{"nl": {"description": "This problem is split into two tasks. In this task, you are required to find the minimum possible answer. In the task Village (Maximum) you are required to find the maximum possible answer. Each task is worth $$$50$$$ points.There are $$$N$$$ houses in a certain village. A single villager lives in each of the houses. The houses are connected by roads. Each road connects two houses and is exactly $$$1$$$ kilometer long. From each house it is possible to reach any other using one or several consecutive roads. In total there are $$$N-1$$$ roads in the village.One day all villagers decided to move to different houses \u2014 that is, after moving each house should again have a single villager living in it, but no villager should be living in the same house as before. We would like to know the smallest possible total length in kilometers of the shortest paths between the old and the new houses for all villagers. Example village with seven houses For example, if there are seven houses connected by roads as shown on the figure, the smallest total length is $$$8$$$ km (this can be achieved by moving $$$1 \\to 6$$$, $$$2 \\to 4$$$, $$$3 \\to 1$$$, $$$4 \\to 2$$$, $$$5 \\to 7$$$, $$$6 \\to 3$$$, $$$7 \\to 5$$$).Write a program that finds the smallest total length of the shortest paths in kilometers and an example assignment of the new houses to the villagers.", "input_spec": "The first line contains an integer $$$N$$$ ($$$1 < N \\le 10^5$$$). Houses are numbered by consecutive integers $$$1, 2, \\ldots, N$$$. Then $$$N-1$$$ lines follow that describe the roads. Each line contains two integers $$$a$$$ and $$$b$$$ ($$$1 \\le a, b \\le N$$$, $$$a \\neq b$$$) denoting that there is a road connecting houses $$$a$$$ and $$$b$$$.", "output_spec": "In the first line output the smallest total length of the shortest paths in kilometers. In the second line describe one valid assignment of the new houses with the smallest total length: $$$N$$$ space-separated distinct integers $$$v_1, v_2, \\ldots, v_N$$$. For each $$$i$$$, $$$v_i$$$ is the house number where the villager from the house $$$i$$$ should move ($$$v_i \\neq i$$$). If there are several valid assignments, output any of those.", "sample_inputs": ["4\n1 2\n2 3\n3 4", "7\n4 2\n5 7\n3 4\n6 3\n1 3\n4 5"], "sample_outputs": ["4\n2 1 4 3", "8\n3 4 6 2 7 1 5"], "notes": null}, "src_uid": "98ded03cdd1870500667f0069d6a84b1"}
{"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": "Petya has an array $$$a$$$ consisting of $$$n$$$ integers. He wants to remove duplicate (equal) elements.Petya wants to leave only the rightmost entry (occurrence) for each element of the array. The relative order of the remaining unique elements should not be changed.", "input_spec": "The first line contains a single integer $$$n$$$ ($$$1 \\le n \\le 50$$$) \u2014 the number of elements in Petya's array. The following line contains a sequence $$$a_1, a_2, \\dots, a_n$$$ ($$$1 \\le a_i \\le 1\\,000$$$) \u2014 the Petya's array.", "output_spec": "In the first line print integer $$$x$$$ \u2014 the number of elements which will be left in Petya's array after he removed the duplicates. In the second line print $$$x$$$ integers separated with a space \u2014 Petya's array after he removed the duplicates. For each unique element only the rightmost entry should be left.", "sample_inputs": ["6\n1 5 5 1 6 1", "5\n2 4 2 4 4", "5\n6 6 6 6 6"], "sample_outputs": ["3\n5 6 1", "2\n2 4", "1\n6"], "notes": "NoteIn the first example you should remove two integers $$$1$$$, which are in the positions $$$1$$$ and $$$4$$$. Also you should remove the integer $$$5$$$, which is in the position $$$2$$$.In the second example you should remove integer $$$2$$$, which is in the position $$$1$$$, and two integers $$$4$$$, which are in the positions $$$2$$$ and $$$4$$$.In the third example you should remove four integers $$$6$$$, which are in the positions $$$1$$$, $$$2$$$, $$$3$$$ and $$$4$$$."}, "src_uid": "1b9d3dfcc2353eac20b84c75c27fab5a"}
{"nl": {"description": "Little Elephant loves magic squares very much.A magic square is a 3\u2009\u00d7\u20093 table, each cell contains some positive integer. At that the sums of integers in all rows, columns and diagonals of the table are equal. The figure below shows the magic square, the sum of integers in all its rows, columns and diagonals equals 15.  The Little Elephant remembered one magic square. He started writing this square on a piece of paper, but as he wrote, he forgot all three elements of the main diagonal of the magic square. Fortunately, the Little Elephant clearly remembered that all elements of the magic square did not exceed 105. Help the Little Elephant, restore the original magic square, given the Elephant's notes.", "input_spec": "The first three lines of the input contain the Little Elephant's notes. The first line contains elements of the first row of the magic square. The second line contains the elements of the second row, the third line is for the third row. The main diagonal elements that have been forgotten by the Elephant are represented by zeroes. It is guaranteed that the notes contain exactly three zeroes and they are all located on the main diagonal. It is guaranteed that all positive numbers in the table do not exceed 105.", "output_spec": "Print three lines, in each line print three integers \u2014 the Little Elephant's magic square. If there are multiple magic squares, you are allowed to print any of them. Note that all numbers you print must be positive and not exceed 105. It is guaranteed that there exists at least one magic square that meets the conditions.", "sample_inputs": ["0 1 1\n1 0 1\n1 1 0", "0 3 6\n5 0 5\n4 7 0"], "sample_outputs": ["1 1 1\n1 1 1\n1 1 1", "6 3 6\n5 5 5\n4 7 4"], "notes": null}, "src_uid": "0c42eafb73d1e30f168958a06a0f9bca"}
{"nl": {"description": "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": "Igor K. always used to trust his favorite Kashpirovsky Antivirus. That is why he didn't hesitate to download the link one of his groupmates sent him via QIP Infinium. The link was said to contain \"some real funny stuff about swine influenza\". The antivirus had no objections and Igor K. run the flash application he had downloaded. Immediately his QIP Infinium said: \"invalid login/password\".Igor K. entered the ISQ from his additional account and looked at the info of his main one. His name and surname changed to \"H1N1\" and \"Infected\" correspondingly, and the \"Additional Information\" field contained a strange-looking binary code 80 characters in length, consisting of zeroes and ones. \"I've been hacked\" \u2014 thought Igor K. and run the Internet Exploiter browser to quickly type his favourite search engine's address.Soon he learned that it really was a virus that changed ISQ users' passwords. Fortunately, he soon found out that the binary code was actually the encrypted password where each group of 10 characters stood for one decimal digit. Accordingly, the original password consisted of 8 decimal digits.Help Igor K. restore his ISQ account by the encrypted password and encryption specification.", "input_spec": "The input data contains 11 lines. The first line represents the binary code 80 characters in length. That is the code written in Igor K.'s ISQ account's info. Next 10 lines contain pairwise distinct binary codes 10 characters in length, corresponding to numbers 0, 1, ..., 9.", "output_spec": "Print one line containing 8 characters \u2014 The password to Igor K.'s ISQ account. It is guaranteed that the solution exists.", "sample_inputs": ["01001100100101100000010110001001011001000101100110010110100001011010100101101100\n0100110000\n0100110010\n0101100000\n0101100010\n0101100100\n0101100110\n0101101000\n0101101010\n0101101100\n0101101110", "10101101111001000010100100011010101101110010110111011000100011011110010110001000\n1001000010\n1101111001\n1001000110\n1010110111\n0010110111\n1101001101\n1011000001\n1110010101\n1011011000\n0110001000"], "sample_outputs": ["12345678", "30234919"], "notes": null}, "src_uid": "0f4f7ca388dd1b2192436c67f9ac74d9"}
{"nl": {"description": "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": "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": "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": "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": "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": " 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": "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": "Pasha has a wooden stick of some positive integer length n. He wants to perform exactly three cuts to get four parts of the stick. Each part must have some positive integer length and the sum of these lengths will obviously be n. Pasha likes rectangles but hates squares, so he wonders, how many ways are there to split a stick into four parts so that it's possible to form a rectangle using these parts, but is impossible to form a square.Your task is to help Pasha and count the number of such ways. Two ways to cut the stick are considered distinct if there exists some integer x, such that the number of parts of length x in the first way differ from the number of parts of length x in the second way.", "input_spec": "The first line of the input contains a positive integer n (1\u2009\u2264\u2009n\u2009\u2264\u20092\u00b7109) \u2014 the length of Pasha's stick.", "output_spec": "The output should contain a single integer\u00a0\u2014 the number of ways to split Pasha's stick into four parts of positive integer length so that it's possible to make a rectangle by connecting the ends of these parts, but is impossible to form a square. ", "sample_inputs": ["6", "20"], "sample_outputs": ["1", "4"], "notes": "NoteThere is only one way to divide the stick in the first sample {1, 1, 2, 2}.Four ways to divide the stick in the second sample are {1, 1, 9, 9}, {2, 2, 8, 8}, {3, 3, 7, 7} and {4, 4, 6, 6}. Note that {5, 5, 5, 5} doesn't work."}, "src_uid": "32b59d23f71800bc29da74a3fe2e2b37"}
{"nl": {"description": "Sarah has always been a lover of nature, and a couple of years ago she saved up enough money to travel the world and explore all the things built by nature over its lifetime on earth. During this time she visited some truly special places which were left untouched for centuries, from watching icebergs in freezing weather to scuba-diving in oceans and admiring the sea life, residing unseen. These experiences were enhanced with breathtaking views built by mountains over time and left there for visitors to see for years on end. Over time, all these expeditions took a toll on Sarah and culminated in her decision to settle down in the suburbs and live a quiet life. However, as Sarah's love for nature never faded, she started growing flowers in her garden in an attempt to stay connected with nature. At the beginning she planted only blue orchids, but over time she started using different flower types to add variety to her collection of flowers. This collection of flowers can be represented as an array of $$$N$$$ flowers and the $$$i$$$-th of them has a type associated with it, denoted as $$$A_i$$$. Each resident, passing by her collection and limited by the width of his view, can only see $$$K$$$ contiguous flowers at each moment in time. To see the whole collection, the resident will look at the first $$$K$$$ contiguous flowers $$$A_1, A_2, ..., A_K$$$, then shift his view by one flower and look at the next section of K contiguous flowers $$$A_2, A_3, ..., A_{K+1}$$$ and so on until they scan the whole collection, ending with section $$$A_{N-K+1}, ..., A_{N-1}, A_N$$$.Each resident determines the beautiness of a section of $$$K$$$ flowers as the number of distinct flower types in that section. Furthermore, the beautiness of the whole collection is calculated by summing the beautiness values of each contiguous section. Formally, beautiness $$$B_i$$$ of a section starting at the $$$i$$$-th position is calculated as $$$B_i = distinct(A_i, A_{i+1}, ..., A_{i+K-1})$$$, and beautiness of the collection $$$B$$$ is calculated as $$$B=B_1 + B_2 + ... + B_{N-K+1}$$$.In addition, as Sarah wants to keep her collection of flowers have a fresh feel, she can also pick two points $$$L$$$ and $$$R$$$, dispose flowers between those two points and plant new flowers, all of them being the same type.You will be given $$$Q$$$ queries and each of those queries will be of the following two types:   You will be given three integers $$$L, R, X$$$ describing that Sarah has planted flowers of type $$$X$$$ between positions $$$L$$$ and $$$R$$$ inclusive. Formally collection is changed such that $$$A[i]=X$$$ for all $$$i$$$ in range $$$[L.. R]$$$.  You will be given integer $$$K$$$, width of the resident's view and you have to determine the beautiness value $$$B$$$ resident has associated with the collection For each query of second type print the result \u2013 beautiness $$$B$$$ of the collection.", "input_spec": "First line contains two integers $$$N$$$ and $$$Q \\;(1 \\leq N, Q \\leq 10^5)\\,$$$ \u2014 number of flowers and the number of queries, respectively. The second line contains $$$N$$$ integers $$$A_1, A_2, ..., A_N\\;(1 \\leq A_i \\leq 10^9)\\,$$$ \u2014 where $$$A_i$$$ represents type of the $$$i$$$-th flower. Each of the next $$$Q$$$ lines describe queries and start with integer $$$T\\in\\{1, 2\\}$$$.    If $$$T = 1$$$, there will be three more integers in the line $$$L, R, X\\;(1 \\leq L, R \\leq N;\\; 1 \\leq X \\leq 10^9)\\,$$$ \u2014 $$$L$$$ and $$$R$$$ describing boundaries and $$$X$$$ describing the flower type  If $$$T = 2$$$, there will be one more integer in the line $$$K\\;(1 \\leq K \\leq N)\\,$$$ \u2014 resident's width of view ", "output_spec": "For each query of the second type print the beautiness $$$B$$$ of the collection.", "sample_inputs": ["5 5\n1 2 3 4 5\n2 3\n1 1 2 5\n2 4\n1 2 4 5\n2 2"], "sample_outputs": ["9\n6\n4"], "notes": "NoteLet's look at the example.Initially the collection is $$$[1, 2, 3, 4, 5]$$$. In the first query $$$K = 3$$$, we consider sections of three flowers with the first being $$$[1, 2, 3]$$$. Since beautiness of the section is the number of distinct flower types in that section, $$$B_1 = 3$$$. Second section is $$$[2, 3, 4]$$$ and $$$B_2 = 3$$$. Third section is $$$[3, 4, 5]$$$ and $$$B_3 = 3$$$, since the flower types are all distinct. The beautiness value resident has associated with the collection is $$$B = B_1 + B_2 + B_3 = 3 + 3 + 3 = 9$$$.After the second query, the collection becomes $$$[5, 5, 3, 4, 5]$$$. For the third query $$$K = 4$$$, so we consider sections of four flowers with the first being $$$[5, 5, 3, 4]$$$. There are three distinct flower types $$$[5, 3, 4]$$$ in this section, so $$$B_1 = 3$$$. Second section $$$[5, 3, 4, 5]$$$ also has $$$3$$$ distinct flower types, so $$$B_2 = 3$$$. The beautiness value resident has associated with the collection is $$$B = B_1 + B_2 = 3 + 3 = 6$$$After the fourth query, the collection becomes $$$[5, 5, 5, 5, 5]$$$.For the fifth query $$$K = 2$$$ and in this case all the four sections are same with each of them being $$$[5, 5]$$$. Beautiness of $$$[5, 5]$$$ is $$$1$$$ since there is only one distinct element in this section $$$[5]$$$. Beautiness of the whole collection is $$$B = B_1 + B_2 + B_3 + B_4 = 1 + 1 + 1 + 1 = 4$$$"}, "src_uid": "ac85e953ff1cce050834f4e793ec1f02"}
{"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": "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": "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": "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": "The main street of Berland is a straight line with n houses built along it (n is an even number). The houses are located at both sides of the street. The houses with odd numbers are at one side of the street and are numbered from 1 to n\u2009-\u20091 in the order from the beginning of the street to the end (in the picture: from left to right). The houses with even numbers are at the other side of the street and are numbered from 2 to n in the order from the end of the street to its beginning (in the picture: from right to left). The corresponding houses with even and odd numbers are strictly opposite each other, that is, house 1 is opposite house n, house 3 is opposite house n\u2009-\u20092, house 5 is opposite house n\u2009-\u20094 and so on.  Vasya needs to get to house number a as quickly as possible. He starts driving from the beginning of the street and drives his car to house a. To get from the beginning of the street to houses number 1 and n, he spends exactly 1 second. He also spends exactly one second to drive the distance between two neighbouring houses. Vasya can park at any side of the road, so the distance between the beginning of the street at the houses that stand opposite one another should be considered the same.Your task is: find the minimum time Vasya needs to reach house a.", "input_spec": "The first line of the input contains two integers, n and a (1\u2009\u2264\u2009a\u2009\u2264\u2009n\u2009\u2264\u2009100\u2009000)\u00a0\u2014 the number of houses on the street and the number of the house that Vasya needs to reach, correspondingly. It is guaranteed that number n is even.", "output_spec": "Print a single integer \u2014 the minimum time Vasya needs to get from the beginning of the street to house a.", "sample_inputs": ["4 2", "8 5"], "sample_outputs": ["2", "3"], "notes": "NoteIn the first sample there are only four houses on the street, two houses at each side. House 2 will be the last at Vasya's right.The second sample corresponds to picture with n\u2009=\u20098. House 5 is the one before last at Vasya's left."}, "src_uid": "aa62dcdc47d0abbba7956284c1561de8"}
{"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": "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": "At the children's festival, children were dancing in a circle. When music stopped playing, the children were still standing in a circle. Then Lena remembered, that her parents gave her a candy box with exactly $$$k$$$ candies \"Wilky\u00a0May\". Lena is not a greedy person, so she decided to present all her candies to her friends in the circle. Lena knows, that some of her friends have a sweet tooth and others do not. Sweet tooth takes out of the box two candies, if the box has at least two candies, and otherwise takes one. The rest of Lena's friends always take exactly one candy from the box.Before starting to give candies, Lena step out of the circle, after that there were exactly $$$n$$$ people remaining there. Lena numbered her friends in a clockwise order with positive integers starting with $$$1$$$ in such a way that index $$$1$$$ was assigned to her best friend Roma.Initially, Lena gave the box to the friend with number $$$l$$$, after that each friend (starting from friend number $$$l$$$) took candies from the box and passed the box to the next friend in clockwise order. The process ended with the friend number $$$r$$$ taking the last candy (or two, who knows) and the empty box. Please note that it is possible that some of Lena's friends took candy from the box several times, that is, the box could have gone several full circles before becoming empty.Lena does not know which of her friends have a sweet tooth, but she is interested in the maximum possible number of friends that can have a sweet tooth. If the situation could not happen, and Lena have been proved wrong in her observations, please tell her about this.", "input_spec": "The only line contains four integers $$$n$$$, $$$l$$$, $$$r$$$ and $$$k$$$ ($$$1 \\le n, k \\le 10^{11}$$$, $$$1 \\le l, r \\le n$$$)\u00a0\u2014 the number of children in the circle, the number of friend, who was given a box with candies, the number of friend, who has taken last candy and the initial number of candies in the box respectively.", "output_spec": "Print exactly one integer\u00a0\u2014 the maximum possible number of sweet tooth among the friends of Lena or \"-1\" (quotes for clarity), if Lena is wrong.", "sample_inputs": ["4 1 4 12", "5 3 4 10", "10 5 5 1", "5 4 5 6"], "sample_outputs": ["2", "3", "10", "-1"], "notes": "NoteIn the first example, any two friends can be sweet tooths, this way each person will receive the box with candies twice and the last person to take sweets will be the fourth friend.In the second example, sweet tooths can be any three friends, except for the friend on the third position.In the third example, only one friend will take candy, but he can still be a sweet tooth, but just not being able to take two candies. All other friends in the circle can be sweet tooths as well, they just will not be able to take a candy even once.In the fourth example, Lena is wrong and this situation couldn't happen."}, "src_uid": "f54cc281033591315b037a400044f1cb"}
{"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": "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": "Ania has a large integer $$$S$$$. Its decimal representation has length $$$n$$$ and doesn't contain any leading zeroes. Ania is allowed to change at most $$$k$$$ digits of $$$S$$$. She wants to do it in such a way that $$$S$$$ still won't contain any leading zeroes and it'll be minimal possible. What integer will Ania finish with?", "input_spec": "The first line contains two integers $$$n$$$ and $$$k$$$ ($$$1 \\leq n \\leq 200\\,000$$$, $$$0 \\leq k \\leq n$$$) \u2014 the number of digits in the decimal representation of $$$S$$$ and the maximum allowed number of changed digits. The second line contains the integer $$$S$$$. It's guaranteed that $$$S$$$ has exactly $$$n$$$ digits and doesn't contain any leading zeroes.", "output_spec": "Output the minimal possible value of $$$S$$$ which Ania can end with. Note that the resulting integer should also have $$$n$$$ digits.", "sample_inputs": ["5 3\n51528", "3 2\n102", "1 1\n1"], "sample_outputs": ["10028", "100", "0"], "notes": "NoteA number has leading zeroes if it consists of at least two digits and its first digit is $$$0$$$. For example, numbers $$$00$$$, $$$00069$$$ and $$$0101$$$ have leading zeroes, while $$$0$$$, $$$3000$$$ and $$$1010$$$ don't have leading zeroes."}, "src_uid": "0515ac888937a4dda30cad5e2383164f"}
{"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": "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": "The last stage of Football World Cup is played using the play-off system.There are n teams left in this stage, they are enumerated from 1 to n. Several rounds are held, in each round the remaining teams are sorted in the order of their ids, then the first in this order plays with the second, the third\u00a0\u2014 with the fourth, the fifth\u00a0\u2014 with the sixth, and so on. It is guaranteed that in each round there is even number of teams. The winner of each game advances to the next round, the loser is eliminated from the tournament, there are no draws. In the last round there is the only game with two remaining teams: the round is called the Final, the winner is called the champion, and the tournament is over.Arkady wants his two favorite teams to play in the Final. Unfortunately, the team ids are already determined, and it may happen that it is impossible for teams to meet in the Final, because they are to meet in some earlier stage, if they are strong enough. Determine, in which round the teams with ids a and b can meet.", "input_spec": "The only line contains three integers n, a and b (2\u2009\u2264\u2009n\u2009\u2264\u2009256, 1\u2009\u2264\u2009a,\u2009b\u2009\u2264\u2009n)\u00a0\u2014 the total number of teams, and the ids of the teams that Arkady is interested in.  It is guaranteed that n is such that in each round an even number of team advance, and that a and b are not equal.", "output_spec": "In the only line print \"Final!\" (without quotes), if teams a and b can meet in the Final. Otherwise, print a single integer\u00a0\u2014 the number of the round in which teams a and b can meet. The round are enumerated from 1.", "sample_inputs": ["4 1 2", "8 2 6", "8 7 5"], "sample_outputs": ["1", "Final!", "2"], "notes": "NoteIn the first example teams 1 and 2 meet in the first round.In the second example teams 2 and 6 can only meet in the third round, which is the Final, if they win all their opponents in earlier rounds.In the third example the teams with ids 7 and 5 can meet in the second round, if they win their opponents in the first round."}, "src_uid": "a753bfa7bde157e108f34a28240f441f"}
{"nl": {"description": "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": "Your task is the exact same as for the easy version. But this time, the marmots subtract the village's population P from their random number before responding to Heidi's request.Also, there are now villages with as few as a single inhabitant, meaning that .Can you help Heidi find out whether a village follows a Poisson or a uniform distribution?", "input_spec": "Same as for the easy and medium versions. But remember that now 1\u2009\u2264\u2009P\u2009\u2264\u20091000 and that the marmots may provide positive as well as negative integers.", "output_spec": "Output one line per village, in the same order as provided in the input. The village's line shall state poisson if the village's distribution is of the Poisson type, and uniform if the answers came from a uniform distribution.", "sample_inputs": [], "sample_outputs": [], "notes": null}, "src_uid": "6ef75e501b318c0799d3cbe8ca998984"}
{"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": "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": "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": "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": "There are two sisters Alice and Betty. You have $$$n$$$ candies. You want to distribute these $$$n$$$ candies between two sisters in such a way that:  Alice will get $$$a$$$ ($$$a > 0$$$) candies;  Betty will get $$$b$$$ ($$$b > 0$$$) candies;  each sister will get some integer number of candies;  Alice will get a greater amount of candies than Betty (i.e. $$$a > b$$$);  all the candies will be given to one of two sisters (i.e. $$$a+b=n$$$). Your task is to calculate the number of ways to distribute exactly $$$n$$$ candies between sisters in a way described above. Candies are indistinguishable.Formally, find the number of ways to represent $$$n$$$ as the sum of $$$n=a+b$$$, where $$$a$$$ and $$$b$$$ are positive integers and $$$a>b$$$.You have to answer $$$t$$$ independent test cases.", "input_spec": "The first line of the input contains one integer $$$t$$$ ($$$1 \\le t \\le 10^4$$$) \u2014 the number of test cases. Then $$$t$$$ test cases follow. The only line of a test case contains one integer $$$n$$$ ($$$1 \\le n \\le 2 \\cdot 10^9$$$) \u2014 the number of candies you have.", "output_spec": "For each test case, print the answer \u2014 the number of ways to distribute exactly $$$n$$$ candies between two sisters in a way described in the problem statement. If there is no way to satisfy all the conditions, print $$$0$$$.", "sample_inputs": ["6\n7\n1\n2\n3\n2000000000\n763243547"], "sample_outputs": ["3\n0\n0\n1\n999999999\n381621773"], "notes": "NoteFor the test case of the example, the $$$3$$$ possible ways to distribute candies are:  $$$a=6$$$, $$$b=1$$$;  $$$a=5$$$, $$$b=2$$$;  $$$a=4$$$, $$$b=3$$$. "}, "src_uid": "b69170c8377623beb66db4706a02ffc6"}
{"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": "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": "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": "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": "Polycarp takes part in a quadcopter competition. According to the rules a flying robot should:  start the race from some point of a field,  go around the flag,  close cycle returning back to the starting point. Polycarp knows the coordinates of the starting point (x1,\u2009y1) and the coordinates of the point where the flag is situated (x2,\u2009y2). Polycarp\u2019s quadcopter can fly only parallel to the sides of the field each tick changing exactly one coordinate by 1. It means that in one tick the quadcopter can fly from the point (x,\u2009y) to any of four points: (x\u2009-\u20091,\u2009y), (x\u2009+\u20091,\u2009y), (x,\u2009y\u2009-\u20091) or (x,\u2009y\u2009+\u20091).Thus the quadcopter path is a closed cycle starting and finishing in (x1,\u2009y1) and containing the point (x2,\u2009y2) strictly inside.    The picture corresponds to the first example: the starting (and finishing) point is in (1,\u20095) and the flag is in (5,\u20092). What is the minimal length of the quadcopter path?", "input_spec": "The first line contains two integer numbers x1 and y1 (\u2009-\u2009100\u2009\u2264\u2009x1,\u2009y1\u2009\u2264\u2009100) \u2014 coordinates of the quadcopter starting (and finishing) point. The second line contains two integer numbers x2 and y2 (\u2009-\u2009100\u2009\u2264\u2009x2,\u2009y2\u2009\u2264\u2009100) \u2014 coordinates of the flag. It is guaranteed that the quadcopter starting point and the flag do not coincide.", "output_spec": "Print the length of minimal path of the quadcopter to surround the flag and return back.", "sample_inputs": ["1 5\n5 2", "0 1\n0 0"], "sample_outputs": ["18", "8"], "notes": null}, "src_uid": "f54ce13fb92e51ebd5e82ffbdd1acbed"}
{"nl": {"description": "Petya and Vasya decided to play a game. They have n cards (n is an even number). A single integer is written on each card.Before the game Petya will choose an integer and after that Vasya will choose another integer (different from the number that Petya chose). During the game each player takes all the cards with number he chose. For example, if Petya chose number 5 before the game he will take all cards on which 5 is written and if Vasya chose number 10 before the game he will take all cards on which 10 is written.The game is considered fair if Petya and Vasya can take all n cards, and the number of cards each player gets is the same.Determine whether Petya and Vasya can choose integer numbers before the game so that the game is fair. ", "input_spec": "The first line contains a single integer n (2\u2009\u2264\u2009n\u2009\u2264\u2009100) \u2014 number of cards. It is guaranteed that n is an even number. The following n lines contain a sequence of integers a1,\u2009a2,\u2009...,\u2009an (one integer per line, 1\u2009\u2264\u2009ai\u2009\u2264\u2009100) \u2014 numbers written on the n cards.", "output_spec": "If it is impossible for Petya and Vasya to choose numbers in such a way that the game will be fair, print \"NO\" (without quotes) in the first line. In this case you should not print anything more. In the other case print \"YES\" (without quotes) in the first line. In the second line print two distinct integers \u2014 number that Petya should choose and the number that Vasya should choose to make the game fair. If there are several solutions, print any of them.", "sample_inputs": ["4\n11\n27\n27\n11", "2\n6\n6", "6\n10\n20\n30\n20\n10\n20", "6\n1\n1\n2\n2\n3\n3"], "sample_outputs": ["YES\n11 27", "NO", "NO", "NO"], "notes": "NoteIn the first example the game will be fair if, for example, Petya chooses number 11, and Vasya chooses number 27. Then the will take all cards \u2014 Petya will take cards 1 and 4, and Vasya will take cards 2 and 3. Thus, each of them will take exactly two cards.In the second example fair game is impossible because the numbers written on the cards are equal, but the numbers that Petya and Vasya should choose should be distinct.In the third example it is impossible to take all cards. Petya and Vasya can take at most five cards \u2014 for example, Petya can choose number 10 and Vasya can choose number 20. But for the game to be fair it is necessary to take 6 cards."}, "src_uid": "2860b4fb22402ea9574c2f9e403d63d8"}
{"nl": {"description": "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": "There are r red and g green blocks for construction of the red-green tower. Red-green tower can be built following next rules:  Red-green tower is consisting of some number of levels;  Let the red-green tower consist of n levels, then the first level of this tower should consist of n blocks, second level \u2014 of n\u2009-\u20091 blocks, the third one \u2014 of n\u2009-\u20092 blocks, and so on \u2014 the last level of such tower should consist of the one block. In other words, each successive level should contain one block less than the previous one;  Each level of the red-green tower should contain blocks of the same color.  Let h be the maximum possible number of levels of red-green tower, that can be built out of r red and g green blocks meeting the rules above. The task is to determine how many different red-green towers having h levels can be built out of the available blocks.Two red-green towers are considered different if there exists some level, that consists of red blocks in the one tower and consists of green blocks in the other tower.You are to write a program that will find the number of different red-green towers of height h modulo\u00a0109\u2009+\u20097.", "input_spec": "The only line of input contains two integers r and g, separated by a single space \u2014 the number of available red and green blocks respectively (0\u2009\u2264\u2009r,\u2009g\u2009\u2264\u20092\u00b7105, r\u2009+\u2009g\u2009\u2265\u20091).", "output_spec": "Output the only integer \u2014 the number of different possible red-green towers of height h modulo\u00a0109\u2009+\u20097.", "sample_inputs": ["4 6", "9 7", "1 1"], "sample_outputs": ["2", "6", "2"], "notes": "NoteThe image in the problem statement shows all possible red-green towers for the first sample."}, "src_uid": "34b6286350e3531c1fbda6b0c184addc"}
{"nl": {"description": "Recently, Berland faces federalization requests more and more often. The proponents propose to divide the country into separate states. Moreover, they demand that there is a state which includes exactly k towns.Currently, Berland has n towns, some pairs of them are connected by bilateral roads. Berland has only n\u2009-\u20091 roads. You can reach any city from the capital, that is, the road network forms a tree.The Ministry of Roads fears that after the reform those roads that will connect the towns of different states will bring a lot of trouble.Your task is to come up with a plan to divide the country into states such that:  each state is connected, i.e. for each state it is possible to get from any town to any other using its roads (that is, the roads that connect the state towns),  there is a state that consisted of exactly k cities,  the number of roads that connect different states is minimum. ", "input_spec": "The first line contains integers n, k (1\u2009\u2264\u2009k\u2009\u2264\u2009n\u2009\u2264\u2009400). Then follow n\u2009-\u20091 lines, each of them describes a road in Berland. The roads are given as pairs of integers xi,\u2009yi (1\u2009\u2264\u2009xi,\u2009yi\u2009\u2264\u2009n;\u00a0xi\u2009\u2260\u2009yi) \u2014 the numbers of towns connected by the road. Assume that the towns are numbered from 1 to n.", "output_spec": "The the first line print the required minimum number of \"problem\" roads t. Then print a sequence of t integers \u2014 their indices in the found division. The roads are numbered starting from 1 in the order they follow in the input. If there are multiple possible solutions, print any of them. If the solution shows that there are no \"problem\" roads at all, print a single integer 0 and either leave the second line empty or do not print it at all.", "sample_inputs": ["5 2\n1 2\n2 3\n3 4\n4 5", "5 3\n1 2\n1 3\n1 4\n1 5", "1 1"], "sample_outputs": ["1\n2", "2\n3 4", "0"], "notes": null}, "src_uid": "56168b28f9ab4830b3d3c5eeb7fc0d3c"}
{"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": "For an array of integers $$$a$$$, let's define $$$|a|$$$ as the number of elements in it.Let's denote two functions: $$$F(a, k)$$$ is a function that takes an array of integers $$$a$$$ and a positive integer $$$k$$$. The result of this function is the array containing $$$|a|$$$ first elements of the array that you get by replacing each element of $$$a$$$ with exactly $$$k$$$ copies of that element.For example, $$$F([2, 2, 1, 3, 5, 6, 8], 2)$$$ is calculated as follows: first, you replace each element of the array with $$$2$$$ copies of it, so you obtain $$$[2, 2, 2, 2, 1, 1, 3, 3, 5, 5, 6, 6, 8, 8]$$$. Then, you take the first $$$7$$$ elements of the array you obtained, so the result of the function is $$$[2, 2, 2, 2, 1, 1, 3]$$$. $$$G(a, x, y)$$$ is a function that takes an array of integers $$$a$$$ and two different integers $$$x$$$ and $$$y$$$. The result of this function is the array $$$a$$$ with every element equal to $$$x$$$ replaced by $$$y$$$, and every element equal to $$$y$$$ replaced by $$$x$$$.For example, $$$G([1, 1, 2, 3, 5], 3, 1) = [3, 3, 2, 1, 5]$$$.An array $$$a$$$ is a parent of the array $$$b$$$ if:  either there exists a positive integer $$$k$$$ such that $$$F(a, k) = b$$$;  or there exist two different integers $$$x$$$ and $$$y$$$ such that $$$G(a, x, y) = b$$$. An array $$$a$$$ is an ancestor of the array $$$b$$$ if there exists a finite sequence of arrays $$$c_0, c_1, \\dots, c_m$$$ ($$$m \\ge 0$$$) such that $$$c_0$$$ is $$$a$$$, $$$c_m$$$ is $$$b$$$, and for every $$$i \\in [1, m]$$$, $$$c_{i-1}$$$ is a parent of $$$c_i$$$.And now, the problem itself.You are given two integers $$$n$$$ and $$$k$$$. Your goal is to construct a sequence of arrays $$$s_1, s_2, \\dots, s_m$$$ in such a way that:  every array $$$s_i$$$ contains exactly $$$n$$$ elements, and all elements are integers from $$$1$$$ to $$$k$$$;  for every array $$$a$$$ consisting of exactly $$$n$$$ integers from $$$1$$$ to $$$k$$$, the sequence contains at least one array $$$s_i$$$ such that $$$s_i$$$ is an ancestor of $$$a$$$. Print the minimum number of arrays in such sequence.", "input_spec": "The only line contains two integers $$$n$$$ and $$$k$$$ ($$$1 \\le n, k \\le 2 \\cdot 10^5$$$).", "output_spec": "Print one integer \u2014 the minimum number of elements in a sequence of arrays meeting the constraints. Since the answer can be large, output it modulo $$$998244353$$$.", "sample_inputs": ["3 2", "4 10", "13 37", "1337 42", "198756 123456", "123456 198756"], "sample_outputs": ["2", "12", "27643508", "211887828", "159489391", "460526614"], "notes": "NoteLet's analyze the first example.One of the possible answers for the first example is the sequence $$$[[2, 1, 2], [1, 2, 2]]$$$. Every array of size $$$3$$$ consisting of elements from $$$1$$$ to $$$2$$$ has an ancestor in this sequence:  for the array $$$[1, 1, 1]$$$, the ancestor is $$$[1, 2, 2]$$$: $$$F([1, 2, 2], 13) = [1, 1, 1]$$$;  for the array $$$[1, 1, 2]$$$, the ancestor is $$$[1, 2, 2]$$$: $$$F([1, 2, 2], 2) = [1, 1, 2]$$$;  for the array $$$[1, 2, 1]$$$, the ancestor is $$$[2, 1, 2]$$$: $$$G([2, 1, 2], 1, 2) = [1, 2, 1]$$$;  for the array $$$[1, 2, 2]$$$, the ancestor is $$$[1, 2, 2]$$$;  for the array $$$[2, 1, 1]$$$, the ancestor is $$$[1, 2, 2]$$$: $$$G([1, 2, 2], 1, 2) = [2, 1, 1]$$$;  for the array $$$[2, 1, 2]$$$, the ancestor is $$$[2, 1, 2]$$$;  for the array $$$[2, 2, 1]$$$, the ancestor is $$$[2, 1, 2]$$$: $$$F([2, 1, 2], 2) = [2, 2, 1]$$$;  for the array $$$[2, 2, 2]$$$, the ancestor is $$$[1, 2, 2]$$$: $$$G(F([1, 2, 2], 4), 1, 2) = G([1, 1, 1], 1, 2) = [2, 2, 2]$$$. "}, "src_uid": "eb9d24070cc5b347d020189d803628ae"}
{"nl": {"description": "Your security guard friend recently got a new job at a new security company. The company requires him to patrol an area of the city encompassing exactly N city blocks, but they let him choose which blocks. That is, your friend must walk the perimeter of a region whose area is exactly N blocks. Your friend is quite lazy and would like your help to find the shortest possible route that meets the requirements. The city is laid out in a square grid pattern, and is large enough that for the sake of the problem it can be considered infinite.", "input_spec": "Input will consist of a single integer N (1\u2009\u2264\u2009N\u2009\u2264\u2009106), the number of city blocks that must be enclosed by the route.", "output_spec": "Print the minimum perimeter that can be achieved.", "sample_inputs": ["4", "11", "22"], "sample_outputs": ["8", "14", "20"], "notes": "NoteHere are some possible shapes for the examples:"}, "src_uid": "414cc57550e31d98c1a6a56be6722a12"}
{"nl": {"description": "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": "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": "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 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": "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": "Several months later Alex finally got his brother Bob's creation by post. And now, in his turn, Alex wants to boast about something to his brother. He thought for a while, and came to the conclusion that he has no ready creations, and decided to write a program for rectangles detection. According to his plan, the program detects if the four given segments form a rectangle of a positive area and with sides parallel to coordinate axes. As Alex does badly at school and can't write this program by himself, he asks you to help him.", "input_spec": "The input data contain four lines. Each of these lines contains four integers x1, y1, x2, y2 (\u2009-\u2009109\u2009\u2264\u2009x1,\u2009y1,\u2009x2,\u2009y2\u2009\u2264\u2009109) \u2014 coordinates of segment's beginning and end positions. The given segments can degenerate into points.", "output_spec": "Output the word \u00abYES\u00bb, if the given four segments form the required rectangle, otherwise output \u00abNO\u00bb.", "sample_inputs": ["1 1 6 1\n1 0 6 0\n6 0 6 1\n1 1 1 0", "0 0 0 3\n2 0 0 0\n2 2 2 0\n0 2 2 2"], "sample_outputs": ["YES", "NO"], "notes": null}, "src_uid": "ad105c08f63e9761fe90f69630628027"}
{"nl": {"description": "This is the easy version of the problem. The only difference is that in this version $$$q=1$$$. You can make hacks only if all versions of the problem are solved.Zookeeper has been teaching his $$$q$$$ sheep how to write and how to add. The $$$i$$$-th sheep has to write exactly $$$k$$$ non-negative integers with the sum $$$n_i$$$.Strangely, sheep have superstitions about digits and believe that the digits $$$3$$$, $$$6$$$, and $$$9$$$ are lucky. To them, the fortune of a number depends on the decimal representation of the number; the fortune of a number is equal to the sum of fortunes of its digits, and the fortune of a digit depends on its value and position and can be described by the following table. For example, the number $$$319$$$ has fortune $$$F_{2} + 3F_{0}$$$.   Each sheep wants to maximize the sum of fortune among all its $$$k$$$ written integers. Can you help them?", "input_spec": "The first line contains a single integer $$$k$$$ ($$$1 \\leq k \\leq 999999$$$): the number of numbers each sheep has to write.   The next line contains six integers $$$F_0$$$, $$$F_1$$$, $$$F_2$$$, $$$F_3$$$, $$$F_4$$$, $$$F_5$$$ ($$$1 \\leq F_i \\leq 10^9$$$): the fortune assigned to each digit.   The next line contains a single integer $$$q$$$ ($$$q = 1$$$): the number of sheep. Each of the next $$$q$$$ lines contains a single integer $$$n_i$$$ ($$$1 \\leq n_i \\leq 999999$$$): the sum of numbers that $$$i$$$-th sheep has to write. In this version, there is only one line.", "output_spec": "Print $$$q$$$ lines, where the $$$i$$$-th line contains the maximum sum of fortune of all numbers of the $$$i$$$-th sheep. In this version, you should print only one line.", "sample_inputs": ["3\n1 2 3 4 5 6\n1\n57", "3\n1 2 3 4 5 6\n1\n63"], "sample_outputs": ["11", "8"], "notes": "NoteIn the first test case, $$$57 = 9 + 9 + 39$$$. The three $$$9$$$'s contribute $$$1 \\cdot 3$$$ and $$$3$$$ at the tens position contributes $$$2 \\cdot 1$$$. Hence the sum of fortune is $$$11$$$.In the second test case, $$$63 = 35 + 19 + 9$$$. The sum of fortune is $$$8$$$."}, "src_uid": "92bcbac3f167a44c235e99afc4de20d2"}
{"nl": {"description": "You are given an array of $$$n$$$ integers: $$$a_1, a_2, \\ldots, a_n$$$. Your task is to find some non-zero integer $$$d$$$ ($$$-10^3 \\leq d \\leq 10^3$$$) such that, after each number in the array is divided by $$$d$$$, the number of positive numbers that are presented in the array is greater than or equal to half of the array size (i.e., at least $$$\\lceil\\frac{n}{2}\\rceil$$$). Note that those positive numbers do not need to be an integer (e.g., a $$$2.5$$$ counts as a positive number). If there are multiple values of $$$d$$$ that satisfy the condition, you may print any of them. In case that there is no such $$$d$$$, print a single integer $$$0$$$.Recall that $$$\\lceil x \\rceil$$$ represents the smallest integer that is not less than $$$x$$$ and that zero ($$$0$$$) is neither positive nor negative.", "input_spec": "The first line contains one integer $$$n$$$ ($$$1 \\le n \\le 100$$$)\u00a0\u2014 the number of elements in the array. The second line contains $$$n$$$ space-separated integers $$$a_1, a_2, \\ldots, a_n$$$ ($$$-10^3 \\le a_i \\le 10^3$$$).", "output_spec": "Print one integer $$$d$$$ ($$$-10^3 \\leq d \\leq 10^3$$$ and $$$d \\neq 0$$$) that satisfies the given condition. If there are multiple values of $$$d$$$ that satisfy the condition, you may print any of them. In case that there is no such $$$d$$$, print a single integer $$$0$$$.", "sample_inputs": ["5\n10 0 -7 2 6", "7\n0 0 1 -1 0 0 2"], "sample_outputs": ["4", "0"], "notes": "NoteIn the first sample, $$$n = 5$$$, so we need at least $$$\\lceil\\frac{5}{2}\\rceil = 3$$$ positive numbers after division. If $$$d = 4$$$, the array after division is $$$[2.5, 0, -1.75, 0.5, 1.5]$$$, in which there are $$$3$$$ positive numbers (namely: $$$2.5$$$, $$$0.5$$$, and $$$1.5$$$).In the second sample, there is no valid $$$d$$$, so $$$0$$$ should be printed."}, "src_uid": "a13cb35197f896cd34614c6c0b369a49"}
{"nl": {"description": "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": "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": "Consider the following equation:  where sign [a] represents the integer part of number a.Let's find all integer z (z\u2009>\u20090), for which this equation is unsolvable in positive integers. The phrase \"unsolvable in positive integers\" means that there are no such positive integers x and y (x,\u2009y\u2009>\u20090), for which the given above equation holds.Let's write out all such z in the increasing order: z1,\u2009z2,\u2009z3, and so on (zi\u2009<\u2009zi\u2009+\u20091). Your task is: given the number n, find the number zn.", "input_spec": "The first line contains a single integer n (1\u2009\u2264\u2009n\u2009\u2264\u200940).", "output_spec": "Print a single integer \u2014 the number zn modulo 1000000007 (109\u2009+\u20097). It is guaranteed that the answer exists.", "sample_inputs": ["1", "2", "3"], "sample_outputs": ["1", "3", "15"], "notes": null}, "src_uid": "c2cbc35012c6ff7ab0d6899e6015e4e7"}
{"nl": {"description": "Kyoya Ootori is selling photobooks of the Ouran High School Host Club. He has 26 photos, labeled \"a\" to \"z\", and he has compiled them into a photo booklet with some photos in some order (possibly with some photos being duplicated). A photo booklet can be described as a string of lowercase letters, consisting of the photos in the booklet in order. He now wants to sell some \"special edition\" photobooks, each with one extra photo inserted anywhere in the book. He wants to make as many distinct photobooks as possible, so he can make more money. He asks Haruhi, how many distinct photobooks can he make by inserting one extra photo into the photobook he already has?Please help Haruhi solve this problem.", "input_spec": "The first line of input will be a single string s (1\u2009\u2264\u2009|s|\u2009\u2264\u200920). String s consists only of lowercase English letters. ", "output_spec": "Output a single integer equal to the number of distinct photobooks Kyoya Ootori can make.", "sample_inputs": ["a", "hi"], "sample_outputs": ["51", "76"], "notes": "NoteIn the first case, we can make 'ab','ac',...,'az','ba','ca',...,'za', and 'aa', producing a total of 51 distinct photo booklets. "}, "src_uid": "556684d96d78264ad07c0cdd3b784bc9"}
{"nl": {"description": "A string a of length m is called antipalindromic iff m is even, and for each i (1\u2009\u2264\u2009i\u2009\u2264\u2009m) ai\u2009\u2260\u2009am\u2009-\u2009i\u2009+\u20091.Ivan has a string s consisting of n lowercase Latin letters; n is even. He wants to form some string t that will be an antipalindromic permutation of s. Also Ivan has denoted the beauty of index i as bi, and the beauty of t as the sum of bi among all indices i such that si\u2009=\u2009ti.Help Ivan to determine maximum possible beauty of t he can get.", "input_spec": "The first line contains one integer n (2\u2009\u2264\u2009n\u2009\u2264\u2009100, n is even) \u2014 the number of characters in s. The second line contains the string s itself. It consists of only lowercase Latin letters, and it is guaranteed that its letters can be reordered to form an antipalindromic string. The third line contains n integer numbers b1, b2, ..., bn (1\u2009\u2264\u2009bi\u2009\u2264\u2009100), where bi is the beauty of index i.", "output_spec": "Print one number \u2014 the maximum possible beauty of t.", "sample_inputs": ["8\nabacabac\n1 1 1 1 1 1 1 1", "8\nabaccaba\n1 2 3 4 5 6 7 8", "8\nabacabca\n1 2 3 4 4 3 2 1"], "sample_outputs": ["8", "26", "17"], "notes": null}, "src_uid": "896555ddb6e1c268cd7b3b6b063fce50"}
{"nl": {"description": "This is the easy version of the problem. The difference between the versions is in the constraints on the array elements. You can make hacks only if all versions of the problem are solved.You are given an array $$$[a_1, a_2, \\dots, a_n]$$$. Your goal is to find the length of the longest subarray of this array such that the most frequent value in it is not unique. In other words, you are looking for a subarray such that if the most frequent value occurs $$$f$$$ times in this subarray, then at least $$$2$$$ different values should occur exactly $$$f$$$ times.An array $$$c$$$ is a subarray of an array $$$d$$$ if $$$c$$$ can be obtained from $$$d$$$ by deletion of several (possibly, zero or all) elements from the beginning and several (possibly, zero or all) elements from the end.", "input_spec": "The first line contains a single integer $$$n$$$ ($$$1 \\le n \\le 200\\,000$$$)\u00a0\u2014 the length of the array. The second line contains $$$n$$$ integers $$$a_1, a_2, \\ldots, a_n$$$ ($$$1 \\le a_i \\le min(n, 100)$$$)\u00a0\u2014 elements of the array.", "output_spec": "You should output exactly one integer \u00a0\u2014 the length of the longest subarray of the array whose most frequent value is not unique. If there is no such subarray, output $$$0$$$.", "sample_inputs": ["7\n1 1 2 2 3 3 3", "10\n1 1 1 5 4 1 3 1 2 2", "1\n1"], "sample_outputs": ["6", "7", "0"], "notes": "NoteIn the first sample, the subarray $$$[1, 1, 2, 2, 3, 3]$$$ is good, but $$$[1, 1, 2, 2, 3, 3, 3]$$$ isn't: in the latter there are $$$3$$$ occurrences of number $$$3$$$, and no other element appears $$$3$$$ times."}, "src_uid": "a06ebb2734365ec97d07cd1b6b3faeed"}
