "notes": "NoteIn the first sample player A is able to complete his goal in 3 steps by always moving a pawn initially located at (4,\u20095). Player B needs at least 5 steps for any of his pawns to reach the row 8. Hence, player A will be the winner."}, "src_uid": "0ddc839e17dee20e1a954c1289de7fbd"}
{"nl": {"description": "A string $$$s$$$ of length $$$n$$$ can be encrypted by the following algorithm:  iterate over all divisors of $$$n$$$ in decreasing order (i.e. from $$$n$$$ to $$$1$$$),  for each divisor $$$d$$$, reverse the substring $$$s[1 \\dots d]$$$ (i.e. the substring which starts at position $$$1$$$ and ends at position $$$d$$$). For example, the above algorithm applied to the string $$$s$$$=\"codeforces\" leads to the following changes: \"codeforces\" $$$\\to$$$ \"secrofedoc\" $$$\\to$$$ \"orcesfedoc\" $$$\\to$$$ \"rocesfedoc\" $$$\\to$$$ \"rocesfedoc\" (obviously, the last reverse operation doesn't change the string because $$$d=1$$$).You are given the encrypted string $$$t$$$. Your task is to decrypt this string, i.e., to find a string $$$s$$$ such that the above algorithm results in string $$$t$$$. It can be proven that this string $$$s$$$ always exists and is unique.", "input_spec": "The first line of input consists of a single integer $$$n$$$ ($$$1 \\le n \\le 100$$$) \u2014 the length of the string $$$t$$$. The second line of input consists of the string $$$t$$$. The length of $$$t$$$ is $$$n$$$, and it consists only of lowercase Latin letters.", "output_spec": "Print a string $$$s$$$ such that the above algorithm results in $$$t$$$.", "sample_inputs": ["10\nrocesfedoc", "16\nplmaetwoxesisiht", "1\nz"], "sample_outputs": ["codeforces", "thisisexampletwo", "z"], "notes": "NoteThe first example is described in the problem statement."}, "src_uid": "1b0b2ee44c63cb0634cb63f2ad65cdd3"}
{"nl": {"description": "Btoh yuo adn yuor roomatme lhoate wianshg disehs, btu stlil sdmoeboy msut peorrfm tihs cohre dialy. Oen dya yuo decdie to idourtcne smoe syestm. Yuor rmmotaoe sstgegus teh fooniwllg dael. Yuo argee on tow arayrs of ientgres M adn R, nmebur upmicnog dyas (induiclng teh cunrret oen) wtih sicsescuve irnegets (teh ceurrnt dya is zreo), adn yuo wsah teh diehss on dya D if adn olny if terhe etsixs an iednx i scuh taht D\u00a0mod\u00a0M[i]\u2009=\u2009R[i], otwsehrie yuor rmootmae deos it. Yuo lkie teh cncepot, btu yuor rmotaome's cuinnng simle meaks yuo ssecupt sthnoemig, so yuo itennd to vefriy teh fnerisas of teh aemnrgeet.Yuo aer geivn ayarrs M adn R. Cuaclatle teh pceanregte of dyas on wchih yuo edn up dnoig teh wisahng. Amsuse taht yuo hvae iiiftlneny mnay dyas aehad of yuo. ", "input_spec": "The first line of input contains a single integer N (1\u2009\u2264\u2009N\u2009\u2264\u200916). The second and third lines of input contain N integers each, all between 0 and 16, inclusive, and represent arrays M and R, respectively. All M[i] are positive, for each i R[i]\u2009<\u2009M[i].", "output_spec": "Output a single real number. The answer is considered to be correct if its absolute or relative error does not exceed 10\u2009-\u20094.", "sample_inputs": ["1\n2\n0", "2\n2 3\n1 0"], "sample_outputs": ["0.500000", "0.666667"], "notes": null}, "src_uid": "14b69f42bc192ea472e82f3a3209f1c1"}
{"nl": {"description": "The Smart Beaver from ABBYY got hooked on square matrices. Now he is busy studying an n\u2009\u00d7\u2009n 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 \u2014 the row which has exactly  rows above it and the same number of rows below it.   Elements of the \"middle\" column \u2014 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\u2009\u00d7\u20095 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\u2009\u2264\u2009aij\u2009\u2264\u2009100) separated by single spaces \u2014 the elements of the given matrix. The input limitations for getting 30 points are:    1\u2009\u2264\u2009n\u2009\u2264\u20095  The input limitations for getting 100 points are:   1\u2009\u2264\u2009n\u2009\u2264\u2009101 ", "output_spec": "Print a single integer \u2014 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": "You have a set of items, each having some integer weight not greater than $$$8$$$. You denote that a subset of items is good if total weight of items in the subset does not exceed $$$W$$$.You want to calculate the maximum possible weight of a good subset of items. Note that you have to consider the empty set and the original set when calculating the answer.", "input_spec": "The first line contains one integer $$$W$$$ ($$$0 \\le W \\le 10^{18}$$$) \u2014 the maximum total weight of a good subset. The second line denotes the set of items you have. It contains $$$8$$$ integers $$$cnt_1$$$, $$$cnt_2$$$, ..., $$$cnt_8$$$ ($$$0 \\le cnt_i \\le 10^{16}$$$), where $$$cnt_i$$$ is the number of items having weight $$$i$$$ in the set.", "output_spec": "Print one integer \u2014 the maximum possible weight of a good subset of items.", "sample_inputs": ["10\n1 2 3 4 5 6 7 8", "0\n0 0 0 0 0 0 0 0", "3\n0 4 1 0 0 9 8 3"], "sample_outputs": ["10", "0", "3"], "notes": null}, "src_uid": "8097e10157320524c0faed56f2bc4880"}
{"nl": {"description": "You are given a string q. A sequence of k strings s1,\u2009s2,\u2009...,\u2009sk is called beautiful, if the concatenation of these strings is string q (formally, s1\u2009+\u2009s2\u2009+\u2009...\u2009+\u2009sk\u2009=\u2009q) 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\u2009\u2264\u2009k\u2009\u2264\u200926) \u2014 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,\u2009s2,\u2009...,\u2009sk. 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\",\u2009\"s\"} and {\"aaa\",\u2009\"cas\"}."}, "src_uid": "c1b071f09ef375f19031ce99d10e90ab"}
{"nl": {"description": "The bear decided to store some raspberry for the winter. He cunningly found out the price for a barrel of honey in kilos of raspberry for each of the following n days. According to the bear's data, on the i-th (1\u2009\u2264\u2009i\u2009\u2264\u2009n) day, the price for one barrel of honey is going to is xi kilos of raspberry.Unfortunately, the bear has neither a honey barrel, nor the raspberry. At the same time, the bear's got a friend who is ready to lend him a barrel of honey for exactly one day for c kilograms of raspberry. That's why the bear came up with a smart plan. He wants to choose some day d (1\u2009\u2264\u2009d\u2009<\u2009n), lent a barrel of honey and immediately (on day d) sell it according to a daily exchange rate. The next day (d\u2009+\u20091) the bear wants to buy a new barrel of honey according to a daily exchange rate (as he's got some raspberry left from selling the previous barrel) and immediately (on day d\u2009+\u20091) give his friend the borrowed barrel of honey as well as c kilograms of raspberry for renting the barrel.The bear wants to execute his plan at most once and then hibernate. What maximum number of kilograms of raspberry can he earn? Note that if at some point of the plan the bear runs out of the raspberry, then he won't execute such a plan.", "input_spec": "The first line contains two space-separated integers, n and c (2\u2009\u2264\u2009n\u2009\u2264\u2009100,\u20090\u2009\u2264\u2009c\u2009\u2264\u2009100), \u2014 the number of days and the number of kilos of raspberry that the bear should give for borrowing the barrel. The second line contains n space-separated integers x1,\u2009x2,\u2009...,\u2009xn (0\u2009\u2264\u2009xi\u2009\u2264\u2009100), the price of a honey barrel on day i.", "output_spec": "Print a single integer \u2014 the answer to the problem.", "sample_inputs": ["5 1\n5 10 7 3 20", "6 2\n100 1 10 40 10 40", "3 0\n1 2 3"], "sample_outputs": ["3", "97", "0"], "notes": "NoteIn the first sample the bear will lend a honey barrel at day 3 and then sell it for 7. Then the bear will buy a barrel for 3 and return it to the friend. So, the profit is (7 - 3 - 1) = 3.In the second sample bear will lend a honey barrel at day 1 and then sell it for 100. Then the bear buy the barrel for 1 at the day 2. So, the profit is (100 - 1 - 2) = 97."}, "src_uid": "411539a86f2e94eb6386bb65c9eb9557"}
{"nl": {"description": "Ujan has been lazy lately, but now has decided to bring his yard to good shape. First, he decided to paint the path from his house to the gate.The path consists of $$$n$$$ consecutive tiles, numbered from $$$1$$$ to $$$n$$$. Ujan will paint each tile in some color. He will consider the path aesthetic if for any two different tiles with numbers $$$i$$$ and $$$j$$$, such that $$$|j - i|$$$ is a divisor of $$$n$$$ greater than $$$1$$$, they have the same color. Formally, the colors of two tiles with numbers $$$i$$$ and $$$j$$$ should be the same if $$$|i-j| > 1$$$ and $$$n \\bmod |i-j| = 0$$$ (where $$$x \\bmod y$$$ is the remainder when dividing $$$x$$$ by $$$y$$$).Ujan wants to brighten up space. What is the maximum number of different colors that Ujan can use, so that the path is aesthetic?", "input_spec": "The first line of input contains a single integer $$$n$$$ ($$$1 \\leq n \\leq 10^{12}$$$), the length of the path.", "output_spec": "Output a single integer, the maximum possible number of colors that the path can be painted in.", "sample_inputs": ["4", "5"], "sample_outputs": ["2", "5"], "notes": "NoteIn the first sample, two colors is the maximum number. Tiles $$$1$$$ and $$$3$$$ should have the same color since $$$4 \\bmod |3-1| = 0$$$. Also, tiles $$$2$$$ and $$$4$$$ should have the same color since $$$4 \\bmod |4-2| = 0$$$.In the second sample, all five colors can be used.  "}, "src_uid": "f553e89e267c223fd5acf0dd2bc1706b"}
{"nl": {"description": "Little Sofia is in fourth grade. Today in the geometry lesson she learned about segments and squares. On the way home, she decided to draw $$$n$$$ squares in the snow with a side length of $$$1$$$. For simplicity, we assume that Sofia lives on a plane and can draw only segments of length $$$1$$$, parallel to the coordinate axes, with vertices at integer points.In order to draw a segment, Sofia proceeds as follows. If she wants to draw a vertical segment with the coordinates of the ends $$$(x, y)$$$ and $$$(x, y+1)$$$. Then Sofia looks if there is already a drawn segment with the coordinates of the ends $$$(x', y)$$$ and $$$(x', y+1)$$$ for some $$$x'$$$. If such a segment exists, then Sofia quickly draws a new segment, using the old one as a guideline. If there is no such segment, then Sofia has to take a ruler and measure a new segment for a long time. Same thing happens when Sofia wants to draw a horizontal segment, but only now she checks for the existence of a segment with the same coordinates $$$x$$$, $$$x+1$$$ and the differing coordinate $$$y$$$.For example, if Sofia needs to draw one square, she will have to draw two segments using a ruler:   After that, she can draw the remaining two segments, using the first two as a guide:   If Sofia needs to draw two squares, she will have to draw three segments using a ruler:   After that, she can draw the remaining four segments, using the first three as a guide:   Sofia is in a hurry, so she wants to minimize the number of segments that she will have to draw with a ruler without a guide. Help her find this minimum number.", "input_spec": "The only line of input contains a single integer $$$n$$$ ($$$1 \\le n \\le 10^{9}$$$), the number of squares that Sofia wants to draw.", "output_spec": "Print single integer, the minimum number of segments that Sofia will have to draw with a ruler without a guide in order to draw $$$n$$$ squares in the manner described above.", "sample_inputs": ["1", "2", "4"], "sample_outputs": ["2", "3", "4"], "notes": null}, "src_uid": "eb8212aec951f8f69b084446da73eaf7"}
{"nl": {"description": "You are given a rectangular cake, represented as an r\u2009\u00d7\u2009c grid. Each cell either has an evil strawberry, or is empty. For example, a 3\u2009\u00d7\u20094 cake may look as follows:  The cakeminator is going to eat the cake! Each time he eats, he chooses a row or a column that does not contain any evil strawberries and contains at least one cake cell that has not been eaten before, and eats all the cake cells there. He may decide to eat any number of times.Please output the maximum number of cake cells that the cakeminator can eat.", "input_spec": "The first line contains two integers r and c (2\u2009\u2264\u2009r,\u2009c\u2009\u2264\u200910), denoting the number of rows and the number of columns of the cake. The next r lines each contains c characters \u2014 the j-th character of the i-th line denotes the content of the cell at row i and column j, and is either one of these:    '.' character denotes a cake cell with no evil strawberry;  'S' character denotes a cake cell with an evil strawberry. ", "output_spec": "Output the maximum number of cake cells that the cakeminator can eat.", "sample_inputs": ["3 4\nS...\n....\n..S."], "sample_outputs": ["8"], "notes": "NoteFor the first example, one possible way to eat the maximum number of cake cells is as follows (perform 3 eats).      "}, "src_uid": "ebaf7d89c623d006a6f1ffd025892102"}
{"nl": {"description": "Monocarp has decided to buy a new TV set and hang it on the wall in his flat. The wall has enough free space so Monocarp can buy a TV set with screen width not greater than $$$a$$$ and screen height not greater than $$$b$$$. Monocarp is also used to TV sets with a certain aspect ratio: formally, if the width of the screen is $$$w$$$, and the height of the screen is $$$h$$$, then the following condition should be met: $$$\\frac{w}{h} = \\frac{x}{y}$$$.There are many different TV sets in the shop. Monocarp is sure that for any pair of positive integers $$$w$$$ and $$$h$$$ there is a TV set with screen width $$$w$$$ and height $$$h$$$ in the shop.Monocarp isn't ready to choose the exact TV set he is going to buy. Firstly he wants to determine the optimal screen resolution. He has decided to try all possible variants of screen size. But he must count the number of pairs of positive integers $$$w$$$ and $$$h$$$, beforehand, such that $$$(w \\le a)$$$, $$$(h \\le b)$$$ and $$$(\\frac{w}{h} = \\frac{x}{y})$$$.In other words, Monocarp wants to determine the number of TV sets having aspect ratio $$$\\frac{x}{y}$$$, screen width not exceeding $$$a$$$, and screen height not exceeding $$$b$$$. Two TV sets are considered different if they have different screen width or different screen height.", "input_spec": "The first line contains four integers $$$a$$$, $$$b$$$, $$$x$$$, $$$y$$$ ($$$1 \\le a, b, x, y \\le 10^{18}$$$)\u00a0\u2014 the constraints on the screen width and height, and on the aspect ratio.", "output_spec": "Print one integer\u00a0\u2014 the number of different variants to choose TV screen width and screen height so that they meet the aforementioned constraints.", "sample_inputs": ["17 15 5 3", "14 16 7 22", "4 2 6 4", "1000000000000000000 1000000000000000000 999999866000004473 999999822000007597"], "sample_outputs": ["3", "0", "1", "1000000063"], "notes": "NoteIn the first example, there are $$$3$$$ possible variants: $$$(5, 3)$$$, $$$(10, 6)$$$, $$$(15, 9)$$$.In the second example, there is no TV set meeting the constraints.In the third example, there is only one variant: $$$(3, 2)$$$."}, "src_uid": "907ac56260e84dbb6d98a271bcb2d62d"}
{"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\u2009\u2264\u2009i\u2009\u2264\u2009k), such that 1\u2009\u2264\u2009k\u2009\u2264\u20093 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\u2009\u2264\u2009n\u2009<\u2009109).", "output_spec": "In the first line print k (1\u2009\u2264\u2009k\u2009\u2264\u20093), 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": "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\u2009\u2264\u2009n\u2009\u2264\u200940,\u20092\u2009\u2264\u2009p\u2009\u2264\u20091000) \u2014 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 \u2014 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": "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\u2009+\u20091 (1\u2009\u2264\u2009i\u2009<\u2009n) 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,\u2009a2,\u2009...,\u2009an 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\u2009\u2264\u2009n\u2009\u2264\u2009100, 1\u2009\u2264\u2009m\u2009\u2264\u2009n, 1\u2009\u2264\u2009k\u2009\u2264\u2009100)\u00a0\u2014 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,\u2009a2,\u2009...,\u2009an (0\u2009\u2264\u2009ai\u2009\u2264\u2009100)\u00a0\u2014 denoting the availability and the prices of the houses. It is guaranteed that am\u2009=\u20090 and that it is possible to purchase some house with no more than k dollars.", "output_spec": "Print one integer\u00a0\u2014 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\u2009=\u200920 dollars, Zane can buy only house 5. The distance from house m\u2009=\u20091 to house 5 is 10\u2009+\u200910\u2009+\u200910\u2009+\u200910\u2009=\u200940 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\u2009=\u20093 and house 6 are only 30 meters away, while house m\u2009=\u20093 and house 7 are 40 meters away."}, "src_uid": "57860e9a5342a29257ce506063d37624"}
{"nl": {"description": "One Sunday Petr went to a bookshop and bought a new book on sports programming. The book had exactly n pages.Petr decided to start reading it starting from the next day, that is, from Monday. Petr's got a very tight schedule and for each day of the week he knows how many pages he will be able to read on that day. Some days are so busy that Petr will have no time to read whatsoever. However, we know that he will be able to read at least one page a week.Assuming that Petr will not skip days and will read as much as he can every day, determine on which day of the week he will read the last page of the book.", "input_spec": "The first input line contains the single integer n (1\u2009\u2264\u2009n\u2009\u2264\u20091000) \u2014 the number of pages in the book. The second line contains seven non-negative space-separated integers that do not exceed 1000 \u2014 those integers represent how many pages Petr can read on Monday, Tuesday, Wednesday, Thursday, Friday, Saturday and Sunday correspondingly. It is guaranteed that at least one of those numbers is larger than zero.", "output_spec": "Print a single number \u2014 the number of the day of the week, when Petr will finish reading the book. The days of the week are numbered starting with one in the natural order: Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday.", "sample_inputs": ["100\n15 20 20 15 10 30 45", "2\n1 0 0 0 0 0 0"], "sample_outputs": ["6", "1"], "notes": "NoteNote to the first sample:By the end of Monday and therefore, by the beginning of Tuesday Petr has 85 pages left. He has 65 pages left by Wednesday, 45 by Thursday, 30 by Friday, 20 by Saturday and on Saturday Petr finishes reading the book (and he also has time to read 10 pages of something else).Note to the second sample:On Monday of the first week Petr will read the first page. On Monday of the second week Petr will read the second page and will finish reading the book."}, "src_uid": "007a779d966e2e9219789d6d9da7002c"}
{"nl": {"description": "Sasha is a very happy guy, that's why he is always on the move. There are $$$n$$$ cities in the country where Sasha lives. They are all located on one straight line, and for convenience, they are numbered from $$$1$$$ to $$$n$$$ in increasing order. The distance between any two adjacent cities is equal to $$$1$$$ kilometer. Since all roads in the country are directed, it's possible to reach the city $$$y$$$ from the city $$$x$$$ only if $$$x < y$$$. Once Sasha decided to go on a trip around the country and to visit all $$$n$$$ cities. He will move with the help of his car, Cheetah-2677. The tank capacity of this model is $$$v$$$ liters, and it spends exactly $$$1$$$ liter of fuel for $$$1$$$ kilometer of the way. At the beginning of the journey, the tank is empty. Sasha is located in the city with the number $$$1$$$ and wants to get to the city with the number $$$n$$$. There is a gas station in each city. In the $$$i$$$-th city, the price of $$$1$$$ liter of fuel is $$$i$$$ dollars. It is obvious that at any moment of time, the tank can contain at most $$$v$$$ liters of fuel.Sasha doesn't like to waste money, that's why he wants to know what is the minimum amount of money is needed to finish the trip if he can buy fuel in any city he wants. Help him to figure it out!", "input_spec": "The first line contains two integers $$$n$$$ and $$$v$$$ ($$$2 \\le n \\le 100$$$, $$$1 \\le v \\le 100$$$) \u00a0\u2014 the number of cities in the country and the capacity of the tank.", "output_spec": "Print one integer\u00a0\u2014 the minimum amount of money that is needed to finish the trip.", "sample_inputs": ["4 2", "7 6"], "sample_outputs": ["4", "6"], "notes": "NoteIn the first example, Sasha can buy $$$2$$$ liters for $$$2$$$ dollars ($$$1$$$ dollar per liter) in the first city, drive to the second city, spend $$$1$$$ liter of fuel on it, then buy $$$1$$$ liter for $$$2$$$ dollars in the second city and then drive to the $$$4$$$-th city. Therefore, the answer is $$$1+1+2=4$$$.In the second example, the capacity of the tank allows to fill the tank completely in the first city, and drive to the last city without stops in other cities."}, "src_uid": "f8eb96deeb82d9f011f13d7dac1e1ab7"}
{"nl": {"description": "Hideo Kojima has just quit his job at Konami. Now he is going to find a new place to work. Despite being such a well-known person, he still needs a CV to apply for a job.During all his career Hideo has produced n games. Some of them were successful, some were not. Hideo wants to remove several of them (possibly zero) from his CV to make a better impression on employers. As a result there should be no unsuccessful game which comes right after successful one in his CV.More formally, you are given an array s1,\u2009s2,\u2009...,\u2009sn of zeros and ones. Zero corresponds to an unsuccessful game, one \u2014 to a successful one. Games are given in order they were produced, and Hideo can't swap these values. He should remove some elements from this array in such a way that no zero comes right after one.Besides that, Hideo still wants to mention as much games in his CV as possible. Help this genius of a man determine the maximum number of games he can leave in his CV.", "input_spec": "The first line contains one integer number n (1\u2009\u2264\u2009n\u2009\u2264\u2009100). The second line contains n space-separated integer numbers s1,\u2009s2,\u2009...,\u2009sn (0\u2009\u2264\u2009si\u2009\u2264\u20091). 0 corresponds to an unsuccessful game, 1 \u2014 to a successful one.", "output_spec": "Print one integer \u2014 the maximum number of games Hideo can leave in his CV so that no unsuccessful game comes after a successful one.", "sample_inputs": ["4\n1 1 0 1", "6\n0 1 0 0 1 0", "1\n0"], "sample_outputs": ["3", "4", "1"], "notes": null}, "src_uid": "c7b1f0b40e310f99936d1c33e4816b95"}
{"nl": {"description": "You are given two strings $$$s$$$ and $$$t$$$ consisting of lowercase Latin letters. The length of $$$t$$$ is $$$2$$$ (i.e. this string consists only of two characters).In one move, you can choose any character of $$$s$$$ and replace it with any lowercase Latin letter. More formally, you choose some $$$i$$$ and replace $$$s_i$$$ (the character at the position $$$i$$$) with some character from 'a' to 'z'.You want to do no more than $$$k$$$ replacements in such a way that maximizes the number of occurrences of $$$t$$$ in $$$s$$$ as a subsequence.Recall that a subsequence is a sequence that can be derived from the given sequence by deleting zero or more elements without changing the order of the remaining elements.", "input_spec": "The first line of the input contains two integers $$$n$$$ and $$$k$$$ ($$$2 \\le n \\le 200$$$; $$$0 \\le k \\le n$$$) \u2014 the length of $$$s$$$ and the maximum number of moves you can make. The second line of the input contains the string $$$s$$$ consisting of $$$n$$$ lowercase Latin letters. The third line of the input contains the string $$$t$$$ consisting of two lowercase Latin letters.", "output_spec": "Print one integer \u2014 the maximum possible number of occurrences of $$$t$$$ in $$$s$$$ as a subsequence if you replace no more than $$$k$$$ characters in $$$s$$$ optimally.", "sample_inputs": ["4 2\nbbaa\nab", "7 3\nasddsaf\nsd", "15 6\nqwertyhgfdsazxc\nqa", "7 2\nabacaba\naa"], "sample_outputs": ["3", "10", "16", "15"], "notes": "NoteIn the first example, you can obtain the string \"abab\" replacing $$$s_1$$$ with 'a' and $$$s_4$$$ with 'b'. Then the answer is $$$3$$$.In the second example, you can obtain the string \"ssddsdd\" and get the answer $$$10$$$.In the fourth example, you can obtain the string \"aaacaaa\" and get the answer $$$15$$$."}, "src_uid": "9c700390ac13942cbde7c3428965b18a"}
{"nl": {"description": "Polycarp loves ciphers. He has invented his own cipher called repeating.Repeating cipher is used for strings. To encrypt the string $$$s=s_{1}s_{2} \\dots s_{m}$$$ ($$$1 \\le m \\le 10$$$), Polycarp uses the following algorithm:  he writes down $$$s_1$$$ ones,  he writes down $$$s_2$$$ twice,  he writes down $$$s_3$$$ three times,  ...  he writes down $$$s_m$$$ $$$m$$$ times. For example, if $$$s$$$=\"bab\" the process is: \"b\" $$$\\to$$$ \"baa\" $$$\\to$$$ \"baabbb\". So the encrypted $$$s$$$=\"bab\" is \"baabbb\".Given string $$$t$$$ \u2014 the result of encryption of some string $$$s$$$. Your task is to decrypt it, i.\u2009e. find the string $$$s$$$.", "input_spec": "The first line contains integer $$$n$$$ ($$$1 \\le n \\le 55$$$) \u2014 the length of the encrypted string. The second line of the input contains $$$t$$$ \u2014 the result of encryption of some string $$$s$$$. It contains only lowercase Latin letters. The length of $$$t$$$ is exactly $$$n$$$. It is guaranteed that the answer to the test exists.", "output_spec": "Print such string $$$s$$$ that after encryption it equals $$$t$$$.", "sample_inputs": ["6\nbaabbb", "10\nooopppssss", "1\nz"], "sample_outputs": ["bab", "oops", "z"], "notes": null}, "src_uid": "08e8c0c37b223f6aae01d5609facdeaf"}
{"nl": {"description": "Vasya has found a strange device. On the front panel of a device there are: a red button, a blue button and a display showing some positive integer. After clicking the red button, device multiplies the displayed number by two. After clicking the blue button, device subtracts one from the number on the display. If at some point the number stops being positive, the device breaks down. The display can show arbitrarily large numbers. Initially, the display shows number n.Bob wants to get number m on the display. What minimum number of clicks he has to make in order to achieve this result?", "input_spec": "The first and the only line of the input contains two distinct integers n and m (1\u2009\u2264\u2009n,\u2009m\u2009\u2264\u2009104), separated by a space .", "output_spec": "Print a single number \u2014 the minimum number of times one needs to push the button required to get the number m out of number n.", "sample_inputs": ["4 6", "10 1"], "sample_outputs": ["2", "9"], "notes": "NoteIn the first example you need to push the blue button once, and then push the red button once.In the second example, doubling the number is unnecessary, so we need to push the blue button nine times."}, "src_uid": "861f8edd2813d6d3a5ff7193a804486f"}
{"nl": {"description": "Apart from Nian, there is a daemon named Sui, which terrifies children and causes them to become sick. Parents give their children money wrapped in red packets and put them under the pillow, so that when Sui tries to approach them, it will be driven away by the fairies inside.Big Banban is hesitating over the amount of money to give out. He considers loops to be lucky since it symbolizes unity and harmony.He would like to find a positive integer n not greater than 1018, such that there are exactly k loops in the decimal representation of n, or determine that such n does not exist.A loop is a planar area enclosed by lines in the digits' decimal representation written in Arabic numerals. For example, there is one loop in digit 4, two loops in 8 and no loops in 5. Refer to the figure below for all exact forms.  ", "input_spec": "The first and only line contains an integer k (1\u2009\u2264\u2009k\u2009\u2264\u2009106)\u00a0\u2014 the desired number of loops.", "output_spec": "Output an integer\u00a0\u2014 if no such n exists, output -1; otherwise output any such n. In the latter case, your output should be a positive decimal integer not exceeding 1018.", "sample_inputs": ["2", "6"], "sample_outputs": ["462", "8080"], "notes": null}, "src_uid": "0c9973792c1976c5710f88e3520cda4e"}
{"nl": {"description": "You have a nuts and lots of boxes. The boxes have a wonderful feature: if you put x (x\u2009\u2265\u20090) divisors (the spacial bars that can divide a box) to it, you get a box, divided into x\u2009+\u20091 sections.You are minimalist. Therefore, on the one hand, you are against dividing some box into more than k sections. On the other hand, you are against putting more than v nuts into some section of the box. What is the minimum number of boxes you have to use if you want to put all the nuts in boxes, and you have b divisors?Please note that you need to minimize the number of used boxes, not sections. You do not have to minimize the number of used divisors.", "input_spec": "The first line contains four space-separated integers k, a, b, v (2\u2009\u2264\u2009k\u2009\u2264\u20091000; 1\u2009\u2264\u2009a,\u2009b,\u2009v\u2009\u2264\u20091000) \u2014 the maximum number of sections in the box, the number of nuts, the number of divisors and the capacity of each section of the box.", "output_spec": "Print a single integer \u2014 the answer to the problem.", "sample_inputs": ["3 10 3 3", "3 10 1 3", "100 100 1 1000"], "sample_outputs": ["2", "3", "1"], "notes": "NoteIn the first sample you can act like this:   Put two divisors to the first box. Now the first box has three sections and we can put three nuts into each section. Overall, the first box will have nine nuts.  Do not put any divisors into the second box. Thus, the second box has one section for the last nut. In the end we've put all the ten nuts into boxes.The second sample is different as we have exactly one divisor and we put it to the first box. The next two boxes will have one section each."}, "src_uid": "7cff20b1c63a694baca69bdf4bdb2652"}
{"nl": {"description": "Little girl Alyona is in a shop to buy some copybooks for school. She study four subjects so she wants to have equal number of copybooks for each of the subjects. There are three types of copybook's packs in the shop: it is possible to buy one copybook for a rubles, a pack of two copybooks for b rubles, and a pack of three copybooks for c rubles. Alyona already has n copybooks.What is the minimum amount of rubles she should pay to buy such number of copybooks k that n\u2009+\u2009k is divisible by 4? There are infinitely many packs of any type in the shop. Alyona can buy packs of different type in the same purchase.", "input_spec": "The only line contains 4 integers n, a, b, c (1\u2009\u2264\u2009n,\u2009a,\u2009b,\u2009c\u2009\u2264\u2009109).", "output_spec": "Print the minimum amount of rubles she should pay to buy such number of copybooks k that n\u2009+\u2009k is divisible by 4.", "sample_inputs": ["1 1 3 4", "6 2 1 1", "4 4 4 4", "999999999 1000000000 1000000000 1000000000"], "sample_outputs": ["3", "1", "0", "1000000000"], "notes": "NoteIn the first example Alyona can buy 3 packs of 1 copybook for 3a\u2009=\u20093 rubles in total. After that she will have 4 copybooks which she can split between the subjects equally. In the second example Alyuna can buy a pack of 2 copybooks for b\u2009=\u20091 ruble. She will have 8 copybooks in total.In the third example Alyona can split the copybooks she already has between the 4 subject equally, so she doesn't need to buy anything.In the fourth example Alyona should buy one pack of one copybook."}, "src_uid": "c74537b7e2032c1d928717dfe15ccfb8"}
{"nl": {"description": "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": "Cucumber boy is fan of Kyubeat, a famous music game.Kyubeat has 16 panels for playing arranged in 4\u2009\u00d7\u20094 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\u2009\u2264\u2009k\u2009\u2264\u20095) \u2014 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) \u2014 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": "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 '.' \u2014 the description of the left desk in the current row; a character '-' \u2014 the aisle; two characters, each is '*' or '.' \u2014 the description of the center desk in the current row; a character '-' \u2014 the aisle; two characters, each is '*' or '.' \u2014 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": "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$$$)\u00a0\u2014 the number of students and the total duration of the exam in minutes, respectively. The second line of the input contains $$$n$$$ integers $$$t_i$$$ ($$$1 \\le t_i \\le 100$$$)\u00a0\u2014 time in minutes that $$$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": "After winning gold and silver in IOI 2014, Akshat and Malvika want to have some fun. Now they are playing a game on a grid made of n horizontal and m vertical sticks.An intersection point is any point on the grid which is formed by the intersection of one horizontal stick and one vertical stick.In the grid shown below, n\u2009=\u20093 and m\u2009=\u20093. There are n\u2009+\u2009m\u2009=\u20096 sticks in total (horizontal sticks are shown in red and vertical sticks are shown in green). There are n\u00b7m\u2009=\u20099 intersection points, numbered from 1 to 9.  The rules of the game are very simple. The players move in turns. Akshat won gold, so he makes the first move. During his/her move, a player must choose any remaining intersection point and remove from the grid all sticks which pass through this point. A player will lose the game if he/she cannot make a move (i.e. there are no intersection points remaining on the grid at his/her move).Assume that both players play optimally. Who will win the game?", "input_spec": "The first line of input contains two space-separated integers, n and m (1\u2009\u2264\u2009n,\u2009m\u2009\u2264\u2009100).", "output_spec": "Print a single line containing \"Akshat\" or \"Malvika\" (without the quotes), depending on the winner of the game.", "sample_inputs": ["2 2", "2 3", "3 3"], "sample_outputs": ["Malvika", "Malvika", "Akshat"], "notes": "NoteExplanation of the first sample:The grid has four intersection points, numbered from 1 to 4.  If Akshat chooses intersection point 1, then he will remove two sticks (1\u2009-\u20092 and 1\u2009-\u20093). The resulting grid will look like this.  Now there is only one remaining intersection point (i.e. 4). Malvika must choose it and remove both remaining sticks. After her move the grid will be empty.In the empty grid, Akshat cannot make any move, hence he will lose.Since all 4 intersection points of the grid are equivalent, Akshat will lose no matter which one he picks."}, "src_uid": "a4b9ce9c9f170a729a97af13e81b5fe4"}
{"nl": {"description": "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\u00a0\u2014 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$$$ students, BeaverKing\u00a0\u2014 by $$$B$$$ students and $$$C$$$ students visited both restaurants. Vasya also knows that there are $$$N$$$ students in his group.Based on this info, Vasya wants to determine either if his data contradicts itself or, if it doesn't, how many students in his group didn't pass the exam. Can you help him so he won't waste his valuable preparation time?", "input_spec": "The first line contains four integers\u00a0\u2014 $$$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$$$ \u2014 BeaverKing, $$$C$$$ \u2014 both of the restaurants and at least one student is left home (it is known that Vasya didn't pass the exam and stayed at home), output one integer\u00a0\u2014 amount of students (including Vasya) who did not pass the exam.  If such a distribution does not exist and Vasya made a mistake while determining the numbers $$$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": "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\u2009\u00d7\u2009m, 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\u2009\u2264\u2009n,\u2009m\u2009\u2264\u2009100)\u00a0\u2014 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": "Petya loves lucky numbers. Everybody knows that positive integers are lucky if their decimal representation doesn't contain digits other than 4 and 7. For example, numbers 47, 744, 4 are lucky and 5, 17, 467 are not.Lucky number is super lucky if it's decimal representation contains equal amount of digits 4 and 7. For example, numbers 47, 7744, 474477 are super lucky and 4, 744, 467 are not.One day Petya came across a positive integer n. Help him to find the least super lucky number which is not less than n.", "input_spec": "The only line contains a positive integer n (1\u2009\u2264\u2009n\u2009\u2264\u200910100000). This number doesn't have leading zeroes.", "output_spec": "Output the least super lucky number that is more than or equal to n.", "sample_inputs": ["4500", "47"], "sample_outputs": ["4747", "47"], "notes": null}, "src_uid": "77b5f83cdadf4b0743618a46b646a849"}
{"nl": {"description": "Iahub and his friend Floyd have started painting a wall. Iahub is painting the wall red and Floyd is painting it pink. You can consider the wall being made of a very large number of bricks, numbered 1, 2, 3 and so on. Iahub has the following scheme of painting: he skips x\u2009-\u20091 consecutive bricks, then he paints the x-th one. That is, he'll paint bricks x, 2\u00b7x, 3\u00b7x and so on red. Similarly, Floyd skips y\u2009-\u20091 consecutive bricks, then he paints the y-th one. Hence he'll paint bricks y, 2\u00b7y, 3\u00b7y and so on pink.After painting the wall all day, the boys observed that some bricks are painted both red and pink. Iahub has a lucky number a and Floyd has a lucky number b. Boys wonder how many bricks numbered no less than a and no greater than b are painted both red and pink. This is exactly your task: compute and print the answer to the question. ", "input_spec": "The input will have a single line containing four integers in this order: x, y, a, b. (1\u2009\u2264\u2009x,\u2009y\u2009\u2264\u20091000, 1\u2009\u2264\u2009a,\u2009b\u2009\u2264\u20092\u00b7109, a\u2009\u2264\u2009b).", "output_spec": "Output a single integer \u2014 the number of bricks numbered no less than a and no greater than b that are painted both red and pink.", "sample_inputs": ["2 3 6 18"], "sample_outputs": ["3"], "notes": "NoteLet's look at the bricks from a to b (a\u2009=\u20096,\u2009b\u2009=\u200918). The bricks colored in red are numbered 6, 8, 10, 12, 14, 16, 18. The bricks colored in pink are numbered 6, 9, 12, 15, 18. The bricks colored in both red and pink are numbered with 6, 12 and 18. "}, "src_uid": "c7aa8a95d5f8832015853cffa1374c48"}
{"nl": {"description": "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\u2009\u2264\u2009n\u2009\u2264\u20091012) \u2014 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": "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\u2009\u2264\u2009n\u2009\u2264\u200924) integers a1,\u2009a2,\u2009...,\u2009an, 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\u2009\u2264\u2009n\u2009\u2264\u200924) \u2014 the number of integers. The second line contains n integers a1,\u2009a2,\u2009...,\u2009an (28\u2009\u2264\u2009ai\u2009\u2264\u200931) \u2014 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) \u2014 March \u2014 April \u2013 May \u2014 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 \u2014 January \u2014 February (non-leap year)."}, "src_uid": "d60c8895cebcc5d0c6459238edbdb945"}
{"nl": {"description": "In mathematics, a subsequence is a sequence that can be derived from another sequence by deleting some elements without changing the order of the remaining elements. For example, the sequence BDF is a subsequence of ABCDEF. A substring of a string is a continuous subsequence of the string. For example, BCD is a substring of ABCDEF.You are given two strings s1, s2 and another string called virus. Your task is to find the longest common subsequence of s1 and s2, such that it doesn't contain virus as a substring.", "input_spec": "The input contains three strings in three separate lines: s1, s2 and virus (1\u2009\u2264\u2009|s1|,\u2009|s2|,\u2009|virus|\u2009\u2264\u2009100). Each string consists only of uppercase English letters.", "output_spec": "Output the longest common subsequence of s1 and s2 without virus as a substring. If there are multiple answers, any of them will be accepted.  If there is no valid common subsequence, output 0.", "sample_inputs": ["AJKEQSLOBSROFGZ\nOVGURWZLWVLUXTH\nOZ", "AA\nA\nA"], "sample_outputs": ["ORZ", "0"], "notes": null}, "src_uid": "391c2abbe862139733fcb997ba1629b8"}
{"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\u2009\u2264\u2009n\u2009\u2264\u2009109).", "output_spec": "Output one integer \u2014 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": "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$$$).", "output_spec": "Output a single integer \u2014 the number of stupid colorings modulo $$$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$$$ colorings.  "}, "src_uid": "1738dc65af1fffa445cb0c3074c6bedb"}
{"nl": {"description": "We consider a positive integer perfect, if and only if the sum of its digits is exactly $$$10$$$. Given a positive integer $$$k$$$, your task is to find the $$$k$$$-th smallest perfect positive integer.", "input_spec": "A single line with a positive integer $$$k$$$ ($$$1 \\leq k \\leq 10\\,000$$$).", "output_spec": "A single number, denoting the $$$k$$$-th smallest perfect integer.", "sample_inputs": ["1", "2"], "sample_outputs": ["19", "28"], "notes": "NoteThe first perfect integer is $$$19$$$ and the second one is $$$28$$$."}, "src_uid": "0a98a6a15e553ce11cb468d3330fc86a"}
{"nl": {"description": "Vasya has n burles. One bottle of Ber-Cola costs a burles and one Bars bar costs b burles. He can buy any non-negative integer number of bottles of Ber-Cola and any non-negative integer number of Bars bars.Find out if it's possible to buy some amount of bottles of Ber-Cola and Bars bars and spend exactly n burles.In other words, you should find two non-negative integers x and y such that Vasya can buy x bottles of Ber-Cola and y Bars bars and x\u00b7a\u2009+\u2009y\u00b7b\u2009=\u2009n or tell that it's impossible.", "input_spec": "First line contains single integer n (1\u2009\u2264\u2009n\u2009\u2264\u200910\u2009000\u2009000)\u00a0\u2014 amount of money, that Vasya has. Second line contains single integer a (1\u2009\u2264\u2009a\u2009\u2264\u200910\u2009000\u2009000)\u00a0\u2014 cost of one bottle of Ber-Cola. Third line contains single integer b (1\u2009\u2264\u2009b\u2009\u2264\u200910\u2009000\u2009000)\u00a0\u2014 cost of one Bars bar.", "output_spec": "If Vasya can't buy Bars and Ber-Cola in such a way to spend exactly n burles print \u00abNO\u00bb (without quotes). Otherwise in first line print \u00abYES\u00bb (without quotes). In second line print two non-negative integers x and y\u00a0\u2014 number of bottles of Ber-Cola and number of Bars bars Vasya should buy in order to spend exactly n burles, i.e. x\u00b7a\u2009+\u2009y\u00b7b\u2009=\u2009n. If there are multiple answers print any of them. Any of numbers x and y can be equal 0.", "sample_inputs": ["7\n2\n3", "100\n25\n10", "15\n4\n8", "9960594\n2551\n2557"], "sample_outputs": ["YES\n2 1", "YES\n0 10", "NO", "YES\n1951 1949"], "notes": "NoteIn first example Vasya can buy two bottles of Ber-Cola and one Bars bar. He will spend exactly 2\u00b72\u2009+\u20091\u00b73\u2009=\u20097 burles.In second example Vasya can spend exactly n burles multiple ways:   buy two bottles of Ber-Cola and five Bars bars;  buy four bottles of Ber-Cola and don't buy Bars bars;  don't buy Ber-Cola and buy 10 Bars bars. In third example it's impossible to but Ber-Cola and Bars bars in order to spend exactly n burles."}, "src_uid": "b031daf3b980e03218167f40f39e7b01"}
{"nl": {"description": "Nowadays all circuses in Berland have a round arena with diameter 13 meters, but in the past things were different.In Ancient Berland arenas in circuses were shaped as a regular (equiangular) polygon, the size and the number of angles could vary from one circus to another. In each corner of the arena there was a special pillar, and the rope strung between the pillars marked the arena edges.Recently the scientists from Berland have discovered the remains of the ancient circus arena. They found only three pillars, the others were destroyed by the time.You are given the coordinates of these three pillars. Find out what is the smallest area that the arena could have.", "input_spec": "The input file consists of three lines, each of them contains a pair of numbers \u2013\u2013 coordinates of the pillar. Any coordinate doesn't exceed 1000 by absolute value, and is given with at most six digits after decimal point.", "output_spec": "Output the smallest possible area of the ancient arena. This number should be accurate to at least 6 digits after the decimal point. It's guaranteed that the number of angles in the optimal polygon is not larger than 100.", "sample_inputs": ["0.000000 0.000000\n1.000000 1.000000\n0.000000 1.000000"], "sample_outputs": ["1.00000000"], "notes": null}, "src_uid": "980f4094b3cfc647d6f74e840b1bfb62"}
{"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\u2009+\u20092\u2009=\u20093 cubes, the third level must have 1\u2009+\u20092\u2009+\u20093\u2009=\u20096 cubes, and so on. Thus, the i-th level of the pyramid must have 1\u2009+\u20092\u2009+\u2009...\u2009+\u2009(i\u2009-\u20091)\u2009+\u2009i 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\u2009\u2264\u2009n\u2009\u2264\u2009104) \u2014 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": "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$$$) \u2014 the number of test cases in the input. Then $$$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$$$-th day. It is guaranteed that the sum of the values \u200b\u200bof $$$n$$$ for all test cases in the input does not exceed $$$100$$$.", "output_spec": "Print $$$t$$$ integers \u2014 the answers to the test cases in the input in the order they follow. The answer to a test case is the minimum number of TV shows for which you need to purchase a subscription so that you can watch episodes of the purchased TV shows on BerTV for $$$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": "n children are standing in a circle and playing a game. Children's numbers in clockwise order form a permutation a1,\u2009a2,\u2009...,\u2009an 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,\u2009l2,\u2009...,\u2009lm \u2014 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,\u2009a2,\u2009...,\u2009an. 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\u2009\u2264\u2009n,\u2009m\u2009\u2264\u2009100). The second line contains m integer numbers l1,\u2009l2,\u2009...,\u2009lm (1\u2009\u2264\u2009li\u2009\u2264\u2009n) \u2014 indices of leaders in the beginning of each step.", "output_spec": "Print such permutation of n numbers a1,\u2009a2,\u2009...,\u2009an that leaders in the game will be exactly l1,\u2009l2,\u2009...,\u2009lm 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\u2009+\u2009a2\u2009=\u20093.  Leadership goes from 3 to 3\u2009+\u2009a3\u2009=\u20095. As it's greater than 4, it's going in a circle to 1.  Leadership goes from 1 to 1\u2009+\u2009a1\u2009=\u20094.  Leadership goes from 4 to 4\u2009+\u2009a4\u2009=\u20098. Thus in circle it still remains at 4. "}, "src_uid": "4a7c959ca279d0a9bd9bbf0ce88cf72b"}
{"nl": {"description": "Kolya loves putting gnomes at the circle table and giving them coins, and Tanya loves studying triplets of gnomes, sitting in the vertexes of an equilateral triangle.More formally, there are 3n gnomes sitting in a circle. Each gnome can have from 1 to 3 coins. Let's number the places in the order they occur in the circle by numbers from 0 to 3n\u2009-\u20091, let the gnome sitting on the i-th place have ai coins. If there is an integer i (0\u2009\u2264\u2009i\u2009<\u2009n) such that ai\u2009+\u2009ai\u2009+\u2009n\u2009+\u2009ai\u2009+\u20092n\u2009\u2260\u20096, then Tanya is satisfied. Count the number of ways to choose ai so that Tanya is satisfied. As there can be many ways of distributing coins, print the remainder of this number modulo 109\u2009+\u20097. Two ways, a and b, are considered distinct if there is index i (0\u2009\u2264\u2009i\u2009<\u20093n), such that ai\u2009\u2260\u2009bi (that is, some gnome got different number of coins in these two ways).", "input_spec": "A single line contains number n (1\u2009\u2264\u2009n\u2009\u2264\u2009105) \u2014 the number of the gnomes divided by three.", "output_spec": "Print a single number \u2014 the remainder of the number of variants of distributing coins that satisfy Tanya modulo 109\u2009+\u20097.", "sample_inputs": ["1", "2"], "sample_outputs": ["20", "680"], "notes": "Note20 ways for n\u2009=\u20091 (gnome with index 0 sits on the top of the triangle, gnome 1 on the right vertex, gnome 2 on the left vertex):   "}, "src_uid": "eae87ec16c284f324d86b7e65fda093c"}
{"nl": {"description": "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\u00a0\u2014 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\u2009\u2264\u2009n\u2009\u2264\u200950)\u00a0\u2014 the number of balls Limak has. The second line contains n integers t1,\u2009t2,\u2009...,\u2009tn (1\u2009\u2264\u2009ti\u2009\u2264\u20091000) 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": "Bear Limak likes watching sports on TV. He is going to watch a game today. The game lasts 90 minutes and there are no breaks.Each minute can be either interesting or boring. If 15 consecutive minutes are boring then Limak immediately turns TV off.You know that there will be n interesting minutes t1,\u2009t2,\u2009...,\u2009tn. Your task is to calculate for how many minutes Limak will watch the game.", "input_spec": "The first line of the input contains one integer n (1\u2009\u2264\u2009n\u2009\u2264\u200990)\u00a0\u2014 the number of interesting minutes. The second line contains n integers t1,\u2009t2,\u2009...,\u2009tn (1\u2009\u2264\u2009t1\u2009<\u2009t2\u2009<\u2009... tn\u2009\u2264\u200990), given in the increasing order.", "output_spec": "Print the number of minutes Limak will watch the game.", "sample_inputs": ["3\n7 20 88", "9\n16 20 30 40 50 60 70 80 90", "9\n15 20 30 40 50 60 70 80 90"], "sample_outputs": ["35", "15", "90"], "notes": "NoteIn the first sample, minutes 21,\u200922,\u2009...,\u200935 are all boring and thus Limak will turn TV off immediately after the 35-th minute. So, he would watch the game for 35 minutes.In the second sample, the first 15 minutes are boring.In the third sample, there are no consecutive 15 boring minutes. So, Limak will watch the whole game."}, "src_uid": "5031b15e220f0ff6cc1dd3731ecdbf27"}
{"nl": {"description": "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\u2009-\u20091, while the second has the smallest possible number of places that is necessary to display any integer from 0 to m\u2009-\u20091. 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\u2009\u2264\u2009n,\u2009m\u2009\u2264\u2009109)\u00a0\u2014 the number of hours in one day and the number of minutes in one hour, respectively.", "output_spec": "Print one integer in decimal notation\u00a0\u2014 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:\u20091), (0:\u20092), (1:\u20090), (1:\u20092).In the second sample, possible pairs are: (02:\u20091), (03:\u20091), (04:\u20091), (05:\u20091), (06:\u20091)."}, "src_uid": "0930c75f57dd88a858ba7bb0f11f1b1c"}
{"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\u2009+\u2009b\u2009=\u2009c, 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\u2009+\u2009102\u2009=\u2009203, if we removed all zeros it will be 11\u2009+\u200912\u2009=\u200923 which is still a correct equation.But if the equation is 105\u2009+\u2009106\u2009=\u2009211, if we removed all zeros it will be 15\u2009+\u200916\u2009=\u2009211 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\u2009\u2264\u2009a,\u2009b\u2009\u2264\u2009109). There won't be any leading zeros in both. The value of c should be calculated as c\u2009=\u2009a\u2009+\u2009b.", "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": "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}$$$) without leading zeroes.", "output_spec": "Output a single number\u00a0\u2014 the number of trains which have departed strictly before the time $$$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$$$.The third example is explained in the statements."}, "src_uid": "d8ca1c83b431466eff6054d3b422ab47"}
{"nl": {"description": "Let us call a pair of integer numbers m-perfect, if at least one number in the pair is greater than or equal to m. Thus, the pairs (3, 3) and (0, 2) are 2-perfect while the pair (-1, 1) is not.Two integers x, y are written on the blackboard. It is allowed to erase one of them and replace it with the sum of the numbers, (x\u2009+\u2009y).What is the minimum number of such operations one has to perform in order to make the given pair of integers m-perfect?", "input_spec": "Single line of the input contains three integers x, y and m (\u2009-\u20091018\u2009\u2264\u2009x, y, m\u2009\u2264\u20091018). Please, do not use the %lld specifier to read or write 64-bit integers in C++. It is preffered to use the cin, cout streams or the %I64d specifier.", "output_spec": "Print the minimum number of operations or \"-1\" (without quotes), if it is impossible to transform the given pair to the m-perfect one.", "sample_inputs": ["1 2 5", "-1 4 15", "0 -1 5"], "sample_outputs": ["2", "4", "-1"], "notes": "NoteIn the first sample the following sequence of operations is suitable: (1, 2)  (3, 2)  (5, 2).In the second sample: (-1, 4)  (3, 4)  (7, 4)  (11, 4)  (15, 4).Finally, in the third sample x, y cannot be made positive, hence there is no proper sequence of operations."}, "src_uid": "82026a3c3d9a6bda2e2ac6e14979d821"}
{"nl": {"description": "Baby Badawy's first words were \"AND 0 SUM BIG\", so he decided to solve the following problem. Given two integers $$$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$$$)\u00a0\u2014 the number of test cases you need to solve. Each test case consists of a line containing two integers $$$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]$$$. "}, "src_uid": "2e7a9f3a97938e4a7e036520d812b97a"}
{"nl": {"description": "The only difference between easy and hard versions is on constraints. In this version constraints are lower. You can make hacks only if all versions of the problem are solved.Koa the Koala is at the beach!The beach consists (from left to right) of a shore, $$$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$$$), the depth of the sea at this point \u00a0\u2014 $$$d_x + p[t \\bmod 2k]$$$ \u00a0\u2014 can't exceed $$$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$$$) \u00a0\u2014 the number of test cases. Description of the test cases follows. The first line of each test case contains three integers $$$n$$$, $$$k$$$ and $$$l$$$ ($$$1 \\le n \\le 100; 1 \\le k \\le 100; 1 \\le l \\le 100$$$)\u00a0\u2014 the number of meters of sea Koa measured and parameters $$$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$$$) \u00a0\u2014 the depths of each meter of sea Koa measured. It is guaranteed that the sum of $$$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": "Two friends are on the coordinate axis Ox in points with integer coordinates. One of them is in the point x1\u2009=\u2009a, another one is in the point x2\u2009=\u2009b. Each of the friends can move by one along the line in any direction unlimited number of times. When a friend moves, the tiredness of a friend changes according to the following rules: the first move increases the tiredness by 1, the second move increases the tiredness by 2, the third\u00a0\u2014 by 3 and so on. For example, if a friend moves first to the left, then to the right (returning to the same point), and then again to the left his tiredness becomes equal to 1\u2009+\u20092\u2009+\u20093\u2009=\u20096.The friends want to meet in a integer point. Determine the minimum total tiredness they should gain, if they meet in the same point.", "input_spec": "The first line contains a single integer a (1\u2009\u2264\u2009a\u2009\u2264\u20091000) \u2014 the initial position of the first friend.  The second line contains a single integer b (1\u2009\u2264\u2009b\u2009\u2264\u20091000) \u2014 the initial position of the second friend. It is guaranteed that a\u2009\u2260\u2009b.", "output_spec": "Print the minimum possible total tiredness if the friends meet in the same point.", "sample_inputs": ["3\n4", "101\n99", "5\n10"], "sample_outputs": ["1", "2", "9"], "notes": "NoteIn the first example the first friend should move by one to the right (then the meeting happens at point 4), or the second friend should move by one to the left (then the meeting happens at point 3). In both cases, the total tiredness becomes 1.In the second example the first friend should move by one to the left, and the second friend should move by one to the right. Then they meet in the point 100, and the total tiredness becomes 1\u2009+\u20091\u2009=\u20092.In the third example one of the optimal ways is the following. The first friend should move three times to the right, and the second friend \u2014 two times to the left. Thus the friends meet in the point 8, and the total tiredness becomes 1\u2009+\u20092\u2009+\u20093\u2009+\u20091\u2009+\u20092\u2009=\u20099."}, "src_uid": "d3f2c6886ed104d7baba8dd7b70058da"}
{"nl": {"description": "\"Contestant who earns a score equal to or greater than the k-th place finisher's score will advance to the next round, as long as the contestant earns a positive score...\" \u2014 an excerpt from contest rules.A total of n participants took part in the contest (n\u2009\u2265\u2009k), and you already know their scores. Calculate how many participants will advance to the next round.", "input_spec": "The first line of the input contains two integers n and k (1\u2009\u2264\u2009k\u2009\u2264\u2009n\u2009\u2264\u200950) separated by a single space. The second line contains n space-separated integers a1,\u2009a2,\u2009...,\u2009an (0\u2009\u2264\u2009ai\u2009\u2264\u2009100), where ai is the score earned by the participant who got the i-th place. The given sequence is non-increasing (that is, for all i from 1 to n\u2009-\u20091 the following condition is fulfilled: ai\u2009\u2265\u2009ai\u2009+\u20091).", "output_spec": "Output the number of participants who advance to the next round.", "sample_inputs": ["8 5\n10 9 8 7 7 7 5 5", "4 2\n0 0 0 0"], "sample_outputs": ["6", "0"], "notes": "NoteIn the first example the participant on the 5th place earned 7 points. As the participant on the 6th place also earned 7 points, there are 6 advancers.In the second example nobody got a positive score."}, "src_uid": "193ec1226ffe07522caf63e84a7d007f"}
{"nl": {"description": "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$$$).", "output_spec": "Print one integer \u2014 the probability that there will be a way to set signal powers so that all constraints are met, taken modulo $$$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": "Gerald is setting the New Year table. The table has the form of a circle; its radius equals R. Gerald invited many guests and is concerned whether the table has enough space for plates for all those guests. Consider all plates to be round and have the same radii that equal r. Each plate must be completely inside the table and must touch the edge of the table. Of course, the plates must not intersect, but they can touch each other. Help Gerald determine whether the table is large enough for n plates.", "input_spec": "The first line contains three integers n, R and r (1\u2009\u2264\u2009n\u2009\u2264\u2009100, 1\u2009\u2264\u2009r,\u2009R\u2009\u2264\u20091000) \u2014 the number of plates, the radius of the table and the plates' radius.", "output_spec": "Print \"YES\" (without the quotes) if it is possible to place n plates on the table by the rules given above. If it is impossible, print \"NO\". Remember, that each plate must touch the edge of the table. ", "sample_inputs": ["4 10 4", "5 10 4", "1 10 10"], "sample_outputs": ["YES", "NO", "YES"], "notes": "NoteThe possible arrangement of the plates for the first sample is:   "}, "src_uid": "2fedbfccd893cde8f2fab2b5bf6fb6f6"}
{"nl": {"description": "From beginning till end, this message has been waiting to be conveyed.For a given unordered multiset of n lowercase English letters (\"multi\" means that a letter may appear more than once), we treat all letters as strings of length 1, and repeat the following operation n\u2009-\u20091 times:  Remove any two elements s and t from the set, and add their concatenation s\u2009+\u2009t to the set. The cost of such operation is defined to be , where f(s,\u2009c) denotes the number of times character c appears in string s.Given a non-negative integer k, construct any valid non-empty set of no more than 100\u2009000 letters, such that the minimum accumulative cost of the whole process is exactly k. It can be shown that a solution always exists.", "input_spec": "The first and only line of input contains a non-negative integer k (0\u2009\u2264\u2009k\u2009\u2264\u2009100\u2009000) \u2014 the required minimum cost.", "output_spec": "Output a non-empty string of no more than 100\u2009000 lowercase English letters \u2014 any multiset satisfying the requirements, concatenated to be a string. Note that the printed string doesn't need to be the final concatenated string. It only needs to represent an unordered multiset of letters.", "sample_inputs": ["12", "3"], "sample_outputs": ["abababab", "codeforces"], "notes": "NoteFor the multiset {'a', 'b', 'a', 'b', 'a', 'b', 'a', 'b'}, one of the ways to complete the process is as follows:  {\"ab\", \"a\", \"b\", \"a\", \"b\", \"a\", \"b\"}, with a cost of 0;  {\"aba\", \"b\", \"a\", \"b\", \"a\", \"b\"}, with a cost of 1;  {\"abab\", \"a\", \"b\", \"a\", \"b\"}, with a cost of 1;  {\"abab\", \"ab\", \"a\", \"b\"}, with a cost of 0;  {\"abab\", \"aba\", \"b\"}, with a cost of 1;  {\"abab\", \"abab\"}, with a cost of 1;  {\"abababab\"}, with a cost of 8. The total cost is 12, and it can be proved to be the minimum cost of the process."}, "src_uid": "b991c064562704b6106a6ff2a297e64a"}
{"nl": {"description": "A big company decided to launch a new series of rectangular displays, and decided that the display must have exactly n pixels. Your task is to determine the size of the rectangular display \u2014 the number of lines (rows) of pixels a and the number of columns of pixels b, so that:  there are exactly n pixels on the display;  the number of rows does not exceed the number of columns, it means a\u2009\u2264\u2009b;  the difference b\u2009-\u2009a is as small as possible. ", "input_spec": "The first line contains the positive integer n (1\u2009\u2264\u2009n\u2009\u2264\u2009106)\u00a0\u2014 the number of pixels display should have.", "output_spec": "Print two integers\u00a0\u2014 the number of rows and columns on the display. ", "sample_inputs": ["8", "64", "5", "999999"], "sample_outputs": ["2 4", "8 8", "1 5", "999 1001"], "notes": "NoteIn the first example the minimum possible difference equals 2, so on the display should be 2 rows of 4 pixels.In the second example the minimum possible difference equals 0, so on the display should be 8 rows of 8 pixels.In the third example the minimum possible difference equals 4, so on the display should be 1 row of 5 pixels."}, "src_uid": "f52af273954798a4ae38a1378bfbf77a"}