{"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": "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": "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": "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": "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": "Consider the following experiment. You have a deck of $$$m$$$ cards, and exactly one card is a joker. $$$n$$$ times, you do the following: shuffle the deck, take the top card of the deck, look at it and return it into the deck.Let $$$x$$$ be the number of times you have taken the joker out of the deck during this experiment. Assuming that every time you shuffle the deck, all $$$m!$$$ possible permutations of cards are equiprobable, what is the expected value of $$$x^k$$$? Print the answer modulo $$$998244353$$$.", "input_spec": "The only line contains three integers $$$n$$$, $$$m$$$ and $$$k$$$ ($$$1 \\le n, m < 998244353$$$, $$$1 \\le k \\le 5000$$$).", "output_spec": "Print one integer \u2014 the expected value of $$$x^k$$$, taken modulo $$$998244353$$$ (the answer can always be represented as an irreducible fraction $$$\\frac{a}{b}$$$, where $$$b \\mod 998244353 \\ne 0$$$; you have to print $$$a \\cdot b^{-1} \\mod 998244353$$$).", "sample_inputs": ["1 1 1", "1 1 5000", "2 2 2", "998244352 1337 5000"], "sample_outputs": ["1", "1", "499122178", "326459680"], "notes": null}, "src_uid": "e6b3e559b5fd4e05adf9f1cd1b22126b"}
{"nl": {"description": "The Cybermen and the Daleks have long been the Doctor's main enemies. Everyone knows that both these species enjoy destroying everything they encounter. However, a little-known fact about them is that they both also love taking Turing tests!Heidi designed a series of increasingly difficult tasks for them to spend their time on, which would allow the Doctor enough time to save innocent lives!The funny part is that these tasks would be very easy for a human to solve.The first task is as follows. There are some points on the plane. All but one of them are on the boundary of an axis-aligned square (its sides are parallel to the axes). Identify that point.", "input_spec": "The first line contains an integer $$$n$$$ ($$$2 \\le n \\le 10$$$). Each of the following $$$4n + 1$$$ lines contains two integers $$$x_i, y_i$$$ ($$$0 \\leq x_i, y_i \\leq 50$$$), describing the coordinates of the next point. It is guaranteed that there are at least $$$n$$$ points on each side of the square and all $$$4n + 1$$$ points are distinct.", "output_spec": "Print two integers\u00a0\u2014 the coordinates of the point that is not on the boundary of the square.", "sample_inputs": ["2\n0 0\n0 1\n0 2\n1 0\n1 1\n1 2\n2 0\n2 1\n2 2", "2\n0 0\n0 1\n0 2\n0 3\n1 0\n1 2\n2 0\n2 1\n2 2"], "sample_outputs": ["1 1", "0 3"], "notes": "NoteIn both examples, the square has four sides $$$x=0$$$, $$$x=2$$$, $$$y=0$$$, $$$y=2$$$."}, "src_uid": "1f9153088dcba9383b1a2dbe592e4d06"}
{"nl": {"description": "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": "Polycarp urgently needs a shovel! He comes to the shop and chooses an appropriate one. The shovel that Policarp chooses is sold for k burles. Assume that there is an unlimited number of such shovels in the shop.In his pocket Polycarp has an unlimited number of \"10-burle coins\" and exactly one coin of r burles (1\u2009\u2264\u2009r\u2009\u2264\u20099).What is the minimum number of shovels Polycarp has to buy so that he can pay for the purchase without any change? It is obvious that he can pay for 10 shovels without any change (by paying the requied amount of 10-burle coins and not using the coin of r burles). But perhaps he can buy fewer shovels and pay without any change. Note that Polycarp should buy at least one shovel.", "input_spec": "The single line of input contains two integers k and r (1\u2009\u2264\u2009k\u2009\u2264\u20091000, 1\u2009\u2264\u2009r\u2009\u2264\u20099)\u00a0\u2014 the price of one shovel and the denomination of the coin in Polycarp's pocket that is different from \"10-burle coins\".  Remember that he has an unlimited number of coins in the denomination of 10, that is, Polycarp has enough money to buy any number of shovels.", "output_spec": "Print the required minimum number of shovels Polycarp has to buy so that he can pay for them without any change. ", "sample_inputs": ["117 3", "237 7", "15 2"], "sample_outputs": ["9", "1", "2"], "notes": "NoteIn the first example Polycarp can buy 9 shovels and pay 9\u00b7117\u2009=\u20091053 burles. Indeed, he can pay this sum by using 10-burle coins and one 3-burle coin. He can't buy fewer shovels without any change.In the second example it is enough for Polycarp to buy one shovel.In the third example Polycarp should buy two shovels and pay 2\u00b715\u2009=\u200930 burles. It is obvious that he can pay this sum without any change. "}, "src_uid": "18cd1cd809df4744bb7bcd7cad94e2d3"}
{"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": "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": "A chainword is a special type of crossword. As most of the crosswords do, it has cells that you put the letters in and some sort of hints to what these letters should be.The letter cells in a chainword are put in a single row. We will consider chainwords of length $$$m$$$ in this task.A hint to a chainword is a sequence of segments such that the segments don't intersect with each other and cover all $$$m$$$ letter cells. Each segment contains a description of the word in the corresponding cells.The twist is that there are actually two hints: one sequence is the row above the letter cells and the other sequence is the row below the letter cells. When the sequences are different, they provide a way to resolve the ambiguity in the answers.You are provided with a dictionary of $$$n$$$ words, each word consists of lowercase Latin letters. All words are pairwise distinct.An instance of a chainword is the following triple:   a string of $$$m$$$ lowercase Latin letters;  the first hint: a sequence of segments such that the letters that correspond to each segment spell a word from the dictionary;  the second hint: another sequence of segments such that the letters that correspond to each segment spell a word from the dictionary. Note that the sequences of segments don't necessarily have to be distinct.Two instances of chainwords are considered different if they have different strings, different first hints or different second hints.Count the number of different instances of chainwords. Since the number might be pretty large, output it modulo $$$998\\,244\\,353$$$.", "input_spec": "The first line contains two integers $$$n$$$ and $$$m$$$ ($$$1 \\le n \\le 8$$$, $$$1 \\le m \\le 10^9$$$)\u00a0\u2014 the number of words in the dictionary and the number of letter cells. Each of the next $$$n$$$ lines contains a word\u00a0\u2014 a non-empty string of no more than $$$5$$$ lowercase Latin letters. All words are pairwise distinct. ", "output_spec": "Print a single integer\u00a0\u2014 the number of different instances of chainwords of length $$$m$$$ for the given dictionary modulo $$$998\\,244\\,353$$$.", "sample_inputs": ["3 5\nababa\nab\na", "2 4\nab\ncd", "5 100\na\naa\naaa\naaaa\naaaaa"], "sample_outputs": ["11", "4", "142528942"], "notes": "NoteHere are all the instances of the valid chainwords for the first example:   The red lines above the letters denote the segments of the first hint, the blue lines below the letters denote the segments of the second hint.In the second example the possible strings are: \"abab\", \"abcd\", \"cdab\" and \"cdcd\". All the hints are segments that cover the first two letters and the last two letters."}, "src_uid": "711d15e11016d0164fb2b0c3756e4857"}
{"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": "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": "An infinitely long Line Chillland Collider (LCC) was built in Chillland. There are $$$n$$$ pipes with coordinates $$$x_i$$$ that are connected to LCC. When the experiment starts at time 0, $$$i$$$-th proton flies from the $$$i$$$-th pipe with speed $$$v_i$$$. It flies to the right with probability $$$p_i$$$ and flies to the left with probability $$$(1 - p_i)$$$. The duration of the experiment is determined as the time of the first collision of any two protons. In case there is no collision, the duration of the experiment is considered to be zero.Find the expected value of the duration of the experiment.Illustration for the first example", "input_spec": "The first line of input contains one integer $$$n$$$\u00a0\u2014 the number of pipes ($$$1 \\le n \\le 10^5$$$). Each of the following $$$n$$$ lines contains three integers $$$x_i$$$, $$$v_i$$$, $$$p_i$$$\u00a0\u2014 the coordinate of the $$$i$$$-th pipe, the speed of the $$$i$$$-th proton and the probability that the $$$i$$$-th proton flies to the right in percentage points ($$$-10^9 \\le x_i \\le 10^9, 1 \\le v \\le 10^6, 0 \\le p_i \\le 100$$$). It is guaranteed that all $$$x_i$$$ are distinct and sorted in increasing order.", "output_spec": "It's possible to prove that the answer can always be represented as a fraction $$$P/Q$$$, where $$$P$$$ is an integer and $$$Q$$$ is a natural number not divisible by $$$998\\,244\\,353$$$. In this case, print $$$P \\cdot Q^{-1}$$$ modulo $$$998\\,244\\,353$$$.", "sample_inputs": ["2\n1 1 100\n3 1 0", "3\n7 10 0\n9 4 86\n14 5 100", "4\n6 4 50\n11 25 50\n13 16 50\n15 8 50"], "sample_outputs": ["1", "0", "150902884"], "notes": null}, "src_uid": "37bb4fe5f6cc2a173e97c033c6fde8c7"}
{"nl": {"description": "You have a rectangular board of size $$$n\\times m$$$ ($$$n$$$ rows, $$$m$$$ columns). The $$$n$$$ rows are numbered from $$$1$$$ to $$$n$$$ from top to bottom, and the $$$m$$$ columns are numbered from $$$1$$$ to $$$m$$$ from left to right. The cell at the intersection of row $$$i$$$ and column $$$j$$$ contains the number $$$i^j$$$ ($$$i$$$ raised to the power of $$$j$$$). For example, if $$$n=3$$$ and $$$m=3$$$ the board is as follows:  Find the number of distinct integers written on the board.", "input_spec": "The only line contains two integers $$$n$$$ and $$$m$$$ ($$$1\\le n,m\\le 10^6$$$)\u00a0\u2014 the number of rows and columns of the board.", "output_spec": "Print one integer, the number of distinct integers on the board.", "sample_inputs": ["3 3", "2 4", "4 2"], "sample_outputs": ["7", "5", "6"], "notes": "NoteThe statement shows the board for the first test case. In this case there are $$$7$$$ distinct integers: $$$1$$$, $$$2$$$, $$$3$$$, $$$4$$$, $$$8$$$, $$$9$$$, and $$$27$$$.In the second test case, the board is as follows:  There are $$$5$$$ distinct numbers: $$$1$$$, $$$2$$$, $$$4$$$, $$$8$$$ and $$$16$$$.In the third test case, the board is as follows:  There are $$$6$$$ distinct numbers: $$$1$$$, $$$2$$$, $$$3$$$, $$$4$$$, $$$9$$$ and $$$16$$$."}, "src_uid": "6ca310cb0b6fc4e62e63a731cd55aead"}
{"nl": {"description": "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": "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": "Iahub is training for the IOI. What is a better way to train than playing a Zuma-like game? There are n balls put in a row. Each ball is colored in one of k colors. Initially the row doesn't contain three or more contiguous balls with the same color. Iahub has a single ball of color x. He can insert his ball at any position in the row (probably, between two other balls). If at any moment there are three or more contiguous balls of the same color in the row, they are destroyed immediately. This rule is applied multiple times, until there are no more sets of 3 or more contiguous balls of the same color. For example, if Iahub has the row of balls [black, black, white, white, black, black] and a white ball, he can insert the ball between two white balls. Thus three white balls are destroyed, and then four black balls become contiguous, so all four balls are destroyed. The row will not contain any ball in the end, so Iahub can destroy all 6 balls.Iahub wants to destroy as many balls as possible. You are given the description of the row of balls, and the color of Iahub's ball. Help Iahub train for the IOI by telling him the maximum number of balls from the row he can destroy.", "input_spec": "The first line of input contains three integers: n (1\u2009\u2264\u2009n\u2009\u2264\u2009100), k (1\u2009\u2264\u2009k\u2009\u2264\u2009100) and x (1\u2009\u2264\u2009x\u2009\u2264\u2009k). The next line contains n space-separated integers c1,\u2009c2,\u2009...,\u2009cn (1\u2009\u2264\u2009ci\u2009\u2264\u2009k). Number ci means that the i-th ball in the row has color ci. It is guaranteed that the initial row of balls will never contain three or more contiguous balls of the same color. ", "output_spec": "Print a single integer \u2014 the maximum number of balls Iahub can destroy.", "sample_inputs": ["6 2 2\n1 1 2 2 1 1", "1 1 1\n1"], "sample_outputs": ["6", "0"], "notes": null}, "src_uid": "d73d9610e3800817a3109314b1e6f88c"}
{"nl": {"description": "You 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": "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": "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": "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": "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": "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": "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": "Not so long ago as a result of combat operations the main Berland place of interest \u2014 the magic clock \u2014 was damaged. The cannon's balls made several holes in the clock, that's why the residents are concerned about the repair. The magic clock can be represented as an infinite Cartesian plane, where the origin corresponds to the clock center. The clock was painted two colors as is shown in the picture:  The picture shows only the central part of the clock. This coloring naturally extends to infinity.The balls can be taken to be points on the plane. Your task is to find the color of the area, damaged by the given ball.All the points located on the border of one of the areas have to be considered painted black.", "input_spec": "The first and single line contains two integers x and y \u2014 the coordinates of the hole made in the clock by the ball. Each of the numbers x and y has an absolute value that does not exceed 1000.", "output_spec": "Find the required color. All the points between which and the origin of coordinates the distance is integral-value are painted black.", "sample_inputs": ["-2 1", "2 1", "4 3"], "sample_outputs": ["white", "black", "black"], "notes": null}, "src_uid": "8c92aac1bef5822848a136a1328346c6"}
{"nl": {"description": "The preferred way to generate user login in Polygon is to concatenate a prefix of the user's first name and a prefix of their last name, in that order. Each prefix must be non-empty, and any of the prefixes can be the full name. Typically there are multiple possible logins for each person.You are given the first and the last name of a user. Return the alphabetically earliest login they can get (regardless of other potential Polygon users).As a reminder, a prefix of a string s is its substring which occurs at the beginning of s: \"a\", \"ab\", \"abc\" etc. are prefixes of string \"{abcdef}\" but \"b\" and 'bc\" are not. A string a is alphabetically earlier than a string b, if a is a prefix of b, or a and b coincide up to some position, and then a has a letter that is alphabetically earlier than the corresponding letter in b: \"a\" and \"ab\" are alphabetically earlier than \"ac\" but \"b\" and \"ba\" are alphabetically later than \"ac\".", "input_spec": "The input consists of a single line containing two space-separated strings: the first and the last names. Each character of each string is a lowercase English letter. The length of each string is between 1 and 10, inclusive. ", "output_spec": "Output a single string\u00a0\u2014 alphabetically earliest possible login formed from these names. The output should be given in lowercase as well.", "sample_inputs": ["harry potter", "tom riddle"], "sample_outputs": ["hap", "tomr"], "notes": null}, "src_uid": "aed892f2bda10b6aee10dcb834a63709"}
{"nl": {"description": "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": "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": "There are $$$n$$$ candy boxes in front of Tania. The boxes are arranged in a row from left to right, numbered from $$$1$$$ to $$$n$$$. The $$$i$$$-th box contains $$$r_i$$$ candies, candies have the color $$$c_i$$$ (the color can take one of three values \u200b\u200b\u2014 red, green, or blue). All candies inside a single box have the same color (and it is equal to $$$c_i$$$).Initially, Tanya is next to the box number $$$s$$$. Tanya can move to the neighbor box (that is, with a number that differs by one) or eat candies in the current box. Tanya eats candies instantly, but the movement takes one second.If Tanya eats candies from the box, then the box itself remains in place, but there is no more candies in it. In other words, Tanya always eats all the candies from the box and candies in the boxes are not refilled.It is known that Tanya cannot eat candies of the same color one after another (that is, the colors of candies in two consecutive boxes from which she eats candies are always different). In addition, Tanya's appetite is constantly growing, so in each next box from which she eats candies, there should be strictly more candies than in the previous one.Note that for the first box from which Tanya will eat candies, there are no restrictions on the color and number of candies.Tanya wants to eat at least $$$k$$$ candies. What is the minimum number of seconds she will need? Remember that she eats candies instantly, and time is spent only on movements.", "input_spec": "The first line contains three integers $$$n$$$, $$$s$$$ and $$$k$$$ ($$$1 \\le n \\le 50$$$, $$$1 \\le s \\le n$$$, $$$1 \\le k \\le 2000$$$) \u2014 number of the boxes, initial position of Tanya and lower bound on number of candies to eat. The following line contains $$$n$$$ integers $$$r_i$$$ ($$$1 \\le r_i \\le 50$$$) \u2014 numbers of candies in the boxes. The third line contains sequence of $$$n$$$ letters 'R', 'G' and 'B', meaning the colors of candies in the correspondent boxes ('R' for red, 'G' for green, 'B' for blue). Recall that each box contains candies of only one color. The third line contains no spaces.", "output_spec": "Print minimal number of seconds to eat at least $$$k$$$ candies. If solution doesn't exist, print \"-1\".", "sample_inputs": ["5 3 10\n1 2 3 4 5\nRGBRR", "2 1 15\n5 6\nRG"], "sample_outputs": ["4", "-1"], "notes": "NoteThe sequence of actions of Tanya for the first example:  move from the box $$$3$$$ to the box $$$2$$$;  eat candies from the box $$$2$$$;  move from the box $$$2$$$ to the box $$$3$$$;  eat candy from the box $$$3$$$;  move from the box $$$3$$$ to the box $$$4$$$;  move from the box $$$4$$$ to the box $$$5$$$;  eat candies from the box $$$5$$$. Since Tanya eats candy instantly, the required time is four seconds."}, "src_uid": "a95e54a7e38cc0d61b39e4a01a6f8d3f"}
{"nl": {"description": "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": "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": "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": "Vasya studies positional numeral systems. Unfortunately, he often forgets to write the base of notation in which the expression is written. Once he saw a note in his notebook saying a\u2009+\u2009b\u2009=\u2009?, and that the base of the positional notation wasn\u2019t written anywhere. Now Vasya has to choose a base p and regard the expression as written in the base p positional notation. Vasya understood that he can get different results with different bases, and some bases are even invalid. For example, expression 78\u2009+\u200987 in the base 16 positional notation is equal to FF16, in the base 15 positional notation it is equal to 11015, in the base 10 one \u2014 to 16510, in the base 9 one \u2014 to 1769, and in the base 8 or lesser-based positional notations the expression is invalid as all the numbers should be strictly less than the positional notation base. Vasya got interested in what is the length of the longest possible expression value. Help him to find this length.The length of a number should be understood as the number of numeric characters in it. For example, the length of the longest answer for 78\u2009+\u200987\u2009=\u2009? is 3. It is calculated like that in the base 15 (11015), base 10 (16510), base 9 (1769) positional notations, for example, and in some other ones.", "input_spec": "The first letter contains two space-separated numbers a and b (1\u2009\u2264\u2009a,\u2009b\u2009\u2264\u20091000) which represent the given summands.", "output_spec": "Print a single number \u2014 the length of the longest answer.", "sample_inputs": ["78 87", "1 1"], "sample_outputs": ["3", "2"], "notes": null}, "src_uid": "8ccfb9b1fef6a992177cc49bd56fab7b"}
{"nl": {"description": "You are given three integers k, pa and pb.You will construct a sequence with the following algorithm: Initially, start with the empty sequence. Each second, you do the following. With probability pa\u2009/\u2009(pa\u2009+\u2009pb), add 'a' to the end of the sequence. Otherwise (with probability pb\u2009/\u2009(pa\u2009+\u2009pb)), add 'b' to the end of the sequence.You stop once there are at least k subsequences that form 'ab'. Determine the expected number of times 'ab' is a subsequence in the resulting sequence. It can be shown that this can be represented by P\u2009/\u2009Q, where P and Q are coprime integers, and . Print the value of .", "input_spec": "The first line will contain three integers integer k,\u2009pa,\u2009pb (1\u2009\u2264\u2009k\u2009\u2264\u20091\u2009000, 1\u2009\u2264\u2009pa,\u2009pb\u2009\u2264\u20091\u2009000\u2009000).", "output_spec": "Print a single integer, the answer to the problem.", "sample_inputs": ["1 1 1", "3 1 4"], "sample_outputs": ["2", "370000006"], "notes": "NoteThe first sample, we will keep appending to our sequence until we get the subsequence 'ab' at least once. For instance, we get the sequence 'ab' with probability 1/4, 'bbab' with probability 1/16, and 'aab' with probability 1/8. Note, it's impossible for us to end with a sequence like 'aabab', since we would have stopped our algorithm once we had the prefix 'aab'. The expected amount of times that 'ab' will occur across all valid sequences is 2. For the second sample, the answer is equal to ."}, "src_uid": "0dc9f5d75143a2bc744480de859188b4"}
{"nl": {"description": "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": "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": "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": "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": "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": "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": "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": "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": "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": "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": "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": "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": "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": "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": "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": "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": "Recall that a binary search tree is a rooted binary tree, whose nodes each store a key and each have at most two distinguished subtrees, left and right. The key in each node must be greater than any key stored in the left subtree, and less than any key stored in the right subtree.The depth of a vertex is the number of edges on the simple path from the vertex to the root. In particular, the depth of the root is $$$0$$$.Let's call a binary search tree perfectly balanced if there doesn't exist a binary search tree with the same number of vertices that has a strictly smaller sum of depths of its vertices.Let's call a binary search tree with integer keys striped if both of the following conditions are satisfied for every vertex $$$v$$$:   If $$$v$$$ has a left subtree whose root is $$$u$$$, then the parity of the key of $$$v$$$ is different from the parity of the key of $$$u$$$.  If $$$v$$$ has a right subtree whose root is $$$w$$$, then the parity of the key of $$$v$$$ is the same as the parity of the key of $$$w$$$. You are given a single integer $$$n$$$. Find the number of perfectly balanced striped binary search trees with $$$n$$$ vertices that have distinct integer keys between $$$1$$$ and $$$n$$$, inclusive. Output this number modulo $$$998\\,244\\,353$$$.", "input_spec": "The only line contains a single integer $$$n$$$ ($$$1 \\le n \\le 10^6$$$), denoting the required number of vertices.", "output_spec": "Output the number of perfectly balanced striped binary search trees with $$$n$$$ vertices and distinct integer keys between $$$1$$$ and $$$n$$$, inclusive, modulo $$$998\\,244\\,353$$$.", "sample_inputs": ["4", "3"], "sample_outputs": ["1", "0"], "notes": "NoteIn the first example, this is the only tree that satisfies the conditions: In the second example, here are various trees that don't satisfy some condition: "}, "src_uid": "821409c1b9bdcd18c4dcf35dc5116501"}
{"nl": {"description": "Anadi has a set of dominoes. Every domino has two parts, and each part contains some dots. For every $$$a$$$ and $$$b$$$ such that $$$1 \\leq a \\leq b \\leq 6$$$, there is exactly one domino with $$$a$$$ dots on one half and $$$b$$$ dots on the other half. The set contains exactly $$$21$$$ dominoes. Here is an exact illustration of his set:  Also, Anadi has an undirected graph without self-loops and multiple edges. He wants to choose some dominoes and place them on the edges of this graph. He can use at most one domino of each type. Each edge can fit at most one domino. It's not necessary to place a domino on each edge of the graph.When placing a domino on an edge, he also chooses its direction. In other words, one half of any placed domino must be directed toward one of the endpoints of the edge and the other half must be directed toward the other endpoint. There's a catch: if there are multiple halves of dominoes directed toward the same vertex, each of these halves must contain the same number of dots.How many dominoes at most can Anadi place on the edges of his graph?", "input_spec": "The first line contains two integers $$$n$$$ and $$$m$$$ ($$$1 \\leq n \\leq 7$$$, $$$0 \\leq m \\leq \\frac{n\\cdot(n-1)}{2}$$$) \u2014 the number of vertices and the number of edges in the graph. The next $$$m$$$ lines contain two integers each. Integers in the $$$i$$$-th line are $$$a_i$$$ and $$$b_i$$$ ($$$1 \\leq a, b \\leq n$$$, $$$a \\neq b$$$) and denote that there is an edge which connects vertices $$$a_i$$$ and $$$b_i$$$. The graph might be disconnected. It's however guaranteed that the graph doesn't contain any self-loops, and that there is at most one edge between any pair of vertices.", "output_spec": "Output one integer which denotes the maximum number of dominoes which Anadi can place on the edges of the graph.", "sample_inputs": ["4 4\n1 2\n2 3\n3 4\n4 1", "7 0", "3 1\n1 3", "7 21\n1 2\n1 3\n1 4\n1 5\n1 6\n1 7\n2 3\n2 4\n2 5\n2 6\n2 7\n3 4\n3 5\n3 6\n3 7\n4 5\n4 6\n4 7\n5 6\n5 7\n6 7"], "sample_outputs": ["4", "0", "1", "16"], "notes": "NoteHere is an illustration of Anadi's graph from the first sample test:  And here is one of the ways to place a domino on each of its edges:  Note that each vertex is faced by the halves of dominoes with the same number of dots. For instance, all halves directed toward vertex $$$1$$$ have three dots."}, "src_uid": "11e6559cfb71b8f6ca88242094b17a2b"}
{"nl": {"description": "A positive integer is called a 2-3-integer, if it is equal to 2x\u00b73y for some non-negative integers x and y. In other words, these integers are such integers that only have 2 and 3 among their prime divisors. For example, integers 1, 6, 9, 16 and 108 \u2014 are 2-3 integers, while 5, 10, 21 and 120 are not.Print the number of 2-3-integers on the given segment [l,\u2009r], i.\u00a0e. the number of sich 2-3-integers t that l\u2009\u2264\u2009t\u2009\u2264\u2009r.", "input_spec": "The only line contains two integers l and r (1\u2009\u2264\u2009l\u2009\u2264\u2009r\u2009\u2264\u20092\u00b7109).", "output_spec": "Print a single integer the number of 2-3-integers on the segment [l,\u2009r].", "sample_inputs": ["1 10", "100 200", "1 2000000000"], "sample_outputs": ["7", "5", "326"], "notes": "NoteIn the first example the 2-3-integers are 1, 2, 3, 4, 6, 8 and 9.In the second example the 2-3-integers are 108, 128, 144, 162 and 192."}, "src_uid": "05fac54ed2064b46338bb18f897a4411"}
{"nl": {"description": "You are a lover of bacteria. You want to raise some bacteria in a box. Initially, the box is empty. Each morning, you can put any number of bacteria into the box. And each night, every bacterium in the box will split into two bacteria. You hope to see exactly x bacteria in the box at some moment. What is the minimum number of bacteria you need to put into the box across those days?", "input_spec": "The only line containing one integer x (1\u2009\u2264\u2009x\u2009\u2264\u2009109).", "output_spec": "The only line containing one integer: the answer.", "sample_inputs": ["5", "8"], "sample_outputs": ["2", "1"], "notes": "NoteFor the first sample, we can add one bacterium in the box in the first day morning and at the third morning there will be 4 bacteria in the box. Now we put one more resulting 5 in the box. We added 2 bacteria in the process so the answer is 2.For the second sample, we can put one in the first morning and in the 4-th morning there will be 8 in the box. So the answer is 1."}, "src_uid": "03e4482d53a059134676f431be4c16d2"}
{"nl": {"description": "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": "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": "There are n children in Jzzhu's school. Jzzhu is going to give some candies to them. Let's number all the children from 1 to n. The i-th child wants to get at least ai candies.Jzzhu asks children to line up. Initially, the i-th child stands at the i-th place of the line. Then Jzzhu start distribution of the candies. He follows the algorithm:  Give m candies to the first child of the line.  If this child still haven't got enough candies, then the child goes to the end of the line, else the child go home.  Repeat the first two steps while the line is not empty. Consider all the children in the order they go home. Jzzhu wants to know, which child will be the last in this order?", "input_spec": "The first line contains two integers n,\u2009m (1\u2009\u2264\u2009n\u2009\u2264\u2009100;\u00a01\u2009\u2264\u2009m\u2009\u2264\u2009100). The second line contains n integers a1,\u2009a2,\u2009...,\u2009an (1\u2009\u2264\u2009ai\u2009\u2264\u2009100).", "output_spec": "Output a single integer, representing the number of the last child.", "sample_inputs": ["5 2\n1 3 1 4 2", "6 4\n1 1 2 2 3 3"], "sample_outputs": ["4", "6"], "notes": "NoteLet's consider the first sample. Firstly child 1 gets 2 candies and go home. Then child 2 gets 2 candies and go to the end of the line. Currently the line looks like [3, 4, 5, 2] (indices of the children in order of the line). Then child 3 gets 2 candies and go home, and then child 4 gets 2 candies and goes to the end of the line. Currently the line looks like [5, 2, 4]. Then child 5 gets 2 candies and goes home. Then child 2 gets two candies and goes home, and finally child 4 gets 2 candies and goes home.Child 4 is the last one who goes home."}, "src_uid": "c0ef1e4d7df360c5c1e52bc6f16ca87c"}
{"nl": {"description": "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": "Consider an array $$$a$$$ of length $$$n$$$ with elements numbered from $$$1$$$ to $$$n$$$. It is possible to remove the $$$i$$$-th element of $$$a$$$ if $$$gcd(a_i, i) = 1$$$, where $$$gcd$$$ denotes the greatest common divisor. After an element is removed, the elements to the right are shifted to the left by one position.An array $$$b$$$ with $$$n$$$ integers such that $$$1 \\le b_i \\le n - i + 1$$$ is a removal sequence for the array $$$a$$$ if it is possible to remove all elements of $$$a$$$, if you remove the $$$b_1$$$-th element, then the $$$b_2$$$-th, ..., then the $$$b_n$$$-th element. For example, let $$$a = [42, 314]$$$:  $$$[1, 1]$$$ is a removal sequence: when you remove the $$$1$$$-st element of the array, the condition $$$gcd(42, 1) = 1$$$ holds, and the array becomes $$$[314]$$$; when you remove the $$$1$$$-st element again, the condition $$$gcd(314, 1) = 1$$$ holds, and the array becomes empty.  $$$[2, 1]$$$ is not a removal sequence: when you try to remove the $$$2$$$-nd element, the condition $$$gcd(314, 2) = 1$$$ is false. An array is ambiguous if it has at least two removal sequences. For example, the array $$$[1, 2, 5]$$$ is ambiguous: it has removal sequences $$$[3, 1, 1]$$$ and $$$[1, 2, 1]$$$. The array $$$[42, 314]$$$ is not ambiguous: the only removal sequence it has is $$$[1, 1]$$$.You are given two integers $$$n$$$ and $$$m$$$. You have to calculate the number of ambiguous arrays $$$a$$$ such that the length of $$$a$$$ is from $$$1$$$ to $$$n$$$ and each $$$a_i$$$ is an integer from $$$1$$$ to $$$m$$$.", "input_spec": "The only line of the input contains two integers $$$n$$$ and $$$m$$$ ($$$2 \\le n \\le 3 \\cdot 10^5$$$; $$$1 \\le m \\le 10^{12}$$$).", "output_spec": "Print one integer \u2014 the number of ambiguous arrays $$$a$$$ such that the length of $$$a$$$ is from $$$1$$$ to $$$n$$$ and each $$$a_i$$$ is an integer from $$$1$$$ to $$$m$$$. Since the answer can be very large, print it modulo $$$998244353$$$.", "sample_inputs": ["2 3", "4 2", "4 6", "1337 424242424242"], "sample_outputs": ["6", "26", "1494", "119112628"], "notes": null}, "src_uid": "0fdd91ed33431848614075ebe9d2ee68"}
{"nl": {"description": "One day, $$$n$$$ people ($$$n$$$ is an even number) met on a plaza and made two round dances, each round dance consists of exactly $$$\\frac{n}{2}$$$ people. Your task is to find the number of ways $$$n$$$ people can make two round dances if each round dance consists of exactly $$$\\frac{n}{2}$$$ people. Each person should belong to exactly one of these two round dances.Round dance is a dance circle consisting of $$$1$$$ or more people. Two round dances are indistinguishable (equal) if one can be transformed to another by choosing the first participant. For example, round dances $$$[1, 3, 4, 2]$$$, $$$[4, 2, 1, 3]$$$ and $$$[2, 1, 3, 4]$$$ are indistinguishable.For example, if $$$n=2$$$ then the number of ways is $$$1$$$: one round dance consists of the first person and the second one of the second person.For example, if $$$n=4$$$ then the number of ways is $$$3$$$. Possible options:  one round dance \u2014 $$$[1,2]$$$, another \u2014 $$$[3,4]$$$;  one round dance \u2014 $$$[2,4]$$$, another \u2014 $$$[3,1]$$$;  one round dance \u2014 $$$[4,1]$$$, another \u2014 $$$[3,2]$$$. Your task is to find the number of ways $$$n$$$ people can make two round dances if each round dance consists of exactly $$$\\frac{n}{2}$$$ people.", "input_spec": "The input contains one integer $$$n$$$ ($$$2 \\le n \\le 20$$$), $$$n$$$ is an even number.", "output_spec": "Print one integer \u2014 the number of ways to make two round dances. It is guaranteed that the answer fits in the $$$64$$$-bit integer data type.", "sample_inputs": ["2", "4", "8", "20"], "sample_outputs": ["1", "3", "1260", "12164510040883200"], "notes": null}, "src_uid": "ad0985c56a207f76afa2ecd642f56728"}
{"nl": {"description": "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": "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": "This problem is split into two tasks. In this task, you are required to find the maximum possible answer. In the task Village (Minimum) you are required to find the minimum possible answer. Each task is worth $$$50$$$ points.There are $$$N$$$ houses in a certain village. A single villager lives in each of the houses. The houses are connected by roads. Each road connects two houses and is exactly $$$1$$$ kilometer long. From each house it is possible to reach any other using one or several consecutive roads. In total there are $$$N-1$$$ roads in the village.One day all villagers decided to move to different houses \u2014 that is, after moving each house should again have a single villager living in it, but no villager should be living in the same house as before. We would like to know the largest possible total length in kilometers of the shortest paths between the old and the new houses for all villagers. Example village with seven houses For example, if there are seven houses connected by roads as shown on the figure, the largest total length is $$$18$$$ km (this can be achieved by moving $$$1 \\to 7$$$, $$$2 \\to 3$$$, $$$3 \\to 4$$$, $$$4 \\to 1$$$, $$$5 \\to 2$$$, $$$6 \\to 5$$$, $$$7 \\to 6$$$).Write a program that finds the largest total length of the shortest paths in kilometers and an example assignment of the new houses to the villagers.", "input_spec": "The first line contains an integer $$$N$$$ ($$$1 < N \\le 10^5$$$). Houses are numbered by consecutive integers $$$1, 2, \\ldots, N$$$. Then $$$N-1$$$ lines follow that describe the roads. Each line contains two integers $$$a$$$ and $$$b$$$ ($$$1 \\le a, b \\le N$$$, $$$a \\neq b$$$) denoting that there is a road connecting houses $$$a$$$ and $$$b$$$.", "output_spec": "In the first line output the largest total length of the shortest paths in kilometers. In the second line describe one valid assignment of the new houses with the largest total length: $$$N$$$ space-separated distinct integers $$$v_1, v_2, \\ldots, v_N$$$. For each $$$i$$$, $$$v_i$$$ is the house number where villager from the house $$$i$$$ should move ($$$v_i \\neq i$$$). If there are several valid assignments, output any of those.", "sample_inputs": ["4\n1 2\n2 3\n3 4", "7\n4 2\n5 7\n3 4\n6 3\n1 3\n4 5"], "sample_outputs": ["8\n4 3 2 1", "18\n2 7 4 1 3 5 6"], "notes": null}, "src_uid": "343dbacbc6bb4981a062dda5a1a13656"}
{"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": "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": "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": "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": "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": "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": "Calculate the number of ways to place $$$n$$$ rooks on $$$n \\times n$$$ chessboard so that both following conditions are met:  each empty cell is under attack;  exactly $$$k$$$ pairs of rooks attack each other. An empty cell is under attack if there is at least one rook in the same row or at least one rook in the same column. Two rooks attack each other if they share the same row or column, and there are no other rooks between them. For example, there are only two pairs of rooks that attack each other in the following picture:  One of the ways to place the rooks for $$$n = 3$$$ and $$$k = 2$$$ Two ways to place the rooks are considered different if there exists at least one cell which is empty in one of the ways but contains a rook in another way.The answer might be large, so print it modulo $$$998244353$$$.", "input_spec": "The only line of the input contains two integers $$$n$$$ and $$$k$$$ ($$$1 \\le n \\le 200000$$$; $$$0 \\le k \\le \\frac{n(n - 1)}{2}$$$).", "output_spec": "Print one integer \u2014 the number of ways to place the rooks, taken modulo $$$998244353$$$.", "sample_inputs": ["3 2", "3 3", "4 0", "1337 42"], "sample_outputs": ["6", "0", "24", "807905441"], "notes": null}, "src_uid": "6c1a9aaa7bdd7de97220b8c6d35740cc"}
{"nl": {"description": "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": "The only difference between easy and hard versions is constraints.Ivan plays a computer game that contains some microtransactions to make characters look cooler. Since Ivan wants his character to be really cool, he wants to use some of these microtransactions \u2014 and he won't start playing until he gets all of them.Each day (during the morning) Ivan earns exactly one burle.There are $$$n$$$ types of microtransactions in the game. Each microtransaction costs $$$2$$$ burles usually and $$$1$$$ burle if it is on sale. Ivan has to order exactly $$$k_i$$$ microtransactions of the $$$i$$$-th type (he orders microtransactions during the evening).Ivan can order any (possibly zero) number of microtransactions of any types during any day (of course, if he has enough money to do it). If the microtransaction he wants to order is on sale then he can buy it for $$$1$$$ burle and otherwise he can buy it for $$$2$$$ burles.There are also $$$m$$$ special offers in the game shop. The $$$j$$$-th offer $$$(d_j, t_j)$$$ means that microtransactions of the $$$t_j$$$-th type are on sale during the $$$d_j$$$-th day.Ivan wants to order all microtransactions as soon as possible. Your task is to calculate the minimum day when he can buy all microtransactions he want and actually start playing.", "input_spec": "The first line of the input contains two integers $$$n$$$ and $$$m$$$ ($$$1 \\le n, m \\le 1000$$$) \u2014 the number of types of microtransactions and the number of special offers in the game shop. The second line of the input contains $$$n$$$ integers $$$k_1, k_2, \\dots, k_n$$$ ($$$0 \\le k_i \\le 1000$$$), where $$$k_i$$$ is the number of copies of microtransaction of the $$$i$$$-th type Ivan has to order. It is guaranteed that sum of all $$$k_i$$$ is not less than $$$1$$$ and not greater than $$$1000$$$. The next $$$m$$$ lines contain special offers. The $$$j$$$-th of these lines contains the $$$j$$$-th special offer. It is given as a pair of integers $$$(d_j, t_j)$$$ ($$$1 \\le d_j \\le 1000, 1 \\le t_j \\le n$$$) and means that microtransactions of the $$$t_j$$$-th type are on sale during the $$$d_j$$$-th day.", "output_spec": "Print one integer \u2014 the minimum day when Ivan can order all microtransactions he wants and actually start playing.", "sample_inputs": ["5 6\n1 2 0 2 0\n2 4\n3 3\n1 5\n1 2\n1 5\n2 3", "5 3\n4 2 1 3 2\n3 5\n4 2\n2 5"], "sample_outputs": ["8", "20"], "notes": null}, "src_uid": "2eb101dcfcc487fe6e44c9b4c0e4024d"}
{"nl": {"description": "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": "    *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": "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": "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": "There is a straight line colored in white. n black segments are added on it one by one.After each segment is added, determine the number of connected components of black segments (i.\u00a0e. the number of black segments in the union of the black segments). In particular, if one segment ends in a point x, and another segment starts in the point x, these two segments belong to the same connected component.", "input_spec": "The first line contains a single integer n (1\u2009\u2264\u2009n\u2009\u2264\u2009200\u2009000) \u2014 the number of segments. The i-th of the next n lines contains two integers li and ri (1\u2009\u2264\u2009li\u2009<\u2009ri\u2009\u2264\u2009109) \u2014 the coordinates of the left and the right ends of the i-th segment. The segments are listed in the order they are added on the white line.", "output_spec": "Print n integers \u2014 the number of connected components of black segments after each segment is added. ", "sample_inputs": ["3\n1 3\n4 5\n2 4", "9\n10 20\n50 60\n30 40\n70 80\n90 100\n60 70\n10 40\n40 50\n80 90"], "sample_outputs": ["1 2 1", "1 2 3 4 5 4 3 2 1"], "notes": "NoteIn the first example there are two components after the addition of the first two segments, because these segments do not intersect. The third added segment intersects the left segment and touches the right segment at the point 4 (these segments belong to the same component, according to the statements). Thus the number of connected components of black segments is equal to 1 after that."}, "src_uid": "3979abbe7bad0f3b5cab15c1cba19f6b"}
{"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": "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": "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": "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": "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": "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": "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": "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": "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": "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": "Modern text editors usually show some information regarding the document being edited. For example, the number of words, the number of pages, or the number of characters.In this problem you should implement the similar functionality.You are given a string which only consists of:  uppercase and lowercase English letters,  underscore symbols (they are used as separators),  parentheses (both opening and closing). It is guaranteed that each opening parenthesis has a succeeding closing parenthesis. Similarly, each closing parentheses has a preceding opening parentheses matching it. For each pair of matching parentheses there are no other parenthesis between them. In other words, each parenthesis in the string belongs to a matching \"opening-closing\" pair, and such pairs can't be nested.For example, the following string is valid: \"_Hello_Vasya(and_Petya)__bye_(and_OK)\".Word is a maximal sequence of consecutive letters, i.e. such sequence that the first character to the left and the first character to the right of it is an underscore, a parenthesis, or it just does not exist. For example, the string above consists of seven words: \"Hello\", \"Vasya\", \"and\", \"Petya\", \"bye\", \"and\" and \"OK\". Write a program that finds:  the length of the longest word outside the parentheses (print 0, if there is no word outside the parentheses),  the number of words inside the parentheses (print 0, if there is no word inside the parentheses). ", "input_spec": "The first line of the input contains a single integer n (1\u2009\u2264\u2009n\u2009\u2264\u2009255)\u00a0\u2014 the length of the given string. The second line contains the string consisting of only lowercase and uppercase English letters, parentheses and underscore symbols. ", "output_spec": "Print two space-separated integers:   the length of the longest word outside the parentheses (print 0, if there is no word outside the parentheses),  the number of words inside the parentheses (print 0, if there is no word inside the parentheses). ", "sample_inputs": ["37\n_Hello_Vasya(and_Petya)__bye_(and_OK)", "37\n_a_(_b___c)__de_f(g_)__h__i(j_k_l)m__", "27\n(LoooonG)__shOrt__(LoooonG)", "5\n(___)"], "sample_outputs": ["5 4", "2 6", "5 2", "0 0"], "notes": "NoteIn the first sample, the words \"Hello\", \"Vasya\" and \"bye\" are outside any of the parentheses, and the words \"and\", \"Petya\", \"and\" and \"OK\" are inside. Note, that the word \"and\" is given twice and you should count it twice in the answer."}, "src_uid": "fc86df4931e787fa3a1a40e2aecf0b92"}
{"nl": {"description": "You are given names of two days of the week.Please, determine whether it is possible that during some non-leap year the first day of some month was equal to the first day of the week you are given, while the first day of the next month was equal to the second day of the week you are given. Both months should belong to one year.In this problem, we consider the Gregorian calendar to be used. The number of months in this calendar is equal to 12. The number of days in months during any non-leap year is: 31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31.Names of the days of the week are given with lowercase English letters: \"monday\", \"tuesday\", \"wednesday\", \"thursday\", \"friday\", \"saturday\", \"sunday\".", "input_spec": "The input consists of two lines, each of them containing the name of exactly one day of the week. It's guaranteed that each string in the input is from the set \"monday\", \"tuesday\", \"wednesday\", \"thursday\", \"friday\", \"saturday\", \"sunday\".", "output_spec": "Print \"YES\" (without quotes) if such situation is possible during some non-leap year. Otherwise, print \"NO\" (without quotes).", "sample_inputs": ["monday\ntuesday", "sunday\nsunday", "saturday\ntuesday"], "sample_outputs": ["NO", "YES", "YES"], "notes": "NoteIn the second sample, one can consider February 1 and March 1 of year 2015. Both these days were Sundays.In the third sample, one can consider July 1 and August 1 of year 2017. First of these two days is Saturday, while the second one is Tuesday."}, "src_uid": "2a75f68a7374b90b80bb362c6ead9a35"}
{"nl": {"description": "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": "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": "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": "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": "Recall that the permutation is an array consisting of $$$n$$$ distinct integers from $$$1$$$ to $$$n$$$ in arbitrary order. For example, $$$[2,3,1,5,4]$$$ is a permutation, but $$$[1,2,2]$$$ is not a permutation ($$$2$$$ appears twice in the array) and $$$[1,3,4]$$$ is also not a permutation ($$$n=3$$$ but there is $$$4$$$ in the array).A sequence $$$a$$$ is a subsegment of a sequence $$$b$$$ if $$$a$$$ can be obtained from $$$b$$$ by deletion of several (possibly, zero or all) elements from the beginning and several (possibly, zero or all) elements from the end. We will denote the subsegments as $$$[l, r]$$$, where $$$l, r$$$ are two integers with $$$1 \\le l \\le r \\le n$$$. This indicates the subsegment where $$$l-1$$$ elements from the beginning and $$$n-r$$$ elements from the end are deleted from the sequence.For a permutation $$$p_1, p_2, \\ldots, p_n$$$, we define a framed segment as a subsegment $$$[l,r]$$$ where $$$\\max\\{p_l, p_{l+1}, \\dots, p_r\\} - \\min\\{p_l, p_{l+1}, \\dots, p_r\\} = r - l$$$. For example, for the permutation $$$(6, 7, 1, 8, 5, 3, 2, 4)$$$ some of its framed segments are: $$$[1, 2], [5, 8], [6, 7], [3, 3], [8, 8]$$$. In particular, a subsegment $$$[i,i]$$$ is always a framed segments for any $$$i$$$ between $$$1$$$ and $$$n$$$, inclusive.We define the happiness of a permutation $$$p$$$ as the number of pairs $$$(l, r)$$$ such that $$$1 \\le l \\le r \\le n$$$, and $$$[l, r]$$$ is a framed segment. For example, the permutation $$$[3, 1, 2]$$$ has happiness $$$5$$$: all segments except $$$[1, 2]$$$ are framed segments.Given integers $$$n$$$ and $$$m$$$, Jongwon wants to compute the sum of happiness for all permutations of length $$$n$$$, modulo the prime number $$$m$$$. Note that there exist $$$n!$$$ (factorial of $$$n$$$) different permutations of length $$$n$$$.", "input_spec": "The only line contains two integers $$$n$$$ and $$$m$$$ ($$$1 \\le n \\le 250\\,000$$$, $$$10^8 \\le m \\le 10^9$$$, $$$m$$$ is prime).", "output_spec": "Print $$$r$$$ ($$$0 \\le r < m$$$), the sum of happiness for all permutations of length $$$n$$$, modulo a prime number $$$m$$$.", "sample_inputs": ["1 993244853", "2 993244853", "3 993244853", "2019 993244853", "2020 437122297"], "sample_outputs": ["1", "6", "32", "923958830", "265955509"], "notes": "NoteFor sample input $$$n=3$$$, let's consider all permutations of length $$$3$$$:  $$$[1, 2, 3]$$$, all subsegments are framed segment. Happiness is $$$6$$$.  $$$[1, 3, 2]$$$, all subsegments except $$$[1, 2]$$$ are framed segment. Happiness is $$$5$$$.  $$$[2, 1, 3]$$$, all subsegments except $$$[2, 3]$$$ are framed segment. Happiness is $$$5$$$.  $$$[2, 3, 1]$$$, all subsegments except $$$[2, 3]$$$ are framed segment. Happiness is $$$5$$$.  $$$[3, 1, 2]$$$, all subsegments except $$$[1, 2]$$$ are framed segment. Happiness is $$$5$$$.  $$$[3, 2, 1]$$$, all subsegments are framed segment. Happiness is $$$6$$$. Thus, the sum of happiness is $$$6+5+5+5+5+6 = 32$$$."}, "src_uid": "020d5dae7157d937c3f58554c9b155f9"}
{"nl": {"description": "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": "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": "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": "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": "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": "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": "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": "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": "Not so long ago company R2 bought company R1 and consequently, all its developments in the field of multicore processors. Now the R2 laboratory is testing one of the R1 processors.The testing goes in n steps, at each step the processor gets some instructions, and then its temperature is measured. The head engineer in R2 is keeping a report record on the work of the processor: he writes down the minimum and the maximum measured temperature in his notebook. His assistant had to write down all temperatures into his notebook, but (for unknown reasons) he recorded only m.The next day, the engineer's assistant filed in a report with all the m temperatures. However, the chief engineer doubts that the assistant wrote down everything correctly (naturally, the chief engineer doesn't doubt his notes). So he asked you to help him. Given numbers n, m, min, max and the list of m temperatures determine whether you can upgrade the set of m temperatures to the set of n temperatures (that is add n\u2009-\u2009m temperatures), so that the minimum temperature was min and the maximum one was max.", "input_spec": "The first line contains four integers n,\u2009m,\u2009min,\u2009max (1\u2009\u2264\u2009m\u2009<\u2009n\u2009\u2264\u2009100;\u00a01\u2009\u2264\u2009min\u2009<\u2009max\u2009\u2264\u2009100). The second line contains m space-separated integers ti (1\u2009\u2264\u2009ti\u2009\u2264\u2009100) \u2014 the temperatures reported by the assistant. Note, that the reported temperatures, and the temperatures you want to add can contain equal temperatures.", "output_spec": "If the data is consistent, print 'Correct' (without the quotes). Otherwise, print 'Incorrect' (without the quotes).", "sample_inputs": ["2 1 1 2\n1", "3 1 1 3\n2", "2 1 1 3\n2"], "sample_outputs": ["Correct", "Correct", "Incorrect"], "notes": "NoteIn the first test sample one of the possible initial configurations of temperatures is [1, 2].In the second test sample one of the possible initial configurations of temperatures is [2, 1, 3].In the third test sample it is impossible to add one temperature to obtain the minimum equal to 1 and the maximum equal to 3."}, "src_uid": "99f9cdc85010bd89434f39b78f15b65e"}
{"nl": {"description": "There are $$$n$$$ candies in a row, they are numbered from left to right from $$$1$$$ to $$$n$$$. The size of the $$$i$$$-th candy is $$$a_i$$$.Alice and Bob play an interesting and tasty game: they eat candy. Alice will eat candy from left to right, and Bob \u2014 from right to left. The game ends if all the candies are eaten.The process consists of moves. During a move, the player eats one or more sweets from her/his side (Alice eats from the left, Bob \u2014 from the right).Alice makes the first move. During the first move, she will eat $$$1$$$ candy (its size is $$$a_1$$$). Then, each successive move the players alternate \u2014 that is, Bob makes the second move, then Alice, then again Bob and so on.On each move, a player counts the total size of candies eaten during the current move. Once this number becomes strictly greater than the total size of candies eaten by the other player on their previous move, the current player stops eating and the move ends. In other words, on a move, a player eats the smallest possible number of candies such that the sum of the sizes of candies eaten on this move is strictly greater than the sum of the sizes of candies that the other player ate on the previous move. If there are not enough candies to make a move this way, then the player eats up all the remaining candies and the game ends.For example, if $$$n=11$$$ and $$$a=[3,1,4,1,5,9,2,6,5,3,5]$$$, then:  move 1: Alice eats one candy of size $$$3$$$ and the sequence of candies becomes $$$[1,4,1,5,9,2,6,5,3,5]$$$.  move 2: Alice ate $$$3$$$ on the previous move, which means Bob must eat $$$4$$$ or more. Bob eats one candy of size $$$5$$$ and the sequence of candies becomes $$$[1,4,1,5,9,2,6,5,3]$$$.  move 3: Bob ate $$$5$$$ on the previous move, which means Alice must eat $$$6$$$ or more. Alice eats three candies with the total size of $$$1+4+1=6$$$ and the sequence of candies becomes $$$[5,9,2,6,5,3]$$$.  move 4: Alice ate $$$6$$$ on the previous move, which means Bob must eat $$$7$$$ or more. Bob eats two candies with the total size of $$$3+5=8$$$ and the sequence of candies becomes $$$[5,9,2,6]$$$.  move 5: Bob ate $$$8$$$ on the previous move, which means Alice must eat $$$9$$$ or more. Alice eats two candies with the total size of $$$5+9=14$$$ and the sequence of candies becomes $$$[2,6]$$$.  move 6 (the last): Alice ate $$$14$$$ on the previous move, which means Bob must eat $$$15$$$ or more. It is impossible, so Bob eats the two remaining candies and the game ends. Print the number of moves in the game and two numbers:  $$$a$$$ \u2014 the total size of all sweets eaten by Alice during the game;  $$$b$$$ \u2014 the total size of all sweets eaten by Bob during the game. ", "input_spec": "The first line contains an integer $$$t$$$ ($$$1 \\le t \\le 5000$$$) \u2014 the number of test cases in the input. The following are descriptions of the $$$t$$$ test cases. Each test case consists of two lines. The first line contains an integer $$$n$$$ ($$$1 \\le n \\le 1000$$$) \u2014 the number of candies. The second line contains a sequence of integers $$$a_1, a_2, \\dots, a_n$$$ ($$$1 \\le a_i \\le 1000$$$) \u2014 the sizes of candies in the order they are arranged from left to right. It is guaranteed that the sum of the values of $$$n$$$ for all sets of input data in a test does not exceed $$$2\\cdot10^5$$$.", "output_spec": "For each set of input data print three integers \u2014 the number of moves in the game and the required values $$$a$$$ and $$$b$$$.", "sample_inputs": ["7\n11\n3 1 4 1 5 9 2 6 5 3 5\n1\n1000\n3\n1 1 1\n13\n1 2 3 4 5 6 7 8 9 10 11 12 13\n2\n2 1\n6\n1 1 1 1 1 1\n7\n1 1 1 1 1 1 1"], "sample_outputs": ["6 23 21\n1 1000 0\n2 1 2\n6 45 46\n2 2 1\n3 4 2\n4 4 3"], "notes": null}, "src_uid": "d70ee6d3574e0f2cac3c683729e2979d"}
{"nl": {"description": "n hobbits are planning to spend the night at Frodo's house. Frodo has n beds standing in a row and m pillows (n\u2009\u2264\u2009m). Each hobbit needs a bed and at least one pillow to sleep, however, everyone wants as many pillows as possible. Of course, it's not always possible to share pillows equally, but any hobbit gets hurt if he has at least two pillows less than some of his neighbors have. Frodo will sleep on the k-th bed in the row. What is the maximum number of pillows he can have so that every hobbit has at least one pillow, every pillow is given to some hobbit and no one is hurt?", "input_spec": "The only line contain three integers n, m and k (1\u2009\u2264\u2009n\u2009\u2264\u2009m\u2009\u2264\u2009109, 1\u2009\u2264\u2009k\u2009\u2264\u2009n)\u00a0\u2014 the number of hobbits, the number of pillows and the number of Frodo's bed.", "output_spec": "Print single integer\u00a0\u2014 the maximum number of pillows Frodo can have so that no one is hurt.", "sample_inputs": ["4 6 2", "3 10 3", "3 6 1"], "sample_outputs": ["2", "4", "3"], "notes": "NoteIn the first example Frodo can have at most two pillows. In this case, he can give two pillows to the hobbit on the first bed, and one pillow to each of the hobbits on the third and the fourth beds.In the second example Frodo can take at most four pillows, giving three pillows to each of the others.In the third example Frodo can take three pillows, giving two pillows to the hobbit in the middle and one pillow to the hobbit on the third bed."}, "src_uid": "da9ddd00f46021e8ee9db4a8deed017c"}
{"nl": {"description": "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": "Recently Vasya found a golden ticket \u2014 a sequence which consists of $$$n$$$ digits $$$a_1a_2\\dots a_n$$$. Vasya considers a ticket to be lucky if it can be divided into two or more non-intersecting segments with equal sums. For example, ticket $$$350178$$$ is lucky since it can be divided into three segments $$$350$$$, $$$17$$$ and $$$8$$$: $$$3+5+0=1+7=8$$$. Note that each digit of sequence should belong to exactly one segment.Help Vasya! Tell him if the golden ticket he found is lucky or not.", "input_spec": "The first line contains one integer $$$n$$$ ($$$2 \\le n \\le 100$$$) \u2014 the number of digits in the ticket. The second line contains $$$n$$$ digits $$$a_1 a_2 \\dots a_n$$$ ($$$0 \\le a_i \\le 9$$$) \u2014 the golden ticket. Digits are printed without spaces.", "output_spec": "If the golden ticket is lucky then print \"YES\", otherwise print \"NO\" (both case insensitive).", "sample_inputs": ["5\n73452", "4\n1248"], "sample_outputs": ["YES", "NO"], "notes": "NoteIn the first example the ticket can be divided into $$$7$$$, $$$34$$$ and $$$52$$$: $$$7=3+4=5+2$$$.In the second example it is impossible to divide ticket into segments with equal sum."}, "src_uid": "410296a01b97a0a39b6683569c84d56c"}
{"nl": {"description": "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": "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": "One day Vasya the Hipster decided to count how many socks he had. It turned out that he had a red socks and b blue socks.According to the latest fashion, hipsters should wear the socks of different colors: a red one on the left foot, a blue one on the right foot.Every day Vasya puts on new socks in the morning and throws them away before going to bed as he doesn't want to wash them.Vasya wonders, what is the maximum number of days when he can dress fashionable and wear different socks, and after that, for how many days he can then wear the same socks until he either runs out of socks or cannot make a single pair from the socks he's got.Can you help him?", "input_spec": "The single line of the input contains two positive integers a and b (1\u2009\u2264\u2009a,\u2009b\u2009\u2264\u2009100) \u2014 the number of red and blue socks that Vasya's got.", "output_spec": "Print two space-separated integers \u2014 the maximum number of days when Vasya can wear different socks and the number of days when he can wear the same socks until he either runs out of socks or cannot make a single pair from the socks he's got. Keep in mind that at the end of the day Vasya throws away the socks that he's been wearing on that day.", "sample_inputs": ["3 1", "2 3", "7 3"], "sample_outputs": ["1 1", "2 0", "3 2"], "notes": "NoteIn the first sample Vasya can first put on one pair of different socks, after that he has two red socks left to wear on the second day."}, "src_uid": "775766790e91e539c1cfaa5030e5b955"}
{"nl": {"description": "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": "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": "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": "Xenia the beginner mathematician is a third year student at elementary school. She is now learning the addition operation.The teacher has written down the sum of multiple numbers. Pupils should calculate the sum. To make the calculation easier, the sum only contains numbers 1, 2 and 3. Still, that isn't enough for Xenia. She is only beginning to count, so she can calculate a sum only if the summands follow in non-decreasing order. For example, she can't calculate sum 1+3+2+1 but she can calculate sums 1+1+2 and 3+3.You've got the sum that was written on the board. Rearrange the summans and print the sum in such a way that Xenia can calculate the sum.", "input_spec": "The first line contains a non-empty string s \u2014 the sum Xenia needs to count. String s contains no spaces. It only contains digits and characters \"+\". Besides, string s is a correct sum of numbers 1, 2 and 3. String s is at most 100 characters long.", "output_spec": "Print the new sum that Xenia can count.", "sample_inputs": ["3+2+1", "1+1+3+1+3", "2"], "sample_outputs": ["1+2+3", "1+1+1+3+3", "2"], "notes": null}, "src_uid": "76c7312733ef9d8278521cf09d3ccbc8"}
{"nl": {"description": "Polycarp really likes writing the word \"kotlin\". He wrote this word several times in a row without spaces. For example, he could write the string like \"kotlinkotlinkotlinkotlin\".Polycarp sliced (cut) the written string into $$$n$$$ pieces and mixed them. As a result, he has $$$n$$$ strings $$$s_1, s_2, \\dots, s_n$$$ and he can arrange them in the right order, concatenate (join) all of them and get a string like \"kotlinkotlin...kotlin\".Help Polycarp to find the right order of strings $$$s_1, s_2, \\dots, s_n$$$, so that if he writes the strings in this order, he will get the word \"kotlin\" or the sequence of this word.Pay attention that you must use all given strings and you must use each string only once.", "input_spec": "The first line of the input contains one integer $$$n$$$ ($$$1 \\le n \\le 10^5$$$) \u2014 the number of Polycarp's strings. Next lines of the input contain $$$n$$$ Polycarp's strings. Total sum of their lengths doesn't exceed $$$3\\cdot10^5$$$. It's guaranteed that there is the right order of arrangement the strings that if you concatenate them into one string, you will get some non-empty sequence of the word \"kotlin\".", "output_spec": "Print $$$n$$$ different integers $$$p_1, p_2, \\dots, p_n$$$ ($$$1 \\le p_i \\le n$$$), where $$$p_i$$$ is an index of the string that should be the $$$i$$$-th in a required concatenation. In other words, the result of concatenation $$$s_{p_1}+s_{p_2}+\\dots+s_{p_n}$$$ must be in the form \"kotlinkotlin...kotlin\". If there are many solutions, print any of them.", "sample_inputs": ["2\nlin\nkot", "4\nlinkotlinkotlinkotl\nkotlin\nin\nkot", "8\ni\nn\ntlin\no\nko\nt\nk\nl"], "sample_outputs": ["2 1", "2 4 1 3", "7 4 3 5 6 8 1 2"], "notes": null}, "src_uid": "a853ca8432d7b8966b12fc85c28ab979"}
{"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": "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": "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": "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": "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": "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": "Mashmokh works in a factory. At the end of each day he must turn off all of the lights. The lights on the factory are indexed from 1 to n. There are n buttons in Mashmokh's room indexed from 1 to n as well. If Mashmokh pushes button with index i, then each light with index not less than i that is still turned on turns off.Mashmokh is not very clever. So instead of pushing the first button he pushes some of the buttons randomly each night. He pushed m distinct buttons b1,\u2009b2,\u2009...,\u2009bm (the buttons were pushed consecutively in the given order) this night. Now he wants to know for each light the index of the button that turned this light off. Please note that the index of button bi is actually bi, not i.Please, help Mashmokh, print these indices.", "input_spec": "The first line of the input contains two space-separated integers n and m (1\u2009\u2264\u2009n,\u2009m\u2009\u2264\u2009100), the number of the factory lights and the pushed buttons respectively. The next line contains m distinct space-separated integers b1,\u2009b2,\u2009...,\u2009bm\u00a0(1\u2009\u2264\u2009bi\u2009\u2264\u2009n). It is guaranteed that all lights will be turned off after pushing all buttons.", "output_spec": "Output n space-separated integers where the i-th number is index of the button that turns the i-th light off.", "sample_inputs": ["5 4\n4 3 1 2", "5 5\n5 4 3 2 1"], "sample_outputs": ["1 1 3 4 4", "1 2 3 4 5"], "notes": "NoteIn the first sample, after pressing button number 4, lights 4 and 5 are turned off and lights 1, 2 and 3 are still on. Then after pressing button number 3, light number 3 is turned off as well. Pressing button number 1 turns off lights number 1 and 2 as well so pressing button number 2 in the end has no effect. Thus button number 4 turned lights 4 and 5 off, button number 3 turned light 3 off and button number 1 turned light 1 and 2 off."}, "src_uid": "2e44c8aabab7ef7b06bbab8719a8d863"}
{"nl": {"description": "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": "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": "Memory and his friend Lexa are competing to get higher score in one popular computer game. Memory starts with score a and Lexa starts with score b. In a single turn, both Memory and Lexa get some integer in the range [\u2009-\u2009k;k] (i.e. one integer among \u2009-\u2009k,\u2009\u2009-\u2009k\u2009+\u20091,\u2009\u2009-\u2009k\u2009+\u20092,\u2009...,\u2009\u2009-\u20092,\u2009\u2009-\u20091,\u20090,\u20091,\u20092,\u2009...,\u2009k\u2009-\u20091,\u2009k) and add them to their current scores. The game has exactly t turns. Memory and Lexa, however, are not good at this game, so they both always get a random integer at their turn.Memory wonders how many possible games exist such that he ends with a strictly higher score than Lexa. Two games are considered to be different if in at least one turn at least one player gets different score. There are (2k\u2009+\u20091)2t games in total. Since the answer can be very large, you should print it modulo 109\u2009+\u20097. Please solve this problem for Memory.", "input_spec": "The first and only line of input contains the four integers a, b, k, and t (1\u2009\u2264\u2009a,\u2009b\u2009\u2264\u2009100, 1\u2009\u2264\u2009k\u2009\u2264\u20091000, 1\u2009\u2264\u2009t\u2009\u2264\u2009100)\u00a0\u2014 the amount Memory and Lexa start with, the number k, and the number of turns respectively.", "output_spec": "Print the number of possible games satisfying the conditions modulo 1\u2009000\u2009000\u2009007 (109\u2009+\u20097) in one line.", "sample_inputs": ["1 2 2 1", "1 1 1 2", "2 12 3 1"], "sample_outputs": ["6", "31", "0"], "notes": "NoteIn the first sample test, Memory starts with 1 and Lexa starts with 2. If Lexa picks \u2009-\u20092, Memory can pick 0, 1, or 2 to win. If Lexa picks \u2009-\u20091, Memory can pick 1 or 2 to win. If Lexa picks 0, Memory can pick 2 to win. If Lexa picks 1 or 2, Memory cannot win. Thus, there are 3\u2009+\u20092\u2009+\u20091\u2009=\u20096 possible games in which Memory wins."}, "src_uid": "8b8327512a318a5b5afd531ff7223bd0"}
{"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": "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": "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": "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": "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": "You are given an array of positive integers a1,\u2009a2,\u2009...,\u2009an\u2009\u00d7\u2009T of length n\u2009\u00d7\u2009T. We know that for any i\u2009>\u2009n it is true that ai\u2009=\u2009ai\u2009-\u2009n. Find the length of the longest non-decreasing sequence of the given array.", "input_spec": "The first line contains two space-separated integers: n, T (1\u2009\u2264\u2009n\u2009\u2264\u2009100, 1\u2009\u2264\u2009T\u2009\u2264\u2009107). The second line contains n space-separated integers a1,\u2009a2,\u2009...,\u2009an (1\u2009\u2264\u2009ai\u2009\u2264\u2009300).", "output_spec": "Print a single number \u2014 the length of a sought sequence.", "sample_inputs": ["4 3\n3 1 4 2"], "sample_outputs": ["5"], "notes": "NoteThe array given in the sample looks like that: 3, 1, 4, 2, 3, 1, 4, 2, 3, 1, 4, 2. The elements in bold form the largest non-decreasing subsequence. "}, "src_uid": "26cf484fa4cb3dc2ab09adce7a3fc9b2"}
{"nl": {"description": "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": "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": "You are given a sequence of integers $$$a_1, a_2, \\dots, a_n$$$. You need to paint elements in colors, so that:   If we consider any color, all elements of this color must be divisible by the minimal element of this color.  The number of used colors must be minimized. For example, it's fine to paint elements $$$[40, 10, 60]$$$ in a single color, because they are all divisible by $$$10$$$. You can use any color an arbitrary amount of times (in particular, it is allowed to use a color only once). The elements painted in one color do not need to be consecutive.For example, if $$$a=[6, 2, 3, 4, 12]$$$ then two colors are required: let's paint $$$6$$$, $$$3$$$ and $$$12$$$ in the first color ($$$6$$$, $$$3$$$ and $$$12$$$ are divisible by $$$3$$$) and paint $$$2$$$ and $$$4$$$ in the second color ($$$2$$$ and $$$4$$$ are divisible by $$$2$$$). For example, if $$$a=[10, 7, 15]$$$ then $$$3$$$ colors are required (we can simply paint each element in an unique color).", "input_spec": "The first line contains an integer $$$n$$$ ($$$1 \\le n \\le 100$$$), where $$$n$$$ is the length of the given sequence. The second line contains $$$n$$$ integers $$$a_1, a_2, \\dots, a_n$$$ ($$$1 \\le a_i \\le 100$$$). These numbers can contain duplicates.", "output_spec": "Print the minimal number of colors to paint all the given numbers in a valid way.", "sample_inputs": ["6\n10 2 3 5 4 2", "4\n100 100 100 100", "8\n7 6 5 4 3 2 2 3"], "sample_outputs": ["3", "1", "4"], "notes": "NoteIn the first example, one possible way to paint the elements in $$$3$$$ colors is:  paint in the first color the elements: $$$a_1=10$$$ and $$$a_4=5$$$,  paint in the second color the element $$$a_3=3$$$,  paint in the third color the elements: $$$a_2=2$$$, $$$a_5=4$$$ and $$$a_6=2$$$. In the second example, you can use one color to paint all the elements.In the third example, one possible way to paint the elements in $$$4$$$ colors is:  paint in the first color the elements: $$$a_4=4$$$, $$$a_6=2$$$ and $$$a_7=2$$$,  paint in the second color the elements: $$$a_2=6$$$, $$$a_5=3$$$ and $$$a_8=3$$$,  paint in the third color the element $$$a_3=5$$$,  paint in the fourth color the element $$$a_1=7$$$. "}, "src_uid": "63d9b7416aa96129c57d20ec6145e0cd"}
{"nl": {"description": "There are $$$n$$$ 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": "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": "Madoka decided to entrust the organization of a major computer game tournament \"OSU\"!In this tournament, matches are held according to the \"Olympic system\". In other words, there are $$$2^n$$$ participants in the tournament, numbered with integers from $$$1$$$ to $$$2^n$$$. There are $$$n$$$ rounds in total in the tournament. In the $$$i$$$-th round there are $$$2^{n - i}$$$ matches between two players (one of whom is right, the other is left), after which the winners go further along the tournament grid, and the losing participants are eliminated from the tournament. Herewith, the relative order in the next round does not change. And the winner of the tournament\u00a0\u2014 is the last remaining participant.But the smaller the participant's number, the more he will pay Madoka if he wins, so Madoka wants the participant with the lowest number to win. To do this, she can arrange the participants in the first round as she likes, and also determine for each match who will win\u00a0\u2014 the participant on the left or right.But Madoka knows that tournament sponsors can change the winner in matches no more than $$$k$$$ times. (That is, if the participant on the left won before the change, then the participant on the right will win after the change, and if the participant on the right won, then the participant on the left will win after the change).  So, the first image shows the tournament grid that Madoka made, where the red lines denote who should win the match. And the second one shows the tournament grid, after one change in the outcome of the match by sponsors (a match between $$$1$$$ and $$$3$$$ players). Print the minimum possible number of the winner in the tournament, which Madoka can get regardless of changes in sponsors. But since the answer can be very large, output it modulo $$$10^9 + 7$$$. Note that we need to minimize the answer, and only then take it modulo.", "input_spec": "The first and the only line contains two integers $$$n$$$ and $$$k$$$ ($$$1 \\le n \\le 10^5, 1 \\le k \\le \\min(2^n - 1, 10^9)$$$)\u00a0\u2014 the number of rounds in the tournament and the number of outcomes that sponsors can change.", "output_spec": "Print exactly one integer\u00a0\u2014 the minimum number of the winner modulo $$$10^9 + 7$$$", "sample_inputs": ["1 1", "2 1", "3 2"], "sample_outputs": ["2", "3", "7"], "notes": "NoteIn the first example, there is only one match between players $$$1$$$ and $$$2$$$, so the sponsors can always make player $$$2$$$ wins.The tournament grid from the second example is shown in the picture in the statement."}, "src_uid": "dc7b887afcc2e95c4e90619ceda63071"}
{"nl": {"description": "Ilya is an experienced player in tic-tac-toe on the 4\u2009\u00d7\u20094 field. He always starts and plays with Xs. He played a lot of games today with his friend Arseny. The friends became tired and didn't finish the last game. It was Ilya's turn in the game when they left it. Determine whether Ilya could have won the game by making single turn or not. The rules of tic-tac-toe on the 4\u2009\u00d7\u20094 field are as follows. Before the first turn all the field cells are empty. The two players take turns placing their signs into empty cells (the first player places Xs, the second player places Os). The player who places Xs goes first, the another one goes second. The winner is the player who first gets three of his signs in a row next to each other (horizontal, vertical or diagonal).", "input_spec": "The tic-tac-toe position is given in four lines. Each of these lines contains four characters. Each character is '.' (empty cell), 'x' (lowercase English letter x), or 'o' (lowercase English letter o). It is guaranteed that the position is reachable playing tic-tac-toe, and it is Ilya's turn now (in particular, it means that the game is not finished). It is possible that all the cells are empty, it means that the friends left without making single turn.", "output_spec": "Print single line: \"YES\" in case Ilya could have won by making single turn, and \"NO\" otherwise.", "sample_inputs": ["xx..\n.oo.\nx...\noox.", "x.ox\nox..\nx.o.\noo.x", "x..x\n..oo\no...\nx.xo", "o.x.\no...\n.x..\nooxx"], "sample_outputs": ["YES", "NO", "YES", "NO"], "notes": "NoteIn the first example Ilya had two winning moves: to the empty cell in the left column and to the leftmost empty cell in the first row.In the second example it wasn't possible to win by making single turn.In the third example Ilya could have won by placing X in the last row between two existing Xs.In the fourth example it wasn't possible to win by making single turn."}, "src_uid": "ca4a77fe9718b8bd0b3cc3d956e22917"}
{"nl": {"description": "So many wall designs to choose from! Even modulo 106\u2009+\u20093, it's an enormous number. Given that recently Heidi acquired an unlimited supply of bricks, her choices are endless! She really needs to do something to narrow them down.Heidi is quick to come up with criteria for a useful wall:  In a useful wall, at least one segment is wider than W bricks. This should give the zombies something to hit their heads against. Or,  in a useful wall, at least one column is higher than H bricks. This provides a lookout from which zombies can be spotted at a distance. This should rule out a fair amount of possibilities, right? Help Heidi compute the number of useless walls that do not confirm to either of these criteria. In other words, a wall is useless if every segment has width at most W and height at most H.Parameter C, the total width of the wall, has the same meaning as in the easy version. However, note that the number of bricks is now unlimited.Output the number of useless walls modulo 106\u2009+\u20093.", "input_spec": "The first and the only line of the input contains three space-separated integers C, W and H (1\u2009\u2264\u2009C\u2009\u2264\u2009108, 1\u2009\u2264\u2009W,\u2009H\u2009\u2264\u2009100).", "output_spec": "Output the number of different walls, modulo 106\u2009+\u20093, which are useless according to Heidi's criteria.", "sample_inputs": ["1 1 1", "1 2 2", "1 2 3", "3 2 2", "5 4 9", "40 37 65"], "sample_outputs": ["2", "3", "4", "19", "40951", "933869"], "notes": "NoteIf there is no brick in any of the columns, the structure is considered as a useless wall."}, "src_uid": "bb1c0ff47186e10e00b7dde6758ff1c1"}
{"nl": {"description": "Uncle Fyodor, Matroskin the Cat and Sharic the Dog live their simple but happy lives in Prostokvashino. Sometimes they receive parcels from Uncle Fyodor\u2019s parents and sometimes from anonymous benefactors, in which case it is hard to determine to which one of them the package has been sent. A photographic rifle is obviously for Sharic who loves hunting and fish is for Matroskin, but for whom was a new video game console meant? Every one of the three friends claimed that the present is for him and nearly quarreled. Uncle Fyodor had an idea how to solve the problem justly: they should suppose that the console was sent to all three of them and play it in turns. Everybody got relieved but then yet another burning problem popped up \u2014 who will play first? This time Matroskin came up with a brilliant solution, suggesting the most fair way to find it out: play rock-paper-scissors together. The rules of the game are very simple. On the count of three every player shows a combination with his hand (or paw). The combination corresponds to one of three things: a rock, scissors or paper. Some of the gestures win over some other ones according to well-known rules: the rock breaks the scissors, the scissors cut the paper, and the paper gets wrapped over the stone. Usually there are two players. Yet there are three friends, that\u2019s why they decided to choose the winner like that: If someone shows the gesture that wins over the other two players, then that player wins. Otherwise, another game round is required. Write a program that will determine the winner by the gestures they have shown.", "input_spec": "The first input line contains the name of the gesture that Uncle Fyodor showed, the second line shows which gesture Matroskin showed and the third line shows Sharic\u2019s gesture. ", "output_spec": "Print \"F\" (without quotes) if Uncle Fyodor wins. Print \"M\" if Matroskin wins and \"S\" if Sharic wins. If it is impossible to find the winner, print \"?\".", "sample_inputs": ["rock\nrock\nrock", "paper\nrock\nrock", "scissors\nrock\nrock", "scissors\npaper\nrock"], "sample_outputs": ["?", "F", "?", "?"], "notes": null}, "src_uid": "072c7d29a1b338609a72ab6b73988282"}
{"nl": {"description": "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": "\u00c6sir - CHAOS \u00c6sir - V.\"Everything has been planned out. No more hidden concerns. The condition of Cytus is also perfect.The time right now...... 00:01:12......It's time.\"The emotion samples are now sufficient. After almost 3 years, it's time for Ivy to awake her bonded sister, Vanessa.The system inside A.R.C.'s Library core can be considered as an undirected graph with infinite number of processing nodes, numbered with all positive integers ($$$1, 2, 3, \\ldots$$$). The node with a number $$$x$$$ ($$$x > 1$$$), is directly connected with a node with number $$$\\frac{x}{f(x)}$$$, with $$$f(x)$$$ being the lowest prime divisor of $$$x$$$.Vanessa's mind is divided into $$$n$$$ fragments. Due to more than 500 years of coma, the fragments have been scattered: the $$$i$$$-th fragment is now located at the node with a number $$$k_i!$$$ (a factorial of $$$k_i$$$).To maximize the chance of successful awakening, Ivy decides to place the samples in a node $$$P$$$, so that the total length of paths from each fragment to $$$P$$$ is smallest possible. If there are multiple fragments located at the same node, the path from that node to $$$P$$$ needs to be counted multiple times.In the world of zeros and ones, such a requirement is very simple for Ivy. Not longer than a second later, she has already figured out such a node.But for a mere human like you, is this still possible?For simplicity, please answer the minimal sum of paths' lengths from every fragment to the emotion samples' assembly node $$$P$$$.", "input_spec": "The first line contains an integer $$$n$$$ ($$$1 \\le n \\le 10^6$$$)\u00a0\u2014 number of fragments of Vanessa's mind. The second line contains $$$n$$$ integers: $$$k_1, k_2, \\ldots, k_n$$$ ($$$0 \\le k_i \\le 5000$$$), denoting the nodes where fragments of Vanessa's mind are located: the $$$i$$$-th fragment is at the node with a number $$$k_i!$$$.", "output_spec": "Print a single integer, denoting the minimal sum of path from every fragment to the node with the emotion samples (a.k.a. node $$$P$$$). As a reminder, if there are multiple fragments at the same node, the distance from that node to $$$P$$$ needs to be counted multiple times as well.", "sample_inputs": ["3\n2 1 4", "4\n3 1 4 4", "4\n3 1 4 1", "5\n3 1 4 1 5"], "sample_outputs": ["5", "6", "6", "11"], "notes": "NoteConsidering the first $$$24$$$ nodes of the system, the node network will look as follows (the nodes $$$1!$$$, $$$2!$$$, $$$3!$$$, $$$4!$$$ are drawn bold):For the first example, Ivy will place the emotion samples at the node $$$1$$$. From here:  The distance from Vanessa's first fragment to the node $$$1$$$ is $$$1$$$.  The distance from Vanessa's second fragment to the node $$$1$$$ is $$$0$$$.  The distance from Vanessa's third fragment to the node $$$1$$$ is $$$4$$$. The total length is $$$5$$$.For the second example, the assembly node will be $$$6$$$. From here:  The distance from Vanessa's first fragment to the node $$$6$$$ is $$$0$$$.  The distance from Vanessa's second fragment to the node $$$6$$$ is $$$2$$$.  The distance from Vanessa's third fragment to the node $$$6$$$ is $$$2$$$.  The distance from Vanessa's fourth fragment to the node $$$6$$$ is again $$$2$$$. The total path length is $$$6$$$."}, "src_uid": "40002052843ca0357dbd3158b16d59f4"}
{"nl": {"description": "You will receive 3 points for solving this problem.Manao is designing the genetic code for a new type of algae to efficiently produce fuel. Specifically, Manao is focusing on a stretch of DNA that encodes one protein. The stretch of DNA is represented by a string containing only the characters 'A', 'T', 'G' and 'C'.Manao has determined that if the stretch of DNA contains a maximal sequence of consecutive identical nucleotides that is of even length, then the protein will be nonfunctional. For example, consider a protein described by DNA string \"GTTAAAG\". It contains four maximal sequences of consecutive identical nucleotides: \"G\", \"TT\", \"AAA\", and \"G\". The protein is nonfunctional because sequence \"TT\" has even length.Manao is trying to obtain a functional protein from the protein he currently has. Manao can insert additional nucleotides into the DNA stretch. Each additional nucleotide is a character from the set {'A', 'T', 'G', 'C'}. Manao wants to determine the minimum number of insertions necessary to make the DNA encode a functional protein.", "input_spec": "The input consists of a single line, containing a string s of length n (1\u2009\u2264\u2009n\u2009\u2264\u2009100). Each character of s will be from the set {'A', 'T', 'G', 'C'}. This problem doesn't have subproblems. You will get 3 points for the correct submission.", "output_spec": "The program should print on one line a single integer representing the minimum number of 'A', 'T', 'G', 'C' characters that are required to be inserted into the input string in order to make all runs of identical characters have odd length.", "sample_inputs": ["GTTAAAG", "AACCAACCAAAAC"], "sample_outputs": ["1", "5"], "notes": "NoteIn the first example, it is sufficient to insert a single nucleotide of any type between the two 'T's in the sequence to restore the functionality of the protein."}, "src_uid": "8b26ca1ca2b28166c3d25dceb1f3d49f"}
{"nl": {"description": "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": "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": "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": "\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": "Petya is a big fan of mathematics, especially its part related to fractions. Recently he learned that a fraction  is called proper iff its numerator is smaller than its denominator (a\u2009<\u2009b) and that the fraction is called irreducible if its numerator and its denominator are coprime (they do not have positive common divisors except 1).During his free time, Petya thinks about proper irreducible fractions and converts them to decimals using the calculator. One day he mistakenly pressed addition button (\u2009+\u2009) instead of division button (\u00f7) and got sum of numerator and denominator that was equal to n instead of the expected decimal notation. Petya wanted to restore the original fraction, but soon he realized that it might not be done uniquely. That's why he decided to determine maximum possible proper irreducible fraction  such that sum of its numerator and denominator equals n. Help Petya deal with this problem. ", "input_spec": "In the only line of input there is an integer n (3\u2009\u2264\u2009n\u2009\u2264\u20091000), the sum of numerator and denominator of the fraction.", "output_spec": "Output two space-separated positive integers a and b, numerator and denominator of the maximum possible proper irreducible fraction satisfying the given sum.", "sample_inputs": ["3", "4", "12"], "sample_outputs": ["1 2", "1 3", "5 7"], "notes": null}, "src_uid": "0af3515ed98d9d01ce00546333e98e77"}
{"nl": {"description": "There are $$$n$$$ cities and $$$n-1$$$ two-way roads in Treeland. Each road connects a pair of different cities. From any city you can drive to any other, moving only along the roads. Cities are numbered from $$$1$$$ to $$$n$$$. Yes, of course, you recognized an undirected tree in this description.There is exactly one flag in each city, in the $$$i$$$-th city the flag color is $$$c_i$$$. The colors of the flags in different cities may be the same.If the King travels along the route $$$[u_1, u_2, u_3, \\dots, u_k]$$$, then this means that he starts in the city $$$u_1$$$, then moves to the city $$$u_2$$$ ($$$u_2$$$ is connected by road with $$$u_1$$$), then from $$$u_2$$$ to $$$u_3$$$ ($$$u_3$$$ is connected by road to $$$u_2$$$), and so on until he arrives in the city of $$$u_k$$$. It is possible that during this route the King will visit the same city more than once. In other words, the route $$$[u_1, u_2, u_3, \\dots, u_k]$$$ does not necessarily consist of different cities. In terms of graph theory \u2014 the King moves from $$$u_1$$$ to $$$u_k$$$ along some path $$$[u_1, u_2, u_3, \\dots, u_k]$$$, which is not necessarily simple (for all $$$j$$$ from $$$1$$$ to $$$k-1$$$ of the city $$$u_j$$$ and $$$u_{j+1}$$$ are connected by road).When the King moves from one city to another, city heads exchange flags as a sign of their friendship.    Example of moving the King along the route $$$[1, 4, 2, 6]$$$. The color of the vertex matches the color of the flag at that vertex. For aesthetic reasons, the King wants the flag color in the city $$$i$$$ to be equal to $$$d_i$$$ for all $$$i$$$ from $$$1$$$ to $$$n$$$. Determine whether the King can choose some route and drive along it so that for each city the flag color in it turns out to be equal to the desired color $$$d_i$$$. Note that the King can choose (and drive) exactly one route. If yes, find the shortest possible route for the King.If the initial colors of the flags already match the King's requirements (i.e. $$$c_i=d_i$$$ for all $$$i$$$), then consider that the King makes a route of length $$$k=0$$$.", "input_spec": "The first line contains an integer $$$t$$$ ($$$1 \\le t \\le 10^5$$$) \u2014 the number of test cases to solve. The following are the cases. Each case begins with a line containing an integer $$$n$$$ ($$$2 \\le n \\le 2\\cdot10^5$$$) \u2014 the number of cities in Treeland. The following is a line of $$$n$$$ integers $$$c_1, c_2, \\dots, c_n$$$ ($$$1 \\le c_i \\le 10^6$$$), where $$$c_i$$$ denotes the color of the flag at the $$$i$$$-th vertex before the King's journey. The following is a line of $$$n$$$ integers $$$d_1, d_2, \\dots, d_n$$$ ($$$1 \\le d_i \\le 10^6$$$), where $$$d_i$$$ denotes the required flag color at the $$$i$$$-th vertex after the completion of the King's journey. Further, in the $$$n-1$$$ line, the Treeland's roads are listed. Each road is given by a line containing two integers $$$x_j, y_j$$$ ($$$1 \\le x_j, y_j \\le n$$$) \u2014 numbers of cities that are connected by the $$$j$$$ th road. It is guaranteed that from every city you can get to any other by road (in other words, the system of cities and roads forms an undirected tree). The sum of all $$$n$$$ values \u200b\u200bfor all cases in one test does not exceed $$$2\\cdot10^5$$$.", "output_spec": "Print the answers to all cases in the order of their appearance in the input data. Each answer must begin with a line containing \"Yes\" (in the case of a positive answer) or \"No\" (in the case that the required route does not exist). In the case of a positive answer, the following line must contain an integer $$$k$$$ \u2014 the number of cities in the shortest possible route of the King. The next line should contain the required route $$$u_1, u_2, \\dots, u_k$$$ ($$$1 \\le u_i \\le n$$$). You can skip the line if $$$k=0$$$.", "sample_inputs": ["1\n7\n2 3 2 7 1 1 3\n7 1 2 3 1 2 3\n1 7\n4 1\n2 6\n2 3\n2 4\n5 4", "1\n5\n1 2 2 2 2\n2 2 2 2 1\n1 2\n2 3\n3 4\n4 5", "3\n4\n10 20 10 20\n20 10 20 10\n1 2\n1 3\n1 4\n2\n1000000 1000000\n1000000 1000000\n1 2\n10\n4 2 2 4 2 4 1 2 3 4\n4 2 4 4 3 2 1 2 4 2\n5 8\n6 9\n10 5\n1 10\n7 10\n3 4\n5 9\n3 10\n2 4"], "sample_outputs": ["Yes\n4\n1 4 2 6", "Yes\n5\n1 2 3 4 5", "No\nYes\n0\nYes\n5\n3 10 5 9 6"], "notes": null}, "src_uid": "78f839ac8cd0a716a0f0211fe3219520"}
{"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": "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": "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": "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": "The Rebel fleet is afraid that the Empire might want to strike back again. Princess Heidi needs to know if it is possible to assign R Rebel spaceships to guard B bases so that every base has exactly one guardian and each spaceship has exactly one assigned base (in other words, the assignment is a perfect matching). Since she knows how reckless her pilots are, she wants to be sure that any two (straight) paths \u2013 from a base to its assigned spaceship \u2013 do not intersect in the galaxy plane (that is, in 2D), and so there is no risk of collision.", "input_spec": "The first line contains two space-separated integers R,\u2009B(1\u2009\u2264\u2009R,\u2009B\u2009\u2264\u200910). For 1\u2009\u2264\u2009i\u2009\u2264\u2009R, the i\u2009+\u20091-th line contains two space-separated integers xi and yi (|xi|,\u2009|yi|\u2009\u2264\u200910000) denoting the coordinates of the i-th Rebel spaceship. The following B lines have the same format, denoting the position of bases. It is guaranteed that no two points coincide and that no three points are on the same line.", "output_spec": "If it is possible to connect Rebel spaceships and bases so as satisfy the constraint, output Yes, otherwise output No (without quote).", "sample_inputs": ["3 3\n0 0\n2 0\n3 1\n-2 1\n0 3\n2 2", "2 1\n1 0\n2 2\n3 1"], "sample_outputs": ["Yes", "No"], "notes": "NoteFor the first example, one possible way is to connect the Rebels and bases in order.For the second example, there is no perfect matching between Rebels and bases."}, "src_uid": "65f81f621c228c09915adcb05256c634"}
{"nl": {"description": "The 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": "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": "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": "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": "Long time ago Alex created an interesting problem about parallelogram. The input data for this problem contained four integer points on the Cartesian plane, that defined the set of vertices of some non-degenerate (positive area) parallelogram. Points not necessary were given in the order of clockwise or counterclockwise traversal.Alex had very nice test for this problem, but is somehow happened that the last line of the input was lost and now he has only three out of four points of the original parallelogram. He remembers that test was so good that he asks you to restore it given only these three points.", "input_spec": "The input consists of three lines, each containing a pair of integer coordinates xi and yi (\u2009-\u20091000\u2009\u2264\u2009xi,\u2009yi\u2009\u2264\u20091000). It's guaranteed that these three points do not lie on the same line and no two of them coincide.", "output_spec": "First print integer k\u00a0\u2014 the number of ways to add one new integer point such that the obtained set defines some parallelogram of positive area. There is no requirement for the points to be arranged in any special order (like traversal), they just define the set of vertices. Then print k lines, each containing a pair of integer\u00a0\u2014 possible coordinates of the fourth point.", "sample_inputs": ["0 0\n1 0\n0 1"], "sample_outputs": ["3\n1 -1\n-1 1\n1 1"], "notes": "NoteIf you need clarification of what parallelogram is, please check Wikipedia page:https://en.wikipedia.org/wiki/Parallelogram"}, "src_uid": "7725f9906a1b87bf4e866df03112f1e0"}
{"nl": {"description": "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": "A chessboard n\u2009\u00d7\u2009m in size is given. During the zero minute we repaint all the black squares to the 0 color. During the i-th minute we repaint to the i color the initially black squares that have exactly four corner-adjacent squares painted i\u2009-\u20091 (all such squares are repainted simultaneously). This process continues ad infinitum. You have to figure out how many squares we repainted exactly x times.The upper left square of the board has to be assumed to be always black. Two squares are called corner-adjacent, if they have exactly one common point.", "input_spec": "The first line contains integers n and m (1\u2009\u2264\u2009n,\u2009m\u2009\u2264\u20095000). The second line contains integer x (1\u2009\u2264\u2009x\u2009\u2264\u2009109).", "output_spec": "Print how many squares will be painted exactly x times.", "sample_inputs": ["3 3\n1", "3 3\n2", "1 1\n1"], "sample_outputs": ["4", "1", "1"], "notes": null}, "src_uid": "fa1ef5f9bceeb7266cc597ba8f2161cb"}
{"nl": {"description": "Maxim loves to fill in a matrix in a special manner. Here is a pseudocode of filling in a matrix of size (m\u2009+\u20091)\u2009\u00d7\u2009(m\u2009+\u20091):Maxim asks you to count, how many numbers m (1\u2009\u2264\u2009m\u2009\u2264\u2009n) are there, such that the sum of values in the cells in the row number m\u2009+\u20091 of the resulting matrix equals t.Expression (x xor y) means applying the operation of bitwise excluding \"OR\" to numbers x and y. The given operation exists in all modern programming languages. For example, in languages C++ and Java it is represented by character \"^\", in Pascal \u2014 by \"xor\".", "input_spec": "A single line contains two integers n and t (1\u2009\u2264\u2009n,\u2009t\u2009\u2264\u20091012,\u2009t\u2009\u2264\u2009n\u2009+\u20091). 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 answer to the problem. ", "sample_inputs": ["1 1", "3 2", "3 3", "1000000000000 1048576"], "sample_outputs": ["1", "1", "0", "118606527258"], "notes": null}, "src_uid": "727d5b601694e5e0f0cf3a9ca25323fc"}
{"nl": {"description": "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": "This night wasn't easy on Vasya. His favorite team lost, and he didn't find himself victorious either\u00a0\u2014 although he played perfectly, his teammates let him down every time. He had to win at least one more time, but the losestreak only grew longer and longer... It's no wonder he didn't get any sleep this night at all.In the morning, Vasya was waiting the bus to the university on the bus stop. Vasya's thoughts were hazy and so he couldn't remember the right bus' number quite right and got onto the bus with the number $$$n$$$.In the bus, Vasya thought that he could get the order of the digits in the number of the bus wrong. Futhermore, he could \"see\" some digits several times, but the digits he saw were definitely in the real number of the bus. For example, if Vasya saw the number 2028, it could mean that the real bus number could be 2028, 8022, 2820 or just 820. However, numbers 80, 22208, 52 definitely couldn't be the number of the bus. Also, real bus number couldn't start with the digit 0, this meaning that, for example, number 082 couldn't be the real bus number too.Given $$$n$$$, determine the total number of possible bus number variants.", "input_spec": "The first line contains one integer $$$n$$$ ($$$1 \\leq n \\leq 10^{18}$$$)\u00a0\u2014 the number of the bus that was seen by Vasya. It is guaranteed that this number does not start with $$$0$$$.", "output_spec": "Output a single integer\u00a0\u2014 the amount of possible variants of the real bus number.", "sample_inputs": ["97", "2028"], "sample_outputs": ["2", "13"], "notes": "NoteIn the first sample, only variants $$$97$$$ and $$$79$$$ are possible.In the second sample, the variants (in the increasing order) are the following: $$$208$$$, $$$280$$$, $$$802$$$, $$$820$$$, $$$2028$$$, $$$2082$$$, $$$2208$$$, $$$2280$$$, $$$2802$$$, $$$2820$$$, $$$8022$$$, $$$8202$$$, $$$8220$$$."}, "src_uid": "7f4e533f49b73cc2b96b4c56847295f2"}
{"nl": {"description": "IT City company developing computer games invented a new way to reward its employees. After a new game release users start buying it actively, and the company tracks the number of sales with precision to each transaction. Every time when the next number of sales is divisible by all numbers from 2 to 10 every developer of this game gets a small bonus.A game designer Petya knows that the company is just about to release a new game that was partly developed by him. On the basis of his experience he predicts that n people will buy the game during the first month. Now Petya wants to determine how many times he will get the bonus. Help him to know it.", "input_spec": "The only line of the input contains one integer n (1\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 divisible by all numbers from 2 to 10.", "sample_inputs": ["3000"], "sample_outputs": ["1"], "notes": null}, "src_uid": "8551308e5ff435e0fc507b89a912408a"}