{"nl": {"description": "You are given two set of points. The first set is determined by the equation A1x\u2009+\u2009B1y\u2009+\u2009C1\u2009=\u20090, and the second one is determined by the equation A2x\u2009+\u2009B2y\u2009+\u2009C2\u2009=\u20090.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,\u2009B1,\u2009C1 separated by space. The second line contains three integer numbers A2,\u2009B2,\u2009C2 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": "Once Volodya was at the museum and saw a regular chessboard as a museum piece. And there were only four chess pieces on it: two white rooks, a white king and a black king. \"Aha, blacks certainly didn't win!\", \u2014 Volodya said and was right for sure. And your task is to say whether whites had won or not.Pieces on the chessboard are guaranteed to represent a correct position (every piece occupies one cell, no two pieces occupy the same cell and kings cannot take each other). Thus, your task is only to decide whether whites mate blacks. We would remind you that it means that the black king can be taken by one of the opponent's pieces at the moment and also it cannot move to an unbeaten position. A rook moves vertically or horizontally by any number of free cells (assuming there are no other pieces on its path), a king \u2014 to the adjacent cells (either by corner or by side). Certainly, pieces cannot leave the board. The black king might be able to take opponent's rooks at his turn (see sample 3).", "input_spec": "The input contains 4 space-separated piece positions: positions of the two rooks, the white king and the black king. Each position on 8\u2009\u00d7\u20098 chessboard is denoted by two symbols \u2014 ('a' - 'h') and ('1' - '8') \u2014 which stand for horizontal and vertical coordinates of the cell occupied by the piece. It is guaranteed, that no two pieces occupy the same cell, and kings cannot take each other.", "output_spec": "Output should contain one word: \"CHECKMATE\" if whites mate blacks, and \"OTHER\" otherwise.", "sample_inputs": ["a6 b4 c8 a8", "a6 c4 b6 b8", "a2 b1 a3 a1"], "sample_outputs": ["CHECKMATE", "OTHER", "OTHER"], "notes": null}, "src_uid": "5d05af36c7ccb0cd26a4ab45966b28a3"}
{"nl": {"description": "One day the Codeforces round author sat exams. He had n exams and he needed to get an integer from 2 to 5 for each exam. He will have to re-sit each failed exam, i.e. the exam that gets mark 2. The author would need to spend too much time and effort to make the sum of his marks strictly more than k. That could have spoilt the Codeforces round. On the other hand, if the sum of his marks is strictly less than k, the author's mum won't be pleased at all. The Codeforces authors are very smart and they always get the mark they choose themselves. Also, the Codeforces authors just hate re-sitting exams. Help the author and find the minimum number of exams he will have to re-sit if he passes the exams in the way that makes the sum of marks for all n exams equal exactly k.", "input_spec": "The single input line contains space-separated integers n and k (1\u2009\u2264\u2009n\u2009\u2264\u200950, 1\u2009\u2264\u2009k\u2009\u2264\u2009250) \u2014 the number of exams and the required sum of marks. It is guaranteed that there exists a way to pass n exams in the way that makes the sum of marks equal exactly k.", "output_spec": "Print the single number \u2014 the minimum number of exams that the author will get a 2 for, considering that the sum of marks for all exams must equal k.", "sample_inputs": ["4 8", "4 10", "1 3"], "sample_outputs": ["4", "2", "0"], "notes": "NoteIn the first sample the author has to get a 2 for all his exams.In the second sample he should get a 3 for two exams and a 2 for two more.In the third sample he should get a 3 for one exam."}, "src_uid": "5a5e46042c3f18529a03cb5c868df7e8"}
{"nl": {"description": "Since most contestants do not read this part, I have to repeat that Bitlandians are quite weird. They have their own jobs, their own working method, their own lives, their own sausages and their own games!Since you are so curious about Bitland, I'll give you the chance of peeking at one of these games.BitLGM and BitAryo are playing yet another of their crazy-looking genius-needed Bitlandish games. They've got a sequence of n non-negative integers a1,\u2009a2,\u2009...,\u2009an. The players make moves in turns. BitLGM moves first. Each player can and must do one of the two following actions in his turn:  Take one of the integers (we'll denote it as ai). Choose integer x (1\u2009\u2264\u2009x\u2009\u2264\u2009ai). And then decrease ai by x, that is, apply assignment: ai\u2009=\u2009ai\u2009-\u2009x.  Choose integer x . And then decrease all ai by x, that is, apply assignment: ai\u2009=\u2009ai\u2009-\u2009x, for all i. The player who cannot make a move loses.You're given the initial sequence a1,\u2009a2,\u2009...,\u2009an. Determine who wins, if both players plays optimally well and if BitLGM and BitAryo start playing the described game in this sequence.", "input_spec": "The first line contains an integer n (1\u2009\u2264\u2009n\u2009\u2264\u20093). The next line contains n integers a1,\u2009a2,\u2009...,\u2009an (0\u2009\u2264\u2009ai\u2009<\u2009300).", "output_spec": "Write the name of the winner (provided that both players play optimally well). Either \"BitLGM\" or \"BitAryo\" (without the quotes).", "sample_inputs": ["2\n1 1", "2\n1 2", "3\n1 2 1"], "sample_outputs": ["BitLGM", "BitAryo", "BitLGM"], "notes": null}, "src_uid": "7a33b4f94082c7ef80d7e87b58497fa7"}
{"nl": {"description": "The following problem is well-known: given integers n and m, calculate , where 2n\u2009=\u20092\u00b72\u00b7...\u00b72 (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\u2009\u2264\u2009n\u2009\u2264\u2009108). The second line contains a single integer m (1\u2009\u2264\u2009m\u2009\u2264\u2009108).", "output_spec": "Output a single integer\u00a0\u2014 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\u2009=\u200916 is equal to 10.In the second example, 58 is divisible by 21\u2009=\u20092 without remainder, and the answer is 0."}, "src_uid": "c649052b549126e600691931b512022f"}
{"nl": {"description": "Natasha is planning an expedition to Mars for $$$n$$$ people. One of the important tasks is to provide food for each participant.The warehouse has $$$m$$$ daily food packages. Each package has some food type $$$a_i$$$.Each participant must eat exactly one food package each day. Due to extreme loads, each participant must eat the same food type throughout the expedition. Different participants may eat different (or the same) types of food.Formally, for each participant $$$j$$$ Natasha should select his food type $$$b_j$$$ and each day $$$j$$$-th participant will eat one food package of type $$$b_j$$$. The values $$$b_j$$$ for different participants may be different.What is the maximum possible number of days the expedition can last, following the requirements above?", "input_spec": "The first line contains two integers $$$n$$$ and $$$m$$$ ($$$1 \\le n \\le 100$$$, $$$1 \\le m \\le 100$$$)\u00a0\u2014 the number of the expedition participants and the number of the daily food packages available. The second line contains sequence of integers $$$a_1, a_2, \\dots, a_m$$$ ($$$1 \\le a_i \\le 100$$$), where $$$a_i$$$ is the type of $$$i$$$-th food package.", "output_spec": "Print the single integer\u00a0\u2014 the number of days the expedition can last. If it is not possible to plan the expedition for even one day, print 0.", "sample_inputs": ["4 10\n1 5 2 1 1 1 2 5 7 2", "100 1\n1", "2 5\n5 4 3 2 1", "3 9\n42 42 42 42 42 42 42 42 42"], "sample_outputs": ["2", "0", "1", "3"], "notes": "NoteIn the first example, Natasha can assign type $$$1$$$ food to the first participant, the same type $$$1$$$ to the second, type $$$5$$$ to the third and type $$$2$$$ to the fourth. In this case, the expedition can last for $$$2$$$ days, since each participant can get two food packages of his food type (there will be used $$$4$$$ packages of type $$$1$$$, two packages of type $$$2$$$ and two packages of type $$$5$$$).In the second example, there are $$$100$$$ participants and only $$$1$$$ food package. In this case, the expedition can't last even $$$1$$$ day."}, "src_uid": "b7ef696a11ff96f2e9c31becc2ff50fe"}
{"nl": {"description": "Nick is interested in prime numbers. Once he read about Goldbach problem. It states that every even integer greater than 2 can be expressed as the sum of two primes. That got Nick's attention and he decided to invent a problem of his own and call it Noldbach problem. Since Nick is interested only in prime numbers, Noldbach problem states that at least k prime numbers from 2 to n inclusively can be expressed as the sum of three integer numbers: two neighboring prime numbers and 1. For example, 19 = 7 + 11 + 1, or 13 = 5 + 7 + 1.Two prime numbers are called neighboring if there are no other prime numbers between them.You are to help Nick, and find out if he is right or wrong.", "input_spec": "The first line of the input contains two integers n (2\u2009\u2264\u2009n\u2009\u2264\u20091000) and k (0\u2009\u2264\u2009k\u2009\u2264\u20091000).", "output_spec": "Output YES if at least k prime numbers from 2 to n inclusively can be expressed as it was described above. Otherwise output NO.", "sample_inputs": ["27 2", "45 7"], "sample_outputs": ["YES", "NO"], "notes": "NoteIn the first sample the answer is YES since at least two numbers can be expressed as it was described (for example, 13 and 19). In the second sample the answer is NO since it is impossible to express 7 prime numbers from 2 to 45 in the desired form."}, "src_uid": "afd2b818ed3e2a931da9d682f6ad660d"}
{"nl": {"description": "Many people are aware of DMCA \u2013 Digital Millennium Copyright Act. But another recently proposed DMCA \u2013 Digital Millennium Calculation Act \u2013 is much less known.In this problem you need to find a root of a number according to this new DMCA law.", "input_spec": "The input contains a single integer $$$a$$$ ($$$1 \\le a \\le 1000000$$$).", "output_spec": "Output the result \u2013 an integer number.", "sample_inputs": ["1", "81"], "sample_outputs": ["1", "9"], "notes": null}, "src_uid": "477a67877367dc68b3bf5143120ff45d"}
{"nl": {"description": "The only difference between easy and hard versions is the number of elements in the array.You are given an array $$$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$$$) \u2014 the number of elements in the array and the number of equal numbers required. The second line of the input contains $$$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$$$.", "output_spec": "Print one integer \u2014 the minimum possible number of operations required to obtain at least $$$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": "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\u00a0\u2014 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!\u2009=\u20091\u2009\u00d7\u20092\u2009\u00d7\u2009...\u2009\u00d7\u2009a. Specifically, 0!\u2009=\u20091.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\u2009\u2265\u2009a 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\u2009\u2264\u2009a\u2009\u2264\u2009b\u2009\u2264\u20091018).", "output_spec": "Output one line containing a single decimal digit\u00a0\u2014 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": "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!\" \u2014 thought Petya. He know for a fact that if he fulfills the parents' task in the i-th (1\u2009\u2264\u2009i\u2009\u2264\u200912) 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\u2009\u2264\u2009k\u2009\u2264\u2009100). The next line contains twelve space-separated integers: the i-th (1\u2009\u2264\u2009i\u2009\u2264\u200912) number in the line represents ai (0\u2009\u2264\u2009ai\u2009\u2264\u2009100). ", "output_spec": "Print the only integer \u2014 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\u2009=\u20090). So, it is possible for Petya not to water the flower at all."}, "src_uid": "59dfa7a4988375febc5dccc27aca90a8"}
{"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\u2009\u2264\u2009n,\u2009k\u2009\u2264\u20091012), 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": "Where do odds begin, and where do they end? Where does hope emerge, and will they ever break?Given an integer sequence a1,\u2009a2,\u2009...,\u2009an 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,\u20094,\u20095} and {1} are subsegments of sequence {1,\u20092,\u20093,\u20094,\u20095,\u20096}, while {1,\u20092,\u20094} and {7} are not.", "input_spec": "The first line of input contains a non-negative integer n (1\u2009\u2264\u2009n\u2009\u2264\u2009100) \u2014 the length of the sequence. The second line contains n space-separated non-negative integers a1,\u2009a2,\u2009...,\u2009an (0\u2009\u2264\u2009ai\u2009\u2264\u2009100) \u2014 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,\u20093,\u20095} and the requirements will be met.In the second example, divide the sequence into 3 subsegments: {1,\u20090,\u20091}, {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,\u20099,\u20099}, {3}, but this is not a valid solution because 2 is an even number."}, "src_uid": "2b8c2deb5d7e49e8e3ededabfd4427db"}
{"nl": {"description": "One day, the Grasshopper was jumping on the lawn and found a piece of paper with a string. Grasshopper became interested what is the minimum jump ability he should have in order to be able to reach the far end of the string, jumping only on vowels of the English alphabet. Jump ability is the maximum possible length of his jump. Formally, consider that at the begginning the Grasshopper is located directly in front of the leftmost character of the string. His goal is to reach the position right after the rightmost character of the string. In one jump the Grasshopper could jump to the right any distance from 1 to the value of his jump ability.    The picture corresponds to the first example. The following letters are vowels: 'A', 'E', 'I', 'O', 'U' and 'Y'.", "input_spec": "The first line contains non-empty string consisting of capital English letters. It is guaranteed that the length of the string does not exceed 100. ", "output_spec": "Print single integer a\u00a0\u2014 the minimum jump ability of the Grasshopper (in the number of symbols) that is needed to overcome the given string, jumping only on vowels.", "sample_inputs": ["ABABBBACFEYUKOTT", "AAA"], "sample_outputs": ["4", "1"], "notes": null}, "src_uid": "1fc7e939cdeb015fe31f3cf1c0982fee"}
{"nl": {"description": "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\u00a0\u2014 the password on the phone. The second line contains single integer n (1\u2009\u2264\u2009n\u2009\u2264\u2009100)\u00a0\u2014 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": "Giga Tower is the tallest and deepest building in Cyberland. There are 17\u2009777\u2009777\u2009777 floors, numbered from \u2009-\u20098\u2009888\u2009888\u2009888 to 8\u2009888\u2009888\u2009888. In particular, there is floor 0 between floor \u2009-\u20091 and floor 1. Every day, thousands of tourists come to this place to enjoy the wonderful view. In Cyberland, it is believed that the number \"8\" is a lucky number (that's why Giga Tower has 8\u2009888\u2009888\u2009888 floors above the ground), and, an integer is lucky, if and only if its decimal notation contains at least one digit \"8\". For example, 8,\u2009\u2009-\u2009180,\u2009808 are all lucky while 42,\u2009\u2009-\u200910 are not. In the Giga Tower, if you write code at a floor with lucky floor number, good luck will always be with you (Well, this round is #278, also lucky, huh?).Tourist Henry goes to the tower to seek good luck. Now he is at the floor numbered a. He wants to find the minimum positive integer b, such that, if he walks b floors higher, he will arrive at a floor with a lucky number. ", "input_spec": "The only line of input contains an integer a (\u2009-\u2009109\u2009\u2264\u2009a\u2009\u2264\u2009109).", "output_spec": "Print the minimum b in a line.", "sample_inputs": ["179", "-1", "18"], "sample_outputs": ["1", "9", "10"], "notes": "NoteFor the first sample, he has to arrive at the floor numbered 180.For the second sample, he will arrive at 8.Note that b should be positive, so the answer for the third sample is 10, not 0."}, "src_uid": "4e57740be015963c190e0bfe1ab74cb9"}
{"nl": {"description": "From \"ftying rats\" to urban saniwation workers - can synthetic biology tronsform how we think of pigeons? The upiquitous pigeon has long been viewed as vermin - spleading disease, scavenging through trush, and defecating in populous urban spases. Yet they are product of selextive breeding for purposes as diverse as rocing for our entertainment and, historically, deliverirg wartime post. Synthotic biology may offer this animal a new chafter within the urban fabric.Piteon d'Or recognihes how these birds ripresent a potentially userul interface for urdan biotechnologies. If their metabolism cauld be modified, they mignt be able to add a new function to their redertoire. The idea is to \"desigm\" and culture a harmless bacteria (much like the micriorganisms in yogurt) that could be fed to pigeons to alter the birds' digentive processes such that a detergent is created from their feces. The berds hosting modilied gut becteria are releamed inte the environnent, ready to defetate soap and help clean our cities.", "input_spec": "The first line of input data contains a single integer $$$n$$$ ($$$5 \\le n \\le 10$$$). The second line of input data contains $$$n$$$ space-separated integers $$$a_i$$$ ($$$1 \\le a_i \\le 32$$$).", "output_spec": "Output a single integer.", "sample_inputs": ["5\n1 2 3 4 5"], "sample_outputs": ["4"], "notes": "NoteWe did not proofread this statement at all."}, "src_uid": "a9eb85dfaa3c50ed488d41da4f29c697"}
{"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,\u2009b2,\u2009...,\u2009bl (1\u2009\u2264\u2009b1\u2009\u2264\u2009b2\u2009\u2264\u2009...\u2009\u2264\u2009bl\u2009\u2264\u2009n) is called good if each number divides (without a remainder) by the next number in the sequence. More formally  for all i (1\u2009\u2264\u2009i\u2009\u2264\u2009l\u2009-\u20091).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\u2009+\u20097).", "input_spec": "The first line of input contains two space-separated integers n,\u2009k\u00a0(1\u2009\u2264\u2009n,\u2009k\u2009\u2264\u20092000).", "output_spec": "Output a single integer \u2014 the number of good sequences of length k modulo 1000000007 (109\u2009+\u20097).", "sample_inputs": ["3 2", "6 4", "2 1"], "sample_outputs": ["5", "39", "2"], "notes": "NoteIn the first sample the good sequences are: [1,\u20091],\u2009[2,\u20092],\u2009[3,\u20093],\u2009[1,\u20092],\u2009[1,\u20093]."}, "src_uid": "c8cbd155d9f20563d37537ef68dde5aa"}
{"nl": {"description": "Bob loves everything sweet. His favorite chocolate bar consists of pieces, each piece may contain a nut. Bob wants to break the bar of chocolate into multiple pieces so that each part would contain exactly one nut and any break line goes between two adjacent pieces.You are asked to calculate the number of ways he can do it. Two ways to break chocolate are considered distinct if one of them contains a break between some two adjacent pieces and the other one doesn't. Please note, that if Bob doesn't make any breaks, all the bar will form one piece and it still has to have exactly one nut.", "input_spec": "The first line of the input contains integer n (1\u2009\u2264\u2009n\u2009\u2264\u2009100)\u00a0\u2014 the number of pieces in the chocolate bar. The second line contains n integers ai (0\u2009\u2264\u2009ai\u2009\u2264\u20091), where 0 represents a piece without the nut and 1 stands for a piece with the nut.", "output_spec": "Print the number of ways to break the chocolate into multiple parts so that each part would contain exactly one nut.", "sample_inputs": ["3\n0 1 0", "5\n1 0 1 0 1"], "sample_outputs": ["1", "4"], "notes": "NoteIn the first sample there is exactly one nut, so the number of ways equals 1\u00a0\u2014 Bob shouldn't make any breaks.In the second sample you can break the bar in four ways:10|10|11|010|110|1|011|01|01"}, "src_uid": "58242665476f1c4fa723848ff0ecda98"}
{"nl": {"description": "Vanya has a scales for weighing loads and weights of masses w0,\u2009w1,\u2009w2,\u2009...,\u2009w100 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,\u2009m (2\u2009\u2264\u2009w\u2009\u2264\u2009109, 1\u2009\u2264\u2009m\u2009\u2264\u2009109) \u2014 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\u2009+\u20093\u2009=\u20099\u2009+\u20091.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": "Recently Ivan the Fool decided to become smarter and study the probability theory. He thinks that he understands the subject fairly well, and so he began to behave like he already got PhD in that area.To prove his skills, Ivan decided to demonstrate his friends a concept of random picture. A picture is a field of $$$n$$$ rows and $$$m$$$ columns, where each cell is either black or white. Ivan calls the picture random if for every cell it has at most one adjacent cell of the same color. Two cells are considered adjacent if they share a side.Ivan's brothers spent some time trying to explain that it's not how the randomness usually works. Trying to convince Ivan, they want to count the number of different random (according to Ivan) pictures. Two pictures are considered different if at least one cell on those two picture is colored differently. Since the number of such pictures may be quite large, print it modulo $$$10^9 + 7$$$.", "input_spec": "The only line contains two integers $$$n$$$ and $$$m$$$ ($$$1 \\le n, m \\le 100\\,000$$$), the number of rows and the number of columns of the field.", "output_spec": "Print one integer, the number of random pictures modulo $$$10^9 + 7$$$.", "sample_inputs": ["2 3"], "sample_outputs": ["8"], "notes": "NoteThe picture below shows all possible random pictures of size $$$2$$$ by $$$3$$$.   "}, "src_uid": "0f1ab296cbe0952faa904f2bebe0567b"}
{"nl": {"description": "Vasya has recently finished writing a book. Now he faces the problem of giving it the title. Vasya wants the title to be vague and mysterious for his book to be noticeable among others. That's why the title should be represented by a single word containing at least once each of the first k Latin letters and not containing any other ones. Also, the title should be a palindrome, that is it should be read similarly from the left to the right and from the right to the left.Vasya has already composed the approximate variant of the title. You are given the title template s consisting of lowercase Latin letters and question marks. Your task is to replace all the question marks by lowercase Latin letters so that the resulting word satisfies the requirements, described above. Each question mark should be replaced by exactly one letter, it is not allowed to delete characters or add new ones to the template. If there are several suitable titles, choose the first in the alphabetical order, for Vasya's book to appear as early as possible in all the catalogues.", "input_spec": "The first line contains an integer k (1\u2009\u2264\u2009k\u2009\u2264\u200926) which is the number of allowed alphabet letters. The second line contains s which is the given template. In s only the first k lowercase letters of Latin alphabet and question marks can be present, the length of s is from 1 to 100 characters inclusively.", "output_spec": "If there is no solution, print IMPOSSIBLE. Otherwise, a single line should contain the required title, satisfying the given template. The title should be a palindrome and it can only contain the first k letters of the Latin alphabet. At that, each of those k letters must be present at least once. If there are several suitable titles, print the lexicographically minimal one.  The lexicographical comparison is performed by the standard < operator in modern programming languages. The line a is lexicographically smaller than the line b, if exists such an i (1\u2009\u2264\u2009i\u2009\u2264\u2009|s|), that ai\u2009<\u2009bi, and for any j (1\u2009\u2264\u2009j\u2009<\u2009i) aj\u2009=\u2009bj. |s| stands for the length of the given template.", "sample_inputs": ["3\na?c", "2\na??a", "2\n?b?a"], "sample_outputs": ["IMPOSSIBLE", "abba", "abba"], "notes": null}, "src_uid": "9d1dd9d722e5fe46823224334b3b208a"}
{"nl": {"description": "The cows have just learned what a primitive root is! Given a prime p, a primitive root  is an integer x (1\u2009\u2264\u2009x\u2009<\u2009p) such that none of integers x\u2009-\u20091,\u2009x2\u2009-\u20091,\u2009...,\u2009xp\u2009-\u20092\u2009-\u20091 are divisible by p, but xp\u2009-\u20091\u2009-\u20091 is. Unfortunately, computing primitive roots can be time consuming, so the cows need your help. Given a prime p, help the cows find the number of primitive roots .", "input_spec": "The input contains a single line containing an integer p (2\u2009\u2264\u2009p\u2009<\u20092000). It is guaranteed that p is a prime.", "output_spec": "Output on a single line the number of primitive roots .", "sample_inputs": ["3", "5"], "sample_outputs": ["1", "2"], "notes": "NoteThe only primitive root  is 2.The primitive roots  are 2 and 3."}, "src_uid": "3bed682b6813f1ddb54410218c233cff"}
{"nl": {"description": "Fox Ciel has n boxes in her room. They have the same size and weight, but they might have different strength. The i-th box can hold at most xi boxes on its top (we'll call xi the strength of the box). Since all the boxes have the same size, Ciel cannot put more than one box directly on the top of some box. For example, imagine Ciel has three boxes: the first has strength 2, the second has strength 1 and the third has strength 1. She cannot put the second and the third box simultaneously directly on the top of the first one. But she can put the second box directly on the top of the first one, and then the third box directly on the top of the second one. We will call such a construction of boxes a pile.Fox Ciel wants to construct piles from all the boxes. Each pile will contain some boxes from top to bottom, and there cannot be more than xi boxes on the top of i-th box. What is the minimal number of piles she needs to construct?", "input_spec": "The first line contains an integer n (1\u2009\u2264\u2009n\u2009\u2264\u2009100). The next line contains n integers x1,\u2009x2,\u2009...,\u2009xn (0\u2009\u2264\u2009xi\u2009\u2264\u2009100).", "output_spec": "Output a single integer \u2014 the minimal possible number of piles.", "sample_inputs": ["3\n0 0 10", "5\n0 1 2 3 4", "4\n0 0 0 0", "9\n0 1 0 2 0 1 1 2 10"], "sample_outputs": ["2", "1", "4", "3"], "notes": "NoteIn example 1, one optimal way is to build 2 piles: the first pile contains boxes 1 and 3 (from top to bottom), the second pile contains only box 2.In example 2, we can build only 1 pile that contains boxes 1, 2, 3, 4, 5 (from top to bottom)."}, "src_uid": "7c710ae68f27f140e7e03564492f7214"}
{"nl": {"description": "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,\u2009y). He wants the circle center to be in new position (x',\u2009y').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\u2009\u2264\u2009r\u2009\u2264\u2009105, \u2009-\u2009105\u2009\u2264\u2009x,\u2009y,\u2009x',\u2009y'\u2009\u2264\u2009105), circle radius, coordinates of original center of the circle and coordinates of destination center of the circle respectively.", "output_spec": "Output a single integer \u2014 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,\u20092) and rotate the circle by 180 degrees counter-clockwise (or clockwise, no matter)."}, "src_uid": "698da80c7d24252b57cca4e4f0ca7031"}
{"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\" \u2014 between them Vasya added two \"WUB\"."}, "src_uid": "edede580da1395fe459a480f6a0a548d"}
{"nl": {"description": "Ternary numeric notation is quite popular in Berland. To telegraph the ternary number the Borze alphabet is used. Digit 0 is transmitted as \u00ab.\u00bb, 1 as \u00ab-.\u00bb and 2 as \u00ab--\u00bb. You are to decode the Borze code, i.e. to find out the ternary number given its representation in Borze alphabet.", "input_spec": "The first line contains a number in Borze code. The length of the string is between 1 and 200 characters. It's guaranteed that the given string is a valid Borze code of some ternary number (this number can have leading zeroes).", "output_spec": "Output the decoded ternary number. It can have leading zeroes.", "sample_inputs": [".-.--", "--.", "-..-.--"], "sample_outputs": ["012", "20", "1012"], "notes": null}, "src_uid": "46b5a1cd1bd2985f2752662b7dbb1869"}
{"nl": {"description": "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,\u20091,\u20092,\u20091,\u20092,\u20091] is at the same time 2-periodic and 6-periodic and array [1,\u20092,\u20091,\u20091,\u20092,\u20091,\u20091,\u20092,\u20091] 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\u2009\u2264\u2009k\u2009\u2264\u2009n\u2009\u2264\u2009100), 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,\u2009a2,\u2009...,\u2009an (1\u2009\u2264\u2009ai\u2009\u2264\u20092), 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,\u20091,\u20092,\u20091,\u20092,\u20091].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,\u20091,\u20091,\u20091,\u20091,\u20091,\u20091,\u20091,\u20091] \u2014 this array is simultaneously 1-, 3- and 9-periodic."}, "src_uid": "5f94c2ecf1cf8fdbb6117cab801ed281"}
{"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 Vi\u010dkopolis and move to Pavlopolis. Thus Leha was left completely alone in a quiet town Vi\u010dkopolis. 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!,\u2009B!). 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!\u2009=\u20091\u00b72\u00b73\u00b7...\u00b7(x\u2009-\u20091)\u00b7x. For example 4!\u2009=\u20091\u00b72\u00b73\u00b74\u2009=\u200924. Recall that GCD(x,\u2009y) 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\u2009\u2264\u2009A,\u2009B\u2009\u2264\u2009109,\u2009min(A,\u2009B)\u2009\u2264\u200912).", "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!\u2009=\u20091\u00b72\u00b73\u00b74\u2009=\u200924. 3!\u2009=\u20091\u00b72\u00b73\u2009=\u20096. The greatest common divisor of integers 24 and 6 is exactly 6."}, "src_uid": "7bf30ceb24b66d91382e97767f9feeb6"}
{"nl": {"description": "In this task Anna and Maria play a game with a very unpleasant rival. Anna and Maria are in the opposite squares of a chessboard (8\u2009\u00d7\u20098): Anna is in the upper right corner, and Maria is in the lower left one. Apart from them, the board has several statues. Each statue occupies exactly one square. A square that contains a statue cannot have anything or anyone \u2014 neither any other statues, nor Anna, nor Maria.Anna is present on the board as a figurant (she stands still and never moves), and Maria has been actively involved in the game. Her goal is \u2014 to come to Anna's square. Maria and statues move in turn, Maria moves first. During one move Maria can go to any adjacent on the side or diagonal cell in which there is no statue, or she can stay in the cell where she is. The statues during their move must go one square down simultaneously, and those statues that were in the bottom row fall from the board and are no longer appeared.At that moment, when one of the statues is in the cell in which the Maria is, the statues are declared winners. At the moment when Maria comes into the cell where Anna has been waiting, Maria is declared the winner.Obviously, nothing depends on the statues, so it all depends on Maria. Determine who will win, if Maria does not make a strategic error.", "input_spec": "You are given the 8 strings whose length equals 8, describing the initial position on the board. The first line represents the top row of the board, the next one \u2014 for the second from the top, and so on, the last line represents the bottom row. Each character string matches a single cell board in the appropriate row, and the characters are in the same manner as that of the corresponding cell. If the cell is empty, the corresponding character is \".\". If a cell has Maria, then it is represented by character \"M\". If a cell has Anna, it is represented by the character \"A\". If a cell has a statue, then the cell is represented by character \"S\". It is guaranteed that the last character of the first row is always \"A\", the first character of the last line is always \"M\". The remaining characters are \".\" or \"S\".", "output_spec": "If Maria wins, print string \"WIN\". If the statues win, print string \"LOSE\".", "sample_inputs": [".......A\n........\n........\n........\n........\n........\n........\nM.......", ".......A\n........\n........\n........\n........\n........\nSS......\nM.......", ".......A\n........\n........\n........\n........\n.S......\nS.......\nMS......"], "sample_outputs": ["WIN", "LOSE", "LOSE"], "notes": null}, "src_uid": "f47e4ab041288ba9567c19930eb9a090"}
{"nl": {"description": "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\u2009-\u2009B is minimum possible. Help the teacher and find the least possible value of A\u2009-\u2009B.", "input_spec": "The first line contains space-separated integers n and m (2\u2009\u2264\u2009n\u2009\u2264\u2009m\u2009\u2264\u200950). The second line contains m space-separated integers f1,\u2009f2,\u2009...,\u2009fm (4\u2009\u2264\u2009fi\u2009\u2264\u20091000) \u2014 the quantities of pieces in the puzzles sold in the shop.", "output_spec": "Print a single integer \u2014 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": "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}$$$).", "output_spec": "Print one integer \u2014 the minimum number of operations required to make the length of decimal representation of $$$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": "Ted has a pineapple. This pineapple is able to bark like a bulldog! At time t (in seconds) it barks for the first time. Then every s seconds after it, it barks twice with 1 second interval. Thus it barks at times t, t\u2009+\u2009s, t\u2009+\u2009s\u2009+\u20091, t\u2009+\u20092s, t\u2009+\u20092s\u2009+\u20091, etc.  Barney woke up in the morning and wants to eat the pineapple, but he can't eat it when it's barking. Barney plans to eat it at time x (in seconds), so he asked you to tell him if it's gonna bark at that time.", "input_spec": "The first and only line of input contains three integers t, s and x (0\u2009\u2264\u2009t,\u2009x\u2009\u2264\u2009109, 2\u2009\u2264\u2009s\u2009\u2264\u2009109)\u00a0\u2014 the time the pineapple barks for the first time, the pineapple barking interval, and the time Barney wants to eat the pineapple respectively.", "output_spec": "Print a single \"YES\" (without quotes) if the pineapple will bark at time x or a single \"NO\" (without quotes) otherwise in the only line of output.", "sample_inputs": ["3 10 4", "3 10 3", "3 8 51", "3 8 52"], "sample_outputs": ["NO", "YES", "YES", "YES"], "notes": "NoteIn the first and the second sample cases pineapple will bark at moments 3, 13, 14, ..., so it won't bark at the moment 4 and will bark at the moment 3.In the third and fourth sample cases pineapple will bark at moments 3, 11, 12, 19, 20, 27, 28, 35, 36, 43, 44, 51, 52, 59, ..., so it will bark at both moments 51 and 52."}, "src_uid": "3baf9d841ff7208c66f6de1b47b0f952"}
{"nl": {"description": "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\u2009>\u20091) 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\u2009\u2264\u2009m\u2009\u2264\u20091015)\u00a0\u2014 the number of ways the thieves might steal the chocolates, as rumours say.", "output_spec": "Print the only integer n\u00a0\u2014 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 \u2009-\u20091.", "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\u2009=\u20098, whereas the amounts of stealed chocolates are (1,\u20092,\u20094,\u20098) (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\u2009=\u200954 with the possibilities: (1,\u20092,\u20094,\u20098),\u2009\u2002(1,\u20093,\u20099,\u200927),\u2009\u2002(2,\u20094,\u20098,\u200916),\u2009\u2002(2,\u20096,\u200918,\u200954),\u2009\u2002(3,\u20096,\u200912,\u200924),\u2009\u2002(4,\u20098,\u200916,\u200932),\u2009\u2002(5,\u200910,\u200920,\u200940),\u2009\u2002(6,\u200912,\u200924,\u200948).There is no n leading to exactly 10 ways of stealing chocolates in the third sample case."}, "src_uid": "602deaad5c66e264997249457d555129"}
{"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,\u2009y1) and the position of the treasure is (x2,\u2009y2).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,\u2009y1,\u2009x2,\u2009y2 (\u2009-\u2009105\u2009\u2264\u2009x1,\u2009y1,\u2009x2,\u2009y2\u2009\u2264\u2009105) \u2014 positions of Captain Bill the Hummingbird and treasure respectively. The second line contains two integer numbers x,\u2009y (1\u2009\u2264\u2009x,\u2009y\u2009\u2264\u2009105) \u2014 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:   \u2014 the first type of move   \u2014 the third type of move "}, "src_uid": "1c80040104e06c9f24abfcfe654a851f"}
{"nl": {"description": "Petya and Vasya decided to play a little. They found n red cubes and m blue cubes. The game goes like that: the players take turns to choose a cube of some color (red or blue) and put it in a line from left to right (overall the line will have n\u2009+\u2009m cubes). Petya moves first. Petya's task is to get as many pairs of neighbouring cubes of the same color as possible. Vasya's task is to get as many pairs of neighbouring cubes of different colors as possible. The number of Petya's points in the game is the number of pairs of neighboring cubes of the same color in the line, the number of Vasya's points in the game is the number of neighbouring cubes of the different color in the line. Your task is to calculate the score at the end of the game (Petya's and Vasya's points, correspondingly), if both boys are playing optimally well. To \"play optimally well\" first of all means to maximize the number of one's points, and second \u2014 to minimize the number of the opponent's points.", "input_spec": "The only line contains two space-separated integers n and m (1\u2009\u2264\u2009n,\u2009m\u2009\u2264\u2009105) \u2014 the number of red and blue cubes, correspondingly.", "output_spec": "On a single line print two space-separated integers \u2014 the number of Petya's and Vasya's points correspondingly provided that both players play optimally well.", "sample_inputs": ["3 1", "2 4"], "sample_outputs": ["2 1", "3 2"], "notes": "NoteIn the first test sample the optimal strategy for Petya is to put the blue cube in the line. After that there will be only red cubes left, so by the end of the game the line of cubes from left to right will look as [blue, red, red, red]. So, Petya gets 2 points and Vasya gets 1 point. If Petya would choose the red cube during his first move, then, provided that both boys play optimally well, Petya would get 1 point and Vasya would get 2 points."}, "src_uid": "c8378e6fcaab30d15469a55419f38b39"}
{"nl": {"description": "You are planning to build housing on a street. There are $$$n$$$ spots available on the street on which you can build a house. The spots are labeled from $$$1$$$ to $$$n$$$ from left to right. In each spot, you can build a house with an integer height between $$$0$$$ and $$$h$$$.In each spot, if a house has height $$$a$$$, you will gain $$$a^2$$$ dollars from it.The city has $$$m$$$ zoning restrictions. The $$$i$$$-th restriction says that the tallest house from spots $$$l_i$$$ to $$$r_i$$$ (inclusive) must be at most $$$x_i$$$.You would like to build houses to maximize your profit. Determine the maximum profit possible.", "input_spec": "The first line contains three integers $$$n$$$, $$$h$$$, and $$$m$$$ ($$$1 \\leq n,h,m \\leq 50$$$)\u00a0\u2014 the number of spots, the maximum height, and the number of restrictions. Each of the next $$$m$$$ lines contains three integers $$$l_i$$$, $$$r_i$$$, and $$$x_i$$$ ($$$1 \\leq l_i \\leq r_i \\leq n$$$, $$$0 \\leq x_i \\leq h$$$)\u00a0\u2014 left and right limits (inclusive) of the $$$i$$$-th restriction and the maximum possible height in that range.", "output_spec": "Print a single integer, the maximum profit you can make.", "sample_inputs": ["3 3 3\n1 1 1\n2 2 3\n3 3 2", "4 10 2\n2 3 8\n3 4 7"], "sample_outputs": ["14", "262"], "notes": "NoteIn the first example, there are $$$3$$$ houses, the maximum height of a house is $$$3$$$, and there are $$$3$$$ restrictions. The first restriction says the tallest house between $$$1$$$ and $$$1$$$ must be at most $$$1$$$. The second restriction says the tallest house between $$$2$$$ and $$$2$$$ must be at most $$$3$$$. The third restriction says the tallest house between $$$3$$$ and $$$3$$$ must be at most $$$2$$$.In this case, it is optimal to build houses with heights $$$[1, 3, 2]$$$. This fits within all the restrictions. The total profit in this case is $$$1^2 + 3^2 + 2^2 = 14$$$.In the second example, there are $$$4$$$ houses, the maximum height of a house is $$$10$$$, and there are $$$2$$$ restrictions. The first restriction says the tallest house from $$$2$$$ to $$$3$$$ must be at most $$$8$$$. The second restriction says the tallest house from $$$3$$$ to $$$4$$$ must be at most $$$7$$$.In this case, it's optimal to build houses with heights $$$[10, 8, 7, 7]$$$. We get a profit of $$$10^2+8^2+7^2+7^2 = 262$$$. Note that there are two restrictions on house $$$3$$$ and both of them must be satisfied. Also, note that even though there isn't any explicit restrictions on house $$$1$$$, we must still limit its height to be at most $$$10$$$ ($$$h=10$$$)."}, "src_uid": "f22b6dab443f63fb8d2d288b702f20ad"}
{"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\u2009000 kilometers. Thus, travelling from North Pole to South Pole or vice versa takes exactly 20\u2009000 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\u2019t 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\u2009\u2264\u2009n\u2009\u2264\u200950). The i-th of next n lines contains an integer ti and a string diri (1\u2009\u2264\u2009ti\u2009\u2264\u2009106, )\u00a0\u2014 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": "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\u2009-\u2009da points, and the second problem will cost b\u2009-\u2009db 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\u2009-\u20091. 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,\u2009t,\u2009a,\u2009b,\u2009da,\u2009db (0\u2009\u2264\u2009x\u2009\u2264\u2009600;\u00a01\u2009\u2264\u2009t,\u2009a,\u2009b,\u2009da,\u2009db\u2009\u2264\u2009300) \u2014 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\u2009-\u2009i\u00b7da\u2009\u2265\u20090 and b\u2009-\u2009i\u00b7db\u2009\u2265\u20090 for all 0\u2009\u2264\u2009i\u2009\u2264\u2009t\u2009-\u20091.", "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 \u2014 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": "Vasya will fancy any number as long as it is an integer power of two. Petya, on the other hand, is very conservative and only likes a single integer $$$p$$$ (which may be positive, negative, or zero). To combine their tastes, they invented $$$p$$$-binary numbers of the form $$$2^x + p$$$, where $$$x$$$ is a non-negative integer.For example, some $$$-9$$$-binary (\"minus nine\" binary) numbers are: $$$-8$$$ (minus eight), $$$7$$$ and $$$1015$$$ ($$$-8=2^0-9$$$, $$$7=2^4-9$$$, $$$1015=2^{10}-9$$$).The boys now use $$$p$$$-binary numbers to represent everything. They now face a problem: given a positive integer $$$n$$$, what's the smallest number of $$$p$$$-binary numbers (not necessarily distinct) they need to represent $$$n$$$ as their sum? It may be possible that representation is impossible altogether. Help them solve this problem.For example, if $$$p=0$$$ we can represent $$$7$$$ as $$$2^0 + 2^1 + 2^2$$$.And if $$$p=-9$$$ we can represent $$$7$$$ as one number $$$(2^4-9)$$$.Note that negative $$$p$$$-binary numbers are allowed to be in the sum (see the Notes section for an example).", "input_spec": "The only line contains two integers $$$n$$$ and $$$p$$$ ($$$1 \\leq n \\leq 10^9$$$, $$$-1000 \\leq p \\leq 1000$$$).", "output_spec": "If it is impossible to represent $$$n$$$ as the sum of any number of $$$p$$$-binary numbers, print a single integer $$$-1$$$. Otherwise, print the smallest possible number of summands.", "sample_inputs": ["24 0", "24 1", "24 -1", "4 -7", "1 1"], "sample_outputs": ["2", "3", "4", "2", "-1"], "notes": "Note$$$0$$$-binary numbers are just regular binary powers, thus in the first sample case we can represent $$$24 = (2^4 + 0) + (2^3 + 0)$$$.In the second sample case, we can represent $$$24 = (2^4 + 1) + (2^2 + 1) + (2^0 + 1)$$$.In the third sample case, we can represent $$$24 = (2^4 - 1) + (2^2 - 1) + (2^2 - 1) + (2^2 - 1)$$$. Note that repeated summands are allowed.In the fourth sample case, we can represent $$$4 = (2^4 - 7) + (2^1 - 7)$$$. Note that the second summand is negative, which is allowed.In the fifth sample case, no representation is possible."}, "src_uid": "9e86d87ce5a75c6a982894af84eb4ba8"}
{"nl": {"description": "Andrey thinks he is truly a successful developer, but in reality he didn't know about the binary search algorithm until recently. After reading some literature Andrey understood that this algorithm allows to quickly find a certain number $$$x$$$ in an array. For an array $$$a$$$ indexed from zero, and an integer $$$x$$$ the pseudocode of the algorithm is as follows:  Note that the elements of the array are indexed from zero, and the division is done in integers (rounding down).Andrey read that the algorithm only works if the array is sorted. However, he found this statement untrue, because there certainly exist unsorted arrays for which the algorithm find $$$x$$$!Andrey wants to write a letter to the book authors, but before doing that he must consider the permutations of size $$$n$$$ such that the algorithm finds $$$x$$$ in them. A permutation of size $$$n$$$ is an array consisting of $$$n$$$ distinct integers between $$$1$$$ and $$$n$$$ in arbitrary order.Help Andrey and find the number of permutations of size $$$n$$$ which contain $$$x$$$ at position $$$pos$$$ and for which the given implementation of the binary search algorithm finds $$$x$$$ (returns true). As the result may be extremely large, print the remainder of its division by $$$10^9+7$$$.", "input_spec": "The only line of input contains integers $$$n$$$, $$$x$$$ and $$$pos$$$ ($$$1 \\le x \\le n \\le 1000$$$, $$$0 \\le pos \\le n - 1$$$) \u2014 the required length of the permutation, the number to search, and the required position of that number, respectively.", "output_spec": "Print a single number\u00a0\u2014 the remainder of the division of the number of valid permutations by $$$10^9+7$$$.", "sample_inputs": ["4 1 2", "123 42 24"], "sample_outputs": ["6", "824071958"], "notes": "NoteAll possible permutations in the first test case: $$$(2, 3, 1, 4)$$$, $$$(2, 4, 1, 3)$$$, $$$(3, 2, 1, 4)$$$, $$$(3, 4, 1, 2)$$$, $$$(4, 2, 1, 3)$$$, $$$(4, 3, 1, 2)$$$."}, "src_uid": "24e2f10463f440affccc2755f4462d8a"}
{"nl": {"description": "In Berland prime numbers are fashionable \u2014 the respectable citizens dwell only on the floors with numbers that are prime numbers. The numismatists value particularly high the coins with prime nominal values. All the prime days are announced holidays!Yet even this is not enough to make the Berland people happy. On the main street of the capital stand n houses, numbered from 1 to n. The government decided to paint every house a color so that the sum of the numbers of the houses painted every color is a prime number.However it turned out that not all the citizens approve of this decision \u2014 many of them protest because they don't want many colored houses on the capital's main street. That's why it is decided to use the minimal possible number of colors. The houses don't have to be painted consecutively, but every one of n houses should be painted some color. The one-colored houses should not stand consecutively, any way of painting is acceptable.There are no more than 5 hours left before the start of painting, help the government find the way when the sum of house numbers for every color is a prime number and the number of used colors is minimal. ", "input_spec": "The single input line contains an integer n (2\u2009\u2264\u2009n\u2009\u2264\u20096000) \u2014 the number of houses on the main streets of the capital.", "output_spec": "Print the sequence of n numbers, where the i-th number stands for the number of color for house number i. Number the colors consecutively starting from 1. Any painting order is allowed. If there are several solutions to that problem, print any of them. If there's no such way of painting print the single number -1.", "sample_inputs": ["8"], "sample_outputs": ["1 2 2 1 1 1 1 2"], "notes": null}, "src_uid": "94ef0d901f21e1945849fd5bfc2d1449"}
{"nl": {"description": "Ivan has number $$$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$$$. Ivan is very lazy, that's why this task bored him soon. But he is interested in how many different numbers he would write on the board if he would finish the task. Help him to find the quantity of different numbers he would write on the board.", "input_spec": "The only line contains one integer\u00a0\u2014 $$$b$$$ $$$(1 \\le b \\le 10^{10})$$$.", "output_spec": "Print one number\u00a0\u2014 answer for the problem.", "sample_inputs": ["1", "2"], "sample_outputs": ["1", "2"], "notes": "NoteIn the first example $$$[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": "One Martian boy called Zorg wants to present a string of beads to his friend from the Earth \u2014 Masha. He knows that Masha likes two colours: blue and red, \u2014 and right in the shop where he has come, there is a variety of adornments with beads of these two colours. All the strings of beads have a small fastener, and if one unfastens it, one might notice that all the strings of beads in the shop are of the same length. Because of the peculiarities of the Martian eyesight, if Zorg sees one blue-and-red string of beads first, and then the other with red beads instead of blue ones, and blue \u2014 instead of red, he regards these two strings of beads as identical. In other words, Zorg regards as identical not only those strings of beads that can be derived from each other by the string turnover, but as well those that can be derived from each other by a mutual replacement of colours and/or by the string turnover.It is known that all Martians are very orderly, and if a Martian sees some amount of objects, he tries to put them in good order. Zorg thinks that a red bead is smaller than a blue one. Let's put 0 for a red bead, and 1 \u2014 for a blue one. From two strings the Martian puts earlier the string with a red bead in the i-th position, providing that the second string has a blue bead in the i-th position, and the first two beads i\u2009-\u20091 are identical.At first Zorg unfastens all the strings of beads, and puts them into small heaps so, that in each heap strings are identical, in his opinion. Then he sorts out the heaps and chooses the minimum string in each heap, in his opinion. He gives the unnecassary strings back to the shop assistant and says he doesn't need them any more. Then Zorg sorts out the remaining strings of beads and buys the string with index k. All these manupulations will take Zorg a lot of time, that's why he asks you to help and find the string of beads for Masha.", "input_spec": "The input file contains two integers n and k (2\u2009\u2264\u2009n\u2009\u2264\u200950;1\u2009\u2264\u2009k\u2009\u2264\u20091016) \u2014the length of a string of beads, and the index of the string, chosen by Zorg. ", "output_spec": "Output the k-th string of beads, putting 0 for a red bead, and 1 \u2014 for a blue one. If it s impossible to find the required string, output the only number -1.", "sample_inputs": ["4 4"], "sample_outputs": ["0101"], "notes": "NoteLet's consider the example of strings of length 4 \u2014 0001, 0010, 0011, 0100, 0101, 0110, 0111, 1000, 1001, 1010, 1011, 1100, 1101, 1110. Zorg will divide them into heaps: {0001, 0111, 1000, 1110}, {0010, 0100, 1011, 1101}, {0011, 1100}, {0101, 1010}, {0110, 1001}. Then he will choose the minimum strings of beads in each heap: 0001, 0010, 0011, 0101, 0110. The forth string \u2014 0101."}, "src_uid": "0a4a418dafaee71f1b31c928fc2ad24a"}
{"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 \u2014 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\u2009+\u2009ki, x\u2009+\u20092ki, x\u2009+\u20093ki 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 \u2014 during x2-th second, and the third one \u2014 during x3-th second, respectively, and during each second starting from max(x1,\u2009x2,\u2009x3) 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\u2009\u2264\u2009ki\u2009\u2264\u20091500) \u2014 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\u2009=\u20091, x2\u2009=\u20092, x3\u2009=\u20091. The first garland will be lit during seconds 1,\u20093,\u20095,\u20097,\u2009..., the second \u2014 2,\u20094,\u20096,\u20098,\u2009..., 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,\u20094,\u20097,\u200910,\u2009..., 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": "\"This problem is rubbish! There is not statement, and there are only 5 test cases. The problemsetter took liberties with this problem!\" \u2014 people complained in the comments to one round on Codeforces. And even more... No, wait, the checker for the problem was alright, that's a mercy.", "input_spec": "The only line of the input contains an integer between 1 and 5, inclusive. All tests for this problem are different. The contents of the test case doesn't need to be equal to its index.", "output_spec": "The only line of the output contains an integer between 1 and 3, inclusive.", "sample_inputs": [], "sample_outputs": [], "notes": "NoteThis problem has no samples, since there so few test cases."}, "src_uid": "c702e07fed684b7741d8337aafa005fb"}
{"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$$$)\u00a0\u2014 the number of manholes and the index of manhole from the left, near which Nastya stays initially. Initially there is exactly one stone near each of the $$$n$$$ manholes. ", "output_spec": "Print a single integer\u00a0\u2014 minimum number of moves which lead Nastya to pick all the coins.", "sample_inputs": ["2 2", "4 2", "5 1"], "sample_outputs": ["6", "13", "15"], "notes": "NoteLet's consider the example where $$$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$$$ moves are required to win."}, "src_uid": "24b02afe8d86314ec5f75a00c72af514"}
{"nl": {"description": "Petya is preparing for IQ test and he has noticed that there many problems like: you are given a sequence, find the next number. Now Petya can solve only problems with arithmetic or geometric progressions.Arithmetic progression is a sequence a1, a1\u2009+\u2009d, a1\u2009+\u20092d, ..., a1\u2009+\u2009(n\u2009-\u20091)d, where a1 and d are any numbers.Geometric progression is a sequence b1, b2\u2009=\u2009b1q, ..., bn\u2009=\u2009bn\u2009-\u20091q, where b1\u2009\u2260\u20090, q\u2009\u2260\u20090, q\u2009\u2260\u20091. Help Petya and write a program to determine if the given sequence is arithmetic or geometric. Also it should found the next number. If the sequence is neither arithmetic nor geometric, print 42 (he thinks it is impossible to find better answer). You should also print 42 if the next element of progression is not integer. So answer is always integer.", "input_spec": "The first line contains exactly four integer numbers between 1 and 1000, inclusively.", "output_spec": "Print the required number. If the given sequence is arithmetic progression, print the next progression element. Similarly, if the given sequence is geometric progression, print the next progression element. Print 42 if the given sequence is not an arithmetic or geometric progression.", "sample_inputs": ["836 624 412 200", "1 334 667 1000"], "sample_outputs": ["-12", "1333"], "notes": "NoteThis problem contains very weak pretests!"}, "src_uid": "68a9508d49fec672f9c61766d6051047"}
{"nl": {"description": "Given an integer $$$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$$$, satisfying the given conditions, separated by a space. If no pair of integers satisfy the conditions above, print \"-1\" (without quotes).", "sample_inputs": ["10", "1"], "sample_outputs": ["6 3", "-1"], "notes": null}, "src_uid": "883f67177474d23d7a320d9dbfa70dd3"}
{"nl": {"description": "You are given an integer sequence $$$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$$$).", "output_spec": "Print one integer \u2014 the minimum possible value of $$$|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": "You know that Japan is the country with almost the largest 'electronic devices per person' ratio. So you might be quite surprised to find out that the primary school in Japan teaches to count using a Soroban \u2014 an abacus developed in Japan. This phenomenon has its reasons, of course, but we are not going to speak about them. Let's have a look at the Soroban's construction.  Soroban consists of some number of rods, each rod contains five beads. We will assume that the rods are horizontal lines. One bead on each rod (the leftmost one) is divided from the others by a bar (the reckoning bar). This single bead is called go-dama and four others are ichi-damas. Each rod is responsible for representing a single digit from 0 to 9. We can obtain the value of a digit by following simple algorithm:  Set the value of a digit equal to 0.  If the go-dama is shifted to the right, add 5.  Add the number of ichi-damas shifted to the left. Thus, the upper rod on the picture shows digit 0, the middle one shows digit 2 and the lower one shows 7. We will consider the top rod to represent the last decimal digit of a number, so the picture shows number 720.Write the program that prints the way Soroban shows the given number n.", "input_spec": "The first line contains a single integer n (0\u2009\u2264\u2009n\u2009<\u2009109).", "output_spec": "Print the description of the decimal digits of number n from the last one to the first one (as mentioned on the picture in the statement), one per line. Print the beads as large English letters 'O', rod pieces as character '-' and the reckoning bar as '|'. Print as many rods, as many digits are in the decimal representation of number n without leading zeroes. We can assume that number 0 has no leading zeroes.", "sample_inputs": ["2", "13", "720"], "sample_outputs": ["O-|OO-OO", "O-|OOO-O\nO-|O-OOO", "O-|-OOOO\nO-|OO-OO\n-O|OO-OO"], "notes": null}, "src_uid": "c2e3aced0bc76b6484360563355d23a7"}
{"nl": {"description": "Vasiliy has a car and he wants to get from home to the post office. The distance which he needs to pass equals to d kilometers.Vasiliy's car is not new \u2014 it breaks after driven every k kilometers and Vasiliy needs t seconds to repair it. After repairing his car Vasiliy can drive again (but after k kilometers it will break again, and so on). In the beginning of the trip the car is just from repair station.To drive one kilometer on car Vasiliy spends a seconds, to walk one kilometer on foot he needs b seconds (a\u2009<\u2009b).Your task is to find minimal time after which Vasiliy will be able to reach the post office. Consider that in every moment of time Vasiliy can left his car and start to go on foot.", "input_spec": "The first line contains 5 positive integers d,\u2009k,\u2009a,\u2009b,\u2009t (1\u2009\u2264\u2009d\u2009\u2264\u20091012; 1\u2009\u2264\u2009k,\u2009a,\u2009b,\u2009t\u2009\u2264\u2009106; a\u2009<\u2009b), where:   d \u2014 the distance from home to the post office;  k \u2014 the distance, which car is able to drive before breaking;  a \u2014 the time, which Vasiliy spends to drive 1 kilometer on his car;  b \u2014 the time, which Vasiliy spends to walk 1 kilometer on foot;  t \u2014 the time, which Vasiliy spends to repair his car. ", "output_spec": "Print the minimal time after which Vasiliy will be able to reach the post office.", "sample_inputs": ["5 2 1 4 10", "5 2 1 4 5"], "sample_outputs": ["14", "13"], "notes": "NoteIn the first example Vasiliy needs to drive the first 2 kilometers on the car (in 2 seconds) and then to walk on foot 3 kilometers (in 12 seconds). So the answer equals to 14 seconds.In the second example Vasiliy needs to drive the first 2 kilometers on the car (in 2 seconds), then repair his car (in 5 seconds) and drive 2 kilometers more on the car (in 2 seconds). After that he needs to walk on foot 1 kilometer (in 4 seconds). So the answer equals to 13 seconds."}, "src_uid": "359ddf1f1aed9b3256836e5856fe3466"}
{"nl": {"description": "A large banner with word CODEFORCES was ordered for the 1000-th onsite round of Codeforces\u03c9 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": "Two participants are each given a pair of distinct numbers from 1 to 9 such that there's exactly one number that is present in both pairs. They want to figure out the number that matches by using a communication channel you have access to without revealing it to you.Both participants communicated to each other a set of pairs of numbers, that includes the pair given to them. Each pair in the communicated sets comprises two different numbers.Determine if you can with certainty deduce the common number, or if you can determine with certainty that both participants know the number but you do not.", "input_spec": "The first line contains two integers $$$n$$$ and $$$m$$$ ($$$1 \\le n, m \\le 12$$$) \u2014 the number of pairs the first participant communicated to the second and vice versa. The second line contains $$$n$$$ pairs of integers, each between $$$1$$$ and $$$9$$$, \u2014 pairs of numbers communicated from first participant to the second. The third line contains $$$m$$$ pairs of integers, each between $$$1$$$ and $$$9$$$, \u2014 pairs of numbers communicated from the second participant to the first. All pairs within each set are distinct (in particular, if there is a pair $$$(1,2)$$$, there will be no pair $$$(2,1)$$$ within the same set), and no pair contains the same number twice. It is guaranteed that the two sets do not contradict the statements, in other words, there is pair from the first set and a pair from the second set that share exactly one number.", "output_spec": "If you can deduce the shared number with certainty, print that number. If you can with certainty deduce that both participants know the shared number, but you do not know it, print $$$0$$$. Otherwise print $$$-1$$$.", "sample_inputs": ["2 2\n1 2 3 4\n1 5 3 4", "2 2\n1 2 3 4\n1 5 6 4", "2 3\n1 2 4 5\n1 2 1 3 2 3"], "sample_outputs": ["1", "0", "-1"], "notes": "NoteIn the first example the first participant communicated pairs $$$(1,2)$$$ and $$$(3,4)$$$, and the second communicated $$$(1,5)$$$, $$$(3,4)$$$. Since we know that the actual pairs they received share exactly one number, it can't be that they both have $$$(3,4)$$$. Thus, the first participant has $$$(1,2)$$$ and the second has $$$(1,5)$$$, and at this point you already know the shared number is $$$1$$$.In the second example either the first participant has $$$(1,2)$$$ and the second has $$$(1,5)$$$, or the first has $$$(3,4)$$$ and the second has $$$(6,4)$$$. In the first case both of them know the shared number is $$$1$$$, in the second case both of them know the shared number is $$$4$$$. You don't have enough information to tell $$$1$$$ and $$$4$$$ apart.In the third case if the first participant was given $$$(1,2)$$$, they don't know what the shared number is, since from their perspective the second participant might have been given either $$$(1,3)$$$, in which case the shared number is $$$1$$$, or $$$(2,3)$$$, in which case the shared number is $$$2$$$. While the second participant does know the number with certainty, neither you nor the first participant do, so the output is $$$-1$$$."}, "src_uid": "cb4de190ae26127df6eeb7a1a1db8a6d"}
{"nl": {"description": "In one of the games Arkady is fond of the game process happens on a rectangular field. In the game process Arkady can buy extensions for his field, each extension enlarges one of the field sizes in a particular number of times. Formally, there are n extensions, the i-th of them multiplies the width or the length (by Arkady's choice) by ai. Each extension can't be used more than once, the extensions can be used in any order.Now Arkady's field has size h\u2009\u00d7\u2009w. He wants to enlarge it so that it is possible to place a rectangle of size a\u2009\u00d7\u2009b on it (along the width or along the length, with sides parallel to the field sides). Find the minimum number of extensions needed to reach Arkady's goal.", "input_spec": "The first line contains five integers a, b, h, w and n (1\u2009\u2264\u2009a,\u2009b,\u2009h,\u2009w,\u2009n\u2009\u2264\u2009100\u2009000)\u00a0\u2014 the sizes of the rectangle needed to be placed, the initial sizes of the field and the number of available extensions. The second line contains n integers a1,\u2009a2,\u2009...,\u2009an (2\u2009\u2264\u2009ai\u2009\u2264\u2009100\u2009000), where ai equals the integer a side multiplies by when the i-th extension is applied.", "output_spec": "Print the minimum number of extensions needed to reach Arkady's goal. If it is not possible to place the rectangle on the field with all extensions, print -1. If the rectangle can be placed on the initial field, print 0.", "sample_inputs": ["3 3 2 4 4\n2 5 4 10", "3 3 3 3 5\n2 3 5 4 2", "5 5 1 2 3\n2 2 3", "3 4 1 1 3\n2 3 2"], "sample_outputs": ["1", "0", "-1", "3"], "notes": "NoteIn the first example it is enough to use any of the extensions available. For example, we can enlarge h in 5 times using the second extension. Then h becomes equal 10 and it is now possible to place the rectangle on the field."}, "src_uid": "18cb436618b2b85c3f5dc348c80882d5"}