{"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": "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": "\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": "Year 2118. Androids are in mass production for decades now, and they do all the work for humans. But androids have to go to school to be able to solve creative tasks. Just like humans before.It turns out that high school struggles are not gone. If someone is not like others, he is bullied. Vasya-8800 is an economy-class android which is produced by a little-known company. His design is not perfect, his characteristics also could be better. So he is bullied by other androids.One of the popular pranks on Vasya is to force him to compare $$$x^y$$$ with $$$y^x$$$. Other androids can do it in milliseconds while Vasya's memory is too small to store such big numbers.Please help Vasya! Write a fast program to compare $$$x^y$$$ with $$$y^x$$$ for Vasya, maybe then other androids will respect him.", "input_spec": "On the only line of input there are two integers $$$x$$$ and $$$y$$$ ($$$1 \\le x, y \\le 10^{9}$$$).", "output_spec": "If $$$x^y < y^x$$$, then print '<' (without quotes). If $$$x^y > y^x$$$, then print '>' (without quotes). If $$$x^y = y^x$$$, then print '=' (without quotes).", "sample_inputs": ["5 8", "10 3", "6 6"], "sample_outputs": [">", "<", "="], "notes": "NoteIn the first example $$$5^8 = 5 \\cdot 5 \\cdot 5 \\cdot 5 \\cdot 5 \\cdot 5 \\cdot 5 \\cdot 5 = 390625$$$, and $$$8^5 = 8 \\cdot 8 \\cdot 8 \\cdot 8 \\cdot 8 = 32768$$$. So you should print '>'.In the second example $$$10^3 = 1000 < 3^{10} = 59049$$$.In the third example $$$6^6 = 46656 = 6^6$$$."}, "src_uid": "ec1e44ff41941f0e6436831b5ae543c6"}
{"nl": {"description": "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": "Fox Ciel is playing a game with numbers now. Ciel has n positive integers: x1, x2, ..., xn. She can do the following operation as many times as needed: select two different indexes i and j such that xi > xj hold, and then apply assignment xi = xi - xj. The goal is to make the sum of all numbers as small as possible.Please help Ciel to find this minimal sum.", "input_spec": "The first line contains an integer n (2\u2009\u2264\u2009n\u2009\u2264\u2009100). Then the second line contains n integers: x1, x2, ..., xn (1\u2009\u2264\u2009xi\u2009\u2264\u2009100).", "output_spec": "Output a single integer \u2014 the required minimal sum.", "sample_inputs": ["2\n1 2", "3\n2 4 6", "2\n12 18", "5\n45 12 27 30 18"], "sample_outputs": ["2", "6", "12", "15"], "notes": "NoteIn the first example the optimal way is to do the assignment: x2 = x2 - x1.In the second example the optimal sequence of operations is: x3 = x3 - x2, x2 = x2 - x1."}, "src_uid": "042cf938dc4a0f46ff33d47b97dc6ad4"}
{"nl": {"description": "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": "Let's call a string good if and only if it consists of only two types of letters\u00a0\u2014 'a' and 'b' and every two consecutive letters are distinct. For example \"baba\" and \"aba\" are good strings and \"abb\" is a bad string.You have $$$a$$$ strings \"a\", $$$b$$$ strings \"b\" and $$$c$$$ strings \"ab\". You want to choose some subset of these strings and concatenate them in any arbitrarily order.What is the length of the longest good string you can obtain this way?", "input_spec": "The first line contains three positive integers $$$a$$$, $$$b$$$, $$$c$$$ ($$$1 \\leq a, b, c \\leq 10^9$$$)\u00a0\u2014 the number of strings \"a\", \"b\" and \"ab\" respectively.", "output_spec": "Print a single number\u00a0\u2014 the maximum possible length of the good string you can obtain.", "sample_inputs": ["1 1 1", "2 1 2", "3 5 2", "2 2 1", "1000000000 1000000000 1000000000"], "sample_outputs": ["4", "7", "11", "6", "4000000000"], "notes": "NoteIn the first example the optimal string is \"baba\".In the second example the optimal string is \"abababa\".In the third example the optimal string is \"bababababab\".In the fourth example the optimal string is \"ababab\"."}, "src_uid": "609f131325c13213aedcf8d55fc3ed77"}
{"nl": {"description": "In Berland a money reform is being prepared. New coins are being introduced. After long economic calculations was decided that the most expensive coin should possess the denomination of exactly n Berland dollars. Also the following restriction has been introduced for comfort: the denomination of each coin should be divisible by the denomination of any cheaper coin. It is known that among all the possible variants the variant with the largest number of new coins will be chosen. Find this variant. Print in the order of decreasing of the coins' denominations.", "input_spec": "The first and only line contains an integer n (1\u2009\u2264\u2009n\u2009\u2264\u2009106) which represents the denomination of the most expensive coin. ", "output_spec": "Print the denominations of all the coins in the order of decreasing. The number of coins must be the largest possible (with the given denomination n of the most expensive coin). Also, the denomination of every coin must be divisible by the denomination of any cheaper coin. Naturally, the denominations of all the coins should be different. If there are several solutins to that problem, print any of them.", "sample_inputs": ["10", "4", "3"], "sample_outputs": ["10 5 1", "4 2 1", "3 1"], "notes": null}, "src_uid": "2fc946bb72f56b6d86eabfaf60f9fa63"}
{"nl": {"description": "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": "Polycarpus has a ribbon, its length is n. He wants to cut the ribbon in a way that fulfils the following two conditions:   After the cutting each ribbon piece should have length a, b or c.  After the cutting the number of ribbon pieces should be maximum. Help Polycarpus and find the number of ribbon pieces after the required cutting.", "input_spec": "The first line contains four space-separated integers n, a, b and c (1\u2009\u2264\u2009n,\u2009a,\u2009b,\u2009c\u2009\u2264\u20094000) \u2014 the length of the original ribbon and the acceptable lengths of the ribbon pieces after the cutting, correspondingly. The numbers a, b and c can coincide.", "output_spec": "Print a single number \u2014 the maximum possible number of ribbon pieces. It is guaranteed that at least one correct ribbon cutting exists.", "sample_inputs": ["5 5 3 2", "7 5 5 2"], "sample_outputs": ["2", "2"], "notes": "NoteIn the first example Polycarpus can cut the ribbon in such way: the first piece has length 2, the second piece has length 3.In the second example Polycarpus can cut the ribbon in such way: the first piece has length 5, the second piece has length 2."}, "src_uid": "062a171cc3ea717ea95ede9d7a1c3a43"}
{"nl": {"description": "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": "Karen is getting ready for a new school day!  It is currently hh:mm, given in a 24-hour format. As you know, Karen loves palindromes, and she believes that it is good luck to wake up when the time is a palindrome.What is the minimum number of minutes she should sleep, such that, when she wakes up, the time is a palindrome?Remember that a palindrome is a string that reads the same forwards and backwards. For instance, 05:39 is not a palindrome, because 05:39 backwards is 93:50. On the other hand, 05:50 is a palindrome, because 05:50 backwards is 05:50.", "input_spec": "The first and only line of input contains a single string in the format hh:mm (00\u2009\u2264\u2009 hh \u2009\u2264\u200923, 00\u2009\u2264\u2009 mm \u2009\u2264\u200959).", "output_spec": "Output a single integer on a line by itself, the minimum number of minutes she should sleep, such that, when she wakes up, the time is a palindrome.", "sample_inputs": ["05:39", "13:31", "23:59"], "sample_outputs": ["11", "0", "1"], "notes": "NoteIn the first test case, the minimum number of minutes Karen should sleep for is 11. She can wake up at 05:50, when the time is a palindrome.In the second test case, Karen can wake up immediately, as the current time, 13:31, is already a palindrome.In the third test case, the minimum number of minutes Karen should sleep for is 1 minute. She can wake up at 00:00, when the time is a palindrome."}, "src_uid": "3ad3b8b700f6f34b3a53fdb63af351a5"}
{"nl": {"description": "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": "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": "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": "THE SxPLAY & KIV\u039b - \u6f02\u6d41 KIV\u039b & Nikki Simmons - PerspectivesWith a new body, our idol Aroma White (or should we call her Kaori Minamiya?) begins to uncover her lost past through the OS space.The space can be considered a 2D plane, with an infinite number of data nodes, indexed from $$$0$$$, with their coordinates defined as follows:  The coordinates of the $$$0$$$-th node is $$$(x_0, y_0)$$$  For $$$i > 0$$$, the coordinates of $$$i$$$-th node is $$$(a_x \\cdot x_{i-1} + b_x, a_y \\cdot y_{i-1} + b_y)$$$ Initially Aroma stands at the point $$$(x_s, y_s)$$$. She can stay in OS space for at most $$$t$$$ seconds, because after this time she has to warp back to the real world. She doesn't need to return to the entry point $$$(x_s, y_s)$$$ to warp home.While within the OS space, Aroma can do the following actions:  From the point $$$(x, y)$$$, Aroma can move to one of the following points: $$$(x-1, y)$$$, $$$(x+1, y)$$$, $$$(x, y-1)$$$ or $$$(x, y+1)$$$. This action requires $$$1$$$ second.  If there is a data node at where Aroma is staying, she can collect it. We can assume this action costs $$$0$$$ seconds. Of course, each data node can be collected at most once. Aroma wants to collect as many data as possible before warping back. Can you help her in calculating the maximum number of data nodes she could collect within $$$t$$$ seconds?", "input_spec": "The first line contains integers $$$x_0$$$, $$$y_0$$$, $$$a_x$$$, $$$a_y$$$, $$$b_x$$$, $$$b_y$$$ ($$$1 \\leq x_0, y_0 \\leq 10^{16}$$$, $$$2 \\leq a_x, a_y \\leq 100$$$, $$$0 \\leq b_x, b_y \\leq 10^{16}$$$), which define the coordinates of the data nodes. The second line contains integers $$$x_s$$$, $$$y_s$$$, $$$t$$$ ($$$1 \\leq x_s, y_s, t \\leq 10^{16}$$$)\u00a0\u2013 the initial Aroma's coordinates and the amount of time available.", "output_spec": "Print a single integer\u00a0\u2014 the maximum number of data nodes Aroma can collect within $$$t$$$ seconds.", "sample_inputs": ["1 1 2 3 1 0\n2 4 20", "1 1 2 3 1 0\n15 27 26", "1 1 2 3 1 0\n2 2 1"], "sample_outputs": ["3", "2", "0"], "notes": "NoteIn all three examples, the coordinates of the first $$$5$$$ data nodes are $$$(1, 1)$$$, $$$(3, 3)$$$, $$$(7, 9)$$$, $$$(15, 27)$$$ and $$$(31, 81)$$$ (remember that nodes are numbered from $$$0$$$).In the first example, the optimal route to collect $$$3$$$ nodes is as follows:   Go to the coordinates $$$(3, 3)$$$ and collect the $$$1$$$-st node. This takes $$$|3 - 2| + |3 - 4| = 2$$$ seconds.  Go to the coordinates $$$(1, 1)$$$ and collect the $$$0$$$-th node. This takes $$$|1 - 3| + |1 - 3| = 4$$$ seconds.  Go to the coordinates $$$(7, 9)$$$ and collect the $$$2$$$-nd node. This takes $$$|7 - 1| + |9 - 1| = 14$$$ seconds. In the second example, the optimal route to collect $$$2$$$ nodes is as follows:   Collect the $$$3$$$-rd node. This requires no seconds.  Go to the coordinates $$$(7, 9)$$$ and collect the $$$2$$$-th node. This takes $$$|15 - 7| + |27 - 9| = 26$$$ seconds. In the third example, Aroma can't collect any nodes. She should have taken proper rest instead of rushing into the OS space like that."}, "src_uid": "d8a7ae2959b3781a8a4566a2f75a4e28"}
{"nl": {"description": "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": "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": "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": "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": "During the breaks between competitions, top-model Izabella tries to develop herself and not to be bored. For example, now she tries to solve Rubik's cube 2x2x2.It's too hard to learn to solve Rubik's cube instantly, so she learns to understand if it's possible to solve the cube in some state using 90-degrees rotation of one face of the cube in any direction.To check her answers she wants to use a program which will for some state of cube tell if it's possible to solve it using one rotation, described above.Cube is called solved if for each face of cube all squares on it has the same color.https://en.wikipedia.org/wiki/Rubik's_Cube", "input_spec": "In first line given a sequence of 24 integers ai (1\u2009\u2264\u2009ai\u2009\u2264\u20096), where ai denotes color of i-th square. There are exactly 4 occurrences of all colors in this sequence.", "output_spec": "Print \u00abYES\u00bb (without quotes) if it's possible to solve cube using one rotation and \u00abNO\u00bb (without quotes) otherwise.", "sample_inputs": ["2 5 4 6 1 3 6 2 5 5 1 2 3 5 3 1 1 2 4 6 6 4 3 4", "5 3 5 3 2 5 2 5 6 2 6 2 4 4 4 4 1 1 1 1 6 3 6 3"], "sample_outputs": ["NO", "YES"], "notes": "NoteIn first test case cube looks like this:  In second test case cube looks like this:   It's possible to solve cube by rotating face with squares with numbers 13, 14, 15, 16."}, "src_uid": "881a820aa8184d9553278a0002a3b7c4"}
{"nl": {"description": "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": "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": "All bus tickets in Berland have their numbers. A number consists of $$$n$$$ digits ($$$n$$$ is even). Only $$$k$$$ decimal digits $$$d_1, d_2, \\dots, d_k$$$ can be used to form ticket numbers. If $$$0$$$ is among these digits, then numbers may have leading zeroes. For example, if $$$n = 4$$$ and only digits $$$0$$$ and $$$4$$$ can be used, then $$$0000$$$, $$$4004$$$, $$$4440$$$ are valid ticket numbers, and $$$0002$$$, $$$00$$$, $$$44443$$$ are not.A ticket is lucky if the sum of first $$$n / 2$$$ digits is equal to the sum of remaining $$$n / 2$$$ digits. Calculate the number of different lucky tickets in Berland. Since the answer may be big, print it modulo $$$998244353$$$.", "input_spec": "The first line contains two integers $$$n$$$ and $$$k$$$ $$$(2 \\le n \\le 2 \\cdot 10^5, 1 \\le k \\le 10)$$$ \u2014 the number of digits in each ticket number, and the number of different decimal digits that may be used. $$$n$$$ is even. The second line contains a sequence of pairwise distinct integers $$$d_1, d_2, \\dots, d_k$$$ $$$(0 \\le d_i \\le 9)$$$ \u2014 the digits that may be used in ticket numbers. The digits are given in arbitrary order.", "output_spec": "Print the number of lucky ticket numbers, taken modulo $$$998244353$$$.", "sample_inputs": ["4 2\n1 8", "20 1\n6", "10 5\n6 1 4 0 3", "1000 7\n5 4 0 1 8 3 2"], "sample_outputs": ["6", "1", "569725", "460571165"], "notes": "NoteIn the first example there are $$$6$$$ lucky ticket numbers: $$$1111$$$, $$$1818$$$, $$$1881$$$, $$$8118$$$, $$$8181$$$ and $$$8888$$$.There is only one ticket number in the second example, it consists of $$$20$$$ digits $$$6$$$. This ticket number is lucky, so the answer is $$$1$$$."}, "src_uid": "279f1f7d250a4be6406c6c7bfc818bbf"}
{"nl": {"description": "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": "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": "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": "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": "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": "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": "Kolya is developing an economy simulator game. His most favourite part of the development process is in-game testing. Once he was entertained by the testing so much, that he found out his game-coin score become equal to 0.Kolya remembers that at the beginning of the game his game-coin score was equal to n and that he have bought only some houses (for 1\u2009234\u2009567 game-coins each), cars (for 123\u2009456 game-coins each) and computers (for 1\u2009234 game-coins each).Kolya is now interested, whether he could have spent all of his initial n game-coins buying only houses, cars and computers or there is a bug in the game. Formally, is there a triple of non-negative integers a, b and c such that a\u2009\u00d7\u20091\u2009234\u2009567\u2009+\u2009b\u2009\u00d7\u2009123\u2009456\u2009+\u2009c\u2009\u00d7\u20091\u2009234\u2009=\u2009n?Please help Kolya answer this question.", "input_spec": "The first line of the input contains a single integer n (1\u2009\u2264\u2009n\u2009\u2264\u2009109)\u00a0\u2014 Kolya's initial game-coin score.", "output_spec": "Print \"YES\" (without quotes) if it's possible that Kolya spent all of his initial n coins buying only houses, cars and computers. Otherwise print \"NO\" (without quotes).", "sample_inputs": ["1359257", "17851817"], "sample_outputs": ["YES", "NO"], "notes": "NoteIn the first sample, one of the possible solutions is to buy one house, one car and one computer, spending 1\u2009234\u2009567\u2009+\u2009123\u2009456\u2009+\u20091234\u2009=\u20091\u2009359\u2009257 game-coins in total."}, "src_uid": "72d7e422a865cc1f85108500bdf2adf2"}
{"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": "The HR manager was disappointed again. The last applicant failed the interview the same way as 24 previous ones. \"Do I give such a hard task?\" \u2014 the HR manager thought. \"Just raise number 5 to the power of n and get last two digits of the number. Yes, of course, n can be rather big, and one cannot find the power using a calculator, but we need people who are able to think, not just follow the instructions.\"Could you pass the interview in the machine vision company in IT City?", "input_spec": "The only line of the input contains a single integer n (2\u2009\u2264\u2009n\u2009\u2264\u20092\u00b71018) \u2014 the power in which you need to raise number 5.", "output_spec": "Output the last two digits of 5n without spaces between them.", "sample_inputs": ["2"], "sample_outputs": ["25"], "notes": null}, "src_uid": "dcaff75492eafaf61d598779d6202c9d"}
{"nl": {"description": "Fox Ciel studies number theory.She thinks a non-empty set S contains non-negative integers is perfect if and only if for any  (a can be equal to b), . Where operation xor means exclusive or operation (http://en.wikipedia.org/wiki/Exclusive_or).Please calculate the number of perfect sets consisting of integers not greater than k. The answer can be very large, so print it modulo 1000000007 (109\u2009+\u20097).", "input_spec": "The first line contains an integer k (0\u2009\u2264\u2009k\u2009\u2264\u2009109).", "output_spec": "Print a single integer \u2014 the number of required sets modulo 1000000007 (109\u2009+\u20097).", "sample_inputs": ["1", "2", "3", "4"], "sample_outputs": ["2", "3", "5", "6"], "notes": "NoteIn example 1, there are 2 such sets: {0} and {0, 1}. Note that {1} is not a perfect set since 1 xor 1 = 0 and {1} doesn't contain zero.In example 4, there are 6 such sets: {0}, {0, 1}, {0, 2}, {0, 3}, {0, 4} and {0, 1, 2, 3}."}, "src_uid": "ead64d8e3134fa8f29881cb487e52f60"}
{"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": "You are given two bracket sequences (not necessarily regular) $$$s$$$ and $$$t$$$ consisting only of characters '(' and ')'. You want to construct the shortest regular bracket sequence that contains both given bracket sequences as subsequences (not necessarily contiguous).Recall what is the regular bracket sequence:  () is the regular bracket sequence;  if $$$S$$$ is the regular bracket sequence, then ($$$S$$$) is a regular bracket sequence;  if $$$S$$$ and $$$T$$$ regular bracket sequences, then $$$ST$$$ (concatenation of $$$S$$$ and $$$T$$$) is a regular bracket sequence. Recall that the subsequence of the string $$$s$$$ is such string $$$t$$$ that can be obtained from $$$s$$$ by removing some (possibly, zero) amount of characters. For example, \"coder\", \"force\", \"cf\" and \"cores\" are subsequences of \"codeforces\", but \"fed\" and \"z\" are not.", "input_spec": "The first line of the input contains one bracket sequence $$$s$$$ consisting of no more than $$$200$$$ characters '(' and ')'. The second line of the input contains one bracket sequence $$$t$$$ consisting of no more than $$$200$$$ characters '(' and ')'.", "output_spec": "Print one line \u2014 the shortest regular bracket sequence that contains both given bracket sequences as subsequences (not necessarily contiguous). If there are several answers, you can print any.", "sample_inputs": ["(())(()\n()))()", ")\n((", ")\n)))", "())\n(()(()(()("], "sample_outputs": ["(())()()", "(())", "((()))", "(()()()(()()))"], "notes": null}, "src_uid": "cc222aab45b3ad3d0e71227592c883f1"}
{"nl": {"description": "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": "At regular competition Vladik and Valera won a and b candies respectively. Vladik offered 1 his candy to Valera. After that Valera gave Vladik 2 his candies, so that no one thought that he was less generous. Vladik for same reason gave 3 candies to Valera in next turn.More formally, the guys take turns giving each other one candy more than they received in the previous turn.This continued until the moment when one of them couldn\u2019t give the right amount of candy. Candies, which guys got from each other, they don\u2019t consider as their own. You need to know, who is the first who can\u2019t give the right amount of candy.", "input_spec": "Single line of input data contains two space-separated integers a, b (1\u2009\u2264\u2009a,\u2009b\u2009\u2264\u2009109) \u2014 number of Vladik and Valera candies respectively.", "output_spec": "Pring a single line \"Vladik\u2019\u2019 in case, if Vladik first who can\u2019t give right amount of candy, or \"Valera\u2019\u2019 otherwise.", "sample_inputs": ["1 1", "7 6"], "sample_outputs": ["Valera", "Vladik"], "notes": "NoteIllustration for first test case:Illustration for second test case:"}, "src_uid": "87e37a82be7e39e433060fd8cdb03270"}
{"nl": {"description": "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": "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": "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": "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": "Marina plays a new rogue-like game. In this game, there are $$$n$$$ different character species and $$$m$$$ different classes. The game is played in runs; for each run, Marina has to select a species and a class for her character. If she selects the $$$i$$$-th species and the $$$j$$$-th class, she will get $$$c_{i, j}$$$ points for this run.Initially, some species and classes are unlocked, all others are locked. To unlock the $$$i$$$-th species, Marina has to get at least $$$a_i$$$ points in total for previous runs \u2014 that is, as soon as her total score for played runs is at least $$$a_i$$$, this species is unlocked. Similarly, to unlock the $$$j$$$-th class, she has to get at least $$$b_j$$$ points in total for previous runs. If $$$a_i = 0$$$ for some $$$i$$$, then this species is unlocked initially (the same applies to classes with $$$b_j = 0$$$).Marina wants to unlock all species and classes in the minimum number of runs. Before playing the game, she can read exactly one guide on some combination of species and class, and reading a guide will increase the score she gets for all runs with that combination by $$$k$$$ (formally, before playing the game, she can increase exactly one value of $$$c_{i, j}$$$ by $$$k$$$).What is the minimum number of runs she has to play to unlock all species and classes if she chooses the combination to read a guide on optimally?", "input_spec": "The first line contains three integers $$$n$$$, $$$m$$$ and $$$k$$$ ($$$1 \\le n, m \\le 1500$$$; $$$0 \\le k \\le 10^9$$$). The second line contains $$$n$$$ integers $$$a_1$$$, $$$a_2$$$, ..., $$$a_n$$$ ($$$0 = a_1 \\le a_2 \\le \\dots \\le a_n \\le 10^{12}$$$), where $$$a_i$$$ is the number of points required to unlock the $$$i$$$-th species (or $$$0$$$, if it is unlocked initially). Note that $$$a_1 = 0$$$, and these values are non-descending. The third line contains $$$m$$$ integers $$$b_1$$$, $$$b_2$$$, ..., $$$b_m$$$ ($$$0 = b_1 \\le b_2 \\le \\dots \\le b_m \\le 10^{12}$$$), where $$$b_i$$$ is the number of points required to unlock the $$$i$$$-th class (or $$$0$$$, if it is unlocked initially). Note that $$$b_1 = 0$$$, and these values are non-descending. Then $$$n$$$ lines follow, each of them contains $$$m$$$ integers. The $$$j$$$-th integer in the $$$i$$$-th line is $$$c_{i, j}$$$ ($$$1 \\le c_{i, j} \\le 10^9$$$) \u2014 the score Marina gets for a run with the $$$i$$$-th species and the $$$j$$$-th class.", "output_spec": "Print one integer \u2014 the minimum number of runs Marina has to play to unlock all species and all classes if she can read exactly one guide before playing the game.", "sample_inputs": ["3 4 2\n0 5 7\n0 2 6 10\n2 5 5 2\n5 3 4 4\n3 4 2 4", "4 2 1\n0 3 9 9\n0 2\n3 3\n5 1\n1 3\n2 3", "3 3 5\n0 8 11\n0 0 3\n3 1 3\n1 2 1\n1 1 3"], "sample_outputs": ["3", "2", "2"], "notes": "NoteThe explanation for the first test:  Marina reads a guide on the combination of the $$$1$$$-st species and the $$$2$$$-nd class. Thus, $$$c_{1, 2}$$$ becomes $$$7$$$. Initially, only the $$$1$$$-st species and the $$$1$$$-st class are unlocked.  Marina plays a run with the $$$1$$$-st species and the $$$1$$$-st class. Her score becomes $$$2$$$, and she unlocks the $$$2$$$-nd class.  Marina plays a run with the $$$1$$$-st species and the $$$2$$$-nd class. Her score becomes $$$9$$$, and she unlocks everything except the $$$4$$$-th class.  Marina plays a run with the $$$3$$$-rd species and the $$$3$$$-rd class. Her score becomes $$$11$$$, and she unlocks the $$$4$$$-th class. She has unlocked everything in $$$3$$$ runs. Note that this way to unlock everything is not the only one.The explanation for the second test:  Marina reads a guide on the combination of the $$$2$$$-nd species and the $$$1$$$-st class. Thus, $$$c_{2, 1}$$$ becomes $$$6$$$. Initially, only the $$$1$$$-st species and the $$$1$$$-st class are unlocked.  Marina plays a run with the $$$1$$$-st species and the $$$1$$$-st class. Her score becomes $$$3$$$, and she unlocks the $$$2$$$-nd species and the $$$2$$$-nd class.  Marina plays a run with the $$$2$$$-nd species and the $$$1$$$-st class. Her score becomes $$$9$$$, and she unlocks the $$$3$$$-rd species and the $$$4$$$-th species. She has unlocked everything in $$$2$$$ runs. As in the $$$1$$$-st example, this is not the only way to unlock everything in $$$2$$$ runs."}, "src_uid": "309d0bc338fafcef050f336a7fa804c7"}
{"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": "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": "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": "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": "Ilya is a very clever lion, he lives in an unusual city ZooVille. In this city all the animals have their rights and obligations. Moreover, they even have their own bank accounts. The state of a bank account is an integer. The state of a bank account can be a negative number. This means that the owner of the account owes the bank money.Ilya the Lion has recently had a birthday, so he got a lot of gifts. One of them (the gift of the main ZooVille bank) is the opportunity to delete the last digit or the digit before last from the state of his bank account no more than once. For example, if the state of Ilya's bank account is -123, then Ilya can delete the last digit and get his account balance equal to -12, also he can remove its digit before last and get the account balance equal to -13. Of course, Ilya is permitted not to use the opportunity to delete a digit from the balance.Ilya is not very good at math, and that's why he asks you to help him maximize his bank account. Find the maximum state of the bank account that can be obtained using the bank's gift.", "input_spec": "The single line contains integer n (10\u2009\u2264\u2009|n|\u2009\u2264\u2009109) \u2014 the state of Ilya's bank account.", "output_spec": "In a single line print an integer \u2014 the maximum state of the bank account that Ilya can get. ", "sample_inputs": ["2230", "-10", "-100003"], "sample_outputs": ["2230", "0", "-10000"], "notes": "NoteIn the first test sample Ilya doesn't profit from using the present.In the second test sample you can delete digit 1 and get the state of the account equal to 0."}, "src_uid": "4b0a8798a6d53351226d4f06e3356b1e"}
{"nl": {"description": "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": "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": "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": "After playing Neo in the legendary \"Matrix\" trilogy, Keanu Reeves started doubting himself: maybe we really live in virtual reality? To find if this is true, he needs to solve the following problem.Let's call a string consisting of only zeroes and ones good if it contains different numbers of zeroes and ones. For example, 1, 101, 0000 are good, while 01, 1001, and 111000 are not good.We are given a string $$$s$$$ of length $$$n$$$ consisting of only zeroes and ones. We need to cut $$$s$$$ into minimal possible number of substrings $$$s_1, s_2, \\ldots, s_k$$$ such that all of them are good. More formally, we have to find minimal by number of strings sequence of good strings $$$s_1, s_2, \\ldots, s_k$$$ such that their concatenation (joining) equals $$$s$$$, i.e. $$$s_1 + s_2 + \\dots + s_k = s$$$.For example, cuttings 110010 into 110 and 010 or into 11 and 0010 are valid, as 110, 010, 11, 0010 are all good, and we can't cut 110010 to the smaller number of substrings as 110010 isn't good itself. At the same time, cutting of 110010 into 1100 and 10 isn't valid as both strings aren't good. Also, cutting of 110010 into 1, 1, 0010 isn't valid, as it isn't minimal, even though all $$$3$$$ strings are good.Can you help Keanu? We can show that the solution always exists. If there are multiple optimal answers, print any.", "input_spec": "The first line of the input contains a single integer $$$n$$$ ($$$1\\le n \\le 100$$$)\u00a0\u2014 the length of the string $$$s$$$. The second line contains the string $$$s$$$ of length $$$n$$$ consisting only from zeros and ones.", "output_spec": "In the first line, output a single integer $$$k$$$ ($$$1\\le k$$$)\u00a0\u2014 a minimal number of strings you have cut $$$s$$$ into. In the second line, output $$$k$$$ strings $$$s_1, s_2, \\ldots, s_k$$$ separated with spaces. The length of each string has to be positive. Their concatenation has to be equal to $$$s$$$ and all of them have to be good. If there are multiple answers, print any.", "sample_inputs": ["1\n1", "2\n10", "6\n100011"], "sample_outputs": ["1\n1", "2\n1 0", "2\n100 011"], "notes": "NoteIn the first example, the string 1 wasn't cut at all. As it is good, the condition is satisfied.In the second example, 1 and 0 both are good. As 10 isn't good, the answer is indeed minimal.In the third example, 100 and 011 both are good. As 100011 isn't good, the answer is indeed minimal."}, "src_uid": "4ebed264d40a449602a26ceef2e849d1"}
{"nl": {"description": "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": "Two chess pieces, a rook and a knight, stand on a standard chessboard 8\u2009\u00d7\u20098 in size. The positions in which they are situated are known. It is guaranteed that none of them beats the other one.Your task is to find the number of ways to place another knight on the board so that none of the three pieces on the board beat another one. A new piece can only be placed on an empty square.", "input_spec": "The first input line contains the description of the rook's position on the board. This description is a line which is 2 in length. Its first symbol is a lower-case Latin letter from a to h, and its second symbol is a number from 1 to 8. The second line contains the description of the knight's position in a similar way. It is guaranteed that their positions do not coincide.", "output_spec": "Print a single number which is the required number of ways.", "sample_inputs": ["a1\nb2", "a8\nd4"], "sample_outputs": ["44", "38"], "notes": null}, "src_uid": "073023c6b72ce923df2afd6130719cfc"}
{"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": "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": "Translator's note: in Russia's most widespread grading system, there are four grades: 5, 4, 3, 2, the higher the better, roughly corresponding to A, B, C and F respectively in American grading system.The term is coming to an end and students start thinking about their grades. Today, a professor told his students that the grades for his course would be given out automatically \u00a0\u2014 he would calculate the simple average (arithmetic mean) of all grades given out for lab works this term and round to the nearest integer. The rounding would be done in favour of the student\u00a0\u2014 $$$4.5$$$ would be rounded up to $$$5$$$ (as in example 3), but $$$4.4$$$ would be rounded down to $$$4$$$.This does not bode well for Vasya who didn't think those lab works would influence anything, so he may receive a grade worse than $$$5$$$ (maybe even the dreaded $$$2$$$). However, the professor allowed him to redo some of his works of Vasya's choosing to increase his average grade. Vasya wants to redo as as few lab works as possible in order to get $$$5$$$ for the course. Of course, Vasya will get $$$5$$$ for the lab works he chooses to redo.Help Vasya\u00a0\u2014 calculate the minimum amount of lab works Vasya has to redo.", "input_spec": "The first line contains a single integer $$$n$$$\u00a0\u2014 the number of Vasya's grades ($$$1 \\leq n \\leq 100$$$). The second line contains $$$n$$$ integers from $$$2$$$ to $$$5$$$\u00a0\u2014 Vasya's grades for his lab works.", "output_spec": "Output a single integer\u00a0\u2014 the minimum amount of lab works that Vasya has to redo. It can be shown that Vasya can always redo enough lab works to get a $$$5$$$.", "sample_inputs": ["3\n4 4 4", "4\n5 4 5 5", "4\n5 3 3 5"], "sample_outputs": ["2", "0", "1"], "notes": "NoteIn the first sample, it is enough to redo two lab works to make two $$$4$$$s into $$$5$$$s.In the second sample, Vasya's average is already $$$4.75$$$ so he doesn't have to redo anything to get a $$$5$$$.In the second sample Vasya has to redo one lab work to get rid of one of the $$$3$$$s, that will make the average exactly $$$4.5$$$ so the final grade would be $$$5$$$."}, "src_uid": "715608282b27a0a25b66f08574a6d5bd"}
{"nl": {"description": "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": "You are developing a new feature for the website which sells airline tickets: being able to sort tickets by price! You have already extracted the tickets' prices, so there's just the last step to be done...You are given an array of integers. Sort it in non-descending order.", "input_spec": "The input consists of a single line of space-separated integers. The first number is n (1\u2009\u2264\u2009n\u2009\u2264\u200910) \u2014 the size of the array. The following n numbers are the elements of the array (1\u2009\u2264\u2009ai\u2009\u2264\u2009100).", "output_spec": "Output space-separated elements of the sorted array.", "sample_inputs": ["3 3 1 2"], "sample_outputs": ["1 2 3"], "notes": "NoteRemember, this is a very important feature, and you have to make sure the customers appreciate it!"}, "src_uid": "29e481abfa9ad1f18e6157c9e833f16e"}
{"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"}
{"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": "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": "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": "Given a positive integer $$$m$$$, we say that a sequence $$$x_1, x_2, \\dots, x_n$$$ of positive integers is $$$m$$$-cute if for every index $$$i$$$ such that $$$2 \\le i \\le n$$$ it holds that $$$x_i = x_{i - 1} + x_{i - 2} + \\dots + x_1 + r_i$$$ for some positive integer $$$r_i$$$ satisfying $$$1 \\le r_i \\le m$$$.You will be given $$$q$$$ queries consisting of three positive integers $$$a$$$, $$$b$$$ and $$$m$$$. For each query you must determine whether or not there exists an $$$m$$$-cute sequence whose first term is $$$a$$$ and whose last term is $$$b$$$. If such a sequence exists, you must additionally find an example of it.", "input_spec": "The first line contains an integer number $$$q$$$ ($$$1 \\le q \\le 10^3$$$)\u00a0\u2014 the number of queries. Each of the following $$$q$$$ lines contains three integers $$$a$$$, $$$b$$$, and $$$m$$$ ($$$1 \\le a, b, m \\le 10^{14}$$$, $$$a \\leq b$$$), describing a single query.", "output_spec": "For each query, if no $$$m$$$-cute sequence whose first term is $$$a$$$ and whose last term is $$$b$$$ exists, print $$$-1$$$. Otherwise print an integer $$$k$$$ ($$$1 \\le k \\leq 50$$$), followed by $$$k$$$ integers $$$x_1, x_2, \\dots, x_k$$$ ($$$1 \\le x_i \\le 10^{14}$$$). These integers must satisfy $$$x_1 = a$$$, $$$x_k = b$$$, and that the sequence $$$x_1, x_2, \\dots, x_k$$$ is $$$m$$$-cute. It can be shown that under the problem constraints, for each query either no $$$m$$$-cute sequence exists, or there exists one with at most $$$50$$$ terms. If there are multiple possible sequences, you may print any of them.", "sample_inputs": ["2\n5 26 2\n3 9 1"], "sample_outputs": ["4 5 6 13 26\n-1"], "notes": "NoteConsider the sample. In the first query, the sequence $$$5, 6, 13, 26$$$ is valid since $$$6 = 5 + \\bf{\\color{blue} 1}$$$, $$$13 = 6 + 5 + {\\bf\\color{blue} 2}$$$ and $$$26 = 13 + 6 + 5 + {\\bf\\color{blue} 2}$$$ have the bold values all between $$$1$$$ and $$$2$$$, so the sequence is $$$2$$$-cute. Other valid sequences, such as $$$5, 7, 13, 26$$$ are also accepted.In the second query, the only possible $$$1$$$-cute sequence starting at $$$3$$$ is $$$3, 4, 8, 16, \\dots$$$, which does not contain $$$9$$$."}, "src_uid": "c9d646762e2e78064bc0670ec7c173c6"}
{"nl": {"description": "You have probably registered on Internet sites many times. And each time you should enter your invented password. Usually the registration form automatically checks the password's crypt resistance. If the user's password isn't complex enough, a message is displayed. Today your task is to implement such an automatic check.Web-developers of the company Q assume that a password is complex enough, if it meets all of the following conditions:  the password length is at least 5 characters;  the password contains at least one large English letter;  the password contains at least one small English letter;  the password contains at least one digit. You are given a password. Please implement the automatic check of its complexity for company Q.", "input_spec": "The first line contains a non-empty sequence of characters (at most 100 characters). Each character is either a large English letter, or a small English letter, or a digit, or one of characters: \"!\", \"?\", \".\", \",\", \"_\".", "output_spec": "If the password is complex enough, print message \"Correct\" (without the quotes), otherwise print message \"Too weak\" (without the quotes).", "sample_inputs": ["abacaba", "X12345", "CONTEST_is_STARTED!!11"], "sample_outputs": ["Too weak", "Too weak", "Correct"], "notes": null}, "src_uid": "42a964b01e269491975965860ec92be7"}
{"nl": {"description": "You are given a string $$$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": "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": "Smart Beaver is careful about his appearance and pays special attention to shoes so he has a huge number of pairs of shoes from the most famous brands of the forest. He's trying to handle his shoes carefully so that each pair stood side by side. But by the end of the week because of his very active lifestyle in his dressing room becomes a mess.Smart Beaver from ABBYY is not only the brightest beaver in the area, but he also is the most domestically oriented. For example, on Mondays the Smart Beaver cleans everything in his home.It's Monday morning. Smart Beaver does not want to spend the whole day cleaning, besides, there is much in to do and it\u2019s the gym day, so he wants to clean up as soon as possible. Now the floors are washed, the dust is wiped off \u2014 it\u2019s time to clean up in the dressing room. But as soon as the Smart Beaver entered the dressing room, all plans for the day were suddenly destroyed: chaos reigned there and it seemed impossible to handle, even in a week. Give our hero some hope: tell him what is the minimum number of shoes need to change the position to make the dressing room neat.The dressing room is rectangular and is divided into n\u2009\u00d7\u2009m equal squares, each square contains exactly one shoe. Each pair of shoes has a unique number that is integer from 1 to , more formally, a square with coordinates (i,\u2009j) contains an integer number of the pair which is lying on it. The Smart Beaver believes that the dressing room is neat only when each pair of sneakers lies together. We assume that the pair of sneakers in squares (i1,\u2009j1) and (i2,\u2009j2) lies together if |i1\u2009-\u2009i2|\u2009+\u2009|j1\u2009-\u2009j2|\u2009=\u20091.", "input_spec": "The first line contains two space-separated integers n and m. They correspond to the dressing room size. Next n lines contain m space-separated integers each. Those numbers describe the dressing room. Each number corresponds to a snicker.  It is guaranteed that:    n\u00b7m is even.  All numbers, corresponding to the numbers of pairs of shoes in the dressing room, will lie between 1 and .  Each number from 1 to  will occur exactly twice.  The input limits for scoring 30 points are (subproblem C1):    2\u2009\u2264\u2009n,\u2009m\u2009\u2264\u20098.  The input limits for scoring 100 points are (subproblems C1+C2):    2\u2009\u2264\u2009n,\u2009m\u2009\u2264\u200980. ", "output_spec": "Print exactly one integer \u2014 the minimum number of the sneakers that need to change their location.", "sample_inputs": ["2 3\n1 1 2\n2 3 3", "3 4\n1 3 2 6\n2 1 5 6\n4 4 5 3"], "sample_outputs": ["2", "4"], "notes": "Note   The second sample.  "}, "src_uid": "1f0e8bbd5bf4fcdea927fbb505a8949b"}
{"nl": {"description": "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": "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": "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": "Recently Adaltik discovered japanese crosswords. Japanese crossword is a picture, represented as a table sized a\u2009\u00d7\u2009b squares, and each square is colored white or black. There are integers to the left of the rows and to the top of the columns, encrypting the corresponding row or column. The number of integers represents how many groups of black squares there are in corresponding row or column, and the integers themselves represents the number of consecutive black squares in corresponding group (you can find more detailed explanation in Wikipedia https://en.wikipedia.org/wiki/Japanese_crossword).Adaltik decided that the general case of japanese crossword is too complicated and drew a row consisting of n squares (e.g. japanese crossword sized 1\u2009\u00d7\u2009n), which he wants to encrypt in the same way as in japanese crossword.    The example of encrypting of a single row of japanese crossword. Help Adaltik find the numbers encrypting the row he drew.", "input_spec": "The first line of the input contains a single integer n (1\u2009\u2264\u2009n\u2009\u2264\u2009100)\u00a0\u2014 the length of the row. The second line of the input contains a single string consisting of n characters 'B' or 'W', ('B' corresponds to black square, 'W'\u00a0\u2014 to white square in the row that Adaltik drew).", "output_spec": "The first line should contain a single integer k\u00a0\u2014 the number of integers encrypting the row, e.g. the number of groups of black squares in the row. The second line should contain k integers, encrypting the row, e.g. corresponding to sizes of groups of consecutive black squares in the order from left to right.", "sample_inputs": ["3\nBBW", "5\nBWBWB", "4\nWWWW", "4\nBBBB", "13\nWBBBBWWBWBBBW"], "sample_outputs": ["1\n2", "3\n1 1 1", "0", "1\n4", "3\n4 1 3"], "notes": "NoteThe last sample case correspond to the picture in the statement."}, "src_uid": "e4b3a2707ba080b93a152f4e6e983973"}
{"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": "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": "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": "For the first time, Polycarp's startup ended the year with a profit! Now he is about to distribute $$$k$$$ burles as a bonus among $$$n$$$ employees.It is known that the current salary of the $$$i$$$-th employee is $$$a_i$$$ and all the values of $$$a_i$$$ in the company are different.Polycarp wants to distribute the $$$k$$$ burles between $$$n$$$ employees so this month the $$$i$$$-th employee will be paid not $$$a_i$$$, but $$$a_i+d_i$$$ ($$$d_i \\ge 0$$$, $$$d_i$$$ is an integer), where $$$d_i$$$ is the bonus for the $$$i$$$-th employee. Of course, $$$d_1+d_2+\\dots+d_n=k$$$.Polycarp will follow two rules for choosing the values $$$d_i$$$:  the relative order of the salaries should not be changed: the employee with originally the highest salary ($$$a_i$$$ is the maximum) should have the highest total payment after receiving their bonus ($$$a_i+d_i$$$ is also the maximum), the employee whose salary was originally the second-largest should receive the second-largest total payment after receiving their bonus and so on.  to emphasize that annual profit is a group effort, Polycarp wants to minimize the maximum total payment to an employee (i.e minimize the maximum value of $$$a_i+d_i$$$). Help Polycarp decide the non-negative integer bonuses $$$d_i$$$ such that:  their sum is $$$k$$$,  for each employee, the number of those who receive strictly more than them remains unchanged (that is, if you sort employees by $$$a_i$$$ and by $$$a_i+d_i$$$, you get the same order of employees),  all $$$a_i + d_i$$$ are different,  the maximum of the values $$$a_i+d_i$$$ is the minimum possible. Help Polycarp and print any of the possible answers $$$d_1, d_2, \\dots, d_n$$$.", "input_spec": "The first line contains an integer $$$t$$$ ($$$1 \\le t \\le 10^4$$$) \u2014 the number of test cases in the input. Then $$$t$$$ test cases follow. The first line of each test case contains two integers $$$n$$$ and $$$k$$$ ($$$1 \\le n \\le 10^5$$$, $$$1 \\le k \\le 10^9$$$)\u00a0\u2014 the number of employees and the total bonus. The second line of each test case contains $$$n$$$ different integers $$$a_1, a_2, \\dots, a_n$$$ ($$$1 \\le a_i \\le 10^9$$$), where $$$a_i$$$ is the current salary of the $$$i$$$-th employee. It is guaranteed that the sum of all $$$n$$$ values in the input does not exceed $$$10^5$$$.", "output_spec": "Print the answers to $$$t$$$ test cases in the order they appear in the input. Print each answer as a sequence of non-negative integers $$$d_1, d_2, \\dots, d_n$$$. If there are several answers, print any of them.", "sample_inputs": ["5\n4 1\n3 1 4 2\n2 3\n10 2\n4 1000000000\n987654321 1000000000 999999999 500000000\n8 9\n5 6 1 8 3 4 2 7\n6 1\n6 3 1 8 5 9"], "sample_outputs": ["0 0 1 0 \n0 3 \n134259259 121913582 121913582 621913577 \n2 2 0 2 0 1 0 2 \n1 0 0 0 0 0"], "notes": null}, "src_uid": "685ecfc7293b4e762863be2e3368e576"}
{"nl": {"description": "One day Misha and Andrew were playing a very simple game. First, each player chooses an integer in the range from 1 to n. Let's assume that Misha chose number m, and Andrew chose number a.Then, by using a random generator they choose a random integer c in the range between 1 and n (any integer from 1 to n is chosen with the same probability), after which the winner is the player, whose number was closer to c. The boys agreed that if m and a are located on the same distance from c, Misha wins.Andrew wants to win very much, so he asks you to help him. You know the number selected by Misha, and number n. You need to determine which value of a Andrew must choose, so that the probability of his victory is the highest possible.More formally, you need to find such integer a (1\u2009\u2264\u2009a\u2009\u2264\u2009n), that the probability that  is maximal, where c is the equiprobably chosen integer from 1 to n (inclusive).", "input_spec": "The first line contains two integers n and m (1\u2009\u2264\u2009m\u2009\u2264\u2009n\u2009\u2264\u2009109) \u2014 the range of numbers in the game, and the number selected by Misha respectively.", "output_spec": "Print a single number \u2014 such value a, that probability that Andrew wins is the highest. If there are multiple such values, print the minimum of them.", "sample_inputs": ["3 1", "4 3"], "sample_outputs": ["2", "2"], "notes": "NoteIn the first sample test: Andrew wins if c is equal to 2 or 3. The probability that Andrew wins is 2\u2009/\u20093. If Andrew chooses a\u2009=\u20093, the probability of winning will be 1\u2009/\u20093. If a\u2009=\u20091, the probability of winning is 0.In the second sample test: Andrew wins if c is equal to 1 and 2. The probability that Andrew wins is 1\u2009/\u20092. For other choices of a the probability of winning is less."}, "src_uid": "f6a80c0f474cae1e201032e1df10e9f7"}
{"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": "Top-model Izabella participates in the competition. She wants to impress judges and show her mathematical skills.Her problem is following: for given string, consisting of only 0 and 1, tell if it's possible to remove some digits in such a way, that remaining number is a representation of some positive integer, divisible by 64, in the binary numerical system.", "input_spec": "In the only line given a non-empty binary string s with length up to 100.", "output_spec": "Print \u00abyes\u00bb (without quotes) if it's possible to remove digits required way and \u00abno\u00bb otherwise.", "sample_inputs": ["100010001", "100"], "sample_outputs": ["yes", "no"], "notes": "NoteIn the first test case, you can get string 1 000 000 after removing two ones which is a representation of number 64 in the binary numerical system.You can read more about binary numeral system representation here: https://en.wikipedia.org/wiki/Binary_system"}, "src_uid": "88364b8d71f2ce2b90bdfaa729eb92ca"}
{"nl": {"description": "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": "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": "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": "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": "There are $$$n$$$ benches in the Berland Central park. It is known that $$$a_i$$$ people are currently sitting on the $$$i$$$-th bench. Another $$$m$$$ people are coming to the park and each of them is going to have a seat on some bench out of $$$n$$$ available.Let $$$k$$$ be the maximum number of people sitting on one bench after additional $$$m$$$ people came to the park. Calculate the minimum possible $$$k$$$ and the maximum possible $$$k$$$.Nobody leaves the taken seat during the whole process.", "input_spec": "The first line contains a single integer $$$n$$$ $$$(1 \\le n \\le 100)$$$ \u2014 the number of benches in the park. The second line contains a single integer $$$m$$$ $$$(1 \\le m \\le 10\\,000)$$$ \u2014 the number of people additionally coming to the park. Each of the next $$$n$$$ lines contains a single integer $$$a_i$$$ $$$(1 \\le a_i \\le 100)$$$ \u2014 the initial number of people on the $$$i$$$-th bench.", "output_spec": "Print the minimum possible $$$k$$$ and the maximum possible $$$k$$$, where $$$k$$$ is the maximum number of people sitting on one bench after additional $$$m$$$ people came to the park.", "sample_inputs": ["4\n6\n1\n1\n1\n1", "1\n10\n5", "3\n6\n1\n6\n5", "3\n7\n1\n6\n5"], "sample_outputs": ["3 7", "15 15", "6 12", "7 13"], "notes": "NoteIn the first example, each of four benches is occupied by a single person. The minimum $$$k$$$ is $$$3$$$. For example, it is possible to achieve if two newcomers occupy the first bench, one occupies the second bench, one occupies the third bench, and two remaining \u2014 the fourth bench. The maximum $$$k$$$ is $$$7$$$. That requires all six new people to occupy the same bench.The second example has its minimum $$$k$$$ equal to $$$15$$$ and maximum $$$k$$$ equal to $$$15$$$, as there is just a single bench in the park and all $$$10$$$ people will occupy it."}, "src_uid": "78f696bd954c9f0f9bb502e515d85a8d"}
{"nl": {"description": "A number is called almost prime if it has exactly two distinct prime divisors. For example, numbers 6, 18, 24 are almost prime, while 4, 8, 9, 42 are not. Find the amount of almost prime numbers which are between 1 and n, inclusive.", "input_spec": "Input contains one integer number n (1\u2009\u2264\u2009n\u2009\u2264\u20093000).", "output_spec": "Output the amount of almost prime numbers between 1 and n, inclusive.", "sample_inputs": ["10", "21"], "sample_outputs": ["2", "8"], "notes": null}, "src_uid": "356666366625bc5358bc8b97c8d67bd5"}
{"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": "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": "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": "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": "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$$$ consists of the same digit.", "output_spec": "For each test case, print the answer: how many digits our character pressed in total.", "sample_inputs": ["4\n22\n9999\n1\n777"], "sample_outputs": ["13\n90\n1\n66"], "notes": null}, "src_uid": "289a55128be89bb86a002d218d31b57f"}
{"nl": {"description": "You are given a string $$$s$$$ consisting of lowercase Latin letters. Let the length of $$$s$$$ be $$$|s|$$$. You may perform several operations on this string.In one operation, you can choose some index $$$i$$$ and remove the $$$i$$$-th character of $$$s$$$ ($$$s_i$$$) if at least one of its adjacent characters is the previous letter in the Latin alphabet for $$$s_i$$$. For example, the previous letter for b is a, the previous letter for s is r, the letter a has no previous letters. Note that after each removal the length of the string decreases by one. So, the index $$$i$$$ should satisfy the condition $$$1 \\le i \\le |s|$$$ during each operation.For the character $$$s_i$$$ adjacent characters are $$$s_{i-1}$$$ and $$$s_{i+1}$$$. The first and the last characters of $$$s$$$ both have only one adjacent character (unless $$$|s| = 1$$$).Consider the following example. Let $$$s=$$$ bacabcab.  During the first move, you can remove the first character $$$s_1=$$$ b because $$$s_2=$$$ a. Then the string becomes $$$s=$$$ acabcab.  During the second move, you can remove the fifth character $$$s_5=$$$ c because $$$s_4=$$$ b. Then the string becomes $$$s=$$$ acabab.  During the third move, you can remove the sixth character $$$s_6=$$$'b' because $$$s_5=$$$ a. Then the string becomes $$$s=$$$ acaba.  During the fourth move, the only character you can remove is $$$s_4=$$$ b, because $$$s_3=$$$ a (or $$$s_5=$$$ a). The string becomes $$$s=$$$ acaa and you cannot do anything with it. Your task is to find the maximum possible number of characters you can remove if you choose the sequence of operations optimally.", "input_spec": "The only line of the input contains one integer $$$|s|$$$ ($$$1 \\le |s| \\le 100$$$) \u2014 the length of $$$s$$$. The second line of the input contains one string $$$s$$$ consisting of $$$|s|$$$ lowercase Latin letters.", "output_spec": "Print one integer \u2014 the maximum possible number of characters you can remove if you choose the sequence of moves optimally.", "sample_inputs": ["8\nbacabcab", "4\nbcda", "6\nabbbbb"], "sample_outputs": ["4", "3", "5"], "notes": "NoteThe first example is described in the problem statement. Note that the sequence of moves provided in the statement is not the only, but it can be shown that the maximum possible answer to this test is $$$4$$$.In the second example, you can remove all but one character of $$$s$$$. The only possible answer follows.  During the first move, remove the third character $$$s_3=$$$ d, $$$s$$$ becomes bca.  During the second move, remove the second character $$$s_2=$$$ c, $$$s$$$ becomes ba.  And during the third move, remove the first character $$$s_1=$$$ b, $$$s$$$ becomes a. "}, "src_uid": "9ce37bc2d361f5bb8a0568fb479b8a38"}
{"nl": {"description": "Makoto has a big blackboard with a positive integer $$$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}$$$."}, "src_uid": "dc466d9c24b7dcb37c0e99337b4124d2"}
{"nl": {"description": "You are given two positive integers $$$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$$$ and NO if you can't.", "sample_inputs": ["3 3", "7 4", "2 8", "34 69", "8935891487501725 71487131900013807"], "sample_outputs": ["YES", "NO", "NO", "YES", "YES"], "notes": "NoteIn the first example, you don't even need to do anything.The fourth example is described in the statement."}, "src_uid": "9f39a3c160087beb0efab2e3cb510e89"}
{"nl": {"description": "While playing with geometric figures Alex has accidentally invented a concept of a $$$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": "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": "Little Johnny has recently learned about set theory. Now he is studying binary relations. You've probably heard the term \"equivalence relation\". These relations are very important in many areas of mathematics. For example, the equality of the two numbers is an equivalence relation.A set \u03c1 of pairs (a,\u2009b) of elements of some set A is called a binary relation on set A. For two elements a and b of the set A we say that they are in relation \u03c1, if pair , in this case we use a notation .Binary relation is equivalence relation, if: It is reflexive (for any a it is true that ); It is symmetric (for any a, b it is true that if , then ); It is transitive (if  and , than ).Little Johnny is not completely a fool and he noticed that the first condition is not necessary! Here is his \"proof\":Take any two elements, a and b. If , then  (according to property (2)), which means  (according to property (3)).It's very simple, isn't it? However, you noticed that Johnny's \"proof\" is wrong, and decided to show him a lot of examples that prove him wrong.Here's your task: count the number of binary relations over a set of size n such that they are symmetric, transitive, but not an equivalence relations (i.e. they are not reflexive).Since their number may be very large (not 0, according to Little Johnny), print the remainder of integer division of this number by 109\u2009+\u20097.", "input_spec": "A single line contains a single integer n (1\u2009\u2264\u2009n\u2009\u2264\u20094000).", "output_spec": "In a single line print the answer to the problem modulo 109\u2009+\u20097.", "sample_inputs": ["1", "2", "3"], "sample_outputs": ["1", "3", "10"], "notes": "NoteIf n\u2009=\u20091 there is only one such relation\u00a0\u2014 an empty one, i.e. . In other words, for a single element x of set A the following is hold: .If n\u2009=\u20092 there are three such relations. Let's assume that set A consists of two elements, x and y. Then the valid relations are , \u03c1\u2009=\u2009{(x,\u2009x)}, \u03c1\u2009=\u2009{(y,\u2009y)}. It is easy to see that the three listed binary relations are symmetric and transitive relations, but they are not equivalence relations."}, "src_uid": "aa2c3e94a44053a0d86f61da06681023"}
{"nl": {"description": "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": "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": "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": "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": "You are given three integers $$$n$$$, $$$k$$$ and $$$f$$$.Consider all binary strings (i.\u2009e. all strings consisting of characters $$$0$$$ and/or $$$1$$$) of length from $$$1$$$ to $$$n$$$. For every such string $$$s$$$, you need to choose an integer $$$c_s$$$ from $$$0$$$ to $$$k$$$.A multiset of binary strings of length exactly $$$n$$$ is considered beautiful if for every binary string $$$s$$$ with length from $$$1$$$ to $$$n$$$, the number of strings in the multiset such that $$$s$$$ is their prefix is not exceeding $$$c_s$$$.For example, let $$$n = 2$$$, $$$c_{0} = 3$$$, $$$c_{00} = 1$$$, $$$c_{01} = 2$$$, $$$c_{1} = 1$$$, $$$c_{10} = 2$$$, and $$$c_{11} = 3$$$. The multiset of strings $$$\\{11, 01, 00, 01\\}$$$ is beautiful, since:  for the string $$$0$$$, there are $$$3$$$ strings in the multiset such that $$$0$$$ is their prefix, and $$$3 \\le c_0$$$;  for the string $$$00$$$, there is one string in the multiset such that $$$00$$$ is its prefix, and $$$1 \\le c_{00}$$$;  for the string $$$01$$$, there are $$$2$$$ strings in the multiset such that $$$01$$$ is their prefix, and $$$2 \\le c_{01}$$$;  for the string $$$1$$$, there is one string in the multiset such that $$$1$$$ is its prefix, and $$$1 \\le c_1$$$;  for the string $$$10$$$, there are $$$0$$$ strings in the multiset such that $$$10$$$ is their prefix, and $$$0 \\le c_{10}$$$;  for the string $$$11$$$, there is one string in the multiset such that $$$11$$$ is its prefix, and $$$1 \\le c_{11}$$$. Now, for the problem itself. You have to calculate the number of ways to choose the integer $$$c_s$$$ for every binary string $$$s$$$ of length from $$$1$$$ to $$$n$$$ in such a way that the maximum possible size of a beautiful multiset is exactly $$$f$$$.", "input_spec": "The only line of input contains three integers $$$n$$$, $$$k$$$ and $$$f$$$ ($$$1 \\le n \\le 15$$$; $$$1 \\le k, f \\le 2 \\cdot 10^5$$$).", "output_spec": "Print one integer \u2014 the number of ways to choose the integer $$$c_s$$$ for every binary string $$$s$$$ of length from $$$1$$$ to $$$n$$$ in such a way that the maximum possible size of a beautiful multiset is exactly $$$f$$$. Since it can be huge, print it modulo $$$998244353$$$.", "sample_inputs": ["1 42 2", "2 37 13", "4 1252 325", "6 153 23699", "15 200000 198756"], "sample_outputs": ["3", "36871576", "861735572", "0", "612404746"], "notes": "NoteIn the first example, the three ways to choose the integers $$$c_s$$$ are:  $$$c_0 = 0$$$, $$$c_1 = 2$$$, then the maximum beautiful multiset is $$$\\{1, 1\\}$$$;  $$$c_0 = 1$$$, $$$c_1 = 1$$$, then the maximum beautiful multiset is $$$\\{0, 1\\}$$$;  $$$c_0 = 2$$$, $$$c_1 = 0$$$, then the maximum beautiful multiset is $$$\\{0, 0\\}$$$. "}, "src_uid": "4b8161259545e44c7d1046be2e4fe014"}
{"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": "Alice and Bob play 5-in-a-row game. They have a playing field of size 10\u2009\u00d7\u200910. In turns they put either crosses or noughts, one at a time. Alice puts crosses and Bob puts noughts.In current match they have made some turns and now it's Alice's turn. She wonders if she can put cross in such empty cell that she wins immediately.Alice wins if some crosses in the field form line of length not smaller than 5. This line can be horizontal, vertical and diagonal.", "input_spec": "You are given matrix 10\u2009\u00d7\u200910 (10 lines of 10 characters each) with capital Latin letters 'X' being a cross, letters 'O' being a nought and '.' being an empty cell. The number of 'X' cells is equal to the number of 'O' cells and there is at least one of each type. There is at least one empty cell. It is guaranteed that in the current arrangement nobody has still won.", "output_spec": "Print 'YES' if it's possible for Alice to win in one turn by putting cross in some empty cell. Otherwise print 'NO'.", "sample_inputs": ["XX.XX.....\n.....OOOO.\n..........\n..........\n..........\n..........\n..........\n..........\n..........\n..........", "XXOXX.....\nOO.O......\n..........\n..........\n..........\n..........\n..........\n..........\n..........\n.........."], "sample_outputs": ["YES", "NO"], "notes": null}, "src_uid": "d5541028a2753c758322c440bdbf9ec6"}
{"nl": {"description": "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$$$ denotes that a suit for this dancer is still to be bought.", "output_spec": "If it is not possible to form a palindrome without swapping dancers and buying new suits for those who have one, then output -1. Otherwise, output the minimal price to get the desired visual effect.", "sample_inputs": ["5 100 1\n0 1 2 1 2", "3 10 12\n1 2 0", "3 12 1\n0 1 0"], "sample_outputs": ["101", "-1", "0"], "notes": "NoteIn the first sample, the cheapest way to obtain palindromic colors is to buy a black suit for the third from left dancer and a white suit for the rightmost dancer.In the second sample, the leftmost dancer's suit already differs from the rightmost dancer's suit so there is no way to obtain the desired coloring.In the third sample, all suits are already bought and their colors form a palindrome."}, "src_uid": "af07223819aeb5bd6ded4340c472b2b6"}
{"nl": {"description": "When preparing a tournament, Codeforces coordinators try treir best to make the first problem as easy as possible. This time the coordinator had chosen some problem and asked $$$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": "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": "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": "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": "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": "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": "On the planet Mars a year lasts exactly n days (there are no leap years on Mars). But Martians have the same weeks as earthlings\u00a0\u2014 5 work days and then 2 days off. Your task is to determine the minimum possible and the maximum possible number of days off per year on Mars.", "input_spec": "The first line of the input contains a positive integer n (1\u2009\u2264\u2009n\u2009\u2264\u20091\u2009000\u2009000)\u00a0\u2014 the number of days in a year on Mars.", "output_spec": "Print two integers\u00a0\u2014 the minimum possible and the maximum possible number of days off per year on Mars.", "sample_inputs": ["14", "2"], "sample_outputs": ["4 4", "0 2"], "notes": "NoteIn the first sample there are 14 days in a year on Mars, and therefore independently of the day a year starts with there will be exactly 4 days off .In the second sample there are only 2 days in a year on Mars, and they can both be either work days or days off."}, "src_uid": "8152daefb04dfa3e1a53f0a501544c35"}
{"nl": {"description": "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": "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": "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": "Nearly each project of the F company has a whole team of developers working on it. They often are in different rooms of the office in different cities and even countries. To keep in touch and track the results of the project, the F company conducts shared online meetings in a Spyke chat.One day the director of the F company got hold of the records of a part of an online meeting of one successful team. The director watched the record and wanted to talk to the team leader. But how can he tell who the leader is? The director logically supposed that the leader is the person who is present at any conversation during a chat meeting. In other words, if at some moment of time at least one person is present on the meeting, then the leader is present on the meeting.You are the assistant director. Given the 'user logged on'/'user logged off' messages of the meeting in the chronological order, help the director determine who can be the leader. Note that the director has the record of only a continuous part of the meeting (probably, it's not the whole meeting).", "input_spec": "The first line contains integers n and m (1\u2009\u2264\u2009n,\u2009m\u2009\u2264\u2009105) \u2014 the number of team participants and the number of messages. Each of the next m lines contains a message in the format:   '+ id': the record means that the person with number id (1\u2009\u2264\u2009id\u2009\u2264\u2009n) has logged on to the meeting.  '- id': the record means that the person with number id (1\u2009\u2264\u2009id\u2009\u2264\u2009n) has logged off from the meeting.  Assume that all the people of the team are numbered from 1 to n and the messages are given in the chronological order. It is guaranteed that the given sequence is the correct record of a continuous part of the meeting. It is guaranteed that no two log on/log off events occurred simultaneously.", "output_spec": "In the first line print integer k (0\u2009\u2264\u2009k\u2009\u2264\u2009n) \u2014 how many people can be leaders. In the next line, print k integers in the increasing order \u2014 the numbers of the people who can be leaders. If the data is such that no member of the team can be a leader, print a single number 0.", "sample_inputs": ["5 4\n+ 1\n+ 2\n- 2\n- 1", "3 2\n+ 1\n- 2", "2 4\n+ 1\n- 1\n+ 2\n- 2", "5 6\n+ 1\n- 1\n- 3\n+ 3\n+ 4\n- 4", "2 4\n+ 1\n- 2\n+ 2\n- 1"], "sample_outputs": ["4\n1 3 4 5", "1\n3", "0", "3\n2 3 5", "0"], "notes": null}, "src_uid": "a3a337c7b919e7dfd7ff45ebf59681b5"}
{"nl": {"description": "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": "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": "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": "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": "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": "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": "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$$$ that Polycarp likes.", "sample_inputs": ["6\n10\n1\n25\n1000000000\n999999999\n500000000"], "sample_outputs": ["4\n1\n6\n32591\n32590\n23125"], "notes": null}, "src_uid": "015afbefe1514a0e18fcb9286c7b6624"}
{"nl": {"description": "From \"ftying rats\" to urban saniwation workers - can synthetic biology tronsform how we think of pigeons? The upiquitous pigeon has long been viewed as vermin - spleading disease, scavenging through trush, and defecating in populous urban spases. Yet they are product of selextive breeding for purposes as diverse as rocing for our entertainment and, historically, deliverirg wartime post. Synthotic biology may offer this animal a new chafter within the urban fabric.Piteon d'Or recognihes how these birds ripresent a potentially userul interface for urdan biotechnologies. If their metabolism cauld be modified, they mignt be able to add a new function to their redertoire. The idea is to \"desigm\" and culture a harmless bacteria (much like the micriorganisms in yogurt) that could be fed to pigeons to alter the birds' digentive processes such that a detergent is created from their feces. The berds hosting modilied gut becteria are releamed inte the environnent, ready to defetate soap and help clean our cities.", "input_spec": "The first line of input data contains a single integer $$$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$$$).", "output_spec": "Output a single integer.", "sample_inputs": ["5\n1 2 3 4 5"], "sample_outputs": ["4"], "notes": "NoteWe did not proofread this statement at all."}, "src_uid": "a9eb85dfaa3c50ed488d41da4f29c697"}
{"nl": {"description": "You're given a row with $$$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": "The princess is going to escape the dragon's cave, and she needs to plan it carefully.The princess runs at vp miles per hour, and the dragon flies at vd miles per hour. The dragon will discover the escape after t hours and will chase the princess immediately. Looks like there's no chance to success, but the princess noticed that the dragon is very greedy and not too smart. To delay him, the princess decides to borrow a couple of bijous from his treasury. Once the dragon overtakes the princess, she will drop one bijou to distract him. In this case he will stop, pick up the item, return to the cave and spend f hours to straighten the things out in the treasury. Only after this will he resume the chase again from the very beginning.The princess is going to run on the straight. The distance between the cave and the king's castle she's aiming for is c miles. How many bijous will she need to take from the treasury to be able to reach the castle? If the dragon overtakes the princess at exactly the same moment she has reached the castle, we assume that she reached the castle before the dragon reached her, and doesn't need an extra bijou to hold him off.", "input_spec": "The input data contains integers vp,\u2009vd,\u2009t,\u2009f and c, one per line (1\u2009\u2264\u2009vp,\u2009vd\u2009\u2264\u2009100, 1\u2009\u2264\u2009t,\u2009f\u2009\u2264\u200910, 1\u2009\u2264\u2009c\u2009\u2264\u20091000).", "output_spec": "Output the minimal number of bijous required for the escape to succeed.", "sample_inputs": ["1\n2\n1\n1\n10", "1\n2\n1\n1\n8"], "sample_outputs": ["2", "1"], "notes": "NoteIn the first case one hour after the escape the dragon will discover it, and the princess will be 1 mile away from the cave. In two hours the dragon will overtake the princess 2 miles away from the cave, and she will need to drop the first bijou. Return to the cave and fixing the treasury will take the dragon two more hours; meanwhile the princess will be 4 miles away from the cave. Next time the dragon will overtake the princess 8 miles away from the cave, and she will need the second bijou, but after this she will reach the castle without any further trouble.The second case is similar to the first one, but the second time the dragon overtakes the princess when she has reached the castle, and she won't need the second bijou."}, "src_uid": "c9c03666278acec35f0e273691fe0fff"}
{"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": "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": "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": "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": "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": "Vasya has recently learned to type and log on to the Internet. He immediately entered a chat room and decided to say hello to everybody. Vasya typed the word s. It is considered that Vasya managed to say hello if several letters can be deleted from the typed word so that it resulted in the word \"hello\". For example, if Vasya types the word \"ahhellllloou\", it will be considered that he said hello, and if he types \"hlelo\", it will be considered that Vasya got misunderstood and he didn't manage to say hello. Determine whether Vasya managed to say hello by the given word s.", "input_spec": "The first and only line contains the word s, which Vasya typed. This word consisits of small Latin letters, its length is no less that 1 and no more than 100 letters.", "output_spec": "If Vasya managed to say hello, print \"YES\", otherwise print \"NO\".", "sample_inputs": ["ahhellllloou", "hlelo"], "sample_outputs": ["YES", "NO"], "notes": null}, "src_uid": "c5d19dc8f2478ee8d9cba8cc2e4cd838"}
{"nl": {"description": "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": "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": "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": "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": "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": "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 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$$$, print -1.", "sample_inputs": ["6\n1 4 4 7 4 1", "5\n2 2 5 2 5", "4\n1 3 3 7", "2\n2 8"], "sample_outputs": ["3", "3", "-1", "3"], "notes": null}, "src_uid": "d486a88939c132848a7efdf257b9b066"}
{"nl": {"description": "You've got a 5\u2009\u00d7\u20095 matrix, consisting of 24 zeroes and a single number one. Let's index the matrix rows by numbers from 1 to 5 from top to bottom, let's index the matrix columns by numbers from 1 to 5 from left to right. In one move, you are allowed to apply one of the two following transformations to the matrix:  Swap two neighboring matrix rows, that is, rows with indexes i and i\u2009+\u20091 for some integer i (1\u2009\u2264\u2009i\u2009<\u20095).  Swap two neighboring matrix columns, that is, columns with indexes j and j\u2009+\u20091 for some integer j (1\u2009\u2264\u2009j\u2009<\u20095). You think that a matrix looks beautiful, if the single number one of the matrix is located in its middle (in the cell that is on the intersection of the third row and the third column). Count the minimum number of moves needed to make the matrix beautiful.", "input_spec": "The input consists of five lines, each line contains five integers: the j-th integer in the i-th line of the input represents the element of the matrix that is located on the intersection of the i-th row and the j-th column. It is guaranteed that the matrix consists of 24 zeroes and a single number one.", "output_spec": "Print a single integer \u2014 the minimum number of moves needed to make the matrix beautiful.", "sample_inputs": ["0 0 0 0 0\n0 0 0 0 1\n0 0 0 0 0\n0 0 0 0 0\n0 0 0 0 0", "0 0 0 0 0\n0 0 0 0 0\n0 1 0 0 0\n0 0 0 0 0\n0 0 0 0 0"], "sample_outputs": ["3", "1"], "notes": null}, "src_uid": "8ba7cedc3f6ae478a0bb3f902440c8e9"}
{"nl": {"description": "We define $$$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": "Vova, the Ultimate Thule new shaman, wants to build a pipeline. As there are exactly n houses in Ultimate Thule, Vova wants the city to have exactly n pipes, each such pipe should be connected to the water supply. A pipe can be connected to the water supply if there's water flowing out of it. Initially Vova has only one pipe with flowing water. Besides, Vova has several splitters.A splitter is a construction that consists of one input (it can be connected to a water pipe) and x output pipes. When a splitter is connected to a water pipe, water flows from each output pipe. You can assume that the output pipes are ordinary pipes. For example, you can connect water supply to such pipe if there's water flowing out from it. At most one splitter can be connected to any water pipe.  The figure shows a 4-output splitter Vova has one splitter of each kind: with 2, 3, 4, ..., k outputs. Help Vova use the minimum number of splitters to build the required pipeline or otherwise state that it's impossible.Vova needs the pipeline to have exactly n pipes with flowing out water. Note that some of those pipes can be the output pipes of the splitters.", "input_spec": "The first line contains two space-separated integers n and k (1\u2009\u2264\u2009n\u2009\u2264\u20091018, 2\u2009\u2264\u2009k\u2009\u2264\u2009109). 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": "Print a single integer \u2014 the minimum number of splitters needed to build the pipeline. If it is impossible to build a pipeline with the given splitters, print -1.", "sample_inputs": ["4 3", "5 5", "8 4"], "sample_outputs": ["2", "1", "-1"], "notes": null}, "src_uid": "83bcfe32db302fbae18e8a95d89cf411"}
{"nl": {"description": "Alice and Bob are playing a game (yet again).They have two sequences of segments of the coordinate axis: a sequence of $$$n$$$ initial segments: $$$[l_1, r_1]$$$, $$$[l_2, r_2]$$$, ..., $$$[l_n, r_n]$$$, and a sequence of $$$m$$$ terminal segments: $$$[L_1, R_1]$$$, $$$[L_2, R_2]$$$, ..., $$$[L_m, R_m]$$$. At the beginning of the game, they choose one of the initial segments and set it as the current segment.Alice and Bob make alternating moves: Alice makes the first move, Bob makes the second move, Alice makes the third one, and so on. During each move, the current player must shrink the current segment either by increasing its left endpoint by $$$1$$$, or by decreasing its right endpoint by $$$1$$$. So, if the current segment is $$$[c_l, c_r]$$$, it becomes either $$$[c_l + 1, c_r]$$$, or $$$[c_l, c_r - 1]$$$.If at the beginning of the game or after Bob's move the current segment coincides with one of the terminal segments, Bob wins. If the current segment becomes degenerate ($$$c_l = c_r$$$), and Bob hasn't won yet, Alice wins. If the current segment coincides with one of the terminal segments after Alice's move, nothing happens \u2014 the game continues.Both players play optimally \u2014 if they can win, they always use a strategy that leads them to victory in the minimum number of turns, and if they cannot win, they try to prolong the game, using the strategy allowing them to make the maximum possible number of moves until their defeat.For each of the initial segments you have to determine who will win the game if this segment is chosen as the current segment at the beginning of the game. If Bob wins, you also have to calculate the number of moves Alice will make before her defeat.", "input_spec": "The first line contains two integers $$$n$$$ and $$$m$$$ ($$$1 \\le n, m \\le 2 \\cdot 10^5$$$) \u2014 the number of initial segments and terminal segments, respectively. Then $$$n$$$ lines follow, the $$$i$$$-th line contains two integers $$$l_i$$$ and $$$r_i$$$ ($$$1 \\le l_i < r_i \\le 10^6$$$) \u2014 the endpoints of the $$$i$$$-th initial segment. Then $$$m$$$ lines follow, the $$$i$$$-th line contains two integers $$$L_i$$$ and $$$R_i$$$ ($$$1 \\le L_i < R_i \\le 10^6$$$) \u2014 the endpoints of the $$$i$$$-th terminal segment. Note that some of the segments given in the input may coincide.", "output_spec": "Print $$$n$$$ integers, the $$$i$$$-th of them should describe the result of the game if the $$$i$$$-th initial segment is chosen at the beginning of the game:   if Alice wins, print $$$-1$$$;  if Bob wins, print the number of moves Alice will make before she is defeated. ", "sample_inputs": ["1 1\n4 7\n4 7", "1 2\n2 5\n2 4\n3 5", "2 1\n1 5\n1 4\n2 3"], "sample_outputs": ["0", "-1", "-1 1"], "notes": null}, "src_uid": "e93431a2908f8cdd367fe5cdfc863c80"}
{"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": "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": "Nothing is eternal in the world, Kostya understood it on the 7-th of January when he saw partially dead four-color garland.Now he has a goal to replace dead light bulbs, however he doesn't know how many light bulbs for each color are required. It is guaranteed that for each of four colors at least one light is working.It is known that the garland contains light bulbs of four colors: red, blue, yellow and green. The garland is made as follows: if you take any four consecutive light bulbs then there will not be light bulbs with the same color among them. For example, the garland can look like \"RYBGRYBGRY\", \"YBGRYBGRYBG\", \"BGRYB\", but can not look like \"BGRYG\", \"YBGRYBYGR\" or \"BGYBGY\". Letters denote colors: 'R'\u00a0\u2014 red, 'B'\u00a0\u2014 blue, 'Y'\u00a0\u2014 yellow, 'G'\u00a0\u2014 green.Using the information that for each color at least one light bulb still works count the number of dead light bulbs of each four colors.", "input_spec": "The first and the only line contains the string s (4\u2009\u2264\u2009|s|\u2009\u2264\u2009100), which describes the garland, the i-th symbol of which describes the color of the i-th light bulb in the order from the beginning of garland:    'R'\u00a0\u2014 the light bulb is red,  'B'\u00a0\u2014 the light bulb is blue,  'Y'\u00a0\u2014 the light bulb is yellow,  'G'\u00a0\u2014 the light bulb is green,  '!'\u00a0\u2014 the light bulb is dead.  The string s can not contain other symbols except those five which were described.  It is guaranteed that in the given string at least once there is each of four letters 'R', 'B', 'Y' and 'G'.  It is guaranteed that the string s is correct garland with some blown light bulbs, it means that for example the line \"GRBY!!!B\" can not be in the input data. ", "output_spec": "In the only line print four integers kr,\u2009kb,\u2009ky,\u2009kg\u00a0\u2014 the number of dead light bulbs of red, blue, yellow and green colors accordingly.", "sample_inputs": ["RYBGRYBGR", "!RGYB", "!!!!YGRB", "!GB!RG!Y!"], "sample_outputs": ["0 0 0 0", "0 1 0 0", "1 1 1 1", "2 1 1 0"], "notes": "NoteIn the first example there are no dead light bulbs.In the second example it is obvious that one blue bulb is blown, because it could not be light bulbs of other colors on its place according to the statements."}, "src_uid": "64fc6e9b458a9ece8ad70a8c72126b33"}
{"nl": {"description": "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)$$$."}, "src_uid": "907ac56260e84dbb6d98a271bcb2d62d"}
{"nl": {"description": "Mashmokh's boss, Bimokh, didn't like Mashmokh. So he fired him. Mashmokh decided to go to university and participate in ACM instead of finding a new job. He wants to become a member of Bamokh's team. In order to join he was given some programming tasks and one week to solve them. Mashmokh is not a very experienced programmer. Actually he is not a programmer at all. So he wasn't able to solve them. That's why he asked you to help him with these tasks. One of these tasks is the following.A sequence of l integers b1,\u2009b2,\u2009...,\u2009bl (1\u2009\u2264\u2009b1\u2009\u2264\u2009b2\u2009\u2264\u2009...\u2009\u2264\u2009bl\u2009\u2264\u2009n) is called good if each number divides (without a remainder) by the next number in the sequence. More formally  for all i (1\u2009\u2264\u2009i\u2009\u2264\u2009l\u2009-\u20091).Given n and k find the number of good sequences of length k. As the answer can be rather large print it modulo 1000000007 (109\u2009+\u20097).", "input_spec": "The first line of input contains two space-separated integers n,\u2009k\u00a0(1\u2009\u2264\u2009n,\u2009k\u2009\u2264\u20092000).", "output_spec": "Output a single integer \u2014 the number of good sequences of length k modulo 1000000007 (109\u2009+\u20097).", "sample_inputs": ["3 2", "6 4", "2 1"], "sample_outputs": ["5", "39", "2"], "notes": "NoteIn the first sample the good sequences are: [1,\u20091],\u2009[2,\u20092],\u2009[3,\u20093],\u2009[1,\u20092],\u2009[1,\u20093]."}, "src_uid": "c8cbd155d9f20563d37537ef68dde5aa"}
{"nl": {"description": "Kurt reaches nirvana when he finds the product of all the digits of some positive integer. Greater value of the product makes the nirvana deeper.Help Kurt find the maximum possible product of digits among all integers from $$$1$$$ to $$$n$$$.", "input_spec": "The only input line contains the integer $$$n$$$ ($$$1 \\le n \\le 2\\cdot10^9$$$).", "output_spec": "Print the maximum product of digits among all integers from $$$1$$$ to $$$n$$$.", "sample_inputs": ["390", "7", "1000000000"], "sample_outputs": ["216", "7", "387420489"], "notes": "NoteIn the first example the maximum product is achieved for $$$389$$$ (the product of digits is $$$3\\cdot8\\cdot9=216$$$).In the second example the maximum product is achieved for $$$7$$$ (the product of digits is $$$7$$$).In the third example the maximum product is achieved for $$$999999999$$$ (the product of digits is $$$9^9=387420489$$$)."}, "src_uid": "38690bd32e7d0b314f701f138ce19dfb"}
{"nl": {"description": "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 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$$$).", "output_spec": "If the records can be consistent output \"Yes\", otherwise output \"No\" (quotes for clarity).", "sample_inputs": ["5\n1 2 3 4 5\n2 1 4 3 5", "5\n1 1 1 1 1\n1 0 1 0 1", "3\n2 3 9\n1 7 9"], "sample_outputs": ["Yes", "Yes", "No"], "notes": "NoteIn the first example, the following could have happened during the night: one of the jury members moved one stone from the second pile to the first pile, and the other jury member moved one stone from the fourth pile to the third pile.In the second example, the jury took stones from the second and fourth piles.It can be proved that it is impossible for the jury members to move and took stones to convert the first array into the second array."}, "src_uid": "e0ddac5c6d3671070860dda10d50c28a"}
{"nl": {"description": "The only difference between easy and hard versions is the length of the string.You are given a string $$$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$$$.", "sample_inputs": ["bbaba\nbb", "baaba\nab", "abcde\nabcde", "asdfasdf\nfasd"], "sample_outputs": ["3", "2", "0", "3"], "notes": null}, "src_uid": "0fd33e1bdfd6c91feb3bf00a2461603f"}
{"nl": {"description": "You are given a positive (greater than zero) integer $$$n$$$.You have to represent $$$n$$$ as the sum of integers (possibly negative) consisting only of ones (digits '1'). For example, $$$24 = 11 + 11 + 1 + 1$$$ and $$$102 = 111 - 11 + 1 + 1$$$. Among all possible representations, you have to find the one that uses the minimum number of ones in total.", "input_spec": "The single line contains one integer $$$n$$$ ($$$1 \\le n < 10^{50}$$$).", "output_spec": "Print one integer $$$x$$$ \u2014 the minimum number of ones, such that there exist a representation of $$$n$$$ as the sum of integers (possibly negative) that uses $$$x$$$ ones in total.", "sample_inputs": ["24", "102"], "sample_outputs": ["6", "7"], "notes": null}, "src_uid": "1961e7c9120ff652b15cad5dd5ca0907"}
{"nl": {"description": "Kavi has $$$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": "Arpa is researching the Mexican wave.There are n spectators in the stadium, labeled from 1 to n. They start the Mexican wave at time 0.   At time 1, the first spectator stands.  At time 2, the second spectator stands.  ...  At time k, the k-th spectator stands.  At time k\u2009+\u20091, the (k\u2009+\u20091)-th spectator stands and the first spectator sits.  At time k\u2009+\u20092, the (k\u2009+\u20092)-th spectator stands and the second spectator sits.  ...  At time n, the n-th spectator stands and the (n\u2009-\u2009k)-th spectator sits.  At time n\u2009+\u20091, the (n\u2009+\u20091\u2009-\u2009k)-th spectator sits.  ...  At time n\u2009+\u2009k, the n-th spectator sits. Arpa wants to know how many spectators are standing at time t.", "input_spec": "The first line contains three integers n, k, t (1\u2009\u2264\u2009n\u2009\u2264\u2009109, 1\u2009\u2264\u2009k\u2009\u2264\u2009n, 1\u2009\u2264\u2009t\u2009<\u2009n\u2009+\u2009k).", "output_spec": "Print single integer: how many spectators are standing at time t.", "sample_inputs": ["10 5 3", "10 5 7", "10 5 12"], "sample_outputs": ["3", "5", "3"], "notes": "NoteIn the following a sitting spectator is represented as -, a standing spectator is represented as ^.  At t\u2009=\u20090\u2002 ----------  number of standing spectators = 0.  At t\u2009=\u20091\u2002 ^---------  number of standing spectators = 1.  At t\u2009=\u20092\u2002 ^^--------  number of standing spectators = 2.  At t\u2009=\u20093\u2002 ^^^-------  number of standing spectators = 3.  At t\u2009=\u20094\u2002 ^^^^------  number of standing spectators = 4.  At t\u2009=\u20095\u2002 ^^^^^-----  number of standing spectators = 5.  At t\u2009=\u20096\u2002 -^^^^^----  number of standing spectators = 5.  At t\u2009=\u20097\u2002 --^^^^^---  number of standing spectators = 5.  At t\u2009=\u20098\u2002 ---^^^^^--  number of standing spectators = 5.  At t\u2009=\u20099\u2002 ----^^^^^-  number of standing spectators = 5.  At t\u2009=\u200910 -----^^^^^  number of standing spectators = 5.  At t\u2009=\u200911 ------^^^^  number of standing spectators = 4.  At t\u2009=\u200912 -------^^^  number of standing spectators = 3.  At t\u2009=\u200913 --------^^  number of standing spectators = 2.  At t\u2009=\u200914 ---------^  number of standing spectators = 1.  At t\u2009=\u200915 ----------  number of standing spectators = 0. "}, "src_uid": "7e614526109a2052bfe7934381e7f6c2"}
{"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$$$."}, "src_uid": "cb4de190ae26127df6eeb7a1a1db8a6d"}
{"nl": {"description": "The numbers of all offices in the new building of the Tax Office of IT City will have lucky numbers.Lucky number is a number that consists of digits 7 and 8 only. Find the maximum number of offices in the new building of the Tax Office given that a door-plate can hold a number not longer than n digits.", "input_spec": "The only line of input contains one integer n (1\u2009\u2264\u2009n\u2009\u2264\u200955) \u2014 the maximum length of a number that a door-plate can hold.", "output_spec": "Output one integer \u2014 the maximum number of offices, than can have unique lucky numbers not longer than n digits.", "sample_inputs": ["2"], "sample_outputs": ["6"], "notes": null}, "src_uid": "f1b43baa14d4c262ba616d892525dfde"}
{"nl": {"description": "There is a binary string $$$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": "  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": "You have $$$n \\times n$$$ square grid and an integer $$$k$$$. Put an integer in each cell while satisfying the conditions below.  All numbers in the grid should be between $$$1$$$ and $$$k$$$ inclusive.  Minimum number of the $$$i$$$-th row is $$$1$$$ ($$$1 \\le i \\le n$$$).  Minimum number of the $$$j$$$-th column is $$$1$$$ ($$$1 \\le j \\le n$$$). Find the number of ways to put integers in the grid. Since the answer can be very large, find the answer modulo $$$(10^{9} + 7)$$$.  These are the examples of valid and invalid grid when $$$n=k=2$$$. ", "input_spec": "The only line contains two integers $$$n$$$ and $$$k$$$ ($$$1 \\le n \\le 250$$$, $$$1 \\le k \\le 10^{9}$$$).", "output_spec": "Print the answer modulo $$$(10^{9} + 7)$$$.", "sample_inputs": ["2 2", "123 456789"], "sample_outputs": ["7", "689974806"], "notes": "NoteIn the first example, following $$$7$$$ cases are possible.  In the second example, make sure you print the answer modulo $$$(10^{9} + 7)$$$."}, "src_uid": "f67173c973c6f83e88bc0ddb0b9bfa93"}
{"nl": {"description": "Polycarp has $$$n$$$ wheels and a car with $$$m$$$ slots for wheels. The initial pressure in the $$$i$$$-th wheel is $$$a_i$$$.Polycarp's goal is to take exactly $$$m$$$ wheels among the given $$$n$$$ wheels and equalize the pressure in them (then he can put these wheels in a car and use it for driving). In one minute he can decrease or increase the pressure in any (single) wheel by $$$1$$$. He can increase the pressure no more than $$$k$$$ times in total because it is hard to pump up wheels.Help Polycarp and say what is the minimum number of minutes he needs to spend to equalize the pressure of at least $$$m$$$ wheels among the given $$$n$$$ wheels.", "input_spec": "The first line of the input contains three integers $$$n, m$$$ and $$$k$$$ ($$$1 \\le m \\le n \\le 2 \\cdot 10^5, 0 \\le k \\le 10^9$$$) \u2014 the number of wheels, the number of slots for wheels in a car and the number of times Polycarp can increase by $$$1$$$ the pressure in a wheel. The second line of the input contains $$$n$$$ integers $$$a_1, a_2, \\dots, a_n$$$ ($$$1 \\le a_i \\le 10^9$$$), where $$$a_i$$$ is the pressure in the $$$i$$$-th wheel.", "output_spec": "Print one integer \u2014 the minimum number of minutes Polycarp needs to spend to equalize the pressure in at least $$$m$$$ wheels among the given $$$n$$$ wheels.", "sample_inputs": ["6 6 7\n6 15 16 20 1 5", "6 3 1\n4 8 15 16 23 42", "5 4 0\n5 5 5 4 5"], "sample_outputs": ["39", "8", "0"], "notes": null}, "src_uid": "9c3abb6508c16d906d16f70acaf155ff"}
{"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": "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$$$ seconds. That means Masha will take the elevator."}, "src_uid": "05cffd59b28b9e026ca3203718b2e6ca"}
{"nl": {"description": "InputThe input contains two integers $$$N$$$, $$$M$$$ ($$$1 \\le N \\le 1024, 2 \\le M \\le 16$$$), separated by a single space.OutputOutput \"YES\" or \"NO\".ExamplesInput\n2 3\nOutput\nYES\nInput\n3 2\nOutput\nNO\nInput\n33 16\nOutput\nYES\nInput\n26 5\nOutput\nNO\n", "input_spec": "The input contains two integers $$$N$$$, $$$M$$$ ($$$1 \\le N \\le 1024, 2 \\le M \\le 16$$$), separated by a single space.", "output_spec": "Output \"YES\" or \"NO\".", "sample_inputs": ["2 3", "3 2", "33 16", "26 5"], "sample_outputs": ["YES", "NO", "YES", "NO"], "notes": null}, "src_uid": "a8945bb1082fefe70e6898a8bec1ce3f"}
{"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": "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$$$ initially, the player can do nothing."}, "src_uid": "c30b372a9cc0df4948dca48ef4c5d80d"}
{"nl": {"description": "You are given three positive integers x,\u2009y,\u2009n. Your task is to find the nearest fraction to fraction  whose denominator is no more than n. Formally, you should find such pair of integers a,\u2009b (1\u2009\u2264\u2009b\u2009\u2264\u2009n;\u00a00\u2009\u2264\u2009a) that the value  is as minimal as possible.If there are multiple \"nearest\" fractions, choose the one with the minimum denominator. If there are multiple \"nearest\" fractions with the minimum denominator, choose the one with the minimum numerator.", "input_spec": "A single line contains three integers x,\u2009y,\u2009n (1\u2009\u2264\u2009x,\u2009y,\u2009n\u2009\u2264\u2009105).", "output_spec": "Print the required fraction in the format \"a/b\" (without quotes).", "sample_inputs": ["3 7 6", "7 2 4"], "sample_outputs": ["2/5", "7/2"], "notes": null}, "src_uid": "827bc6f120aff6a6f04271bc84e863ee"}
{"nl": {"description": "Natasha is going to fly to Mars. She needs to build a rocket, which consists of several stages in some order. Each of the stages is defined by a lowercase Latin letter. This way, the rocket can be described by the string\u00a0\u2014 concatenation of letters, which correspond to the stages.There are $$$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$$$, so the rocket must have both stages: 'a' and 'b'. This rocket doesn't satisfy the condition, because these letters are adjacent in the alphabet. Answer is -1."}, "src_uid": "56b13d313afef9dc6c6ba2758b5ea313"}
{"nl": {"description": "The only difference between easy and hard versions is the number of elements in the array.You are given an array $$$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": "Vasily has a number a, which he wants to turn into a number b. For this purpose, he can do two types of operations:  multiply the current number by 2 (that is, replace the number x by 2\u00b7x);  append the digit 1 to the right of current number (that is, replace the number x by 10\u00b7x\u2009+\u20091). You need to help Vasily to transform the number a into the number b using only the operations described above, or find that it is impossible.Note that in this task you are not required to minimize the number of operations. It suffices to find any way to transform a into b.", "input_spec": "The first line contains two positive integers a and b (1\u2009\u2264\u2009a\u2009<\u2009b\u2009\u2264\u2009109)\u00a0\u2014 the number which Vasily has and the number he wants to have.", "output_spec": "If there is no way to get b from a, print \"NO\" (without quotes). Otherwise print three lines. On the first line print \"YES\" (without quotes). The second line should contain single integer k\u00a0\u2014 the length of the transformation sequence. On the third line print the sequence of transformations x1,\u2009x2,\u2009...,\u2009xk, where:   x1 should be equal to a,  xk should be equal to b,  xi should be obtained from xi\u2009-\u20091 using any of two described operations (1\u2009<\u2009i\u2009\u2264\u2009k).  If there are multiple answers, print any of them.", "sample_inputs": ["2 162", "4 42", "100 40021"], "sample_outputs": ["YES\n5\n2 4 8 81 162", "NO", "YES\n5\n100 200 2001 4002 40021"], "notes": null}, "src_uid": "fc3adb1a9a7f1122b567b4d8afd7b3f3"}
{"nl": {"description": "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": "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": "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": "Misha and Vasya participated in a Codeforces contest. Unfortunately, each of them solved only one problem, though successfully submitted it at the first attempt. Misha solved the problem that costs a points and Vasya solved the problem that costs b points. Besides, Misha submitted the problem c minutes after the contest started and Vasya submitted the problem d minutes after the contest started. As you know, on Codeforces the cost of a problem reduces as a round continues. That is, if you submit a problem that costs p points t minutes after the contest started, you get  points. Misha and Vasya are having an argument trying to find out who got more points. Help them to find out the truth.", "input_spec": "The first line contains four integers a, b, c, d (250\u2009\u2264\u2009a,\u2009b\u2009\u2264\u20093500, 0\u2009\u2264\u2009c,\u2009d\u2009\u2264\u2009180).  It is guaranteed that numbers a and b are divisible by 250 (just like on any real Codeforces round).", "output_spec": "Output on a single line:  \"Misha\" (without the quotes), if Misha got more points than Vasya. \"Vasya\" (without the quotes), if Vasya got more points than Misha. \"Tie\" (without the quotes), if both of them got the same number of points.", "sample_inputs": ["500 1000 20 30", "1000 1000 1 1", "1500 1000 176 177"], "sample_outputs": ["Vasya", "Tie", "Misha"], "notes": null}, "src_uid": "95b19d7569d6b70bd97d46a8541060d0"}
{"nl": {"description": "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": "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": "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": "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": "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": "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": "A mouse encountered a nice big cake and decided to take a walk across it, eating the berries on top of the cake on its way. The cake is rectangular, neatly divided into squares; some of the squares have a berry in them, and some don't.The mouse is in a bit of a hurry, though, so once she enters the cake from its northwest corner (the top left cell in the input data), she will only go east (right) or south (down), until she reaches the southeast corner (the bottom right cell). She will eat every berry in the squares she passes through, but not in the other squares.The mouse tries to choose her path so as to maximize the number of berries consumed. However, her haste and hunger might be clouding her judgement, leading her to suboptimal decisions...", "input_spec": "The first line of input contains two integers $$$H$$$ and $$$W$$$ ($$$1 \\le H, W \\le 5$$$), separated by a space, \u2014 the height and the width of the cake. The next $$$H$$$ lines contain a string of $$$W$$$ characters each, representing the squares of the cake in that row: '.' represents an empty square, and '*' represents a square with a berry.", "output_spec": "Output the number of berries the mouse will eat following her strategy.", "sample_inputs": ["4 3\n*..\n.*.\n..*\n...", "4 4\n.*..\n*...\n...*\n..*.", "3 4\n..**\n*...\n....", "5 5\n..*..\n.....\n**...\n**...\n**..."], "sample_outputs": ["3", "2", "1", "1"], "notes": null}, "src_uid": "f985d7a6e7650a9b855a4cef26fd9b0d"}