{"nl": {"description": "There are n bears in the inn and p places to sleep. Bears will party together for some number of nights (and days).Bears love drinking juice. They don't like wine but they can't distinguish it from juice by taste or smell.A bear doesn't sleep unless he drinks wine. A bear must go to sleep a few hours after drinking a wine. He will wake up many days after the party is over.Radewoosh is the owner of the inn. He wants to put some number of barrels in front of bears. One barrel will contain wine and all other ones will contain juice. Radewoosh will challenge bears to find a barrel with wine.Each night, the following happens in this exact order:  Each bear must choose a (maybe empty) set of barrels. The same barrel may be chosen by many bears.  Each bear drinks a glass from each barrel he chose.  All bears who drink wine go to sleep (exactly those bears who chose a barrel with wine). They will wake up many days after the party is over. If there are not enough places to sleep then bears lose immediately. At the end, if it's sure where wine is and there is at least one awake bear then bears win (unless they have lost before because of the number of places to sleep).Radewoosh wants to allow bears to win. He considers q scenarios. In the i-th scenario the party will last for i nights. Then, let Ri denote the maximum number of barrels for which bears surely win if they behave optimally. Let's define . Your task is to find , where  denotes the exclusive or (also denoted as XOR).Note that the same barrel may be chosen by many bears and all of them will go to sleep at once.", "input_spec": "The only line of the input contains three integers n, p and q (1\u2009\u2264\u2009n\u2009\u2264\u2009109, 1\u2009\u2264\u2009p\u2009\u2264\u2009130, 1\u2009\u2264\u2009q\u2009\u2264\u20092\u2009000\u2009000)\u00a0\u2014 the number of bears, the number of places to sleep and the number of scenarios, respectively.", "output_spec": "Print one integer, equal to .", "sample_inputs": ["5 1 3", "1 100 4", "3 2 1", "100 100 100"], "sample_outputs": ["32", "4", "7", "381863924"], "notes": "NoteIn the first sample, there are 5 bears and only 1 place to sleep. We have R1\u2009=\u20096,\u2009R2\u2009=\u200911,\u2009R3\u2009=\u200916 so the answer is . Let's analyze the optimal strategy for scenario with 2 days. There are R2\u2009=\u200911 barrels and 10 of them contain juice.  In the first night, the i-th bear chooses a barrel i only.   If one of the first 5 barrels contains wine then one bear goes to sleep. Then, bears win because they know where wine is and there is at least one awake bear.  But let's say none of the first 5 barrels contains wine. In the second night, the i-th bear chooses a barrel 5\u2009+\u2009i.   If one of barrels 6\u2009\u2013\u200910 contains wine then one bear goes to sleep. And again, bears win in such a situation.  If nobody went to sleep then wine is in a barrel 11.   In the second sample, there is only one bear. He should choose an empty set of barrels in each night. Otherwise, he would maybe get wine and bears would lose (because there must be at least one awake bear). So, for any number of days we have Ri\u2009=\u20091. The answer is ."}, "src_uid": "28cf4ff955d089318ea08d17bc4f43da"}
{"nl": {"description": "Santa Claus is the first who came to the Christmas Olympiad, and he is going to be the first to take his place at a desk! In the classroom there are n lanes of m desks each, and there are two working places at each of the desks. The lanes are numbered from 1 to n from the left to the right, the desks in a lane are numbered from 1 to m starting from the blackboard. Note that the lanes go perpendicularly to the blackboard, not along it (see picture).The organizers numbered all the working places from 1 to 2nm. The places are numbered by lanes (i.\u00a0e. all the places of the first lane go first, then all the places of the second lane, and so on), in a lane the places are numbered starting from the nearest to the blackboard (i.\u00a0e. from the first desk in the lane), at each desk, the place on the left is numbered before the place on the right.    The picture illustrates the first and the second samples. Santa Clause knows that his place has number k. Help him to determine at which lane at which desk he should sit, and whether his place is on the left or on the right!", "input_spec": "The only line contains three integers n, m and k (1\u2009\u2264\u2009n,\u2009m\u2009\u2264\u200910\u2009000, 1\u2009\u2264\u2009k\u2009\u2264\u20092nm)\u00a0\u2014 the number of lanes, the number of desks in each lane and the number of Santa Claus' place.", "output_spec": "Print two integers: the number of lane r, the number of desk d, and a character s, which stands for the side of the desk Santa Claus. The character s should be \"L\", if Santa Clause should sit on the left, and \"R\" if his place is on the right.", "sample_inputs": ["4 3 9", "4 3 24", "2 4 4"], "sample_outputs": ["2 2 L", "4 3 R", "1 2 R"], "notes": "NoteThe first and the second samples are shown on the picture. The green place corresponds to Santa Claus' place in the first example, the blue place corresponds to Santa Claus' place in the second example.In the third sample there are two lanes with four desks in each, and Santa Claus has the fourth place. Thus, his place is in the first lane at the second desk on the right."}, "src_uid": "d6929926b44c2d5b1a8e6b7f965ca1bb"}
{"nl": {"description": "Vasya likes to solve equations. Today he wants to solve $$$(x~\\mathrm{div}~k) \\cdot (x \\bmod k) = n$$$, where $$$\\mathrm{div}$$$ and $$$\\mathrm{mod}$$$ stand for integer division and modulo operations (refer to the Notes below for exact definition). In this equation, $$$k$$$ and $$$n$$$ are positive integer parameters, and $$$x$$$ is a positive integer unknown. If there are several solutions, Vasya wants to find the smallest possible $$$x$$$. Can you help him?", "input_spec": "The first line contains two integers $$$n$$$ and $$$k$$$ ($$$1 \\leq n \\leq 10^6$$$, $$$2 \\leq k \\leq 1000$$$).", "output_spec": "Print a single integer $$$x$$$\u00a0\u2014 the smallest positive integer solution to $$$(x~\\mathrm{div}~k) \\cdot (x \\bmod k) = n$$$. It is guaranteed that this equation has at least one positive integer solution.", "sample_inputs": ["6 3", "1 2", "4 6"], "sample_outputs": ["11", "3", "10"], "notes": "NoteThe result of integer division $$$a~\\mathrm{div}~b$$$ is equal to the largest integer $$$c$$$ such that $$$b \\cdot c \\leq a$$$. $$$a$$$ modulo $$$b$$$ (shortened $$$a \\bmod b$$$) is the only integer $$$c$$$ such that $$$0 \\leq c < b$$$, and $$$a - c$$$ is divisible by $$$b$$$.In the first sample, $$$11~\\mathrm{div}~3 = 3$$$ and $$$11 \\bmod 3 = 2$$$. Since $$$3 \\cdot 2 = 6$$$, then $$$x = 11$$$ is a solution to $$$(x~\\mathrm{div}~3) \\cdot (x \\bmod 3) = 6$$$. One can see that $$$19$$$ is the only other positive integer solution, hence $$$11$$$ is the smallest one."}, "src_uid": "ed0ebc1e484fcaea875355b5b7944c57"}
{"nl": {"description": "Let's introduce the designation , where x is a string, n is a positive integer and operation \"\u2009+\u2009\" is the string concatenation operation. For example, [abc,\u20092]\u2009=\u2009abcabc.We'll say that string s can be obtained from string t, if we can remove some characters from string t and obtain string s. For example, strings ab and a\u0441ba can be obtained from string xacbac, and strings bx and aaa cannot be obtained from it.Sereja has two strings, w\u2009=\u2009[a,\u2009b] and q\u2009=\u2009[c,\u2009d]. He wants to find such maximum integer p (p\u2009>\u20090), that [q,\u2009p] can be obtained from string w.", "input_spec": "The first line contains two integers b, d (1\u2009\u2264\u2009b,\u2009d\u2009\u2264\u2009107). The second line contains string a. The third line contains string c. The given strings are not empty and consist of lowercase English letters. Their lengths do not exceed 100.", "output_spec": "In a single line print an integer \u2014 the largest number p. If the required value of p doesn't exist, print 0.", "sample_inputs": ["10 3\nabab\nbab"], "sample_outputs": ["3"], "notes": null}, "src_uid": "5ea0351ac9f949dedae1928bfb7ebffa"}
{"nl": {"description": "An n\u2009\u00d7\u2009n table a is defined as follows:  The first row and the first column contain ones, that is: ai,\u20091\u2009=\u2009a1,\u2009i\u2009=\u20091 for all i\u2009=\u20091,\u20092,\u2009...,\u2009n.  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,\u2009j\u2009=\u2009ai\u2009-\u20091,\u2009j\u2009+\u2009ai,\u2009j\u2009-\u20091. 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\u2009\u00d7\u2009n table defined by the rules above.", "input_spec": "The only line of input contains a positive integer n (1\u2009\u2264\u2009n\u2009\u2264\u200910) \u2014 the number of rows and columns of the table.", "output_spec": "Print a single line containing a positive integer m \u2014 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,\u20091,\u20091,\u20091,\u20091},\u2009 {1,\u20092,\u20093,\u20094,\u20095},\u2009 {1,\u20093,\u20096,\u200910,\u200915},\u2009 {1,\u20094,\u200910,\u200920,\u200935},\u2009 {1,\u20095,\u200915,\u200935,\u200970}."}, "src_uid": "2f650aae9dfeb02533149ced402b60dc"}
{"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\u2009-\u2009C?", "input_spec": "The first line contains one integer n (1\u2009\u2264\u2009n\u2009\u2264\u2009100) \u2014 the number of elements in a. The second line contains n integers a1, a2, ..., an (\u2009-\u2009100\u2009\u2264\u2009ai\u2009\u2264\u2009100) \u2014 the elements of sequence a.", "output_spec": "Print the maximum possible value of B\u2009-\u2009C, 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\u2009=\u2009{1,\u20090}, c\u2009=\u2009{\u2009-\u20092}. Then B\u2009=\u20091, C\u2009=\u2009\u2009-\u20092, B\u2009-\u2009C\u2009=\u20093.In the second example we choose b\u2009=\u2009{16,\u200923,\u200916,\u200915,\u200942,\u20098}, c\u2009=\u2009{} (an empty sequence). Then B\u2009=\u2009120, C\u2009=\u20090, B\u2009-\u2009C\u2009=\u2009120."}, "src_uid": "4b5d14833f9b51bfd336cc0e661243a5"}
{"nl": {"description": "A car moves from point A to point B at speed v meters per second. The action takes place on the X-axis. At the distance d meters from A there are traffic lights. Starting from time 0, for the first g seconds the green light is on, then for the following r seconds the red light is on, then again the green light is on for the g seconds, and so on.The car can be instantly accelerated from 0 to v and vice versa, can instantly slow down from the v to 0. Consider that it passes the traffic lights at the green light instantly. If the car approaches the traffic lights at the moment when the red light has just turned on, it doesn't have time to pass it. But if it approaches the traffic lights at the moment when the green light has just turned on, it can move. The car leaves point A at the time 0.What is the minimum time for the car to get from point A to point B without breaking the traffic rules?", "input_spec": "The first line contains integers l, d, v, g, r (1\u2009\u2264\u2009l,\u2009d,\u2009v,\u2009g,\u2009r\u2009\u2264\u20091000,\u2009d\u2009<\u2009l) \u2014 the distance between A and B (in meters), the distance from A to the traffic lights, car's speed, the duration of green light and the duration of red light.", "output_spec": "Output a single number \u2014 the minimum time that the car needs to get from point A to point B. Your output must have relative or absolute error less than 10\u2009-\u20096.", "sample_inputs": ["2 1 3 4 5", "5 4 3 1 1"], "sample_outputs": ["0.66666667", "2.33333333"], "notes": null}, "src_uid": "e4a4affb439365c843c9f9828d81b42c"}
{"nl": {"description": "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\u2009>\u20090 exist such that:  Decimal representation of x (without leading zeroes) consists of exactly n digits;  There exists some integer y\u2009>\u20090 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,\u2009k,\u2009m (1\u2009\u2264\u2009n\u2009\u2264\u20091000, 1\u2009\u2264\u2009k\u2009\u2264\u2009100, 1\u2009\u2264\u2009m\u2009\u2264\u2009109).", "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": "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\u2009+\u20097).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\u2009\u2264\u2009a\u2009<\u2009b\u2009\u2264\u20099,\u20091\u2009\u2264\u2009n\u2009\u2264\u2009106).", "output_spec": "Print a single integer \u2014 the answer to the problem modulo 1000000007 (109\u2009+\u20097).", "sample_inputs": ["1 3 3", "2 3 10"], "sample_outputs": ["1", "165"], "notes": null}, "src_uid": "d3e3da5b6ba37c8ac5f22b18c140ce81"}
{"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\u2009\u2264\u2009x1,\u2009x2,\u2009x3\u2009\u2264\u2009100)\u00a0\u2014 the coordinates of the houses of the first, the second and the third friends respectively. ", "output_spec": "Print one integer\u00a0\u2014 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": "You are given an alphabet consisting of n letters, your task is to make a string of the maximum possible length so that the following conditions are satisfied:   the i-th letter occurs in the string no more than ai times;  the number of occurrences of each letter in the string must be distinct for all the letters that occurred in the string at least once. ", "input_spec": "The first line of the input contains a single integer n (2\u2009\u2009\u2264\u2009\u2009n\u2009\u2009\u2264\u2009\u200926)\u00a0\u2014 the number of letters in the alphabet. The next line contains n integers ai (1\u2009\u2264\u2009ai\u2009\u2264\u2009109)\u00a0\u2014 i-th of these integers gives the limitation on the number of occurrences of the i-th character in the string.", "output_spec": "Print a single integer \u2014 the maximum length of the string that meets all the requirements.", "sample_inputs": ["3\n2 5 5", "3\n1 1 2"], "sample_outputs": ["11", "3"], "notes": "NoteFor convenience let's consider an alphabet consisting of three letters: \"a\", \"b\", \"c\". In the first sample, some of the optimal strings are: \"cccaabbccbb\", \"aabcbcbcbcb\". In the second sample some of the optimal strings are: \"acc\", \"cbc\"."}, "src_uid": "3c4b2d1c9440515bc3002eddd2b89f6f"}
{"nl": {"description": "Pasha has two hamsters: Arthur and Alexander. Pasha put n apples in front of them. Pasha knows which apples Arthur likes. Similarly, Pasha knows which apples Alexander likes. Pasha doesn't want any conflict between the hamsters (as they may like the same apple), so he decided to distribute the apples between the hamsters on his own. He is going to give some apples to Arthur and some apples to Alexander. It doesn't matter how many apples each hamster gets but it is important that each hamster gets only the apples he likes. It is possible that somebody doesn't get any apples.Help Pasha distribute all the apples between the hamsters. Note that Pasha wants to distribute all the apples, not just some of them.", "input_spec": "The first line contains integers n, a, b (1\u2009\u2264\u2009n\u2009\u2264\u2009100;\u00a01\u2009\u2264\u2009a,\u2009b\u2009\u2264\u2009n) \u2014 the number of apples Pasha has, the number of apples Arthur likes and the number of apples Alexander likes, correspondingly. The next line contains a distinct integers \u2014 the numbers of the apples Arthur likes. The next line contains b distinct integers \u2014 the numbers of the apples Alexander likes. Assume that the apples are numbered from 1 to n. The input is such that the answer exists.", "output_spec": "Print n characters, each of them equals either 1 or 2. If the i-h character equals 1, then the i-th apple should be given to Arthur, otherwise it should be given to Alexander. If there are multiple correct answers, you are allowed to print any of them.", "sample_inputs": ["4 2 3\n1 2\n2 3 4", "5 5 2\n3 4 1 2 5\n2 3"], "sample_outputs": ["1 1 2 2", "1 1 1 1 1"], "notes": null}, "src_uid": "a35a27754c9c095c6f1b2d4adccbfe93"}
{"nl": {"description": "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.   \u00a0It'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\u00a0\u2014 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\u2009\u2264\u2009n\u2009\u2264\u20091018) 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\u00a0\u2014 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\u2009+\u20091\u2009+\u20093\u2009=\u200910."}, "src_uid": "069d0cb9b7c798a81007fb5b63fa0f45"}
{"nl": {"description": "Each of you probably has your personal experience of riding public transportation and buying tickets. After a person buys a ticket (which traditionally has an even number of digits), he usually checks whether the ticket is lucky. Let us remind you that a ticket is lucky if the sum of digits in its first half matches the sum of digits in its second half.But of course, not every ticket can be lucky. Far from it! Moreover, sometimes one look at a ticket can be enough to say right away that the ticket is not lucky. So, let's consider the following unluckiness criterion that can definitely determine an unlucky ticket. We'll say that a ticket is definitely unlucky if each digit from the first half corresponds to some digit from the second half so that each digit from the first half is strictly less than the corresponding digit from the second one or each digit from the first half is strictly more than the corresponding digit from the second one. Each digit should be used exactly once in the comparisons. In other words, there is such bijective correspondence between the digits of the first and the second half of the ticket, that either each digit of the first half turns out strictly less than the corresponding digit of the second half or each digit of the first half turns out strictly more than the corresponding digit from the second half.For example, ticket 2421 meets the following unluckiness criterion and will not be considered lucky (the sought correspondence is 2\u2009>\u20091 and 4\u2009>\u20092), ticket 0135 also meets the criterion (the sought correspondence is 0\u2009<\u20093 and 1\u2009<\u20095), and ticket 3754 does not meet the criterion. You have a ticket in your hands, it contains 2n digits. Your task is to check whether it meets the unluckiness criterion.", "input_spec": "The first line contains an integer n (1\u2009\u2264\u2009n\u2009\u2264\u2009100). The second line contains a string that consists of 2n digits and defines your ticket.", "output_spec": "In the first line print \"YES\" if the ticket meets the unluckiness criterion. Otherwise, print \"NO\" (without the quotes).", "sample_inputs": ["2\n2421", "2\n0135", "2\n3754"], "sample_outputs": ["YES", "YES", "NO"], "notes": null}, "src_uid": "e4419bca9d605dbd63f7884377e28769"}
{"nl": {"description": "Manao has a monitor. The screen of the monitor has horizontal to vertical length ratio a:b. Now he is going to watch a movie. The movie's frame has horizontal to vertical length ratio c:d. Manao adjusts the view in such a way that the movie preserves the original frame ratio, but also occupies as much space on the screen as possible and fits within it completely. Thus, he may have to zoom the movie in or out, but Manao will always change the frame proportionally in both dimensions.Calculate the ratio of empty screen (the part of the screen not occupied by the movie) to the total screen size. Print the answer as an irreducible fraction p\u2009/\u2009q.", "input_spec": "A single line contains four space-separated integers a, b, c, d (1\u2009\u2264\u2009a,\u2009b,\u2009c,\u2009d\u2009\u2264\u20091000).", "output_spec": "Print the answer to the problem as \"p/q\", where p is a non-negative integer, q is a positive integer and numbers p and q don't have a common divisor larger than 1.", "sample_inputs": ["1 1 3 2", "4 3 2 2"], "sample_outputs": ["1/3", "1/4"], "notes": "NoteSample 1. Manao's monitor has a square screen. The movie has 3:2 horizontal to vertical length ratio. Obviously, the movie occupies most of the screen if the width of the picture coincides with the width of the screen. In this case, only 2/3 of the monitor will project the movie in the horizontal dimension: Sample 2. This time the monitor's width is 4/3 times larger than its height and the movie's frame is square. In this case, the picture must take up the whole monitor in the vertical dimension and only 3/4 in the horizontal dimension: "}, "src_uid": "b0f435fc2f7334aee0d07524bc37cb1e"}
{"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\u2009+\u20097). 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\u2009\u2264\u2009n,\u2009m,\u2009k\u2009\u2264\u20092000).", "output_spec": "Print a single integer \u2014 the number of strings of the described type modulo 1000000007 (109\u2009+\u20097).", "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": "Let's consider a table consisting of n rows and n columns. The cell located at the intersection of i-th row and j-th column contains number i\u2009\u00d7\u2009j. The rows and columns are numbered starting from 1.You are given a positive integer x. Your task is to count the number of cells in a table that contain number x.", "input_spec": "The single line contains numbers n and x (1\u2009\u2264\u2009n\u2009\u2264\u2009105, 1\u2009\u2264\u2009x\u2009\u2264\u2009109) \u2014 the size of the table and the number that we are looking for in the table.", "output_spec": "Print a single number: the number of times x occurs in the table.", "sample_inputs": ["10 5", "6 12", "5 13"], "sample_outputs": ["2", "4", "0"], "notes": "NoteA table for the second sample test is given below. The occurrences of number 12 are marked bold.   "}, "src_uid": "c4b139eadca94201596f1305b2f76496"}
{"nl": {"description": "The whole world got obsessed with robots,and to keep pace with the progress, great Berland's programmer Draude decided to build his own robot. He was working hard at the robot. He taught it to walk the shortest path from one point to another, to record all its movements, but like in many Draude's programs, there was a bug \u2014 the robot didn't always walk the shortest path. Fortunately, the robot recorded its own movements correctly. Now Draude wants to find out when his robot functions wrong. Heh, if Draude only remembered the map of the field, where he tested the robot, he would easily say if the robot walked in the right direction or not. But the field map was lost never to be found, that's why he asks you to find out if there exist at least one map, where the path recorded by the robot is the shortest.The map is an infinite checkered field, where each square is either empty, or contains an obstruction. It is also known that the robot never tries to run into the obstruction. By the recorded robot's movements find out if there exist at least one such map, that it is possible to choose for the robot a starting square (the starting square should be empty) such that when the robot moves from this square its movements coincide with the recorded ones (the robot doesn't run into anything, moving along empty squares only), and the path from the starting square to the end one is the shortest.In one movement the robot can move into the square (providing there are no obstrutions in this square) that has common sides with the square the robot is currently in.", "input_spec": "The first line of the input file contains the recording of the robot's movements. This recording is a non-empty string, consisting of uppercase Latin letters L, R, U and D, standing for movements left, right, up and down respectively. The length of the string does not exceed 100.", "output_spec": "In the first line output the only word OK (if the above described map exists), or BUG (if such a map does not exist).", "sample_inputs": ["LLUUUR", "RRUULLDD"], "sample_outputs": ["OK", "BUG"], "notes": null}, "src_uid": "bb7805cc9d1cc907b64371b209c564b3"}
{"nl": {"description": "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$$$) \u2014 the number of daily rations of fish food, rabbit stew and chicken stakes in Polycarps backpack correspondingly.", "output_spec": "Print the maximum number of days the cat can eat in a trip without additional food purchases, if Polycarp chooses the day of the week to start his trip optimally.", "sample_inputs": ["2 1 1", "3 2 2", "1 100 1", "30 20 10"], "sample_outputs": ["4", "7", "3", "39"], "notes": "NoteIn the first example the best day for start of the trip is Sunday. In this case, during Sunday and Monday the cat will eat fish food, during Tuesday \u2014 rabbit stew and during Wednesday \u2014 chicken stake. So, after four days of the trip all food will be eaten.In the second example Polycarp can start his trip in any day of the week. In any case there are food supplies only for one week in Polycarps backpack.In the third example Polycarp can start his trip in any day, excluding Wednesday, Saturday and Sunday. In this case, the cat will eat three different dishes in three days. Nevertheless that after three days of a trip there will be $$$99$$$ portions of rabbit stew in a backpack, can cannot eat anything in fourth day of a trip."}, "src_uid": "e17df52cc0615585e4f8f2d31d2daafb"}
{"nl": {"description": "HQ9+ is a joke programming language which has only four one-character instructions: \"H\" prints \"Hello, World!\", \"Q\" prints the source code of the program itself, \"9\" prints the lyrics of \"99 Bottles of Beer\" song,  \"+\" increments the value stored in the internal accumulator.Instructions \"H\" and \"Q\" are case-sensitive and must be uppercase. The characters of the program which are not instructions are ignored.You are given a program written in HQ9+. You have to figure out whether executing this program will produce any output.", "input_spec": "The input will consist of a single line p which will give a program in HQ9+. String p will contain between 1 and 100 characters, inclusive. ASCII-code of each character of p will be between 33 (exclamation mark) and 126 (tilde), inclusive.", "output_spec": "Output \"YES\", if executing the program will produce any output, and \"NO\" otherwise.", "sample_inputs": ["Hi!", "Codeforces"], "sample_outputs": ["YES", "NO"], "notes": "NoteIn the first case the program contains only one instruction \u2014 \"H\", which prints \"Hello, World!\".In the second case none of the program characters are language instructions."}, "src_uid": "1baf894c1c7d5aeea01129c7900d3c12"}
{"nl": {"description": "Student Andrey has been skipping physical education lessons for the whole term, and now he must somehow get a passing grade on this subject. Obviously, it is impossible to do this by legal means, but Andrey doesn't give up. Having obtained an empty certificate from a local hospital, he is going to use his knowledge of local doctor's handwriting to make a counterfeit certificate of illness. However, after writing most of the certificate, Andrey suddenly discovered that doctor's signature is impossible to forge. Or is it?For simplicity, the signature is represented as an $$$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)$$$."}, "src_uid": "49e5eabe8d69b3d27a251cccc001ab25"}
{"nl": {"description": "Array of integers is unimodal, if:  it is strictly increasing in the beginning;  after that it is constant;  after that it is strictly decreasing. The first block (increasing) and the last block (decreasing) may be absent. It is allowed that both of this blocks are absent.For example, the following three arrays are unimodal: [5,\u20097,\u200911,\u200911,\u20092,\u20091], [4,\u20094,\u20092], [7], but the following three are not unimodal: [5,\u20095,\u20096,\u20096,\u20091], [1,\u20092,\u20091,\u20092], [4,\u20095,\u20095,\u20096].Write a program that checks if an array is unimodal.", "input_spec": "The first line contains integer n (1\u2009\u2264\u2009n\u2009\u2264\u2009100) \u2014 the number of elements in the array. The second line contains n integers a1,\u2009a2,\u2009...,\u2009an (1\u2009\u2264\u2009ai\u2009\u2264\u20091\u2009000) \u2014 the elements of the array.", "output_spec": "Print \"YES\" if the given array is unimodal. Otherwise, print \"NO\". You can output each letter in any case (upper or lower).", "sample_inputs": ["6\n1 5 5 5 4 2", "5\n10 20 30 20 10", "4\n1 2 1 2", "7\n3 3 3 3 3 3 3"], "sample_outputs": ["YES", "YES", "NO", "YES"], "notes": "NoteIn the first example the array is unimodal, because it is strictly increasing in the beginning (from position 1 to position 2, inclusively), that it is constant (from position 2 to position 4, inclusively) and then it is strictly decreasing (from position 4 to position 6, inclusively)."}, "src_uid": "5482ed8ad02ac32d28c3888299bf3658"}
{"nl": {"description": "Alice and Bob are decorating a Christmas Tree. Alice wants only $$$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$$$)\u00a0\u2014 the number of yellow, blue and red ornaments.  It is guaranteed that it is possible to choose at least $$$6$$$ ($$$1+2+3=6$$$) ornaments.", "output_spec": "Print one number\u00a0\u2014 the maximum number of ornaments that can be used. ", "sample_inputs": ["8 13 9", "13 3 6"], "sample_outputs": ["24", "9"], "notes": "NoteIn the first example, the answer is $$$7+8+9=24$$$.In the second example, the answer is $$$2+3+4=9$$$."}, "src_uid": "03ac8efe10de17590e1ae151a7bae1a5"}
{"nl": {"description": "Valeric and Valerko missed the last Euro football game, so they decided to watch the game's key moments on the Net. They want to start watching as soon as possible but the connection speed is too low. If they turn on the video right now, it will \"hang up\" as the size of data to watch per second will be more than the size of downloaded data per second.The guys want to watch the whole video without any pauses, so they have to wait some integer number of seconds for a part of the video to download. After this number of seconds passes, they can start watching. Waiting for the whole video to download isn't necessary as the video can download after the guys started to watch.Let's suppose that video's length is c seconds and Valeric and Valerko wait t seconds before the watching. Then for any moment of time t0, t\u2009\u2264\u2009t0\u2009\u2264\u2009c\u2009+\u2009t, the following condition must fulfill: the size of data received in t0 seconds is not less than the size of data needed to watch t0\u2009-\u2009t seconds of the video.Of course, the guys want to wait as little as possible, so your task is to find the minimum integer number of seconds to wait before turning the video on. The guys must watch the video without pauses.", "input_spec": "The first line contains three space-separated integers a, b and c (1\u2009\u2264\u2009a,\u2009b,\u2009c\u2009\u2264\u20091000,\u2009a\u2009>\u2009b). The first number (a) denotes the size of data needed to watch one second of the video. The second number (b) denotes the size of data Valeric and Valerko can download from the Net per second. The third number (c) denotes the video's length in seconds.", "output_spec": "Print a single number \u2014 the minimum integer number of seconds that Valeric and Valerko must wait to watch football without pauses.", "sample_inputs": ["4 1 1", "10 3 2", "13 12 1"], "sample_outputs": ["3", "5", "1"], "notes": "NoteIn the first sample video's length is 1 second and it is necessary 4 units of data for watching 1 second of video, so guys should download 4 \u00b7 1 = 4 units of data to watch the whole video. The most optimal way is to wait 3 seconds till 3 units of data will be downloaded and then start watching. While guys will be watching video 1 second, one unit of data will be downloaded and Valerik and Valerko will have 4 units of data by the end of watching. Also every moment till the end of video guys will have more data then necessary for watching.In the second sample guys need 2 \u00b7 10 = 20 units of data, so they have to wait 5 seconds and after that they will have 20 units before the second second ends. However, if guys wait 4 seconds, they will be able to watch first second of video without pauses, but they will download 18 units of data by the end of second second and it is less then necessary."}, "src_uid": "7dd098ec3ad5b29ad681787173eba341"}
{"nl": {"description": "Polycarp knows that if the sum of the digits of a number is divisible by $$$3$$$, then the number itself is divisible by $$$3$$$. He assumes that the numbers, the sum of the digits of which is divisible by $$$4$$$, are also somewhat interesting. Thus, he considers a positive integer $$$n$$$ interesting if its sum of digits is divisible by $$$4$$$.Help Polycarp find the nearest larger or equal interesting number for the given number $$$a$$$. That is, find the interesting number $$$n$$$ such that $$$n \\ge a$$$ and $$$n$$$ is minimal.", "input_spec": "The only line in the input contains an integer $$$a$$$ ($$$1 \\le a \\le 1000$$$).", "output_spec": "Print the nearest greater or equal interesting number for the given number $$$a$$$. In other words, print the interesting number $$$n$$$ such that $$$n \\ge a$$$ and $$$n$$$ is minimal.", "sample_inputs": ["432", "99", "237", "42"], "sample_outputs": ["435", "103", "237", "44"], "notes": null}, "src_uid": "bb6fb9516b2c55d1ee47a30d423562d7"}
{"nl": {"description": "You are given a string $$$s$$$ of length $$$n$$$ consisting of lowercase Latin letters. You may apply some operations to this string: in one operation you can delete some contiguous substring of this string, if all letters in the substring you delete are equal. For example, after deleting substring bbbb from string abbbbaccdd we get the string aaccdd.Calculate the minimum number of operations to delete the whole string $$$s$$$.", "input_spec": "The first line contains one integer $$$n$$$ ($$$1 \\le n \\le 500$$$) \u2014 the length of string $$$s$$$. The second line contains the string $$$s$$$ ($$$|s| = n$$$) consisting of lowercase Latin letters.", "output_spec": "Output a single integer \u2014 the minimal number of operation to delete string $$$s$$$.", "sample_inputs": ["5\nabaca", "8\nabcddcba"], "sample_outputs": ["3", "4"], "notes": null}, "src_uid": "516a89f4d1ae867fc1151becd92471e6"}
{"nl": {"description": "We define $$$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$$$).", "output_spec": "Print one integer \u2014 the number of stable arrays $$$[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$$$.", "sample_inputs": ["7 3", "3 7", "1337 42", "1 1", "500000 1"], "sample_outputs": ["16", "0", "95147305", "1", "500000"], "notes": null}, "src_uid": "8e8eb64a047cb970a549ee870c3d280d"}
{"nl": {"description": "Petya collects beautiful matrix.A matrix of size $$$n \\times n$$$ is beautiful if:   All elements of the matrix are integers between $$$1$$$ and $$$n$$$;  For every row of the matrix, all elements of this row are different;  For every pair of vertically adjacent elements, these elements are different. Today Petya bought a beautiful matrix $$$a$$$ of size $$$n \\times n$$$, and now he wants to determine its rarity.The rarity of the matrix is its index in the list of beautiful matrices of size $$$n \\times n$$$, sorted in lexicographical order. Matrix comparison is done row by row. (The index of lexicographically smallest matrix is zero).Since the number of beautiful matrices may be huge, Petya wants you to calculate the rarity of the matrix $$$a$$$ modulo $$$998\\,244\\,353$$$.", "input_spec": "The first line contains one integer $$$n$$$ ($$$1 \\le n \\le 2000$$$) \u2014 the number of rows and columns in $$$a$$$. Each of the next $$$n$$$ lines contains $$$n$$$ integers $$$a_{i,j}$$$ ($$$1 \\le a_{i,j} \\le n$$$) \u2014 the elements of $$$a$$$. It is guaranteed that $$$a$$$ is a beautiful matrix.", "output_spec": "Print one integer \u2014 the rarity of matrix $$$a$$$, taken modulo $$$998\\,244\\,353$$$.", "sample_inputs": ["2\n2 1\n1 2", "3\n1 2 3\n2 3 1\n3 1 2", "3\n1 2 3\n3 1 2\n2 3 1"], "sample_outputs": ["1", "1", "3"], "notes": "NoteThere are only $$$2$$$ beautiful matrices of size $$$2 \\times 2$$$:  There are the first $$$5$$$ beautiful matrices of size $$$3 \\times 3$$$ in lexicographical order:  "}, "src_uid": "46253becfda9a45ce670dc7d835beaf3"}
{"nl": {"description": "Let's consider equation:x2\u2009+\u2009s(x)\u00b7x\u2009-\u2009n\u2009=\u20090,\u2009 where x,\u2009n are positive integers, s(x) is the function, equal to the sum of digits of number x in the decimal number system.You are given an integer n, find the smallest positive integer root of equation x, or else determine that there are no such roots.", "input_spec": "A single line contains integer n (1\u2009\u2264\u2009n\u2009\u2264\u20091018) \u2014 the equation parameter. Please, do not use the %lld specifier to read or write 64-bit integers in \u0421++. It is preferred to use cin, cout streams or the %I64d specifier. ", "output_spec": "Print -1, if the equation doesn't have integer positive roots. Otherwise print such smallest integer x (x\u2009>\u20090), that the equation given in the statement holds.", "sample_inputs": ["2", "110", "4"], "sample_outputs": ["1", "10", "-1"], "notes": "NoteIn the first test case x\u2009=\u20091 is the minimum root. As s(1)\u2009=\u20091 and 12\u2009+\u20091\u00b71\u2009-\u20092\u2009=\u20090.In the second test case x\u2009=\u200910 is the minimum root. As s(10)\u2009=\u20091\u2009+\u20090\u2009=\u20091 and 102\u2009+\u20091\u00b710\u2009-\u2009110\u2009=\u20090.In the third test case the equation has no roots."}, "src_uid": "e1070ad4383f27399d31b8d0e87def59"}
{"nl": {"description": "You are given an undirected graph consisting of $$$n$$$ vertices and $$$m$$$ edges. Initially there is a single integer written on every vertex: the vertex $$$i$$$ has $$$p_i$$$ written on it. All $$$p_i$$$ are distinct integers from $$$1$$$ to $$$n$$$.You have to process $$$q$$$ queries of two types:  $$$1$$$ $$$v$$$ \u2014 among all vertices reachable from the vertex $$$v$$$ using the edges of the graph (including the vertex $$$v$$$ itself), find a vertex $$$u$$$ with the largest number $$$p_u$$$ written on it, print $$$p_u$$$ and replace $$$p_u$$$ with $$$0$$$;  $$$2$$$ $$$i$$$ \u2014 delete the $$$i$$$-th edge from the graph.  Note that, in a query of the first type, it is possible that all vertices reachable from $$$v$$$ have $$$0$$$ written on them. In this case, $$$u$$$ is not explicitly defined, but since the selection of $$$u$$$ does not affect anything, you can choose any vertex reachable from $$$v$$$ and print its value (which is $$$0$$$). ", "input_spec": "The first line contains three integers $$$n$$$, $$$m$$$ and $$$q$$$ ($$$1 \\le n \\le 2 \\cdot 10^5$$$; $$$1 \\le m \\le 3 \\cdot 10^5$$$; $$$1 \\le q \\le 5 \\cdot 10^5$$$). The second line contains $$$n$$$ distinct integers $$$p_1$$$, $$$p_2$$$, ..., $$$p_n$$$, where $$$p_i$$$ is the number initially written on vertex $$$i$$$ ($$$1 \\le p_i \\le n$$$). Then $$$m$$$ lines follow, the $$$i$$$-th of them contains two integers $$$a_i$$$ and $$$b_i$$$ ($$$1 \\le a_i, b_i \\le n$$$, $$$a_i \\ne b_i$$$) and means that the $$$i$$$-th edge connects vertices $$$a_i$$$ and $$$b_i$$$. It is guaranteed that the graph does not contain multi-edges. Then $$$q$$$ lines follow, which describe the queries. Each line is given by one of the following formats:   $$$1$$$ $$$v$$$ \u2014 denotes a query of the first type with a vertex $$$v$$$ ($$$1 \\le v \\le n$$$).  $$$2$$$ $$$i$$$ \u2014 denotes a query of the second type with an edge $$$i$$$ ($$$1 \\le i \\le m$$$). For each query of the second type, it is guaranteed that the corresponding edge is not deleted from the graph yet. ", "output_spec": "For every query of the first type, print the value of $$$p_u$$$ written on the chosen vertex $$$u$$$.", "sample_inputs": ["5 4 6\n1 2 5 4 3\n1 2\n2 3\n1 3\n4 5\n1 1\n2 1\n2 3\n1 1\n1 2\n1 2"], "sample_outputs": ["5\n1\n2\n0"], "notes": null}, "src_uid": "ad014bde729222db14f38caa521e4167"}
{"nl": {"description": "A few years ago Sajjad left his school and register to another one due to security reasons. Now he wishes to find Amir, one of his schoolmates and good friends.There are n schools numerated from 1 to n. One can travel between each pair of them, to do so, he needs to buy a ticket. The ticker between schools i and j costs  and can be used multiple times. Help Sajjad to find the minimum cost he needs to pay for tickets to visit all schools. He can start and finish in any school.", "input_spec": "The first line contains a single integer n (1\u2009\u2264\u2009n\u2009\u2264\u2009105)\u00a0\u2014 the number of schools.", "output_spec": "Print single integer: the minimum cost of tickets needed to visit all schools.", "sample_inputs": ["2", "10"], "sample_outputs": ["0", "4"], "notes": "NoteIn the first example we can buy a ticket between the schools that costs ."}, "src_uid": "dfe9446431325c73e88b58ba204d0e47"}
{"nl": {"description": "Today's morning was exceptionally snowy. Meshanya decided to go outside and noticed a huge snowball rolling down the mountain! Luckily, there are two stones on that mountain.Initially, snowball is at height $$$h$$$ and it has weight $$$w$$$. Each second the following sequence of events happens: snowball's weights increases by $$$i$$$, where $$$i$$$\u00a0\u2014 is the current height of snowball, then snowball hits the stone (if it's present at the current height), then snowball moves one meter down. If the snowball reaches height zero, it stops.There are exactly two stones on the mountain. First stone has weight $$$u_1$$$ and is located at height $$$d_1$$$, the second one\u00a0\u2014 $$$u_2$$$ and $$$d_2$$$ respectively. When the snowball hits either of two stones, it loses weight equal to the weight of that stone. If after this snowball has negative weight, then its weight becomes zero, but the snowball continues moving as before.  Find the weight of the snowball when it stops moving, that is, it reaches height\u00a00.", "input_spec": "First line contains two integers $$$w$$$ and $$$h$$$\u00a0\u2014 initial weight and height of the snowball ($$$0 \\le w \\le 100$$$; $$$1 \\le h \\le 100$$$). Second line contains two integers $$$u_1$$$ and $$$d_1$$$\u00a0\u2014 weight and height of the first stone ($$$0 \\le u_1 \\le 100$$$; $$$1 \\le d_1 \\le h$$$). Third line contains two integers $$$u_2$$$ and $$$d_2$$$\u00a0\u2014 weight and heigth of the second stone ($$$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\u00a0\u2014 final weight of the snowball after it reaches height\u00a00.", "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": "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\u2009<\u2009ai\u2009+\u20091 for all i from 1 to n\u2009-\u20091; 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,\u20092,\u20093,\u20094,\u20095) and remove the third element from it, we obtain the sequence (1,\u20092,\u20094,\u20095)). 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\u2009\u2264\u2009n\u2009\u2264\u2009100)\u00a0\u2014 the number of holds. The next line contains n space-separated integers ai (1\u2009\u2264\u2009ai\u2009\u2264\u20091000), 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 \u2014 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,\u20096), 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,\u20093,\u20097,\u20098), (1,\u20092,\u20097,\u20098), (1,\u20092,\u20093,\u20098), for which the difficulty is 4, 5 and 5, respectively. Thus, after removing the second element we obtain the optimal answer \u2014 4."}, "src_uid": "8a8013f960814040ac4bf229a0bd5437"}
{"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\u2009\u00d7\u20098 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 \u2014 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": "Imp likes his plush toy a lot.  Recently, he found a machine that can clone plush toys. Imp knows that if he applies the machine to an original toy, he additionally gets one more original toy and one copy, and if he applies the machine to a copied toy, he gets two additional copies.Initially, Imp has only one original toy. He wants to know if it is possible to use machine to get exactly x copied toys and y original toys? He can't throw toys away, and he can't apply the machine to a copy if he doesn't currently have any copies.", "input_spec": "The only line contains two integers x and y (0\u2009\u2264\u2009x,\u2009y\u2009\u2264\u2009109)\u00a0\u2014 the number of copies and the number of original toys Imp wants to get (including the initial one).", "output_spec": "Print \"Yes\", if the desired configuration is possible, and \"No\" otherwise. You can print each letter in arbitrary case (upper or lower).", "sample_inputs": ["6 3", "4 2", "1000 1001"], "sample_outputs": ["Yes", "No", "Yes"], "notes": "NoteIn the first example, Imp has to apply the machine twice to original toys and then twice to copies."}, "src_uid": "1527171297a0b9c5adf356a549f313b9"}
{"nl": {"description": "After seeing the \"ALL YOUR BASE ARE BELONG TO US\" meme for the first time, numbers X and Y realised that they have different bases, which complicated their relations.You're given a number X represented in base bx and a number Y represented in base by. Compare those two numbers.", "input_spec": "The first line of the input contains two space-separated integers n and bx (1\u2009\u2264\u2009n\u2009\u2264\u200910, 2\u2009\u2264\u2009bx\u2009\u2264\u200940), where n is the number of digits in the bx-based representation of X.  The second line contains n space-separated integers x1,\u2009x2,\u2009...,\u2009xn (0\u2009\u2264\u2009xi\u2009<\u2009bx) \u2014 the digits of X. They are given in the order from the most significant digit to the least significant one. The following two lines describe Y in the same way: the third line contains two space-separated integers m and by (1\u2009\u2264\u2009m\u2009\u2264\u200910, 2\u2009\u2264\u2009by\u2009\u2264\u200940, bx\u2009\u2260\u2009by), where m is the number of digits in the by-based representation of Y, and the fourth line contains m space-separated integers y1,\u2009y2,\u2009...,\u2009ym (0\u2009\u2264\u2009yi\u2009<\u2009by) \u2014 the digits of Y. There will be no leading zeroes. Both X and Y will be positive. All digits of both numbers are given in the standard decimal numeral system.", "output_spec": "Output a single character (quotes for clarity):    '<' if X\u2009<\u2009Y  '>' if X\u2009>\u2009Y  '=' if X\u2009=\u2009Y ", "sample_inputs": ["6 2\n1 0 1 1 1 1\n2 10\n4 7", "3 3\n1 0 2\n2 5\n2 4", "7 16\n15 15 4 0 0 7 10\n7 9\n4 8 0 3 1 5 0"], "sample_outputs": ["=", "<", ">"], "notes": "NoteIn the first sample, X\u2009=\u20091011112\u2009=\u20094710\u2009=\u2009Y.In the second sample, X\u2009=\u20091023\u2009=\u2009215 and Y\u2009=\u2009245\u2009=\u20091123, thus X\u2009<\u2009Y.In the third sample,  and Y\u2009=\u200948031509. We may notice that X starts with much larger digits and bx is much larger than by, so X is clearly larger than Y."}, "src_uid": "d6ab5f75a7bee28f0af2bf168a0b2e67"}
{"nl": {"description": "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\u2009\u2264\u2009N\u2009\u2264\u200950), 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": "Luba has a ticket consisting of 6 digits. In one move she can choose digit in any position and replace it with arbitrary digit. She wants to know the minimum number of digits she needs to replace in order to make the ticket lucky.The ticket is considered lucky if the sum of first three digits equals to the sum of last three digits.", "input_spec": "You are given a string consisting of 6 characters (all characters are digits from 0 to 9) \u2014 this string denotes Luba's ticket. The ticket can start with the digit 0.", "output_spec": "Print one number \u2014 the minimum possible number of digits Luba needs to replace to make the ticket lucky.", "sample_inputs": ["000000", "123456", "111000"], "sample_outputs": ["0", "2", "1"], "notes": "NoteIn the first example the ticket is already lucky, so the answer is 0.In the second example Luba can replace 4 and 5 with zeroes, and the ticket will become lucky. It's easy to see that at least two replacements are required.In the third example Luba can replace any zero with 3. It's easy to see that at least one replacement is required."}, "src_uid": "09601fd1742ffdc9f822950f1d3e8494"}
{"nl": {"description": "Luke Skywalker got locked up in a rubbish shredder between two presses. R2D2 is already working on his rescue, but Luke needs to stay alive as long as possible. For simplicity we will assume that everything happens on a straight line, the presses are initially at coordinates 0 and L, and they move towards each other with speed v1 and v2, respectively. Luke has width d and is able to choose any position between the presses. Luke dies as soon as the distance between the presses is less than his width. Your task is to determine for how long Luke can stay alive.", "input_spec": "The first line of the input contains four integers d, L, v1, v2 (1\u2009\u2264\u2009d,\u2009L,\u2009v1,\u2009v2\u2009\u2264\u200910\u2009000,\u2009d\u2009<\u2009L)\u00a0\u2014 Luke's width, the initial position of the second press and the speed of the first and second presses, respectively.", "output_spec": "Print a single real value\u00a0\u2014 the maximum period of time Luke can stay alive for. Your answer will be considered correct if its absolute or relative error does not exceed 10\u2009-\u20096.  Namely: let's assume that your answer is a, and the answer of the jury is b. The checker program will consider your answer correct, if .", "sample_inputs": ["2 6 2 2", "1 9 1 2"], "sample_outputs": ["1.00000000000000000000", "2.66666666666666650000"], "notes": "NoteIn the first sample Luke should stay exactly in the middle of the segment, that is at coordinates [2;4], as the presses move with the same speed.In the second sample he needs to occupy the position . In this case both presses move to his edges at the same time."}, "src_uid": "f34f3f974a21144b9f6e8615c41830f5"}
{"nl": {"description": "Vasya is very upset that many people on the Net mix uppercase and lowercase letters in one word. That's why he decided to invent an extension for his favorite browser that would change the letters' register in every word so that it either only consisted of lowercase letters or, vice versa, only of uppercase ones. At that as little as possible letters should be changed in the word. For example, the word HoUse must be replaced with house, and the word ViP \u2014 with VIP. If a word contains an equal number of uppercase and lowercase letters, you should replace all the letters with lowercase ones. For example, maTRIx should be replaced by matrix. Your task is to use the given method on one given word.", "input_spec": "The first line contains a word s \u2014 it consists of uppercase and lowercase Latin letters and possesses the length from 1 to 100.", "output_spec": "Print the corrected word s. If the given word s has strictly more uppercase letters, make the word written in the uppercase register, otherwise - in the lowercase one.", "sample_inputs": ["HoUse", "ViP", "maTRIx"], "sample_outputs": ["house", "VIP", "matrix"], "notes": null}, "src_uid": "b432dfa66bae2b542342f0b42c0a2598"}
{"nl": {"description": "Mister B once received a gift: it was a book about aliens, which he started read immediately. This book had c pages.At first day Mister B read v0 pages, but after that he started to speed up. Every day, starting from the second, he read a pages more than on the previous day (at first day he read v0 pages, at second\u00a0\u2014 v0\u2009+\u2009a pages, at third\u00a0\u2014 v0\u2009+\u20092a pages, and so on). But Mister B is just a human, so he physically wasn't able to read more than v1 pages per day.Also, to refresh his memory, every day, starting from the second, Mister B had to reread last l pages he read on the previous day. Mister B finished the book when he read the last page for the first time.Help Mister B to calculate how many days he needed to finish the book.", "input_spec": "First and only line contains five space-separated integers: c, v0, v1, a and l (1\u2009\u2264\u2009c\u2009\u2264\u20091000, 0\u2009\u2264\u2009l\u2009<\u2009v0\u2009\u2264\u2009v1\u2009\u2264\u20091000, 0\u2009\u2264\u2009a\u2009\u2264\u20091000) \u2014 the length of the book in pages, the initial reading speed, the maximum reading speed, the acceleration in reading speed and the number of pages for rereading.", "output_spec": "Print one integer \u2014 the number of days Mister B needed to finish the book.", "sample_inputs": ["5 5 10 5 4", "12 4 12 4 1", "15 1 100 0 0"], "sample_outputs": ["1", "3", "15"], "notes": "NoteIn the first sample test the book contains 5 pages, so Mister B read it right at the first day.In the second sample test at first day Mister B read pages number 1\u2009-\u20094, at second day\u00a0\u2014 4\u2009-\u200911, at third day\u00a0\u2014 11\u2009-\u200912 and finished the book.In third sample test every day Mister B read 1 page of the book, so he finished in 15 days."}, "src_uid": "b743110117ce13e2090367fd038d3b50"}
{"nl": {"description": "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,\u2009ri] 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\u2009-\u2009bi|\u2009\u2264\u20091.Iahub thinks that point x belongs to segment [l,\u2009r], if inequality l\u2009\u2264\u2009x\u2009\u2264\u2009r 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\u2009\u2264\u2009n\u2009\u2264\u2009100) and m (1\u2009\u2264\u2009m\u2009\u2264\u2009100). The next line contains n space-separated integers x1,\u2009x2,\u2009...,\u2009xn (0\u2009\u2264\u2009xi\u2009\u2264\u2009100) \u2014 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\u2009\u2264\u2009li\u2009\u2264\u2009ri\u2009\u2264\u2009100) \u2014 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": "Nastya received a gift on New Year\u00a0\u2014 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\u2009+\u20091 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\u2009+\u20097, because it is easy to see that it is always integer.", "input_spec": "The only line contains two integers x and k (0\u2009\u2264\u2009x,\u2009k\u2009\u2264\u20091018), where x is the initial number of dresses and k\u2009+\u20091 is the number of months in a year in Byteland.", "output_spec": "In the only line print a single integer\u00a0\u2014 the expected number of dresses Nastya will own one year later modulo 109\u2009+\u20097.", "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\u2009+\u20098)\u2009/\u20092\u2009=\u20097."}, "src_uid": "e0e017e8c8872fc1957242ace739464d"}
{"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}$$$) \u2014 the number of toys and the expected total cost of the pair of toys.", "output_spec": "Print the number of ways to choose the pair of toys satisfying the condition above. Print 0, if Tanechka can choose no pair of toys in such a way that their total cost is $$$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$$$."}, "src_uid": "98624ab2fcd2a50a75788a29e04999ad"}
{"nl": {"description": "Polycarp is preparing the first programming contest for robots. There are $$$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$$$.Two corporations specializing in problem-solving robot manufacturing, \"Robo-Coder Inc.\" and \"BionicSolver Industries\", are going to register two robots (one for each corporation) for participation as well. Polycarp knows the advantages and flaws of robots produced by these companies, so, for each problem, he knows precisely whether each robot will solve it during the competition. Knowing this, he can try predicting the results \u2014 or manipulating them. For some reason (which absolutely cannot involve bribing), Polycarp wants the \"Robo-Coder Inc.\" robot to outperform the \"BionicSolver Industries\" robot in the competition. Polycarp wants to set the values of $$$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$$$ will be large, it may look very suspicious \u2014 so Polycarp wants to minimize the maximum value of $$$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$$$) \u2014 the number of problems. The second line contains $$$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$$$ points, the \"BionicSolver\" \u2014 $$$6$$$ points.In the second example, both robots get $$$0$$$ points, and the score distribution does not matter.In the third example, both robots solve all problems, so their points are equal."}, "src_uid": "b62338bff0cbb4df4e5e27e1a3ffaa07"}
{"nl": {"description": "Alice and Bob have decided to play the game \"Rock, Paper, Scissors\". The game consists of several rounds, each round is independent of each other. In each round, both players show one of the following things at the same time: rock, paper or scissors. If both players showed the same things then the round outcome is a draw. Otherwise, the following rules applied:  if one player showed rock and the other one showed scissors, then the player who showed rock is considered the winner and the other one is considered the loser;  if one player showed scissors and the other one showed paper, then the player who showed scissors is considered the winner and the other one is considered the loser;  if one player showed paper and the other one showed rock, then the player who showed paper is considered the winner and the other one is considered the loser. Alice and Bob decided to play exactly $$$n$$$ rounds of the game described above. Alice decided to show rock $$$a_1$$$ times, show scissors $$$a_2$$$ times and show paper $$$a_3$$$ times. Bob decided to show rock $$$b_1$$$ times, show scissors $$$b_2$$$ times and show paper $$$b_3$$$ times. Though, both Alice and Bob did not choose the sequence in which they show things. It is guaranteed that $$$a_1 + a_2 + a_3 = n$$$ and $$$b_1 + b_2 + b_3 = n$$$.Your task is to find two numbers:  the minimum number of round Alice can win;  the maximum number of rounds Alice can win. ", "input_spec": "The first line of the input contains one integer $$$n$$$ ($$$1 \\le n \\le 10^{9}$$$) \u2014 the number of rounds. The second line of the input contains three integers $$$a_1, a_2, a_3$$$ ($$$0 \\le a_i \\le n$$$) \u2014 the number of times Alice will show rock, scissors and paper, respectively. It is guaranteed that $$$a_1 + a_2 + a_3 = n$$$. The third line of the input contains three integers $$$b_1, b_2, b_3$$$ ($$$0 \\le b_j \\le n$$$) \u2014 the number of times Bob will show rock, scissors and paper, respectively. It is guaranteed that $$$b_1 + b_2 + b_3 = n$$$.", "output_spec": "Print two integers: the minimum and the maximum number of rounds Alice can win.", "sample_inputs": ["2\n0 1 1\n1 1 0", "15\n5 5 5\n5 5 5", "3\n0 0 3\n3 0 0", "686\n479 178 29\n11 145 530", "319\n10 53 256\n182 103 34"], "sample_outputs": ["0 1", "0 15", "3 3", "22 334", "119 226"], "notes": "NoteIn the first example, Alice will not win any rounds if she shows scissors and then paper and Bob shows rock and then scissors. In the best outcome, Alice will win one round if she shows paper and then scissors, and Bob shows rock and then scissors.In the second example, Alice will not win any rounds if Bob shows the same things as Alice each round.In the third example, Alice always shows paper and Bob always shows rock so Alice will win all three rounds anyway."}, "src_uid": "e6dc3bc64fc66b6127e2b32cacc06402"}
{"nl": {"description": "Theatre Square in the capital city of Berland has a rectangular shape with the size n\u2009\u00d7\u2009m 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\u2009\u00d7\u2009a.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,\u2009\u2009m and a (1\u2009\u2264\u2009\u2009n,\u2009m,\u2009a\u2009\u2264\u2009109).", "output_spec": "Write the needed number of flagstones.", "sample_inputs": ["6 6 4"], "sample_outputs": ["4"], "notes": null}, "src_uid": "ef971874d8c4da37581336284b688517"}
{"nl": {"description": "The Easter Rabbit laid n eggs in a circle and is about to paint them. Each egg should be painted one color out of 7: red, orange, yellow, green, blue, indigo or violet. Also, the following conditions should be satisfied:  Each of the seven colors should be used to paint at least one egg.  Any four eggs lying sequentially should be painted different colors. Help the Easter Rabbit paint the eggs in the required manner. We know that it is always possible.", "input_spec": "The only line contains an integer n \u2014 the amount of eggs (7\u2009\u2264\u2009n\u2009\u2264\u2009100).", "output_spec": "Print one line consisting of n characters. The i-th character should describe the color of the i-th egg in the order they lie in the circle. The colors should be represented as follows: \"R\" stands for red, \"O\" stands for orange, \"Y\" stands for yellow, \"G\" stands for green, \"B\" stands for blue, \"I\" stands for indigo, \"V\" stands for violet. If there are several answers, print any of them.", "sample_inputs": ["8", "13"], "sample_outputs": ["ROYGRBIV", "ROYGBIVGBIVYG"], "notes": "NoteThe way the eggs will be painted in the first sample is shown on the picture:   "}, "src_uid": "dc3817c71b1fa5606f316e5e94732296"}
{"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,\u20092,\u2009...,\u2009v. 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\u2009\u2264\u2009cnt1,\u2009cnt2\u2009<\u2009109; cnt1\u2009+\u2009cnt2\u2009\u2264\u2009109; 2\u2009\u2264\u2009x\u2009<\u2009y\u2009\u2264\u20093\u00b7104)\u00a0\u2014 the numbers that are described in the statement. It is guaranteed that numbers x, y are prime.", "output_spec": "Print a single integer \u2014 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,\u20093,\u20095} to the first friend and the set of numbers {2} to the second friend. Note that if you give set {1,\u20093,\u20095} 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,\u20092,\u20094} to the second friend. Thus, the answer to the problem is 4."}, "src_uid": "ff3c39b759a049580a6e96c66c904fdc"}
{"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\u2009\u2264\u2009n\u2009\u2264\u20098) \u2013 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": "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\u2009\u2264\u2009a,\u2009b\u2009<\u2009n\u2009\u2264\u2009100).", "output_spec": "Print the single number \u2014 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": "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\u2009\u2264\u2009n,\u2009k\u2009\u2264\u20091018, k\u2009\u2264\u2009n)\u00a0\u2014 the number of sticks drawn by Sasha and the number k\u00a0\u2014 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": "Someday, Drazil wanted to go on date with Varda. Drazil and Varda live on Cartesian plane. Drazil's home is located in point (0,\u20090) and Varda's home is located in point (a,\u2009b). In each step, he can move in a unit distance in horizontal or vertical direction. In other words, from position (x,\u2009y) he can go to positions (x\u2009+\u20091,\u2009y), (x\u2009-\u20091,\u2009y), (x,\u2009y\u2009+\u20091) or (x,\u2009y\u2009-\u20091). 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,\u2009b) and continue travelling. Luckily, Drazil arrived to the position (a,\u2009b) 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,\u20090) to (a,\u2009b) 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 (\u2009-\u2009109\u2009\u2264\u2009a,\u2009b\u2009\u2264\u2009109, 1\u2009\u2264\u2009s\u2009\u2264\u20092\u00b7109) 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": "Tokitsukaze is one of the characters in the game \"Kantai Collection\". In this game, every character has a common attribute\u00a0\u2014 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$$$)\u00a0\u2014 the value Tokitsukaze's HP currently.", "output_spec": "Print an integer $$$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": "Santa Claus has n candies, he dreams to give them as gifts to children.What is the maximal number of children for whose he can give candies if Santa Claus want each kid should get distinct positive integer number of candies. Santa Class wants to give all n candies he has.", "input_spec": "The only line contains positive integer number n (1\u2009\u2264\u2009n\u2009\u2264\u20091000) \u2014 number of candies Santa Claus has.", "output_spec": "Print to the first line integer number k \u2014 maximal number of kids which can get candies. Print to the second line k distinct integer numbers: number of candies for each of k kid. The sum of k printed numbers should be exactly n. If there are many solutions, print any of them.", "sample_inputs": ["5", "9", "2"], "sample_outputs": ["2\n2 3", "3\n3 5 1", "1\n2"], "notes": null}, "src_uid": "356a7bcebbbd354c268cddbb5454d5fc"}
{"nl": {"description": "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 \u2014 the commands Drazil sends to Dreamoon, this string consists of only the characters in the set {'+', '-'}.  The second line contains a string s2 \u2014 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\u2009-\u20099.", "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 \u2009+\u20091. 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 \u2009+\u20093 is 0."}, "src_uid": "f7f68a15cfd33f641132fac265bc5299"}
{"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$$$ since that is the maximum number of characters that can remain.In the second example, we don't need to erase any characters."}, "src_uid": "84cb9ad2ae3ba7e912920d7feb4f6219"}
{"nl": {"description": "Berland Football Cup starts really soon! Commentators from all over the world come to the event.Organizers have already built $$$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": "On the Literature lesson Sergei noticed an awful injustice, it seems that some students are asked more often than others.Seating in the class looks like a rectangle, where n rows with m pupils in each. The teacher asks pupils in the following order: at first, she asks all pupils from the first row in the order of their seating, then she continues to ask pupils from the next row. If the teacher asked the last row, then the direction of the poll changes, it means that she asks the previous row. The order of asking the rows looks as follows: the 1-st row, the 2-nd row, ..., the n\u2009-\u20091-st row, the n-th row, the n\u2009-\u20091-st row, ..., the 2-nd row, the 1-st row, the 2-nd row, ...The order of asking of pupils on the same row is always the same: the 1-st pupil, the 2-nd pupil, ..., the m-th pupil.During the lesson the teacher managed to ask exactly k questions from pupils in order described above. Sergei seats on the x-th row, on the y-th place in the row. Sergei decided to prove to the teacher that pupils are asked irregularly, help him count three values:  the maximum number of questions a particular pupil is asked,  the minimum number of questions a particular pupil is asked,  how many times the teacher asked Sergei. If there is only one row in the class, then the teacher always asks children from this row.", "input_spec": "The first and the only line contains five integers n, m, k, x and y (1\u2009\u2264\u2009n,\u2009m\u2009\u2264\u2009100,\u20091\u2009\u2264\u2009k\u2009\u2264\u20091018,\u20091\u2009\u2264\u2009x\u2009\u2264\u2009n,\u20091\u2009\u2264\u2009y\u2009\u2264\u2009m).", "output_spec": "Print three integers:   the maximum number of questions a particular pupil is asked,  the minimum number of questions a particular pupil is asked,  how many times the teacher asked Sergei. ", "sample_inputs": ["1 3 8 1 1", "4 2 9 4 2", "5 5 25 4 3", "100 100 1000000000000000000 100 100"], "sample_outputs": ["3 2 3", "2 1 1", "1 1 1", "101010101010101 50505050505051 50505050505051"], "notes": "NoteThe order of asking pupils in the first test:   the pupil from the first row who seats at the first table, it means it is Sergei;  the pupil from the first row who seats at the second table;  the pupil from the first row who seats at the third table;  the pupil from the first row who seats at the first table, it means it is Sergei;  the pupil from the first row who seats at the second table;  the pupil from the first row who seats at the third table;  the pupil from the first row who seats at the first table, it means it is Sergei;  the pupil from the first row who seats at the second table; The order of asking pupils in the second test:   the pupil from the first row who seats at the first table;  the pupil from the first row who seats at the second table;  the pupil from the second row who seats at the first table;  the pupil from the second row who seats at the second table;  the pupil from the third row who seats at the first table;  the pupil from the third row who seats at the second table;  the pupil from the fourth row who seats at the first table;  the pupil from the fourth row who seats at the second table, it means it is Sergei;  the pupil from the third row who seats at the first table; "}, "src_uid": "e61debcad37eaa9a6e21d7a2122b8b21"}
{"nl": {"description": "A string is called bracket sequence if it does not contain any characters other than \"(\" and \")\". A bracket sequence is called regular if it it is possible to obtain correct arithmetic expression by inserting characters \"+\" and \"1\" into this sequence. For example, \"\", \"(())\" and \"()()\" are regular bracket sequences; \"))\" and \")((\" are bracket sequences (but not regular ones), and \"(a)\" and \"(1)+(1)\" are not bracket sequences at all.You have a number of strings; each string is a bracket sequence of length $$$2$$$. So, overall you have $$$cnt_1$$$ strings \"((\", $$$cnt_2$$$ strings \"()\", $$$cnt_3$$$ strings \")(\" and $$$cnt_4$$$ strings \"))\". You want to write all these strings in some order, one after another; after that, you will get a long bracket sequence of length $$$2(cnt_1 + cnt_2 + cnt_3 + cnt_4)$$$. You wonder: is it possible to choose some order of the strings you have such that you will get a regular bracket sequence? Note that you may not remove any characters or strings, and you may not add anything either.", "input_spec": "The input consists of four lines, $$$i$$$-th of them contains one integer $$$cnt_i$$$ ($$$0 \\le cnt_i \\le 10^9$$$).", "output_spec": "Print one integer: $$$1$$$ if it is possible to form a regular bracket sequence by choosing the correct order of the given strings, $$$0$$$ otherwise.", "sample_inputs": ["3\n1\n4\n3", "0\n0\n0\n0", "1\n2\n3\n4"], "sample_outputs": ["1", "1", "0"], "notes": "NoteIn the first example it is possible to construct a string \"(())()(()((()()()())))\", which is a regular bracket sequence.In the second example it is possible to construct a string \"\", which is a regular bracket sequence."}, "src_uid": "b99578086043537297d374dc01eeb6f8"}
{"nl": {"description": "Paul is at the orchestra. The string section is arranged in an r\u2009\u00d7\u2009c 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\u2009\u2264\u2009r,\u2009c,\u2009n\u2009\u2264\u20093000, 1\u2009\u2264\u2009k\u2009\u2264\u2009min(n,\u200910))\u00a0\u2014 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\u2009\u2264\u2009xi\u2009\u2264\u2009r, 1\u2009\u2264\u2009yi\u2009\u2264\u2009c): 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\u00a0\u2014 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\u2009\u00d7\u20092 column containing the viola, the 2\u2009\u00d7\u20091 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": "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,\u2009c2,\u2009c3,\u2009c4 and c5 \u2014 the number of coins that the first, second, third, fourth and fifth players respectively have at the end of the game (0\u2009\u2264\u2009c1,\u2009c2,\u2009c3,\u2009c4,\u2009c5\u2009\u2264\u2009100).", "output_spec": "Print the only line containing a single positive integer b \u2014 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": "Panic is rising in the committee for doggo standardization\u00a0\u2014 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$$$)\u00a0\u2014 the number of puppies. The second line contains a string $$$s$$$ of length $$$n$$$ consisting of lowercase Latin letters, where the $$$i$$$-th symbol denotes the $$$i$$$-th puppy's color.", "output_spec": "If it's possible to recolor all puppies into one color, print \"Yes\". Otherwise print \"No\". Output the answer without quotation signs.", "sample_inputs": ["6\naabddc", "3\nabc", "3\njjj"], "sample_outputs": ["Yes", "No", "Yes"], "notes": "NoteIn the first example Slava can perform the following steps:   take all puppies of color 'a' (a total of two) and recolor them into 'b';  take all puppies of color 'd' (a total of two) and recolor them into 'c';  take all puppies of color 'b' (three puppies for now) and recolor them into 'c'. In the second example it's impossible to recolor any of the puppies.In the third example all the puppies' colors are the same; thus there's no need to recolor anything."}, "src_uid": "6b22e93f7e429693dcfe3c099346dcda"}
{"nl": {"description": "Polycarp has $$$n$$$ coins, the value of the $$$i$$$-th coin is $$$a_i$$$. Polycarp wants to distribute all the coins between his pockets, but he cannot put two coins with the same value into the same pocket.For example, if Polycarp has got six coins represented as an array $$$a = [1, 2, 4, 3, 3, 2]$$$, he can distribute the coins into two pockets as follows: $$$[1, 2, 3], [2, 3, 4]$$$.Polycarp wants to distribute all the coins with the minimum number of used pockets. Help him to do that.", "input_spec": "The first line of the input contains one integer $$$n$$$ ($$$1 \\le n \\le 100$$$) \u2014 the number of coins. The second line of the input contains $$$n$$$ integers $$$a_1, a_2, \\dots, a_n$$$ ($$$1 \\le a_i \\le 100$$$) \u2014 values of coins.", "output_spec": "Print only one integer \u2014 the minimum number of pockets Polycarp needs to distribute all the coins so no two coins with the same value are put into the same pocket.", "sample_inputs": ["6\n1 2 4 3 3 2", "1\n100"], "sample_outputs": ["2", "1"], "notes": null}, "src_uid": "f30329023e84b4c50b1b118dc98ae73c"}
{"nl": {"description": "Karl likes Codeforces and subsequences. He wants to find a string of lowercase English letters that contains at least $$$k$$$ subsequences codeforces. Out of all possible strings, Karl wants to find a shortest one.Formally, a codeforces subsequence of a string $$$s$$$ is a subset of ten characters of $$$s$$$ that read codeforces from left to right. For example, codeforces contains codeforces a single time, while codeforcesisawesome contains codeforces four times: codeforcesisawesome, codeforcesisawesome, codeforcesisawesome, codeforcesisawesome.Help Karl find any shortest string that contains at least $$$k$$$ codeforces subsequences.", "input_spec": "The only line contains a single integer $$$k$$$ ($$$1 \\leq k \\leq 10^{16})$$$.", "output_spec": "Print a shortest string of lowercase English letters that contains at least $$$k$$$ codeforces subsequences. If there are several such strings, print any of them.", "sample_inputs": ["1", "3"], "sample_outputs": ["codeforces", "codeforcesss"], "notes": null}, "src_uid": "8001a7570766cadcc538217e941b3031"}
{"nl": {"description": "There are three doors in front of you, numbered from $$$1$$$ to $$$3$$$ from left to right. Each door has a lock on it, which can only be opened with a key with the same number on it as the number on the door.There are three keys\u00a0\u2014 one for each door. Two of them are hidden behind the doors, so that there is no more than one key behind each door. So two doors have one key behind them, one door doesn't have a key behind it. To obtain a key hidden behind a door, you should first unlock that door. The remaining key is in your hands.Can you open all the doors?", "input_spec": "The first line contains a single integer $$$t$$$ ($$$1 \\le t \\le 18$$$)\u00a0\u2014 the number of testcases. The first line of each testcase contains a single integer $$$x$$$ ($$$1 \\le x \\le 3$$$)\u00a0\u2014 the number on the key in your hands. The second line contains three integers $$$a, b$$$ and $$$c$$$ ($$$0 \\le a, b, c \\le 3$$$)\u00a0\u2014 the number on the key behind each of the doors. If there is no key behind the door, the number is equal to $$$0$$$. Values $$$1, 2$$$ and $$$3$$$ appear exactly once among $$$x, a, b$$$ and $$$c$$$.", "output_spec": "For each testcase, print \"YES\" if you can open all the doors. Otherwise, print \"NO\".", "sample_inputs": ["4\n\n3\n\n0 1 2\n\n1\n\n0 3 2\n\n2\n\n3 1 0\n\n2\n\n1 3 0"], "sample_outputs": ["YES\nNO\nYES\nNO"], "notes": null}, "src_uid": "5cd113a30bbbb93d8620a483d4da0349"}
{"nl": {"description": "Let's call a string a phone number if it has length 11 and fits the pattern \"8xxxxxxxxxx\", where each \"x\" is replaced by a digit.For example, \"80123456789\" and \"80000000000\" are phone numbers, while \"8012345678\" and \"79000000000\" are not.You have $$$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$$$\u00a0\u2014 the number of cards with digits that you have ($$$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$$$. The string will not contain any other characters, such as leading or trailing spaces.", "output_spec": "If at least one phone number can be made from these cards, output the maximum number of phone numbers that can be made. Otherwise, output 0.", "sample_inputs": ["11\n00000000008", "22\n0011223344556677889988", "11\n31415926535"], "sample_outputs": ["1", "2", "0"], "notes": "NoteIn the first example, one phone number, \"8000000000\", can be made from these cards.In the second example, you can make two phone numbers from the cards, for example, \"80123456789\" and \"80123456789\".In the third example you can't make any phone number from the given cards."}, "src_uid": "259d01b81bef5536b969247ff2c2d776"}
{"nl": {"description": "In Omkar's last class of math, he learned about the least common multiple, or $$$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$$$."}, "src_uid": "3fd60db24b1873e906d6dee9c2508ac5"}
{"nl": {"description": "After passing a test, Vasya got himself a box of $$$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\\%$$$ of the candies remaining in the box. If there are still candies left in the box, the process repeats\u00a0\u2014 next day Vasya eats $$$k$$$ candies again, and Petya\u00a0\u2014 $$$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}$$$)\u00a0\u2014 the initial amount of candies in the box.", "output_spec": "Output a single integer\u00a0\u2014 the minimal amount of $$$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$$$ candies, while Petya\u00a0\u2014 $$$29$$$."}, "src_uid": "db1a50da538fa82038f8db6104d2ab93"}
{"nl": {"description": "Let's introduce some definitions that will be needed later.Let $$$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}$$$)\u00a0\u2014 the numbers used in formula.", "output_spec": "Print the answer.", "sample_inputs": ["10 2", "20190929 1605", "947 987654321987654321"], "sample_outputs": ["2", "363165664", "593574252"], "notes": "NoteIn the first example, $$$f(10, 1) = g(1, 2) \\cdot g(1, 5) = 1$$$, $$$f(10, 2) = g(2, 2) \\cdot g(2, 5) = 2$$$.In the second example, actual value of formula is approximately $$$1.597 \\cdot 10^{171}$$$. Make sure you print the answer modulo $$$(10^{9} + 7)$$$.In the third example, be careful about overflow issue."}, "src_uid": "04610fbaa746c083dda30e21fa6e1a0c"}
{"nl": {"description": "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\u2009\u2264\u2009n\u2009\u2264\u200925) \u2014 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": "InputThe input contains a single integer a (1\u2009\u2264\u2009a\u2009\u2264\u200940).OutputOutput a single string.ExamplesInput2OutputAdamsInput8OutputVan BurenInput29OutputHarding", "input_spec": "The input contains a single integer a (1\u2009\u2264\u2009a\u2009\u2264\u200940).", "output_spec": "Output a single string.", "sample_inputs": ["2", "8", "29"], "sample_outputs": ["Adams", "Van Buren", "Harding"], "notes": null}, "src_uid": "0b51a8318c9ec0c80c0f4dc04fe0bfb3"}
{"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\u2009\u2264\u2009n\u2009\u2264\u2009100)\u00a0\u2014 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 \u03c0 in binary representation. Not very useful information though."}, "src_uid": "ab8a2070ea758d118b3c09ee165d9517"}
{"nl": {"description": "    *The two images are equivalent, feel free to use either one.", "input_spec": "The input contains a single integer $$$a$$$ ($$$-100 \\le a \\le 100$$$).", "output_spec": "Output the result \u2013 an integer number.", "sample_inputs": ["1"], "sample_outputs": ["1"], "notes": null}, "src_uid": "f76005f888df46dac38b0f159ca04d5f"}
{"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\u2009\u2264\u2009n\u2009\u2264\u2009100), the number of the columns in the box. The next line contains n space-separated integer numbers. The i-th number ai (1\u2009\u2264\u2009ai\u2009\u2264\u2009100) 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": "There was once young lass called Mary,  Whose jokes were occasionally scary.  On this April's Fool  Fixed limerick rules  Allowed her to trip the unwary.Can she fill all the linesTo work at all times?On juggling the wordsRight around two-thirdsShe nearly ran out of rhymes.", "input_spec": "The input contains a single integer $$$a$$$ ($$$4 \\le a \\le 998$$$). Not every integer in the range is a valid input for the problem; you are guaranteed that the input will be a valid integer.", "output_spec": "Output a single number.", "sample_inputs": ["35", "57", "391"], "sample_outputs": ["57", "319", "1723"], "notes": null}, "src_uid": "7220f2da5081547a12118595bbeda4f6"}
{"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\u2009\u2264\u2009n\u2009\u2264\u2009100, 1\u2009\u2264\u2009k\u2009\u2264\u200910000). The second line contains n integers a1,\u2009a2,\u2009a3,\u2009...,\u2009an (1\u2009\u2264\u2009ai\u2009\u2264\u2009100).", "output_spec": "If it is impossible for Arya to give Bran k candies within n days, print -1. Otherwise print a single integer\u00a0\u2014 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": "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... \u221e.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\u2009=\u2009 \"What are you doing while sending \"fi\u2009-\u20091\"? Are you busy? Will you send \"fi\u2009-\u20091\"?\" for all i\u2009\u2265\u20091.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\u2009\u2264\u2009q\u2009\u2264\u200910)\u00a0\u2014 the number of Nephren's questions. Each of the next q lines describes Nephren's question and contains two integers n and k (0\u2009\u2264\u2009n\u2009\u2264\u2009105,\u20091\u2009\u2264\u2009k\u2009\u2264\u20091018).", "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": "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,\u2009x2,\u2009x3 and three more integers y1,\u2009y2,\u2009y3, such that x1\u2009<\u2009x2\u2009<\u2009x3, y1\u2009<\u2009y2\u2009<\u2009y3 and the eight point set consists of all points (xi,\u2009yj) (1\u2009\u2264\u2009i,\u2009j\u2009\u2264\u20093), except for point (x2,\u2009y2).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\u2009\u2264\u2009xi,\u2009yi\u2009\u2264\u2009106). 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": "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$$$)\u00a0\u2014 the length.", "output_spec": "Print the number of ways to fill.", "sample_inputs": ["4", "1"], "sample_outputs": ["4", "0"], "notes": "NoteIn the first example, there are $$$4$$$ possible cases of filling.In the second example, you cannot fill the shapes in $$$3 \\times 1$$$ tiles."}, "src_uid": "4b7ff467ed5907e32fd529fb39b708db"}
{"nl": {"description": "Jack is working on his jumping skills recently. Currently he's located at point zero of the number line. He would like to get to the point x. In order to train, he has decided that he'll first jump by only one unit, and each subsequent jump will be exactly one longer than the previous one. He can go either left or right with each jump. He wonders how many jumps he needs to reach x.", "input_spec": "The input data consists of only one integer x (\u2009-\u2009109\u2009\u2264\u2009x\u2009\u2264\u2009109).", "output_spec": "Output the minimal number of jumps that Jack requires to reach x.", "sample_inputs": ["2", "6", "0"], "sample_outputs": ["3", "3", "0"], "notes": null}, "src_uid": "18644c9df41b9960594fdca27f1d2fec"}
{"nl": {"description": "There are n boys and m girls attending a theatre club. To set a play \"The Big Bang Theory\", they need to choose a group containing exactly t actors containing no less than 4 boys and no less than one girl. How many ways are there to choose a group? Of course, the variants that only differ in the composition of the troupe are considered different.Perform all calculations in the 64-bit type: long long for \u0421/\u0421++, int64 for Delphi and long for Java.", "input_spec": "The only line of the input data contains three integers n, m, t (4\u2009\u2264\u2009n\u2009\u2264\u200930,\u20091\u2009\u2264\u2009m\u2009\u2264\u200930,\u20095\u2009\u2264\u2009t\u2009\u2264\u2009n\u2009+\u2009m).", "output_spec": "Find the required number of ways. Please do not use the %lld specificator to read or write 64-bit integers in \u0421++. It is preferred to use cin, cout streams or the %I64d specificator.", "sample_inputs": ["5 2 5", "4 3 5"], "sample_outputs": ["10", "3"], "notes": null}, "src_uid": "489e69c7a2fba5fac34e89d7388ed4b8"}
{"nl": {"description": "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\u2009-\u20091 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\u2009\u2264\u2009n\u2009\u2264\u200930; 1\u2009\u2264\u2009L\u2009\u2264\u2009109)\u00a0\u2014 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,\u2009c2,\u2009...,\u2009cn (1\u2009\u2264\u2009ci\u2009\u2264\u2009109)\u00a0\u2014 the costs of bottles of different types.", "output_spec": "Output a single integer\u00a0\u2014 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": "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\u2009\u2264\u2009a\u2009\u2264\u20091018). The second line contains integer b (1\u2009\u2264\u2009b\u2009\u2264\u20091018). 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": "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\u2009\u2264\u2009a,\u2009b,\u2009n\u2009\u2264\u2009100) \u2014 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,\u2009b) represent the operation of calculating the greatest common divisor of numbers a and b. Specifically, gcd(x,\u20090)\u2009=\u2009gcd(0,\u2009x)\u2009=\u2009x.In the first sample the game will go like that: Simon should take gcd(3,\u20099)\u2009=\u20093 stones from the heap. After his move the heap has 6 stones left. Antisimon should take gcd(5,\u20096)\u2009=\u20091 stone from the heap. After his move the heap has 5 stones left. Simon should take gcd(3,\u20095)\u2009=\u20091 stone from the heap. After his move the heap has 4 stones left. Antisimon should take gcd(5,\u20094)\u2009=\u20091 stone from the heap. After his move the heap has 3 stones left. Simon should take gcd(3,\u20093)\u2009=\u20093 stones from the heap. After his move the heap has 0 stones left. Antisimon should take gcd(5,\u20090)\u2009=\u20095 stones from the heap. As 0\u2009<\u20095, 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": "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,\u2009y) 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,\u20091), that is top left corner of the matrix. Then she goes down all the way to cell (n,\u20091) \u2014 the bottom left corner. Then she starts moving in the snake fashion \u2014 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,\u20092).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\u2009\u2264\u2009n,\u2009m\u2009\u2264\u2009109, n is always even, 0\u2009\u2264\u2009k\u2009<\u2009n\u00b7m). 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": "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\u2009-\u2009x 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\u2009\u2264\u2009n,\u2009x,\u2009y\u2009\u2264\u2009104,\u2009x\u2009\u2264\u2009n) \u2014 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 (\u2009>\u2009n).", "output_spec": "Print a single integer \u2014 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": "This year, as in previous years, MemSQL is inviting the top 25 competitors from the Start[c]up qualification round to compete onsite for the final round. Not everyone who is eligible to compete onsite can afford to travel to the office, though. Initially the top 25 contestants are invited to come onsite. Each eligible contestant must either accept or decline the invitation. Whenever a contestant declines, the highest ranked contestant not yet invited is invited to take the place of the one that declined. This continues until 25 contestants have accepted invitations.After the qualifying round completes, you know K of the onsite finalists, as well as their qualifying ranks (which start at 1, there are no ties). Determine the minimum possible number of contestants that declined the invitation to compete onsite in the final round.", "input_spec": "The first line of input contains K (1\u2009\u2264\u2009K\u2009\u2264\u200925), the number of onsite finalists you know. The second line of input contains r1,\u2009r2,\u2009...,\u2009rK (1\u2009\u2264\u2009ri\u2009\u2264\u2009106), the qualifying ranks of the finalists you know. All these ranks are distinct.", "output_spec": "Print the minimum possible number of contestants that declined the invitation to compete onsite.", "sample_inputs": ["25\n2 3 4 5 6 7 8 9 10 11 12 14 15 16 17 18 19 20 21 22 23 24 25 26 28", "5\n16 23 8 15 4", "3\n14 15 92"], "sample_outputs": ["3", "0", "67"], "notes": "NoteIn the first example, you know all 25 onsite finalists. The contestants who ranked 1-st, 13-th, and 27-th must have declined, so the answer is 3."}, "src_uid": "ef657588b4f2fe8b2ff5f8edc0ab8afd"}
{"nl": {"description": "A girl named Sonya is studying in the scientific lyceum of the Kingdom of Kremland. The teacher of computer science (Sonya's favorite subject!) invented a task for her.Given an array $$$a$$$ of length $$$n$$$, consisting only of the numbers $$$0$$$ and $$$1$$$, and the number $$$k$$$. Exactly $$$k$$$ times the following happens:   Two numbers $$$i$$$ and $$$j$$$ are chosen equiprobable such that ($$$1 \\leq i < j \\leq n$$$).  The numbers in the $$$i$$$ and $$$j$$$ positions are swapped. Sonya's task is to find the probability that after all the operations are completed, the $$$a$$$ array will be sorted in non-decreasing order. She turned to you for help. Help Sonya solve this problem.It can be shown that the desired probability is either $$$0$$$ or it can be represented as $$$\\dfrac{P}{Q}$$$, where $$$P$$$ and $$$Q$$$ are coprime integers and $$$Q \\not\\equiv 0~\\pmod {10^9+7}$$$.", "input_spec": "The first line contains two integers $$$n$$$ and $$$k$$$ ($$$2 \\leq n \\leq 100, 1 \\leq k \\leq 10^9$$$)\u00a0\u2014 the length of the array $$$a$$$ and the number of operations. The second line contains $$$n$$$ integers $$$a_1, a_2, \\ldots, a_n$$$ ($$$0 \\le a_i \\le 1$$$)\u00a0\u2014 the description of the array $$$a$$$.", "output_spec": "If the desired probability is $$$0$$$, print $$$0$$$, otherwise print the value $$$P \\cdot Q^{-1}$$$ $$$\\pmod {10^9+7}$$$, where $$$P$$$ and $$$Q$$$ are defined above.", "sample_inputs": ["3 2\n0 1 0", "5 1\n1 1 1 0 0", "6 4\n1 0 0 1 1 0"], "sample_outputs": ["333333336", "0", "968493834"], "notes": "NoteIn the first example, all possible variants of the final array $$$a$$$, after applying exactly two operations: $$$(0, 1, 0)$$$, $$$(0, 0, 1)$$$, $$$(1, 0, 0)$$$, $$$(1, 0, 0)$$$, $$$(0, 1, 0)$$$, $$$(0, 0, 1)$$$, $$$(0, 0, 1)$$$, $$$(1, 0, 0)$$$, $$$(0, 1, 0)$$$. Therefore, the answer is $$$\\dfrac{3}{9}=\\dfrac{1}{3}$$$.In the second example, the array will not be sorted in non-decreasing order after one operation, therefore the answer is $$$0$$$."}, "src_uid": "77f28d155a632ceaabd9f5a9d846461a"}
{"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\u2009\u2264\u2009p\u2009\u2264\u2009500; 1\u2009\u2264\u2009y\u2009\u2264\u2009x\u2009\u2264\u200920000)\u00a0\u2014 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\u00a0\u2014 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": "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": "Alice is the leader of the State Refactoring Party, and she is about to become the prime minister. The elections have just taken place. There are $$$n$$$ parties, numbered from $$$1$$$ to $$$n$$$. The $$$i$$$-th party has received $$$a_i$$$ seats in the parliament.Alice's party has number $$$1$$$. In order to become the prime minister, she needs to build a coalition, consisting of her party and possibly some other parties. There are two conditions she needs to fulfil:   The total number of seats of all parties in the coalition must be a strict majority of all the seats, i.e. it must have strictly more than half of the seats. For example, if the parliament has $$$200$$$ (or $$$201$$$) seats, then the majority is $$$101$$$ or more seats.  Alice's party must have at least $$$2$$$ times more seats than any other party in the coalition. For example, to invite a party with $$$50$$$ seats, Alice's party must have at least $$$100$$$ seats. For example, if $$$n=4$$$ and $$$a=[51, 25, 99, 25]$$$ (note that Alice'a party has $$$51$$$ seats), then the following set $$$[a_1=51, a_2=25, a_4=25]$$$ can create a coalition since both conditions will be satisfied. However, the following sets will not create a coalition:  $$$[a_2=25, a_3=99, a_4=25]$$$ since Alice's party is not there;  $$$[a_1=51, a_2=25]$$$ since coalition should have a strict majority;  $$$[a_1=51, a_2=25, a_3=99]$$$ since Alice's party should have at least $$$2$$$ times more seats than any other party in the coalition. Alice does not have to minimise the number of parties in a coalition. If she wants, she can invite as many parties as she wants (as long as the conditions are satisfied). If Alice's party has enough people to create a coalition on her own, she can invite no parties.Note that Alice can either invite a party as a whole or not at all. It is not possible to invite only some of the deputies (seats) from another party. In other words, if Alice invites a party, she invites all its deputies.Find and print any suitable coalition.", "input_spec": "The first line contains a single integer $$$n$$$ ($$$2 \\leq n \\leq 100$$$)\u00a0\u2014 the number of parties. The second line contains $$$n$$$ space separated integers $$$a_1, a_2, \\dots, a_n$$$ ($$$1 \\leq a_i \\leq 100$$$)\u00a0\u2014 the number of seats the $$$i$$$-th party has.", "output_spec": "If no coalition satisfying both conditions is possible, output a single line with an integer $$$0$$$. Otherwise, suppose there are $$$k$$$ ($$$1 \\leq k \\leq n$$$) parties in the coalition (Alice does not have to minimise the number of parties in a coalition), and their indices are $$$c_1, c_2, \\dots, c_k$$$ ($$$1 \\leq c_i \\leq n$$$). Output two lines, first containing the integer $$$k$$$, and the second the space-separated indices $$$c_1, c_2, \\dots, c_k$$$.  You may print the parties in any order. Alice's party (number $$$1$$$) must be on that list. If there are multiple solutions, you may print any of them.", "sample_inputs": ["3\n100 50 50", "3\n80 60 60", "2\n6 5", "4\n51 25 99 25"], "sample_outputs": ["2\n1 2", "0", "1\n1", "3\n1 2 4"], "notes": "NoteIn the first example, Alice picks the second party. Note that she can also pick the third party or both of them. However, she cannot become prime minister without any of them, because $$$100$$$ is not a strict majority out of $$$200$$$.In the second example, there is no way of building a majority, as both other parties are too large to become a coalition partner.In the third example, Alice already has the majority. The fourth example is described in the problem statement."}, "src_uid": "0a71fdaaf08c18396324ad762b7379d7"}
{"nl": {"description": "You have r red, g green and b blue balloons. To decorate a single table for the banquet you need exactly three balloons. Three balloons attached to some table shouldn't have the same color. What maximum number t of tables can be decorated if we know number of balloons of each color?Your task is to write a program that for given values r, g and b will find the maximum number t of tables, that can be decorated in the required manner.", "input_spec": "The single line contains three integers r, g and b (0\u2009\u2264\u2009r,\u2009g,\u2009b\u2009\u2264\u20092\u00b7109) \u2014 the number of red, green and blue baloons respectively. The numbers are separated by exactly one space.", "output_spec": "Print a single integer t \u2014 the maximum number of tables that can be decorated in the required manner.", "sample_inputs": ["5 4 3", "1 1 1", "2 3 3"], "sample_outputs": ["4", "1", "2"], "notes": "NoteIn the first sample you can decorate the tables with the following balloon sets: \"rgg\", \"gbb\", \"brr\", \"rrg\", where \"r\", \"g\" and \"b\" represent the red, green and blue balls, respectively."}, "src_uid": "bae7cbcde19114451b8712d6361d2b01"}
{"nl": {"description": "Your friend has recently learned about coprime numbers. A pair of numbers {a,\u2009b} is called coprime if the maximum number that divides both a and b is equal to one. Your friend often comes up with different statements. He has recently supposed that if the pair (a,\u2009b) is coprime and the pair (b,\u2009c) is coprime, then the pair (a,\u2009c) is coprime. You want to find a counterexample for your friend's statement. Therefore, your task is to find three distinct numbers (a,\u2009b,\u2009c), for which the statement is false, and the numbers meet the condition l\u2009\u2264\u2009a\u2009<\u2009b\u2009<\u2009c\u2009\u2264\u2009r. More specifically, you need to find three numbers (a,\u2009b,\u2009c), such that l\u2009\u2264\u2009a\u2009<\u2009b\u2009<\u2009c\u2009\u2264\u2009r, pairs (a,\u2009b) and (b,\u2009c) are coprime, and pair (a,\u2009c) is not coprime.", "input_spec": "The single line contains two positive space-separated integers l, r (1\u2009\u2264\u2009l\u2009\u2264\u2009r\u2009\u2264\u20091018; r\u2009-\u2009l\u2009\u2264\u200950).", "output_spec": "Print three positive space-separated integers a, b, c\u00a0\u2014 three distinct numbers (a,\u2009b,\u2009c) that form the counterexample. If there are several solutions, you are allowed to print any of them. The numbers must be printed in ascending order.  If the counterexample does not exist, print the single number -1.", "sample_inputs": ["2 4", "10 11", "900000000000000009 900000000000000029"], "sample_outputs": ["2 3 4", "-1", "900000000000000009 900000000000000010 900000000000000021"], "notes": "NoteIn the first sample pair (2,\u20094) is not coprime and pairs (2,\u20093) and (3,\u20094) are. In the second sample you cannot form a group of three distinct integers, so the answer is -1. In the third sample it is easy to see that numbers 900000000000000009 and 900000000000000021 are divisible by three. "}, "src_uid": "6c1ad1cc1fbecff69be37b1709a5236d"}
{"nl": {"description": "You are given n rectangles. The corners of rectangles have integer coordinates and their edges are parallel to the Ox and Oy axes. The rectangles may touch each other, but they do not overlap (that is, there are no points that belong to the interior of more than one rectangle). Your task is to determine if the rectangles form a square. In other words, determine if the set of points inside or on the border of at least one rectangle is precisely equal to the set of points inside or on the border of some square.", "input_spec": "The first line contains a single integer n (1\u2009\u2264\u2009n\u2009\u2264\u20095). Next n lines contain four integers each, describing a single rectangle: x1, y1, x2, y2 (0\u2009\u2264\u2009x1\u2009<\u2009x2\u2009\u2264\u200931400,\u20090\u2009\u2264\u2009y1\u2009<\u2009y2\u2009\u2264\u200931400) \u2014 x1 and x2 are x-coordinates of the left and right edges of the rectangle, and y1 and y2 are y-coordinates of the bottom and top edges of the rectangle.  No two rectangles overlap (that is, there are no points that belong to the interior of more than one rectangle).", "output_spec": "In a single line print \"YES\", if the given rectangles form a square, or \"NO\" otherwise.", "sample_inputs": ["5\n0 0 2 3\n0 3 3 5\n2 0 5 2\n3 2 5 5\n2 2 3 3", "4\n0 0 2 3\n0 3 3 5\n2 0 5 2\n3 2 5 5"], "sample_outputs": ["YES", "NO"], "notes": null}, "src_uid": "f63fc2d97fd88273241fce206cc217f2"}
{"nl": {"description": "So, the New Year holidays are over. Santa Claus and his colleagues can take a rest and have guests at last. When two \"New Year and Christmas Men\" meet, thear assistants cut out of cardboard the letters from the guest's name and the host's name in honor of this event. Then the hung the letters above the main entrance. One night, when everyone went to bed, someone took all the letters of our characters' names. Then he may have shuffled the letters and put them in one pile in front of the door.The next morning it was impossible to find the culprit who had made the disorder. But everybody wondered whether it is possible to restore the names of the host and his guests from the letters lying at the door? That is, we need to verify that there are no extra letters, and that nobody will need to cut more letters.Help the \"New Year and Christmas Men\" and their friends to cope with this problem. You are given both inscriptions that hung over the front door the previous night, and a pile of letters that were found at the front door next morning.", "input_spec": "The input file consists of three lines: the first line contains the guest's name, the second line contains the name of the residence host and the third line contains letters in a pile that were found at the door in the morning. All lines are not empty and contain only uppercase Latin letters. The length of each line does not exceed 100.", "output_spec": "Print \"YES\" without the quotes, if the letters in the pile could be permuted to make the names of the \"New Year and Christmas Men\". Otherwise, print \"NO\" without the quotes.", "sample_inputs": ["SANTACLAUS\nDEDMOROZ\nSANTAMOROZDEDCLAUS", "PAPAINOEL\nJOULUPUKKI\nJOULNAPAOILELUPUKKI", "BABBONATALE\nFATHERCHRISTMAS\nBABCHRISTMASBONATALLEFATHER"], "sample_outputs": ["YES", "NO", "NO"], "notes": "NoteIn the first sample the letters written in the last line can be used to write the names and there won't be any extra letters left.In the second sample letter \"P\" is missing from the pile and there's an extra letter \"L\".In the third sample there's an extra letter \"L\"."}, "src_uid": "b6456a39d38fabcd25267793ed94d90c"}
{"nl": {"description": "Let's define the permutation of length n as an array p\u2009=\u2009[p1,\u2009p2,\u2009...,\u2009pn] 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\u2009=\u2009[4,\u20091,\u20096,\u20092,\u20095,\u20093] 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,\u20091,\u20096,\u20092,\u20095,\u20093] 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,\u20091,\u20096,\u20092,\u20095,\u20093] will become [4,\u20092,\u20091,\u20095,\u20096,\u20093].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\u2009\u2264\u2009n\u2009\u2264\u200950, 1\u2009\u2264\u2009k\u2009\u2264\u2009min{1018,\u2009l} 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,\u20092,\u20093,\u20094], while the second permutation would be [1,\u20092,\u20094,\u20093]."}, "src_uid": "e03c6d3bb8cf9119530668765691a346"}
{"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\u2009+\u2009r 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,\u2009h (1\u2009\u2264\u2009r,\u2009h\u2009\u2264\u2009107).", "output_spec": "Print a single integer \u2014 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": "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\u2009\u2264\u2009n\u2009\u2264\u20091000)\u00a0\u2014 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": "Little Petya was given this problem for homework:You are given function  (here  represents the operation of taking the remainder). His task is to count the number of integers x in range [a;b] with property f(x)\u2009=\u2009x.It is a pity that Petya forgot the order in which the remainders should be taken and wrote down only 4 numbers. Each of 24 possible orders of taking the remainder has equal probability of being chosen. For example, if Petya has numbers 1, 2, 3, 4 then he can take remainders in that order or first take remainder modulo 4, then modulo 2, 3, 1. There also are 22 other permutations of these numbers that represent orders in which remainder can be taken. In this problem 4 numbers wrote down by Petya will be pairwise distinct.Now it is impossible for Petya to complete the task given by teacher but just for fun he decided to find the number of integers  with property that probability that f(x)\u2009=\u2009x is not less than 31.4159265352718281828459045%. In other words, Petya will pick up the number x if there exist at least 7 permutations of numbers p1,\u2009p2,\u2009p3,\u2009p4, for which f(x)\u2009=\u2009x.", "input_spec": "First line of the input will contain 6 integers, separated by spaces: p1,\u2009p2,\u2009p3,\u2009p4,\u2009a,\u2009b (1\u2009\u2264\u2009p1,\u2009p2,\u2009p3,\u2009p4\u2009\u2264\u20091000,\u20090\u2009\u2264\u2009a\u2009\u2264\u2009b\u2009\u2264\u200931415).  It is guaranteed that numbers p1,\u2009p2,\u2009p3,\u2009p4 will be pairwise distinct.", "output_spec": "Output the number of integers in the given range that have the given property.", "sample_inputs": ["2 7 1 8 2 8", "20 30 40 50 0 100", "31 41 59 26 17 43"], "sample_outputs": ["0", "20", "9"], "notes": null}, "src_uid": "63b9dc70e6ad83d89a487ffebe007b0a"}
{"nl": {"description": "Imp is watching a documentary about cave painting.  Some numbers, carved in chaotic order, immediately attracted his attention. Imp rapidly proposed a guess that they are the remainders of division of a number n by all integers i from 1 to k. Unfortunately, there are too many integers to analyze for Imp.Imp wants you to check whether all these remainders are distinct. Formally, he wants to check, if all , 1\u2009\u2264\u2009i\u2009\u2264\u2009k, are distinct, i.\u00a0e. there is no such pair (i,\u2009j) that:   1\u2009\u2264\u2009i\u2009<\u2009j\u2009\u2264\u2009k,  , where  is the remainder of division x by y. ", "input_spec": "The only line contains two integers n, k (1\u2009\u2264\u2009n,\u2009k\u2009\u2264\u20091018).", "output_spec": "Print \"Yes\", if all the remainders are distinct, and \"No\" otherwise. You can print each letter in arbitrary case (lower or upper).", "sample_inputs": ["4 4", "5 3"], "sample_outputs": ["No", "Yes"], "notes": "NoteIn the first sample remainders modulo 1 and 4 coincide."}, "src_uid": "5271c707c9c72ef021a0baf762bf3eb2"}
{"nl": {"description": "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\u2009\u2264\u2009n\u2009\u2264\u20091000, 1\u2009\u2264\u2009m\u2009\u2264\u200910, 1\u2009\u2264\u2009c0,\u2009d0\u2009\u2264\u2009100). Each of the following m lines contains 4 integers. The i-th line contains numbers ai, bi, ci and di (1\u2009\u2264\u2009ai,\u2009bi,\u2009ci,\u2009di\u2009\u2264\u2009100).", "output_spec": "Print the only number \u2014 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": "Calvin the robot lies in an infinite rectangular grid. Calvin's source code contains a list of n commands, each either 'U', 'R', 'D', or 'L'\u00a0\u2014 instructions to move a single square up, right, down, or left, respectively. How many ways can Calvin execute a non-empty contiguous substrings of commands and return to the same square he starts in? Two substrings are considered different if they have different starting or ending indices.", "input_spec": "The first line of the input contains a single positive integer, n (1\u2009\u2264\u2009n\u2009\u2264\u2009200)\u00a0\u2014 the number of commands. The next line contains n characters, each either 'U', 'R', 'D', or 'L'\u00a0\u2014 Calvin's source code.", "output_spec": "Print a single integer\u00a0\u2014 the number of contiguous substrings that Calvin can execute and return to his starting square.", "sample_inputs": ["6\nURLLDR", "4\nDLUU", "7\nRLRLRLR"], "sample_outputs": ["2", "0", "12"], "notes": "NoteIn the first case, the entire source code works, as well as the \"RL\" substring in the second and third characters.Note that, in the third case, the substring \"LR\" appears three times, and is therefore counted three times to the total result."}, "src_uid": "7bd5521531950e2de9a7b0904353184d"}
{"nl": {"description": "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 \u2014 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\u2009\u2264\u2009a,\u2009b,\u2009c\u2009\u2264\u2009106) \u2014 the valence numbers of the given atoms.", "output_spec": "If such a molecule can be built, print three space-separated integers \u2014 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": "In Berland each high school student is characterized by academic performance \u2014 integer value between 1 and 5.In high school 0xFF there are two groups of pupils: the group A and the group B. Each group consists of exactly n students. An academic performance of each student is known \u2014 integer value between 1 and 5.The school director wants to redistribute students between groups so that each of the two groups has the same number of students whose academic performance is equal to 1, the same number of students whose academic performance is 2 and so on. In other words, the purpose of the school director is to change the composition of groups, so that for each value of academic performance the numbers of students in both groups are equal.To achieve this, there is a plan to produce a series of exchanges of students between groups. During the single exchange the director selects one student from the class A and one student of class B. After that, they both change their groups.Print the least number of exchanges, in order to achieve the desired equal numbers of students for each academic performance.", "input_spec": "The first line of the input contains integer number n (1\u2009\u2264\u2009n\u2009\u2264\u2009100) \u2014 number of students in both groups. The second line contains sequence of integer numbers a1,\u2009a2,\u2009...,\u2009an (1\u2009\u2264\u2009ai\u2009\u2264\u20095), where ai is academic performance of the i-th student of the group A. The third line contains sequence of integer numbers b1,\u2009b2,\u2009...,\u2009bn (1\u2009\u2264\u2009bi\u2009\u2264\u20095), where bi is academic performance of the i-th student of the group B.", "output_spec": "Print the required minimum number of exchanges or -1, if the desired distribution of students can not be obtained.", "sample_inputs": ["4\n5 4 4 4\n5 5 4 5", "6\n1 1 1 1 1 1\n5 5 5 5 5 5", "1\n5\n3", "9\n3 2 5 5 2 3 3 3 2\n4 1 4 1 1 2 4 4 1"], "sample_outputs": ["1", "3", "-1", "4"], "notes": null}, "src_uid": "47da1dd95cd015acb8c7fd6ae5ec22a3"}
{"nl": {"description": "Right now she actually isn't. But she will be, if you don't solve this problem.You are given integers n, k, A and B. There is a number x, which is initially equal to n. You are allowed to perform two types of operations:   Subtract 1 from x. This operation costs you A coins.  Divide x by k. Can be performed only if x is divisible by k. This operation costs you B coins.  What is the minimum amount of coins you have to pay to make x equal to 1?", "input_spec": "The first line contains a single integer n (1\u2009\u2264\u2009n\u2009\u2264\u20092\u00b7109). The second line contains a single integer k (1\u2009\u2264\u2009k\u2009\u2264\u20092\u00b7109). The third line contains a single integer A (1\u2009\u2264\u2009A\u2009\u2264\u20092\u00b7109). The fourth line contains a single integer B (1\u2009\u2264\u2009B\u2009\u2264\u20092\u00b7109).", "output_spec": "Output a single integer\u00a0\u2014 the minimum amount of coins you have to pay to make x equal to 1.", "sample_inputs": ["9\n2\n3\n1", "5\n5\n2\n20", "19\n3\n4\n2"], "sample_outputs": ["6", "8", "12"], "notes": "NoteIn the first testcase, the optimal strategy is as follows:   Subtract 1 from x (9\u2009\u2192\u20098) paying 3 coins.  Divide x by 2 (8\u2009\u2192\u20094) paying 1 coin.  Divide x by 2 (4\u2009\u2192\u20092) paying 1 coin.  Divide x by 2 (2\u2009\u2192\u20091) paying 1 coin. The total cost is 6 coins.In the second test case the optimal strategy is to subtract 1 from x 4 times paying 8 coins in total."}, "src_uid": "f838fae7c98bf51cfa0b9bd158650b10"}
{"nl": {"description": "The only difference between easy and hard versions is constraints.Polycarp loves to listen to music, so he never leaves the player, even on the way home from the university. Polycarp overcomes the distance from the university to the house in exactly $$$T$$$ minutes.In the player, Polycarp stores $$$n$$$ songs, each of which is characterized by two parameters: $$$t_i$$$ and $$$g_i$$$, where $$$t_i$$$ is the length of the song in minutes ($$$1 \\le t_i \\le 15$$$), $$$g_i$$$ is its genre ($$$1 \\le g_i \\le 3$$$).Polycarp wants to create such a playlist so that he can listen to music all the time on the way from the university to his home, and at the time of his arrival home, the playlist is over. Polycarp never interrupts songs and always listens to them from beginning to end. Thus, if he started listening to the $$$i$$$-th song, he would spend exactly $$$t_i$$$ minutes on its listening. Polycarp also does not like when two songs of the same genre play in a row (i.e. successively/adjacently) or when the songs in his playlist are repeated.Help Polycarpus count the number of different sequences of songs (their order matters), the total duration is exactly $$$T$$$, such that there are no two consecutive songs of the same genre in them and all the songs in the playlist are different.", "input_spec": "The first line of the input contains two integers $$$n$$$ and $$$T$$$ ($$$1 \\le n \\le 15, 1 \\le T \\le 225$$$) \u2014 the number of songs in the player and the required total duration, respectively. Next, the $$$n$$$ lines contain descriptions of songs: the $$$i$$$-th line contains two integers $$$t_i$$$ and $$$g_i$$$ ($$$1 \\le t_i \\le 15, 1 \\le g_i \\le 3$$$) \u2014 the duration of the $$$i$$$-th song and its genre, respectively.", "output_spec": "Output one integer \u2014 the number of different sequences of songs, the total length of exactly $$$T$$$, such that there are no two consecutive songs of the same genre in them and all the songs in the playlist are different. Since the answer may be huge, output it modulo $$$10^9 + 7$$$ (that is, the remainder when dividing the quantity by $$$10^9 + 7$$$).", "sample_inputs": ["3 3\n1 1\n1 2\n1 3", "3 3\n1 1\n1 1\n1 3", "4 10\n5 3\n2 1\n3 2\n5 1"], "sample_outputs": ["6", "2", "10"], "notes": "NoteIn the first example, Polycarp can make any of the $$$6$$$ possible playlist by rearranging the available songs: $$$[1, 2, 3]$$$, $$$[1, 3, 2]$$$, $$$[2, 1, 3]$$$, $$$[2, 3, 1]$$$, $$$[3, 1, 2]$$$ and $$$[3, 2, 1]$$$ (indices of the songs are given).In the second example, the first and second songs cannot go in succession (since they have the same genre). Thus, Polycarp can create a playlist in one of $$$2$$$ possible ways: $$$[1, 3, 2]$$$ and $$$[2, 3, 1]$$$ (indices of the songs are given).In the third example, Polycarp can make the following playlists: $$$[1, 2, 3]$$$, $$$[1, 3, 2]$$$, $$$[2, 1, 3]$$$, $$$[2, 3, 1]$$$, $$$[3, 1, 2]$$$, $$$[3, 2, 1]$$$, $$$[1, 4]$$$, $$$[4, 1]$$$, $$$[2, 3, 4]$$$ and $$$[4, 3, 2]$$$ (indices of the songs are given)."}, "src_uid": "ac2a37ff4c7e89a345b189e4891bbf56"}
{"nl": {"description": "Petya loves lucky numbers very much. Everybody knows that lucky numbers are positive integers whose decimal record contains only the lucky digits 4 and 7. For example, numbers 47, 744, 4 are lucky and 5, 17, 467 are not.Petya calls a mask of a positive integer n the number that is obtained after successive writing of all lucky digits of number n from the left to the right. For example, the mask of number 72174994 is number 7744, the mask of 7 is 7, the mask of 9999047 is 47. Obviously, mask of any number is always a lucky number.Petya has two numbers \u2014 an arbitrary integer a and a lucky number b. Help him find the minimum number c (c\u2009>\u2009a) such that the mask of number c equals b.", "input_spec": "The only line contains two integers a and b (1\u2009\u2264\u2009a,\u2009b\u2009\u2264\u2009105). It is guaranteed that number b is lucky.", "output_spec": "In the only line print a single number \u2014 the number c that is sought by Petya.", "sample_inputs": ["1 7", "100 47"], "sample_outputs": ["7", "147"], "notes": null}, "src_uid": "e5e4ea7a5bf785e059e10407b25d73fb"}
{"nl": {"description": "Two bored soldiers are playing card war. Their card deck consists of exactly n cards, numbered from 1 to n, all values are different. They divide cards between them in some manner, it's possible that they have different number of cards. Then they play a \"war\"-like card game. The rules are following. On each turn a fight happens. Each of them picks card from the top of his stack and puts on the table. The one whose card value is bigger wins this fight and takes both cards from the table to the bottom of his stack. More precisely, he first takes his opponent's card and puts to the bottom of his stack, and then he puts his card to the bottom of his stack. If after some turn one of the player's stack becomes empty, he loses and the other one wins. You have to calculate how many fights will happen and who will win the game, or state that game won't end.", "input_spec": "First line contains a single integer n (2\u2009\u2264\u2009n\u2009\u2264\u200910), the number of cards. Second line contains integer k1 (1\u2009\u2264\u2009k1\u2009\u2264\u2009n\u2009-\u20091), the number of the first soldier's cards. Then follow k1 integers that are the values on the first soldier's cards, from top to bottom of his stack. Third line contains integer k2 (k1\u2009+\u2009k2\u2009=\u2009n), the number of the second soldier's cards. Then follow k2 integers that are the values on the second soldier's cards, from top to bottom of his stack. All card values are different.", "output_spec": "If somebody wins in this game, print 2 integers where the first one stands for the number of fights before end of game and the second one is 1 or 2 showing which player has won. If the game won't end and will continue forever output \u2009-\u20091.", "sample_inputs": ["4\n2 1 3\n2 4 2", "3\n1 2\n2 1 3"], "sample_outputs": ["6 2", "-1"], "notes": "NoteFirst sample:   Second sample:   "}, "src_uid": "f587b1867754e6958c3d7e0fe368ec6e"}
{"nl": {"description": "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\u00a0\u2014\u00a0a 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$$$ tiles. As each tile can be rotated in one of four ways, he still needs to decide on how exactly he will tile the floor. There is a single aesthetic criterion that he wants to fulfil: two adjacent tiles must not share a colour on the edge\u00a0\u2014\u00a0i.e. one of the tiles must have a white colour on the shared border, and the second one must be black.    The picture on the left shows one valid tiling of a $$$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$$$\u00a0($$$1 \\leq w,h \\leq 1\\,000$$$)\u00a0\u2014\u00a0the width and height of the kitchen, measured in tiles.", "output_spec": "Output a single integer $$$n$$$\u00a0\u2014\u00a0the remainder of the number of tilings when divided by $$$998244353$$$.", "sample_inputs": ["2 2", "2 4"], "sample_outputs": ["16", "64"], "notes": null}, "src_uid": "8b2a9ae21740c89079a6011a30cd6aee"}
{"nl": {"description": "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\u2009\u00d7\u20098 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 \u2014 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 \u2014 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 \u2014 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": "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$$$)\u00a0\u2014 the size of the lost array and the range of numbers in the array.", "output_spec": "Print the remainder when dividing by $$$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": "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\u2009\u2264\u2009t\u2009\u2264\u200910000). 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": "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 \u2014 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\u2009\u2264\u2009n,\u2009s\u2009\u2264\u20091018).", "output_spec": "Print one integer \u2014 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\u2009-\u20093\u2009\u2265\u200920).In the third example 10 is the only really big number (10\u2009-\u20091\u2009\u2265\u20099)."}, "src_uid": "9704e2ac6a158d5ced8fd1dc1edb356b"}
{"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": "InputThe input consists of a single string of uppercase letters A-Z. The length of the string is between 1 and 10 characters, inclusive.OutputOutput \"YES\" or \"NO\".ExamplesInput\nHELP\nOutput\nYES\nInput\nAID\nOutput\nNO\nInput\nMARY\nOutput\nNO\nInput\nANNA\nOutput\nYES\nInput\nMUG\nOutput\nYES\nInput\nCUP\nOutput\nNO\nInput\nSUM\nOutput\nYES\nInput\nPRODUCT\nOutput\nNO\n", "input_spec": "The input consists of a single string of uppercase letters A-Z. The length of the string is between 1 and 10 characters, inclusive.", "output_spec": "Output \"YES\" or \"NO\".", "sample_inputs": ["HELP", "AID", "MARY", "ANNA", "MUG", "CUP", "SUM", "PRODUCT"], "sample_outputs": ["YES", "NO", "NO", "YES", "YES", "NO", "YES", "NO"], "notes": null}, "src_uid": "27e977b41f5b6970a032d13e53db2a6a"}
{"nl": {"description": "Mr. Bender has a digital table of size n\u2009\u00d7\u2009n, each cell can be switched on or off. He wants the field to have at least c switched on squares. When this condition is fulfilled, Mr Bender will be happy.We'll consider the table rows numbered from top to bottom from 1 to n, and the columns \u2014 numbered from left to right from 1 to n. Initially there is exactly one switched on cell with coordinates (x,\u2009y) (x is the row number, y is the column number), and all other cells are switched off. Then each second we switch on the cells that are off but have the side-adjacent cells that are on.For a cell with coordinates (x,\u2009y) the side-adjacent cells are cells with coordinates (x\u2009-\u20091,\u2009y), (x\u2009+\u20091,\u2009y), (x,\u2009y\u2009-\u20091), (x,\u2009y\u2009+\u20091).In how many seconds will Mr. Bender get happy?", "input_spec": "The first line contains four space-separated integers n,\u2009x,\u2009y,\u2009c (1\u2009\u2264\u2009n,\u2009c\u2009\u2264\u2009109;\u00a01\u2009\u2264\u2009x,\u2009y\u2009\u2264\u2009n;\u00a0c\u2009\u2264\u2009n2).", "output_spec": "In a single line print a single integer \u2014 the answer to the problem.", "sample_inputs": ["6 4 3 1", "9 3 8 10"], "sample_outputs": ["0", "2"], "notes": "NoteInitially the first test has one painted cell, so the answer is 0. In the second test all events will go as is shown on the figure. ."}, "src_uid": "232c5206ee7c1903556c3625e0b0efc6"}
{"nl": {"description": "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 \u2014 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 \u2014 as 'R', the bishop \u2014 as'B', the knight \u2014 as 'N', the pawn \u2014 as 'P', the king \u2014 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": "Mr. Santa asks all the great programmers of the world to solve a trivial problem. He gives them an integer m and asks for the number of positive integers n, such that the factorial of n ends with exactly m zeroes. Are you among those great programmers who can solve this problem?", "input_spec": "The only line of input contains an integer m (1\u2009\u2264\u2009m\u2009\u2264\u2009100\u2009000)\u00a0\u2014 the required number of trailing zeroes in factorial.", "output_spec": "First print k\u00a0\u2014 the number of values of n such that the factorial of n ends with m zeroes. Then print these k integers in increasing order.", "sample_inputs": ["1", "5"], "sample_outputs": ["5\n5 6 7 8 9", "0"], "notes": "NoteThe factorial of n is equal to the product of all integers from 1 to n inclusive, that is n!\u2009=\u20091\u00b72\u00b73\u00b7...\u00b7n.In the first sample, 5!\u2009=\u2009120, 6!\u2009=\u2009720, 7!\u2009=\u20095040, 8!\u2009=\u200940320 and 9!\u2009=\u2009362880."}, "src_uid": "c27ecc6e4755b21f95a6b1b657ef0744"}
{"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\u2009\u2264\u2009n\u2009\u2264\u20092\u00b7108) and integer m (1\u2009\u2264\u2009m\u2009\u2264\u200920). The i\u2009+\u20091-th line contains a pair of numbers ai and bi (1\u2009\u2264\u2009ai\u2009\u2264\u2009108,\u20091\u2009\u2264\u2009bi\u2009\u2264\u200910). All the input numbers are integer.", "output_spec": "Output the only number \u2014 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": "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$$$) and describes Bob's lucky days. It is guaranteed that both Alice and Bob have some unlucky days.", "output_spec": "Print one integer: the maximum number of days in the row that are lucky for both Alice and Bob.", "sample_inputs": ["0 2 5\n1 3 5", "0 1 3\n2 3 6"], "sample_outputs": ["2", "1"], "notes": "NoteThe graphs below correspond to the two sample tests and show the lucky and unlucky days of Alice and Bob as well as the possible solutions for these tests."}, "src_uid": "faa75751c05c3ff919ddd148c6784910"}
{"nl": {"description": "Petr has just bought a new car. He's just arrived at the most known Petersburg's petrol station to refuel it when he suddenly discovered that the petrol tank is secured with a combination lock! The lock has a scale of $$$360$$$ degrees and a pointer which initially points at zero:  Petr called his car dealer, who instructed him to rotate the lock's wheel exactly $$$n$$$ times. The $$$i$$$-th rotation should be $$$a_i$$$ degrees, either clockwise or counterclockwise, and after all $$$n$$$ rotations the pointer should again point at zero.This confused Petr a little bit as he isn't sure which rotations should be done clockwise and which should be done counterclockwise. As there are many possible ways of rotating the lock, help him and find out whether there exists at least one, such that after all $$$n$$$ rotations the pointer will point at zero again.", "input_spec": "The first line contains one integer $$$n$$$ ($$$1 \\leq n \\leq 15$$$) \u2014 the number of rotations. Each of the following $$$n$$$ lines contains one integer $$$a_i$$$ ($$$1 \\leq a_i \\leq 180$$$) \u2014 the angle of the $$$i$$$-th rotation in degrees.", "output_spec": "If it is possible to do all the rotations so that the pointer will point at zero after all of them are performed, print a single word \"YES\". Otherwise, print \"NO\". Petr will probably buy a new car in this case. You can print each letter in any case (upper or lower).", "sample_inputs": ["3\n10\n20\n30", "3\n10\n10\n10", "3\n120\n120\n120"], "sample_outputs": ["YES", "NO", "YES"], "notes": "NoteIn the first example, we can achieve our goal by applying the first and the second rotation clockwise, and performing the third rotation counterclockwise.In the second example, it's impossible to perform the rotations in order to make the pointer point at zero in the end.In the third example, Petr can do all three rotations clockwise. In this case, the whole wheel will be rotated by $$$360$$$ degrees clockwise and the pointer will point at zero again."}, "src_uid": "01b50fcba4185ceb1eb8e4ba04a0cc10"}
{"nl": {"description": "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\u2009+\u20091)-th position, then at time x\u2009+\u20091 the i-th position will have a girl and the (i\u2009+\u20091)-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\u2009\u2264\u2009n,\u2009t\u2009\u2264\u200950), 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": "Polycarpus is an amateur businessman. Recently he was surprised to find out that the market for paper scissors is completely free! Without further ado, Polycarpus decided to start producing and selling such scissors.Polycaprus calculated that the optimal celling price for such scissors would be p bourles. However, he read somewhere that customers are attracted by prices that say something like \"Special Offer! Super price 999 bourles!\". So Polycarpus decided to lower the price a little if it leads to the desired effect.Polycarpus agrees to lower the price by no more than d bourles so that the number of nines at the end of the resulting price is maximum. If there are several ways to do it, he chooses the maximum possible price.Note, Polycarpus counts only the trailing nines in a price.", "input_spec": "The first line contains two integers p and d (1\u2009\u2264\u2009p\u2009\u2264\u20091018; 0\u2009\u2264\u2009d\u2009<\u2009p) \u2014 the initial price of scissors and the maximum possible price reduction. Please, do not use the %lld specifier to read or write 64-bit integers in \u0421++. It is preferred to use cin, cout streams or the %I64d specifier.", "output_spec": "Print the required price \u2014 the maximum price that ends with the largest number of nines and that is less than p by no more than d. The required number shouldn't have leading zeroes.", "sample_inputs": ["1029 102", "27191 17"], "sample_outputs": ["999", "27189"], "notes": null}, "src_uid": "c706cfcd4c37fbc1b1631aeeb2c02b6a"}