{"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": "This version of the problem differs from the next one only in the constraint on $$$n$$$.Note that the memory limit in this problem is lower than in others.You have a vertical strip with $$$n$$$ cells, numbered consecutively from $$$1$$$ to $$$n$$$ from top to bottom.You also have a token that is initially placed in cell $$$n$$$. You will move the token up until it arrives at cell $$$1$$$.Let the token be in cell $$$x > 1$$$ at some moment. One shift of the token can have either of the following kinds:   Subtraction: you choose an integer $$$y$$$ between $$$1$$$ and $$$x-1$$$, inclusive, and move the token from cell $$$x$$$ to cell $$$x - y$$$.  Floored division: you choose an integer $$$z$$$ between $$$2$$$ and $$$x$$$, inclusive, and move the token from cell $$$x$$$ to cell $$$\\lfloor \\frac{x}{z} \\rfloor$$$ ($$$x$$$ divided by $$$z$$$ rounded down). Find the number of ways to move the token from cell $$$n$$$ to cell $$$1$$$ using one or more shifts, and print it modulo $$$m$$$. Note that if there are several ways to move the token from one cell to another in one shift, all these ways are considered distinct (check example explanation for a better understanding).", "input_spec": "The only line contains two integers $$$n$$$ and $$$m$$$ ($$$2 \\le n \\le 2 \\cdot 10^5$$$; $$$10^8 < m < 10^9$$$; $$$m$$$ is a prime number)\u00a0\u2014 the length of the strip and the modulo.", "output_spec": "Print the number of ways to move the token from cell $$$n$$$ to cell $$$1$$$, modulo $$$m$$$.", "sample_inputs": ["3 998244353", "5 998244353", "42 998244353"], "sample_outputs": ["5", "25", "793019428"], "notes": "NoteIn the first test, there are three ways to move the token from cell $$$3$$$ to cell $$$1$$$ in one shift: using subtraction of $$$y = 2$$$, or using division by $$$z = 2$$$ or $$$z = 3$$$.There are also two ways to move the token from cell $$$3$$$ to cell $$$1$$$ via cell $$$2$$$: first subtract $$$y = 1$$$, and then either subtract $$$y = 1$$$ again or divide by $$$z = 2$$$.Therefore, there are five ways in total."}, "src_uid": "a524aa54e83fd0223489a19531bf0e79"}
{"nl": {"description": "One day Alex was creating a contest about his friends, but accidentally deleted it. Fortunately, all the problems were saved, but now he needs to find them among other problems.But there are too many problems, to do it manually. Alex asks you to write a program, which will determine if a problem is from this contest by its name.It is known, that problem is from this contest if and only if its name contains one of Alex's friends' name exactly once. His friends' names are \"Danil\", \"Olya\", \"Slava\", \"Ann\" and \"Nikita\".Names are case sensitive.", "input_spec": "The only line contains string from lowercase and uppercase letters and \"_\" symbols of length, not more than 100 \u2014 the name of the problem.", "output_spec": "Print \"YES\", if problem is from this contest, and \"NO\" otherwise.", "sample_inputs": ["Alex_and_broken_contest", "NikitaAndString", "Danil_and_Olya"], "sample_outputs": ["NO", "YES", "NO"], "notes": null}, "src_uid": "db2dc7500ff4d84dcc1a37aebd2b3710"}
{"nl": {"description": "Given 2 integers $$$u$$$ and $$$v$$$, find the shortest array such that bitwise-xor of its elements is $$$u$$$, and the sum of its elements is $$$v$$$.", "input_spec": "The only line contains 2 integers $$$u$$$ and $$$v$$$ $$$(0 \\le u,v \\le 10^{18})$$$.", "output_spec": "If there's no array that satisfies the condition, print \"-1\". Otherwise: The first line should contain one integer, $$$n$$$, representing the length of the desired array. The next line should contain $$$n$$$ positive integers, the array itself. If there are multiple possible answers, print any.", "sample_inputs": ["2 4", "1 3", "8 5", "0 0"], "sample_outputs": ["2\n3 1", "3\n1 1 1", "-1", "0"], "notes": "NoteIn the first sample, $$$3\\oplus 1 = 2$$$ and $$$3 + 1 = 4$$$. There is no valid array of smaller length.Notice that in the fourth sample the array is empty."}, "src_uid": "490f23ced6c43f9e12f1bcbecbb14904"}
{"nl": {"description": "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": "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": "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": "As you have noticed, there are lovely girls in Arpa\u2019s land.People in Arpa's land are numbered from 1 to n. Everyone has exactly one crush, i-th person's crush is person with the number crushi.  Someday Arpa shouted Owf loudly from the top of the palace and a funny game started in Arpa's land. The rules are as follows.The game consists of rounds. Assume person x wants to start a round, he calls crushx and says: \"Oww...wwf\" (the letter w is repeated t times) and cuts off the phone immediately. If t\u2009>\u20091 then crushx calls crushcrushx and says: \"Oww...wwf\" (the letter w is repeated t\u2009-\u20091 times) and cuts off the phone immediately. The round continues until some person receives an \"Owf\" (t\u2009=\u20091). This person is called the Joon-Joon of the round. There can't be two rounds at the same time.Mehrdad has an evil plan to make the game more funny, he wants to find smallest t (t\u2009\u2265\u20091) such that for each person x, if x starts some round and y becomes the Joon-Joon of the round, then by starting from y, x would become the Joon-Joon of the round. Find such t for Mehrdad if it's possible.Some strange fact in Arpa's land is that someone can be himself's crush (i.e. crushi\u2009=\u2009i).", "input_spec": "The first line of input contains integer n (1\u2009\u2264\u2009n\u2009\u2264\u2009100)\u00a0\u2014 the number of people in Arpa's land. The second line contains n integers, i-th of them is crushi (1\u2009\u2264\u2009crushi\u2009\u2264\u2009n)\u00a0\u2014 the number of i-th person's crush.", "output_spec": "If there is no t satisfying the condition, print -1. Otherwise print such smallest t.", "sample_inputs": ["4\n2 3 1 4", "4\n4 4 4 4", "4\n2 1 4 3"], "sample_outputs": ["3", "-1", "1"], "notes": "NoteIn the first sample suppose t\u2009=\u20093. If the first person starts some round:The first person calls the second person and says \"Owwwf\", then the second person calls the third person and says \"Owwf\", then the third person calls the first person and says \"Owf\", so the first person becomes Joon-Joon of the round. So the condition is satisfied if x is 1.The process is similar for the second and the third person.If the fourth person starts some round:The fourth person calls himself and says \"Owwwf\", then he calls himself again and says \"Owwf\", then he calls himself for another time and says \"Owf\", so the fourth person becomes Joon-Joon of the round. So the condition is satisfied when x is 4.In the last example if the first person starts a round, then the second person becomes the Joon-Joon, and vice versa."}, "src_uid": "149221131a978298ac56b58438df46c9"}
{"nl": {"description": "On his free time, Chouti likes doing some housework. He has got one new task, paint some bricks in the yard.There are $$$n$$$ bricks lined in a row on the ground. Chouti has got $$$m$$$ paint buckets of different colors at hand, so he painted each brick in one of those $$$m$$$ colors.Having finished painting all bricks, Chouti was satisfied. He stood back and decided to find something fun with these bricks. After some counting, he found there are $$$k$$$ bricks with a color different from the color of the brick on its left (the first brick is not counted, for sure).So as usual, he needs your help in counting how many ways could he paint the bricks. Two ways of painting bricks are different if there is at least one brick painted in different colors in these two ways. Because the answer might be quite big, you only need to output the number of ways modulo $$$998\\,244\\,353$$$.", "input_spec": "The first and only line contains three integers $$$n$$$, $$$m$$$ and $$$k$$$ ($$$1 \\leq n,m \\leq 2000, 0 \\leq k \\leq n-1$$$)\u00a0\u2014 the number of bricks, the number of colors, and the number of bricks, such that its color differs from the color of brick to the left of it.", "output_spec": "Print one integer\u00a0\u2014 the number of ways to color bricks modulo $$$998\\,244\\,353$$$.", "sample_inputs": ["3 3 0", "3 2 1"], "sample_outputs": ["3", "4"], "notes": "NoteIn the first example, since $$$k=0$$$, the color of every brick should be the same, so there will be exactly $$$m=3$$$ ways to color the bricks.In the second example, suppose the two colors in the buckets are yellow and lime, the following image shows all $$$4$$$ possible colorings.  "}, "src_uid": "b2b9bee53e425fab1aa4d5468b9e578b"}
{"nl": {"description": "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": "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": "Manao works on a sports TV. He's spent much time watching the football games of some country. After a while he began to notice different patterns. For example, each team has two sets of uniforms: home uniform and guest uniform. When a team plays a game at home, the players put on the home uniform. When a team plays as a guest on somebody else's stadium, the players put on the guest uniform. The only exception to that rule is: when the home uniform color of the host team matches the guests' uniform, the host team puts on its guest uniform as well. For each team the color of the home and guest uniform is different.There are n teams taking part in the national championship. The championship consists of n\u00b7(n\u2009-\u20091) games: each team invites each other team to its stadium. At this point Manao wondered: how many times during the championship is a host team going to put on the guest uniform? Note that the order of the games does not affect this number.You know the colors of the home and guest uniform for each team. For simplicity, the colors are numbered by integers in such a way that no two distinct colors have the same number. Help Manao find the answer to his question.", "input_spec": "The first line contains an integer n (2\u2009\u2264\u2009n\u2009\u2264\u200930). Each of the following n lines contains a pair of distinct space-separated integers hi, ai (1\u2009\u2264\u2009hi,\u2009ai\u2009\u2264\u2009100) \u2014 the colors of the i-th team's home and guest uniforms, respectively.", "output_spec": "In a single line print the number of games where the host team is going to play in the guest uniform.", "sample_inputs": ["3\n1 2\n2 4\n3 4", "4\n100 42\n42 100\n5 42\n100 5", "2\n1 2\n1 2"], "sample_outputs": ["1", "5", "0"], "notes": "NoteIn the first test case the championship consists of 6 games. The only game with the event in question is the game between teams 2 and 1 on the stadium of team 2.In the second test sample the host team will have to wear guest uniform in the games between teams: 1 and 2, 2 and 1, 2 and 3, 3 and 4, 4 and 2 (the host team is written first)."}, "src_uid": "745f81dcb4f23254bf6602f9f389771b"}
{"nl": {"description": "Ehab is interested in the bitwise-xor operation and the special graphs. Mahmoud gave him a problem that combines both. He has a complete graph consisting of n vertices numbered from 0 to n\u2009-\u20091. For all 0\u2009\u2264\u2009u\u2009<\u2009v\u2009<\u2009n, vertex u and vertex v are connected with an undirected edge that has weight  (where  is the bitwise-xor operation). Can you find the weight of the minimum spanning tree of that graph?You can read about complete graphs in https://en.wikipedia.org/wiki/Complete_graphYou can read about the minimum spanning tree in https://en.wikipedia.org/wiki/Minimum_spanning_treeThe weight of the minimum spanning tree is the sum of the weights on the edges included in it.", "input_spec": "The only line contains an integer n (2\u2009\u2264\u2009n\u2009\u2264\u20091012), the number of vertices in the graph.", "output_spec": "The only line contains an integer x, the weight of the graph's minimum spanning tree.", "sample_inputs": ["4"], "sample_outputs": ["4"], "notes": "NoteIn the first sample:  The weight of the minimum spanning tree is 1+2+1=4."}, "src_uid": "a98f0d924ea52cafe0048f213f075891"}
{"nl": {"description": "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": "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": "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": "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)$$$. Note that the second summand is negative, which is allowed.In the fifth sample case, no representation is possible."}, "src_uid": "9e86d87ce5a75c6a982894af84eb4ba8"}
{"nl": {"description": "Joker returns to Gotham City to execute another evil plan. In Gotham City, there are $$$N$$$ street junctions (numbered from $$$1$$$ to $$$N$$$) and $$$M$$$ streets (numbered from $$$1$$$ to $$$M$$$). Each street connects two distinct junctions, and two junctions are connected by at most one street.For his evil plan, Joker needs to use an odd number of streets that together form a cycle. That is, for a junction $$$S$$$ and an even positive integer $$$k$$$, there is a sequence of junctions $$$S, s_1, \\ldots, s_k, S$$$ such that there are streets connecting (a) $$$S$$$ and $$$s_1$$$, (b) $$$s_k$$$ and $$$S$$$, and (c) $$$s_{i-1}$$$ and $$$s_i$$$ for each $$$i = 2, \\ldots, k$$$.However, the police are controlling the streets of Gotham City. On each day $$$i$$$, they monitor a different subset of all streets with consecutive numbers $$$j$$$: $$$l_i \\leq j \\leq r_i$$$. These monitored streets cannot be a part of Joker's plan, of course. Unfortunately for the police, Joker has spies within the Gotham City Police Department; they tell him which streets are monitored on which day. Now Joker wants to find out, for some given number of days, whether he can execute his evil plan. On such a day there must be a cycle of streets, consisting of an odd number of streets which are not monitored on that day.", "input_spec": "The first line of the input contains three integers $$$N$$$, $$$M$$$, and $$$Q$$$ ($$$1 \\leq N, M, Q \\leq 200\\,000$$$): the number of junctions, the number of streets, and the number of days to be investigated. The following $$$M$$$ lines describe the streets. The $$$j$$$-th of these lines ($$$1 \\le j \\le M$$$) contains two junction numbers $$$u$$$ and $$$v$$$ ($$$u \\neq v$$$), saying that street $$$j$$$ connects these two junctions. It is guaranteed that any two junctions are connected by at most one street. The following $$$Q$$$ lines contain two integers $$$l_i$$$ and $$$r_i$$$, saying that all streets $$$j$$$ with $$$l_i \\leq j \\leq r_i$$$ are checked by the police on day $$$i$$$ ($$$1 \\leq i \\leq Q$$$).", "output_spec": "Your output is to contain $$$Q$$$ lines. Line $$$i$$$ ($$$1 \\leq i \\leq Q$$$) contains \"YES\" if Joker can execute his plan on day $$$i$$$, or \"NO\" otherwise.", "sample_inputs": ["6 8 2\n1 3\n1 5\n1 6\n2 5\n2 6\n3 4\n3 5\n5 6\n4 8\n4 7"], "sample_outputs": ["NO\nYES"], "notes": "NoteThe graph in the example test:   "}, "src_uid": "57ad95bb938906f7550f7eb6422130f7"}
{"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": "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": "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": "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": "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": "Tonio has a keyboard with only two letters, \"V\" and \"K\".One day, he has typed out a string s with only these two letters. He really likes it when the string \"VK\" appears, so he wishes to change at most one letter in the string (or do no changes) to maximize the number of occurrences of that string. Compute the maximum number of times \"VK\" can appear as a substring (i.\u00a0e. a letter \"K\" right after a letter \"V\") in the resulting string.", "input_spec": "The first line will contain a string s consisting only of uppercase English letters \"V\" and \"K\" with length not less than 1 and not greater than 100.", "output_spec": "Output a single integer, the maximum number of times \"VK\" can appear as a substring of the given string after changing at most one character.", "sample_inputs": ["VK", "VV", "V", "VKKKKKKKKKVVVVVVVVVK", "KVKV"], "sample_outputs": ["1", "1", "0", "3", "1"], "notes": "NoteFor the first case, we do not change any letters. \"VK\" appears once, which is the maximum number of times it could appear.For the second case, we can change the second character from a \"V\" to a \"K\". This will give us the string \"VK\". This has one occurrence of the string \"VK\" as a substring.For the fourth case, we can change the fourth character from a \"K\" to a \"V\". This will give us the string \"VKKVKKKKKKVVVVVVVVVK\". This has three occurrences of the string \"VK\" as a substring. We can check no other moves can give us strictly more occurrences."}, "src_uid": "578bae0fe6634882227ac371ebb38fc9"}
{"nl": {"description": "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$$$ is the smallest prime divisor at both steps."}, "src_uid": "a1e80ddd97026835a84f91bac8eb21e6"}
{"nl": {"description": "There is a field of size $$$2 \\times 2$$$. Each cell of this field can either contain grass or be empty. The value $$$a_{i, j}$$$ is $$$1$$$ if the cell $$$(i, j)$$$ contains grass, or $$$0$$$ otherwise.In one move, you can choose one row and one column and cut all the grass in this row and this column. In other words, you choose the row $$$x$$$ and the column $$$y$$$, then you cut the grass in all cells $$$a_{x, i}$$$ and all cells $$$a_{i, y}$$$ for all $$$i$$$ from $$$1$$$ to $$$2$$$. After you cut the grass from a cell, it becomes empty (i.\u2009e. its value is replaced by $$$0$$$).Your task is to find the minimum number of moves required to cut the grass in all non-empty cells of the field (i.\u2009e. make all $$$a_{i, j}$$$ zeros).You have to answer $$$t$$$ independent test cases.", "input_spec": "The first line of the input contains one integer $$$t$$$ ($$$1 \\le t \\le 16$$$) \u2014 the number of test cases. Then $$$t$$$ test cases follow. The test case consists of two lines, each of these lines contains two integers. The $$$j$$$-th integer in the $$$i$$$-th row is $$$a_{i, j}$$$. If $$$a_{i, j} = 0$$$ then the cell $$$(i, j)$$$ is empty, and if $$$a_{i, j} = 1$$$ the cell $$$(i, j)$$$ contains grass.", "output_spec": "For each test case, print one integer \u2014 the minimum number of moves required to cut the grass in all non-empty cells of the field (i.\u2009e. make all $$$a_{i, j}$$$ zeros) in the corresponding test case.", "sample_inputs": ["3\n\n0 0\n\n0 0\n\n1 0\n\n0 1\n\n1 1\n\n1 1"], "sample_outputs": ["0\n1\n2"], "notes": null}, "src_uid": "7336b8becd2438f0439240ee8f9610ec"}
{"nl": {"description": "Neko loves divisors. During the latest number theory lesson, he got an interesting exercise from his math teacher.Neko has two integers $$$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$$$, which is the smallest least common multiple possible."}, "src_uid": "414149fadebe25ab6097fc67663177c3"}
{"nl": {"description": "The only difference between the easy and the hard versions is constraints.A subsequence is a string that can be derived from another string by deleting some or no symbols without changing the order of the remaining symbols. Characters to be deleted are not required to go successively, there can be any gaps between them. For example, for the string \"abaca\" the following strings are subsequences: \"abaca\", \"aba\", \"aaa\", \"a\" and \"\" (empty string). But the following strings are not subsequences: \"aabaca\", \"cb\" and \"bcaa\".You are given a string $$$s$$$ consisting of $$$n$$$ lowercase Latin letters.In one move you can take any subsequence $$$t$$$ of the given string and add it to the set $$$S$$$. The set $$$S$$$ can't contain duplicates. This move costs $$$n - |t|$$$, where $$$|t|$$$ is the length of the added subsequence (i.e. the price equals to the number of the deleted characters).Your task is to find out the minimum possible total cost to obtain a set $$$S$$$ of size $$$k$$$ or report that it is impossible to do so.", "input_spec": "The first line of the input contains two integers $$$n$$$ and $$$k$$$ ($$$1 \\le n, k \\le 100$$$) \u2014 the length of the string and the size of the set, correspondingly. The second line of the input contains a string $$$s$$$ consisting of $$$n$$$ lowercase Latin letters.", "output_spec": "Print one integer \u2014 if it is impossible to obtain the set $$$S$$$ of size $$$k$$$, print -1. Otherwise, print the minimum possible total cost to do it.", "sample_inputs": ["4 5\nasdf", "5 6\naaaaa", "5 7\naaaaa", "10 100\najihiushda"], "sample_outputs": ["4", "15", "-1", "233"], "notes": "NoteIn the first example we can generate $$$S$$$ = { \"asdf\", \"asd\", \"adf\", \"asf\", \"sdf\" }. The cost of the first element in $$$S$$$ is $$$0$$$ and the cost of the others is $$$1$$$. So the total cost of $$$S$$$ is $$$4$$$."}, "src_uid": "ae5d21919ecac431ea7507cb1b6dc72b"}
{"nl": {"description": "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": "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": "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": "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": "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": "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": "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": "One day Vasya came across three Berland coins. They didn't have any numbers that's why Vasya didn't understand how their denominations differ. He supposed that if one coin is heavier than the other one, then it should be worth more. Vasya weighed all the three pairs of coins on pan balance scales and told you the results. Find out how the deminations of the coins differ or if Vasya has a mistake in the weighting results. No two coins are equal.", "input_spec": "The input data contains the results of all the weighting, one result on each line. It is guaranteed that every coin pair was weighted exactly once. Vasya labelled the coins with letters \u00abA\u00bb, \u00abB\u00bb and \u00abC\u00bb. Each result is a line that appears as (letter)(> or < sign)(letter). For example, if coin \"A\" proved lighter than coin \"B\", the result of the weighting is A<B.", "output_spec": "It the results are contradictory, print Impossible. Otherwise, print without spaces the rearrangement of letters \u00abA\u00bb, \u00abB\u00bb and \u00abC\u00bb which represent the coins in the increasing order of their weights.", "sample_inputs": ["A>B\nC<B\nA>C", "A<B\nB>C\nC>A"], "sample_outputs": ["CBA", "ACB"], "notes": null}, "src_uid": "97fd9123d0fb511da165b900afbde5dc"}
{"nl": {"description": "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": "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": "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": "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": "Kicker (table football) is a board game based on football, in which players control the footballers' figures mounted on rods by using bars to get the ball into the opponent's goal. When playing two on two, one player of each team controls the goalkeeper and the full-backs (plays defence), the other player controls the half-backs and forwards (plays attack).Two teams of company Q decided to battle each other. Let's enumerate players from both teams by integers from 1 to 4. The first and second player play in the first team, the third and the fourth one play in the second team. For each of the four players we know their game skills in defence and attack. The defence skill of the i-th player is ai, the attack skill is bi.Before the game, the teams determine how they will play. First the players of the first team decide who will play in the attack, and who will play in the defence. Then the second team players do the same, based on the choice of their opponents.We will define a team's defence as the defence skill of player of the team who plays defence. Similarly, a team's attack is the attack skill of the player of the team who plays attack. We assume that one team is guaranteed to beat the other one, if its defence is strictly greater than the opponent's attack and its attack is strictly greater than the opponent's defence.The teams of company Q know each other's strengths and therefore arrange their teams optimally. Identify the team that is guaranteed to win (if both teams act optimally) or tell that there is no such team.", "input_spec": "The input contain the players' description in four lines. The i-th line contains two space-separated integers ai and bi (1\u2009\u2264\u2009ai,\u2009bi\u2009\u2264\u2009100) \u2014 the defence and the attack skill of the i-th player, correspondingly.", "output_spec": "If the first team can win, print phrase \"Team 1\" (without the quotes), if the second team can win, print phrase \"Team 2\" (without the quotes). If no of the teams can definitely win, print \"Draw\" (without the quotes).", "sample_inputs": ["1 100\n100 1\n99 99\n99 99", "1 1\n2 2\n3 3\n2 2", "3 3\n2 2\n1 1\n2 2"], "sample_outputs": ["Team 1", "Team 2", "Draw"], "notes": "NoteLet consider the first test sample. The first team can definitely win if it will choose the following arrangement: the first player plays attack, the second player plays defence.Consider the second sample. The order of the choosing roles for players makes sense in this sample. As the members of the first team choose first, the members of the second team can beat them (because they know the exact defence value and attack value of the first team)."}, "src_uid": "1a70ed6f58028a7c7a86e73c28ff245f"}
{"nl": {"description": "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": "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": "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": "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": "Imagine a city with n horizontal streets crossing m vertical streets, forming an (n\u2009-\u20091)\u2009\u00d7\u2009(m\u2009-\u20091) grid. In order to increase the traffic flow, mayor of the city has decided to make each street one way. This means in each horizontal street, the traffic moves only from west to east or only from east to west. Also, traffic moves only from north to south or only from south to north in each vertical street. It is possible to enter a horizontal street from a vertical street, or vice versa, at their intersection.  The mayor has received some street direction patterns. Your task is to check whether it is possible to reach any junction from any other junction in the proposed street direction pattern.", "input_spec": "The first line of input contains two integers n and m, (2\u2009\u2264\u2009n,\u2009m\u2009\u2264\u200920), denoting the number of horizontal streets and the number of vertical streets. The second line contains a string of length n, made of characters '<' and '>', denoting direction of each horizontal street. If the i-th character is equal to '<', the street is directed from east to west otherwise, the street is directed from west to east. Streets are listed in order from north to south. The third line contains a string of length m, made of characters '^' and 'v', denoting direction of each vertical street. If the i-th character is equal to '^', the street is directed from south to north, otherwise the street is directed from north to south. Streets are listed in order from west to east.", "output_spec": "If the given pattern meets the mayor's criteria, print a single line containing \"YES\", otherwise print a single line containing \"NO\".", "sample_inputs": ["3 3\n><>\nv^v", "4 6\n<><>\nv^v^v^"], "sample_outputs": ["NO", "YES"], "notes": "NoteThe figure above shows street directions in the second sample test case."}, "src_uid": "eab5c84c9658eb32f5614cd2497541cf"}
{"nl": {"description": "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$$$ boxes."}, "src_uid": "c05d753b35545176ad468b99ff13aa39"}
{"nl": {"description": "You are given two integers n and k. Find k-th smallest divisor of n, or report that it doesn't exist.Divisor of n is any such natural number, that n can be divided by it without remainder.", "input_spec": "The first line contains two integers n and k (1\u2009\u2264\u2009n\u2009\u2264\u20091015, 1\u2009\u2264\u2009k\u2009\u2264\u2009109).", "output_spec": "If n has less than k divisors, output -1. Otherwise, output the k-th smallest divisor of n.", "sample_inputs": ["4 2", "5 3", "12 5"], "sample_outputs": ["2", "-1", "6"], "notes": "NoteIn the first example, number 4 has three divisors: 1, 2 and 4. The second one is 2.In the second example, number 5 has only two divisors: 1 and 5. The third divisor doesn't exist, so the answer is -1."}, "src_uid": "6ba39b428a2d47b7d199879185797ffb"}
{"nl": {"description": "This is an easy version of the problem. The actual problems are different, but the easy version is almost a subtask of the hard version. Note that the constraints and the output format are different.You are given a string $$$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": "A prime number is a number which has exactly two distinct divisors: one and itself. For example, numbers 2, 7, 3 are prime, and 1, 6, 4 are not.The next prime number after x is the smallest prime number greater than x. For example, the next prime number after 2 is 3, and the next prime number after 3 is 5. Note that there is exactly one next prime number after each number. So 5 is\u00a0not the next prime number for 2.One cold April morning Panoramix predicted that soon Kakofonix will break free from his straitjacket, and this will be a black day for the residents of the Gallic countryside.Panoramix's prophecy tells that if some day Asterix and Obelix beat exactly x Roman soldiers, where x is a prime number, and next day they beat exactly y Roman soldiers, where y is the next prime number after x, then it's time to wait for Armageddon, for nothing can shut Kakofonix up while he sings his infernal song.Yesterday the Gauls beat n Roman soldiers and it turned out that the number n was prime! Today their victims were a troop of m Romans (m\u2009>\u2009n). Determine whether the Gauls should wait for the black day after today's victory of Asterix and Obelix?", "input_spec": "The first and only input line contains two positive integers \u2014 n and m (2\u2009\u2264\u2009n\u2009<\u2009m\u2009\u2264\u200950). It is guaranteed that n is prime. Pretests contain all the cases with restrictions 2\u2009\u2264\u2009n\u2009<\u2009m\u2009\u2264\u20094.", "output_spec": "Print YES, if m is the next prime number after n, or NO otherwise.", "sample_inputs": ["3 5", "7 11", "7 9"], "sample_outputs": ["YES", "YES", "NO"], "notes": null}, "src_uid": "9d52ff51d747bb59aa463b6358258865"}
{"nl": {"description": "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": "The Smart Beaver from ABBYY decided to have a day off. But doing nothing the whole day turned out to be too boring, and he decided to play a game with pebbles. Initially, the Beaver has n pebbles. He arranges them in a equal rows, each row has b pebbles (a\u2009>\u20091). Note that the Beaver must use all the pebbles he has, i. e. n\u2009=\u2009a\u00b7b.   10 pebbles are arranged in two rows, each row has 5 pebbles  Once the Smart Beaver has arranged the pebbles, he takes back any of the resulting rows (that is, b pebbles) and discards all other pebbles. Then he arranges all his pebbles again (possibly choosing other values of a and b) and takes back one row, and so on. The game continues until at some point the Beaver ends up with exactly one pebble. The game process can be represented as a finite sequence of integers c1,\u2009...,\u2009ck, where:   c1\u2009=\u2009n  ci\u2009+\u20091 is the number of pebbles that the Beaver ends up with after the i-th move, that is, the number of pebbles in a row after some arrangement of ci pebbles (1\u2009\u2264\u2009i\u2009<\u2009k). Note that ci\u2009>\u2009ci\u2009+\u20091.  ck\u2009=\u20091 The result of the game is the sum of numbers ci. You are given n. Find the maximum possible result of the game.", "input_spec": "The single line of the input contains a single integer n \u2014 the initial number of pebbles the Smart Beaver has. The input limitations for getting 30 points are:    2\u2009\u2264\u2009n\u2009\u2264\u200950  The input limitations for getting 100 points are:    2\u2009\u2264\u2009n\u2009\u2264\u2009109 ", "output_spec": "Print a single number \u2014 the maximum possible result of the game.", "sample_inputs": ["10", "8"], "sample_outputs": ["16", "15"], "notes": "NoteConsider the first example (c1\u2009=\u200910). The possible options for the game development are:  Arrange the pebbles in 10 rows, one pebble per row. Then c2\u2009=\u20091, and the game ends after the first move with the result of 11.  Arrange the pebbles in 5 rows, two pebbles per row. Then c2\u2009=\u20092, and the game continues. During the second move we have two pebbles which can be arranged in a unique way (remember that you are not allowed to put all the pebbles in the same row!) \u2014 2 rows, one pebble per row. c3\u2009=\u20091, and the game ends with the result of 13.  Finally, arrange the pebbles in two rows, five pebbles per row. The same logic leads us to c2\u2009=\u20095,\u2009c3\u2009=\u20091, and the game ends with the result of 16 \u2014 the maximum possible result. "}, "src_uid": "821c0e3b5fad197a47878bba5e520b6e"}
{"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$$$ and the second character is m, p or s.", "output_spec": "Print a single integer\u00a0\u2014 the minimum number of extra suited tiles she needs to draw.", "sample_inputs": ["1s 2s 3s", "9m 9m 9m", "3p 9m 2p"], "sample_outputs": ["0", "0", "1"], "notes": "NoteIn the first example, Tokitsukaze already has a shuntsu.In the second example, Tokitsukaze already has a koutsu.In the third example, Tokitsukaze can get a shuntsu by drawing one suited tile\u00a0\u2014 1p or 4p. The resulting tiles will be [3p, 9m, 2p, 1p] or [3p, 9m, 2p, 4p]."}, "src_uid": "7e42cebc670e76ace967e01021f752d3"}
{"nl": {"description": "Tanechka is shopping in the toy shop. There are exactly $$$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$$$."}, "src_uid": "98624ab2fcd2a50a75788a29e04999ad"}
{"nl": {"description": "You are given a mysterious language (codenamed \"Secret\") available in \"Custom Test\" tab. Find out what this language is and write a program which outputs its name. Note that the program must be written in this language.", "input_spec": "This program has only one test, and it's empty (it doesn't give your program anything to read).", "output_spec": "Output the name of the mysterious language.", "sample_inputs": [], "sample_outputs": [], "notes": null}, "src_uid": "ef8239a0f77c538d2d9b246b86be63fe"}
{"nl": {"description": "You are given the sequence $$$a_1, a_2, \\dots, a_n$$$. You can choose any subset of elements and then reorder them to create a \"saw\".The sequence $$$b_1, b_2, \\dots, b_m$$$ is called a \"saw\" if the elements satisfy one of the following series of inequalities: $$$b_1>b_2<b_3>b_4<\\dots$$$ or $$$b_1<b_2>b_3<b_4>\\dots$$$.Find the longest saw which can be obtained from a given array.Note that both the given sequence $$$a$$$ and the required saw $$$b$$$ can contain duplicated (non-unique) values.", "input_spec": "The first line contains an integer $$$t$$$ ($$$1 \\le t \\le 10^5$$$) \u2014 the number of test cases in the input. Then the descriptions of the $$$t$$$ test cases follow. Each test case begins with a line containing integer $$$n$$$ ($$$1 \\le n \\le 2\\cdot10^5$$$). Then a line containing $$$n$$$ integers $$$a_1, a_2, \\dots, a_n$$$ ($$$1 \\le a_i \\le 10^9$$$) follows. It's guaranteed that $$$\\sum{n}$$$ doesn't exceed $$$2 \\cdot 10^5$$$.", "output_spec": "For each test case, print two lines: print the length of the longest saw in the first line, and the saw itself in the second line. If there are several solutions, print any of them.", "sample_inputs": ["3\n10\n10 9 8 7 6 5 4 3 2 1\n7\n1 2 2 2 3 2 2\n3\n100 100 100"], "sample_outputs": ["10\n1 6 2 7 3 8 4 9 5 10 \n4\n2 1 3 2 \n1\n100"], "notes": null}, "src_uid": "4e679d176597052498b7b8f14d81f63f"}
{"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": "InputThe input contains two integers a1,\u2009a2 (0\u2009\u2264\u2009ai\u2009\u2264\u2009109), separated by a single space.OutputOutput a single integer.ExamplesInput3 14Output44Input27 12Output48Input100 200Output102", "input_spec": "The input contains two integers a1,\u2009a2 (0\u2009\u2264\u2009ai\u2009\u2264\u2009109), separated by a single space.", "output_spec": "Output a single integer.", "sample_inputs": ["3 14", "27 12", "100 200"], "sample_outputs": ["44", "48", "102"], "notes": null}, "src_uid": "69b219054cad0844fc4f15df463e09c0"}
{"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": "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": "\"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": "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": "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": "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": "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": "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": "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$$$ integers \u2014 the answers to the given test cases.", "sample_inputs": ["4\n\n20\n\n8\n\n45\n\n10"], "sample_outputs": ["389\n8\n123456789\n19"], "notes": null}, "src_uid": "fe126aaa93acaca8c8559bc9e7e27b9f"}
{"nl": {"description": "A necklace can be described as a string of links ('-') and pearls ('o'), with the last link or pearl connected to the first one.  You can remove a link or a pearl and insert it between two other existing links or pearls (or between a link and a pearl) on the necklace. This process can be repeated as many times as you like, but you can't throw away any parts.Can you make the number of links between every two adjacent pearls equal? Two pearls are considered to be adjacent if there is no other pearl between them.Note that the final necklace should remain as one circular part of the same length as the initial necklace.", "input_spec": "The only line of input contains a string $$$s$$$ ($$$3 \\leq |s| \\leq 100$$$), representing the necklace, where a dash '-' represents a link and the lowercase English letter 'o' represents a pearl.", "output_spec": "Print \"YES\" if the links and pearls can be rejoined such that the number of links between adjacent pearls is equal. Otherwise print \"NO\". You can print each letter in any case (upper or lower).", "sample_inputs": ["-o-o--", "-o---", "-o---o-", "ooo"], "sample_outputs": ["YES", "YES", "NO", "YES"], "notes": null}, "src_uid": "6e006ae3df3bcd24755358a5f584ec03"}
{"nl": {"description": "Allen has a LOT of money. He has $$$n$$$ dollars in the bank. For security reasons, he wants to withdraw it in cash (we will not disclose the reasons here). The denominations for dollar bills are $$$1$$$, $$$5$$$, $$$10$$$, $$$20$$$, $$$100$$$. What is the minimum number of bills Allen could receive after withdrawing his entire balance?", "input_spec": "The first and only line of input contains a single integer $$$n$$$ ($$$1 \\le n \\le 10^9$$$).", "output_spec": "Output the minimum number of bills that Allen could receive.", "sample_inputs": ["125", "43", "1000000000"], "sample_outputs": ["3", "5", "10000000"], "notes": "NoteIn the first sample case, Allen can withdraw this with a $$$100$$$ dollar bill, a $$$20$$$ dollar bill, and a $$$5$$$ dollar bill. There is no way for Allen to receive $$$125$$$ dollars in one or two bills.In the second sample case, Allen can withdraw two $$$20$$$ dollar bills and three $$$1$$$ dollar bills.In the third sample case, Allen can withdraw $$$100000000$$$ (ten million!) $$$100$$$ dollar bills."}, "src_uid": "8e81ad7110552c20297f08ad3e5f8ddc"}
{"nl": {"description": "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": "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": "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": "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": "Rikhail Mubinchik believes that the current definition of prime numbers is obsolete as they are too complex and unpredictable. A palindromic number is another matter. It is aesthetically pleasing, and it has a number of remarkable properties. Help Rikhail to convince the scientific community in this!Let us remind you that a number is called prime if it is integer larger than one, and is not divisible by any positive integer other than itself and one.Rikhail calls a number a palindromic if it is integer, positive, and its decimal representation without leading zeros is a palindrome, i.e. reads the same from left to right and right to left.One problem with prime numbers is that there are too many of them. Let's introduce the following notation: \u03c0(n)\u00a0\u2014 the number of primes no larger than n, rub(n)\u00a0\u2014 the number of palindromic numbers no larger than n. Rikhail wants to prove that there are a lot more primes than palindromic ones.He asked you to solve the following problem: for a given value of the coefficient A find the maximum n, such that \u03c0(n)\u2009\u2264\u2009A\u00b7rub(n).", "input_spec": "The input consists of two positive integers p, q, the numerator and denominator of the fraction that is the value of A\u00a0(,\u00a0).", "output_spec": "If such maximum number exists, then print it. Otherwise, print \"Palindromic tree is better than splay tree\" (without the quotes).", "sample_inputs": ["1 1", "1 42", "6 4"], "sample_outputs": ["40", "1", "172"], "notes": null}, "src_uid": "e6e760164882b9e194a17663625be27d"}
{"nl": {"description": "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": "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": "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": "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": "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": "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": "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": "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": "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": "The 9-th grade student Gabriel noticed a caterpillar on a tree when walking around in a forest after the classes. The caterpillar was on the height h1 cm from the ground. On the height h2 cm (h2\u2009>\u2009h1) on the same tree hung an apple and the caterpillar was crawling to the apple.Gabriel is interested when the caterpillar gets the apple. He noted that the caterpillar goes up by a cm per hour by day and slips down by b cm per hour by night.In how many days Gabriel should return to the forest to see the caterpillar get the apple. You can consider that the day starts at 10 am and finishes at 10 pm. Gabriel's classes finish at 2 pm. You can consider that Gabriel noticed the caterpillar just after the classes at 2 pm.Note that the forest is magic so the caterpillar can slip down under the ground and then lift to the apple.", "input_spec": "The first line contains two integers h1,\u2009h2 (1\u2009\u2264\u2009h1\u2009<\u2009h2\u2009\u2264\u2009105) \u2014 the heights of the position of the caterpillar and the apple in centimeters. The second line contains two integers a,\u2009b (1\u2009\u2264\u2009a,\u2009b\u2009\u2264\u2009105) \u2014 the distance the caterpillar goes up by day and slips down by night, in centimeters per hour.", "output_spec": "Print the only integer k \u2014 the number of days Gabriel should wait to return to the forest and see the caterpillar getting the apple. If the caterpillar can't get the apple print the only integer \u2009-\u20091.", "sample_inputs": ["10 30\n2 1", "10 13\n1 1", "10 19\n1 2", "1 50\n5 4"], "sample_outputs": ["1", "0", "-1", "1"], "notes": "NoteIn the first example at 10 pm of the first day the caterpillar gets the height 26. At 10 am of the next day it slips down to the height 14. And finally at 6 pm of the same day the caterpillar gets the apple.Note that in the last example the caterpillar was slipping down under the ground and getting the apple on the next day."}, "src_uid": "2c39638f07c3d789ba4c323a205487d7"}
{"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": "The final match of the Berland Football Cup has been held recently. The referee has shown $$$n$$$ yellow cards throughout the match. At the beginning of the match there were $$$a_1$$$ players in the first team and $$$a_2$$$ players in the second team.The rules of sending players off the game are a bit different in Berland football. If a player from the first team receives $$$k_1$$$ yellow cards throughout the match, he can no longer participate in the match \u2014 he's sent off. And if a player from the second team receives $$$k_2$$$ yellow cards, he's sent off. After a player leaves the match, he can no longer receive any yellow cards. Each of $$$n$$$ yellow cards was shown to exactly one player. Even if all players from one team (or even from both teams) leave the match, the game still continues.The referee has lost his records on who has received each yellow card. Help him to determine the minimum and the maximum number of players that could have been thrown out of the game.", "input_spec": "The first line contains one integer $$$a_1$$$ $$$(1 \\le a_1 \\le 1\\,000)$$$ \u2014 the number of players in the first team. The second line contains one integer $$$a_2$$$ $$$(1 \\le a_2 \\le 1\\,000)$$$ \u2014 the number of players in the second team. The third line contains one integer $$$k_1$$$ $$$(1 \\le k_1 \\le 1\\,000)$$$ \u2014 the maximum number of yellow cards a player from the first team can receive (after receiving that many yellow cards, he leaves the game). The fourth line contains one integer $$$k_2$$$ $$$(1 \\le k_2 \\le 1\\,000)$$$ \u2014 the maximum number of yellow cards a player from the second team can receive (after receiving that many yellow cards, he leaves the game). The fifth line contains one integer $$$n$$$ $$$(1 \\le n \\le a_1 \\cdot k_1 + a_2 \\cdot k_2)$$$ \u2014 the number of yellow cards that have been shown during the match.", "output_spec": "Print two integers \u2014 the minimum and the maximum number of players that could have been thrown out of the game.", "sample_inputs": ["2\n3\n5\n1\n8", "3\n1\n6\n7\n25", "6\n4\n9\n10\n89"], "sample_outputs": ["0 4", "4 4", "5 9"], "notes": "NoteIn the first example it could be possible that no player left the game, so the first number in the output is $$$0$$$. The maximum possible number of players that could have been forced to leave the game is $$$4$$$ \u2014 one player from the first team, and three players from the second.In the second example the maximum possible number of yellow cards has been shown $$$(3 \\cdot 6 + 1 \\cdot 7 = 25)$$$, so in any case all players were sent off."}, "src_uid": "2be8e0b8ad4d3de2930576c0209e8b91"}
{"nl": {"description": "Polycarp decided to relax on his weekend and visited to the performance of famous ropewalkers: Agafon, Boniface and Konrad.The rope is straight and infinite in both directions. At the beginning of the performance, Agafon, Boniface and Konrad are located in positions $$$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$$$, so the performance could be finished within 2 seconds."}, "src_uid": "47c07e46517dbc937e2e779ec0d74eb3"}
{"nl": {"description": "Hideo Kojima has just quit his job at Konami. Now he is going to find a new place to work. Despite being such a well-known person, he still needs a CV to apply for a job.During all his career Hideo has produced n games. Some of them were successful, some were not. Hideo wants to remove several of them (possibly zero) from his CV to make a better impression on employers. As a result there should be no unsuccessful game which comes right after successful one in his CV.More formally, you are given an array s1,\u2009s2,\u2009...,\u2009sn of zeros and ones. Zero corresponds to an unsuccessful game, one \u2014 to a successful one. Games are given in order they were produced, and Hideo can't swap these values. He should remove some elements from this array in such a way that no zero comes right after one.Besides that, Hideo still wants to mention as much games in his CV as possible. Help this genius of a man determine the maximum number of games he can leave in his CV.", "input_spec": "The first line contains one integer number n (1\u2009\u2264\u2009n\u2009\u2264\u2009100). The second line contains n space-separated integer numbers s1,\u2009s2,\u2009...,\u2009sn (0\u2009\u2264\u2009si\u2009\u2264\u20091). 0 corresponds to an unsuccessful game, 1 \u2014 to a successful one.", "output_spec": "Print one integer \u2014 the maximum number of games Hideo can leave in his CV so that no unsuccessful game comes after a successful one.", "sample_inputs": ["4\n1 1 0 1", "6\n0 1 0 0 1 0", "1\n0"], "sample_outputs": ["3", "4", "1"], "notes": null}, "src_uid": "c7b1f0b40e310f99936d1c33e4816b95"}
{"nl": {"description": "The only difference between easy and hard versions is constraints.The BerTV channel every day broadcasts one episode of one of the $$$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": "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": "Mahmoud has n line segments, the i-th of them has length ai. Ehab challenged him to use exactly 3 line segments to form a non-degenerate triangle. Mahmoud doesn't accept challenges unless he is sure he can win, so he asked you to tell him if he should accept the challenge. Given the lengths of the line segments, check if he can choose exactly 3 of them to form a non-degenerate triangle.Mahmoud should use exactly 3 line segments, he can't concatenate two line segments or change any length. A non-degenerate triangle is a triangle with positive area.", "input_spec": "The first line contains single integer n (3\u2009\u2264\u2009n\u2009\u2264\u2009105)\u00a0\u2014 the number of line segments Mahmoud has. The second line contains n integers a1,\u2009a2,\u2009...,\u2009an (1\u2009\u2264\u2009ai\u2009\u2264\u2009109)\u00a0\u2014 the lengths of line segments Mahmoud has.", "output_spec": "In the only line print \"YES\" if he can choose exactly three line segments and form a non-degenerate triangle with them, and \"NO\" otherwise.", "sample_inputs": ["5\n1 5 3 2 4", "3\n4 1 2"], "sample_outputs": ["YES", "NO"], "notes": "NoteFor the first example, he can use line segments with lengths 2, 4 and 5 to form a non-degenerate triangle."}, "src_uid": "897bd80b79df7b1143b652655b9a6790"}
{"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": "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": "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": "You are given an array a consisting of n integers, and additionally an integer m. You have to choose some sequence of indices b1,\u2009b2,\u2009...,\u2009bk (1\u2009\u2264\u2009b1\u2009<\u2009b2\u2009<\u2009...\u2009<\u2009bk\u2009\u2264\u2009n) in such a way that the value of  is maximized. Chosen sequence can be empty.Print the maximum possible value of .", "input_spec": "The first line contains two integers n and m (1\u2009\u2264\u2009n\u2009\u2264\u200935, 1\u2009\u2264\u2009m\u2009\u2264\u2009109). The second line contains n integers a1, a2, ..., an (1\u2009\u2264\u2009ai\u2009\u2264\u2009109).", "output_spec": "Print the maximum possible value of .", "sample_inputs": ["4 4\n5 2 4 1", "3 20\n199 41 299"], "sample_outputs": ["3", "19"], "notes": "NoteIn the first example you can choose a sequence b\u2009=\u2009{1,\u20092}, so the sum  is equal to 7 (and that's 3 after taking it modulo 4).In the second example you can choose a sequence b\u2009=\u2009{3}."}, "src_uid": "d3a8a3e69a55936ee33aedd66e5b7f4a"}
{"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": "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": "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": "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": "To celebrate the opening of the Winter Computer School the organizers decided to buy in n liters of cola. However, an unexpected difficulty occurred in the shop: it turned out that cola is sold in bottles 0.5, 1 and 2 liters in volume. At that, there are exactly a bottles 0.5 in volume, b one-liter bottles and c of two-liter ones. The organizers have enough money to buy any amount of cola. What did cause the heated arguments was how many bottles of every kind to buy, as this question is pivotal for the distribution of cola among the participants (and organizers as well).Thus, while the organizers are having the argument, discussing different variants of buying cola, the Winter School can't start. Your task is to count the number of all the possible ways to buy exactly n liters of cola and persuade the organizers that this number is too large, and if they keep on arguing, then the Winter Computer School will have to be organized in summer.All the bottles of cola are considered indistinguishable, i.e. two variants of buying are different from each other only if they differ in the number of bottles of at least one kind.", "input_spec": "The first line contains four integers \u2014 n, a, b, c (1\u2009\u2264\u2009n\u2009\u2264\u200910000, 0\u2009\u2264\u2009a,\u2009b,\u2009c\u2009\u2264\u20095000).", "output_spec": "Print the unique number \u2014 the solution to the problem. If it is impossible to buy exactly n liters of cola, print 0. ", "sample_inputs": ["10 5 5 5", "3 0 0 2"], "sample_outputs": ["9", "0"], "notes": null}, "src_uid": "474e527d41040446a18186596e8bdd83"}
{"nl": {"description": "Tonight is brain dinner night and all zombies will gather together to scarf down some delicious brains. The artful Heidi plans to crash the party, incognito, disguised as one of them. Her objective is to get away with at least one brain, so she can analyze the zombies' mindset back home and gain a strategic advantage.They will be N guests tonight: N\u2009-\u20091 real zombies and a fake one, our Heidi. The living-dead love hierarchies as much as they love brains: each one has a unique rank in the range 1 to N\u2009-\u20091, and Heidi, who still appears slightly different from the others, is attributed the highest rank, N. Tonight there will be a chest with brains on display and every attendee sees how many there are. These will then be split among the attendees according to the following procedure:The zombie of the highest rank makes a suggestion on who gets how many brains (every brain is an indivisible entity). A vote follows. If at least half of the attendees accept the offer, the brains are shared in the suggested way and the feast begins. But if majority is not reached, then the highest-ranked zombie is killed, and the next zombie in hierarchy has to make a suggestion. If he is killed too, then the third highest-ranked makes one, etc. (It's enough to have exactly half of the votes \u2013 in case of a tie, the vote of the highest-ranked alive zombie counts twice, and he will of course vote in favor of his own suggestion in order to stay alive.)You should know that zombies are very greedy and sly, and they know this too \u2013 basically all zombie brains are alike. Consequently, a zombie will never accept an offer which is suboptimal for him. That is, if an offer is not strictly better than a potential later offer, he will vote against it. And make no mistake: while zombies may normally seem rather dull, tonight their intellects are perfect. Each zombie's priorities for tonight are, in descending order:   survive the event (they experienced death already once and know it is no fun),  get as many brains as possible. Heidi goes first and must make an offer which at least half of the attendees will accept, and which allocates at least one brain for Heidi herself.What is the smallest number of brains that have to be in the chest for this to be possible?", "input_spec": "The only line of input contains one integer: N, the number of attendees (1\u2009\u2264\u2009N\u2009\u2264\u2009109).", "output_spec": "Output one integer: the smallest number of brains in the chest which allows Heidi to take one brain home.", "sample_inputs": ["1", "4"], "sample_outputs": ["1", "2"], "notes": "Note"}, "src_uid": "30e95770f12c631ce498a2b20c2931c7"}
{"nl": {"description": "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)$$$."}, "src_uid": "24e2f10463f440affccc2755f4462d8a"}
{"nl": {"description": "Carl is a beginner magician. He has a blue, b violet and c orange magic spheres. In one move he can transform two spheres of the same color into one sphere of any other color. To make a spell that has never been seen before, he needs at least x blue, y violet and z orange spheres. Can he get them (possible, in multiple actions)?", "input_spec": "The first line of the input contains three integers a, b and c (0\u2009\u2264\u2009a,\u2009b,\u2009c\u2009\u2264\u20091\u2009000\u2009000)\u00a0\u2014 the number of blue, violet and orange spheres that are in the magician's disposal. The second line of the input contains three integers, x, y and z (0\u2009\u2264\u2009x,\u2009y,\u2009z\u2009\u2264\u20091\u2009000\u2009000)\u00a0\u2014 the number of blue, violet and orange spheres that he needs to get.", "output_spec": "If the wizard is able to obtain the required numbers of spheres, print \"Yes\". Otherwise, print \"No\".", "sample_inputs": ["4 4 0\n2 1 2", "5 6 1\n2 7 2", "3 3 3\n2 2 2"], "sample_outputs": ["Yes", "No", "Yes"], "notes": "NoteIn the first sample the wizard has 4 blue and 4 violet spheres. In his first action he can turn two blue spheres into one violet one. After that he will have 2 blue and 5 violet spheres. Then he turns 4 violet spheres into 2 orange spheres and he ends up with 2 blue, 1 violet and 2 orange spheres, which is exactly what he needs."}, "src_uid": "1db4ba9dc1000e26532bb73336cf12c3"}
{"nl": {"description": "Let's denote a function $$$f(x)$$$ in such a way: we add $$$1$$$ to $$$x$$$, then, while there is at least one trailing zero in the resulting number, we remove that zero. For example,   $$$f(599) = 6$$$: $$$599 + 1 = 600 \\rightarrow 60 \\rightarrow 6$$$;  $$$f(7) = 8$$$: $$$7 + 1 = 8$$$;  $$$f(9) = 1$$$: $$$9 + 1 = 10 \\rightarrow 1$$$;  $$$f(10099) = 101$$$: $$$10099 + 1 = 10100 \\rightarrow 1010 \\rightarrow 101$$$. We say that some number $$$y$$$ is reachable from $$$x$$$ if we can apply function $$$f$$$ to $$$x$$$ some (possibly zero) times so that we get $$$y$$$ as a result. For example, $$$102$$$ is reachable from $$$10098$$$ because $$$f(f(f(10098))) = f(f(10099)) = f(101) = 102$$$; and any number is reachable from itself.You are given a number $$$n$$$; your task is to count how many different numbers are reachable from $$$n$$$.", "input_spec": "The first line contains one integer $$$n$$$ ($$$1 \\le n \\le 10^9$$$).", "output_spec": "Print one integer: the number of different numbers that are reachable from $$$n$$$.", "sample_inputs": ["1098", "10"], "sample_outputs": ["20", "19"], "notes": "NoteThe numbers that are reachable from $$$1098$$$ are:$$$1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 14, 15, 16, 17, 18, 19, 1098, 1099$$$."}, "src_uid": "055fbbde4b9ffd4473e6e716da6da899"}
{"nl": {"description": "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": "International Abbreviation Olympiad takes place annually starting from 1989. Each year the competition receives an abbreviation of form IAO'y, where y stands for some number of consequent last digits of the current year. Organizers always pick an abbreviation with non-empty string y that has never been used before. Among all such valid abbreviations they choose the shortest one and announce it to be the abbreviation of this year's competition.For example, the first three Olympiads (years 1989, 1990 and 1991, respectively) received the abbreviations IAO'9, IAO'0 and IAO'1, while the competition in 2015 received an abbreviation IAO'15, as IAO'5 has been already used in 1995.You are given a list of abbreviations. For each of them determine the year it stands for.", "input_spec": "The first line of the input contains a single integer n (1\u2009\u2264\u2009n\u2009\u2264\u20091000)\u00a0\u2014 the number of abbreviations to process.  Then n lines follow, each containing a single abbreviation. It's guaranteed that each abbreviation contains at most nine digits.", "output_spec": "For each abbreviation given in the input, find the year of the corresponding Olympiad.", "sample_inputs": ["5\nIAO'15\nIAO'2015\nIAO'1\nIAO'9\nIAO'0", "4\nIAO'9\nIAO'99\nIAO'999\nIAO'9999"], "sample_outputs": ["2015\n12015\n1991\n1989\n1990", "1989\n1999\n2999\n9999"], "notes": null}, "src_uid": "31be4d38a8b5ea8738a65bfee24a5a21"}
{"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": "The \"Bulls and Cows\" game needs two people to play. The thinker thinks of a number and the guesser tries to guess it.The thinker thinks of a four-digit number in the decimal system. All the digits in the number are different and the number may have a leading zero. It can't have more than one leading zero, because all it's digits should be different. The guesser tries to guess the number. He makes a series of guesses, trying experimental numbers and receives answers from the first person in the format \"x bulls y cows\". x represents the number of digits in the experimental number that occupy the same positions as in the sought number. y represents the number of digits of the experimental number that present in the sought number, but occupy different positions. Naturally, the experimental numbers, as well as the sought number, are represented by four-digit numbers where all digits are different and a leading zero can be present.For example, let's suppose that the thinker thought of the number 0123. Then the guessers' experimental number 1263 will receive a reply \"1 bull 2 cows\" (3 occupies the same positions in both numbers and 1 and 2 are present in both numbers but they occupy different positions). Also, the answer to number 8103 will be \"2 bulls 1 cow\" (analogically, 1 and 3 occupy the same positions and 0 occupies a different one). When the guesser is answered \"4 bulls 0 cows\", the game is over.Now the guesser has already made several guesses and wants to know whether his next guess can possibly be the last one.", "input_spec": "The first input line contains an integer n (1\u2009\u2264\u2009n\u2009\u2264\u200910) which represents the number of already made guesses. Then follow n lines in the form of \"ai bi ci\", where ai is the i-th experimental number, bi is the number of bulls, ci is the number of cows (1\u2009\u2264\u2009i\u2009\u2264\u2009n, 0\u2009\u2264\u2009bi,\u2009ci,\u2009bi\u2009+\u2009ci\u2009\u2264\u20094). The experimental numbers are correct, i.e., each of them contains exactly four digits, in each of them all the four digits are different, and there can be a leading zero. All the experimental numbers are different. As the guesser hasn't guessed the number yet, the answer \"4 bulls 0 cows\" is not present.", "output_spec": "If the input data is enough to determine the sought number, print the number with four digits on a single line. If it has less than four digits, add leading zero. If the data is not enough, print \"Need more data\" without the quotes. If the thinker happens to have made a mistake in his replies, print \"Incorrect data\" without the quotes.", "sample_inputs": ["2\n1263 1 2\n8103 2 1", "2\n1234 2 2\n1256 0 2", "2\n0123 1 1\n4567 1 2"], "sample_outputs": ["Need more data", "2134", "Incorrect data"], "notes": null}, "src_uid": "142e5f2f08724e53c234fc2379216b4c"}
{"nl": {"description": "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": "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": "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": "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 sweet little monster Om Nom loves candies very much. One day he found himself in a rather tricky situation that required him to think a bit in order to enjoy candies the most. Would you succeed with the same task if you were on his place?  One day, when he came to his friend Evan, Om Nom didn't find him at home but he found two bags with candies. The first was full of blue candies and the second bag was full of red candies. Om Nom knows that each red candy weighs Wr grams and each blue candy weighs Wb grams. Eating a single red candy gives Om Nom Hr joy units and eating a single blue candy gives Om Nom Hb joy units.Candies are the most important thing in the world, but on the other hand overeating is not good. Om Nom knows if he eats more than C grams of candies, he will get sick. Om Nom thinks that it isn't proper to leave candy leftovers, so he can only eat a whole candy. Om Nom is a great mathematician and he quickly determined how many candies of what type he should eat in order to get the maximum number of joy units. Can you repeat his achievement? You can assume that each bag contains more candies that Om Nom can eat.", "input_spec": "The single line contains five integers C,\u2009Hr,\u2009Hb,\u2009Wr,\u2009Wb (1\u2009\u2264\u2009C,\u2009Hr,\u2009Hb,\u2009Wr,\u2009Wb\u2009\u2264\u2009109).", "output_spec": "Print a single integer \u2014 the maximum number of joy units that Om Nom can get.", "sample_inputs": ["10 3 5 2 3"], "sample_outputs": ["16"], "notes": "NoteIn the sample test Om Nom can eat two candies of each type and thus get 16 joy units."}, "src_uid": "eb052ca12ca293479992680581452399"}
{"nl": {"description": "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": "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": "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": "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]$$$. "}, "src_uid": "ae0320a57d73fab1d05f5d10fbdb9e1a"}
{"nl": {"description": "Let's define a function $$$f(p)$$$ on a permutation $$$p$$$ as follows. Let $$$g_i$$$ be the greatest common divisor (GCD) of elements $$$p_1$$$, $$$p_2$$$, ..., $$$p_i$$$ (in other words, it is the GCD of the prefix of length $$$i$$$). Then $$$f(p)$$$ is the number of distinct elements among $$$g_1$$$, $$$g_2$$$, ..., $$$g_n$$$.Let $$$f_{max}(n)$$$ be the maximum value of $$$f(p)$$$ among all permutations $$$p$$$ of integers $$$1$$$, $$$2$$$, ..., $$$n$$$.Given an integers $$$n$$$, count the number of permutations $$$p$$$ of integers $$$1$$$, $$$2$$$, ..., $$$n$$$, such that $$$f(p)$$$ is equal to $$$f_{max}(n)$$$. Since the answer may be large, print the remainder of its division by $$$1000\\,000\\,007 = 10^9 + 7$$$.", "input_spec": "The only line contains the integer $$$n$$$ ($$$2 \\le n \\le 10^6$$$)\u00a0\u2014 the length of the permutations.", "output_spec": "The only line should contain your answer modulo $$$10^9+7$$$.", "sample_inputs": ["2", "3", "6"], "sample_outputs": ["1", "4", "120"], "notes": "NoteConsider the second example: these are the permutations of length $$$3$$$:  $$$[1,2,3]$$$, $$$f(p)=1$$$.  $$$[1,3,2]$$$, $$$f(p)=1$$$.  $$$[2,1,3]$$$, $$$f(p)=2$$$.  $$$[2,3,1]$$$, $$$f(p)=2$$$.  $$$[3,1,2]$$$, $$$f(p)=2$$$.  $$$[3,2,1]$$$, $$$f(p)=2$$$. The maximum value $$$f_{max}(3) = 2$$$, and there are $$$4$$$ permutations $$$p$$$ such that $$$f(p)=2$$$."}, "src_uid": "b2d59b1279d891dba9372a52364bced2"}
{"nl": {"description": "You are given two integer numbers, $$$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$$$. "}, "src_uid": "cedcc3cee864bf8684148df93804d029"}
{"nl": {"description": "Masha has three sticks of length $$$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$$$ minutes. One can show that it is impossible to get a valid triangle faster."}, "src_uid": "3dc56bc08606a39dd9ca40a43c452f09"}
{"nl": {"description": "Welcome to Codeforces Stock Exchange! We're pretty limited now as we currently allow trading on one stock, Codeforces Ltd. We hope you'll still be able to make profit from the market!In the morning, there are $$$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": "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": "Johnny has a younger sister Anne, who is very clever and smart. As she came home from the kindergarten, she told his brother about the task that her kindergartener asked her to solve. The task was just to construct a triangle out of four sticks of different colours. Naturally, one of the sticks is extra. It is not allowed to break the sticks or use their partial length. Anne has perfectly solved this task, now she is asking Johnny to do the same.The boy answered that he would cope with it without any difficulty. However, after a while he found out that different tricky things can occur. It can happen that it is impossible to construct a triangle of a positive area, but it is possible to construct a degenerate triangle. It can be so, that it is impossible to construct a degenerate triangle even. As Johnny is very lazy, he does not want to consider such a big amount of cases, he asks you to help him.", "input_spec": "The first line of the input contains four space-separated positive integer numbers not exceeding 100 \u2014 lengthes of the sticks.", "output_spec": "Output TRIANGLE if it is possible to construct a non-degenerate triangle. Output SEGMENT if the first case cannot take place and it is possible to construct a degenerate triangle. Output IMPOSSIBLE if it is impossible to construct any triangle. Remember that you are to use three sticks. It is not allowed to break the sticks or use their partial length.", "sample_inputs": ["4 2 1 3", "7 2 2 4", "3 5 9 1"], "sample_outputs": ["TRIANGLE", "SEGMENT", "IMPOSSIBLE"], "notes": null}, "src_uid": "8f5df9a41e6e100aa65b9fc1d26e447a"}
{"nl": {"description": "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$$$ is the winner."}, "src_uid": "d5e66e34601cad6d78c3f02898fa09f4"}
{"nl": {"description": "$$$k$$$ people want to split $$$n$$$ candies between them. Each candy should be given to exactly one of them or be thrown away.The people are numbered from $$$1$$$ to $$$k$$$, and Arkady is the first of them. To split the candies, Arkady will choose an integer $$$x$$$ and then give the first $$$x$$$ candies to himself, the next $$$x$$$ candies to the second person, the next $$$x$$$ candies to the third person and so on in a cycle. The leftover (the remainder that is not divisible by $$$x$$$) will be thrown away.Arkady can't choose $$$x$$$ greater than $$$M$$$ as it is considered greedy. Also, he can't choose such a small $$$x$$$ that some person will receive candies more than $$$D$$$ times, as it is considered a slow splitting.Please find what is the maximum number of candies Arkady can receive by choosing some valid $$$x$$$.", "input_spec": "The only line contains four integers $$$n$$$, $$$k$$$, $$$M$$$ and $$$D$$$ ($$$2 \\le n \\le 10^{18}$$$, $$$2 \\le k \\le n$$$, $$$1 \\le M \\le n$$$, $$$1 \\le D \\le \\min{(n, 1000)}$$$, $$$M \\cdot D \\cdot k \\ge n$$$)\u00a0\u2014 the number of candies, the number of people, the maximum number of candies given to a person at once, the maximum number of times a person can receive candies.", "output_spec": "Print a single integer\u00a0\u2014 the maximum possible number of candies Arkady can give to himself. Note that it is always possible to choose some valid $$$x$$$.", "sample_inputs": ["20 4 5 2", "30 9 4 1"], "sample_outputs": ["8", "4"], "notes": "NoteIn the first example Arkady should choose $$$x = 4$$$. He will give $$$4$$$ candies to himself, $$$4$$$ candies to the second person, $$$4$$$ candies to the third person, then $$$4$$$ candies to the fourth person and then again $$$4$$$ candies to himself. No person is given candies more than $$$2$$$ times, and Arkady receives $$$8$$$ candies in total.Note that if Arkady chooses $$$x = 5$$$, he will receive only $$$5$$$ candies, and if he chooses $$$x = 3$$$, he will receive only $$$3 + 3 = 6$$$ candies as well as the second person, the third and the fourth persons will receive $$$3$$$ candies, and $$$2$$$ candies will be thrown away. He can't choose $$$x = 1$$$ nor $$$x = 2$$$ because in these cases he will receive candies more than $$$2$$$ times.In the second example Arkady has to choose $$$x = 4$$$, because any smaller value leads to him receiving candies more than $$$1$$$ time."}, "src_uid": "ac2e795cd44061db8da13e3947ba791b"}
{"nl": {"description": "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": "Vasya has a pile, that consists of some number of stones. $$$n$$$ times he either took one stone from the pile or added one stone to the pile. The pile was non-empty before each operation of taking one stone from the pile.You are given $$$n$$$ operations which Vasya has made. Find the minimal possible number of stones that can be in the pile after making these operations.", "input_spec": "The first line contains one positive integer $$$n$$$\u00a0\u2014 the number of operations, that have been made by Vasya ($$$1 \\leq n \\leq 100$$$). The next line contains the string $$$s$$$, consisting of $$$n$$$ symbols, equal to \"-\" (without quotes) or \"+\" (without quotes). If Vasya took the stone on $$$i$$$-th operation, $$$s_i$$$ is equal to \"-\" (without quotes), if added, $$$s_i$$$ is equal to \"+\" (without quotes).", "output_spec": "Print one integer\u00a0\u2014 the minimal possible number of stones that can be in the pile after these $$$n$$$ operations.", "sample_inputs": ["3\n---", "4\n++++", "2\n-+", "5\n++-++"], "sample_outputs": ["0", "4", "1", "3"], "notes": "NoteIn the first test, if Vasya had $$$3$$$ stones in the pile at the beginning, after making operations the number of stones will be equal to $$$0$$$. It is impossible to have less number of piles, so the answer is $$$0$$$. Please notice, that the number of stones at the beginning can't be less, than $$$3$$$, because in this case, Vasya won't be able to take a stone on some operation (the pile will be empty).In the second test, if Vasya had $$$0$$$ stones in the pile at the beginning, after making operations the number of stones will be equal to $$$4$$$. It is impossible to have less number of piles because after making $$$4$$$ operations the number of stones in the pile increases on $$$4$$$ stones. So, the answer is $$$4$$$.In the third test, if Vasya had $$$1$$$ stone in the pile at the beginning, after making operations the number of stones will be equal to $$$1$$$. It can be proved, that it is impossible to have less number of stones after making the operations.In the fourth test, if Vasya had $$$0$$$ stones in the pile at the beginning, after making operations the number of stones will be equal to $$$3$$$."}, "src_uid": "a593016e4992f695be7c7cd3c920d1ed"}
{"nl": {"description": "Bear Limak wants to become the largest of bears, or at least to become larger than his brother Bob.Right now, Limak and Bob weigh a and b respectively. It's guaranteed that Limak's weight is smaller than or equal to his brother's weight.Limak eats a lot and his weight is tripled after every year, while Bob's weight is doubled after every year.After how many full years will Limak become strictly larger (strictly heavier) than Bob?", "input_spec": "The only line of the input contains two integers a and b (1\u2009\u2264\u2009a\u2009\u2264\u2009b\u2009\u2264\u200910)\u00a0\u2014 the weight of Limak and the weight of Bob respectively.", "output_spec": "Print one integer, denoting the integer number of years after which Limak will become strictly larger than Bob.", "sample_inputs": ["4 7", "4 9", "1 1"], "sample_outputs": ["2", "3", "1"], "notes": "NoteIn the first sample, Limak weighs 4 and Bob weighs 7 initially. After one year their weights are 4\u00b73\u2009=\u200912 and 7\u00b72\u2009=\u200914 respectively (one weight is tripled while the other one is doubled). Limak isn't larger than Bob yet. After the second year weights are 36 and 28, so the first weight is greater than the second one. Limak became larger than Bob after two years so you should print 2.In the second sample, Limak's and Bob's weights in next years are: 12 and 18, then 36 and 36, and finally 108 and 72 (after three years). The answer is 3. Remember that Limak wants to be larger than Bob and he won't be satisfied with equal weights.In the third sample, Limak becomes larger than Bob after the first year. Their weights will be 3 and 2 then."}, "src_uid": "a1583b07a9d093e887f73cc5c29e444a"}
{"nl": {"description": "Recently you have received two positive integer numbers $$$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": "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": "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": "The protection of a popular program developed by one of IT City companies is organized the following way. After installation it outputs a random five digit number which should be sent in SMS to a particular phone number. In response an SMS activation code arrives.A young hacker Vasya disassembled the program and found the algorithm that transforms the shown number into the activation code. Note: it is clear that Vasya is a law-abiding hacker, and made it for a noble purpose \u2014 to show the developer the imperfection of their protection.The found algorithm looks the following way. At first the digits of the number are shuffled in the following order <first digit><third digit><fifth digit><fourth digit><second digit>. For example the shuffle of 12345 should lead to 13542. On the second stage the number is raised to the fifth power. The result of the shuffle and exponentiation of the number 12345 is 455\u00a0422\u00a0043\u00a0125\u00a0550\u00a0171\u00a0232. The answer is the 5 last digits of this result. For the number 12345 the answer should be 71232.Vasya is going to write a keygen program implementing this algorithm. Can you do the same?", "input_spec": "The only line of the input contains a positive integer five digit number for which the activation code should be found.", "output_spec": "Output exactly 5 digits without spaces between them \u2014 the found activation code of the program.", "sample_inputs": ["12345"], "sample_outputs": ["71232"], "notes": null}, "src_uid": "51b1c216948663fff721c28d131bf18f"}
{"nl": {"description": "A magic number is a number formed by concatenation of numbers 1, 14 and 144. We can use each of these numbers any number of times. Therefore 14144, 141414 and 1411 are magic numbers but 1444, 514 and 414 are not.You're given a number. Determine if it is a magic number or not.", "input_spec": "The first line of input contains an integer n, (1\u2009\u2264\u2009n\u2009\u2264\u2009109). This number doesn't contain leading zeros.", "output_spec": "Print \"YES\" if n is a magic number or print \"NO\" if it's not.", "sample_inputs": ["114114", "1111", "441231"], "sample_outputs": ["YES", "YES", "NO"], "notes": null}, "src_uid": "3153cfddae27fbd817caaf2cb7a6a4b5"}
{"nl": {"description": "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": "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": "Polycarp is the project manager in the IT-company. Right now, he needs to choose developers for his team to start a new project. The company has $$$n$$$ developers \"on the bench\" (i.e not involved in other projects). Polycarp assessed the skills of each of them: $$$a_i$$$ ($$$-10^4 \\le a_i \\le 10^4$$$) \u2014 an integer characteristic of the $$$i$$$-th developer. This value can be either positive, zero or even negative (some developers cause distractions).After Polycarp chooses a subset of developers for his team, the strength of the team will be determined by the sum of $$$a_i$$$ values for all selected developers.Polycarp fears that if he chooses a team in such a way that maximizes the sum of the characteristics of $$$a_i$$$, other managers may find this unacceptable. For this reason, he plans to create such a team that the sum of the $$$a_i$$$ values for it is strictly less than the maximum possible value.Help Polycarp choose any team that:  the sum of the characteristics $$$a_i$$$ for all members of the selected team is strictly less than the maximum value that can be achieved by choosing the team in some other way  and at the same time, the sum of the characteristics of $$$a_i$$$ for all members of the selected team is the greatest possible. If, following the requirements above, you can select a team in several ways, then just find any of them. It's guaranteed that the sum of the characteristics in the desired subset is strictly positive (i.e. Polycarp can always choose a non-empty team).", "input_spec": "The first line contains one integer $$$t$$$ ($$$1 \\le t \\le 10^4$$$) \u2014 the number of test cases. Then $$$t$$$ test cases follow. Each test case begins with a line containing one integer $$$n$$$ ($$$2 \\le n \\le 10^5$$$) \u2014 the number of developers \"on the bench\". The second line of a test case contains a sequence of integers $$$a_1, a_2, \\dots, a_n$$$ ($$$-10^4 \\le a_i \\le 10^4$$$) \u2014 the characteristics of the $$$n$$$ developers. It is guaranteed that the characteristics are such that the sum of the characteristics in the answer is strictly positive. It is guaranteed that the sum of $$$n$$$ over all test cases in the input doesn't exceed $$$10^5$$$.", "output_spec": "Print the answers for the given $$$t$$$ test cases in the order that they appear in the input. In the first line of each answer, print a positive integer $$$s$$$ \u2014 the sum of the characteristics in the desired subset. The second line should contain only the characters 0 and 1 and match the answer:   the character in the $$$i$$$-th position should be equal to 1 if the $$$i$$$-th developer belongs to the team;  the character in the $$$i$$$-th position should be equal to 0 if the $$$i$$$-th developer does not belong to the team.  If there are several answers, print any of them.", "sample_inputs": ["5\n5\n1 -1 1 -1 1\n2\n11 1\n3\n5 -3 4\n3\n5 3 -4\n5\n-1 0 3 -3 0"], "sample_outputs": ["2\n11101\n11\n10\n6\n111\n5\n100\n2\n10100"], "notes": "NoteIn the first test case, the maximum subset $$$a_1, a_3, a_5$$$ has a sum equal to $$$3$$$, so Polycarp should choose a team with the maximum total sum which is less than $$$3$$$.In the second test case, the maximum subset $$$a_1, a_2$$$ has a sum equal to $$$12$$$, so Polycarp should choose a team with the maximum total sum which is less than $$$12$$$.In the third test case, the maximum subset $$$a_1, a_3$$$ has a sum equal to $$$9$$$.In the fourth test case, the maximum subset $$$a_1, a_2$$$ has a sum equal to $$$8$$$.In the fifth test case, there are several subsets with a maximum sum equal to $$$3$$$, so Polycarp should choose a team with a lower total sum."}, "src_uid": "52b86006d324475ffcd1259f8e68fc54"}
{"nl": {"description": "For a given positive integer $$$m$$$, a positive number is called a $$$m$$$-number if the product of its digits is $$$m$$$. For example, the beginning of a series of $$$24$$$-numbers are as follows: $$$38$$$, $$$46$$$, $$$64$$$, $$$83$$$, $$$138$$$, $$$146$$$, $$$164$$$, $$$183$$$, $$$226$$$ ...You are given a positive integer $$$m$$$ and $$$k$$$. Print $$$k$$$-th among $$$m$$$-numbers if all $$$m$$$-numbers are sorted in ascending order.", "input_spec": "A single line of input contains two integers $$$m$$$ and $$$k$$$ ($$$2 \\le m \\le 10^9$$$, $$$1 \\le k \\le 10^9$$$).", "output_spec": "Print the desired number\u00a0\u2014 $$$k$$$-th among all $$$m$$$-numbers if $$$m$$$-numbers are sorted in ascending order. If the answer does not exist, print -1.", "sample_inputs": ["24 9", "24 1", "5040 1000000000", "2020 2020"], "sample_outputs": ["226", "38", "111121111315213227111", "-1"], "notes": null}, "src_uid": "d38877179ddbc55028d8f0a4da43cd46"}
{"nl": {"description": "Your program fails again. This time it gets \"Wrong answer on test 233\".This is the harder version of the problem. In this version, $$$1 \\le n \\le 2\\cdot10^5$$$. You can hack this problem if you locked it. But you can hack the previous problem only if you locked both problems.The problem is to finish $$$n$$$ one-choice-questions. Each of the questions contains $$$k$$$ options, and only one of them is correct. The answer to the $$$i$$$-th question is $$$h_{i}$$$, and if your answer of the question $$$i$$$ is $$$h_{i}$$$, you earn $$$1$$$ point, otherwise, you earn $$$0$$$ points for this question. The values $$$h_1, h_2, \\dots, h_n$$$ are known to you in this problem.However, you have a mistake in your program. It moves the answer clockwise! Consider all the $$$n$$$ answers are written in a circle. Due to the mistake in your program, they are shifted by one cyclically.Formally, the mistake moves the answer for the question $$$i$$$ to the question $$$i \\bmod n + 1$$$. So it moves the answer for the question $$$1$$$ to question $$$2$$$, the answer for the question $$$2$$$ to the question $$$3$$$, ..., the answer for the question $$$n$$$ to the question $$$1$$$.We call all the $$$n$$$ answers together an answer suit. There are $$$k^n$$$ possible answer suits in total.You're wondering, how many answer suits satisfy the following condition: after moving clockwise by $$$1$$$, the total number of points of the new answer suit is strictly larger than the number of points of the old one. You need to find the answer modulo $$$998\\,244\\,353$$$.For example, if $$$n = 5$$$, and your answer suit is $$$a=[1,2,3,4,5]$$$, it will submitted as $$$a'=[5,1,2,3,4]$$$ because of a mistake. If the correct answer suit is $$$h=[5,2,2,3,4]$$$, the answer suit $$$a$$$ earns $$$1$$$ point and the answer suite $$$a'$$$ earns $$$4$$$ points. Since $$$4 > 1$$$, the answer suit $$$a=[1,2,3,4,5]$$$ should be counted.", "input_spec": "The first line contains two integers $$$n$$$, $$$k$$$ ($$$1 \\le n \\le 2\\cdot10^5$$$, $$$1 \\le k \\le 10^9$$$)\u00a0\u2014 the number of questions and the number of possible answers to each question. The following line contains $$$n$$$ integers $$$h_1, h_2, \\dots, h_n$$$, ($$$1 \\le h_{i} \\le k)$$$\u00a0\u2014 answers to the questions.", "output_spec": "Output one integer: the number of answers suits satisfying the given condition, modulo $$$998\\,244\\,353$$$.", "sample_inputs": ["3 3\n1 3 1", "5 5\n1 1 4 2 2", "6 2\n1 1 2 2 1 1"], "sample_outputs": ["9", "1000", "16"], "notes": "NoteFor the first example, valid answer suits are $$$[2,1,1], [2,1,2], [2,1,3], [3,1,1], [3,1,2], [3,1,3], [3,2,1], [3,2,2], [3,2,3]$$$."}, "src_uid": "63c4006a0a6284f9825aaabfc4c28fd1"}
{"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": "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": "You've got a rectangular parallelepiped with integer edge lengths. You know the areas of its three faces that have a common vertex. Your task is to find the sum of lengths of all 12 edges of this parallelepiped.", "input_spec": "The first and the single line contains three space-separated integers \u2014 the areas of the parallelepiped's faces. The area's values are positive (\u2009>\u20090) and do not exceed 104. It is guaranteed that there exists at least one parallelepiped that satisfies the problem statement.", "output_spec": "Print a single number \u2014 the sum of all edges of the parallelepiped.", "sample_inputs": ["1 1 1", "4 6 6"], "sample_outputs": ["12", "28"], "notes": "NoteIn the first sample the parallelepiped has sizes 1\u2009\u00d7\u20091\u2009\u00d7\u20091, in the second one\u00a0\u2014 2\u2009\u00d7\u20092\u2009\u00d7\u20093."}, "src_uid": "c0a3290be3b87f3a232ec19d4639fefc"}
{"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": "You are given an integer N. Consider all possible segments on the coordinate axis with endpoints at integer points with coordinates between 0 and N, inclusive; there will be  of them.You want to draw these segments in several layers so that in each layer the segments don't overlap (they might touch at the endpoints though). You can not move the segments to a different location on the coordinate axis. Find the minimal number of layers you have to use for the given N.", "input_spec": "The only input line contains a single integer N (1\u2009\u2264\u2009N\u2009\u2264\u2009100).", "output_spec": "Output a single integer - the minimal number of layers required to draw the segments for the given N.", "sample_inputs": ["2", "3", "4"], "sample_outputs": ["2", "4", "6"], "notes": "NoteAs an example, here are the segments and their optimal arrangement into layers for N\u2009=\u20094.  "}, "src_uid": "f8af5dfcf841a7f105ac4c144eb51319"}
{"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": "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": "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": "One day Kefa found n baloons. For convenience, we denote color of i-th baloon as si \u2014 lowercase letter of the Latin alphabet. Also Kefa has k friends. Friend will be upset, If he get two baloons of the same color. Kefa want to give out all baloons to his friends. Help Kefa to find out, can he give out all his baloons, such that no one of his friens will be upset \u2014 print \u00abYES\u00bb, if he can, and \u00abNO\u00bb, otherwise. Note, that Kefa's friend will not upset, if he doesn't get baloons at all.", "input_spec": "The first line contains two integers n and k (1\u2009\u2264\u2009n,\u2009k\u2009\u2264\u2009100) \u2014 the number of baloons and friends. Next line contains string s \u2014 colors of baloons.", "output_spec": "Answer to the task \u2014 \u00abYES\u00bb or \u00abNO\u00bb in a single line. You can choose the case (lower or upper) for each letter arbitrary.", "sample_inputs": ["4 2\naabb", "6 3\naacaab"], "sample_outputs": ["YES", "NO"], "notes": "NoteIn the first sample Kefa can give 1-st and 3-rd baloon to the first friend, and 2-nd and 4-th to the second.In the second sample Kefa needs to give to all his friends baloons of color a, but one baloon will stay, thats why answer is \u00abNO\u00bb."}, "src_uid": "ceb3807aaffef60bcdbcc9a17a1391be"}
{"nl": {"description": "Johny likes numbers n and k very much. Now Johny wants to find the smallest integer x greater than n, so it is divisible by the number k.", "input_spec": "The only line contains two integers n and k (1\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": "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": "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": "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": "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": "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": "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": "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": "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": "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": "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": "Good job! Now that Heidi is able to distinguish between Poisson and uniform distributions, she is in a good position to actually estimate the populations.Can you help Heidi estimate each village's population?", "input_spec": "Same as the easy version.", "output_spec": "Output one line per village, in the same order as provided in the input, containing your (integer) population estimate. Your answer is considered correct if it is an integer that falls into the interval , where P is the real population of the village, used to create the distribution (either Poisson or uniform) from which the marmots drew their answers.", "sample_inputs": [], "sample_outputs": [], "notes": null}, "src_uid": "18bf2c587415f85df83fb090e16b8351"}
{"nl": {"description": "Unlucky year in Berland is such a year that its number n can be represented as n\u2009=\u2009xa\u2009+\u2009yb, where a and b are non-negative integer numbers. For example, if x\u2009=\u20092 and y\u2009=\u20093 then the years 4 and 17 are unlucky (4\u2009=\u200920\u2009+\u200931, 17\u2009=\u200923\u2009+\u200932\u2009=\u200924\u2009+\u200930) and year 18 isn't unlucky as there is no such representation for it.Such interval of years that there are no unlucky years in it is called The Golden Age.You should write a program which will find maximum length of The Golden Age which starts no earlier than the year l and ends no later than the year r. If all years in the interval [l,\u2009r] are unlucky then the answer is 0.", "input_spec": "The first line contains four integer numbers x, y, l and r (2\u2009\u2264\u2009x,\u2009y\u2009\u2264\u20091018, 1\u2009\u2264\u2009l\u2009\u2264\u2009r\u2009\u2264\u20091018).", "output_spec": "Print the maximum length of The Golden Age within the interval [l,\u2009r]. If all years in the interval [l,\u2009r] are unlucky then print 0.", "sample_inputs": ["2 3 1 10", "3 5 10 22", "2 3 3 5"], "sample_outputs": ["1", "8", "0"], "notes": "NoteIn the first example the unlucky years are 2, 3, 4, 5, 7, 9 and 10. So maximum length of The Golden Age is achived in the intervals [1,\u20091], [6,\u20096] and [8,\u20098].In the second example the longest Golden Age is the interval [15,\u200922]."}, "src_uid": "68ca8a8730db27ac2230f9fe9b120f5f"}
{"nl": {"description": "You can find anything whatsoever in our Galaxy! A cubical planet goes round an icosahedral star. Let us introduce a system of axes so that the edges of the cubical planet are parallel to the coordinate axes and two opposite vertices lay in the points (0,\u20090,\u20090) and (1,\u20091,\u20091). Two flies live on the planet. At the moment they are sitting on two different vertices of the cubical planet. Your task is to determine whether they see each other or not. The flies see each other when the vertices they occupy lie on the same face of the cube.", "input_spec": "The first line contains three space-separated integers (0 or 1) \u2014 the coordinates of the first fly, the second line analogously contains the coordinates of the second fly.", "output_spec": "Output \"YES\" (without quotes) if the flies see each other. Otherwise, output \"NO\".", "sample_inputs": ["0 0 0\n0 1 0", "1 1 0\n0 1 0", "0 0 0\n1 1 1"], "sample_outputs": ["YES", "YES", "NO"], "notes": null}, "src_uid": "91c9dbbceb467d5fd420e92c2919ecb6"}
{"nl": {"description": "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": "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": "A stowaway and a controller play the following game. The train is represented by n wagons which are numbered with positive integers from 1 to n from the head to the tail. The stowaway and the controller are initially in some two different wagons. Every minute the train can be in one of two conditions \u2014 moving or idle. Every minute the players move.The controller's move is as follows. The controller has the movement direction \u2014 to the train's head or to its tail. During a move the controller moves to the neighbouring wagon correspondingly to its movement direction. If at the end of his move the controller enters the 1-st or the n-th wagon, that he changes the direction of his movement into the other one. In other words, the controller cyclically goes from the train's head to its tail and back again during all the time of a game, shifting during each move by one wagon. Note, that the controller always have exactly one possible move.The stowaway's move depends from the state of the train. If the train is moving, then the stowaway can shift to one of neighbouring wagons or he can stay where he is without moving. If the train is at a station and is idle, then the stowaway leaves the train (i.e. he is now not present in any train wagon) and then, if it is not the terminal train station, he enters the train again into any of n wagons (not necessarily into the one he's just left and not necessarily into the neighbouring one). If the train is idle for several minutes then each such minute the stowaway leaves the train and enters it back.Let's determine the order of the players' moves. If at the given minute the train is moving, then first the stowaway moves and then the controller does. If at this minute the train is idle, then first the stowaway leaves the train, then the controller moves and then the stowaway enters the train.If at some point in time the stowaway and the controller happen to be in one wagon, then the controller wins: he makes the stowaway pay fine. If after a while the stowaway reaches the terminal train station, then the stowaway wins: he simply leaves the station during his move and never returns there again.At any moment of time the players know each other's positions. The players play in the optimal way. Specifically, if the controller wins, then the stowaway plays so as to lose as late as possible. As all the possible moves for the controller are determined uniquely, then he is considered to play optimally always. Determine the winner.", "input_spec": "The first line contains three integers n, m and k. They represent the number of wagons in the train, the stowaway's and the controller's initial positions correspondingly (2\u2009\u2264\u2009n\u2009\u2264\u200950, 1\u2009\u2264\u2009m,\u2009k\u2009\u2264\u2009n, m\u2009\u2260\u2009k). The second line contains the direction in which a controller moves. \"to head\" means that the controller moves to the train's head and \"to tail\" means that the controller moves to its tail. It is guaranteed that in the direction in which the controller is moving, there is at least one wagon. Wagon 1 is the head, and wagon n is the tail. The third line has the length from 1 to 200 and consists of symbols \"0\" and \"1\". The i-th symbol contains information about the train's state at the i-th minute of time. \"0\" means that in this very minute the train moves and \"1\" means that the train in this very minute stands idle. The last symbol of the third line is always \"1\" \u2014 that's the terminal train station.", "output_spec": "If the stowaway wins, print \"Stowaway\" without quotes. Otherwise, print \"Controller\" again without quotes, then, separated by a space, print the number of a minute, at which the stowaway will be caught.", "sample_inputs": ["5 3 2\nto head\n0001001", "3 2 1\nto tail\n0001"], "sample_outputs": ["Stowaway", "Controller 2"], "notes": null}, "src_uid": "2222ce16926fdc697384add731819f75"}
{"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": "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": "Consider some square matrix A with side n consisting of zeros and ones. There are n rows numbered from 1 to n from top to bottom and n columns numbered from 1 to n from left to right in this matrix. We'll denote the element of the matrix which is located at the intersection of the i-row and the j-th column as Ai,\u2009j.Let's call matrix A clear if no two cells containing ones have a common side.Let's call matrix A symmetrical if it matches the matrices formed from it by a horizontal and/or a vertical reflection. Formally, for each pair (i,\u2009j) (1\u2009\u2264\u2009i,\u2009j\u2009\u2264\u2009n) both of the following conditions must be met: Ai,\u2009j\u2009=\u2009An\u2009-\u2009i\u2009+\u20091,\u2009j and Ai,\u2009j\u2009=\u2009Ai,\u2009n\u2009-\u2009j\u2009+\u20091.Let's define the sharpness of matrix A as the number of ones in it.Given integer x, your task is to find the smallest positive integer n such that there exists a clear symmetrical matrix A with side n and sharpness x.", "input_spec": "The only line contains a single integer x (1\u2009\u2264\u2009x\u2009\u2264\u2009100) \u2014 the required sharpness of the matrix.", "output_spec": "Print a single number \u2014 the sought value of n.", "sample_inputs": ["4", "9"], "sample_outputs": ["3", "5"], "notes": "NoteThe figure below shows the matrices that correspond to the samples:  "}, "src_uid": "01eccb722b09a0474903b7e5abc4c47a"}
{"nl": {"description": "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": "Your search for Heidi is over \u2013 you finally found her at a library, dressed up as a human. In fact, she has spent so much time there that she now runs the place! Her job is to buy books and keep them at the library so that people can borrow and read them. There are n different books, numbered 1 through n.We will look at the library's operation during n consecutive days. Heidi knows in advance that on the i-th day (1\u2009\u2264\u2009i\u2009\u2264\u2009n) precisely one person will come to the library, request to borrow the book ai, read it in a few hours, and return the book later on the same day.Heidi desperately wants to please all her guests, so she will make sure to always have the book ai available in the library on the i-th day. During the night before the i-th day, she has the option of going to the bookstore (which operates at nights to avoid competition with the library) and buying any book for the price of 1 CHF. Of course, if she already has a book at the library, she does not need to buy it again. Initially, the library contains no books.There is a problem, though. The capacity of the library is k \u2013 this means that at any time, there can be at most k books at the library. If buying a new book would cause Heidi to have more than k books, she must first get rid of some book that she already has, in order to make room for the new book. If she later needs a book that she got rid of, she will need to buy that book again.You are given k and the sequence of requests for books a1,\u2009a2,\u2009...,\u2009an. What is the minimum cost (in CHF) of buying new books to satisfy all the requests?", "input_spec": "The first line of input will contain two integers n and k (1\u2009\u2264\u2009n,\u2009k\u2009\u2264\u200980). The second line will contain n integers a1,\u2009a2,\u2009...,\u2009an (1\u2009\u2264\u2009ai\u2009\u2264\u2009n) \u2013 the sequence of book requests.", "output_spec": "On a single line print the minimum cost of buying books at the store so as to satisfy all requests.", "sample_inputs": ["4 80\n1 2 2 1", "4 1\n1 2 2 1", "4 2\n1 2 3 1"], "sample_outputs": ["2", "3", "3"], "notes": "NoteIn the first test case, Heidi is able to keep all books forever. Therefore, she only needs to buy the book 1 before the first day and the book 2 before the second day.In the second test case, she can only keep one book at a time. Therefore she will need to buy new books on the first, second and fourth day.In the third test case, before buying book 3 on the third day, she must decide which of the books 1 and 2 she should get rid of. Of course, she should keep the book 1, which will be requested on the fourth day."}, "src_uid": "956228e31679caa9952b216e010f9773"}
{"nl": {"description": "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": "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": "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": "Petya loves lucky numbers. Everybody knows that lucky numbers are positive integers whose decimal representation contains only the lucky digits 4 and 7. For example, numbers 47, 744, 4 are lucky and 5, 17, 467 are not.Let next(x) be the minimum lucky number which is larger than or equals x. Petya is interested what is the value of the expression next(l)\u2009+\u2009next(l\u2009+\u20091)\u2009+\u2009...\u2009+\u2009next(r\u2009-\u20091)\u2009+\u2009next(r). Help him solve this problem.", "input_spec": "The single line contains two integers l and r (1\u2009\u2264\u2009l\u2009\u2264\u2009r\u2009\u2264\u2009109) \u2014 the left and right interval limits.", "output_spec": "In the single line print the only number \u2014 the sum next(l)\u2009+\u2009next(l\u2009+\u20091)\u2009+\u2009...\u2009+\u2009next(r\u2009-\u20091)\u2009+\u2009next(r). Please do not use the %lld specificator to read or write 64-bit integers in C++. It is preferred to use the cin, cout streams or the %I64d specificator.", "sample_inputs": ["2 7", "7 7"], "sample_outputs": ["33", "7"], "notes": "NoteIn the first sample: next(2)\u2009+\u2009next(3)\u2009+\u2009next(4)\u2009+\u2009next(5)\u2009+\u2009next(6)\u2009+\u2009next(7)\u2009=\u20094\u2009+\u20094\u2009+\u20094\u2009+\u20097\u2009+\u20097\u2009+\u20097\u2009=\u200933In the second sample: next(7)\u2009=\u20097"}, "src_uid": "8a45fe8956d3ac9d501f4a13b55638dd"}