{"nl": {"description": "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$$$) \u2014 the number of test cases. Then $$$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) \u2014 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": "In some game by Playrix it takes t minutes for an oven to bake k carrot cakes, all cakes are ready at the same moment t minutes after they started baking. Arkady needs at least n cakes to complete a task, but he currently don't have any. However, he has infinitely many ingredients and one oven. Moreover, Arkady can build one more similar oven to make the process faster, it would take d minutes to build the oven. While the new oven is being built, only old one can bake cakes, after the new oven is built, both ovens bake simultaneously. Arkady can't build more than one oven.Determine if it is reasonable to build the second oven, i.e. will it decrease the minimum time needed to get n cakes or not. If the time needed with the second oven is the same as with one oven, then it is unreasonable.", "input_spec": "The only line contains four integers n, t, k, d (1\u2009\u2264\u2009n,\u2009t,\u2009k,\u2009d\u2009\u2264\u20091\u2009000)\u00a0\u2014 the number of cakes needed, the time needed for one oven to bake k cakes, the number of cakes baked at the same time, the time needed to build the second oven. ", "output_spec": "If it is reasonable to build the second oven, print \"YES\". Otherwise print \"NO\".", "sample_inputs": ["8 6 4 5", "8 6 4 6", "10 3 11 4", "4 2 1 4"], "sample_outputs": ["YES", "NO", "NO", "YES"], "notes": "NoteIn the first example it is possible to get 8 cakes in 12 minutes using one oven. The second oven can be built in 5 minutes, so after 6 minutes the first oven bakes 4 cakes, the second oven bakes 4 more ovens after 11 minutes. Thus, it is reasonable to build the second oven. In the second example it doesn't matter whether we build the second oven or not, thus it takes 12 minutes to bake 8 cakes in both cases. Thus, it is unreasonable to build the second oven.In the third example the first oven bakes 11 cakes in 3 minutes, that is more than needed 10. It is unreasonable to build the second oven, because its building takes more time that baking the needed number of cakes using the only oven."}, "src_uid": "32c866d3d394e269724b4930df5e4407"}
{"nl": {"description": "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\u2009-\u20091, inclusively.    Consider an example. Let L\u2009=\u20098, blue points are barriers, and green points are Kefa's start (A) and Sasha's start (B). Then Kefa writes down the sequence [2,\u20094,\u20096], and Sasha writes down [1,\u20095,\u20097]. 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 \u2014 counterclockwise, if you look on a track from above. ", "input_spec": "The first line contains two integers n and L (1\u2009\u2264\u2009n\u2009\u2264\u200950, n\u2009\u2264\u2009L\u2009\u2264\u2009100) \u2014 the number of barriers on a track and its length.  The second line contains n distinct integers in the ascending order \u2014 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\u2009-\u20091 inclusively. The second line contains n distinct integers in the ascending order \u2014 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\u2009-\u20091 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": "This winter is so cold in Nvodsk! A group of n friends decided to buy k bottles of a soft drink called \"Take-It-Light\" to warm up a bit. Each bottle has l milliliters of the drink. Also they bought c limes and cut each of them into d slices. After that they found p grams of salt.To make a toast, each friend needs nl milliliters of the drink, a slice of lime and np grams of salt. The friends want to make as many toasts as they can, provided they all drink the same amount. How many toasts can each friend make?", "input_spec": "The first and only line contains positive integers n, k, l, c, d, p, nl, np, not exceeding 1000 and no less than 1. The numbers are separated by exactly one space.", "output_spec": "Print a single integer \u2014 the number of toasts each friend can make.", "sample_inputs": ["3 4 5 10 8 100 3 1", "5 100 10 1 19 90 4 3", "10 1000 1000 25 23 1 50 1"], "sample_outputs": ["2", "3", "0"], "notes": "NoteA comment to the first sample: Overall the friends have 4\u2009*\u20095\u2009=\u200920 milliliters of the drink, it is enough to make 20\u2009/\u20093\u2009=\u20096 toasts. The limes are enough for 10\u2009*\u20098\u2009=\u200980 toasts and the salt is enough for 100\u2009/\u20091\u2009=\u2009100 toasts. However, there are 3 friends in the group, so the answer is min(6,\u200980,\u2009100)\u2009/\u20093\u2009=\u20092."}, "src_uid": "67410b7d36b9d2e6a97ca5c7cff317c1"}
{"nl": {"description": "The recent All-Berland Olympiad in Informatics featured n participants with each scoring a certain amount of points.As the head of the programming committee, you are to determine the set of participants to be awarded with diplomas with respect to the following criteria:   At least one participant should get a diploma.  None of those with score equal to zero should get awarded.  When someone is awarded, all participants with score not less than his score should also be awarded. Determine the number of ways to choose a subset of participants that will receive the diplomas.", "input_spec": "The first line contains a single integer n (1\u2009\u2264\u2009n\u2009\u2264\u2009100)\u00a0\u2014 the number of participants. The next line contains a sequence of n integers a1,\u2009a2,\u2009...,\u2009an (0\u2009\u2264\u2009ai\u2009\u2264\u2009600)\u00a0\u2014 participants' scores. It's guaranteed that at least one participant has non-zero score.", "output_spec": "Print a single integer\u00a0\u2014 the desired number of ways.", "sample_inputs": ["4\n1 3 3 2", "3\n1 1 1", "4\n42 0 0 42"], "sample_outputs": ["3", "1", "1"], "notes": "NoteThere are three ways to choose a subset in sample case one.  Only participants with 3 points will get diplomas.  Participants with 2 or 3 points will get diplomas.  Everyone will get a diploma! The only option in sample case two is to award everyone.Note that in sample case three participants with zero scores cannot get anything."}, "src_uid": "3b520c15ea9a11b16129da30dcfb5161"}
{"nl": {"description": "Reca company makes monitors, the most popular of their models is AB999 with the screen size a\u2009\u00d7\u2009b centimeters. Because of some production peculiarities a screen parameters are integer numbers. Recently the screen sides ratio x:\u2009y became popular with users. That's why the company wants to reduce monitor AB999 size so that its screen sides ratio becomes x:\u2009y, at the same time they want its total area to be maximal of all possible variants. Your task is to find the screen parameters of the reduced size model, or find out that such a reduction can't be performed.", "input_spec": "The first line of the input contains 4 integers \u2014 a, b, x and y (1\u2009\u2264\u2009a,\u2009b,\u2009x,\u2009y\u2009\u2264\u20092\u00b7109).", "output_spec": "If the answer exists, output 2 positive integers \u2014 screen parameters of the reduced size model. Output 0 0 otherwise.", "sample_inputs": ["800 600 4 3", "1920 1200 16 9", "1 1 1 2"], "sample_outputs": ["800 600", "1920 1080", "0 0"], "notes": null}, "src_uid": "97999cd7c6de79a4e39f56a41ff59e7a"}
{"nl": {"description": "Count the number of distinct sequences a1,\u2009a2,\u2009...,\u2009an (1\u2009\u2264\u2009ai) consisting of positive integers such that gcd(a1,\u2009a2,\u2009...,\u2009an)\u2009=\u2009x and . As this number could be large, print the answer modulo 109\u2009+\u20097.gcd here means the greatest common divisor.", "input_spec": "The only line contains two positive integers x and y (1\u2009\u2264\u2009x,\u2009y\u2009\u2264\u2009109).", "output_spec": "Print the number of such sequences modulo 109\u2009+\u20097.", "sample_inputs": ["3 9", "5 8"], "sample_outputs": ["3", "0"], "notes": "NoteThere are three suitable sequences in the first test: (3,\u20093,\u20093), (3,\u20096), (6,\u20093).There are no suitable sequences in the second test."}, "src_uid": "de7731ce03735b962ee033613192f7bc"}
{"nl": {"description": "Petya is having a party soon, and he has decided to invite his $$$n$$$ friends.He wants to make invitations in the form of origami. For each invitation, he needs two red sheets, five green sheets, and eight blue sheets. The store sells an infinite number of notebooks of each color, but each notebook consists of only one color with $$$k$$$ sheets. That is, each notebook contains $$$k$$$ sheets of either red, green, or blue.Find the minimum number of notebooks that Petya needs to buy to invite all $$$n$$$ of his friends.", "input_spec": "The first line contains two integers $$$n$$$ and $$$k$$$ ($$$1\\leq n, k\\leq 10^8$$$)\u00a0\u2014 the number of Petya's friends and the number of sheets in each notebook respectively.", "output_spec": "Print one number\u00a0\u2014 the minimum number of notebooks that Petya needs to buy.", "sample_inputs": ["3 5", "15 6"], "sample_outputs": ["10", "38"], "notes": "NoteIn the first example, we need $$$2$$$ red notebooks, $$$3$$$ green notebooks, and $$$5$$$ blue notebooks.In the second example, we need $$$5$$$ red notebooks, $$$13$$$ green notebooks, and $$$20$$$ blue notebooks."}, "src_uid": "d259a3a5c38af34b2a15d61157cc0a39"}
{"nl": {"description": "The only difference between easy and hard versions is the length of the string.You are given a string $$$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$$$.", "output_spec": "Print one integer \u2014 the maximum possible length of the substring you can remove so that $$$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": "User ainta is making a web site. This time he is going to make a navigation of the pages. In his site, there are n pages numbered by integers from 1 to n. Assume that somebody is on the p-th page now. The navigation will look like this: << p\u2009-\u2009k p\u2009-\u2009k\u2009+\u20091 ... p\u2009-\u20091 (p) p\u2009+\u20091 ... p\u2009+\u2009k\u2009-\u20091 p\u2009+\u2009k >> When someone clicks the button \"<<\" he is redirected to page 1, and when someone clicks the button \">>\" he is redirected to page n. Of course if someone clicks on a number, he is redirected to the corresponding page.There are some conditions in the navigation:  If page 1 is in the navigation, the button \"<<\" must not be printed.  If page n is in the navigation, the button \">>\" must not be printed.  If the page number is smaller than 1 or greater than n, it must not be printed.  \u00a0You can see some examples of the navigations. Make a program that prints the navigation.", "input_spec": "The first and the only line contains three integers n, p, k (3\u2009\u2264\u2009n\u2009\u2264\u2009100; 1\u2009\u2264\u2009p\u2009\u2264\u2009n; 1\u2009\u2264\u2009k\u2009\u2264\u2009n)", "output_spec": "Print the proper navigation. Follow the format of the output from the test samples.", "sample_inputs": ["17 5 2", "6 5 2", "6 1 2", "6 2 2", "9 6 3", "10 6 3", "8 5 4"], "sample_outputs": ["<< 3 4 (5) 6 7 >>", "<< 3 4 (5) 6", "(1) 2 3 >>", "1 (2) 3 4 >>", "<< 3 4 5 (6) 7 8 9", "<< 3 4 5 (6) 7 8 9 >>", "1 2 3 4 (5) 6 7 8"], "notes": null}, "src_uid": "526e2cce272e42a3220e33149b1c9c84"}
{"nl": {"description": "There is a legend in the IT City college. A student that failed to answer all questions on the game theory exam is given one more chance by his professor. The student has to play a game with the professor.The game is played on a square field consisting of n\u2009\u00d7\u2009n cells. Initially all cells are empty. On each turn a player chooses and paint an empty cell that has no common sides with previously painted cells. Adjacent corner of painted cells is allowed. On the next turn another player does the same, then the first one and so on. The player with no cells to paint on his turn loses.The professor have chosen the field size n and allowed the student to choose to be the first or the second player in the game. What should the student choose to win the game? Both players play optimally.", "input_spec": "The only line of the input contains one integer n (1\u2009\u2264\u2009n\u2009\u2264\u20091018) \u2014 the size of the field.", "output_spec": "Output number 1, if the player making the first turn wins when both players play optimally, otherwise print number 2.", "sample_inputs": ["1", "2"], "sample_outputs": ["1", "2"], "notes": null}, "src_uid": "816ec4cd9736f3113333ef05405b8e81"}
{"nl": {"description": "You are given an integer array $$$a_0, a_1, \\dots, a_{n - 1}$$$, and an integer $$$k$$$. You perform the following code with it:long long ans = 0; // create a 64-bit signed variable which is initially equal to 0for(int i = 1; i <= k; i++){  int idx = rnd.next(0, n - 1); // generate a random integer between 0 and n - 1, both inclusive                                // each integer from 0 to n - 1 has the same probability of being chosen  ans += a[idx];  a[idx] -= (a[idx] % i);}Your task is to calculate the expected value of the variable ans after performing this code.Note that the input is generated according to special rules (see the input format section).", "input_spec": "The only line contains six integers $$$n$$$, $$$a_0$$$, $$$x$$$, $$$y$$$, $$$k$$$ and $$$M$$$ ($$$1 \\le n \\le 10^7$$$; $$$1 \\le a_0, x, y < M \\le 998244353$$$; $$$1 \\le k \\le 17$$$). The array $$$a$$$ in the input is constructed as follows:   $$$a_0$$$ is given in the input;  for every $$$i$$$ from $$$1$$$ to $$$n - 1$$$, the value of $$$a_i$$$ can be calculated as $$$a_i = (a_{i - 1} \\cdot x + y) \\bmod M$$$. ", "output_spec": "Let the expected value of the variable ans after performing the code be $$$E$$$. It can be shown that $$$E \\cdot n^k$$$ is an integer. You have to output this integer modulo $$$998244353$$$.", "sample_inputs": ["3 10 3 5 13 88", "2 15363 270880 34698 17 2357023"], "sample_outputs": ["382842030", "319392398"], "notes": "NoteThe array in the first example test is $$$[10, 35, 22]$$$. In the second example, it is $$$[15363, 1418543]$$$."}, "src_uid": "1d45491e28d24e2b318605cd328d6ecf"}
{"nl": {"description": "Andrey received a postcard from Irina. It contained only the words \"Hello, Andrey!\", and a strange string consisting of lowercase Latin letters, snowflakes and candy canes. Andrey thought that this string is an encrypted message, and decided to decrypt it.Andrey noticed that snowflakes and candy canes always stand after the letters, so he supposed that the message was encrypted as follows. Candy cane means that the letter before it can be removed, or can be left. A snowflake means that the letter before it can be removed, left, or repeated several times.For example, consider the following string:   This string can encode the message \u00abhappynewyear\u00bb. For this, candy canes and snowflakes should be used as follows:   candy cane 1: remove the letter w,  snowflake 1: repeat the letter p twice,  candy cane 2: leave the letter n,  snowflake 2: remove the letter w,  snowflake 3: leave the letter e.   Please note that the same string can encode different messages. For example, the string above can encode \u00abhayewyar\u00bb, \u00abhapppppynewwwwwyear\u00bb, and other messages.Andrey knows that messages from Irina usually have a length of $$$k$$$ letters. Help him to find out if a given string can encode a message of $$$k$$$ letters, and if so, give an example of such a message.", "input_spec": "The first line contains the string received in the postcard. The string consists only of lowercase Latin letters, as well as the characters \u00ab*\u00bb and \u00ab?\u00bb, meaning snowflake and candy cone, respectively. These characters can only appear immediately after the letter. The length of the string does not exceed $$$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 \u00abImpossible\u00bb 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": "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 \u2014 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\u2009\u2264\u2009n\u2009\u2264\u2009100) \u2014 the number of testcases. The i-th of the following n lines contains one integer xi (1\u2009\u2264\u2009xi\u2009\u2264\u2009100) \u2014 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": "Some days ago, I learned the concept of LCM (least common multiple). I've played with it for several times and I want to make a big number with it.But I also don't want to use many numbers, so I'll choose three positive integers (they don't have to be distinct) which are not greater than n. Can you help me to find the maximum possible least common multiple of these three integers?", "input_spec": "The first line contains an integer n (1\u2009\u2264\u2009n\u2009\u2264\u2009106) \u2014 the n mentioned in the statement.", "output_spec": "Print a single integer \u2014 the maximum possible LCM of three not necessarily distinct positive integers that are not greater than n.", "sample_inputs": ["9", "7"], "sample_outputs": ["504", "210"], "notes": "NoteThe least common multiple of some positive integers is the least positive integer which is multiple for each of them.The result may become very large, 32-bit integer won't be enough. So using 64-bit integers is recommended.For the last example, we can chose numbers 7, 6, 5 and the LCM of them is 7\u00b76\u00b75\u2009=\u2009210. It is the maximum value we can get."}, "src_uid": "25e5afcdf246ee35c9cef2fcbdd4566e"}
{"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\u2009\u2264\u2009n\u2009\u2264\u20099)\u00a0\u2014 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": "Polycarpus has got n candies and m friends (n\u2009\u2265\u2009m). 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\u2009\u2264\u2009n,\u2009m\u2009\u2264\u2009100;n\u2009\u2265\u2009m) \u2014 the number of candies and the number of Polycarpus's friends.", "output_spec": "Print the required sequence a1,\u2009a2,\u2009...,\u2009am, 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": "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\u2009\u2264\u2009n\u2009\u2264\u2009100) \u2014 the number of letters in word s before the correction. The second line contains a string s consisting of exactly n lowercase Latin letters \u2014 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": "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\u2009\u00d7\u2009m 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,\u2009j) 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,\u2009y) on the board to position (x\u2009-\u2009a,\u2009y\u2009-\u2009b);  move the candy from position (x,\u2009y) on the board to position (x\u2009+\u2009a,\u2009y\u2009-\u2009b);  move the candy from position (x,\u2009y) on the board to position (x\u2009-\u2009a,\u2009y\u2009+\u2009b);  move the candy from position (x,\u2009y) on the board to position (x\u2009+\u2009a,\u2009y\u2009+\u2009b). 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,\u2009j) to one of the chessboard corners. Help them cope with the task! ", "input_spec": "The first line of the input contains six integers n,\u2009m,\u2009i,\u2009j,\u2009a,\u2009b (1\u2009\u2264\u2009n,\u2009m\u2009\u2264\u2009106;\u00a01\u2009\u2264\u2009i\u2009\u2264\u2009n;\u00a01\u2009\u2264\u2009j\u2009\u2264\u2009m;\u00a01\u2009\u2264\u2009a,\u2009b\u2009\u2264\u2009106). 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,\u2009j) 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,\u2009m), (n,\u20091), (n,\u2009m), (1,\u20091).", "output_spec": "In a single line print a single integer \u2014 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\u2009+\u20092,\u20093\u2009+\u20092)\u2009=\u2009(3,\u20095), from there they can move it to positions (3\u2009-\u20092,\u20095\u2009+\u20092)\u2009=\u2009(1,\u20097) and (3\u2009+\u20092,\u20095\u2009+\u20092)\u2009=\u2009(5,\u20097). 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": "Dante is engaged in a fight with \"The Savior\". Before he can fight it with his sword, he needs to break its shields. He has two guns, Ebony and Ivory, each of them is able to perform any non-negative number of shots.For every bullet that hits the shield, Ebony deals a units of damage while Ivory deals b units of damage. In order to break the shield Dante has to deal exactly c units of damage. Find out if this is possible.", "input_spec": "The first line of the input contains three integers a, b, c (1\u2009\u2264\u2009a,\u2009b\u2009\u2264\u2009100,\u20091\u2009\u2264\u2009c\u2009\u2264\u200910\u2009000)\u00a0\u2014 the number of units of damage dealt by Ebony gun and Ivory gun, and the total number of damage required to break the shield, respectively.", "output_spec": "Print \"Yes\" (without quotes) if Dante can deal exactly c damage to the shield and \"No\" (without quotes) otherwise.", "sample_inputs": ["4 6 15", "3 2 7", "6 11 6"], "sample_outputs": ["No", "Yes", "Yes"], "notes": "NoteIn the second sample, Dante can fire 1 bullet from Ebony and 2 from Ivory to deal exactly 1\u00b73\u2009+\u20092\u00b72\u2009=\u20097 damage. In the third sample, Dante can fire 1 bullet from ebony and no bullets from ivory to do 1\u00b76\u2009+\u20090\u00b711\u2009=\u20096 damage. "}, "src_uid": "e66ecb0021a34042885442b336f3d911"}
{"nl": {"description": "A long time ago (probably even in the first book), Nicholas Flamel, a great alchemist and the creator of the Philosopher's Stone, taught Harry Potter three useful spells. The first one allows you to convert a grams of sand into b grams of lead, the second one allows you to convert c grams of lead into d grams of gold and third one allows you to convert e grams of gold into f grams of sand. When Harry told his friends about these spells, Ron Weasley was amazed. After all, if they succeed in turning sand into lead, lead into gold, and then turning part of the gold into sand again and so on, then it will be possible to start with a small amount of sand and get huge amounts of gold! Even an infinite amount of gold! Hermione Granger, by contrast, was skeptical about that idea. She argues that according to the law of conservation of matter getting an infinite amount of matter, even using magic, is impossible. On the contrary, the amount of matter may even decrease during transformation, being converted to magical energy. Though Hermione's theory seems convincing, Ron won't believe her. As far as Ron is concerned, Hermione made up her law of conservation of matter to stop Harry and Ron wasting their time with this nonsense, and to make them go and do homework instead. That's why Ron has already collected a certain amount of sand for the experiments. A quarrel between the friends seems unavoidable...Help Harry to determine which one of his friends is right, and avoid the quarrel after all. To do this you have to figure out whether it is possible to get the amount of gold greater than any preassigned number from some finite amount of sand.", "input_spec": "The first line contains 6 integers a, b, c, d, e, f (0\u2009\u2264\u2009a,\u2009b,\u2009c,\u2009d,\u2009e,\u2009f\u2009\u2264\u20091000).", "output_spec": "Print \"Ron\", if it is possible to get an infinitely large amount of gold having a certain finite amount of sand (and not having any gold and lead at all), i.e., Ron is right. Otherwise, print \"Hermione\".", "sample_inputs": ["100 200 250 150 200 250", "100 50 50 200 200 100", "100 10 200 20 300 30", "0 0 0 0 0 0", "1 1 0 1 1 1", "1 0 1 2 1 2", "100 1 100 1 0 1"], "sample_outputs": ["Ron", "Hermione", "Hermione", "Hermione", "Ron", "Hermione", "Ron"], "notes": "NoteConsider the first sample. Let's start with the 500 grams of sand. Apply the first spell 5 times and turn the sand into 1000 grams of lead. Then apply the second spell 4 times to get 600 grams of gold. Let\u2019s take 400 grams from the resulting amount of gold turn them back into sand. We get 500 grams of sand and 200 grams of gold. If we apply the same operations to 500 grams of sand again, we can get extra 200 grams of gold every time. Thus, you can get 200, 400, 600 etc. grams of gold, i.e., starting with a finite amount of sand (500 grams), you can get the amount of gold which is greater than any preassigned number.In the forth sample it is impossible to get sand, or lead, or gold, applying the spells.In the fifth sample an infinitely large amount of gold can be obtained by using only the second spell, which allows you to receive 1 gram of gold out of nothing. Note that if such a second spell is available, then the first and the third one do not affect the answer at all.The seventh sample is more interesting. We can also start with a zero amount of sand there. With the aid of the third spell you can get sand out of nothing. We get 10000 grams of sand in this manner. Let's get 100 grams of lead using the first spell 100 times. Then make 1 gram of gold from them. We managed to receive 1 gram of gold, starting with a zero amount of sand! Clearly, in this manner you can get an infinitely large amount of gold."}, "src_uid": "44d608de3e1447f89070e707ba550150"}
{"nl": {"description": "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$$$)\u00a0\u2014 the total number of moves and the number of candies in the box at the end.  It's guaranteed, that for the given $$$n$$$ and $$$k$$$ the answer exists.", "output_spec": "Print a single integer\u00a0\u2014 the number of candies, which Alya ate. Please note, that in this problem there aren't multiple possible answers\u00a0\u2014 the answer is unique for any input data. ", "sample_inputs": ["1 1", "9 11", "5 0", "3 2"], "sample_outputs": ["0", "4", "3", "1"], "notes": "NoteIn the first example, Alya has made one move only. According to the statement, the first move is always putting one candy in the box. Hence Alya ate $$$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": "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\u2009\u2264\u2009n,\u2009m,\u2009a,\u2009b\u2009\u2264\u20091000) \u2014 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 \u2014 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": "Manao is trying to open a rather challenging lock. The lock has n buttons on it and to open it, you should press the buttons in a certain order to open the lock. When you push some button, it either stays pressed into the lock (that means that you've guessed correctly and pushed the button that goes next in the sequence), or all pressed buttons return to the initial position. When all buttons are pressed into the lock at once, the lock opens.Consider an example with three buttons. Let's say that the opening sequence is: {2, 3, 1}. If you first press buttons 1 or 3, the buttons unpress immediately. If you first press button 2, it stays pressed. If you press 1 after 2, all buttons unpress. If you press 3 after 2, buttons 3 and 2 stay pressed. As soon as you've got two pressed buttons, you only need to press button 1 to open the lock.Manao doesn't know the opening sequence. But he is really smart and he is going to act in the optimal way. Calculate the number of times he's got to push a button in order to open the lock in the worst-case scenario.", "input_spec": "A single line contains integer n (1\u2009\u2264\u2009n\u2009\u2264\u20092000) \u2014 the number of buttons the lock has.", "output_spec": "In a single line print the number of times Manao has to push a button in the worst-case scenario.", "sample_inputs": ["2", "3"], "sample_outputs": ["3", "7"], "notes": "NoteConsider the first test sample. Manao can fail his first push and push the wrong button. In this case he will already be able to guess the right one with his second push. And his third push will push the second right button. Thus, in the worst-case scenario he will only need 3 pushes."}, "src_uid": "6df251ac8bf27427a24bc23d64cb9884"}
{"nl": {"description": "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\u2009\u2264\u2009n\u2009\u2264\u200915) \u2014 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": "Greg is a beginner bodybuilder. Today the gym coach gave him the training plan. All it had was n integers a1,\u2009a2,\u2009...,\u2009an. These numbers mean that Greg needs to do exactly n exercises today. Besides, Greg should repeat the i-th in order exercise ai times.Greg now only does three types of exercises: \"chest\" exercises, \"biceps\" exercises and \"back\" exercises. Besides, his training is cyclic, that is, the first exercise he does is a \"chest\" one, the second one is \"biceps\", the third one is \"back\", the fourth one is \"chest\", the fifth one is \"biceps\", and so on to the n-th exercise.Now Greg wonders, which muscle will get the most exercise during his training. We know that the exercise Greg repeats the maximum number of times, trains the corresponding muscle the most. Help Greg, determine which muscle will get the most training.", "input_spec": "The first line contains integer n (1\u2009\u2264\u2009n\u2009\u2264\u200920). The second line contains n integers a1,\u2009a2,\u2009...,\u2009an (1\u2009\u2264\u2009ai\u2009\u2264\u200925) \u2014 the number of times Greg repeats the exercises.", "output_spec": "Print word \"chest\" (without the quotes), if the chest gets the most exercise, \"biceps\" (without the quotes), if the biceps gets the most exercise and print \"back\" (without the quotes) if the back gets the most exercise. It is guaranteed that the input is such that the answer to the problem is unambiguous.", "sample_inputs": ["2\n2 8", "3\n5 1 10", "7\n3 3 2 7 9 6 8"], "sample_outputs": ["biceps", "back", "chest"], "notes": "NoteIn the first sample Greg does 2 chest, 8 biceps and zero back exercises, so the biceps gets the most exercises.In the second sample Greg does 5 chest, 1 biceps and 10 back exercises, so the back gets the most exercises.In the third sample Greg does 18 chest, 12 biceps and 8 back exercises, so the chest gets the most exercise."}, "src_uid": "579021de624c072f5e0393aae762117e"}
{"nl": {"description": "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$$$)\u00a0\u2014 the number of participants, the number of pens, and the number of notebooks respectively.", "output_spec": "Print \"Yes\" if it possible to reward all the participants. Otherwise, print \"No\". You can print each letter in any case (upper or lower).", "sample_inputs": ["5 8 6", "3 9 3", "8 5 20"], "sample_outputs": ["Yes", "Yes", "No"], "notes": "NoteIn the first example, there are $$$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": "Vector Willman and Array Bolt are the two most famous athletes of Byteforces. They are going to compete in a race with a distance of L meters today.  Willman and Bolt have exactly the same speed, so when they compete the result is always a tie. That is a problem for the organizers because they want a winner. While watching previous races the organizers have noticed that Willman can perform only steps of length equal to w meters, and Bolt can perform only steps of length equal to b meters. Organizers decided to slightly change the rules of the race. Now, at the end of the racetrack there will be an abyss, and the winner will be declared the athlete, who manages to run farther from the starting point of the the racetrack (which is not the subject to change by any of the athletes). Note that none of the athletes can run infinitely far, as they both will at some moment of time face the point, such that only one step further will cause them to fall in the abyss. In other words, the athlete will not fall into the abyss if the total length of all his steps will be less or equal to the chosen distance L.Since the organizers are very fair, the are going to set the length of the racetrack as an integer chosen randomly and uniformly in range from 1 to t (both are included). What is the probability that Willman and Bolt tie again today?", "input_spec": "The first line of the input contains three integers t, w and b (1\u2009\u2264\u2009t,\u2009w,\u2009b\u2009\u2264\u20095\u00b71018) \u2014 the maximum possible length of the racetrack, the length of Willman's steps and the length of Bolt's steps respectively.", "output_spec": "Print the answer to the problem as an irreducible fraction . Follow the format of the samples output. The fraction  (p and q are integers, and both p\u2009\u2265\u20090 and q\u2009>\u20090 holds) is called irreducible, if there is no such integer d\u2009>\u20091, that both p and q are divisible by d.", "sample_inputs": ["10 3 2", "7 1 2"], "sample_outputs": ["3/10", "3/7"], "notes": "NoteIn the first sample Willman and Bolt will tie in case 1, 6 or 7 are chosen as the length of the racetrack."}, "src_uid": "7a1d8ca25bce0073c4eb5297b94501b5"}
{"nl": {"description": "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": "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\u2009\u2264\u2009k\u2009\u2264\u2009109, 0\u2009\u2264\u2009a,\u2009b\u2009\u2264\u2009109, a\u2009+\u2009b\u2009>\u20090).", "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": "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$$$ share an edge. "}, "src_uid": "3dc1ee09016a25421ae371fa8005fce1"}
{"nl": {"description": "Welcome to Codeforces Stock Exchange! We're pretty limited now as we currently allow trading on one stock, Codeforces Ltd. We hope you'll still be able to make profit from the market!In the morning, there are $$$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$$$) \u2014 the number of ways to buy the shares on the market, the number of ways to sell the shares on the market, and the number of bourles you hold now. The next line contains $$$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$$$ bourles.", "output_spec": "Output a single integer \u2014 the maximum number of bourles you can hold after the evening.", "sample_inputs": ["3 4 11\n4 2 5\n4 4 5 4", "2 2 50\n5 7\n4 2"], "sample_outputs": ["26", "50"], "notes": "NoteIn the first example test, you have $$$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$$$ bourles after the evening.In the second example test, it's optimal not to take any action."}, "src_uid": "42f25d492bddc12d3d89d39315d63cb9"}
{"nl": {"description": "Yet another Armageddon is coming! This time the culprit is the Julya tribe calendar. The beavers in this tribe knew math very well. Smart Beaver, an archaeologist, got a sacred plate with a magic integer on it. The translation from Old Beaverish is as follows: \"May the Great Beaver bless you! May your chacres open and may your third eye never turn blind from beholding the Truth! Take the magic number, subtract a digit from it (the digit must occur in the number) and get a new magic number. Repeat this operation until a magic number equals zero. The Earth will stand on Three Beavers for the time, equal to the number of subtractions you perform!\"Distinct subtraction sequences can obviously get you different number of operations. But the Smart Beaver is ready to face the worst and is asking you to count the minimum number of operations he needs to reduce the magic number to zero.", "input_spec": "The single line contains the magic integer n, 0\u2009\u2264\u2009n.   to get 20 points, you need to solve the problem with constraints: n\u2009\u2264\u2009106 (subproblem C1);  to get 40 points, you need to solve the problem with constraints: n\u2009\u2264\u20091012 (subproblems C1+C2);  to get 100 points, you need to solve the problem with constraints: n\u2009\u2264\u20091018 (subproblems C1+C2+C3). ", "output_spec": "Print a single integer \u2014 the minimum number of subtractions that turns the magic number to a zero.", "sample_inputs": ["24"], "sample_outputs": ["5"], "notes": "NoteIn the first test sample the minimum number of operations can be reached by the following sequence of subtractions:  24\u2009\u2192\u200920\u2009\u2192\u200918\u2009\u2192\u200910\u2009\u2192\u20099\u2009\u2192\u20090 "}, "src_uid": "fc5765b9bd18dc7555fa76e91530c036"}
{"nl": {"description": "Kavi has $$$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": "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\u2009=\u2009{x1,\u2009x2,\u2009...,\u2009xk} (1\u2009\u2264\u2009xi\u2009\u2264\u2009n, 0\u2009<\u2009k\u2009<\u2009n) the sums of elements on that positions in a and b are different, i.\u00a0e. ", "input_spec": "The first line contains one integer n (1\u2009\u2264\u2009n\u2009\u2264\u200922)\u00a0\u2014 the size of the array. The second line contains n space-separated distinct integers a1,\u2009a2,\u2009...,\u2009an (0\u2009\u2264\u2009ai\u2009\u2264\u2009109)\u00a0\u2014 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,\u2009b2,\u2009...,\u2009bn. 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": "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": "The tram in Berland goes along a straight line from the point 0 to the point s and back, passing 1 meter per t1 seconds in both directions. It means that the tram is always in the state of uniform rectilinear motion, instantly turning around at points x\u2009=\u20090 and x\u2009=\u2009s.Igor is at the point x1. He should reach the point x2. Igor passes 1 meter per t2 seconds. Your task is to determine the minimum time Igor needs to get from the point x1 to the point x2, if it is known where the tram is and in what direction it goes at the moment Igor comes to the point x1.Igor can enter the tram unlimited number of times at any moment when his and the tram's positions coincide. It is not obligatory that points in which Igor enter and exit the tram are integers. Assume that any boarding and unboarding happens instantly. Igor can move arbitrary along the line (but not faster than 1 meter per t2 seconds). He can also stand at some point for some time.", "input_spec": "The first line contains three integers s, x1 and x2 (2\u2009\u2264\u2009s\u2009\u2264\u20091000, 0\u2009\u2264\u2009x1,\u2009x2\u2009\u2264\u2009s, x1\u2009\u2260\u2009x2)\u00a0\u2014 the maximum coordinate of the point to which the tram goes, the point Igor is at, and the point he should come to. The second line contains two integers t1 and t2 (1\u2009\u2264\u2009t1,\u2009t2\u2009\u2264\u20091000)\u00a0\u2014 the time in seconds in which the tram passes 1 meter and the time in seconds in which Igor passes 1 meter. The third line contains two integers p and d (1\u2009\u2264\u2009p\u2009\u2264\u2009s\u2009-\u20091, d is either 1 or )\u00a0\u2014 the position of the tram in the moment Igor came to the point x1 and the direction of the tram at this moment. If , the tram goes in the direction from the point s to the point 0. If d\u2009=\u20091, the tram goes in the direction from the point 0 to the point s.", "output_spec": "Print the minimum time in seconds which Igor needs to get from the point x1 to the point x2.", "sample_inputs": ["4 2 4\n3 4\n1 1", "5 4 0\n1 2\n3 1"], "sample_outputs": ["8", "7"], "notes": "NoteIn the first example it is profitable for Igor to go by foot and not to wait the tram. Thus, he has to pass 2 meters and it takes 8 seconds in total, because he passes 1 meter per 4 seconds. In the second example Igor can, for example, go towards the point x2 and get to the point 1 in 6 seconds (because he has to pass 3 meters, but he passes 1 meters per 2 seconds). At that moment the tram will be at the point 1, so Igor can enter the tram and pass 1 meter in 1 second. Thus, Igor will reach the point x2 in 7 seconds in total."}, "src_uid": "fb3aca6eba3a952e9d5736c5d8566821"}
{"nl": {"description": "On the way to Rio de Janeiro Ostap kills time playing with a grasshopper he took with him in a special box. Ostap builds a line of length n such that some cells of this line are empty and some contain obstacles. Then, he places his grasshopper to one of the empty cells and a small insect in another empty cell. The grasshopper wants to eat the insect.Ostap knows that grasshopper is able to jump to any empty cell that is exactly k cells away from the current (to the left or to the right). Note that it doesn't matter whether intermediate cells are empty or not as the grasshopper makes a jump over them. For example, if k\u2009=\u20091 the grasshopper can jump to a neighboring cell only, and if k\u2009=\u20092 the grasshopper can jump over a single cell.Your goal is to determine whether there is a sequence of jumps such that grasshopper will get from his initial position to the cell with an insect.", "input_spec": "The first line of the input contains two integers n and k (2\u2009\u2264\u2009n\u2009\u2264\u2009100, 1\u2009\u2264\u2009k\u2009\u2264\u2009n\u2009-\u20091)\u00a0\u2014 the number of cells in the line and the length of one grasshopper's jump. The second line contains a string of length n consisting of characters '.', '#', 'G' and 'T'. Character '.' means that the corresponding cell is empty, character '#' means that the corresponding cell contains an obstacle and grasshopper can't jump there. Character 'G' means that the grasshopper starts at this position and, finally, 'T' means that the target insect is located at this cell. It's guaranteed that characters 'G' and 'T' appear in this line exactly once.", "output_spec": "If there exists a sequence of jumps (each jump of length k), such that the grasshopper can get from his initial position to the cell with the insect, print \"YES\" (without quotes) in the only line of the input. Otherwise, print \"NO\" (without quotes).", "sample_inputs": ["5 2\n#G#T#", "6 1\nT....G", "7 3\nT..#..G", "6 2\n..GT.."], "sample_outputs": ["YES", "YES", "NO", "NO"], "notes": "NoteIn the first sample, the grasshopper can make one jump to the right in order to get from cell 2 to cell 4.In the second sample, the grasshopper is only able to jump to neighboring cells but the way to the insect is free\u00a0\u2014 he can get there by jumping left 5 times.In the third sample, the grasshopper can't make a single jump.In the fourth sample, the grasshopper can only jump to the cells with odd indices, thus he won't be able to reach the insect."}, "src_uid": "189a9b5ce669bdb04b9d371d74a5dd41"}
{"nl": {"description": null, "input_spec": null, "output_spec": null, "sample_inputs": [], "sample_outputs": [], "notes": null}, "src_uid": "b6a30a725754a4b4daeb6e87986e28a4"}
{"nl": {"description": "When new students come to the Specialized Educational and Scientific Centre (SESC) they need to start many things from the beginning. Sometimes the teachers say (not always unfairly) that we cannot even count. So our teachers decided to teach us arithmetics from the start. And what is the best way to teach students add and subtract? \u2014 That's right, using counting sticks! An here's our new task: An expression of counting sticks is an expression of type:[ A sticks][sign +][B sticks][sign =][C sticks] (1\u2009\u2264\u2009A,\u2009B,\u2009C).  Sign + consists of two crossed sticks: one vertical and one horizontal. Sign = consists of two horizontal sticks. The expression is arithmetically correct if A\u2009+\u2009B\u2009=\u2009C.We've got an expression that looks like A\u2009+\u2009B\u2009=\u2009C given by counting sticks. Our task is to shift at most one stick (or we can shift nothing) so that the expression became arithmetically correct. Note that we cannot remove the sticks from the expression, also we cannot shift the sticks from the signs + and =.We really aren't fabulous at arithmetics. Can you help us?", "input_spec": "The single line contains the initial expression. It is guaranteed that the expression looks like A\u2009+\u2009B\u2009=\u2009C, where 1\u2009\u2264\u2009A,\u2009B,\u2009C\u2009\u2264\u2009100.", "output_spec": "If there isn't a way to shift the stick so the expression becomes correct, print on a single line \"Impossible\" (without the quotes). If there is a way, print the resulting expression. Follow the format of the output from the test samples. Don't print extra space characters. If there are multiple correct answers, print any of them. For clarifications, you are recommended to see the test samples.", "sample_inputs": ["||+|=|||||", "|||||+||=||", "|+|=||||||", "||||+||=||||||"], "sample_outputs": ["|||+|=||||", "Impossible", "Impossible", "||||+||=||||||"], "notes": "NoteIn the first sample we can shift stick from the third group of sticks to the first one.In the second sample we cannot shift vertical stick from + sign to the second group of sticks. So we cannot make a - sign.There is no answer in the third sample because we cannot remove sticks from the expression.In the forth sample the initial expression is already arithmetically correct and that is why we don't have to shift sticks."}, "src_uid": "ee0aaa7acf127e9f3a9edafc58f4e2d6"}
{"nl": {"description": "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,\u2009a].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\u2009000\u2009000\u2009007 (109\u2009+\u20097). Can you compute it faster than Dreamoon?", "input_spec": "The single line of the input contains two integers a, b (1\u2009\u2264\u2009a,\u2009b\u2009\u2264\u2009107).", "output_spec": "Print a single integer representing the answer modulo 1\u2009000\u2009000\u2009007 (109\u2009+\u20097).", "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,\u20095}."}, "src_uid": "cd351d1190a92d094b2d929bf1e5c44f"}
{"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\u2009\u2264\u2009n\u2009\u2264\u2009100)\u00a0\u2014 number of visits. Second line contains an integer a (1\u2009\u2264\u2009a\u2009\u2264\u2009100)\u00a0\u2014 distance between Rabbit's and Owl's houses. Third line contains an integer b (1\u2009\u2264\u2009b\u2009\u2264\u2009100)\u00a0\u2014 distance between Rabbit's and Eeyore's houses. Fourth line contains an integer c (1\u2009\u2264\u2009c\u2009\u2264\u2009100)\u00a0\u2014 distance between Owl's and Eeyore's houses.", "output_spec": "Output one number\u00a0\u2014 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\u2009+\u20091\u2009=\u20093.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": "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$$$) \u2014 the number from which Tanya will subtract and the number of subtractions correspondingly.", "output_spec": "Print one integer number \u2014 the result of the decreasing $$$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": "Numbers k-bonacci (k is integer, k\u2009>\u20091) are a generalization of Fibonacci numbers and are determined as follows:  F(k,\u2009n)\u2009=\u20090, for integer n, 1\u2009\u2264\u2009n\u2009<\u2009k;  F(k,\u2009k)\u2009=\u20091;  F(k,\u2009n)\u2009=\u2009F(k,\u2009n\u2009-\u20091)\u2009+\u2009F(k,\u2009n\u2009-\u20092)\u2009+\u2009...\u2009+\u2009F(k,\u2009n\u2009-\u2009k), for integer n, n\u2009>\u2009k. Note that we determine the k-bonacci numbers, F(k,\u2009n), only for integer values of n and k.You've got a number s, represent it as a sum of several (at least two) distinct k-bonacci numbers. ", "input_spec": "The first line contains two integers s and k (1\u2009\u2264\u2009s,\u2009k\u2009\u2264\u2009109;\u00a0k\u2009>\u20091).", "output_spec": "In the first line print an integer m (m\u2009\u2265\u20092) that shows how many numbers are in the found representation. In the second line print m distinct integers a1,\u2009a2,\u2009...,\u2009am. Each printed integer should be a k-bonacci number. The sum of printed integers must equal s. It is guaranteed that the answer exists. If there are several possible answers, print any of them.", "sample_inputs": ["5 2", "21 5"], "sample_outputs": ["3\n0 2 3", "3\n4 1 16"], "notes": null}, "src_uid": "da793333b977ed179fdba900aa604b52"}
{"nl": {"description": "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\u2009\u2264\u2009n\u2009\u2264\u200992)\u00a0\u2014 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\u2009\u2264\u2009ai\u2009\u2264\u200915)\u00a0\u2014 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\u2009+\u20091 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": "Mishka started participating in a programming contest. There are $$$n$$$ problems in the contest. Mishka's problem-solving skill is equal to $$$k$$$.Mishka arranges all problems from the contest into a list. Because of his weird principles, Mishka only solves problems from one of the ends of the list. Every time, he chooses which end (left or right) he will solve the next problem from. Thus, each problem Mishka solves is either the leftmost or the rightmost problem in the list.Mishka cannot solve a problem with difficulty greater than $$$k$$$. When Mishka solves the problem, it disappears from the list, so the length of the list decreases by $$$1$$$. Mishka stops when he is unable to solve any problem from any end of the list.How many problems can Mishka solve?", "input_spec": "The first line of input contains two integers $$$n$$$ and $$$k$$$ ($$$1 \\le n, k \\le 100$$$) \u2014 the number of problems in the contest and Mishka's problem-solving skill. The second line of input contains $$$n$$$ integers $$$a_1, a_2, \\dots, a_n$$$ ($$$1 \\le a_i \\le 100$$$), where $$$a_i$$$ is the difficulty of the $$$i$$$-th problem. The problems are given in order from the leftmost to the rightmost in the list.", "output_spec": "Print one integer \u2014 the maximum number of problems Mishka can solve.", "sample_inputs": ["8 4\n4 2 3 1 5 1 6 4", "5 2\n3 1 2 1 3", "5 100\n12 34 55 43 21"], "sample_outputs": ["5", "0", "5"], "notes": "NoteIn the first example, Mishka can solve problems in the following order: $$$[4, 2, 3, 1, 5, 1, 6, 4] \\rightarrow [2, 3, 1, 5, 1, 6, 4] \\rightarrow [2, 3, 1, 5, 1, 6] \\rightarrow [3, 1, 5, 1, 6] \\rightarrow [1, 5, 1, 6] \\rightarrow [5, 1, 6]$$$, so the number of solved problems will be equal to $$$5$$$.In the second example, Mishka can't solve any problem because the difficulties of problems from both ends are greater than $$$k$$$.In the third example, Mishka's solving skill is so amazing that he can solve all the problems."}, "src_uid": "ecf0ead308d8a581dd233160a7e38173"}
{"nl": {"description": "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\u2009\u2264\u2009k\u2009\u2264\u2009n\u2009\u2264\u20091012). 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": "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\u2009-\u20091) 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\u2009\u2264\u2009n\u2009\u2264\u2009100;\u00a01\u2009\u2264\u2009s\u2009\u2264\u20091000) \u2014 the number of mugs and the volume of the cup. The next line contains n integers a1, a2, ..., an (1\u2009\u2264\u2009ai\u2009\u2264\u200910). 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 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\u2009\u2264\u2009a\u2009<\u2009b\u2009\u2264\u2009105, 0\u2009\u2264\u2009c\u2009\u2264\u20099).", "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": "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": "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\u2009\u2264\u2009x\u2009\u2264\u200999) 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\u2009\u2264\u2009n\u2009\u2264\u200999). 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,\u200908,\u200909,\u200933,\u200938,\u200939,\u200973,\u200978,\u200979,\u200983,\u200988,\u200989,\u200993,\u200998,\u200999."}, "src_uid": "76c8bfa6789db8364a8ece0574cd31f5"}
{"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\u2009\u00d7\u20093 grid (one player always draws crosses, the other \u2014 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\u2009\u00d7\u20093 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 \u2014 if the given board layout can't appear during a valid game;  the first player won \u2014 if in the given board layout the first player has just won;  the second player won \u2014 if in the given board layout the second player has just won;  draw \u2014 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": "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)$$$)\u00a0\u2014 an array's size, the minimal number and the maximal number of distinct elements in an array.", "output_spec": "Output two numbers\u00a0\u2014 the minimal and the maximal possible sums of all elements in an array.", "sample_inputs": ["4 2 2", "5 1 5"], "sample_outputs": ["5 7", "5 31"], "notes": "NoteIn the first example, an array could be the one of the following: $$$[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]$$$."}, "src_uid": "ce220726392fb0cacf0ec44a7490084a"}
{"nl": {"description": "Find the minimum number with the given sum of digits $$$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$$$) \u2014 the number of test cases. Each test case is specified by a line that contains the only integer $$$s$$$ ($$$1 \\le s \\le 45$$$).", "output_spec": "Print $$$t$$$ integers \u2014 the answers to the given test cases.", "sample_inputs": ["4\n\n20\n\n8\n\n45\n\n10"], "sample_outputs": ["389\n8\n123456789\n19"], "notes": null}, "src_uid": "fe126aaa93acaca8c8559bc9e7e27b9f"}
{"nl": {"description": "You have a plate and you want to add some gilding to it. The plate is a rectangle that we split into $$$w\\times h$$$ cells. There should be $$$k$$$ gilded rings, the first one should go along the edge of the plate, the second one\u00a0\u2014 $$$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) \u2014 the number of rows, columns and the number of rings, respectively.", "output_spec": "Print a single positive integer\u00a0\u2014 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": "Consider the infinite sequence of integers: 1,\u20091,\u20092,\u20091,\u20092,\u20093,\u20091,\u20092,\u20093,\u20094,\u20091,\u20092,\u20093,\u20094,\u20095.... The sequence is built in the following way: at first the number 1 is written out, then the numbers from 1 to 2, then the numbers from 1 to 3, then the numbers from 1 to 4 and so on. Note that the sequence contains numbers, not digits. For example number 10 first appears in the sequence in position 55 (the elements are numerated from one).Find the number on the n-th position of the sequence.", "input_spec": "The only line contains integer n (1\u2009\u2264\u2009n\u2009\u2264\u20091014) \u2014 the position of the number to find. Note that the given number is too large, so you should use 64-bit integer type to store it. In C++ you can use the long long integer type and in Java you can use long integer type.", "output_spec": "Print the element in the n-th position of the sequence (the elements are numerated from one).", "sample_inputs": ["3", "5", "10", "55", "56"], "sample_outputs": ["2", "2", "4", "10", "1"], "notes": null}, "src_uid": "1db5631847085815461c617854b08ee5"}
{"nl": {"description": "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\u2009\u2264\u2009n\u2009\u2264\u2009100) \u2014 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 \u2014 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 \u2014 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": "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\u2009\u00d7\u2009m multiplication table, where the element on the intersection of the i-th row and j-th column equals i\u00b7j (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\u00b7m 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\u2009\u2264\u2009n,\u2009m\u2009\u2264\u20095\u00b7105;\u00a01\u2009\u2264\u2009k\u2009\u2264\u2009n\u00b7m).", "output_spec": "Print the k-th largest number in a n\u2009\u00d7\u2009m multiplication table.", "sample_inputs": ["2 2 2", "2 3 4", "1 10 5"], "sample_outputs": ["2", "3", "5"], "notes": "NoteA 2\u2009\u00d7\u20093 multiplication table looks like this:1 2 32 4 6"}, "src_uid": "13a918eca30799b240ceb9de47507a26"}
{"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\u2009\u2264\u2009|s|\u2009\u2264\u200910). 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": "InputThe input contains a single integer $$$a$$$ ($$$1 \\le a \\le 99$$$).OutputOutput \"YES\" or \"NO\".ExamplesInput\n5\nOutput\nYES\nInput\n13\nOutput\nNO\nInput\n24\nOutput\nNO\nInput\n46\nOutput\nYES\n", "input_spec": "The input contains a single integer $$$a$$$ ($$$1 \\le a \\le 99$$$).", "output_spec": "Output \"YES\" or \"NO\".", "sample_inputs": ["5", "13", "24", "46"], "sample_outputs": ["YES", "NO", "NO", "YES"], "notes": null}, "src_uid": "821529a4644b74483bcdf80fc318d1f8"}
{"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\u2009\u2264\u2009w,\u2009b\u2009\u2264\u20091000).", "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\u2009-\u20099.", "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 \u2014 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": "Vasya likes everything infinite. Now he is studying the properties of a sequence s, such that its first element is equal to a (s1\u2009=\u2009a), and the difference between any two neighbouring elements is equal to c (si\u2009-\u2009si\u2009-\u20091\u2009=\u2009c). In particular, Vasya wonders if his favourite integer b appears in this sequence, that is, there exists a positive integer i, such that si\u2009=\u2009b. Of course, you are the person he asks for a help.", "input_spec": "The first line of the input contain three integers a, b and c (\u2009-\u2009109\u2009\u2264\u2009a,\u2009b,\u2009c\u2009\u2264\u2009109)\u00a0\u2014 the first element of the sequence, Vasya's favorite number and the difference between any two neighbouring elements of the sequence, respectively.", "output_spec": "If b appears in the sequence s print \"YES\" (without quotes), otherwise print \"NO\" (without quotes).", "sample_inputs": ["1 7 3", "10 10 0", "1 -4 5", "0 60 50"], "sample_outputs": ["YES", "YES", "NO", "NO"], "notes": "NoteIn the first sample, the sequence starts from integers 1, 4, 7, so 7 is its element.In the second sample, the favorite integer of Vasya is equal to the first element of the sequence.In the third sample all elements of the sequence are greater than Vasya's favorite integer.In the fourth sample, the sequence starts from 0, 50, 100, and all the following elements are greater than Vasya's favorite integer."}, "src_uid": "9edf42c20ddf22a251b84553d7305a7d"}
{"nl": {"description": "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\u2009<\u2009n\u2009\u2264\u200910000,\u20091\u2009<\u2009m\u2009\u2264\u200910).", "output_spec": "Print a single integer \u2014 the minimal number of moves being a multiple of m. If there is no way he can climb satisfying condition print \u2009-\u20091 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": "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,\u2009y1,\u2009x2,\u2009y2,\u2009x3,\u2009y3 \u2014 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 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 \u00abtranslation\u00bb. 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": "Vasilisa the Wise from the Kingdom of Far Far Away got a magic box with a secret as a present from her friend Hellawisa the Wise from the Kingdom of A Little Closer. However, Vasilisa the Wise does not know what the box's secret is, since she cannot open it again. She hopes that you will help her one more time with that.The box's lock looks as follows: it contains 4 identical deepenings for gems as a 2\u2009\u00d7\u20092 square, and some integer numbers are written at the lock's edge near the deepenings. The example of a lock is given on the picture below.  The box is accompanied with 9 gems. Their shapes match the deepenings' shapes and each gem contains one number from 1 to 9 (each number is written on exactly one gem). The box will only open after it is decorated with gems correctly: that is, each deepening in the lock should be filled with exactly one gem. Also, the sums of numbers in the square's rows, columns and two diagonals of the square should match the numbers written at the lock's edge. For example, the above lock will open if we fill the deepenings with gems with numbers as is shown on the picture below.  Now Vasilisa the Wise wants to define, given the numbers on the box's lock, which gems she should put in the deepenings to open the box. Help Vasilisa to solve this challenging task.", "input_spec": "The input contains numbers written on the edges of the lock of the box. The first line contains space-separated integers r1 and r2 that define the required sums of numbers in the rows of the square. The second line contains space-separated integers c1 and c2 that define the required sums of numbers in the columns of the square. The third line contains space-separated integers d1 and d2 that define the required sums of numbers on the main and on the side diagonals of the square (1\u2009\u2264\u2009r1,\u2009r2,\u2009c1,\u2009c2,\u2009d1,\u2009d2\u2009\u2264\u200920). Correspondence between the above 6 variables and places where they are written is shown on the picture below. For more clarifications please look at the second sample test that demonstrates the example given in the problem statement.   ", "output_spec": "Print the scheme of decorating the box with stones: two lines containing two space-separated integers from 1 to 9. The numbers should be pairwise different. If there is no solution for the given lock, then print the single number \"-1\" (without the quotes). If there are several solutions, output any.", "sample_inputs": ["3 7\n4 6\n5 5", "11 10\n13 8\n5 16", "1 2\n3 4\n5 6", "10 10\n10 10\n10 10"], "sample_outputs": ["1 2\n3 4", "4 7\n9 1", "-1", "-1"], "notes": "NotePay attention to the last test from the statement: it is impossible to open the box because for that Vasilisa the Wise would need 4 identical gems containing number \"5\". However, Vasilisa only has one gem with each number from 1 to 9."}, "src_uid": "6821f502f5b6ec95c505e5dd8f3cd5d3"}
{"nl": {"description": "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\u2009+\u20091.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\u2009\u2264\u2009n\u2009\u2264\u200945, 1\u2009\u2264\u2009k\u2009\u2264\u200945, 0\u2009\u2264\u2009M\u2009\u2264\u20092\u00b7109). The second line contains k integer numbers, values tj (1\u2009\u2264\u2009tj\u2009\u2264\u20091000000), 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\u2009+\u20092\u2009+\u20093\u2009+\u20094\u2009=\u200910 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\u00b71\u2009=\u20095 minutes. Also he can solve the second subtasks of two tasks and spend 2\u00b72\u2009=\u20094 minutes. Thus, he earns 5\u2009+\u20092\u2009=\u20097 points in total."}, "src_uid": "d659e92a410c1bc836be64fc1c0db160"}
{"nl": {"description": "There is an old tradition of keeping 4 boxes of candies in the house in Cyberland. The numbers of candies are special if their arithmetic mean, their median and their range are all equal. By definition, for a set {x1,\u2009x2,\u2009x3,\u2009x4} (x1\u2009\u2264\u2009x2\u2009\u2264\u2009x3\u2009\u2264\u2009x4) arithmetic mean is , median is  and range is x4\u2009-\u2009x1. The arithmetic mean and median are not necessary integer. It is well-known that if those three numbers are same, boxes will create a \"debugging field\" and codes in the field will have no bugs.For example, 1,\u20091,\u20093,\u20093 is the example of 4 numbers meeting the condition because their mean, median and range are all equal to 2.Jeff has 4 special boxes of candies. However, something bad has happened! Some of the boxes could have been lost and now there are only n (0\u2009\u2264\u2009n\u2009\u2264\u20094) boxes remaining. The i-th remaining box contains ai candies.Now Jeff wants to know: is there a possible way to find the number of candies of the 4\u2009-\u2009n missing boxes, meeting the condition above (the mean, median and range are equal)?", "input_spec": "The first line of input contains an only integer n (0\u2009\u2264\u2009n\u2009\u2264\u20094). The next n lines contain integers ai, denoting the number of candies in the i-th box (1\u2009\u2264\u2009ai\u2009\u2264\u2009500).", "output_spec": "In the first output line, print \"YES\" if a solution exists, or print \"NO\" if there is no solution. If a solution exists, you should output 4\u2009-\u2009n more lines, each line containing an integer b, denoting the number of candies in a missing box. All your numbers b must satisfy inequality 1\u2009\u2264\u2009b\u2009\u2264\u2009106. It is guaranteed that if there exists a positive integer solution, you can always find such b's meeting the condition. If there are multiple answers, you are allowed to print any of them. Given numbers ai may follow in any order in the input, not necessary in non-decreasing. ai may have stood at any positions in the original set, not necessary on lowest n first positions.", "sample_inputs": ["2\n1\n1", "3\n1\n1\n1", "4\n1\n2\n2\n3"], "sample_outputs": ["YES\n3\n3", "NO", "YES"], "notes": "NoteFor the first sample, the numbers of candies in 4 boxes can be 1,\u20091,\u20093,\u20093. The arithmetic mean, the median and the range of them are all 2.For the second sample, it's impossible to find the missing number of candies.In the third example no box has been lost and numbers satisfy the condition.You may output b in any order."}, "src_uid": "230e613abf0f6a768829cbc1f1a09219"}
{"nl": {"description": "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,\u2009a2,\u2009a3,\u2009a4,\u2009a5 and a6 (1\u2009\u2264\u2009ai\u2009\u2264\u20091000) \u2014 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 \u2014 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": "Once upon a time there were several little pigs and several wolves on a two-dimensional grid of size n\u2009\u00d7\u2009m. 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\u2009\u2264\u2009n,\u2009m\u2009\u2264\u200910) which denotes the number of rows and columns in our two-dimensional grid, respectively. Then follow n lines containing m characters each \u2014 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 \u2014 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": "Ilya got tired of sports programming, left university and got a job in the subway. He was given the task to determine the escalator load factor. Let's assume that n people stand in the queue for the escalator. At each second one of the two following possibilities takes place: either the first person in the queue enters the escalator with probability p, or the first person in the queue doesn't move with probability (1\u2009-\u2009p), paralyzed by his fear of escalators and making the whole queue wait behind him.Formally speaking, the i-th person in the queue cannot enter the escalator until people with indices from 1 to i\u2009-\u20091 inclusive enter it. In one second only one person can enter the escalator. The escalator is infinite, so if a person enters it, he never leaves it, that is he will be standing on the escalator at any following second. Ilya needs to count the expected value of the number of people standing on the escalator after t seconds. Your task is to help him solve this complicated task.", "input_spec": "The first line of the input contains three numbers n,\u2009p,\u2009t (1\u2009\u2264\u2009n,\u2009t\u2009\u2264\u20092000, 0\u2009\u2264\u2009p\u2009\u2264\u20091). Numbers n and t are integers, number p is real, given with exactly two digits after the decimal point.", "output_spec": "Print a single real number \u2014 the expected number of people who will be standing on the escalator after t seconds. The absolute or relative error mustn't exceed 10\u2009-\u20096.", "sample_inputs": ["1 0.50 1", "1 0.50 4", "4 0.20 2"], "sample_outputs": ["0.5", "0.9375", "0.4"], "notes": null}, "src_uid": "20873b1e802c7aa0e409d9f430516c1e"}
{"nl": {"description": "One day student Vasya was sitting on a lecture and mentioned a string s1s2... sn, consisting of letters \"a\", \"b\" and \"c\" that was written on his desk. As the lecture was boring, Vasya decided to complete the picture by composing a graph G with the following properties:   G has exactly n vertices, numbered from 1 to n.  For all pairs of vertices i and j, where i\u2009\u2260\u2009j, there is an edge connecting them if and only if characters si and sj are either equal or neighbouring in the alphabet. That is, letters in pairs \"a\"-\"b\" and \"b\"-\"c\" are neighbouring, while letters \"a\"-\"c\" are not. Vasya painted the resulting graph near the string and then erased the string. Next day Vasya's friend Petya came to a lecture and found some graph at his desk. He had heard of Vasya's adventure and now he wants to find out whether it could be the original graph G, painted by Vasya. In order to verify this, Petya needs to know whether there exists a string s, such that if Vasya used this s he would produce the given graph G.", "input_spec": "The first line of the input contains two integers n and m \u00a0\u2014 the number of vertices and edges in the graph found by Petya, respectively. Each of the next m lines contains two integers ui and vi (1\u2009\u2264\u2009ui,\u2009vi\u2009\u2264\u2009n,\u2009ui\u2009\u2260\u2009vi)\u00a0\u2014 the edges of the graph G. It is guaranteed, that there are no multiple edges, that is any pair of vertexes appear in this list no more than once.", "output_spec": "In the first line print \"Yes\" (without the quotes), if the string s Petya is interested in really exists and \"No\" (without the quotes) otherwise. If the string s exists, then print it on the second line of the output. The length of s must be exactly n, it must consist of only letters \"a\", \"b\" and \"c\" only, and the graph built using this string must coincide with G. If there are multiple possible answers, you may print any of them.", "sample_inputs": ["2 1\n1 2", "4 3\n1 2\n1 3\n1 4"], "sample_outputs": ["Yes\naa", "No"], "notes": "NoteIn the first sample you are given a graph made of two vertices with an edge between them. So, these vertices can correspond to both the same and adjacent letters. Any of the following strings \"aa\", \"ab\", \"ba\", \"bb\", \"bc\", \"cb\", \"cc\" meets the graph's conditions. In the second sample the first vertex is connected to all three other vertices, but these three vertices are not connected with each other. That means that they must correspond to distinct letters that are not adjacent, but that is impossible as there are only two such letters: a and c."}, "src_uid": "e71640f715f353e49745eac5f72e682a"}
{"nl": {"description": "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$$$).", "output_spec": "Output one integer\u00a0\u2014 the answer to the problem.", "sample_inputs": ["7", "8", "9"], "sample_outputs": ["4", "5", "5"], "notes": "NoteIn the first sample, there are following possible weights of splits of $$$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": "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 \u200b\u200bof 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\u2009\u2264\u2009n\u2009\u2264\u2009100) \u2014 the number of bits in the cell. The second line contains a string consisting of n characters \u2014 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 \u2014 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 \u2014 with 0000."}, "src_uid": "54cb2e987f2cc06c02c7638ea879a1ab"}
{"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\u2009\u2264\u2009n\u2009\u2264\u2009109).", "output_spec": "In the first line print one integer k\u00a0\u2014 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\u2009=\u200915 there is only one variant: 15\u2009+\u20091\u2009+\u20095\u2009=\u200921.In the second test case there are no such x."}, "src_uid": "ae20ae2a16273a0d379932d6e973f878"}
{"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,\u2009b) (0\u2009\u2264\u2009a,\u2009b) which satisfy the system.", "input_spec": "A single line contains two integers n,\u2009m (1\u2009\u2264\u2009n,\u2009m\u2009\u2264\u20091000) \u2014 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,\u20090). In the second sample the suitable pair is integers (3,\u20095). In the third sample there is no suitable pair."}, "src_uid": "03caf4ddf07c1783e42e9f9085cc6efd"}
{"nl": {"description": "There is a building consisting of $$$10~000$$$ apartments numbered from $$$1$$$ to $$$10~000$$$, inclusive.Call an apartment boring, if its number consists of the same digit. Examples of boring apartments are $$$11, 2, 777, 9999$$$ and so on.Our character is a troublemaker, and he calls the intercoms of all boring apartments, till someone answers the call, in the following order:  First he calls all apartments consisting of digit $$$1$$$, in increasing order ($$$1, 11, 111, 1111$$$).  Next he calls all apartments consisting of digit $$$2$$$, in increasing order ($$$2, 22, 222, 2222$$$)  And so on. The resident of the boring apartment $$$x$$$ answers the call, and our character stops calling anyone further.Our character wants to know how many digits he pressed in total and your task is to help him to count the total number of keypresses.For example, if the resident of boring apartment $$$22$$$ answered, then our character called apartments with numbers $$$1, 11, 111, 1111, 2, 22$$$ and the total number of digits he pressed is $$$1 + 2 + 3 + 4 + 1 + 2 = 13$$$.You have to answer $$$t$$$ independent test cases.", "input_spec": "The first line of the input contains one integer $$$t$$$ ($$$1 \\le t \\le 36$$$) \u2014 the number of test cases. The only line of the test case contains one integer $$$x$$$ ($$$1 \\le x \\le 9999$$$) \u2014 the apartment number of the resident who answered the call. It is guaranteed that $$$x$$$ consists of the same digit.", "output_spec": "For each test case, print the answer: how many digits our character pressed in total.", "sample_inputs": ["4\n22\n9999\n1\n777"], "sample_outputs": ["13\n90\n1\n66"], "notes": null}, "src_uid": "289a55128be89bb86a002d218d31b57f"}
{"nl": {"description": "  ", "input_spec": "The input contains two integers a,\u2009b (1\u2009\u2264\u2009a\u2009\u2264\u200910,\u20090\u2009\u2264\u2009b\u2009\u2264\u200922\u00b7a\u2009-\u20091) separated by a single space.", "output_spec": "Output two integers separated by a single space.", "sample_inputs": ["1 0", "2 15", "4 160"], "sample_outputs": ["0 0", "3 0", "12 12"], "notes": null}, "src_uid": "879ac20ae5d3e7f1002afe907d9887df"}
{"nl": {"description": "Petya loves lucky numbers very much. Everybody knows that lucky numbers are positive integers whose decimal record contains only the lucky digits 4 and 7. For example, numbers 47, 744, 4 are lucky and 5, 17, 467 are not.Petya loves tickets very much. As we know, each ticket has a number that is a positive integer. Its length equals n (n is always even). Petya calls a ticket lucky if the ticket's number is a lucky number and the sum of digits in the first half (the sum of the first n\u2009/\u20092 digits) equals the sum of digits in the second half (the sum of the last n\u2009/\u20092 digits). Check if the given ticket is lucky.", "input_spec": "The first line contains an even integer n (2\u2009\u2264\u2009n\u2009\u2264\u200950) \u2014 the length of the ticket number that needs to be checked. The second line contains an integer whose length equals exactly n \u2014 the ticket number. The number may contain leading zeros.", "output_spec": "On the first line print \"YES\" if the given ticket number is lucky. Otherwise, print \"NO\" (without the quotes).", "sample_inputs": ["2\n47", "4\n4738", "4\n4774"], "sample_outputs": ["NO", "NO", "YES"], "notes": "NoteIn the first sample the sum of digits in the first half does not equal the sum of digits in the second half (4\u2009\u2260\u20097).In the second sample the ticket number is not the lucky number."}, "src_uid": "435b6d48f99d90caab828049a2c9e2a7"}
{"nl": {"description": "An elephant decided to visit his friend. It turned out that the elephant's house is located at point 0 and his friend's house is located at point x(x\u2009>\u20090) of the coordinate line. In one step the elephant can move 1, 2, 3, 4 or 5 positions forward. Determine, what is the minimum number of steps he need to make in order to get to his friend's house.", "input_spec": "The first line of the input contains an integer x (1\u2009\u2264\u2009x\u2009\u2264\u20091\u2009000\u2009000)\u00a0\u2014 The coordinate of the friend's house.", "output_spec": "Print the minimum number of steps that elephant needs to make to get from point 0 to point x.", "sample_inputs": ["5", "12"], "sample_outputs": ["1", "3"], "notes": "NoteIn the first sample the elephant needs to make one step of length 5 to reach the point x.In the second sample the elephant can get to point x if he moves by 3, 5 and 4. There are other ways to get the optimal answer but the elephant cannot reach x in less than three moves."}, "src_uid": "4b3d65b1b593829e92c852be213922b6"}
{"nl": {"description": "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\u2009\u2264\u2009li\u2009\u2264\u20099) \u2014 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\" (w\u0131thout 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": "After Fox Ciel won an onsite round of a programming contest, she took a bus to return to her castle. The fee of the bus was 220 yen. She met Rabbit Hanako in the bus. They decided to play the following game because they got bored in the bus.  Initially, there is a pile that contains x 100-yen coins and y 10-yen coins.  They take turns alternatively. Ciel takes the first turn.  In each turn, they must take exactly 220 yen from the pile. In Ciel's turn, if there are multiple ways to take 220 yen, she will choose the way that contains the maximal number of 100-yen coins. In Hanako's turn, if there are multiple ways to take 220 yen, she will choose the way that contains the maximal number of 10-yen coins.  If Ciel or Hanako can't take exactly 220 yen from the pile, she loses.  Determine the winner of the game.", "input_spec": "The first line contains two integers x (0\u2009\u2264\u2009x\u2009\u2264\u2009106) and y (0\u2009\u2264\u2009y\u2009\u2264\u2009106), separated by a single space.", "output_spec": "If Ciel wins, print \"Ciel\". Otherwise, print \"Hanako\".", "sample_inputs": ["2 2", "3 22"], "sample_outputs": ["Ciel", "Hanako"], "notes": "NoteIn the first turn (Ciel's turn), she will choose 2 100-yen coins and 2 10-yen coins. In the second turn (Hanako's turn), she will choose 1 100-yen coin and 12 10-yen coins. In the third turn (Ciel's turn), she can't pay exactly 220 yen, so Ciel will lose."}, "src_uid": "8ffee18bbc4bb281027f91193002b7f5"}
{"nl": {"description": "Makoto has a big blackboard with a positive integer $$$n$$$ written on it. He will perform the following action exactly $$$k$$$ times:Suppose the number currently written on the blackboard is $$$v$$$. He will randomly pick one of the divisors of $$$v$$$ (possibly $$$1$$$ and $$$v$$$) and replace $$$v$$$ with this divisor. As Makoto uses his famous random number generator (RNG) and as he always uses $$$58$$$ as his generator seed, each divisor is guaranteed to be chosen with equal probability.He now wonders what is the expected value of the number written on the blackboard after $$$k$$$ steps.It can be shown that this value can be represented as $$$\\frac{P}{Q}$$$ where $$$P$$$ and $$$Q$$$ are coprime integers and $$$Q \\not\\equiv 0 \\pmod{10^9+7}$$$. Print the value of $$$P \\cdot Q^{-1}$$$ modulo $$$10^9+7$$$.", "input_spec": "The only line of the input contains two integers $$$n$$$ and $$$k$$$ ($$$1 \\leq n \\leq 10^{15}$$$, $$$1 \\leq k \\leq 10^4$$$).", "output_spec": "Print a single integer \u2014 the expected value of the number on the blackboard after $$$k$$$ steps as $$$P \\cdot Q^{-1} \\pmod{10^9+7}$$$ for $$$P$$$, $$$Q$$$ defined above.", "sample_inputs": ["6 1", "6 2", "60 5"], "sample_outputs": ["3", "875000008", "237178099"], "notes": "NoteIn the first example, after one step, the number written on the blackboard is $$$1$$$, $$$2$$$, $$$3$$$ or $$$6$$$ \u2014 each occurring with equal probability. Hence, the answer is $$$\\frac{1+2+3+6}{4}=3$$$.In the second example, the answer is equal to $$$1 \\cdot \\frac{9}{16}+2 \\cdot \\frac{3}{16}+3 \\cdot \\frac{3}{16}+6 \\cdot \\frac{1}{16}=\\frac{15}{8}$$$."}, "src_uid": "dc466d9c24b7dcb37c0e99337b4124d2"}
{"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\u00a0\u2014 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\u00a0\u2014 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\u00a0  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\u2009+\u20095\u2009+\u200910\u2009+\u20092\u2009=\u200918 rotations are required."}, "src_uid": "ecc890b3bdb9456441a2a265c60722dd"}
{"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\" \u2014 the duration of George's sleep. It is guaranteed that the input contains the correct time in the 24-hour format, that is, 00\u2009\u2264\u2009hh\u2009\u2264\u200923, 00\u2009\u2264\u2009mm\u2009\u2264\u200959.", "output_spec": "In the single line print time p \u2014 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": "Valera has got n domino pieces in a row. Each piece consists of two halves \u2014 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\u2009\u2264\u2009n\u2009\u2264\u2009100), denoting the number of dominoes Valera has. Next n lines contain two space-separated integers xi,\u2009yi (1\u2009\u2264\u2009xi,\u2009yi\u2009\u2264\u20096). 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 \u2014 the minimum required number of seconds. If Valera can't do the task in any time, print \u2009-\u20091.", "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": "Imagine you have an infinite 2D plane with Cartesian coordinate system. Some of the integral points are blocked, and others are not. Two integral points A and B on the plane are 4-connected if and only if:  the Euclidean distance between A and B is one unit and neither A nor B is blocked;  or there is some integral point C, such that A is 4-connected with C, and C is 4-connected with B. Let's assume that the plane doesn't contain blocked points. Consider all the integral points of the plane whose Euclidean distance from the origin is no more than n, we'll name these points special. Chubby Yang wants to get the following property: no special point is 4-connected to some non-special point. To get the property she can pick some integral points of the plane and make them blocked. What is the minimum number of points she needs to pick?", "input_spec": "The first line contains an integer n (0\u2009\u2264\u2009n\u2009\u2264\u20094\u00b7107).", "output_spec": "Print a single integer \u2014 the minimum number of points that should be blocked.", "sample_inputs": ["1", "2", "3"], "sample_outputs": ["4", "8", "16"], "notes": null}, "src_uid": "d87ce09acb8401e910ca6ef3529566f4"}
{"nl": {"description": "Recently Luba learned about a special kind of numbers that she calls beautiful numbers. The number is called beautiful iff its binary representation consists of k\u2009+\u20091 consecutive ones, and then k consecutive zeroes.Some examples of beautiful numbers:   12 (110);  1102 (610);  11110002 (12010);  1111100002 (49610). More formally, the number is beautiful iff there exists some positive integer k such that the number is equal to (2k\u2009-\u20091)\u2009*\u2009(2k\u2009-\u20091).Luba has got an integer number n, and she wants to find its greatest beautiful divisor. Help her to find it!", "input_spec": "The only line of input contains one number n (1\u2009\u2264\u2009n\u2009\u2264\u2009105) \u2014 the number Luba has got.", "output_spec": "Output one number \u2014 the greatest beautiful divisor of Luba's number. It is obvious that the answer always exists.", "sample_inputs": ["3", "992"], "sample_outputs": ["1", "496"], "notes": null}, "src_uid": "339246a1be81aefe19290de0d1aead84"}
{"nl": {"description": "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\u00a0\u2014 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,\u2009a2,\u2009...,\u2009am 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\u2009\u2264\u2009k\u2009\u2264\u2009n\u2009\u2264\u20091018).", "output_spec": "Output one number\u00a0\u2014 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": "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$$$)\u00a0\u2014 the floor Masha is at, the floor Masha wants to get to, the floor the elevator is located on, the time it takes Masha to pass between two floors by stairs, the time it takes the elevator to pass between two floors and the time it takes for the elevator to close or open the doors. It is guaranteed that $$$x \\ne y$$$.", "output_spec": "If the time it will take to use the elevator is not greater than the time it will take to use the stairs, print \u00abYES\u00bb (without quotes), otherwise print \u00abNO> (without quotes). You can print each letter in any case (upper or lower).", "sample_inputs": ["5 1 4 4 2 1", "1 6 6 2 1 1", "4 1 7 4 1 2"], "sample_outputs": ["YES", "NO", "YES"], "notes": "NoteIn the first example:If Masha goes by the stairs, the time she spends is $$$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$$$ seconds. That means Masha will take the elevator."}, "src_uid": "05cffd59b28b9e026ca3203718b2e6ca"}
{"nl": {"description": "Polycarp is going to participate in the contest. It starts at $$$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$$$) corresponding to the midpoint of the contest in the format hh:mm. Print each number as exactly two digits (prepend a number with leading zero if needed), separate them with ':'.", "sample_inputs": ["10:00\n11:00", "11:10\n11:12", "01:02\n03:02"], "sample_outputs": ["10:30", "11:11", "02:02"], "notes": null}, "src_uid": "f7a32a8325ce97c4c50ce3a5c282ec50"}
{"nl": {"description": "Vasya has got an undirected graph consisting of $$$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$$$ \u2014 the minimum and maximum number of isolated vertices, respectively.", "sample_inputs": ["4 2", "3 1"], "sample_outputs": ["0 1", "1 1"], "notes": "NoteIn the first example it is possible to construct a graph with $$$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)$$$. In the second example the graph will always contain exactly one isolated vertex."}, "src_uid": "daf0dd781bf403f7c1bb668925caa64d"}
{"nl": {"description": "There are $$$n$$$ heroes fighting in the arena. Initially, the $$$i$$$-th hero has $$$a_i$$$ health points.The fight in the arena takes place in several rounds. At the beginning of each round, each alive hero deals $$$1$$$ damage to all other heroes. Hits of all heroes occur simultaneously. Heroes whose health is less than $$$1$$$ at the end of the round are considered killed.If exactly $$$1$$$ hero remains alive after a certain round, then he is declared the winner. Otherwise, there is no winner.Your task is to calculate the number of ways to choose the initial health points for each hero $$$a_i$$$, where $$$1 \\le a_i \\le x$$$, so that there is no winner of the fight. The number of ways can be very large, so print it modulo $$$998244353$$$. Two ways are considered different if at least one hero has a different amount of health. For example, $$$[1, 2, 1]$$$ and $$$[2, 1, 1]$$$ are different.", "input_spec": "The only line contains two integers $$$n$$$ and $$$x$$$ ($$$2 \\le n \\le 500; 1 \\le x \\le 500$$$).", "output_spec": "Print one integer\u00a0\u2014 the number of ways to choose the initial health points for each hero $$$a_i$$$, where $$$1 \\le a_i \\le x$$$, so that there is no winner of the fight, taken modulo $$$998244353$$$. ", "sample_inputs": ["2 5", "3 3", "5 4", "13 37"], "sample_outputs": ["5", "15", "1024", "976890680"], "notes": null}, "src_uid": "1908d1c8c6b122a4c6633a7af094f17f"}
{"nl": {"description": "\"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 \u732b\u5c4b 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\u2009\u2264\u2009n\u2009\u2264\u2009100). It's guaranteed that the string only contains uppercase English letters.", "output_spec": "Print a single integer\u00a0\u2014 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": "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\u2009\u2264\u2009r,\u2009g,\u2009b\u2009\u2264\u2009109) \u2014 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": "JATC's math teacher always gives the class some interesting math problems so that they don't get bored. Today the problem is as follows. Given an integer $$$n$$$, you can perform the following operations zero or more times:  mul $$$x$$$: multiplies $$$n$$$ by $$$x$$$ (where $$$x$$$ is an arbitrary positive integer).  sqrt: replaces $$$n$$$ with $$$\\sqrt{n}$$$ (to apply this operation, $$$\\sqrt{n}$$$ must be an integer). You can perform these operations as many times as you like. What is the minimum value of $$$n$$$, that can be achieved and what is the minimum number of operations, to achieve that minimum value?Apparently, no one in the class knows the answer to this problem, maybe you can help them?", "input_spec": "The only line of the input contains a single integer $$$n$$$ ($$$1 \\le n \\le 10^6$$$)\u00a0\u2014 the initial number.", "output_spec": "Print two integers: the minimum integer $$$n$$$ that can be achieved using the described operations and the minimum number of operations required.", "sample_inputs": ["20", "5184"], "sample_outputs": ["10 2", "6 4"], "notes": "NoteIn the first example, you can apply the operation mul $$$5$$$ to get $$$100$$$ and then sqrt to get $$$10$$$.In the second example, you can first apply sqrt to get $$$72$$$, then mul $$$18$$$ to get $$$1296$$$ and finally two more sqrt and you get $$$6$$$.Note, that even if the initial value of $$$n$$$ is less or equal $$$10^6$$$, it can still become greater than $$$10^6$$$ after applying one or more operations."}, "src_uid": "212cda3d9d611cd45332bb10b80f0b56"}
{"nl": {"description": "At a geometry lesson Gerald was given a task: to get vector B out of vector A. Besides, the teacher permitted him to perform the following operations with vector \u0410: Turn the vector by 90 degrees clockwise. Add to the vector a certain vector C.Operations could be performed in any order any number of times.Can Gerald cope with the task?", "input_spec": "The first line contains integers x1 \u0438 y1 \u2014 the coordinates of the vector A (\u2009-\u2009108\u2009\u2264\u2009x1,\u2009y1\u2009\u2264\u2009108). The second and the third line contain in the similar manner vectors B and C (their coordinates are integers; their absolute value does not exceed 108).", "output_spec": "Print \"YES\" (without the quotes) if it is possible to get vector B using the given operations. Otherwise print \"NO\" (without the quotes).", "sample_inputs": ["0 0\n1 1\n0 1", "0 0\n1 1\n1 1", "0 0\n1 1\n2 2"], "sample_outputs": ["YES", "YES", "NO"], "notes": null}, "src_uid": "cc8a8af1ba2b19bf081e379139542883"}
{"nl": {"description": "In this problem you will meet the simplified model of game King of Thieves.In a new ZeptoLab game called \"King of Thieves\" your aim is to reach a chest with gold by controlling your character, avoiding traps and obstacles on your way.  An interesting feature of the game is that you can design your own levels that will be available to other players. Let's consider the following simple design of a level.A dungeon consists of n segments located at a same vertical level, each segment is either a platform that character can stand on, or a pit with a trap that makes player lose if he falls into it. All segments have the same length, platforms on the scheme of the level are represented as '*' and pits are represented as '.'. One of things that affects speedrun characteristics of the level is a possibility to perform a series of consecutive jumps of the same length. More formally, when the character is on the platform number i1, he can make a sequence of jumps through the platforms i1\u2009<\u2009i2\u2009<\u2009...\u2009<\u2009ik, if i2\u2009-\u2009i1\u2009=\u2009i3\u2009-\u2009i2\u2009=\u2009...\u2009=\u2009ik\u2009-\u2009ik\u2009-\u20091. Of course, all segments i1,\u2009i2,\u2009... ik should be exactly the platforms, not pits. Let's call a level to be good if you can perform a sequence of four jumps of the same length or in the other words there must be a sequence i1,\u2009i2,\u2009...,\u2009i5, consisting of five platforms so that the intervals between consecutive platforms are of the same length. Given the scheme of the level, check if it is good.", "input_spec": "The first line contains integer n (1\u2009\u2264\u2009n\u2009\u2264\u2009100) \u2014 the number of segments on the level. Next line contains the scheme of the level represented as a string of n characters '*' and '.'.", "output_spec": "If the level is good, print the word \"yes\" (without the quotes), otherwise print the word \"no\" (without the quotes).", "sample_inputs": ["16\n.**.*..*.***.**.", "11\n.*.*...*.*."], "sample_outputs": ["yes", "no"], "notes": "NoteIn the first sample test you may perform a sequence of jumps through platforms 2,\u20095,\u20098,\u200911,\u200914."}, "src_uid": "12d451eb1b401a8f426287c4c6909e4b"}
{"nl": {"description": "Students Vasya and Petya are studying at the BSU (Byteland State University). At one of the breaks they decided to order a pizza. In this problem pizza is a circle of some radius. The pizza was delivered already cut into n pieces. The i-th piece is a sector of angle equal to ai. Vasya and Petya want to divide all pieces of pizza into two continuous sectors in such way that the difference between angles of these sectors is minimal. Sector angle is sum of angles of all pieces in it. Pay attention, that one of sectors can be empty.", "input_spec": "The first line contains one integer n (1\u2009\u2264\u2009n\u2009\u2264\u2009360) \u00a0\u2014 the number of pieces into which the delivered pizza was cut. The second line contains n integers ai (1\u2009\u2264\u2009ai\u2009\u2264\u2009360) \u00a0\u2014 the angles of the sectors into which the pizza was cut. The sum of all ai is 360.", "output_spec": "Print one integer \u00a0\u2014 the minimal difference between angles of sectors that will go to Vasya and Petya.", "sample_inputs": ["4\n90 90 90 90", "3\n100 100 160", "1\n360", "4\n170 30 150 10"], "sample_outputs": ["0", "40", "360", "0"], "notes": "NoteIn first sample Vasya can take 1 and 2 pieces, Petya can take 3 and 4 pieces. Then the answer is |(90\u2009+\u200990)\u2009-\u2009(90\u2009+\u200990)|\u2009=\u20090.In third sample there is only one piece of pizza that can be taken by only one from Vasya and Petya. So the answer is |360\u2009-\u20090|\u2009=\u2009360.In fourth sample Vasya can take 1 and 4 pieces, then Petya will take 2 and 3 pieces. So the answer is |(170\u2009+\u200910)\u2009-\u2009(30\u2009+\u2009150)|\u2009=\u20090.Picture explaning fourth sample:Both red and green sectors consist of two adjacent pieces of pizza. So Vasya can take green sector, then Petya will take red sector."}, "src_uid": "1b6a6aff81911865356ec7cbf6883e82"}
{"nl": {"description": "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\u2009\u2264\u2009|s|\u2009\u2264\u200915).", "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": "There is a binary string $$$t$$$ of length $$$10^{100}$$$, and initally all of its bits are $$$\\texttt{0}$$$. You are given a binary string $$$s$$$, and perform the following operation some times:   Select some substring of $$$t$$$, and replace it with its XOR with $$$s$$$.$$$^\\dagger$$$  After several operations, the string $$$t$$$ has exactly two bits $$$\\texttt{1}$$$; that is, there are exactly two distinct indices $$$p$$$ and $$$q$$$ such that the $$$p$$$-th and $$$q$$$-th bits of $$$t$$$ are $$$\\texttt{1}$$$, and the rest of the bits are $$$\\texttt{0}$$$. Find the lexicographically largest$$$^\\ddagger$$$ string $$$t$$$ satisfying these constraints, or report that no such string exists.$$$^\\dagger$$$ Formally, choose an index $$$i$$$ such that $$$0 \\leq i \\leq 10^{100}-|s|$$$. For all $$$1 \\leq j \\leq |s|$$$, if $$$s_j = \\texttt{1}$$$, then toggle $$$t_{i+j}$$$. That is, if $$$t_{i+j}=\\texttt{0}$$$, set $$$t_{i+j}=\\texttt{1}$$$. Otherwise if $$$t_{i+j}=\\texttt{1}$$$, set $$$t_{i+j}=\\texttt{0}$$$.$$$^\\ddagger$$$ A binary string $$$a$$$ is lexicographically larger than a binary string $$$b$$$ of the same length if in the first position where $$$a$$$ and $$$b$$$ differ, the string $$$a$$$ has a bit $$$\\texttt{1}$$$ and the corresponding bit in $$$b$$$ is $$$\\texttt{0}$$$.", "input_spec": "The only line of each test contains a single binary string $$$s$$$ ($$$1 \\leq |s| \\leq 35$$$).", "output_spec": "If no string $$$t$$$ exists as described in the statement, output -1. Otherwise, output the integers $$$p$$$ and $$$q$$$ ($$$1 \\leq p < q \\leq 10^{100}$$$) such that the $$$p$$$-th and $$$q$$$-th bits of the lexicographically maximal $$$t$$$ are $$$\\texttt{1}$$$.", "sample_inputs": ["1", "001", "1111", "00000", "00000111110000011111000001111101010"], "sample_outputs": ["1 2", "3 4", "1 5", "-1", "6 37452687"], "notes": "NoteIn the first test, you can perform the following operations. $$$$$$\\texttt{00000}\\ldots \\to \\color{red}{\\texttt{1}}\\texttt{0000}\\ldots \\to \\texttt{1}\\color{red}{\\texttt{1}}\\texttt{000}\\ldots$$$$$$In the second test, you can perform the following operations. $$$$$$\\texttt{00000}\\ldots \\to \\color{red}{\\texttt{001}}\\texttt{00}\\ldots \\to \\texttt{0}\\color{red}{\\texttt{011}}\\texttt{0}\\ldots$$$$$$In the third test, you can perform the following operations. $$$$$$\\texttt{00000}\\ldots \\to \\color{red}{\\texttt{1111}}\\texttt{0}\\ldots \\to \\texttt{1}\\color{red}{\\texttt{0001}}\\ldots$$$$$$It can be proven that these strings $$$t$$$ are the lexicographically largest ones.In the fourth test, you can't make a single bit $$$\\texttt{1}$$$, so it is impossible."}, "src_uid": "6bf798edef30db7d0ce2130e40084e6b"}
{"nl": {"description": "Arkady and his friends love playing checkers on an $$$n \\times n$$$ field. The rows and the columns of the field are enumerated from $$$1$$$ to $$$n$$$.The friends have recently won a championship, so Arkady wants to please them with some candies. Remembering an old parable (but not its moral), Arkady wants to give to his friends one set of candies per each cell of the field: the set of candies for cell $$$(i, j)$$$ will have exactly $$$(i^2 + j^2)$$$ candies of unique type.There are $$$m$$$ friends who deserve the present. How many of these $$$n \\times n$$$ sets of candies can be split equally into $$$m$$$ parts without cutting a candy into pieces? Note that each set has to be split independently since the types of candies in different sets are different.", "input_spec": "The only line contains two integers $$$n$$$ and $$$m$$$ ($$$1 \\le n \\le 10^9$$$, $$$1 \\le m \\le 1000$$$)\u00a0\u2014 the size of the field and the number of parts to split the sets into.", "output_spec": "Print a single integer\u00a0\u2014 the number of sets that can be split equally.", "sample_inputs": ["3 3", "6 5", "1000000000 1"], "sample_outputs": ["1", "13", "1000000000000000000"], "notes": "NoteIn the first example, only the set for cell $$$(3, 3)$$$ can be split equally ($$$3^2 + 3^2 = 18$$$, which is divisible by $$$m=3$$$).In the second example, the sets for the following cells can be divided equally:   $$$(1, 2)$$$ and $$$(2, 1)$$$, since $$$1^2 + 2^2 = 5$$$, which is divisible by $$$5$$$;  $$$(1, 3)$$$ and $$$(3, 1)$$$;  $$$(2, 4)$$$ and $$$(4, 2)$$$;  $$$(2, 6)$$$ and $$$(6, 2)$$$;  $$$(3, 4)$$$ and $$$(4, 3)$$$;  $$$(3, 6)$$$ and $$$(6, 3)$$$;  $$$(5, 5)$$$. In the third example, sets in all cells can be divided equally, since $$$m = 1$$$."}, "src_uid": "2ec9e7cddc634d7830575e14363a4657"}
{"nl": {"description": "Several ages ago Berland was a kingdom. The King of Berland adored math. That's why, when he first visited one of his many palaces, he first of all paid attention to the floor in one hall. The floor was tiled with hexagonal tiles.The hall also turned out hexagonal in its shape. The King walked along the perimeter of the hall and concluded that each of the six sides has a, b, c, a, b and c adjacent tiles, correspondingly.To better visualize the situation, look at the picture showing a similar hexagon for a\u2009=\u20092, b\u2009=\u20093 and c\u2009=\u20094.  According to the legend, as the King of Berland obtained the values a, b and c, he almost immediately calculated the total number of tiles on the hall floor. Can you do the same?", "input_spec": "The first line contains three integers: a, b and c (2\u2009\u2264\u2009a,\u2009b,\u2009c\u2009\u2264\u20091000).", "output_spec": "Print a single number \u2014 the total number of tiles on the hall floor.", "sample_inputs": ["2 3 4"], "sample_outputs": ["18"], "notes": null}, "src_uid": "8ab25ed4955d978fe20f6872cb94b0da"}
{"nl": {"description": "Polycarpus likes giving presents to Paraskevi. He has bought two chocolate bars, each of them has the shape of a segmented rectangle. The first bar is a1\u2009\u00d7\u2009b1 segments large and the second one is a2\u2009\u00d7\u2009b2 segments large.Polycarpus wants to give Paraskevi one of the bars at the lunch break and eat the other one himself. Besides, he wants to show that Polycarpus's mind and Paraskevi's beauty are equally matched, so the two bars must have the same number of squares.To make the bars have the same number of squares, Polycarpus eats a little piece of chocolate each minute. Each minute he does the following:  he either breaks one bar exactly in half (vertically or horizontally) and eats exactly a half of the bar,  or he chips of exactly one third of a bar (vertically or horizontally) and eats exactly a third of the bar. In the first case he is left with a half, of the bar and in the second case he is left with two thirds of the bar.Both variants aren't always possible, and sometimes Polycarpus cannot chip off a half nor a third. For example, if the bar is 16\u2009\u00d7\u200923, then Polycarpus can chip off a half, but not a third. If the bar is 20\u2009\u00d7\u200918, then Polycarpus can chip off both a half and a third. If the bar is 5\u2009\u00d7\u20097, then Polycarpus cannot chip off a half nor a third.What is the minimum number of minutes Polycarpus needs to make two bars consist of the same number of squares? Find not only the required minimum number of minutes, but also the possible sizes of the bars after the process.", "input_spec": "The first line of the input contains integers a1,\u2009b1 (1\u2009\u2264\u2009a1,\u2009b1\u2009\u2264\u2009109) \u2014 the initial sizes of the first chocolate bar. The second line of the input contains integers a2,\u2009b2 (1\u2009\u2264\u2009a2,\u2009b2\u2009\u2264\u2009109) \u2014 the initial sizes of the second bar. You can use the data of type int64 (in Pascal), long long (in \u0421++), long (in Java) to process large integers (exceeding 231\u2009-\u20091).", "output_spec": "In the first line print m \u2014 the sought minimum number of minutes. In the second and third line print the possible sizes of the bars after they are leveled in m minutes. Print the sizes using the format identical to the input format. Print the sizes (the numbers in the printed pairs) in any order. The second line must correspond to the first bar and the third line must correspond to the second bar. If there are multiple solutions, print any of them. If there is no solution, print a single line with integer -1.", "sample_inputs": ["2 6\n2 3", "36 5\n10 16", "3 5\n2 1"], "sample_outputs": ["1\n1 6\n2 3", "3\n16 5\n5 16", "-1"], "notes": null}, "src_uid": "4fcd8c4955a47661462c326cbb3429bd"}
{"nl": {"description": "A few years ago, Hitagi encountered a giant crab, who stole the whole of her body weight. Ever since, she tried to avoid contact with others, for fear that this secret might be noticed.To get rid of the oddity and recover her weight, a special integer sequence is needed. Hitagi's sequence has been broken for a long time, but now Kaiki provides an opportunity.Hitagi's sequence a has a length of n. Lost elements in it are denoted by zeros. Kaiki provides another sequence b, whose length k equals the number of lost elements in a (i.e. the number of zeros). Hitagi is to replace each zero in a with an element from b so that each element in b should be used exactly once. Hitagi knows, however, that, apart from 0, no integer occurs in a and b more than once in total.If the resulting sequence is not an increasing sequence, then it has the power to recover Hitagi from the oddity. You are to determine whether this is possible, or Kaiki's sequence is just another fake. In other words, you should detect whether it is possible to replace each zero in a with an integer from b so that each integer from b is used exactly once, and the resulting sequence is not increasing.", "input_spec": "The first line of input contains two space-separated positive integers n (2\u2009\u2264\u2009n\u2009\u2264\u2009100) and k (1\u2009\u2264\u2009k\u2009\u2264\u2009n) \u2014 the lengths of sequence a and b respectively. The second line contains n space-separated integers a1,\u2009a2,\u2009...,\u2009an (0\u2009\u2264\u2009ai\u2009\u2264\u2009200) \u2014 Hitagi's broken sequence with exactly k zero elements. The third line contains k space-separated integers b1,\u2009b2,\u2009...,\u2009bk (1\u2009\u2264\u2009bi\u2009\u2264\u2009200) \u2014 the elements to fill into Hitagi's sequence. Input guarantees that apart from 0, no integer occurs in a and b more than once in total.", "output_spec": "Output \"Yes\" if it's possible to replace zeros in a with elements in b and make the resulting sequence not increasing, and \"No\" otherwise.", "sample_inputs": ["4 2\n11 0 0 14\n5 4", "6 1\n2 3 0 8 9 10\n5", "4 1\n8 94 0 4\n89", "7 7\n0 0 0 0 0 0 0\n1 2 3 4 5 6 7"], "sample_outputs": ["Yes", "No", "Yes", "Yes"], "notes": "NoteIn the first sample:   Sequence a is 11,\u20090,\u20090,\u200914.  Two of the elements are lost, and the candidates in b are 5 and 4.  There are two possible resulting sequences: 11,\u20095,\u20094,\u200914 and 11,\u20094,\u20095,\u200914, both of which fulfill the requirements. Thus the answer is \"Yes\". In the second sample, the only possible resulting sequence is 2,\u20093,\u20095,\u20098,\u20099,\u200910, which is an increasing sequence and therefore invalid."}, "src_uid": "40264e84c041fcfb4f8c0af784df102a"}
{"nl": {"description": "There are n walruses sitting in a circle. All of them are numbered in the clockwise order: the walrus number 2 sits to the left of the walrus number 1, the walrus number 3 sits to the left of the walrus number 2, ..., the walrus number 1 sits to the left of the walrus number n.The presenter has m chips. The presenter stands in the middle of the circle and starts giving the chips to the walruses starting from walrus number 1 and moving clockwise. The walrus number i gets i chips. If the presenter can't give the current walrus the required number of chips, then the presenter takes the remaining chips and the process ends. Determine by the given n and m how many chips the presenter will get in the end.", "input_spec": "The first line contains two integers n and m (1\u2009\u2264\u2009n\u2009\u2264\u200950, 1\u2009\u2264\u2009m\u2009\u2264\u2009104) \u2014 the number of walruses and the number of chips correspondingly.", "output_spec": "Print the number of chips the presenter ended up with.", "sample_inputs": ["4 11", "17 107", "3 8"], "sample_outputs": ["0", "2", "1"], "notes": "NoteIn the first sample the presenter gives one chip to the walrus number 1, two chips to the walrus number 2, three chips to the walrus number 3, four chips to the walrus number 4, then again one chip to the walrus number 1. After that the presenter runs out of chips. He can't give anything to the walrus number 2 and the process finishes.In the third sample the presenter gives one chip to the walrus number 1, two chips to the walrus number 2, three chips to the walrus number 3, then again one chip to the walrus number 1. The presenter has one chip left and he can't give two chips to the walrus number 2, that's why the presenter takes the last chip."}, "src_uid": "5dd5ee90606d37cae5926eb8b8d250bb"}
{"nl": {"description": "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": "Two best friends Serozha and Gena play a game.Initially there is one pile consisting of n stones on the table. During one move one pile should be taken and divided into an arbitrary number of piles consisting of a1\u2009>\u2009a2\u2009>\u2009...\u2009>\u2009ak\u2009>\u20090 stones. The piles should meet the condition a1\u2009-\u2009a2\u2009=\u2009a2\u2009-\u2009a3\u2009=\u2009...\u2009=\u2009ak\u2009-\u20091\u2009-\u2009ak\u2009=\u20091. Naturally, the number of piles k should be no less than two.The friends play in turns. The player who cannot make a move loses. Serozha makes the first move. Who will win if both players play in the optimal way?", "input_spec": "The single line contains a single integer n (1\u2009\u2264\u2009n\u2009\u2264\u2009105).", "output_spec": "If Serozha wins, print k, which represents the minimal number of piles into which he can split the initial one during the first move in order to win the game. If Gena wins, print \"-1\" (without the quotes).", "sample_inputs": ["3", "6", "100"], "sample_outputs": ["2", "-1", "8"], "notes": null}, "src_uid": "63262317ba572d78163c91b853c05506"}
{"nl": {"description": "Anton has the integer x. He is interested what positive integer, which doesn't exceed x, has the maximum sum of digits.Your task is to help Anton and to find the integer that interests him. If there are several such integers, determine the biggest of them. ", "input_spec": "The first line contains the positive integer x (1\u2009\u2264\u2009x\u2009\u2264\u20091018) \u2014 the integer which Anton has. ", "output_spec": "Print the positive integer which doesn't exceed x and has the maximum sum of digits. If there are several such integers, print the biggest of them. Printed integer must not contain leading zeros.", "sample_inputs": ["100", "48", "521"], "sample_outputs": ["99", "48", "499"], "notes": null}, "src_uid": "e55b0debbf33c266091e6634494356b8"}
{"nl": {"description": "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$$$), representing the necklace, where a dash '-' represents a link and the lowercase English letter 'o' represents a pearl.", "output_spec": "Print \"YES\" if the links and pearls can be rejoined such that the number of links between adjacent pearls is equal. Otherwise print \"NO\". You can print each letter in any case (upper or lower).", "sample_inputs": ["-o-o--", "-o---", "-o---o-", "ooo"], "sample_outputs": ["YES", "YES", "NO", "YES"], "notes": null}, "src_uid": "6e006ae3df3bcd24755358a5f584ec03"}
{"nl": {"description": "Natasha is going to fly to Mars. She needs to build a rocket, which consists of several stages in some order. Each of the stages is defined by a lowercase Latin letter. This way, the rocket can be described by the string\u00a0\u2014 concatenation of letters, which correspond to the stages.There are $$$n$$$ stages available. The rocket must contain exactly $$$k$$$ of them. Stages in the rocket should be ordered by their weight. So, after the stage with some letter can go only stage with a letter, which is at least two positions after in the alphabet (skipping one letter in between, or even more). For example, after letter 'c' can't go letters 'a', 'b', 'c' and 'd', but can go letters 'e', 'f', ..., 'z'.For the rocket to fly as far as possible, its weight should be minimal. The weight of the rocket is equal to the sum of the weights of its stages. The weight of the stage is the number of its letter in the alphabet. For example, the stage 'a 'weighs one ton,' b 'weighs two tons, and' z'\u00a0\u2014 $$$26$$$ tons.Build the rocket with the minimal weight or determine, that it is impossible to build a rocket at all. Each stage can be used at most once.", "input_spec": "The first line of input contains two integers\u00a0\u2014 $$$n$$$ and $$$k$$$ ($$$1 \\le k \\le n \\le 50$$$)\u00a0\u2013 the number of available stages and the number of stages to use in the rocket. The second line contains string $$$s$$$, which consists of exactly $$$n$$$ lowercase Latin letters. Each letter defines a new stage, which can be used to build the rocket. Each stage can be used at most once.", "output_spec": "Print a single integer\u00a0\u2014 the minimal total weight of the rocket or -1, if it is impossible to build the rocket at all.", "sample_inputs": ["5 3\nxyabd", "7 4\nproblem", "2 2\nab", "12 1\nabaabbaaabbb"], "sample_outputs": ["29", "34", "-1", "1"], "notes": "NoteIn the first example, the following rockets satisfy the condition: \"adx\" (weight is $$$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$$$, so the rocket must have both stages: 'a' and 'b'. This rocket doesn't satisfy the condition, because these letters are adjacent in the alphabet. Answer is -1."}, "src_uid": "56b13d313afef9dc6c6ba2758b5ea313"}
{"nl": {"description": "Neko is playing with his toys on the backyard of Aki's house. Aki decided to play a prank on him, by secretly putting catnip into Neko's toys. Unfortunately, he went overboard and put an entire bag of catnip into the toys...It took Neko an entire day to turn back to normal. Neko reported to Aki that he saw a lot of weird things, including a trie of all correct bracket sequences of length $$$2n$$$.The definition of correct bracket sequence is as follows:  The empty sequence is a correct bracket sequence,  If $$$s$$$ is a correct bracket sequence, then $$$(\\,s\\,)$$$ is a correct bracket sequence,  If $$$s$$$ and $$$t$$$ are a correct bracket sequence, then $$$st$$$ is also a correct bracket sequence. For example, the strings \"(())\", \"()()\" form a correct bracket sequence, while \")(\" and \"((\" not.Aki then came up with an interesting problem: What is the size of the maximum matching (the largest set of edges such that there are no two edges with a common vertex) in this trie? Since the answer can be quite large, print it modulo $$$10^9 + 7$$$.", "input_spec": "The only line contains a single integer $$$n$$$ ($$$1 \\le n \\le 1000$$$).", "output_spec": "Print exactly one integer\u00a0\u2014 the size of the maximum matching in the trie. Since the answer can be quite large, print it modulo $$$10^9 + 7$$$.", "sample_inputs": ["1", "2", "3"], "sample_outputs": ["1", "3", "9"], "notes": "NoteThe pictures below illustrate tries in the first two examples (for clarity, the round brackets are replaced with angle brackets). The maximum matching is highlighted with blue. \u00a0 "}, "src_uid": "8218255989e5eab73ac7107072c3b2af"}
{"nl": {"description": "Little Petya is learning to play chess. He has already learned how to move a king, a rook and a bishop. Let us remind you the rules of moving chess pieces. A chessboard is 64 square fields organized into an 8\u2009\u00d7\u20098 table. A field is represented by a pair of integers (r,\u2009c) \u2014 the number of the row and the number of the column (in a classical game the columns are traditionally indexed by letters). Each chess piece takes up exactly one field. To make a move is to move a chess piece, the pieces move by the following rules:  A rook moves any number of fields horizontally or vertically.  A bishop moves any number of fields diagonally.  A king moves one field in any direction \u2014 horizontally, vertically or diagonally.     The pieces move like that Petya is thinking about the following problem: what minimum number of moves is needed for each of these pieces to move from field (r1,\u2009c1) to field (r2,\u2009c2)? At that, we assume that there are no more pieces besides this one on the board. Help him solve this problem.", "input_spec": "The input contains four integers r1,\u2009c1,\u2009r2,\u2009c2 (1\u2009\u2264\u2009r1,\u2009c1,\u2009r2,\u2009c2\u2009\u2264\u20098) \u2014 the coordinates of the starting and the final field. The starting field doesn't coincide with the final one. You can assume that the chessboard rows are numbered from top to bottom 1 through 8, and the columns are numbered from left to right 1 through 8.", "output_spec": "Print three space-separated integers: the minimum number of moves the rook, the bishop and the king (in this order) is needed to move from field (r1,\u2009c1) to field (r2,\u2009c2). If a piece cannot make such a move, print a 0 instead of the corresponding number.", "sample_inputs": ["4 3 1 6", "5 5 5 6"], "sample_outputs": ["2 1 3", "1 0 1"], "notes": null}, "src_uid": "7dbf58806db185f0fe70c00b60973f4b"}
{"nl": {"description": "Polycarpus has recently got interested in sequences of pseudorandom numbers. He learned that many programming languages generate such sequences in a similar way:  (for i\u2009\u2265\u20091). Here a, b, m are constants, fixed for the given realization of the pseudorandom numbers generator, r0 is the so-called randseed (this value can be set from the program using functions like RandSeed(r) or srand(n)), and  denotes the operation of taking the remainder of division.For example, if a\u2009=\u20092,\u2009b\u2009=\u20096,\u2009m\u2009=\u200912,\u2009r0\u2009=\u200911, the generated sequence will be: 4,\u20092,\u200910,\u20092,\u200910,\u20092,\u200910,\u20092,\u200910,\u20092,\u200910,\u2009....Polycarpus realized that any such sequence will sooner or later form a cycle, but the cycle may occur not in the beginning, so there exist a preperiod and a period. The example above shows a preperiod equal to 1 and a period equal to 2.Your task is to find the period of a sequence defined by the given values of a,\u2009b,\u2009m and r0. Formally, you have to find such minimum positive integer t, for which exists such positive integer k, that for any i\u2009\u2265\u2009k: ri\u2009=\u2009ri\u2009+\u2009t.", "input_spec": "The single line of the input contains four integers a, b, m and r0 (1\u2009\u2264\u2009m\u2009\u2264\u2009105,\u20090\u2009\u2264\u2009a,\u2009b\u2009\u2264\u20091000,\u20090\u2009\u2264\u2009r0\u2009<\u2009m), separated by single spaces.", "output_spec": "Print a single integer \u2014 the period of the sequence.", "sample_inputs": ["2 6 12 11", "2 3 5 1", "3 6 81 9"], "sample_outputs": ["2", "4", "1"], "notes": "NoteThe first sample is described above. In the second sample the sequence is (starting from the first element): 0,\u20093,\u20094,\u20091,\u20090,\u20093,\u20094,\u20091,\u20090,\u2009...In the third sample the sequence is (starting from the first element): 33,\u200924,\u200978,\u200978,\u200978,\u200978,\u2009..."}, "src_uid": "9137197ee1b781cd5cc77c46f50b9012"}
{"nl": {"description": "Karlsson has visited Lillebror again. They found a box of chocolates and a big whipped cream cake at Lillebror's place. Karlsson immediately suggested to divide the sweets fairly between Lillebror and himself. Specifically, to play together a game he has just invented with the chocolates. The winner will get the cake as a reward.The box of chocolates has the form of a hexagon. It contains 19 cells for the chocolates, some of which contain a chocolate. The players move in turns. During one move it is allowed to eat one or several chocolates that lay in the neighboring cells on one line, parallel to one of the box's sides. The picture below shows the examples of allowed moves and of an unacceptable one. The player who cannot make a move loses.  Karlsson makes the first move as he is Lillebror's guest and not vice versa. The players play optimally. Determine who will get the cake.", "input_spec": "The input data contains 5 lines, containing 19 words consisting of one symbol. The word \"O\" means that the cell contains a chocolate and a \".\" stands for an empty cell. It is guaranteed that the box contains at least one chocolate. See the examples for better understanding.", "output_spec": "If Karlsson gets the cake, print \"Karlsson\" (without the quotes), otherwise print \"Lillebror\" (yet again without the quotes).", "sample_inputs": [". . .\n . . O .\n. . O O .\n . . . .\n  . . .", ". . .\n . . . O\n. . . O .\n O . O .\n  . O ."], "sample_outputs": ["Lillebror", "Karlsson"], "notes": null}, "src_uid": "eaa022cc7846c983a826900dc6dd919f"}
{"nl": {"description": "The only difference between easy and hard versions is 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$$$) \u2014 the number of cups of coffee and the number of pages in the coursework. The second line of the input contains $$$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": "Polycarp loves lowercase letters and dislikes uppercase ones. Once he got a string s consisting only of lowercase and uppercase Latin letters.Let A be a set of positions in the string. Let's call it pretty if following conditions are met:  letters on positions from A in the string are all distinct and lowercase;  there are no uppercase letters in the string which are situated between positions from A (i.e. there is no such j that s[j] is an uppercase letter, and a1\u2009<\u2009j\u2009<\u2009a2 for some a1 and a2 from A). Write a program that will determine the maximum number of elements in a pretty set of positions.", "input_spec": "The first line contains a single integer n (1\u2009\u2264\u2009n\u2009\u2264\u2009200) \u2014 length of string s. The second line contains a string s consisting of lowercase and uppercase Latin letters.", "output_spec": "Print maximum number of elements in pretty set of positions for string s.", "sample_inputs": ["11\naaaaBaabAbA", "12\nzACaAbbaazzC", "3\nABC"], "sample_outputs": ["2", "3", "0"], "notes": "NoteIn the first example the desired positions might be 6 and 8 or 7 and 8. Positions 6 and 7 contain letters 'a', position 8 contains letter 'b'. The pair of positions 1 and 8 is not suitable because there is an uppercase letter 'B' between these position.In the second example desired positions can be 7, 8 and 11. There are other ways to choose pretty set consisting of three elements.In the third example the given string s does not contain any lowercase letters, so the answer is 0."}, "src_uid": "567ce65f87d2fb922b0f7e0957fbada3"}
{"nl": {"description": "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 \u2014 the number of moves permitted for the king.", "sample_inputs": ["e4"], "sample_outputs": ["8"], "notes": null}, "src_uid": "6994331ca6282669cbb7138eb7e55e01"}
{"nl": {"description": "Buses run between the cities A and B, the first one is at 05:00 AM and the last one departs not later than at 11:59 PM. A bus from the city A departs every a minutes and arrives to the city B in a ta minutes, and a bus from the city B departs every b minutes and arrives to the city A in a tb minutes.The driver Simion wants to make his job diverse, so he counts the buses going towards him. Simion doesn't count the buses he meet at the start and finish.You know the time when Simion departed from the city A to the city B. Calculate the number of buses Simion will meet to be sure in his counting.", "input_spec": "The first line contains two integers a,\u2009ta (1\u2009\u2264\u2009a,\u2009ta\u2009\u2264\u2009120) \u2014 the frequency of the buses from the city A to the city B and the travel time. Both values are given in minutes. The second line contains two integers b,\u2009tb (1\u2009\u2264\u2009b,\u2009tb\u2009\u2264\u2009120) \u2014 the frequency of the buses from the city B to the city A and the travel time. Both values are given in minutes. The last line contains the departure time of Simion from the city A in the format hh:mm. It is guaranteed that there are a bus from the city A at that time. Note that the hours and the minutes are given with exactly two digits.", "output_spec": "Print the only integer z \u2014 the number of buses Simion will meet on the way. Note that you should not count the encounters in cities A and B.", "sample_inputs": ["10 30\n10 35\n05:20", "60 120\n24 100\n13:00"], "sample_outputs": ["5", "9"], "notes": "NoteIn the first example Simion departs form the city A at 05:20 AM and arrives to the city B at 05:50 AM. He will meet the first 5 buses from the city B that departed in the period [05:00 AM - 05:40 AM]. Also Simion will meet a bus in the city B at 05:50 AM, but he will not count it.Also note that the first encounter will be between 05:26 AM and 05:27 AM (if we suggest that the buses are go with the sustained speed)."}, "src_uid": "1c4cf1c3cb464a483511a8a61f8685a7"}
{"nl": {"description": "So nearly half of the winter is over and Maria is dreaming about summer. She's fed up with skates and sleds, she was dreaming about Hopscotch all night long. It's a very popular children's game. The game field, the court, looks as is shown in the figure (all blocks are square and are numbered from bottom to top, blocks in the same row are numbered from left to right). Let us describe the hopscotch with numbers that denote the number of squares in the row, staring from the lowest one: 1-1-2-1-2-1-2-(1-2)..., where then the period is repeated (1-2).  The coordinate system is defined as shown in the figure. Side of all the squares are equal and have length a.Maria is a very smart and clever girl, and she is concerned with quite serious issues: if she throws a stone into a point with coordinates (x,\u2009y), then will she hit some square? If the answer is positive, you are also required to determine the number of the square.It is believed that the stone has fallen into the square if it is located strictly inside it. In other words a stone that has fallen on the square border is not considered a to hit a square.", "input_spec": "The only input line contains three integers: a, x, y, where a (1\u2009\u2264\u2009a\u2009\u2264\u2009100) is the side of the square, x and y (\u2009-\u2009106\u2009\u2264\u2009x\u2009\u2264\u2009106,\u20090\u2009\u2264\u2009y\u2009\u2264\u2009106) are coordinates of the stone.", "output_spec": "Print the number of the square, inside which the stone fell. If the stone is on a border of some stone or outside the court, print \"-1\" without the quotes.", "sample_inputs": ["1 0 0", "3 1 1", "3 0 10", "3 0 7", "3 4 0"], "sample_outputs": ["-1", "1", "5", "-1", "-1"], "notes": null}, "src_uid": "cf48ff6ba3e77ba5d4afccb8f775fb02"}
{"nl": {"description": "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\u2009\u2264\u2009n\u2009\u2264\u2009100, 0\u2009\u2264\u2009k\u2009\u2264\u200910\u2009000), the number of instruments and number of days respectively. The second line contains n integers ai (1\u2009\u2264\u2009ai\u2009\u2264\u2009100), 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,\u20093,\u20095} or {3,\u20094,\u20095}.In the third test Amr doesn't have enough time to learn the only presented instrument."}, "src_uid": "dbb164a8dd190e63cceba95a31690a7c"}
{"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$$$)\u00a0\u2014 the initial number of cats at the party and the number of cats who left the circle at the moment Katie observes, respectively.", "output_spec": "Print a single integer\u00a0\u2014 the maximum number of groups of cats at the moment Katie observes.", "sample_inputs": ["7 4", "6 2", "3 0", "2 2"], "sample_outputs": ["3", "2", "1", "0"], "notes": "NoteIn the first example, originally there are $$$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": "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": "A bus moves along the coordinate line Ox from the point x\u2009=\u20090 to the point x\u2009=\u2009a. After starting from the point x\u2009=\u20090, it reaches the point x\u2009=\u2009a, immediately turns back and then moves to the point x\u2009=\u20090. After returning to the point x\u2009=\u20090 it immediately goes back to the point x\u2009=\u2009a and so on. Thus, the bus moves from x\u2009=\u20090 to x\u2009=\u2009a and back. Moving from the point x\u2009=\u20090 to x\u2009=\u2009a or from the point x\u2009=\u2009a to x\u2009=\u20090 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\u2009=\u2009f. This point is between points x\u2009=\u20090 and x\u2009=\u2009a. 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\u2009=\u2009f to make k journeys? The first journey starts in the point x\u2009=\u20090.", "input_spec": "The first line contains four integers a, b, f, k (0\u2009<\u2009f\u2009<\u2009a\u2009\u2264\u2009106, 1\u2009\u2264\u2009b\u2009\u2264\u2009109, 1\u2009\u2264\u2009k\u2009\u2264\u2009104) \u2014 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": "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,\u2009ATKY\u2009-\u2009DEFM), while Yang's HP decreases by max(0,\u2009ATKM\u2009-\u2009DEFY), where index Y denotes Master Yang and index M denotes monster. Both decreases happen simultaneously Once monster's HP\u2009\u2264\u20090 and the same time Master Yang's HP\u2009>\u20090, 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,\u2009ATKY,\u2009DEFY, separated by a space, denoting the initial HP, ATK and DEF of Master Yang. The second line contains three integers HPM,\u2009ATKM,\u2009DEFM, separated by a space, denoting the HP, ATK and DEF of the monster. The third line contains three integers h,\u2009a,\u2009d, separated by a space, denoting the price of 1\u00a0HP, 1\u00a0ATK and 1\u00a0DEF. 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": "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$$$)", "output_spec": "Print exactly one integer\u00a0\u2014 the minimum number of coins required to obtain sum $$$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": "Our bear's forest has a checkered field. The checkered field is an n\u2009\u00d7\u2009n table, the rows are numbered from 1 to n from top to bottom, the columns are numbered from 1 to n from left to right. Let's denote a cell of the field on the intersection of row x and column y by record (x,\u2009y). Each cell of the field contains growing raspberry, at that, the cell (x,\u2009y) of the field contains x\u2009+\u2009y raspberry bushes.The bear came out to walk across the field. At the beginning of the walk his speed is (dx,\u2009dy). Then the bear spends exactly t seconds on the field. Each second the following takes place:  Let's suppose that at the current moment the bear is in cell (x,\u2009y).  First the bear eats the raspberry from all the bushes he has in the current cell. After the bear eats the raspberry from k bushes, he increases each component of his speed by k. In other words, if before eating the k bushes of raspberry his speed was (dx,\u2009dy), then after eating the berry his speed equals (dx\u2009+\u2009k,\u2009dy\u2009+\u2009k).  Let's denote the current speed of the bear (dx,\u2009dy) (it was increased after the previous step). Then the bear moves from cell (x,\u2009y) to cell (((x\u2009+\u2009dx\u2009-\u20091)\u00a0mod\u00a0n)\u2009+\u20091,\u2009((y\u2009+\u2009dy\u2009-\u20091)\u00a0mod\u00a0n)\u2009+\u20091).  Then one additional raspberry bush grows in each cell of the field. You task is to predict the bear's actions. Find the cell he ends up in if he starts from cell (sx,\u2009sy). Assume that each bush has infinitely much raspberry and the bear will never eat all of it.", "input_spec": "The first line of the input contains six space-separated integers: n, sx, sy, dx, dy, t (1\u2009\u2264\u2009n\u2009\u2264\u2009109;\u00a01\u2009\u2264\u2009sx,\u2009sy\u2009\u2264\u2009n;\u00a0\u2009-\u2009100\u2009\u2264\u2009dx,\u2009dy\u2009\u2264\u2009100;\u00a00\u2009\u2264\u2009t\u2009\u2264\u20091018).", "output_spec": "Print two integers \u2014 the coordinates of the cell the bear will end up in after t seconds.", "sample_inputs": ["5 1 2 0 1 2", "1 1 1 -1 -1 2"], "sample_outputs": ["3 1", "1 1"], "notes": "NoteOperation a\u00a0mod\u00a0b means taking the remainder after dividing a by b. Note that the result of the operation is always non-negative. For example, (\u2009-\u20091)\u00a0mod\u00a03\u2009=\u20092.In the first sample before the first move the speed vector will equal (3,4) and the bear will get to cell (4,1). Before the second move the speed vector will equal (9,10) and he bear will get to cell (3,1). Don't forget that at the second move, the number of berry bushes increased by 1.In the second sample before the first move the speed vector will equal (1,1) and the bear will get to cell (1,1). Before the second move, the speed vector will equal (4,4) and the bear will get to cell (1,1). Don't forget that at the second move, the number of berry bushes increased by 1."}, "src_uid": "ee9fa8be2ae05a4e831a4f608c0cc785"}
{"nl": {"description": "After finishing eating her bun, Alyona came up with two integers n and m. She decided to write down two columns of integers\u00a0\u2014 the first column containing integers from 1 to n and the second containing integers from 1 to m. Now the girl wants to count how many pairs of integers she can choose, one from the first column and the other from the second column, such that their sum is divisible by 5.Formally, Alyona wants to count the number of pairs of integers (x,\u2009y) such that 1\u2009\u2264\u2009x\u2009\u2264\u2009n, 1\u2009\u2264\u2009y\u2009\u2264\u2009m and  equals 0.As usual, Alyona has some troubles and asks you to help.", "input_spec": "The only line of the input contains two integers n and m (1\u2009\u2264\u2009n,\u2009m\u2009\u2264\u20091\u2009000\u2009000).", "output_spec": "Print the only integer\u00a0\u2014 the number of pairs of integers (x,\u2009y) such that 1\u2009\u2264\u2009x\u2009\u2264\u2009n, 1\u2009\u2264\u2009y\u2009\u2264\u2009m and (x\u2009+\u2009y) is divisible by 5.", "sample_inputs": ["6 12", "11 14", "1 5", "3 8", "5 7", "21 21"], "sample_outputs": ["14", "31", "1", "5", "7", "88"], "notes": "NoteFollowing pairs are suitable in the first sample case:   for x\u2009=\u20091 fits y equal to 4 or 9;  for x\u2009=\u20092 fits y equal to 3 or 8;  for x\u2009=\u20093 fits y equal to 2, 7 or 12;  for x\u2009=\u20094 fits y equal to 1, 6 or 11;  for x\u2009=\u20095 fits y equal to 5 or 10;  for x\u2009=\u20096 fits y equal to 4 or 9. Only the pair (1,\u20094) is suitable in the third sample case."}, "src_uid": "df0879635b59e141c839d9599abd77d2"}
{"nl": {"description": "You are given two lists of non-zero digits.Let's call an integer pretty if its (base 10) representation has at least one digit from the first list and at least one digit from the second list. What is the smallest positive pretty integer?", "input_spec": "The first line contains two integers n and m (1\u2009\u2264\u2009n,\u2009m\u2009\u2264\u20099) \u2014 the lengths of the first and the second lists, respectively. The second line contains n distinct digits a1,\u2009a2,\u2009...,\u2009an (1\u2009\u2264\u2009ai\u2009\u2264\u20099) \u2014 the elements of the first list. The third line contains m distinct digits b1,\u2009b2,\u2009...,\u2009bm (1\u2009\u2264\u2009bi\u2009\u2264\u20099) \u2014 the elements of the second list.", "output_spec": "Print the smallest pretty integer.", "sample_inputs": ["2 3\n4 2\n5 7 6", "8 8\n1 2 3 4 5 6 7 8\n8 7 6 5 4 3 2 1"], "sample_outputs": ["25", "1"], "notes": "NoteIn the first example 25, 46, 24567 are pretty, as well as many other integers. The smallest among them is 25. 42 and 24 are not pretty because they don't have digits from the second list.In the second example all integers that have at least one digit different from 9 are pretty. It's obvious that the smallest among them is 1, because it's the smallest positive integer."}, "src_uid": "3a0c1b6d710fd8f0b6daf420255d76ee"}
{"nl": {"description": "Maxim wants to buy an apartment in a new house at Line Avenue of Metropolis. The house has n apartments that are numbered from 1 to n and are arranged in a row. Two apartments are adjacent if their indices differ by 1. Some of the apartments can already be inhabited, others are available for sale.Maxim often visits his neighbors, so apartment is good for him if it is available for sale and there is at least one already inhabited apartment adjacent to it. Maxim knows that there are exactly k already inhabited apartments, but he doesn't know their indices yet.Find out what could be the minimum possible and the maximum possible number of apartments that are good for Maxim.", "input_spec": "The only line of the input contains two integers: n and k (1\u2009\u2264\u2009n\u2009\u2264\u2009109, 0\u2009\u2264\u2009k\u2009\u2264\u2009n).", "output_spec": "Print the minimum possible and the maximum possible number of apartments good for Maxim.", "sample_inputs": ["6 3"], "sample_outputs": ["1 3"], "notes": "NoteIn the sample test, the number of good apartments could be minimum possible if, for example, apartments with indices 1, 2 and 3 were inhabited. In this case only apartment 4 is good. The maximum possible number could be, for example, if apartments with indices 1, 3 and 5 were inhabited. In this case all other apartments: 2, 4 and 6 are good."}, "src_uid": "bdccf34b5a5ae13238c89a60814b9f86"}
{"nl": {"description": "The hero of our story, Valera, and his best friend Arcady are still in school, and therefore they spend all the free time playing turn-based strategy \"GAGA: Go And Go Again\". The gameplay is as follows. There are two armies on the playing field each of which consists of n men (n is always even). The current player specifies for each of her soldiers an enemy's soldier he will shoot (a target) and then all the player's soldiers shot simultaneously. This is a game world, and so each soldier shoots perfectly, that is he absolutely always hits the specified target. If an enemy soldier is hit, he will surely die. It may happen that several soldiers had been indicated the same target. Killed soldiers do not participate in the game anymore. The game \"GAGA\" consists of three steps: first Valera makes a move, then Arcady, then Valera again and the game ends. You are asked to calculate the maximum total number of soldiers that may be killed during the game. ", "input_spec": "The input data consist of a single integer n (2\u2009\u2264\u2009n\u2009\u2264\u2009108, n is even). Please note that before the game starts there are 2n soldiers on the fields. ", "output_spec": "Print a single number \u2014 a maximum total number of soldiers that could be killed in the course of the game in three turns.", "sample_inputs": ["2", "4"], "sample_outputs": ["3", "6"], "notes": "NoteThe first sample test:1) Valera's soldiers 1 and 2 shoot at Arcady's soldier 1.2) Arcady's soldier 2 shoots at Valera's soldier 1.3) Valera's soldier 1 shoots at Arcady's soldier 2.There are 3 soldiers killed in total: Valera's soldier 1 and Arcady's soldiers 1 and 2."}, "src_uid": "031e53952e76cff8fdc0988bb0d3239c"}
{"nl": {"description": "Yakko, Wakko and Dot, world-famous animaniacs, decided to rest from acting in cartoons, and take a leave to travel a bit. Yakko dreamt to go to Pennsylvania, his Motherland and the Motherland of his ancestors. Wakko thought about Tasmania, its beaches, sun and sea. Dot chose Transylvania as the most mysterious and unpredictable place.But to their great regret, the leave turned to be very short, so it will be enough to visit one of the three above named places. That's why Yakko, as the cleverest, came up with a truly genius idea: let each of the three roll an ordinary six-sided die, and the one with the highest amount of points will be the winner, and will take the other two to the place of his/her dreams.Yakko thrown a die and got Y points, Wakko \u2014 W points. It was Dot's turn. But she didn't hurry. Dot wanted to know for sure what were her chances to visit Transylvania.It is known that Yakko and Wakko are true gentlemen, that's why if they have the same amount of points with Dot, they will let Dot win.", "input_spec": "The only line of the input file contains two natural numbers Y and W \u2014 the results of Yakko's and Wakko's die rolls.", "output_spec": "Output the required probability in the form of irreducible fraction in format \u00abA/B\u00bb, where A \u2014 the numerator, and B \u2014 the denominator. If the required probability equals to zero, output \u00ab0/1\u00bb. If the required probability equals to 1, output \u00ab1/1\u00bb. ", "sample_inputs": ["4 2"], "sample_outputs": ["1/2"], "notes": "NoteDot will go to Transylvania, if she is lucky to roll 4, 5 or 6 points."}, "src_uid": "f97eb4ecffb6cbc8679f0c621fd59414"}
{"nl": {"description": "Gerald bought two very rare paintings at the Sotheby's auction and he now wants to hang them on the wall. For that he bought a special board to attach it to the wall and place the paintings on the board. The board has shape of an a1\u2009\u00d7\u2009b1 rectangle, the paintings have shape of a a2\u2009\u00d7\u2009b2 and a3\u2009\u00d7\u2009b3 rectangles.Since the paintings are painted in the style of abstract art, it does not matter exactly how they will be rotated, but still, one side of both the board, and each of the paintings must be parallel to the floor. The paintings can touch each other and the edges of the board, but can not overlap or go beyond the edge of the board. Gerald asks whether it is possible to place the paintings on the board, or is the board he bought not large enough?", "input_spec": "The first line contains two space-separated numbers a1 and b1 \u2014 the sides of the board. Next two lines contain numbers a2,\u2009b2,\u2009a3 and b3 \u2014 the sides of the paintings. All numbers ai,\u2009bi in the input are integers and fit into the range from 1 to 1000.", "output_spec": "If the paintings can be placed on the wall, print \"YES\" (without the quotes), and if they cannot, print \"NO\" (without the quotes).", "sample_inputs": ["3 2\n1 3\n2 1", "5 5\n3 3\n3 3", "4 2\n2 3\n1 2"], "sample_outputs": ["YES", "NO", "YES"], "notes": "NoteThat's how we can place the pictures in the first test:And that's how we can do it in the third one."}, "src_uid": "2ff30d9c4288390fd7b5b37715638ad9"}
{"nl": {"description": "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\u00a0\u2014 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\u2009\u2264\u2009A,\u2009B\u2009\u2264\u2009109), denoting the number of yellow and blue crystals respectively at Grisha's disposal. The next line contains three integers x, y and z (0\u2009\u2264\u2009x,\u2009y,\u2009z\u2009\u2264\u2009109)\u00a0\u2014 the respective amounts of yellow, green and blue balls to be obtained.", "output_spec": "Print a single integer\u00a0\u2014 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": "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\u2009\u2264\u2009m\u2009\u2264\u2009n\u2009\u2264\u2009109) \u2014 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 \u2014 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": "There are a lot of things which could be cut\u00a0\u2014 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$$$)\u00a0\u2014 the number of elements in the sequence and the number of bitcoins you have. Second line contains $$$n$$$ integers: $$$a_1$$$, $$$a_2$$$, ..., $$$a_n$$$ ($$$1 \\le a_i \\le 100$$$)\u00a0\u2014 elements of the sequence, which contains the equal number of even and odd numbers", "output_spec": "Print the maximum possible number of cuts which can be made while spending no more than $$$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$$$ bitcoins."}, "src_uid": "b3f8e769ee7719ea5c9f458428b16a4e"}
{"nl": {"description": "A word or a sentence in some language is called a pangram if all the characters of the alphabet of this language appear in it at least once. Pangrams are often used to demonstrate fonts in printing or test the output devices.You are given a string consisting of lowercase and uppercase Latin letters. Check whether this string is a pangram. We say that the string contains a letter of the Latin alphabet if this letter occurs in the string in uppercase or lowercase.", "input_spec": "The first line contains a single integer n (1\u2009\u2264\u2009n\u2009\u2264\u2009100)\u00a0\u2014 the number of characters in the string. The second line contains the string. The string consists only of uppercase and lowercase Latin letters.", "output_spec": "Output \"YES\", if the string is a pangram and \"NO\" otherwise.", "sample_inputs": ["12\ntoosmallword", "35\nTheQuickBrownFoxJumpsOverTheLazyDog"], "sample_outputs": ["NO", "YES"], "notes": null}, "src_uid": "f13eba0a0fb86e20495d218fc4ad532d"}
{"nl": {"description": "Gennady owns a small hotel in the countryside where he lives a peaceful life. He loves to take long walks, watch sunsets and play cards with tourists staying in his hotel. His favorite game is called \"Mau-Mau\".To play Mau-Mau, you need a pack of $$$52$$$ cards. Each card has a suit (Diamonds \u2014 D, Clubs \u2014 C, Spades \u2014 S, or Hearts \u2014 H), and a rank (2, 3, 4, 5, 6, 7, 8, 9, T, J, Q, K, or A).At the start of the game, there is one card on the table and you have five cards in your hand. You can play a card from your hand if and only if it has the same rank or the same suit as the card on the table.In order to check if you'd be a good playing partner, Gennady has prepared a task for you. Given the card on the table and five cards in your hand, check if you can play at least one card.", "input_spec": "The first line of the input contains one string which describes the card on the table. The second line contains five strings which describe the cards in your hand. Each string is two characters long. The first character denotes the rank and belongs to the set $$$\\{{\\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": "Alice likes word \"nineteen\" very much. She has a string s and wants the string to contain as many such words as possible. For that reason she can rearrange the letters of the string.For example, if she has string \"xiineteenppnnnewtnee\", she can get string \"xnineteenppnineteenw\", containing (the occurrences marked) two such words. More formally, word \"nineteen\" occurs in the string the number of times you can read it starting from some letter of the string. Of course, you shouldn't skip letters.Help her to find the maximum number of \"nineteen\"s that she can get in her string.", "input_spec": "The first line contains a non-empty string s, consisting only of lowercase English letters. The length of string s doesn't exceed 100.", "output_spec": "Print a single integer \u2014 the maximum number of \"nineteen\"s that she can get in her string.", "sample_inputs": ["nniinneetteeeenn", "nneteenabcnneteenabcnneteenabcnneteenabcnneteenabcii", "nineteenineteen"], "sample_outputs": ["2", "2", "2"], "notes": null}, "src_uid": "bb433cdb8299afcf46cb2797cbfbf724"}
{"nl": {"description": "There exists an island called Arpa\u2019s land, some beautiful girls live there, as ugly ones do.Mehrdad wants to become minister of Arpa\u2019s land. Arpa has prepared an exam. Exam has only one question, given n, print the last digit of 1378n.   Mehrdad has become quite confused and wants you to help him. Please help, although it's a naive cheat.", "input_spec": "The single line of input contains one integer n (0\u2009\u2009\u2264\u2009\u2009n\u2009\u2009\u2264\u2009\u2009109).", "output_spec": "Print single integer\u00a0\u2014 the last digit of 1378n.", "sample_inputs": ["1", "2"], "sample_outputs": ["8", "4"], "notes": "NoteIn the first example, last digit of 13781\u2009=\u20091378 is 8.In the second example, last digit of 13782\u2009=\u20091378\u00b71378\u2009=\u20091898884 is 4."}, "src_uid": "4b51b99d1dea367bf37dc5ead08ca48f"}
{"nl": {"description": "Greatest common divisor GCD(a,\u2009b) of two positive integers a and b is equal to the biggest integer d such that both integers a and b are divisible by d. There are many efficient algorithms to find greatest common divisor GCD(a,\u2009b), for example, Euclid algorithm. Formally, find the biggest integer d, such that all integers a,\u2009a\u2009+\u20091,\u2009a\u2009+\u20092,\u2009...,\u2009b are divisible by d. To make the problem even more complicated we allow a and b to be up to googol, 10100\u00a0\u2014 such number do not fit even in 64-bit integer type!", "input_spec": "The only line of the input contains two integers a and b (1\u2009\u2264\u2009a\u2009\u2264\u2009b\u2009\u2264\u200910100).", "output_spec": "Output one integer\u00a0\u2014 greatest common divisor of all integers from a to b inclusive.", "sample_inputs": ["1 2", "61803398874989484820458683436563811772030917980576 61803398874989484820458683436563811772030917980576"], "sample_outputs": ["1", "61803398874989484820458683436563811772030917980576"], "notes": null}, "src_uid": "9c5b6d8a20414d160069010b2965b896"}
{"nl": {"description": "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,\u2009t2,\u2009...,\u2009tn. 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\u2009-\u20091 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\u00a0\u2014 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\u2009\u2264\u2009n\u2009\u2264\u200930)\u00a0\u2014 the total depth of the recursion. The second line contains n integers t1,\u2009t2,\u2009...,\u2009tn (1\u2009\u2264\u2009ti\u2009\u2264\u20095). On the i-th level each of 2i\u2009-\u20091 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\u2009=\u20094 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\u2009+\u20094\u2009+\u20098\u2009+\u200923\u2009=\u200939.  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": "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\u2009\u2264\u2009n\u2009\u2264\u2009100) \u2014 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\u2009\u2264\u2009ai\u2009\u2264\u20093) 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": "Dima and his friends have been playing hide and seek at Dima's place all night. As a result, Dima's place got messy. In the morning they decided that they need to clean the place.To decide who exactly would clean the apartment, the friends want to play a counting-out game. First, all the guys stand in a circle, and then each of them shows some number of fingers on one hand (one to five), and then the boys count in a circle, starting from Dima, the number of people, respective to the total number of fingers shown. The person on who the countdown stops will clean the apartment.For example, if Dima and one of his friends played hide and seek, and 7 fingers were shown during the counting-out, then Dima would clean the place. If there were 2 or say, 8 fingers shown, then his friend would clean the place.Dima knows how many fingers each of his friends will show during the counting-out. Now he is interested in the number of ways to show some number of fingers on one hand (one to five), so that he did not have to clean the place. Help Dima.", "input_spec": "The first line contains integer n (1\u2009\u2264\u2009n\u2009\u2264\u2009100) \u2014 the number of Dima's friends. Dima himself isn't considered to be his own friend. The second line contains n positive integers, not exceeding 5, representing, how many fingers the Dima's friends will show.  The numbers in the lines are separated by a single space.", "output_spec": "In a single line print the answer to the problem.", "sample_inputs": ["1\n1", "1\n2", "2\n3 5"], "sample_outputs": ["3", "2", "3"], "notes": "NoteIn the first sample Dima can show 1, 3 or 5 fingers. If Dima shows 3 fingers, then the counting-out will go like that: Dima, his friend, Dima, his friend.In the second sample Dima can show 2 or 4 fingers."}, "src_uid": "ff6b3fd358c758324c19a26283ab96a4"}
{"nl": {"description": "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$$$)\u00a0\u2014 the number of floors. The second line contains $$$n$$$ integers $$$a_1, a_2, \\ldots, a_n$$$ ($$$0 \\leq a_i \\leq 100$$$)\u00a0\u2014 the number of people on each floor.", "output_spec": "In a single line, print the answer to the problem\u00a0\u2014 the minimum number of electricity units.", "sample_inputs": ["3\n0 2 1", "2\n1 1"], "sample_outputs": ["16", "4"], "notes": "NoteIn the first example, the answer can be achieved by choosing the second floor as the $$$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": "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\u2009\u2264\u2009a,\u2009b\u2009\u2264\u2009109) 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": "There is a very secret base in Potatoland where potato mash is made according to a special recipe. The neighbours from Porridgia decided to seize this recipe and to sell it to Pilauland. For this mission they have been preparing special agent Pearlo for many years. When, finally, Pearlo learned all secrets of espionage, he penetrated into the Potatoland territory and reached the secret base.Now he is standing at the entrance, but to get inside he need to pass combination lock. Minute ago one of the workers entered the password on the terminal and opened the door. The terminal is a square digital keyboard 3\u2009\u00d7\u20093 with digits from 1 to 9.Pearlo knows that the password consists from distinct digits and is probably symmetric with respect to the central button of the terminal. He has heat sensor which allowed him to detect the digits which the worker pressed. Now he wants to check whether the password entered by the worker is symmetric with respect to the central button of the terminal. This fact can Help Pearlo to reduce the number of different possible password combinations.", "input_spec": "Input contains the matrix of three rows of three symbols each. Symbol \u00abX\u00bb means that the corresponding button was pressed, and \u00ab.\u00bb means that is was not pressed. The matrix may contain no \u00abX\u00bb, also it may contain no \u00ab.\u00bb.", "output_spec": "Print YES if the password is symmetric with respect to the central button of the terminal and NO otherwise.", "sample_inputs": ["XX.\n...\n.XX", "X.X\nX..\n..."], "sample_outputs": ["YES", "NO"], "notes": "NoteIf you are not familiar with the term \u00abcentral symmetry\u00bb, you may look into http://en.wikipedia.org/wiki/Central_symmetry"}, "src_uid": "6a5fe5fac8a4e3993dc3423180cdd6a9"}
{"nl": {"description": "  You can preview the image in better quality by the link: http://assets.codeforces.com/files/656/without-text.png", "input_spec": "The only line of the input is a string (between 1 and 50 characters long, inclusive). Each character will be an alphanumeric character or a full stop \".\".", "output_spec": "Output the required answer.", "sample_inputs": ["Codeforces", "APRIL.1st"], "sample_outputs": ["-87", "17"], "notes": null}, "src_uid": "d3fa5a3a008048dc4a9fbce1ebc61d67"}
{"nl": {"description": "Any resemblance to any real championship and sport is accidental.The Berland National team takes part in the local Football championship which now has a group stage. Let's describe the formal rules of the local championship:   the team that kicked most balls in the enemy's goal area wins the game;  the victory gives 3 point to the team, the draw gives 1 point and the defeat gives 0 points;  a group consists of four teams, the teams are ranked by the results of six games: each team plays exactly once with each other team;  the teams that get places 1 and 2 in the group stage results, go to the next stage of the championship. In the group stage the team's place is defined by the total number of scored points: the more points, the higher the place is. If two or more teams have the same number of points, then the following criteria are used (the criteria are listed in the order of falling priority, starting from the most important one):   the difference between the total number of scored goals and the total number of missed goals in the championship: the team with a higher value gets a higher place;  the total number of scored goals in the championship: the team with a higher value gets a higher place;  the lexicographical order of the name of the teams' countries: the country with the lexicographically smaller name gets a higher place. The Berland team plays in the group where the results of 5 out of 6 games are already known. To be exact, there is the last game left. There the Berand national team plays with some other team. The coach asks you to find such score X:Y (where X is the number of goals Berland scored and Y is the number of goals the opponent scored in the game), that fulfills the following conditions:   X > Y, that is, Berland is going to win this game;  after the game Berland gets the 1st or the 2nd place in the group;  if there are multiple variants, you should choose such score X:Y, where value X\u2009-\u2009Y is minimum;  if it is still impossible to come up with one score, you should choose the score where value Y (the number of goals Berland misses) is minimum. ", "input_spec": "The input has five lines. Each line describes a game as \"team1 team2 goals1:goals2\" (without the quotes), what means that team team1 played a game with team team2, besides, team1 scored goals1 goals and team2 scored goals2 goals. The names of teams team1 and team2 are non-empty strings, consisting of uppercase English letters, with length of no more than 20 characters; goals1,\u2009goals2 are integers from 0 to 9.  The Berland team is called \"BERLAND\". It is guaranteed that the Berland team and one more team played exactly 2 games and the the other teams played exactly 3 games.", "output_spec": "Print the required score in the last game as X:Y, where X is the number of goals Berland scored and Y is the number of goals the opponent scored. If the Berland team does not get the first or the second place in the group, whatever this game's score is, then print on a single line \"IMPOSSIBLE\" (without the quotes). Note, that the result score can be very huge, 10:0 for example.", "sample_inputs": ["AERLAND DERLAND 2:1\nDERLAND CERLAND 0:3\nCERLAND AERLAND 0:1\nAERLAND BERLAND 2:0\nDERLAND BERLAND 4:0", "AERLAND DERLAND 2:2\nDERLAND CERLAND 2:3\nCERLAND AERLAND 1:3\nAERLAND BERLAND 2:1\nDERLAND BERLAND 4:1"], "sample_outputs": ["6:0", "IMPOSSIBLE"], "notes": "NoteIn the first sample \"BERLAND\" plays the last game with team \"CERLAND\". If Berland wins with score 6:0, the results' table looks like that in the end:   AERLAND (points: 9, the difference between scored and missed goals: 4, scored goals: 5)  BERLAND (points: 3, the difference between scored and missed goals: 0, scored goals: 6)  DERLAND (points: 3, the difference between scored and missed goals: 0, scored goals: 5)  CERLAND (points: 3, the difference between scored and missed goals: -4, scored goals: 3) In the second sample teams \"AERLAND\" and \"DERLAND\" have already won 7 and 4 points, respectively. The Berland team wins only 3 points, which is not enough to advance to the next championship stage."}, "src_uid": "5033d51c67b7ae0b1a2d9fd292fdced1"}
{"nl": {"description": "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\u00b7n people in the group (including Vadim), and they have exactly n\u2009-\u20091 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 \u2014 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\u2009\u2264\u2009n\u2009\u2264\u200950). The second line contains 2\u00b7n integer numbers w1, w2, ..., w2n, where wi is weight of person i (1\u2009\u2264\u2009wi\u2009\u2264\u20091000).", "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": "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": "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\u2009\u2264\u2009|S|\u2009\u2264\u2009500)\u00a0\u2014 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": "For a positive integer n let's define a function f:f(n)\u2009=\u2009\u2009-\u20091\u2009+\u20092\u2009-\u20093\u2009+\u2009..\u2009+\u2009(\u2009-\u20091)nn Your task is to calculate f(n) for a given integer n.", "input_spec": "The single line contains the positive integer n (1\u2009\u2264\u2009n\u2009\u2264\u20091015).", "output_spec": "Print f(n) in a single line.", "sample_inputs": ["4", "5"], "sample_outputs": ["2", "-3"], "notes": "Notef(4)\u2009=\u2009\u2009-\u20091\u2009+\u20092\u2009-\u20093\u2009+\u20094\u2009=\u20092f(5)\u2009=\u2009\u2009-\u20091\u2009+\u20092\u2009-\u20093\u2009+\u20094\u2009-\u20095\u2009=\u2009\u2009-\u20093"}, "src_uid": "689e7876048ee4eb7479e838c981f068"}
{"nl": {"description": "Soon a school Olympiad in Informatics will be held in Berland, n schoolchildren will participate there.At a meeting of the jury of the Olympiad it was decided that each of the n participants, depending on the results, will get a diploma of the first, second or third degree. Thus, each student will receive exactly one diploma.They also decided that there must be given at least min1 and at most max1 diplomas of the first degree, at least min2 and at most max2 diplomas of the second degree, and at least min3 and at most max3 diplomas of the third degree.After some discussion it was decided to choose from all the options of distributing diplomas satisfying these limitations the one that maximizes the number of participants who receive diplomas of the first degree. Of all these options they select the one which maximizes the number of the participants who receive diplomas of the second degree. If there are multiple of these options, they select the option that maximizes the number of diplomas of the third degree.Choosing the best option of distributing certificates was entrusted to Ilya, one of the best programmers of Berland. However, he found more important things to do, so it is your task now to choose the best option of distributing of diplomas, based on the described limitations.It is guaranteed that the described limitations are such that there is a way to choose such an option of distributing diplomas that all n participants of the Olympiad will receive a diploma of some degree.", "input_spec": "The first line of the input contains a single integer n (3\u2009\u2264\u2009n\u2009\u2264\u20093\u00b7106)\u00a0\u2014\u00a0the number of schoolchildren who will participate in the Olympiad. The next line of the input contains two integers min1 and max1 (1\u2009\u2264\u2009min1\u2009\u2264\u2009max1\u2009\u2264\u2009106)\u00a0\u2014\u00a0the minimum and maximum limits on the number of diplomas of the first degree that can be distributed. The third line of the input contains two integers min2 and max2 (1\u2009\u2264\u2009min2\u2009\u2264\u2009max2\u2009\u2264\u2009106)\u00a0\u2014\u00a0the minimum and maximum limits on the number of diplomas of the second degree that can be distributed.  The next line of the input contains two integers min3 and max3 (1\u2009\u2264\u2009min3\u2009\u2264\u2009max3\u2009\u2264\u2009106)\u00a0\u2014\u00a0the minimum and maximum limits on the number of diplomas of the third degree that can be distributed.  It is guaranteed that min1\u2009+\u2009min2\u2009+\u2009min3\u2009\u2264\u2009n\u2009\u2264\u2009max1\u2009+\u2009max2\u2009+\u2009max3.", "output_spec": "In the first line of the output print three numbers, showing how many diplomas of the first, second and third degree will be given to students in the optimal variant of distributing diplomas. The optimal variant of distributing diplomas is the one that maximizes the number of students who receive diplomas of the first degree. Of all the suitable options, the best one is the one which maximizes the number of participants who receive diplomas of the second degree. If there are several of these options, the best one is the one that maximizes the number of diplomas of the third degree.", "sample_inputs": ["6\n1 5\n2 6\n3 7", "10\n1 2\n1 3\n1 5", "6\n1 3\n2 2\n2 2"], "sample_outputs": ["1 2 3", "2 3 5", "2 2 2"], "notes": null}, "src_uid": "3cd092b6507079518cf206deab21cf97"}
{"nl": {"description": "Hongcow is learning to spell! One day, his teacher gives him a word that he needs to learn to spell. Being a dutiful student, he immediately learns how to spell the word.Hongcow has decided to try to make new words from this one. He starts by taking the word he just learned how to spell, and moves the last character of the word to the beginning of the word. He calls this a cyclic shift. He can apply cyclic shift many times. For example, consecutively applying cyclic shift operation to the word \"abracadabra\" Hongcow will get words \"aabracadabr\", \"raabracadab\" and so on.Hongcow is now wondering how many distinct words he can generate by doing the cyclic shift arbitrarily many times. The initial string is also counted.", "input_spec": "The first line of input will be a single string s (1\u2009\u2264\u2009|s|\u2009\u2264\u200950), the word Hongcow initially learns how to spell. The string s consists only of lowercase English letters ('a'\u2013'z').", "output_spec": "Output a single integer equal to the number of distinct strings that Hongcow can obtain by applying the cyclic shift arbitrarily many times to the given string.", "sample_inputs": ["abcd", "bbb", "yzyz"], "sample_outputs": ["4", "1", "2"], "notes": "NoteFor the first sample, the strings Hongcow can generate are \"abcd\", \"dabc\", \"cdab\", and \"bcda\".For the second sample, no matter how many times Hongcow does the cyclic shift, Hongcow can only generate \"bbb\".For the third sample, the two strings Hongcow can generate are \"yzyz\" and \"zyzy\"."}, "src_uid": "8909ac99ed4ab2ee4d681ec864c7831e"}
{"nl": {"description": "This is the easy version of the problem. The only difference between the easy version and the hard version is the constraints on $$$n$$$. You can only make hacks if both versions are solved.A permutation of $$$1, 2, \\ldots, n$$$ is a sequence of $$$n$$$ integers, where each integer from $$$1$$$ to $$$n$$$ appears exactly once. For example, $$$[2,3,1,4]$$$ is a permutation of $$$1, 2, 3, 4$$$, but $$$[1,4,2,2]$$$ isn't because $$$2$$$ appears twice in it.Recall that the number of inversions in a permutation $$$a_1, a_2, \\ldots, a_n$$$ is the number of pairs of indices $$$(i, j)$$$ such that $$$i < j$$$ and $$$a_i > a_j$$$.Let $$$p$$$ and $$$q$$$ be two permutations of $$$1, 2, \\ldots, n$$$. Find the number of permutation pairs $$$(p,q)$$$ that satisfy the following conditions:  $$$p$$$ is lexicographically smaller than $$$q$$$.  the number of inversions in $$$p$$$ is greater than the number of inversions in $$$q$$$. Print the number of such pairs modulo $$$mod$$$. Note that $$$mod$$$ may not be a prime.", "input_spec": "The only line contains two integers $$$n$$$ and $$$mod$$$ ($$$1\\le n\\le 50$$$, $$$1\\le mod\\le 10^9$$$).", "output_spec": "Print one integer, which is the answer modulo $$$mod$$$.", "sample_inputs": ["4 403458273"], "sample_outputs": ["17"], "notes": "NoteThe following are all valid pairs $$$(p,q)$$$ when $$$n=4$$$.  $$$p=[1,3,4,2]$$$, $$$q=[2,1,3,4]$$$,  $$$p=[1,4,2,3]$$$, $$$q=[2,1,3,4]$$$,  $$$p=[1,4,3,2]$$$, $$$q=[2,1,3,4]$$$,  $$$p=[1,4,3,2]$$$, $$$q=[2,1,4,3]$$$,  $$$p=[1,4,3,2]$$$, $$$q=[2,3,1,4]$$$,  $$$p=[1,4,3,2]$$$, $$$q=[3,1,2,4]$$$,  $$$p=[2,3,4,1]$$$, $$$q=[3,1,2,4]$$$,  $$$p=[2,4,1,3]$$$, $$$q=[3,1,2,4]$$$,  $$$p=[2,4,3,1]$$$, $$$q=[3,1,2,4]$$$,  $$$p=[2,4,3,1]$$$, $$$q=[3,1,4,2]$$$,  $$$p=[2,4,3,1]$$$, $$$q=[3,2,1,4]$$$,  $$$p=[2,4,3,1]$$$, $$$q=[4,1,2,3]$$$,  $$$p=[3,2,4,1]$$$, $$$q=[4,1,2,3]$$$,  $$$p=[3,4,1,2]$$$, $$$q=[4,1,2,3]$$$,  $$$p=[3,4,2,1]$$$, $$$q=[4,1,2,3]$$$,  $$$p=[3,4,2,1]$$$, $$$q=[4,1,3,2]$$$,  $$$p=[3,4,2,1]$$$, $$$q=[4,2,1,3]$$$. "}, "src_uid": "ae0320a57d73fab1d05f5d10fbdb9e1a"}
{"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,\u2009y) in the 2D plane such that x and y are integers and 0\u2009\u2264\u2009x,\u2009y. There is a tree in such a point, and it has x\u2009+\u2009y 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\u2009\u2264\u2009m\u2009\u2264\u20091000, 1\u2009\u2264\u2009b\u2009\u2264\u200910000).", "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": "Bear Limak wants to become the largest of bears, or at least to become larger than his brother Bob.Right now, Limak and Bob weigh a and b respectively. It's guaranteed that Limak's weight is smaller than or equal to his brother's weight.Limak eats a lot and his weight is tripled after every year, while Bob's weight is doubled after every year.After how many full years will Limak become strictly larger (strictly heavier) than Bob?", "input_spec": "The only line of the input contains two integers a and b (1\u2009\u2264\u2009a\u2009\u2264\u2009b\u2009\u2264\u200910)\u00a0\u2014 the weight of Limak and the weight of Bob respectively.", "output_spec": "Print one integer, denoting the integer number of years after which Limak will become strictly larger than Bob.", "sample_inputs": ["4 7", "4 9", "1 1"], "sample_outputs": ["2", "3", "1"], "notes": "NoteIn the first sample, Limak weighs 4 and Bob weighs 7 initially. After one year their weights are 4\u00b73\u2009=\u200912 and 7\u00b72\u2009=\u200914 respectively (one weight is tripled while the other one is doubled). Limak isn't larger than Bob yet. After the second year weights are 36 and 28, so the first weight is greater than the second one. Limak became larger than Bob after two years so you should print 2.In the second sample, Limak's and Bob's weights in next years are: 12 and 18, then 36 and 36, and finally 108 and 72 (after three years). The answer is 3. Remember that Limak wants to be larger than Bob and he won't be satisfied with equal weights.In the third sample, Limak becomes larger than Bob after the first year. Their weights will be 3 and 2 then."}, "src_uid": "a1583b07a9d093e887f73cc5c29e444a"}
{"nl": {"description": "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\u2009\u2264\u2009n\u2009\u2264\u20091000) \u2014 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": "One day Igor K. stopped programming and took up math. One late autumn evening he was sitting at a table reading a book and thinking about something. The following statement caught his attention: \"Among any six people there are either three pairwise acquainted people or three pairwise unacquainted people\"Igor just couldn't get why the required minimum is 6 people. \"Well, that's the same for five people, too!\" \u2014 he kept on repeating in his mind. \u2014 \"Let's take, say, Max, Ilya, Vova \u2014 here, they all know each other! And now let's add Dima and Oleg to Vova \u2014 none of them is acquainted with each other! Now, that math is just rubbish!\"Igor K. took 5 friends of his and wrote down who of them is friends with whom. Now he wants to check whether it is true for the five people that among them there are either three pairwise acquainted or three pairwise not acquainted people.", "input_spec": "The first line contains an integer m (0\u2009\u2264\u2009m\u2009\u2264\u200910), which is the number of relations of acquaintances among the five friends of Igor's. Each of the following m lines contains two integers ai and bi (1\u2009\u2264\u2009ai,\u2009bi\u2009\u2264\u20095;ai\u2009\u2260\u2009bi), where (ai,\u2009bi) is a pair of acquainted people. It is guaranteed that each pair of the acquaintances is described exactly once. The acquaintance relation is symmetrical, i.e. if x is acquainted with y, then y is also acquainted with x.", "output_spec": "Print \"FAIL\", if among those five people there are no either three pairwise acquainted or three pairwise unacquainted people. Otherwise print \"WIN\".", "sample_inputs": ["4\n1 3\n2 3\n1 4\n5 3", "5\n1 2\n2 3\n3 4\n4 5\n5 1"], "sample_outputs": ["WIN", "FAIL"], "notes": null}, "src_uid": "2bc18799c85ecaba87564a86a94e0322"}
{"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,\u2009b) good, if GCD(a,\u2009b)\u2009=\u2009x and LCM(a,\u2009b)\u2009=\u2009y, where GCD(a,\u2009b) denotes the greatest common divisor of a and b, and LCM(a,\u2009b) 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,\u2009b) such that l\u2009\u2264\u2009a,\u2009b\u2009\u2264\u2009r. Note that pairs (a,\u2009b) and (b,\u2009a) are considered different if a\u2009\u2260\u2009b.", "input_spec": "The only line contains four integers l,\u2009r,\u2009x,\u2009y (1\u2009\u2264\u2009l\u2009\u2264\u2009r\u2009\u2264\u2009109, 1\u2009\u2264\u2009x\u2009\u2264\u2009y\u2009\u2264\u2009109).", "output_spec": "In the only line print the only integer\u00a0\u2014 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,\u2009b): (1,\u20092) and (2,\u20091).In the second example there are four suitable good pairs of integers (a,\u2009b): (1,\u200912), (12,\u20091), (3,\u20094) and (4,\u20093).In the third example there are good pairs of integers, for example, (3,\u200930), but none of them fits the condition l\u2009\u2264\u2009a,\u2009b\u2009\u2264\u2009r."}, "src_uid": "d37dde5841116352c9b37538631d0b15"}
{"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\u2009+\u20097).", "input_spec": "The first line contains two integers x and y (|x|,\u2009|y|\u2009\u2264\u2009109). The second line contains a single integer n (1\u2009\u2264\u2009n\u2009\u2264\u20092\u00b7109).", "output_spec": "Output a single integer representing fn modulo 1000000007 (109\u2009+\u20097).", "sample_inputs": ["2 3\n3", "0 -1\n2"], "sample_outputs": ["1", "1000000006"], "notes": "NoteIn the first sample, f2\u2009=\u2009f1\u2009+\u2009f3, 3\u2009=\u20092\u2009+\u2009f3, f3\u2009=\u20091.In the second sample, f2\u2009=\u2009\u2009-\u20091; \u2009-\u20091 modulo (109\u2009+\u20097) equals (109\u2009+\u20096)."}, "src_uid": "2ff85140e3f19c90e587ce459d64338b"}
{"nl": {"description": "Polycarp loves ciphers. He has invented his own cipher called Right-Left.Right-Left cipher is used for strings. To encrypt the string $$$s=s_{1}s_{2} \\dots s_{n}$$$ Polycarp uses the following algorithm:  he writes down $$$s_1$$$,  he appends the current word with $$$s_2$$$ (i.e. writes down $$$s_2$$$ to the right of the current result),  he prepends the current word with $$$s_3$$$ (i.e. writes down $$$s_3$$$ to the left of the current result),  he appends the current word with $$$s_4$$$ (i.e. writes down $$$s_4$$$ to the right of the current result),  he prepends the current word with $$$s_5$$$ (i.e. writes down $$$s_5$$$ to the left of the current result),  and so on for each position until the end of $$$s$$$. For example, if $$$s$$$=\"techno\" the process is: \"t\" $$$\\to$$$ \"te\" $$$\\to$$$ \"cte\" $$$\\to$$$ \"cteh\" $$$\\to$$$ \"ncteh\" $$$\\to$$$ \"ncteho\". So the encrypted $$$s$$$=\"techno\" is \"ncteho\".Given string $$$t$$$ \u2014 the result of encryption of some string $$$s$$$. Your task is to decrypt it, i.e. find the string $$$s$$$.", "input_spec": "The only line of the input contains $$$t$$$ \u2014 the result of encryption of some string $$$s$$$. It contains only lowercase Latin letters. The length of $$$t$$$ is between $$$1$$$ and $$$50$$$, inclusive.", "output_spec": "Print such string $$$s$$$ that after encryption it equals $$$t$$$.", "sample_inputs": ["ncteho", "erfdcoeocs", "z"], "sample_outputs": ["techno", "codeforces", "z"], "notes": null}, "src_uid": "992ae43e66f1808f19c86b1def1f6b41"}
{"nl": {"description": "In mathematics, the Pythagorean theorem \u2014 is a relation in Euclidean geometry among the three sides of a right-angled triangle. In terms of areas, it states: \u007fIn any right-angled triangle, the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares whose sides are the two legs (the two sides that meet at a right angle). The theorem can be written as an equation relating the lengths of the sides a, b and c, often called the Pythagorean equation:a2\u2009+\u2009b2\u2009=\u2009c2where c represents the length of the hypotenuse, and a and b represent the lengths of the other two sides.  Given n, your task is to count how many right-angled triangles with side-lengths a, b and c that satisfied an inequality 1\u2009\u2264\u2009a\u2009\u2264\u2009b\u2009\u2264\u2009c\u2009\u2264\u2009n.", "input_spec": "The only line contains one integer n\u00a0(1\u2009\u2264\u2009n\u2009\u2264\u2009104) as we mentioned above.", "output_spec": "Print a single integer \u2014 the answer to the problem.", "sample_inputs": ["5", "74"], "sample_outputs": ["1", "35"], "notes": null}, "src_uid": "36a211f7814e77339eb81dc132e115e1"}
{"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,\u20092}, {3,\u20094}, {4,\u20095}, {5,\u20096} or {7,\u20098}.  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\u2009\u2264\u2009n\u2009\u2264\u200910000, 1\u2009\u2264\u2009k\u2009\u2264\u2009100)\u00a0\u2014 the number of rows and the number of groups of soldiers, respectively. The second line contains k integers a1,\u2009a2,\u2009a3,\u2009...,\u2009ak (1\u2009\u2264\u2009ai\u2009\u2264\u200910000), where ai denotes the number of soldiers in the i-th group. It is guaranteed that a1\u2009+\u2009a2\u2009+\u2009...\u2009+\u2009ak\u2009\u2264\u20098\u00b7n.", "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,\u20092,\u20097,\u20098), and the second group an all the remaining seats.In the fourth example she can place the first two groups on seats (1,\u20092) and (7,\u20098), the third group on seats (3), and the fourth group on seats (5,\u20096)."}, "src_uid": "d1f88a97714d6c13309c88fcf7d86821"}
{"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\u2009\u2264\u2009n\u2009\u2264\u20091018) \u2014 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": "Professor GukiZ makes a new robot. The robot are in the point with coordinates (x1,\u2009y1) and should go to the point (x2,\u2009y2). 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,\u2009y1 (\u2009-\u2009109\u2009\u2264\u2009x1,\u2009y1\u2009\u2264\u2009109) \u2014 the start position of the robot. The second line contains two integers x2,\u2009y2 (\u2009-\u2009109\u2009\u2264\u2009x2,\u2009y2\u2009\u2264\u2009109) \u2014 the finish position of the robot.", "output_spec": "Print the only integer d \u2014 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,\u20094). 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": "Two-gram is an ordered pair (i.e. string of length two) of capital Latin letters. For example, \"AZ\", \"AA\", \"ZA\" \u2014 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$$$) \u2014 the length of string $$$s$$$. The second line of the input contains the string $$$s$$$ consisting of $$$n$$$ capital Latin letters.", "output_spec": "Print the only line containing exactly two capital Latin letters \u2014 any two-gram contained in the given string $$$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": "Vasya is an active Internet user. One day he came across an Internet resource he liked, so he wrote its address in the notebook. We know that the address of the written resource has format: <protocol>://<domain>.ru[/<context>] where:  <protocol> can equal either \"http\" (without the quotes) or \"ftp\" (without the quotes),  <domain> is a non-empty string, consisting of lowercase English letters,  the /<context> part may not be present. If it is present, then <context> is a non-empty string, consisting of lowercase English letters. If string <context> isn't present in the address, then the additional character \"/\" isn't written. Thus, the address has either two characters \"/\" (the ones that go before the domain), or three (an extra one in front of the context).When the boy came home, he found out that the address he wrote in his notebook had no punctuation marks. Vasya must have been in a lot of hurry and didn't write characters \":\", \"/\", \".\".Help Vasya to restore the possible address of the recorded Internet resource.", "input_spec": "The first line contains a non-empty string that Vasya wrote out in his notebook. This line consists of lowercase English letters only.  It is guaranteed that the given string contains at most 50 letters. It is guaranteed that the given string can be obtained from some correct Internet resource address, described above.", "output_spec": "Print a single line \u2014 the address of the Internet resource that Vasya liked. If there are several addresses that meet the problem limitations, you are allowed to print any of them.", "sample_inputs": ["httpsunrux", "ftphttprururu"], "sample_outputs": ["http://sun.ru/x", "ftp://http.ru/ruru"], "notes": "NoteIn the second sample there are two more possible answers: \"ftp://httpruru.ru\" and \"ftp://httpru.ru/ru\"."}, "src_uid": "4c999b7854a8a08960b6501a90b3bba3"}
{"nl": {"description": "Melody Pond was stolen from her parents as a newborn baby by Madame Kovarian, to become a weapon of the Silence in their crusade against the Doctor. Madame Kovarian changed Melody's name to River Song, giving her a new identity that allowed her to kill the Eleventh Doctor.Heidi figured out that Madame Kovarian uses a very complicated hashing function in order to change the names of the babies she steals. In order to prevent this from happening to future Doctors, Heidi decided to prepare herself by learning some basic hashing techniques.The first hashing function she designed is as follows.Given two positive integers $$$(x, y)$$$ she defines $$$H(x,y):=x^2+2xy+x+1$$$.Now, Heidi wonders if the function is reversible. That is, given a positive integer $$$r$$$, can you find a pair $$$(x, y)$$$ (of positive integers) such that $$$H(x, y) = r$$$?If multiple such pairs exist, output the one with smallest possible $$$x$$$. If there is no such pair, output \"NO\".", "input_spec": "The first and only line contains an integer $$$r$$$ ($$$1 \\le r \\le 10^{12}$$$).", "output_spec": "Output integers $$$x, y$$$ such that $$$H(x,y) = r$$$ and $$$x$$$ is smallest possible, or \"NO\" if no such pair exists.", "sample_inputs": ["19", "16"], "sample_outputs": ["1 8", "NO"], "notes": null}, "src_uid": "3ff1c25a1026c90aeb14d148d7fb96ba"}
{"nl": {"description": "InputThe input contains a single integer $$$a$$$ ($$$0 \\le a \\le 63$$$).OutputOutput a single number.ExamplesInput\n2\nOutput\n2\nInput\n5\nOutput\n24\nInput\n35\nOutput\n50\n", "input_spec": "The input contains a single integer $$$a$$$ ($$$0 \\le a \\le 63$$$).", "output_spec": "Output a single number.", "sample_inputs": ["2", "5", "35"], "sample_outputs": ["2", "24", "50"], "notes": null}, "src_uid": "db5e54f466e1f3d69a51ea0b346e667c"}
{"nl": {"description": "There is an infinite board of square tiles. Initially all tiles are white.Vova has a red marker and a blue marker. Red marker can color $$$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}$$$) \u2014 the number of tiles red marker should color and the number of tiles blue marker should color, respectively.", "output_spec": "Print a single integer \u2014 the minimal perimeter of a colored rectangle Vova can obtain by coloring exactly $$$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": "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\u2009\u2264\u2009s,\u2009v1,\u2009v2,\u2009t1,\u2009t2\u2009\u2264\u20091000)\u00a0\u2014 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\u00a0\u2014 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\u00a0\u2014 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\u00a0\u2014 in 22 milliseconds. So, it is be a draw."}, "src_uid": "10226b8efe9e3c473239d747b911a1ef"}
{"nl": {"description": "Mad scientist Mike is building a time machine in his spare time. To finish the work, he needs a resistor with a certain resistance value.However, all Mike has is lots of identical resistors with unit resistance R0\u2009=\u20091. Elements with other resistance can be constructed from these resistors. In this problem, we will consider the following as elements:   one resistor;  an element and one resistor plugged in sequence;  an element and one resistor plugged in parallel.   With the consecutive connection the resistance of the new element equals R\u2009=\u2009Re\u2009+\u2009R0. With the parallel connection the resistance of the new element equals . In this case Re equals the resistance of the element being connected.Mike needs to assemble an element with a resistance equal to the fraction . Determine the smallest possible number of resistors he needs to make such an element.", "input_spec": "The single input line contains two space-separated integers a and b (1\u2009\u2264\u2009a,\u2009b\u2009\u2264\u20091018). It is guaranteed that the fraction  is irreducible. It is guaranteed that a solution always exists.", "output_spec": "Print a single number \u2014 the answer to the problem. Please do not use the %lld specifier to read or write 64-bit integers in \u0421++. It is recommended to use the cin, cout streams or the %I64d specifier.", "sample_inputs": ["1 1", "3 2", "199 200"], "sample_outputs": ["1", "3", "200"], "notes": "NoteIn the first sample, one resistor is enough.In the second sample one can connect the resistors in parallel, take the resulting element and connect it to a third resistor consecutively. Then, we get an element with resistance . We cannot make this element using two resistors."}, "src_uid": "792efb147f3668a84c866048361970f8"}
{"nl": {"description": "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\u2009+\u2009b 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\u2009\u2264\u2009k,\u2009b,\u2009n,\u2009t\u2009\u2264\u2009106) \u2014 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 \u2014 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": "Lenny is playing a game on a 3\u2009\u00d7\u20093 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": "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\u2009\u2264\u2009n\u2009\u2264\u200989) \u2014 length of the string s. The second line contains string s \u2014 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": "In a small but very proud high school it was decided to win ACM ICPC. This goal requires to compose as many teams of three as possible, but since there were only 6 students who wished to participate, the decision was to build exactly two teams.After practice competition, participant number i got a score of ai. Team score is defined as sum of scores of its participants. High school management is interested if it's possible to build two teams with equal scores. Your task is to answer that question.", "input_spec": "The single line contains six integers a1,\u2009...,\u2009a6 (0\u2009\u2264\u2009ai\u2009\u2264\u20091000) \u2014 scores of the participants", "output_spec": "Print \"YES\" (quotes for clarity), if it is possible to build teams with equal score, and \"NO\" otherwise. You can print each character either upper- or lowercase (\"YeS\" and \"yes\" are valid when the answer is \"YES\").", "sample_inputs": ["1 3 2 1 2 1", "1 1 1 1 1 99"], "sample_outputs": ["YES", "NO"], "notes": "NoteIn the first sample, first team can be composed of 1st, 2nd and 6th participant, second \u2014 of 3rd, 4th and 5th: team scores are 1\u2009+\u20093\u2009+\u20091\u2009=\u20092\u2009+\u20091\u2009+\u20092\u2009=\u20095.In the second sample, score of participant number 6 is too high: his team score will be definitely greater."}, "src_uid": "2acf686862a34c337d1d2cbc0ac3fd11"}
{"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\u2009=\u20090, F1\u2009=\u20091, and all the next numbers are Fi\u2009=\u2009Fi\u2009-\u20092\u2009+\u2009Fi\u2009-\u20091.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\u2009\u2264\u2009n\u2009<\u2009109) \u2014 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": "There is the faculty of Computer Science in Berland. In the social net \"TheContact!\" for each course of this faculty there is the special group whose name equals the year of university entrance of corresponding course of students at the university. Each of students joins the group of his course and joins all groups for which the year of student's university entrance differs by no more than x from the year of university entrance of this student, where x \u2014 some non-negative integer. A value x is not given, but it can be uniquely determined from the available data. Note that students don't join other groups. You are given the list of groups which the student Igor joined. According to this information you need to determine the year of Igor's university entrance.", "input_spec": "The first line contains the positive odd integer n (1\u2009\u2264\u2009n\u2009\u2264\u20095) \u2014 the number of groups which Igor joined.  The next line contains n distinct integers a1,\u2009a2,\u2009...,\u2009an (2010\u2009\u2264\u2009ai\u2009\u2264\u20092100) \u2014 years of student's university entrance for each group in which Igor is the member. It is guaranteed that the input data is correct and the answer always exists. Groups are given randomly.", "output_spec": "Print the year of Igor's university entrance. ", "sample_inputs": ["3\n2014 2016 2015", "1\n2050"], "sample_outputs": ["2015", "2050"], "notes": "NoteIn the first test the value x\u2009=\u20091. Igor entered the university in 2015. So he joined groups members of which are students who entered the university in 2014, 2015 and 2016.In the second test the value x\u2009=\u20090. Igor entered only the group which corresponds to the year of his university entrance. "}, "src_uid": "f03773118cca29ff8d5b4281d39e7c63"}
{"nl": {"description": "You want to arrange n integers a1,\u2009a2,\u2009...,\u2009an in some order in a row. Let's define the value of an arrangement as the sum of differences between all pairs of adjacent integers.More formally, let's denote some arrangement as a sequence of integers x1,\u2009x2,\u2009...,\u2009xn, where sequence x is a permutation of sequence a. The value of such an arrangement is (x1\u2009-\u2009x2)\u2009+\u2009(x2\u2009-\u2009x3)\u2009+\u2009...\u2009+\u2009(xn\u2009-\u20091\u2009-\u2009xn).Find the largest possible value of an arrangement. Then, output the lexicographically smallest sequence x that corresponds to an arrangement of the largest possible value.", "input_spec": "The first line of the input contains integer n (2\u2009\u2264\u2009n\u2009\u2264\u2009100). The second line contains n space-separated integers a1, a2, ..., an (|ai|\u2009\u2264\u20091000).", "output_spec": "Print the required sequence x1,\u2009x2,\u2009...,\u2009xn. Sequence x should be the lexicographically smallest permutation of a that corresponds to an arrangement of the largest possible value.", "sample_inputs": ["5\n100 -100 50 0 -50"], "sample_outputs": ["100 -50 0 50 -100"], "notes": "NoteIn the sample test case, the value of the output arrangement is (100\u2009-\u2009(\u2009-\u200950))\u2009+\u2009((\u2009-\u200950)\u2009-\u20090)\u2009+\u2009(0\u2009-\u200950)\u2009+\u2009(50\u2009-\u2009(\u2009-\u2009100))\u2009=\u2009200. No other arrangement has a larger value, and among all arrangements with the value of 200, the output arrangement is the lexicographically smallest one.Sequence x1,\u2009x2,\u2009... ,\u2009xp is lexicographically smaller than sequence y1,\u2009y2,\u2009... ,\u2009yp if there exists an integer r (0\u2009\u2264\u2009r\u2009<\u2009p) such that x1\u2009=\u2009y1,\u2009x2\u2009=\u2009y2,\u2009... ,\u2009xr\u2009=\u2009yr and xr\u2009+\u20091\u2009<\u2009yr\u2009+\u20091."}, "src_uid": "4408eba2c5c0693e6b70bdcbe2dda2f4"}
{"nl": {"description": "You are given a binary string $$$s$$$.Find the number of distinct cyclical binary strings of length $$$n$$$ which contain $$$s$$$ as a substring.The cyclical string $$$t$$$ contains $$$s$$$ as a substring if there is some cyclical shift of string $$$t$$$, such that $$$s$$$ is a substring of this cyclical shift of $$$t$$$.For example, the cyclical string \"000111\" contains substrings \"001\", \"01110\" and \"10\", but doesn't contain \"0110\" and \"10110\".Two cyclical strings are called different if they differ from each other as strings. For example, two different strings, which differ from each other by a cyclical shift, are still considered different cyclical strings.", "input_spec": "The first line contains a single integer $$$n$$$ ($$$1 \\le n \\le 40$$$)\u00a0\u2014 the length of the target string $$$t$$$. The next line contains the string $$$s$$$ ($$$1 \\le |s| \\le n$$$)\u00a0\u2014 the string which must be a substring of cyclical string $$$t$$$. String $$$s$$$ contains only characters '0' and '1'.", "output_spec": "Print the only integer\u00a0\u2014 the number of distinct cyclical binary strings $$$t$$$, which contain $$$s$$$ as a substring.", "sample_inputs": ["2\n0", "4\n1010", "20\n10101010101010"], "sample_outputs": ["3", "2", "962"], "notes": "NoteIn the first example, there are three cyclical strings, which contain \"0\"\u00a0\u2014 \"00\", \"01\" and \"10\".In the second example, there are only two such strings\u00a0\u2014 \"1010\", \"0101\"."}, "src_uid": "0034806908c9794086736a2d07fc654c"}
{"nl": {"description": "This is an easy version of the problem. The actual problems are different, but the easy version is almost a subtask of the hard version. Note that the constraints and the output format are different.You are given a string $$$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$$$) \u2014 the length of $$$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": "Tomorrow Peter has a Biology exam. He does not like this subject much, but d days ago he learnt that he would have to take this exam. Peter's strict parents made him prepare for the exam immediately, for this purpose he has to study not less than minTimei and not more than maxTimei hours per each i-th day. Moreover, they warned Peter that a day before the exam they would check how he has followed their instructions.So, today is the day when Peter's parents ask him to show the timetable of his preparatory studies. But the boy has counted only the sum of hours sumTime spent him on preparation, and now he wants to know if he can show his parents a timetable s\u0441hedule with d numbers, where each number s\u0441hedulei stands for the time in hours spent by Peter each i-th day on biology studies, and satisfying the limitations imposed by his parents, and at the same time the sum total of all schedulei should equal to sumTime.", "input_spec": "The first input line contains two integer numbers d,\u2009sumTime (1\u2009\u2264\u2009d\u2009\u2264\u200930,\u20090\u2009\u2264\u2009sumTime\u2009\u2264\u2009240) \u2014 the amount of days, during which Peter studied, and the total amount of hours, spent on preparation. Each of the following d lines contains two integer numbers minTimei,\u2009maxTimei (0\u2009\u2264\u2009minTimei\u2009\u2264\u2009maxTimei\u2009\u2264\u20098), separated by a space \u2014 minimum and maximum amount of hours that Peter could spent in the i-th day.", "output_spec": "In the first line print YES, and in the second line print d numbers (separated by a space), each of the numbers \u2014 amount of hours, spent by Peter on preparation in the corresponding day, if he followed his parents' instructions; or print NO in the unique line. If there are many solutions, print any of them.", "sample_inputs": ["1 48\n5 7", "2 5\n0 1\n3 5"], "sample_outputs": ["NO", "YES\n1 4"], "notes": null}, "src_uid": "f48ff06e65b70f49eee3d7cba5a6aed0"}
{"nl": {"description": "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\u2009\u2264\u2009n\u2009\u2264\u2009500) \u2014 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": "Awruk is taking part in elections in his school. It is the final round. He has only one opponent\u00a0\u2014 Elodreip. The are $$$n$$$ students in the school. Each student has exactly $$$k$$$ votes and is obligated to use all of them. So Awruk knows that if a person gives $$$a_i$$$ votes for Elodreip, than he will get exactly $$$k - a_i$$$ votes from this person. Of course $$$0 \\le k - a_i$$$ holds.Awruk knows that if he loses his life is over. He has been speaking a lot with his friends and now he knows $$$a_1, a_2, \\dots, a_n$$$ \u2014 how many votes for Elodreip each student wants to give. Now he wants to change the number $$$k$$$ to win the elections. Of course he knows that bigger $$$k$$$ means bigger chance that somebody may notice that he has changed something and then he will be disqualified.So, Awruk knows $$$a_1, a_2, \\dots, a_n$$$ \u2014 how many votes each student will give to his opponent. Help him select the smallest winning number $$$k$$$. In order to win, Awruk needs to get strictly more votes than Elodreip.", "input_spec": "The first line contains integer $$$n$$$ ($$$1 \\le n \\le 100$$$)\u00a0\u2014 the number of students in the school. The second line contains $$$n$$$ integers $$$a_1, a_2, \\ldots, a_n$$$ ($$$1 \\leq a_i \\leq 100$$$)\u00a0\u2014 the number of votes each student gives to Elodreip.", "output_spec": "Output the smallest integer $$$k$$$ ($$$k \\ge \\max a_i$$$) which gives Awruk the victory. In order to win, Awruk needs to get strictly more votes than Elodreip.", "sample_inputs": ["5\n1 1 1 5 1", "5\n2 2 3 2 2"], "sample_outputs": ["5", "5"], "notes": "NoteIn the first example, Elodreip gets $$$1 + 1 + 1 + 5 + 1 = 9$$$ votes. The smallest possible $$$k$$$ is $$$5$$$ (it surely can't be less due to the fourth person), and it leads to $$$4 + 4 + 4 + 0 + 4 = 16$$$ votes for Awruk, which is enough to win.In the second example, Elodreip gets $$$11$$$ votes. If $$$k = 4$$$, Awruk gets $$$9$$$ votes and loses to Elodreip."}, "src_uid": "d215b3541d6d728ad01b166aae64faa2"}
{"nl": {"description": "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\u2009\u2264\u2009A\u2009\u2264\u2009105), the desired number of ways.", "output_spec": "In the first line print integers N and M (1\u2009\u2264\u2009N\u2009\u2264\u2009106,\u20091\u2009\u2264\u2009M\u2009\u2264\u200910), the amount of change to be made, and the number of denominations, respectively. Then print M integers D1,\u2009D2,\u2009...,\u2009DM (1\u2009\u2264\u2009Di\u2009\u2264\u2009106), the denominations of the coins. All denominations must be distinct: for any i\u2009\u2260\u2009j we must have Di\u2009\u2260\u2009Dj. 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": "You found a mysterious function f. The function takes two strings s1 and s2. These strings must consist only of lowercase English letters, and must be the same length.The output of the function f is another string of the same length. The i-th character of the output is equal to the minimum of the i-th character of s1 and the i-th character of s2.For example, f(\"ab\", \"ba\") = \"aa\", and f(\"nzwzl\", \"zizez\") = \"niwel\".You found two strings x and y of the same length and consisting of only lowercase English letters. Find any string z such that f(x,\u2009z)\u2009=\u2009y, or print -1 if no such string z exists.", "input_spec": "The first line of input contains the string x. The second line of input contains the string y. Both x and y consist only of lowercase English letters, x and y have same length and this length is between 1 and 100.", "output_spec": "If there is no string z such that f(x,\u2009z)\u2009=\u2009y, print -1. Otherwise, print a string z such that f(x,\u2009z)\u2009=\u2009y. If there are multiple possible answers, print any of them. The string z should be the same length as x and y and consist only of lowercase English letters.", "sample_inputs": ["ab\naa", "nzwzl\nniwel", "ab\nba"], "sample_outputs": ["ba", "xiyez", "-1"], "notes": "NoteThe first case is from the statement.Another solution for the second case is \"zizez\"There is no solution for the third case. That is, there is no z such that f(\"ab\", z)\u2009=\u2009 \"ba\"."}, "src_uid": "ce0cb995e18501f73e34c76713aec182"}
{"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 \u2014 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\u2009\u2264\u2009a,\u2009b\u2009\u2264\u2009100, 2\u2009\u2264\u2009n\u2009\u2264\u2009a\u2009+\u2009b) \u2014 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": "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\u2009\u2264\u2009ti\u2009\u2264\u2009100)\u00a0\u2014 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\u2009+\u20093\u2009+\u20097\u2009+\u20093\u2009+\u200920\u2009=\u200940.  Remove two cards with a number 7. The remaining sum would be 3\u2009+\u20093\u2009+\u200920\u2009=\u200926.  Remove two cards with a number 3. The remaining sum would be 7\u2009+\u20097\u2009+\u200920\u2009=\u200934. 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\u2009+\u20099\u2009+\u20091\u2009+\u20093\u2009+\u20098\u2009=\u200928.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\u2009+\u200910\u2009=\u200920."}, "src_uid": "a9c17ce5fd5f39ffd70917127ce3408a"}
{"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\u00a0\u2013 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\u00a0\u2013 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\u2009\u2264\u2009n\u2009\u2264\u2009109)\u00a0\u2013 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\u00a0\u2013 if counter-clockwise, and undefined otherwise.", "sample_inputs": ["^ >\n1", "< ^\n3", "^ v\n6"], "sample_outputs": ["cw", "ccw", "undefined"], "notes": null}, "src_uid": "fb99ef80fd21f98674fe85d80a2e5298"}
{"nl": {"description": "One cold winter evening Alice and her older brother Bob was sitting at home near the fireplace and giving each other interesting problems to solve. When it was Alice's turn, she told the number n to Bob and said:\u2014Shuffle the digits in this number in order to obtain the smallest possible number without leading zeroes.\u2014No problem! \u2014 said Bob and immediately gave her an answer.Alice said a random number, so she doesn't know whether Bob's answer is correct. Help her to find this out, because impatient brother is waiting for the verdict.", "input_spec": "The first line contains one integer n (0\u2009\u2264\u2009n\u2009\u2264\u2009109) without leading zeroes. The second lines contains one integer m (0\u2009\u2264\u2009m\u2009\u2264\u2009109) \u2014 Bob's answer, possibly with leading zeroes.", "output_spec": "Print OK if Bob's answer is correct and WRONG_ANSWER otherwise.", "sample_inputs": ["3310\n1033", "4\n5"], "sample_outputs": ["OK", "WRONG_ANSWER"], "notes": null}, "src_uid": "d1e381b72a6c09a0723cfe72c0917372"}
{"nl": {"description": "Pak Chanek has a grid that has $$$N$$$ rows and $$$M$$$ columns. Each row is numbered from $$$1$$$ to $$$N$$$ from top to bottom. Each column is numbered from $$$1$$$ to $$$M$$$ from left to right.Each tile in the grid contains a number. The numbers are arranged as follows:   Row $$$1$$$ contains integers from $$$1$$$ to $$$M$$$ from left to right.  Row $$$2$$$ contains integers from $$$M+1$$$ to $$$2 \\times M$$$ from left to right.  Row $$$3$$$ contains integers from $$$2 \\times M+1$$$ to $$$3 \\times M$$$ from left to right.  And so on until row $$$N$$$. A domino is defined as two different tiles in the grid that touch by their sides. A domino is said to be tight if and only if the two numbers in the domino have a difference of exactly $$$1$$$. Count the number of distinct tight dominoes in the grid.Two dominoes are said to be distinct if and only if there exists at least one tile that is in one domino, but not in the other.", "input_spec": "The only line contains two integers $$$N$$$ and $$$M$$$ ($$$1 \\leq N, M \\leq 10^9$$$) \u2014 the number of rows and columns in the grid.", "output_spec": "An integer representing the number of distinct tight dominoes in the grid.", "sample_inputs": ["3 4", "2 1"], "sample_outputs": ["9", "1"], "notes": "NoteThe picture below is the grid that Pak Chanek has in the first example.  The picture below is an example of a tight domino in the grid.  "}, "src_uid": "a91aab4c0618d036c81022232814ef44"}
{"nl": {"description": "Reziba has many magic gems. Each magic gem can be split into $$$M$$$ normal gems. The amount of space each magic (and normal) gem takes is $$$1$$$ unit. A normal gem cannot be split.Reziba wants to choose a set of magic gems and split some of them, so the total space occupied by the resulting set of gems is $$$N$$$ units. If a magic gem is chosen and split, it takes $$$M$$$ units of space (since it is split into $$$M$$$ gems); if a magic gem is not split, it takes $$$1$$$ unit.How many different configurations of the resulting set of gems can Reziba have, such that the total amount of space taken is $$$N$$$ units? Print the answer modulo $$$1000000007$$$ ($$$10^9+7$$$). Two configurations are considered different if the number of magic gems Reziba takes to form them differs, or the indices of gems Reziba has to split differ.", "input_spec": "The input contains a single line consisting of $$$2$$$ integers $$$N$$$ and $$$M$$$ ($$$1 \\le N \\le 10^{18}$$$, $$$2 \\le M \\le 100$$$).", "output_spec": "Print one integer, the total number of configurations of the resulting set of gems, given that the total amount of space taken is $$$N$$$ units. Print the answer modulo $$$1000000007$$$ ($$$10^9+7$$$).", "sample_inputs": ["4 2", "3 2"], "sample_outputs": ["5", "3"], "notes": "NoteIn the first example each magic gem can split into $$$2$$$ normal gems, and we know that the total amount of gems are $$$4$$$.Let $$$1$$$ denote a magic gem, and $$$0$$$ denote a normal gem.The total configurations you can have is:   $$$1 1 1 1$$$ (None of the gems split);  $$$0 0 1 1$$$ (First magic gem splits into $$$2$$$ normal gems);  $$$1 0 0 1$$$ (Second magic gem splits into $$$2$$$ normal gems);  $$$1 1 0 0$$$ (Third magic gem splits into $$$2$$$ normal gems);  $$$0 0 0 0$$$ (First and second magic gems split into total $$$4$$$ normal gems). Hence, answer is $$$5$$$."}, "src_uid": "e7b9eec21d950f5d963ff50619c6f119"}
{"nl": {"description": "You are given a text of single-space separated words, consisting of small and capital Latin letters.Volume of the word is number of capital letters in the word. Volume of the text is maximum volume of all words in the text.Calculate the volume of the given text.", "input_spec": "The first line contains one integer number n (1\u2009\u2264\u2009n\u2009\u2264\u2009200) \u2014 length of the text. The second line contains text of single-space separated words s1,\u2009s2,\u2009...,\u2009si, consisting only of small and capital Latin letters.", "output_spec": "Print one integer number \u2014 volume of text.", "sample_inputs": ["7\nNonZERO", "24\nthis is zero answer text", "24\nHarbour Space University"], "sample_outputs": ["5", "0", "1"], "notes": "NoteIn the first example there is only one word, there are 5 capital letters in it.In the second example all of the words contain 0 capital letters."}, "src_uid": "d3929a9acf1633475ab16f5dfbead13c"}
{"nl": {"description": "You are given a regular polygon with $$$n$$$ vertices labeled from $$$1$$$ to $$$n$$$ in counter-clockwise order. The triangulation of a given polygon is a set of triangles such that each vertex of each triangle is a vertex of the initial polygon, there is no pair of triangles such that their intersection has non-zero area, and the total area of all triangles is equal to the area of the given polygon. The weight of a triangulation is the sum of weigths of triangles it consists of, where the weight of a triagle is denoted as the product of labels of its vertices.Calculate the minimum weight among all triangulations of the polygon.", "input_spec": "The first line contains single integer $$$n$$$ ($$$3 \\le n \\le 500$$$) \u2014 the number of vertices in the regular polygon.", "output_spec": "Print one integer \u2014 the minimum weight among all triangulations of the given polygon.", "sample_inputs": ["3", "4"], "sample_outputs": ["6", "18"], "notes": "NoteAccording to Wiki: polygon triangulation is the decomposition of a polygonal area (simple polygon) $$$P$$$ into a set of triangles, i.\u2009e., finding a set of triangles with pairwise non-intersecting interiors whose union is $$$P$$$.In the first example the polygon is a triangle, so we don't need to cut it further, so the answer is $$$1 \\cdot 2 \\cdot 3 = 6$$$.In the second example the polygon is a rectangle, so it should be divided into two triangles. It's optimal to cut it using diagonal $$$1-3$$$ so answer is $$$1 \\cdot 2 \\cdot 3 + 1 \\cdot 3 \\cdot 4 = 6 + 12 = 18$$$."}, "src_uid": "1bd29d7a8793c22e81a1f6fd3991307a"}
{"nl": {"description": "Not long ago Billy came across such a problem, where there were given three natural numbers A, B and C from the range [1,\u2009N], and it was asked to check whether the equation AB\u2009=\u2009C is correct. Recently Billy studied the concept of a digital root of a number. We should remind you that a digital root d(x) of the number x is the sum s(x) of all the digits of this number, if s(x)\u2009\u2264\u20099, otherwise it is d(s(x)). For example, a digital root of the number 6543 is calculated as follows: d(6543)\u2009=\u2009d(6\u2009+\u20095\u2009+\u20094\u2009+\u20093)\u2009=\u2009d(18)\u2009=\u20099. Billy has counted that the digital root of a product of numbers is equal to the digital root of the product of the factors' digital roots, i.e. d(xy)\u2009=\u2009d(d(x)d(y)). And the following solution to the problem came to his mind: to calculate the digital roots and check if this condition is met. However, Billy has doubts that this condition is sufficient. That's why he asks you to find out the amount of test examples for the given problem such that the algorithm proposed by Billy makes mistakes.", "input_spec": "The first line contains the only number N (1\u2009\u2264\u2009N\u2009\u2264\u2009106).", "output_spec": "Output one number \u2014 the amount of required A, B and C from the range [1,\u2009N].", "sample_inputs": ["4", "5"], "sample_outputs": ["2", "6"], "notes": "NoteFor the first sample the required triples are (3,\u20094,\u20093) and (4,\u20093,\u20093)."}, "src_uid": "fc133fe6353089a0ebee08dec919f608"}
{"nl": {"description": "One day Vasya heard a story: \"In the city of High Bertown a bus number 62 left from the bus station. It had n grown-ups and m kids...\"The latter events happen to be of no importance to us. Vasya is an accountant and he loves counting money. So he wondered what maximum and minimum sum of money these passengers could have paid for the ride.The bus fare equals one berland ruble in High Bertown. However, not everything is that easy \u2014 no more than one child can ride for free with each grown-up passenger. That means that a grown-up passenger who rides with his k (k\u2009>\u20090) children, pays overall k rubles: a ticket for himself and (k\u2009-\u20091) tickets for his children. Also, a grown-up can ride without children, in this case he only pays one ruble.We know that in High Bertown children can't ride in a bus unaccompanied by grown-ups.Help Vasya count the minimum and the maximum sum in Berland rubles, that all passengers of this bus could have paid in total.", "input_spec": "The input file consists of a single line containing two space-separated numbers n and m (0\u2009\u2264\u2009n,\u2009m\u2009\u2264\u2009105) \u2014 the number of the grown-ups and the number of the children in the bus, correspondingly.", "output_spec": "If n grown-ups and m children could have ridden in the bus, then print on a single line two space-separated integers \u2014 the minimum and the maximum possible total bus fare, correspondingly.  Otherwise, print \"Impossible\" (without the quotes).", "sample_inputs": ["1 2", "0 5", "2 2"], "sample_outputs": ["2 2", "Impossible", "2 3"], "notes": "NoteIn the first sample a grown-up rides with two children and pays two rubles.In the second sample there are only children in the bus, so the situation is impossible. In the third sample there are two cases:  Each of the two grown-ups rides with one children and pays one ruble for the tickets. In this case the passengers pay two rubles in total.  One of the grown-ups ride with two children's and pays two rubles, the another one rides alone and pays one ruble for himself. So, they pay three rubles in total. "}, "src_uid": "1e865eda33afe09302bda9077d613763"}
{"nl": {"description": "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\u2009\u2264\u2009y\u2009\u2264\u20099000) \u2014 the year number.", "output_spec": "Print a single integer \u2014 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": "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,\u2009s2,\u2009s3,\u2009s4 (1\u2009\u2264\u2009s1,\u2009s2,\u2009s3,\u2009s4\u2009\u2264\u2009109) \u2014 the colors of horseshoes Valera has. Consider all possible colors indexed with integers.", "output_spec": "Print a single integer \u2014 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": "You are given two integers n and k. Find k-th smallest divisor of n, or report that it doesn't exist.Divisor of n is any such natural number, that n can be divided by it without remainder.", "input_spec": "The first line contains two integers n and k (1\u2009\u2264\u2009n\u2009\u2264\u20091015, 1\u2009\u2264\u2009k\u2009\u2264\u2009109).", "output_spec": "If n has less than k divisors, output -1. Otherwise, output the k-th smallest divisor of n.", "sample_inputs": ["4 2", "5 3", "12 5"], "sample_outputs": ["2", "-1", "6"], "notes": "NoteIn the first example, number 4 has three divisors: 1, 2 and 4. The second one is 2.In the second example, number 5 has only two divisors: 1 and 5. The third divisor doesn't exist, so the answer is -1."}, "src_uid": "6ba39b428a2d47b7d199879185797ffb"}
{"nl": {"description": "The king Copa often has been reported about the Codeforces site, which is rapidly getting more and more popular among the brightest minds of the humanity, who are using it for training and competing. Recently Copa understood that to conquer the world he needs to organize the world Codeforces tournament. He hopes that after it the brightest minds will become his subordinates, and the toughest part of conquering the world will be completed.The final round of the Codeforces World Finals 20YY is scheduled for DD.MM.YY, where DD is the day of the round, MM is the month and YY are the last two digits of the year. Bob is lucky to be the first finalist form Berland. But there is one problem: according to the rules of the competition, all participants must be at least 18 years old at the moment of the finals. Bob was born on BD.BM.BY. This date is recorded in his passport, the copy of which he has already mailed to the organizers. But Bob learned that in different countries the way, in which the dates are written, differs. For example, in the US the month is written first, then the day and finally the year. Bob wonders if it is possible to rearrange the numbers in his date of birth so that he will be at least 18 years old on the day DD.MM.YY. He can always tell that in his motherland dates are written differently. Help him.According to another strange rule, eligible participant must be born in the same century as the date of the finals. If the day of the finals is participant's 18-th birthday, he is allowed to participate. As we are considering only the years from 2001 to 2099 for the year of the finals, use the following rule: the year is leap if it's number is divisible by four.", "input_spec": "The first line contains the date DD.MM.YY, the second line contains the date BD.BM.BY. It is guaranteed that both dates are correct, and YY and BY are always in [01;99]. It could be that by passport Bob was born after the finals. In this case, he can still change the order of numbers in date.", "output_spec": "If it is possible to rearrange the numbers in the date of birth so that Bob will be at least 18 years old on the DD.MM.YY, output YES. In the other case, output NO.  Each number contains exactly two digits and stands for day, month or year in a date. Note that it is permitted to rearrange only numbers, not digits.", "sample_inputs": ["01.01.98\n01.01.80", "20.10.20\n10.02.30", "28.02.74\n28.02.64"], "sample_outputs": ["YES", "NO", "NO"], "notes": null}, "src_uid": "5418c98fe362909f7b28f95225837d33"}
{"nl": {"description": "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\u2009\\leq\u2009l\u2009\\leq\u2009r\u2009\\leq\u2009|s|$$$) of a string $$$s\u2009=\u2009s_{1}s_{2} \\ldots s_{|s|}$$$ is the string $$$s_{l}s_{l\u2009+\u20091} \\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": "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\u2009-\u2009A,\u20090) red tokens, and max(bi\u2009-\u2009B,\u20090) 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\u2009\u2264\u2009n\u2009\u2264\u200916). 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\u2009\u2264\u2009ri,\u2009bi\u2009\u2264\u2009107).", "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": "There are $$$n$$$ students in a university. The number of students is even. The $$$i$$$-th student has programming skill equal to $$$a_i$$$. The coach wants to form $$$\\frac{n}{2}$$$ teams. Each team should consist of exactly two students, and each student should belong to exactly one team. Two students can form a team only if their skills are equal (otherwise they cannot understand each other and cannot form a team).Students can solve problems to increase their skill. One solved problem increases the skill by one.The coach wants to know the minimum total number of problems students should solve to form exactly $$$\\frac{n}{2}$$$ teams (i.e. each pair of students should form a team). Your task is to find this number.", "input_spec": "The first line of the input contains one integer $$$n$$$ ($$$2 \\le n \\le 100$$$) \u2014 the number of students. It is guaranteed that $$$n$$$ is even. The second line of the input contains $$$n$$$ integers $$$a_1, a_2, \\dots, a_n$$$ ($$$1 \\le a_i \\le 100$$$), where $$$a_i$$$ is the skill of the $$$i$$$-th student.", "output_spec": "Print one number \u2014 the minimum total number of problems students should solve to form exactly $$$\\frac{n}{2}$$$ teams.", "sample_inputs": ["6\n5 10 2 3 14 5", "2\n1 100"], "sample_outputs": ["5", "99"], "notes": "NoteIn the first example the optimal teams will be: $$$(3, 4)$$$, $$$(1, 6)$$$ and $$$(2, 5)$$$, where numbers in brackets are indices of students. Then, to form the first team the third student should solve $$$1$$$ problem, to form the second team nobody needs to solve problems and to form the third team the second student should solve $$$4$$$ problems so the answer is $$$1 + 4 = 5$$$.In the second example the first student should solve $$$99$$$ problems to form a team with the second one."}, "src_uid": "55485fe203a114374f0aae93006278d3"}
{"nl": {"description": "Two players play a simple game. Each player is provided with a box with balls. First player's box contains exactly n1 balls and second player's box contains exactly n2 balls. In one move first player can take from 1 to k1 balls from his box and throw them away. Similarly, the second player can take from 1 to k2 balls from his box in his move. Players alternate turns and the first player starts the game. The one who can't make a move loses. Your task is to determine who wins if both players play optimally.", "input_spec": "The first line contains four integers n1,\u2009n2,\u2009k1,\u2009k2. All numbers in the input are from 1 to 50. This problem doesn't have subproblems. You will get 3 points for the correct submission.", "output_spec": "Output \"First\" if the first player wins and \"Second\" otherwise.", "sample_inputs": ["2 2 1 2", "2 1 1 1"], "sample_outputs": ["Second", "First"], "notes": "NoteConsider the first sample test. Each player has a box with 2 balls. The first player draws a single ball from his box in one move and the second player can either take 1 or 2 balls from his box in one move. No matter how the first player acts, the second player can always win if he plays wisely."}, "src_uid": "aed24ebab3ed9fd1741eea8e4200f86b"}
{"nl": {"description": "Seven boys and seven girls from Athens were brought before King Minos. The evil king laughed and said \"I hope you enjoy your stay in Crete\".With a loud clang, the doors behind them shut, and darkness reigned. The terrified children huddled together. In the distance they heard a bellowing, unholy roar.Bravely, they advanced forward, to their doom.", "input_spec": "$$$n$$$ ($$$1 \\le n \\le 100$$$) \u2014 the dimensions of the labyrinth.  Each of the next $$$n$$$ lines contains a string of lowercase English letters of length $$$n$$$.", "output_spec": null, "sample_inputs": ["10\natzxcodera\nmzhappyayc\nmineodteri\ntrxesonaac\nmtollexcxc\nhjikeoutlc\neascripsni\nrgvymnjcxm\nonzazwswwg\ngeothermal"], "sample_outputs": ["YES"], "notes": null}, "src_uid": "efb72baf6759f7bc5ac0f3099b7177d0"}
{"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 \u221e (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 \u2014 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": "Polycarp decided to relax on his weekend and visited to the performance of famous ropewalkers: Agafon, Boniface and Konrad.The rope is straight and infinite in both directions. At the beginning of the performance, Agafon, Boniface and Konrad are located in positions $$$a$$$, $$$b$$$ and $$$c$$$ respectively. At the end of the performance, the distance between each pair of ropewalkers was at least $$$d$$$.Ropewalkers can walk on the rope. In one second, only one ropewalker can change his position. Every ropewalker can change his position exactly by $$$1$$$ (i. e. shift by $$$1$$$ to the left or right direction on the rope). Agafon, Boniface and Konrad can not move at the same time (Only one of them can move at each moment). Ropewalkers can be at the same positions at the same time and can \"walk past each other\".You should find the minimum duration (in seconds) of the performance. In other words, find the minimum number of seconds needed so that the distance between each pair of ropewalkers can be greater or equal to $$$d$$$.Ropewalkers can walk to negative coordinates, due to the rope is infinite to both sides.", "input_spec": "The only line of the input contains four integers $$$a$$$, $$$b$$$, $$$c$$$, $$$d$$$ ($$$1 \\le a, b, c, d \\le 10^9$$$). It is possible that any two (or all three) ropewalkers are in the same position at the beginning of the performance.", "output_spec": "Output one integer \u2014 the minimum duration (in seconds) of the performance.", "sample_inputs": ["5 2 6 3", "3 1 5 6", "8 3 3 2", "2 3 10 4"], "sample_outputs": ["2", "8", "2", "3"], "notes": "NoteIn the first example: in the first two seconds Konrad moves for 2 positions to the right (to the position $$$8$$$), while Agafon and Boniface stay at their positions. Thus, the distance between Agafon and Boniface will be $$$|5 - 2| = 3$$$, the distance between Boniface and Konrad will be $$$|2 - 8| = 6$$$ and the distance between Agafon and Konrad will be $$$|5 - 8| = 3$$$. Therefore, all three pairwise distances will be at least $$$d=3$$$, so the performance could be finished within 2 seconds."}, "src_uid": "47c07e46517dbc937e2e779ec0d74eb3"}
{"nl": {"description": "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\u2009-\u20091) 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,\u20092,\u20091] after the first step, the sequence [1,\u20092,\u20091,\u20093,\u20091,\u20092,\u20091] 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.\u00a0e. after (n\u2009-\u20091) steps.Please help Chloe to solve the problem!", "input_spec": "The only line contains two integers n and k (1\u2009\u2264\u2009n\u2009\u2264\u200950, 1\u2009\u2264\u2009k\u2009\u2264\u20092n\u2009-\u20091).", "output_spec": "Print single integer\u00a0\u2014 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,\u20092,\u20091,\u20093,\u20091,\u20092,\u20091]. The number on the second position is 2.In the second sample the obtained sequence is [1,\u20092,\u20091,\u20093,\u20091,\u20092,\u20091,\u20094,\u20091,\u20092,\u20091,\u20093,\u20091,\u20092,\u20091]. The number on the eighth position is 4."}, "src_uid": "0af400ea8e25b1a36adec4cc08912b71"}
{"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\u2009\u2264\u2009n,\u2009k\u2009\u2264\u2009100) \u2014 the number of buckets and the length of the garden, respectively. The second line of input contains n integer numbers ai (1\u2009\u2264\u2009ai\u2009\u2264\u2009100) \u2014 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 \u2014 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": "Bomboslav likes to look out of the window in his room and watch lads outside playing famous shell game. The game is played by two persons: operator and player. Operator takes three similar opaque shells and places a ball beneath one of them. Then he shuffles the shells by swapping some pairs and the player has to guess the current position of the ball.Bomboslav noticed that guys are not very inventive, so the operator always swaps the left shell with the middle one during odd moves (first, third, fifth, etc.) and always swaps the middle shell with the right one during even moves (second, fourth, etc.).Let's number shells from 0 to 2 from left to right. Thus the left shell is assigned number 0, the middle shell is 1 and the right shell is 2. Bomboslav has missed the moment when the ball was placed beneath the shell, but he knows that exactly n movements were made by the operator and the ball was under shell x at the end. Now he wonders, what was the initial position of the ball?", "input_spec": "The first line of the input contains an integer n (1\u2009\u2264\u2009n\u2009\u2264\u20092\u00b7109)\u00a0\u2014 the number of movements made by the operator. The second line contains a single integer x (0\u2009\u2264\u2009x\u2009\u2264\u20092)\u00a0\u2014 the index of the shell where the ball was found after n movements.", "output_spec": "Print one integer from 0 to 2\u00a0\u2014 the index of the shell where the ball was initially placed.", "sample_inputs": ["4\n2", "1\n1"], "sample_outputs": ["1", "0"], "notes": "NoteIn the first sample, the ball was initially placed beneath the middle shell and the operator completed four movements.  During the first move operator swapped the left shell and the middle shell. The ball is now under the left shell.  During the second move operator swapped the middle shell and the right one. The ball is still under the left shell.  During the third move operator swapped the left shell and the middle shell again. The ball is again in the middle.  Finally, the operators swapped the middle shell and the right shell. The ball is now beneath the right shell. "}, "src_uid": "7853e03d520cd71571a6079cdfc4c4b0"}
{"nl": {"description": "Little C loves number \u00ab3\u00bb very much. He loves all things about it.Now he is playing a game on a chessboard of size $$$n \\times m$$$. The cell in the $$$x$$$-th row and in the $$$y$$$-th column is called $$$(x,y)$$$. Initially, The chessboard is empty. Each time, he places two chessmen on two different empty cells, the Manhattan distance between which is exactly $$$3$$$. The Manhattan distance between two cells $$$(x_i,y_i)$$$ and $$$(x_j,y_j)$$$ is defined as $$$|x_i-x_j|+|y_i-y_j|$$$.He want to place as many chessmen as possible on the chessboard. Please help him find the maximum number of chessmen he can place.", "input_spec": "A single line contains two integers $$$n$$$ and $$$m$$$ ($$$1 \\leq n,m \\leq 10^9$$$) \u2014 the number of rows and the number of columns of the chessboard.", "output_spec": "Print one integer \u2014 the maximum number of chessmen Little C can place.", "sample_inputs": ["2 2", "3 3"], "sample_outputs": ["0", "8"], "notes": "NoteIn the first example, the Manhattan distance between any two cells is smaller than $$$3$$$, so the answer is $$$0$$$.In the second example, a possible solution is $$$(1,1)(3,2)$$$, $$$(1,2)(3,3)$$$, $$$(2,1)(1,3)$$$, $$$(3,1)(2,3)$$$."}, "src_uid": "02ce135a4b276d1e9ba6a4ce37f2fe70"}
{"nl": {"description": "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\u2009\u2264\u2009n\u2009\u2264\u2009109).", "output_spec": "Output the only number \u2014 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": "Ari the monster always wakes up very early with the first ray of the sun and the first thing she does is feeding her squirrel.Ari draws a regular convex polygon on the floor and numbers it's vertices 1,\u20092,\u2009...,\u2009n in clockwise order. Then starting from the vertex 1 she draws a ray in the direction of each other vertex. The ray stops when it reaches a vertex or intersects with another ray drawn before. Ari repeats this process for vertex 2,\u20093,\u2009...,\u2009n (in this particular order). And then she puts a walnut in each region inside the polygon.  Ada the squirrel wants to collect all the walnuts, but she is not allowed to step on the lines drawn by Ari. That means Ada have to perform a small jump if she wants to go from one region to another. Ada can jump from one region P to another region Q if and only if P and Q share a side or a corner.Assuming that Ada starts from outside of the picture, what is the minimum number of jumps she has to perform in order to collect all the walnuts?", "input_spec": "The first and only line of the input contains a single integer n (3\u2009\u2264\u2009n\u2009\u2264\u200954321) - the number of vertices of the regular polygon drawn by Ari.", "output_spec": "Print the minimum number of jumps Ada should make to collect all the walnuts. Note, that she doesn't need to leave the polygon after.", "sample_inputs": ["5", "3"], "sample_outputs": ["9", "1"], "notes": "NoteOne of the possible solutions for the first sample is shown on the picture above."}, "src_uid": "efa8e7901a3084d34cfb1a6b18067f2b"}
{"nl": {"description": "Let's denote d(n) as the number of divisors of a positive integer n. You are given three integers a, b and c. Your task is to calculate the following sum:Find the sum modulo 1073741824 (230).", "input_spec": "The first line contains three space-separated integers a, b and c (1\u2009\u2264\u2009a,\u2009b,\u2009c\u2009\u2264\u20092000).", "output_spec": "Print a single integer \u2014 the required sum modulo 1073741824 (230).", "sample_inputs": ["2 2 2", "4 4 4", "10 10 10"], "sample_outputs": ["20", "328", "11536"], "notes": "NoteFor the first example.  d(1\u00b71\u00b71)\u2009=\u2009d(1)\u2009=\u20091;  d(1\u00b71\u00b72)\u2009=\u2009d(2)\u2009=\u20092;  d(1\u00b72\u00b71)\u2009=\u2009d(2)\u2009=\u20092;  d(1\u00b72\u00b72)\u2009=\u2009d(4)\u2009=\u20093;  d(2\u00b71\u00b71)\u2009=\u2009d(2)\u2009=\u20092;  d(2\u00b71\u00b72)\u2009=\u2009d(4)\u2009=\u20093;  d(2\u00b72\u00b71)\u2009=\u2009d(4)\u2009=\u20093;  d(2\u00b72\u00b72)\u2009=\u2009d(8)\u2009=\u20094. So the result is 1\u2009+\u20092\u2009+\u20092\u2009+\u20093\u2009+\u20092\u2009+\u20093\u2009+\u20093\u2009+\u20094\u2009=\u200920."}, "src_uid": "4fdd4027dd9cd688fcc70e1076c9b401"}
{"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\u2009\u2264\u2009n\u2009\u2264\u200950) \u2014 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 \u2014 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": "We've got no test cases. A big olympiad is coming up. But the problemsetters' number one priority should be adding another problem to the round. The diameter of a multiset of points on the line is the largest distance between two points from this set. For example, the diameter of the multiset {1,\u20093,\u20092,\u20091} is 2.Diameter of multiset consisting of one point is 0.You are given n points on the line. What is the minimum number of points you have to remove, so that the diameter of the multiset of the remaining points will not exceed d?", "input_spec": "The first line contains two integers n and d (1\u2009\u2264\u2009n\u2009\u2264\u2009100,\u20090\u2009\u2264\u2009d\u2009\u2264\u2009100)\u00a0\u2014 the amount of points and the maximum allowed diameter respectively. The second line contains n space separated integers (1\u2009\u2264\u2009xi\u2009\u2264\u2009100)\u00a0\u2014 the coordinates of the points.", "output_spec": "Output a single integer\u00a0\u2014 the minimum number of points you have to remove.", "sample_inputs": ["3 1\n2 1 4", "3 0\n7 7 7", "6 3\n1 3 4 6 9 10"], "sample_outputs": ["1", "0", "3"], "notes": "NoteIn the first test case the optimal strategy is to remove the point with coordinate 4. The remaining points will have coordinates 1 and 2, so the diameter will be equal to 2\u2009-\u20091\u2009=\u20091.In the second test case the diameter is equal to 0, so its is unnecessary to remove any points. In the third test case the optimal strategy is to remove points with coordinates 1, 9 and 10. The remaining points will have coordinates 3, 4 and 6, so the diameter will be equal to 6\u2009-\u20093\u2009=\u20093."}, "src_uid": "6bcb324c072f796f4d50bafea5f624b2"}
{"nl": {"description": "Vasya has a pack of 54 cards (52 standard cards and 2 distinct jokers). That is all he has at the moment. Not to die from boredom, Vasya plays Solitaire with them.Vasya lays out nm cards as a rectangle n\u2009\u00d7\u2009m. If there are jokers among them, then Vasya should change them with some of the rest of 54\u2009-\u2009nm cards (which are not layed out) so that there were no jokers left. Vasya can pick the cards to replace the jokers arbitrarily. Remember, that each card presents in pack exactly once (i. e. in a single copy). Vasya tries to perform the replacements so that the solitaire was solved.Vasya thinks that the solitaire is solved if after the jokers are replaced, there exist two non-overlapping squares 3\u2009\u00d7\u20093, inside each of which all the cards either have the same suit, or pairwise different ranks.Determine by the initial position whether the solitaire can be solved or not. If it can be solved, show the way in which it is possible.", "input_spec": "The first line contains integers n and m (3\u2009\u2264\u2009n,\u2009m\u2009\u2264\u200917, n\u2009\u00d7\u2009m\u2009\u2264\u200952). Next n lines contain m words each. Each word consists of two letters. The jokers are defined as \"J1\" and \"J2\" correspondingly. For the rest of the cards, the first letter stands for the rank and the second one \u2014 for the suit. The possible ranks are: \"2\", \"3\", \"4\", \"5\", \"6\", \"7\", \"8\", \"9\", \"T\", \"J\", \"Q\", \"K\" and \"A\". The possible suits are: \"C\", \"D\", \"H\" and \"S\". All the cards are different.", "output_spec": "If the Solitaire can be solved, print on the first line \"Solution exists.\" without the quotes. On the second line print in what way the jokers can be replaced. Three variants are possible:   \"There are no jokers.\", if there are no jokers in the input data. \"Replace Jx with y.\", if there is one joker. x is its number, and y is the card it should be replaced with. \"Replace J1 with x and J2 with y.\", if both jokers are present in the input data. x and y here represent distinct cards with which one should replace the first and the second jokers correspondingly. On the third line print the coordinates of the upper left corner of the first square 3\u2009\u00d7\u20093 in the format \"Put the first square to (r, c).\", where r and c are the row and the column correspondingly. In the same manner print on the fourth line the coordinates of the second square 3\u2009\u00d7\u20093 in the format \"Put the second square to (r, c).\". If there are several solutions to that problem, print any of them. If there are no solutions, print of the single line \"No solution.\" without the quotes. See the samples to understand the output format better.", "sample_inputs": ["4 6\n2S 3S 4S 7S 8S AS\n5H 6H 7H 5S TC AC\n8H 9H TH 7C 8C 9C\n2D 2C 3C 4C 5C 6C", "4 6\n2S 3S 4S 7S 8S AS\n5H 6H 7H J1 TC AC\n8H 9H TH 7C 8C 9C\n2D 2C 3C 4C 5C 6C", "4 6\n2S 3S 4S 7S 8S AS\n5H 6H 7H QC TC AC\n8H 9H TH 7C 8C 9C\n2D 2C 3C 4C 5C 6C"], "sample_outputs": ["No solution.", "Solution exists.\nReplace J1 with 2H.\nPut the first square to (1, 1).\nPut the second square to (2, 4).", "Solution exists.\nThere are no jokers.\nPut the first square to (1, 1).\nPut the second square to (2, 4)."], "notes": "NoteThe pretests cover all the possible output formats."}, "src_uid": "b3f29d9c27cbfeadb96b6ac9ffd6bc8f"}
{"nl": {"description": "You are given a chessboard of size 1\u2009\u00d7\u2009n. It is guaranteed that n is even. The chessboard is painted like this: \"BWBW...BW\".Some cells of the board are occupied by the chess pieces. Each cell contains no more than one chess piece. It is known that the total number of pieces equals to .In one step you can move one of the pieces one cell to the left or to the right. You cannot move pieces beyond the borders of the board. You also cannot move pieces to the cells that are already occupied.Your task is to place all the pieces in the cells of the same color using the minimum number of moves (all the pieces must occupy only the black cells or only the white cells after all the moves are made).", "input_spec": "The first line of the input contains one integer n (2\u2009\u2264\u2009n\u2009\u2264\u2009100, n is even) \u2014 the size of the chessboard.  The second line of the input contains  integer numbers  (1\u2009\u2264\u2009pi\u2009\u2264\u2009n) \u2014 initial positions of the pieces. It is guaranteed that all the positions are distinct.", "output_spec": "Print one integer \u2014 the minimum number of moves you have to make to place all the pieces in the cells of the same color.", "sample_inputs": ["6\n1 2 6", "10\n1 2 3 4 5"], "sample_outputs": ["2", "10"], "notes": "NoteIn the first example the only possible strategy is to move the piece at the position 6 to the position 5 and move the piece at the position 2 to the position 3. Notice that if you decide to place the pieces in the white cells the minimum number of moves will be 3.In the second example the possible strategy is to move  in 4 moves, then  in 3 moves,  in 2 moves and  in 1 move."}, "src_uid": "0efe9afd8e6be9e00f7949be93f0ca1a"}
{"nl": {"description": "In this problem, we will consider complete undirected graphs consisting of $$$n$$$ vertices with weighted edges. The weight of each edge is an integer from $$$1$$$ to $$$k$$$.An undirected graph is considered beautiful if the sum of weights of all edges incident to vertex $$$1$$$ is equal to the weight of MST in the graph. MST is the minimum spanning tree\u00a0\u2014 a tree consisting of $$$n-1$$$ edges of the graph, which connects all $$$n$$$ vertices and has the minimum sum of weights among all such trees; the weight of MST is the sum of weights of all edges in it.Calculate the number of complete beautiful graphs having exactly $$$n$$$ vertices and the weights of edges from $$$1$$$ to $$$k$$$. Since the answer might be large, print it modulo $$$998244353$$$.", "input_spec": "The only line contains two integers $$$n$$$ and $$$k$$$ ($$$2 \\le n \\le 250$$$; $$$1 \\le k \\le 250$$$).", "output_spec": "Print one integer\u00a0\u2014 the number of complete beautiful graphs having exactly $$$n$$$ vertices and the weights of edges from $$$1$$$ to $$$k$$$. Since the answer might be large, print it modulo $$$998244353$$$.", "sample_inputs": ["3 2", "4 4", "6 9", "42 13"], "sample_outputs": ["5", "571", "310640163", "136246935"], "notes": null}, "src_uid": "b2d7ac8e75cbdb828067aeafd803ac62"}
{"nl": {"description": "Johny likes numbers n and k very much. Now Johny wants to find the smallest integer x greater than n, so it is divisible by the number k.", "input_spec": "The only line contains two integers n and k (1\u2009\u2264\u2009n,\u2009k\u2009\u2264\u2009109).", "output_spec": "Print the smallest integer x\u2009>\u2009n, so it is divisible by the number k.", "sample_inputs": ["5 3", "25 13", "26 13"], "sample_outputs": ["6", "26", "39"], "notes": null}, "src_uid": "75f3835c969c871a609b978e04476542"}
{"nl": {"description": "Duff is in love with lovely numbers! A positive integer x is called lovely if and only if there is no such positive integer a\u2009>\u20091 such that a2 is a divisor of x.  Malek has a number store! In his store, he has only divisors of positive integer n (and he has all of them). As a birthday present, Malek wants to give her a lovely number from his store. He wants this number to be as big as possible.Malek always had issues in math, so he asked for your help. Please tell him what is the biggest lovely number in his store.", "input_spec": "The first and only line of input contains one integer, n (1\u2009\u2264\u2009n\u2009\u2264\u20091012).", "output_spec": "Print the answer in one line.", "sample_inputs": ["10", "12"], "sample_outputs": ["10", "6"], "notes": "NoteIn first sample case, there are numbers 1, 2, 5 and 10 in the shop. 10 isn't divisible by any perfect square, so 10 is lovely.In second sample case, there are numbers 1, 2, 3, 4, 6 and 12 in the shop. 12 is divisible by 4\u2009=\u200922, so 12 is not lovely, while 6 is indeed lovely."}, "src_uid": "6d0da975fa0961acfdbe75f2f29aeb92"}
{"nl": {"description": "There are $$$n$$$ students in a school class, the rating of the $$$i$$$-th student on Codehorses is $$$a_i$$$. You have to form a team consisting of $$$k$$$ students ($$$1 \\le k \\le n$$$) such that the ratings of all team members are distinct.If it is impossible to form a suitable team, print \"NO\" (without quotes). Otherwise print \"YES\", and then print $$$k$$$ distinct numbers which should be the indices of students in the team you form. If there are multiple answers, print any of them.", "input_spec": "The first line contains two integers $$$n$$$ and $$$k$$$ ($$$1 \\le k \\le n \\le 100$$$) \u2014 the number of students and the size of the team you have to form. The second line contains $$$n$$$ integers $$$a_1, a_2, \\dots, a_n$$$ ($$$1 \\le a_i \\le 100$$$), where $$$a_i$$$ is the rating of $$$i$$$-th student.", "output_spec": "If it is impossible to form a suitable team, print \"NO\" (without quotes). Otherwise print \"YES\", and then print $$$k$$$ distinct integers from $$$1$$$ to $$$n$$$ which should be the indices of students in the team you form. All the ratings of the students in the team should be distinct. You may print the indices in any order. If there are multiple answers, print any of them. Assume that the students are numbered from $$$1$$$ to $$$n$$$.", "sample_inputs": ["5 3\n15 13 15 15 12", "5 4\n15 13 15 15 12", "4 4\n20 10 40 30"], "sample_outputs": ["YES\n1 2 5", "NO", "YES\n1 2 3 4"], "notes": "NoteAll possible answers for the first example:   {1 2 5}  {2 3 5}  {2 4 5} Note that the order does not matter."}, "src_uid": "5de6574d57ab04ca195143e08d28d0ad"}
{"nl": {"description": "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 \u2009-\u20091.", "input_spec": "The single line contains two numbers, n and t (1\u2009\u2264\u2009n\u2009\u2264\u2009100, 2\u2009\u2264\u2009t\u2009\u2264\u200910) \u2014 the length of the number and the number it should be divisible by.", "output_spec": "Print one such positive number without leading zeroes, \u2014 the answer to the problem, or \u2009-\u20091, 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": "To quickly hire highly skilled specialists one of the new IT City companies made an unprecedented move. Every employee was granted a car, and an employee can choose one of four different car makes.The parking lot before the office consists of one line of (2n\u2009-\u20092) parking spaces. Unfortunately the total number of cars is greater than the parking lot capacity. Furthermore even amount of cars of each make is greater than the amount of parking spaces! That's why there are no free spaces on the parking lot ever.Looking on the straight line of cars the company CEO thought that parking lot would be more beautiful if it contained exactly n successive cars of the same make. Help the CEO determine the number of ways to fill the parking lot this way.", "input_spec": "The only line of the input contains one integer n (3\u2009\u2264\u2009n\u2009\u2264\u200930) \u2014 the amount of successive cars of the same make.", "output_spec": "Output one integer \u2014 the number of ways to fill the parking lot by cars of four makes using the described way.", "sample_inputs": ["3"], "sample_outputs": ["24"], "notes": "NoteLet's denote car makes in the following way: A \u2014 Aston Martin, B \u2014   Bentley, M \u2014 Mercedes-Maybach, Z \u2014 Zaporozhets. For n\u2009=\u20093 there are the following appropriate ways to fill the parking lot: AAAB AAAM AAAZ ABBB AMMM AZZZ BBBA BBBM BBBZ BAAA BMMM BZZZ MMMA MMMB MMMZ MAAA MBBB MZZZ ZZZA ZZZB ZZZM ZAAA ZBBB ZMMMOriginally it was planned to grant sport cars of Ferrari, Lamborghini, Maserati and Bugatti makes but this idea was renounced because it is impossible to drive these cars having small road clearance on the worn-down roads of IT City."}, "src_uid": "3b02cbb38d0b4ddc1a6467f7647d53a9"}
{"nl": {"description": "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$$$)\u00a0\u2014 the number of fast food restaurants on the circle and the distance between the neighboring restaurants, respectively. The second line contains two integers $$$a$$$ and $$$b$$$ ($$$0 \\le a, b \\le \\frac{k}{2}$$$)\u00a0\u2014 the distances to the nearest fast food restaurants from the initial city and from the city Sergey made the first stop at, respectively.", "output_spec": "Print the two integers $$$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$$$."}, "src_uid": "5bb4adff1b332f43144047955eefba0c"}
{"nl": {"description": "We all know that GukiZ often plays with arrays. Now he is thinking about this problem: how many arrays a, of length n, with non-negative elements strictly less then 2l meet the following condition: ? Here operation  means bitwise AND (in Pascal it is equivalent to and, in C/C++/Java/Python it is equivalent to &), operation  means bitwise OR (in Pascal it is equivalent to , in C/C++/Java/Python it is equivalent to |). Because the answer can be quite large, calculate it modulo m. This time GukiZ hasn't come up with solution, and needs you to help him!", "input_spec": "First and the only line of input contains four integers n, k, l, m (2\u2009\u2264\u2009n\u2009\u2264\u20091018, 0\u2009\u2264\u2009k\u2009\u2264\u20091018, 0\u2009\u2264\u2009l\u2009\u2264\u200964, 1\u2009\u2264\u2009m\u2009\u2264\u2009109\u2009+\u20097).", "output_spec": "In the single line print the number of arrays satisfying the condition above modulo m.", "sample_inputs": ["2 1 2 10", "2 1 1 3", "3 3 2 10"], "sample_outputs": ["3", "1", "9"], "notes": "NoteIn the first sample, satisfying arrays are {1,\u20091},\u2009{3,\u20091},\u2009{1,\u20093}.In the second sample, only satisfying array is {1,\u20091}.In the third sample, satisfying arrays are {0,\u20093,\u20093},\u2009{1,\u20093,\u20092},\u2009{1,\u20093,\u20093},\u2009{2,\u20093,\u20091},\u2009{2,\u20093,\u20093},\u2009{3,\u20093,\u20090},\u2009{3,\u20093,\u20091},\u2009{3,\u20093,\u20092},\u2009{3,\u20093,\u20093}."}, "src_uid": "2163eec2ea1eed5da8231d1882cb0f8e"}
{"nl": {"description": "Seryozha conducts a course dedicated to building a map of heights of Stepanovo recreation center. He laid a rectangle grid of size $$$n \\times m$$$ cells on a map (rows of grid are numbered from $$$1$$$ to $$$n$$$ from north to south, and columns are numbered from $$$1$$$ to $$$m$$$ from west to east). After that he measured the average height of each cell above Rybinsk sea level and obtained a matrix of heights of size $$$n \\times m$$$. The cell $$$(i, j)$$$ lies on the intersection of the $$$i$$$-th row and the $$$j$$$-th column and has height $$$h_{i, j}$$$. Seryozha is going to look at the result of his work in the browser. The screen of Seryozha's laptop can fit a subrectangle of size $$$a \\times b$$$ of matrix of heights ($$$1 \\le a \\le n$$$, $$$1 \\le b \\le m$$$). Seryozha tries to decide how the weather can affect the recreation center \u2014 for example, if it rains, where all the rainwater will gather. To do so, he is going to find the cell having minimum height among all cells that are shown on the screen of his laptop.Help Seryozha to calculate the sum of heights of such cells for all possible subrectangles he can see on his screen. In other words, you have to calculate the sum of minimum heights in submatrices of size $$$a \\times b$$$ with top left corners in $$$(i, j)$$$ over all $$$1 \\le i \\le n - a + 1$$$ and $$$1 \\le j \\le m - b + 1$$$.Consider the sequence $$$g_i = (g_{i - 1} \\cdot x + y) \\bmod z$$$. You are given integers $$$g_0$$$, $$$x$$$, $$$y$$$ and $$$z$$$. By miraculous coincidence, $$$h_{i, j} = g_{(i - 1) \\cdot m + j - 1}$$$ ($$$(i - 1) \\cdot m + j - 1$$$ is the index).", "input_spec": "The first line of the input contains four integers $$$n$$$, $$$m$$$, $$$a$$$ and $$$b$$$ ($$$1 \\le n, m \\le 3\\,000$$$, $$$1 \\le a \\le n$$$, $$$1 \\le b \\le m$$$) \u2014 the number of rows and columns in the matrix Seryozha has, and the number of rows and columns that can be shown on the screen of the laptop, respectively. The second line of the input contains four integers $$$g_0$$$, $$$x$$$, $$$y$$$ and $$$z$$$ ($$$0 \\le g_0, x, y < z \\le 10^9$$$).", "output_spec": "Print a single integer \u2014 the answer to the problem.", "sample_inputs": ["3 4 2 1\n1 2 3 59"], "sample_outputs": ["111"], "notes": "NoteThe matrix from the first example:   "}, "src_uid": "4618fbffb2b9d321a6d22c11590a4773"}
{"nl": {"description": "To make a paper airplane, one has to use a rectangular piece of paper. From a sheet of standard size you can make $$$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$$$)\u00a0\u2014 the number of people, the number of airplanes each should make, the number of airplanes that can be made using one sheet and the number of sheets in one pack, respectively.", "output_spec": "Print a single integer\u00a0\u2014 the minimum number of packs they should buy.", "sample_inputs": ["5 3 2 3", "5 3 100 1"], "sample_outputs": ["4", "5"], "notes": "NoteIn the first sample they have to buy $$$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": "Many students live in a dormitory. A dormitory is a whole new world of funny amusements and possibilities but it does have its drawbacks. There is only one shower and there are multiple students who wish to have a shower in the morning. That's why every morning there is a line of five people in front of the dormitory shower door. As soon as the shower opens, the first person from the line enters the shower. After a while the first person leaves the shower and the next person enters the shower. The process continues until everybody in the line has a shower.Having a shower takes some time, so the students in the line talk as they wait. At each moment of time the students talk in pairs: the (2i\u2009-\u20091)-th man in the line (for the current moment) talks with the (2i)-th one. Let's look at this process in more detail. Let's number the people from 1 to 5. Let's assume that the line initially looks as 23154 (person number 2 stands at the beginning of the line). Then, before the shower opens, 2 talks with 3, 1 talks with 5, 4 doesn't talk with anyone. Then 2 enters the shower. While 2 has a shower, 3 and 1 talk, 5 and 4 talk too. Then, 3 enters the shower. While 3 has a shower, 1 and 5 talk, 4 doesn't talk to anyone. Then 1 enters the shower and while he is there, 5 and 4 talk. Then 5 enters the shower, and then 4 enters the shower.We know that if students i and j talk, then the i-th student's happiness increases by gij and the j-th student's happiness increases by gji. Your task is to find such initial order of students in the line that the total happiness of all students will be maximum in the end. Please note that some pair of students may have a talk several times. In the example above students 1 and 5 talk while they wait for the shower to open and while 3 has a shower.", "input_spec": "The input consists of five lines, each line contains five space-separated integers: the j-th number in the i-th line shows gij (0\u2009\u2264\u2009gij\u2009\u2264\u2009105). It is guaranteed that gii\u2009=\u20090 for all i. Assume that the students are numbered from 1 to 5.", "output_spec": "Print a single integer \u2014 the maximum possible total happiness of the students.", "sample_inputs": ["0 0 0 0 9\n0 0 0 0 0\n0 0 0 0 0\n0 0 0 0 0\n7 0 0 0 0", "0 43 21 18 2\n3 0 21 11 65\n5 2 0 1 4\n54 62 12 0 99\n87 64 81 33 0"], "sample_outputs": ["32", "620"], "notes": "NoteIn the first sample, the optimal arrangement of the line is 23154. In this case, the total happiness equals:(g23\u2009+\u2009g32\u2009+\u2009g15\u2009+\u2009g51)\u2009+\u2009(g13\u2009+\u2009g31\u2009+\u2009g54\u2009+\u2009g45)\u2009+\u2009(g15\u2009+\u2009g51)\u2009+\u2009(g54\u2009+\u2009g45)\u2009=\u200932."}, "src_uid": "be6d4df20e9a48d183dd8f34531df246"}
{"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\u2009\u2264\u2009m,  k participants compete in the current round and a half of them passes to the next round, the other m\u2009-\u2009k 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,\u2009b,\u2009p (1\u2009\u2264\u2009n,\u2009b,\u2009p\u2009\u2264\u2009500) \u2014 the number of participants and the parameters described in the problem statement.", "output_spec": "Print two integers x and y \u2014 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": "Vadim loves decorating the Christmas tree, so he got a beautiful garland as a present. It consists of $$$n$$$ light bulbs in a single row. Each bulb has a number from $$$1$$$ to $$$n$$$ (in arbitrary order), such that all the numbers are distinct. While Vadim was solving problems, his home Carp removed some light bulbs from the garland. Now Vadim wants to put them back on.Vadim wants to put all bulb back on the garland. Vadim defines complexity of a garland to be the number of pairs of adjacent bulbs with numbers with different parity (remainder of the division by $$$2$$$). For example, the complexity of 1 4 2 3 5 is $$$2$$$ and the complexity of 1 3 5 7 6 4 2 is $$$1$$$.No one likes complexity, so Vadim wants to minimize the number of such pairs. Find the way to put all bulbs back on the garland, such that the complexity is as small as possible.", "input_spec": "The first line contains a single integer $$$n$$$ ($$$1 \\le n \\le 100$$$)\u00a0\u2014 the number of light bulbs on the garland. The second line contains $$$n$$$ integers $$$p_1,\\ p_2,\\ \\ldots,\\ p_n$$$ ($$$0 \\le p_i \\le n$$$)\u00a0\u2014 the number on the $$$i$$$-th bulb, or $$$0$$$ if it was removed.", "output_spec": "Output a single number\u00a0\u2014 the minimum complexity of the garland.", "sample_inputs": ["5\n0 5 0 2 3", "7\n1 0 0 5 0 0 2"], "sample_outputs": ["2", "1"], "notes": "NoteIn the first example, one should place light bulbs as 1 5 4 2 3. In that case, the complexity would be equal to 2, because only $$$(5, 4)$$$ and $$$(2, 3)$$$ are the pairs of adjacent bulbs that have different parity.In the second case, one of the correct answers is 1 7 3 5 6 4 2. "}, "src_uid": "90db6b6548512acfc3da162144169dba"}
{"nl": {"description": "Statistics claims that students sleep no more than three hours a day. But even in the world of their dreams, while they are snoring peacefully, the sense of impending doom is still upon them.A poor student is dreaming that he is sitting the mathematical analysis exam. And he is examined by the most formidable professor of all times, a three times Soviet Union Hero, a Noble Prize laureate in student expulsion, venerable Petr Palych.The poor student couldn't answer a single question. Thus, instead of a large spacious office he is going to apply for a job to thorium mines. But wait a minute! Petr Palych decided to give the student the last chance! Yes, that is possible only in dreams. So the professor began: \"Once a Venusian girl and a Marsian boy met on the Earth and decided to take a walk holding hands. But the problem is the girl has al fingers on her left hand and ar fingers on the right one. The boy correspondingly has bl and br fingers. They can only feel comfortable when holding hands, when no pair of the girl's fingers will touch each other. That is, they are comfortable when between any two girl's fingers there is a boy's finger. And in addition, no three fingers of the boy should touch each other. Determine if they can hold hands so that the both were comfortable.\"The boy any the girl don't care who goes to the left and who goes to the right. The difference is only that if the boy goes to the left of the girl, he will take her left hand with his right one, and if he goes to the right of the girl, then it is vice versa.", "input_spec": "The first line contains two positive integers not exceeding 100. They are the number of fingers on the Venusian girl's left and right hand correspondingly. The second line contains two integers not exceeding 100. They are the number of fingers on the Marsian boy's left and right hands correspondingly.", "output_spec": "Print YES or NO, that is, the answer to Petr Palych's question.", "sample_inputs": ["5 1\n10 5", "4 5\n3 3", "1 2\n11 6"], "sample_outputs": ["YES", "YES", "NO"], "notes": "NoteThe boy and the girl don't really care who goes to the left."}, "src_uid": "36b7478e162be6e985613b2dad0974dd"}
{"nl": {"description": "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$$$)\u00a0\u2014 the number of coins you have.", "output_spec": "Output a single integer\u00a0\u2014 the minimum possible number of packets, satisfying the condition above.", "sample_inputs": ["6", "2"], "sample_outputs": ["3", "2"], "notes": "NoteIn the first example, three packets with $$$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": "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\u2009\u2264\u2009n,\u2009m\u2009\u2264\u20095\u00b7105) \u2014 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": "Katie, Kuro and Shiro are best friends. They have known each other since kindergarten. That's why they often share everything with each other and work together on some very hard problems.Today is Shiro's birthday. She really loves pizza so she wants to invite her friends to the pizza restaurant near her house to celebrate her birthday, including her best friends Katie and Kuro.She has ordered a very big round pizza, in order to serve her many friends. Exactly $$$n$$$ of Shiro's friends are here. That's why she has to divide the pizza into $$$n + 1$$$ slices (Shiro also needs to eat). She wants the slices to be exactly the same size and shape. If not, some of her friends will get mad and go home early, and the party will be over.Shiro is now hungry. She wants to cut the pizza with minimum of straight cuts. A cut is a straight segment, it might have ends inside or outside the pizza. But she is too lazy to pick up the calculator.As usual, she will ask Katie and Kuro for help. But they haven't come yet. Could you help Shiro with this problem?", "input_spec": "A single line contains one non-negative integer $$$n$$$ ($$$0 \\le n \\leq 10^{18}$$$)\u00a0\u2014 the number of Shiro's friends. The circular pizza has to be sliced into $$$n + 1$$$ pieces.", "output_spec": "A single integer\u00a0\u2014 the number of straight cuts Shiro needs.", "sample_inputs": ["3", "4"], "sample_outputs": ["2", "5"], "notes": "NoteTo cut the round pizza into quarters one has to make two cuts through the center with angle $$$90^{\\circ}$$$ between them.To cut the round pizza into five equal parts one has to make five cuts."}, "src_uid": "236177ff30dafe68295b5d33dc501828"}
{"nl": {"description": "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) \u0438 'C' (cheese). The ingredients in the recipe go from bottom to top, for example, recipe \"\u0412SCBS\" 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\u2009\u2264\u2009nb,\u2009ns,\u2009nc\u2009\u2264\u2009100) \u2014 the number of the pieces of bread, sausage and cheese on Polycarpus' kitchen. The third line contains three integers pb, ps, pc (1\u2009\u2264\u2009pb,\u2009ps,\u2009pc\u2009\u2264\u2009100) \u2014 the price of one piece of bread, sausage and cheese in the shop. Finally, the fourth line contains integer r (1\u2009\u2264\u2009r\u2009\u2264\u20091012) \u2014 the number of rubles Polycarpus has. Please, do not write the %lld specifier to read or write 64-bit integers in \u0421++. 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": "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\u2009\u2264\u2009n\u2009\u2264\u20091018)\u00a0\u2014 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,\u20092) and (3,\u20094) and then clash the winners."}, "src_uid": "3d3432b4f7c6a3b901161fa24b415b14"}
{"nl": {"description": "Recently Anton found a box with digits in his room. There are k2 digits 2, k3 digits 3, k5 digits 5 and k6 digits 6.Anton's favorite integers are 32 and 256. He decided to compose this integers from digits he has. He wants to make the sum of these integers as large as possible. Help him solve this task!Each digit can be used no more than once, i.e. the composed integers should contain no more than k2 digits 2, k3 digits 3 and so on. Of course, unused digits are not counted in the sum.", "input_spec": "The only line of the input contains four integers k2, k3, k5 and k6\u00a0\u2014 the number of digits 2, 3, 5 and 6 respectively (0\u2009\u2264\u2009k2,\u2009k3,\u2009k5,\u2009k6\u2009\u2264\u20095\u00b7106).", "output_spec": "Print one integer\u00a0\u2014 maximum possible sum of Anton's favorite integers that can be composed using digits from the box.", "sample_inputs": ["5 1 3 4", "1 1 1 1"], "sample_outputs": ["800", "256"], "notes": "NoteIn the first sample, there are five digits 2, one digit 3, three digits 5 and four digits 6. Anton can compose three integers 256 and one integer 32 to achieve the value 256\u2009+\u2009256\u2009+\u2009256\u2009+\u200932\u2009=\u2009800. Note, that there is one unused integer 2 and one unused integer 6. They are not counted in the answer.In the second sample, the optimal answer is to create on integer 256, thus the answer is 256."}, "src_uid": "082b31cc156a7ba1e0a982f07ecc207e"}