{"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 have $$$c_1$$$ letters 'a', $$$c_2$$$ letters 'b', ..., $$$c_{26}$$$ letters 'z'. You want to build a beautiful string of length $$$n$$$ from them (obviously, you cannot use the $$$i$$$-th letter more than $$$c_i$$$ times). Each $$$c_i$$$ is greater than $$$\\frac{n}{3}$$$.A string is called beautiful if there are no palindromic contiguous substrings of odd length greater than $$$1$$$ in it. For example, the string \"abacaba\" is not beautiful, it has several palindromic substrings of odd length greater than $$$1$$$ (for example, \"aca\"). Another example: the string \"abcaa\" is beautiful.Calculate the number of different strings you can build, and print the answer modulo $$$998244353$$$.", "input_spec": "The first line contains one integer $$$n$$$ ($$$3 \\le n \\le 400$$$). The second line contains $$$26$$$ integers $$$c_1$$$, $$$c_2$$$, ..., $$$c_{26}$$$ ($$$\\frac{n}{3} < c_i \\le n$$$).", "output_spec": "Print one integer \u2014 the number of strings you can build, taken modulo $$$998244353$$$.", "sample_inputs": ["4\n2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2", "3\n2 2 2 2 2 2 3 3 3 2 2 2 2 2 2 3 3 3 2 2 3 2 2 3 2 2", "400\n348 322 247 158 209 134 151 267 268 176 214 379 372 291 388 135 147 304 169 149 193 351 380 368 181 340"], "sample_outputs": ["422500", "16900", "287489790"], "notes": null}, "src_uid": "1f012349f4b229dc98faadf1ca732355"}
{"nl": {"description": "Vasya has a non-negative integer n. He wants to round it to nearest integer, which ends up with 0. If n already ends up with 0, Vasya considers it already rounded.For example, if n\u2009=\u20094722 answer is 4720. If n\u2009=\u20095 Vasya can round it to 0 or to 10. Both ways are correct.For given n find out to which integer will Vasya round it.", "input_spec": "The first line contains single integer n (0\u2009\u2264\u2009n\u2009\u2264\u2009109)\u00a0\u2014 number that Vasya has.", "output_spec": "Print result of rounding n. Pay attention that in some cases answer isn't unique. In that case print any correct answer.", "sample_inputs": ["5", "113", "1000000000", "5432359"], "sample_outputs": ["0", "110", "1000000000", "5432360"], "notes": "NoteIn the first example n\u2009=\u20095. Nearest integers, that ends up with zero are 0 and 10. Any of these answers is correct, so you can print 0 or 10."}, "src_uid": "29c4d5fdf1328bbc943fa16d54d97aa9"}
{"nl": {"description": "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": "One day, BThero decided to play around with arrays and came up with the following problem:You are given an array $$$a$$$, which consists of $$$n$$$ positive integers. The array is numerated $$$1$$$ through $$$n$$$. You execute the following procedure exactly once:  You create a new array $$$b$$$ which consists of $$$2n$$$ positive integers, where for each $$$1 \\le i \\le n$$$ the condition $$$b_{2i-1}+b_{2i} = a_i$$$ holds. For example, for the array $$$a = [6, 8, 2]$$$ you can create $$$b = [2, 4, 4, 4, 1, 1]$$$.  You merge consecutive equal numbers in $$$b$$$. For example, $$$b = [2, 4, 4, 4, 1, 1]$$$ becomes $$$b = [2, 4, 1]$$$. Find and print the minimum possible value of $$$|b|$$$ (size of $$$b$$$) which can be achieved at the end of the procedure. It can be shown that under the given constraints there is at least one way to construct $$$b$$$.", "input_spec": "The first line of the input file contains a single integer $$$T$$$ ($$$1 \\le T \\le 5 \\cdot 10^5$$$) denoting the number of test cases. The description of $$$T$$$ test cases follows. The first line of each test contains a single integer $$$n$$$ ($$$1 \\le n \\le 5 \\cdot 10^5$$$). The second line contains $$$n$$$ space-separated integers $$$a_1$$$, $$$a_2$$$, ..., $$$a_n$$$ ($$$2 \\le a_i \\le 10^9$$$). It is guaranteed that $$$\\sum{n}$$$ over all test cases does not exceed $$$5 \\cdot 10^5$$$.", "output_spec": "For each test case, print a single line containing one integer \u2014 the minimum possible value of $$$|b|$$$.", "sample_inputs": ["3\n3\n6 8 2\n1\n4\n3\n5 6 6"], "sample_outputs": ["3\n1\n2"], "notes": null}, "src_uid": "e809d068b3ae47eb5ecfb9ac69892254"}
{"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": "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": "Natasha's favourite numbers are $$$n$$$ and $$$1$$$, and Sasha's favourite numbers are $$$m$$$ and $$$-1$$$. One day Natasha and Sasha met and wrote down every possible array of length $$$n+m$$$ such that some $$$n$$$ of its elements are equal to $$$1$$$ and another $$$m$$$ elements are equal to $$$-1$$$. For each such array they counted its maximal prefix sum, probably an empty one which is equal to $$$0$$$ (in another words, if every nonempty prefix sum is less to zero, then it is considered equal to zero). Formally, denote as $$$f(a)$$$ the maximal prefix sum of an array $$$a_{1, \\ldots ,l}$$$ of length $$$l \\geq 0$$$. Then: $$$$$$f(a) = \\max (0, \\smash{\\displaystyle\\max_{1 \\leq i \\leq l}} \\sum_{j=1}^{i} a_j )$$$$$$Now they want to count the sum of maximal prefix sums for each such an array and they are asking you to help. As this sum can be very large, output it modulo $$$998\\: 244\\: 853$$$.", "input_spec": "The only line contains two integers $$$n$$$ and $$$m$$$ ($$$0 \\le n,m \\le 2\\,000$$$).", "output_spec": "Output the answer to the problem modulo $$$998\\: 244\\: 853$$$.", "sample_inputs": ["0 2", "2 0", "2 2", "2000 2000"], "sample_outputs": ["0", "2", "5", "674532367"], "notes": "NoteIn the first example the only possible array is [-1,-1], its maximal prefix sum is equal to $$$0$$$. In the second example the only possible array is [1,1], its maximal prefix sum is equal to $$$2$$$. There are $$$6$$$ possible arrays in the third example:[1,1,-1,-1], f([1,1,-1,-1]) = 2[1,-1,1,-1], f([1,-1,1,-1]) = 1[1,-1,-1,1], f([1,-1,-1,1]) = 1[-1,1,1,-1], f([-1,1,1,-1]) = 1[-1,1,-1,1], f([-1,1,-1,1]) = 0[-1,-1,1,1], f([-1,-1,1,1]) = 0So the answer for the third example is $$$2+1+1+1+0+0 = 5$$$."}, "src_uid": "a2fcad987e9b2bb3e6395654cd4fcfbb"}
{"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": "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": "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": "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": "  It's the end of July\u00a0\u2013 the time when a festive evening is held at Jelly Castle! Guests from all over the kingdom gather here to discuss new trends in the world of confectionery. Yet some of the things discussed here are not supposed to be disclosed to the general public: the information can cause discord in the kingdom of Sweetland in case it turns out to reach the wrong hands. So it's a necessity to not let any uninvited guests in.There are 26 entrances in Jelly Castle, enumerated with uppercase English letters from A to Z. Because of security measures, each guest is known to be assigned an entrance he should enter the castle through. The door of each entrance is opened right before the first guest's arrival and closed right after the arrival of the last guest that should enter the castle through this entrance. No two guests can enter the castle simultaneously.For an entrance to be protected from possible intrusion, a candy guard should be assigned to it. There are k such guards in the castle, so if there are more than k opened doors, one of them is going to be left unguarded! Notice that a guard can't leave his post until the door he is assigned to is closed.Slastyona had a suspicion that there could be uninvited guests at the evening. She knows the order in which the invited guests entered the castle, and wants you to help her check whether there was a moment when more than k doors were opened.", "input_spec": "Two integers are given in the first string: the number of guests n and the number of guards k (1\u2009\u2264\u2009n\u2009\u2264\u2009106, 1\u2009\u2264\u2009k\u2009\u2264\u200926). In the second string, n uppercase English letters s1s2... sn are given, where si is the entrance used by the i-th guest.", "output_spec": "Output \u00abYES\u00bb if at least one door was unguarded during some time, and \u00abNO\u00bb otherwise. You can output each letter in arbitrary case (upper or lower).", "sample_inputs": ["5 1\nAABBB", "5 1\nABABB"], "sample_outputs": ["NO", "YES"], "notes": "NoteIn the first sample case, the door A is opened right before the first guest's arrival and closed when the second guest enters the castle. The door B is opened right before the arrival of the third guest, and closed after the fifth one arrives. One guard can handle both doors, as the first one is closed before the second one is opened.In the second sample case, the door B is opened before the second guest's arrival, but the only guard can't leave the door A unattended, as there is still one more guest that should enter the castle through this door. "}, "src_uid": "216323563f5b2dd63edc30cb9b4849a5"}
{"nl": {"description": "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": "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 three integers $$$a$$$, $$$b$$$ and $$$x$$$. Your task is to construct a binary string $$$s$$$ of length $$$n = a + b$$$ such that there are exactly $$$a$$$ zeroes, exactly $$$b$$$ ones and exactly $$$x$$$ indices $$$i$$$ (where $$$1 \\le i < n$$$) such that $$$s_i \\ne s_{i + 1}$$$. It is guaranteed that the answer always exists.For example, for the string \"01010\" there are four indices $$$i$$$ such that $$$1 \\le i < n$$$ and $$$s_i \\ne s_{i + 1}$$$ ($$$i = 1, 2, 3, 4$$$). For the string \"111001\" there are two such indices $$$i$$$ ($$$i = 3, 5$$$).Recall that binary string is a non-empty sequence of characters where each character is either 0 or 1.", "input_spec": "The first line of the input contains three integers $$$a$$$, $$$b$$$ and $$$x$$$ ($$$1 \\le a, b \\le 100, 1 \\le x < a + b)$$$.", "output_spec": "Print only one string $$$s$$$, where $$$s$$$ is any binary string satisfying conditions described above. It is guaranteed that the answer always exists.", "sample_inputs": ["2 2 1", "3 3 3", "5 3 6"], "sample_outputs": ["1100", "101100", "01010100"], "notes": "NoteAll possible answers for the first example:   1100;  0011. All possible answers for the second example:   110100;  101100;  110010;  100110;  011001;  001101;  010011;  001011. "}, "src_uid": "ef4123b8f3f3b511fde8b79ea9a6b20c"}
{"nl": {"description": "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": "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": "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": "As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as , where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!", "input_spec": "The first input line contains an integer n (1\u2009\u2264\u2009n\u2009\u2264\u2009109).", "output_spec": "Print \"YES\" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print \"NO\" (without the quotes).", "sample_inputs": ["256", "512"], "sample_outputs": ["YES", "NO"], "notes": "NoteIn the first sample number .In the second sample number 512 can not be represented as a sum of two triangular numbers."}, "src_uid": "245ec0831cd817714a4e5c531bffd099"}
{"nl": {"description": "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": "You have an initially empty cauldron, and you want to brew a potion in it. The potion consists of two ingredients: magic essence and water. The potion you want to brew should contain exactly $$$k\\ \\%$$$ magic essence and $$$(100 - k)\\ \\%$$$ water.In one step, you can pour either one liter of magic essence or one liter of water into the cauldron. What is the minimum number of steps to brew a potion? You don't care about the total volume of the potion, only about the ratio between magic essence and water in it.A small reminder: if you pour $$$e$$$ liters of essence and $$$w$$$ liters of water ($$$e + w > 0$$$) into the cauldron, then it contains $$$\\frac{e}{e + w} \\cdot 100\\ \\%$$$ (without rounding) magic essence and $$$\\frac{w}{e + w} \\cdot 100\\ \\%$$$ water.", "input_spec": "The first line contains the single $$$t$$$ ($$$1 \\le t \\le 100$$$)\u00a0\u2014 the number of test cases. The first and only line of each test case contains a single integer $$$k$$$ ($$$1 \\le k \\le 100$$$)\u00a0\u2014 the percentage of essence in a good potion.", "output_spec": "For each test case, print the minimum number of steps to brew a good potion. It can be proved that it's always possible to achieve it in a finite number of steps.", "sample_inputs": ["3\n3\n100\n25"], "sample_outputs": ["100\n1\n4"], "notes": "NoteIn the first test case, you should pour $$$3$$$ liters of magic essence and $$$97$$$ liters of water into the cauldron to get a potion with $$$3\\ \\%$$$ of magic essence.In the second test case, you can pour only $$$1$$$ liter of essence to get a potion with $$$100\\ \\%$$$ of magic essence.In the third test case, you can pour $$$1$$$ liter of magic essence and $$$3$$$ liters of water."}, "src_uid": "19a2bcb727510c729efe442a13c2ff7c"}
{"nl": {"description": "Apart from having lots of holidays throughout the year, residents of Berland also have whole lucky years. Year is considered lucky if it has no more than 1 non-zero digit in its number. So years 100, 40000, 5 are lucky and 12, 3001 and 12345 are not.You are given current year in Berland. Your task is to find how long will residents of Berland wait till the next lucky year.", "input_spec": "The first line contains integer number n (1\u2009\u2264\u2009n\u2009\u2264\u2009109) \u2014 current year in Berland.", "output_spec": "Output amount of years from the current year to the next lucky one.", "sample_inputs": ["4", "201", "4000"], "sample_outputs": ["1", "99", "1000"], "notes": "NoteIn the first example next lucky year is 5. In the second one \u2014 300. In the third \u2014 5000."}, "src_uid": "a3e15c0632e240a0ef6fe43a5ab3cc3e"}
{"nl": {"description": "Vanya got an important task \u2014 he should enumerate books in the library and label each book with its number. Each of the n books should be assigned with a number from 1 to n. Naturally, distinct books should be assigned distinct numbers.Vanya wants to know how many digits he will have to write down as he labels the books.", "input_spec": "The first line contains integer n (1\u2009\u2264\u2009n\u2009\u2264\u2009109) \u2014 the number of books in the library.", "output_spec": "Print the number of digits needed to number all the books.", "sample_inputs": ["13", "4"], "sample_outputs": ["17", "4"], "notes": "NoteNote to the first test. The books get numbers 1,\u20092,\u20093,\u20094,\u20095,\u20096,\u20097,\u20098,\u20099,\u200910,\u200911,\u200912,\u200913, which totals to 17 digits.Note to the second sample. The books get numbers 1,\u20092,\u20093,\u20094, which totals to 4 digits."}, "src_uid": "4e652ccb40632bf4b9dd95b9f8ae1ec9"}
{"nl": {"description": "Today, Osama gave Fadi an integer $$$X$$$, and Fadi was wondering about the minimum possible value of $$$max(a, b)$$$ such that $$$LCM(a, b)$$$ equals $$$X$$$. Both $$$a$$$ and $$$b$$$ should be positive integers.$$$LCM(a, b)$$$ is the smallest positive integer that is divisible by both $$$a$$$ and $$$b$$$. For example, $$$LCM(6, 8) = 24$$$, $$$LCM(4, 12) = 12$$$, $$$LCM(2, 3) = 6$$$.Of course, Fadi immediately knew the answer. Can you be just like Fadi and find any such pair?", "input_spec": "The first and only line contains an integer $$$X$$$ ($$$1 \\le X \\le 10^{12}$$$).", "output_spec": "Print two positive integers, $$$a$$$ and $$$b$$$, such that the value of $$$max(a, b)$$$ is minimum possible and $$$LCM(a, b)$$$ equals $$$X$$$. If there are several possible such pairs, you can print any.", "sample_inputs": ["2", "6", "4", "1"], "sample_outputs": ["1 2", "2 3", "1 4", "1 1"], "notes": null}, "src_uid": "e504a04cefef3da093573f9df711bcea"}
{"nl": {"description": "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": "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": "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": "You are locked in a room with a door that has a keypad with 10 keys corresponding to digits from 0 to 9. To escape from the room, you need to enter a correct code. You also have a sequence of digits.Some keys on the keypad have fingerprints. You believe the correct code is the longest not necessarily contiguous subsequence of the sequence you have that only contains digits with fingerprints on the corresponding keys. Find such code.", "input_spec": "The first line contains two integers $$$n$$$ and $$$m$$$ ($$$1 \\le n, m \\le 10$$$) representing the number of digits in the sequence you have and the number of keys on the keypad that have fingerprints. The next line contains $$$n$$$ distinct space-separated integers $$$x_1, x_2, \\ldots, x_n$$$ ($$$0 \\le x_i \\le 9$$$) representing the sequence. The next line contains $$$m$$$ distinct space-separated integers $$$y_1, y_2, \\ldots, y_m$$$ ($$$0 \\le y_i \\le 9$$$) \u2014 the keys with fingerprints.", "output_spec": "In a single line print a space-separated sequence of integers representing the code. If the resulting sequence is empty, both printing nothing and printing a single line break is acceptable.", "sample_inputs": ["7 3\n3 5 7 1 6 2 8\n1 2 7", "4 4\n3 4 1 0\n0 1 7 9"], "sample_outputs": ["7 1 2", "1 0"], "notes": "NoteIn the first example, the only digits with fingerprints are $$$1$$$, $$$2$$$ and $$$7$$$. All three of them appear in the sequence you know, $$$7$$$ first, then $$$1$$$ and then $$$2$$$. Therefore the output is 7 1 2. Note that the order is important, and shall be the same as the order in the original sequence.In the second example digits $$$0$$$, $$$1$$$, $$$7$$$ and $$$9$$$ have fingerprints, however only $$$0$$$ and $$$1$$$ appear in the original sequence. $$$1$$$ appears earlier, so the output is 1 0. Again, the order is important."}, "src_uid": "f9044a4b4c3a0c2751217d9b31cd0c72"}
{"nl": {"description": "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": "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": "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": "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": "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": "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": "Today Patrick waits for a visit from his friend Spongebob. To prepare for the visit, Patrick needs to buy some goodies in two stores located near his house. There is a d1 meter long road between his house and the first shop and a d2 meter long road between his house and the second shop. Also, there is a road of length d3 directly connecting these two shops to each other. Help Patrick calculate the minimum distance that he needs to walk in order to go to both shops and return to his house.  Patrick always starts at his house. He should visit both shops moving only along the three existing roads and return back to his house. He doesn't mind visiting the same shop or passing the same road multiple times. The only goal is to minimize the total distance traveled.", "input_spec": "The first line of the input contains three integers d1, d2, d3 (1\u2009\u2264\u2009d1,\u2009d2,\u2009d3\u2009\u2264\u2009108)\u00a0\u2014 the lengths of the paths.    d1 is the length of the path connecting Patrick's house and the first shop;  d2 is the length of the path connecting Patrick's house and the second shop;  d3 is the length of the path connecting both shops. ", "output_spec": "Print the minimum distance that Patrick will have to walk in order to visit both shops and return to his house.", "sample_inputs": ["10 20 30", "1 1 5"], "sample_outputs": ["60", "4"], "notes": "NoteThe first sample is shown on the picture in the problem statement. One of the optimal routes is: house  first shop  second shop  house.In the second sample one of the optimal routes is: house  first shop  house  second shop  house."}, "src_uid": "26cd7954a21866dbb2824d725473673e"}
{"nl": {"description": "One spring day on his way to university Lesha found an array A. Lesha likes to split arrays into several parts. This time Lesha decided to split the array A into several, possibly one, new arrays so that the sum of elements in each of the new arrays is not zero. One more condition is that if we place the new arrays one after another they will form the old array A.Lesha is tired now so he asked you to split the array. Help Lesha!", "input_spec": "The first line contains single integer n (1\u2009\u2264\u2009n\u2009\u2264\u2009100)\u00a0\u2014 the number of elements in the array A. The next line contains n integers a1,\u2009a2,\u2009...,\u2009an (\u2009-\u2009103\u2009\u2264\u2009ai\u2009\u2264\u2009103)\u00a0\u2014 the elements of the array A.", "output_spec": "If it is not possible to split the array A and satisfy all the constraints, print single line containing \"NO\" (without quotes). Otherwise in the first line print \"YES\" (without quotes). In the next line print single integer k\u00a0\u2014 the number of new arrays. In each of the next k lines print two integers li and ri which denote the subarray A[li... ri] of the initial array A being the i-th new array. Integers li, ri should satisfy the following conditions:   l1\u2009=\u20091  rk\u2009=\u2009n  ri\u2009+\u20091\u2009=\u2009li\u2009+\u20091 for each 1\u2009\u2264\u2009i\u2009<\u2009k.  If there are multiple answers, print any of them.", "sample_inputs": ["3\n1 2 -3", "8\n9 -12 3 4 -4 -10 7 3", "1\n0", "4\n1 2 3 -5"], "sample_outputs": ["YES\n2\n1 2\n3 3", "YES\n2\n1 2\n3 8", "NO", "YES\n4\n1 1\n2 2\n3 3\n4 4"], "notes": null}, "src_uid": "3a9258070ff179daf33a4515def9897a"}
{"nl": {"description": "Vasily the Bear loves beautiful strings. String s is beautiful if it meets the following criteria:   String s only consists of characters 0 and 1, at that character 0 must occur in string s exactly n times, and character 1 must occur exactly m times.  We can obtain character g from string s with some (possibly, zero) number of modifications. The character g equals either zero or one. A modification of string with length at least two is the following operation: we replace two last characters from the string by exactly one other character. This character equals one if it replaces two zeros, otherwise it equals zero. For example, one modification transforms string \"01010\" into string \"0100\", two modifications transform it to \"011\". It is forbidden to modify a string with length less than two.Help the Bear, count the number of beautiful strings. As the number of beautiful strings can be rather large, print the remainder after dividing the number by 1000000007 (109\u2009+\u20097). ", "input_spec": "The first line of the input contains three space-separated integers n,\u2009m,\u2009g (0\u2009\u2264\u2009n,\u2009m\u2009\u2264\u2009105,\u2009n\u2009+\u2009m\u2009\u2265\u20091,\u20090\u2009\u2264\u2009g\u2009\u2264\u20091).", "output_spec": "Print a single integer \u2014 the answer to the problem modulo 1000000007 (109\u2009+\u20097).", "sample_inputs": ["1 1 0", "2 2 0", "1 1 1"], "sample_outputs": ["2", "4", "0"], "notes": "NoteIn the first sample the beautiful strings are: \"01\", \"10\".In the second sample the beautiful strings are: \"0011\", \"1001\", \"1010\", \"1100\".In the third sample there are no beautiful strings."}, "src_uid": "066dd9e6091238edf2912a6af4d29e7f"}
{"nl": {"description": "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 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": "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": "\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": "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": "Sasha and Ira are two best friends. But they aren\u2019t just friends, they are software engineers and experts in artificial intelligence. They are developing an algorithm for two bots playing a two-player game. The game is cooperative and turn based. In each turn, one of the players makes a move (it doesn\u2019t matter which player, it's possible that players turns do not alternate). Algorithm for bots that Sasha and Ira are developing works by keeping track of the state the game is in. Each time either bot makes a move, the state changes. And, since the game is very dynamic, it will never go back to the state it was already in at any point in the past.Sasha and Ira are perfectionists and want their algorithm to have an optimal winning strategy. They have noticed that in the optimal winning strategy, both bots make exactly N moves each. But, in order to find the optimal strategy, their algorithm needs to analyze all possible states of the game (they haven\u2019t learned about alpha-beta pruning yet) and pick the best sequence of moves.They are worried about the efficiency of their algorithm and are wondering what is the total number of states of the game that need to be analyzed? ", "input_spec": "The first and only line contains integer N.   1\u2009\u2264\u2009N\u2009\u2264\u2009106 ", "output_spec": "Output should contain a single integer \u2013 number of possible states modulo 109\u2009+\u20097.", "sample_inputs": ["2"], "sample_outputs": ["19"], "notes": "NoteStart: Game is in state A.   Turn 1: Either bot can make a move (first bot is red and second bot is blue), so there are two possible states after the first turn \u2013 B and C.  Turn 2: In both states B and C, either bot can again make a turn, so the list of possible states is expanded to include D, E, F and G.  Turn 3: Red bot already did N=2 moves when in state D, so it cannot make any more moves there. It can make moves when in state E, F and G, so states I, K and M are added to the list. Similarly, blue bot cannot make a move when in state G, but can when in D, E and F, so states H, J and L are added.  Turn 4: Red bot already did N=2 moves when in states H, I and K, so it can only make moves when in J, L and M, so states P, R and S are added. Blue bot cannot make a move when in states J, L and M, but only when in H, I and K, so states N, O and Q are added. Overall, there are 19 possible states of the game their algorithm needs to analyze."}, "src_uid": "a18833c987fd7743e8021196b5dcdd1b"}
{"nl": {"description": "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}\\}$$$. All the cards in the input are different.", "output_spec": "If it is possible to play a card from your hand, print one word \"YES\". Otherwise, print \"NO\". You can print each letter in any case (upper or lower).", "sample_inputs": ["AS\n2H 4C TH JH AD", "2H\n3D 4C AC KD AS", "4D\nAS AC AD AH 5H"], "sample_outputs": ["YES", "NO", "YES"], "notes": "NoteIn the first example, there is an Ace of Spades (AS) on the table. You can play an Ace of Diamonds (AD) because both of them are Aces.In the second example, you cannot play any card.In the third example, you can play an Ace of Diamonds (AD) because it has the same suit as a Four of Diamonds (4D), which lies on the table."}, "src_uid": "699444eb6366ad12bc77e7ac2602d74b"}
{"nl": {"description": "On a chessboard with a width of $$$n$$$ and a height of $$$n$$$, rows are numbered from bottom to top from $$$1$$$ to $$$n$$$, columns are numbered from left to right from $$$1$$$ to $$$n$$$. Therefore, for each cell of the chessboard, you can assign the coordinates $$$(r,c)$$$, where $$$r$$$ is the number of the row, and $$$c$$$ is the number of the column.The white king has been sitting in a cell with $$$(1,1)$$$ coordinates for a thousand years, while the black king has been sitting in a cell with $$$(n,n)$$$ coordinates. They would have sat like that further, but suddenly a beautiful coin fell on the cell with coordinates $$$(x,y)$$$...Each of the monarchs wanted to get it, so they decided to arrange a race according to slightly changed chess rules:As in chess, the white king makes the first move, the black king makes the second one, the white king makes the third one, and so on. However, in this problem, kings can stand in adjacent cells or even in the same cell at the same time.The player who reaches the coin first will win, that is to say, the player who reaches the cell with the coordinates $$$(x,y)$$$ first will win.Let's recall that the king is such a chess piece that can move one cell in all directions, that is, if the king is in the $$$(a,b)$$$ cell, then in one move he can move from $$$(a,b)$$$ to the cells $$$(a + 1,b)$$$, $$$(a - 1,b)$$$, $$$(a,b + 1)$$$, $$$(a,b - 1)$$$, $$$(a + 1,b - 1)$$$, $$$(a + 1,b + 1)$$$, $$$(a - 1,b - 1)$$$, or $$$(a - 1,b + 1)$$$. Going outside of the field is prohibited.Determine the color of the king, who will reach the cell with the coordinates $$$(x,y)$$$ first, if the white king moves first.", "input_spec": "The first line contains a single integer $$$n$$$ ($$$2 \\le n \\le 10^{18}$$$)\u00a0\u2014 the length of the side of the chess field. The second line contains two integers $$$x$$$ and $$$y$$$ ($$$1 \\le x,y \\le n$$$)\u00a0\u2014 coordinates of the cell, where the coin fell.", "output_spec": "In a single line print the answer \"White\" (without quotes), if the white king will win, or \"Black\" (without quotes), if the black king will win. You can print each letter in any case (upper or lower).", "sample_inputs": ["4\n2 3", "5\n3 5", "2\n2 2"], "sample_outputs": ["White", "Black", "Black"], "notes": "NoteAn example of the race from the first sample where both the white king and the black king move optimally: The white king moves from the cell $$$(1,1)$$$ into the cell $$$(2,2)$$$. The black king moves form the cell $$$(4,4)$$$ into the cell $$$(3,3)$$$. The white king moves from the cell $$$(2,2)$$$ into the cell $$$(2,3)$$$. This is cell containing the coin, so the white king wins.  An example of the race from the second sample where both the white king and the black king move optimally: The white king moves from the cell $$$(1,1)$$$ into the cell $$$(2,2)$$$. The black king moves form the cell $$$(5,5)$$$ into the cell $$$(4,4)$$$. The white king moves from the cell $$$(2,2)$$$ into the cell $$$(3,3)$$$. The black king moves from the cell $$$(4,4)$$$ into the cell $$$(3,5)$$$. This is the cell, where the coin fell, so the black king wins.  In the third example, the coin fell in the starting cell of the black king, so the black king immediately wins.  "}, "src_uid": "b8ece086b35a36ca873e2edecc674557"}
{"nl": {"description": "Vasya plays the sleuth with his friends. The rules of the game are as follows: those who play for the first time, that is Vasya is the sleuth, he should investigate a \"crime\" and find out what is happening. He can ask any questions whatsoever that can be answered with \"Yes\" or \"No\". All the rest agree beforehand to answer the questions like that: if the question\u2019s last letter is a vowel, they answer \"Yes\" and if the last letter is a consonant, they answer \"No\". Of course, the sleuth knows nothing about it and his task is to understand that.Unfortunately, Vasya is not very smart. After 5 hours of endless stupid questions everybody except Vasya got bored. That\u2019s why Vasya\u2019s friends ask you to write a program that would give answers instead of them.The English alphabet vowels are: A, E, I, O, U, YThe English alphabet consonants are: B, C, D, F, G, H, J, K, L, M, N, P, Q, R, S, T, V, W, X, Z", "input_spec": "The single line contains a question represented by a non-empty line consisting of large and small Latin letters, spaces and a question mark. The line length does not exceed 100. It is guaranteed that the question mark occurs exactly once in the line \u2014 as the last symbol and that the line contains at least one letter.", "output_spec": "Print answer for the question in a single line: YES if the answer is \"Yes\", NO if the answer is \"No\". Remember that in the reply to the question the last letter, not the last character counts. I. e. the spaces and the question mark do not count as letters.", "sample_inputs": ["Is it a melon?", "Is it an apple?", "Is     it a banana ?", "Is   it an apple  and a  banana   simultaneouSLY?"], "sample_outputs": ["NO", "YES", "YES", "YES"], "notes": null}, "src_uid": "dea7eb04e086a4c1b3924eff255b9648"}
{"nl": {"description": "This is a harder version of the problem. In this version, $$$n \\le 300\\,000$$$.Vasya is an experienced developer of programming competitions' problems. As all great minds at some time, Vasya faced a creative crisis. To improve the situation, Petya gifted him a string consisting of opening and closing brackets only. Petya believes, that the beauty of the bracket string is a number of its cyclical shifts, which form a correct bracket sequence.To digress from his problems, Vasya decided to select two positions of the string (not necessarily distinct) and swap characters located at this positions with each other. Vasya will apply this operation exactly once. He is curious what is the maximum possible beauty he can achieve this way. Please help him.We remind that bracket sequence $$$s$$$ is called correct if:   $$$s$$$ is empty;  $$$s$$$ is equal to \"($$$t$$$)\", where $$$t$$$ is correct bracket sequence;  $$$s$$$ is equal to $$$t_1 t_2$$$, i.e. concatenation of $$$t_1$$$ and $$$t_2$$$, where $$$t_1$$$ and $$$t_2$$$ are correct bracket sequences. For example, \"(()())\", \"()\" are correct, while \")(\" and \"())\" are not.The cyclical shift of the string $$$s$$$ of length $$$n$$$ by $$$k$$$ ($$$0 \\leq k < n$$$) is a string formed by a concatenation of the last $$$k$$$ symbols of the string $$$s$$$ with the first $$$n - k$$$ symbols of string $$$s$$$. For example, the cyclical shift of string \"(())()\" by $$$2$$$ equals \"()(())\".Cyclical shifts $$$i$$$ and $$$j$$$ are considered different, if $$$i \\ne j$$$.", "input_spec": "The first line contains an integer $$$n$$$ ($$$1 \\le n \\le 300\\,000$$$), the length of the string. The second line contains a string, consisting of exactly $$$n$$$ characters, where each of the characters is either \"(\" or \")\".", "output_spec": "The first line should contain a single integer\u00a0\u2014 the largest beauty of the string, which can be achieved by swapping some two characters. The second line should contain integers $$$l$$$ and $$$r$$$ ($$$1 \\leq l, r \\leq n$$$)\u00a0\u2014 the indices of two characters, which should be swapped in order to maximize the string's beauty. In case there are several possible swaps, print any of them.", "sample_inputs": ["10\n()()())(()", "12\n)(()(()())()", "6\n)))(()"], "sample_outputs": ["5\n8 7", "4\n5 10", "0\n1 1"], "notes": "NoteIn the first example, we can swap $$$7$$$-th and $$$8$$$-th character, obtaining a string \"()()()()()\". The cyclical shifts by $$$0, 2, 4, 6, 8$$$ of this string form a correct bracket sequence.In the second example, after swapping $$$5$$$-th and $$$10$$$-th character, we obtain a string \")(())()()(()\". The cyclical shifts by $$$11, 7, 5, 3$$$ of this string form a correct bracket sequence.In the third example, swap of any two brackets results in $$$0$$$ cyclical shifts being correct bracket sequences. "}, "src_uid": "be820239276b5e1a346309f9dd21c5cb"}
{"nl": {"description": "This is an interactive problem. In the interaction section below you will find the information about flushing the output.The New Year tree of height h is a perfect binary tree with vertices numbered 1 through 2h\u2009-\u20091 in some order. In this problem we assume that h is at least 2. The drawing below shows one example New Year tree of height 3:  Polar bears love decorating the New Year tree and Limak is no exception. To decorate the tree, he must first find its root, i.e. a vertex with exactly two neighbours (assuming that h\u2009\u2265\u20092). It won't be easy because Limak is a little bear and he doesn't even see the whole tree. Can you help him?There are t testcases. In each testcase, you should first read h from the input. Then you can ask at most 16 questions of format \"? x\" (without quotes), where x is an integer between 1 and 2h\u2009-\u20091, inclusive. As a reply you will get the list of neighbours of vertex x (more details in the \"Interaction\" section below). For example, for a tree on the drawing above after asking \"? 1\" you would get a response with 3 neighbours: 4, 5 and 7. Your goal is to find the index of the root y and print it in the format \"! y\". You will be able to read h for a next testcase only after printing the answer in a previous testcase and flushing the output.Each tree is fixed from the beginning and it doesn't change during your questions.", "input_spec": "The first line of the input contains a single integer t (1\u2009\u2264\u2009t\u2009\u2264\u2009500)\u00a0\u2014 the number of testcases. At the beginning of each testcase you should read from the input a single integer h (2\u2009\u2264\u2009h\u2009\u2264\u20097)\u00a0\u2014 the height of the tree. You can't read the value of h in a next testcase until you answer a previous testcase.", "output_spec": null, "sample_inputs": ["1\n3\n3\n4 5 7\n2\n1 2\n1\n2", "2\n2\n1\n3\n2\n1 2\n2\n1 2\n4\n3\n3 12 13"], "sample_outputs": ["? 1\n? 5\n? 6\n! 5", "? 1\n? 3\n? 3\n! 3\n? 6\n! 1"], "notes": "NoteIn the first sample, a tree corresponds to the drawing from the statement.In the second sample, there are two two testcases. A tree in the first testcase has height 2 and thus 3 vertices. A tree in the second testcase has height 4 and thus 15 vertices. You can see both trees on the drawing below.  "}, "src_uid": "5c0db518fa326b1e405479313216426a"}
{"nl": {"description": "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": "\"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": "PolandBall is standing in a row with Many Other Balls. More precisely, there are exactly n Balls. Balls are proud of their home land\u00a0\u2014 and they want to prove that it's strong.The Balls decided to start with selecting exactly m groups of Balls, each consisting either of single Ball or two neighboring Balls. Each Ball can join no more than one group.The Balls really want to impress their Enemies. They kindly asked you to calculate number of such divisions for all m where 1\u2009\u2264\u2009m\u2009\u2264\u2009k. Output all these values modulo 998244353, the Enemies will be impressed anyway.", "input_spec": "There are exactly two numbers n and k (1\u2009\u2264\u2009n\u2009\u2264\u2009109, 1\u2009\u2264\u2009k\u2009<\u2009215), denoting the number of Balls and the maximim number of groups, respectively.", "output_spec": "You should output a sequence of k values. The i-th of them should represent the sought number of divisions into exactly i groups, according to PolandBall's rules.", "sample_inputs": ["3 3", "1 1", "5 10"], "sample_outputs": ["5 5 1", "1", "9 25 25 9 1 0 0 0 0 0"], "notes": "NoteIn the first sample case we can divide Balls into groups as follows: {1}, {2}, {3}, {12}, {23}.{12}{3}, {1}{23}, {1}{2}, {1}{3}, {2}{3}.{1}{2}{3}.Therefore, output is: 5 5 1."}, "src_uid": "266cc96acf6287f92a3bb0f8eccc5cf1"}
{"nl": {"description": "Mary has just graduated from one well-known University and is now attending celebration party. Students like to dream of a beautiful life, so they used champagne glasses to construct a small pyramid. The height of the pyramid is n. The top level consists of only 1 glass, that stands on 2 glasses on the second level (counting from the top), then 3 glasses on the third level and so on.The bottom level consists of n glasses.Vlad has seen in the movies many times how the champagne beautifully flows from top levels to bottom ones, filling all the glasses simultaneously. So he took a bottle and started to pour it in the glass located at the top of the pyramid.Each second, Vlad pours to the top glass the amount of champagne equal to the size of exactly one glass. If the glass is already full, but there is some champagne flowing in it, then it pours over the edge of the glass and is equally distributed over two glasses standing under. If the overflowed glass is at the bottom level, then the champagne pours on the table. For the purpose of this problem we consider that champagne is distributed among pyramid glasses immediately. Vlad is interested in the number of completely full glasses if he stops pouring champagne in t seconds.Pictures below illustrate the pyramid consisting of three levels.   ", "input_spec": "The only line of the input contains two integers n and t (1\u2009\u2264\u2009n\u2009\u2264\u200910,\u20090\u2009\u2264\u2009t\u2009\u2264\u200910\u2009000)\u00a0\u2014 the height of the pyramid and the number of seconds Vlad will be pouring champagne from the bottle.", "output_spec": "Print the single integer\u00a0\u2014 the number of completely full glasses after t seconds.", "sample_inputs": ["3 5", "4 8"], "sample_outputs": ["4", "6"], "notes": "NoteIn the first sample, the glasses full after 5 seconds are: the top glass, both glasses on the second level and the middle glass at the bottom level. Left and right glasses of the bottom level will be half-empty."}, "src_uid": "b2b49b7f6e3279d435766085958fb69d"}
{"nl": {"description": "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": "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": "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": "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": "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": "Vasya decided to learn to play chess. Classic chess doesn't seem interesting to him, so he plays his own sort of chess.The queen is the piece that captures all squares on its vertical, horizontal and diagonal lines. If the cell is located on the same vertical, horizontal or diagonal line with queen, and the cell contains a piece of the enemy color, the queen is able to move to this square. After that the enemy's piece is removed from the board. The queen cannot move to a cell containing an enemy piece if there is some other piece between it and the queen. There is an n\u2009\u00d7\u2009n chessboard. We'll denote a cell on the intersection of the r-th row and c-th column as (r,\u2009c). The square (1,\u20091) contains the white queen and the square (1,\u2009n) contains the black queen. All other squares contain green pawns that don't belong to anyone.The players move in turns. The player that moves first plays for the white queen, his opponent plays for the black queen.On each move the player has to capture some piece with his queen (that is, move to a square that contains either a green pawn or the enemy queen). The player loses if either he cannot capture any piece during his move or the opponent took his queen during the previous move. Help Vasya determine who wins if both players play with an optimal strategy on the board n\u2009\u00d7\u2009n.", "input_spec": "The input contains a single number n (2\u2009\u2264\u2009n\u2009\u2264\u2009109) \u2014 the size of the board.", "output_spec": "On the first line print the answer to problem \u2014 string \"white\" or string \"black\", depending on who wins if the both players play optimally.  If the answer is \"white\", then you should also print two integers r and c representing the cell (r,\u2009c), where the first player should make his first move to win. If there are multiple such cells, print the one with the minimum r. If there are still multiple squares, print the one with the minimum c.", "sample_inputs": ["2", "3"], "sample_outputs": ["white\n1 2", "black"], "notes": "NoteIn the first sample test the white queen can capture the black queen at the first move, so the white player wins.In the second test from the statement if the white queen captures the green pawn located on the central vertical line, then it will be captured by the black queen during the next move. So the only move for the white player is to capture the green pawn located at (2,\u20091). Similarly, the black queen doesn't have any other options but to capture the green pawn located at (2,\u20093), otherwise if it goes to the middle vertical line, it will be captured by the white queen.During the next move the same thing happens \u2014 neither the white, nor the black queen has other options rather than to capture green pawns situated above them. Thus, the white queen ends up on square (3,\u20091), and the black queen ends up on square (3,\u20093). In this situation the white queen has to capture any of the green pawns located on the middle vertical line, after that it will be captured by the black queen. Thus, the player who plays for the black queen wins."}, "src_uid": "52e07d176aa1d370788f94ee2e61df93"}
{"nl": {"description": "You are given an integer $$$n$$$ from $$$1$$$ to $$$10^{18}$$$ without leading zeroes.In one move you can swap any two adjacent digits in the given number in such a way that the resulting number will not contain leading zeroes. In other words, after each move the number you have cannot contain any leading zeroes.What is the minimum number of moves you have to make to obtain a number that is divisible by $$$25$$$? Print -1 if it is impossible to obtain a number that is divisible by $$$25$$$.", "input_spec": "The first line contains an integer $$$n$$$ ($$$1 \\le n \\le 10^{18}$$$). It is guaranteed that the first (left) digit of the number $$$n$$$ is not a zero.", "output_spec": "If it is impossible to obtain a number that is divisible by $$$25$$$, print -1. Otherwise print the minimum number of moves required to obtain such number. Note that you can swap only adjacent digits in the given number.", "sample_inputs": ["5071", "705", "1241367"], "sample_outputs": ["4", "1", "-1"], "notes": "NoteIn the first example one of the possible sequences of moves is 5071 $$$\\rightarrow$$$ 5701 $$$\\rightarrow$$$ 7501 $$$\\rightarrow$$$ 7510 $$$\\rightarrow$$$ 7150."}, "src_uid": "ea1c737956f88be94107f2565ca8bbfd"}
{"nl": {"description": "Vus the Cossack holds a programming competition, in which $$$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$$$ pens. Since the Cossack does not have enough pens, the answer is \"No\"."}, "src_uid": "6cd07298b23cc6ce994bb1811b9629c4"}
{"nl": {"description": "Petya loves lucky numbers. Everybody knows that lucky numbers are positive integers whose decimal representation contains only the lucky digits 4 and 7. For example, numbers 47, 744, 4 are lucky and 5, 17, 467 are not.Petya calls a number almost lucky if it could be evenly divided by some lucky number. Help him find out if the given number n is almost lucky.", "input_spec": "The single line contains an integer n (1\u2009\u2264\u2009n\u2009\u2264\u20091000) \u2014 the number that needs to be checked.", "output_spec": "In the only line print \"YES\" (without the quotes), if number n is almost lucky. Otherwise, print \"NO\" (without the quotes).", "sample_inputs": ["47", "16", "78"], "sample_outputs": ["YES", "YES", "NO"], "notes": "NoteNote that all lucky numbers are almost lucky as any number is evenly divisible by itself.In the first sample 47 is a lucky number. In the second sample 16 is divisible by 4."}, "src_uid": "78cf8bc7660dbd0602bf6e499bc6bb0d"}
{"nl": {"description": "InputThe first line of the input contains a single integer $$$N$$$ ($$$1 \\le N \\le 24$$$). The next $$$N$$$ lines contain $$$5$$$ space-separated integers each. The first three integers will be between 0 and 2, inclusive. The last two integers will be between 0 and 3, inclusive. The sum of the first three integers will be equal to the sum of the last two integers.OutputOutput the result \u2013 a string of lowercase English letters.ExamplesInput\n1\n1 0 0 1 0\nOutput\na\nInput\n10\n2 0 0 1 1\n1 1 1 2 1\n2 1 0 1 2\n1 1 0 1 1\n2 1 0 2 1\n1 1 1 2 1\n1 2 1 3 1\n2 0 0 1 1\n1 1 0 1 1\n1 1 2 2 2\nOutput\ncodeforcez\n", "input_spec": "The first line of the input contains a single integer $$$N$$$ ($$$1 \\le N \\le 24$$$). The next $$$N$$$ lines contain $$$5$$$ space-separated integers each. The first three integers will be between 0 and 2, inclusive. The last two integers will be between 0 and 3, inclusive. The sum of the first three integers will be equal to the sum of the last two integers.", "output_spec": "Output the result \u2013 a string of lowercase English letters.", "sample_inputs": ["1\n1 0 0 1 0", "10\n2 0 0 1 1\n1 1 1 2 1\n2 1 0 1 2\n1 1 0 1 1\n2 1 0 2 1\n1 1 1 2 1\n1 2 1 3 1\n2 0 0 1 1\n1 1 0 1 1\n1 1 2 2 2"], "sample_outputs": ["a", "codeforcez"], "notes": null}, "src_uid": "a3603f5ed0d8bdb7fe829342991b78e6"}
{"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": "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": "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": "You are given a weighted undirected tree on $$$n$$$ vertices and a list of $$$q$$$ updates. Each update changes the weight of one edge. The task is to output the diameter of the tree after each update.(The distance between two vertices is the sum of the weights on the unique simple path that connects them. The diameter is the largest of all those distances.)", "input_spec": "The first line contains three space-separated integers $$$n$$$, $$$q$$$ and $$$w$$$\u00a0($$$2 \\leq n \\leq 100,000, 1 \\leq q \\leq 100,000$$$, $$$1 \\leq w \\leq 20,000,000,000,000$$$) \u2013 the number of vertices in the tree, the number of updates and the limit on the weights of edges. The vertices are numbered $$$1$$$ through $$$n$$$. Next, $$$n-1$$$ lines describing the initial tree follow. The $$$i$$$-th of these lines contains three space-separated integers $$$a_i$$$, $$$b_i$$$, $$$c_i$$$\u00a0($$$1 \\leq a_i, b_i \\leq n$$$, $$$0 \\leq c_i < w$$$) meaning that initially, there is an edge between vertices $$$a_i$$$ and $$$b_i$$$ with weight $$$c_i$$$. It is guaranteed that these $$$n-1$$$ lines describe a tree. Finally, $$$q$$$ lines describing queries follow. The $$$j$$$-th of these lines contains two space-separated integers $$$d_j$$$, $$$e_j$$$\u00a0($$$0 \\leq d_j < n - 1, 0 \\leq e_j < w$$$). These two integers are then transformed according to the following scheme:    $$$d'_j = (d_j + last) \\bmod (n - 1)$$$  $$$e'_j = (e_j + last) \\bmod w$$$ ", "output_spec": "Output $$$q$$$ lines. For each $$$i$$$, line $$$i$$$ should contain the diameter of the tree after the $$$i$$$-th update.", "sample_inputs": ["4 3 2000\n1 2 100\n2 3 1000\n2 4 1000\n2 1030\n1 1020\n1 890", "10 10 10000\n1 9 1241\n5 6 1630\n10 5 1630\n2 6 853\n10 1 511\n5 3 760\n8 3 1076\n4 10 1483\n7 10 40\n8 2051\n5 6294\n5 4168\n7 1861\n0 5244\n6 5156\n3 3001\n8 5267\n5 3102\n8 3623"], "sample_outputs": ["2030\n2080\n2050", "6164\n7812\n8385\n6737\n6738\n7205\n6641\n7062\n6581\n5155"], "notes": "NoteThe first sample is depicted in the figure below. The left-most picture shows the initial state of the graph. Each following picture depicts the situation after an update. The weight of the updated edge is painted green, and the diameter is red.The first query changes the weight of the $$$3$$$rd edge, i.e. $$$\\{2, 4\\}$$$, to $$$1030$$$. The largest distance between any pair of vertices is $$$2030$$$ \u2013 the distance between $$$3$$$ and $$$4$$$.As the answer is $$$2030$$$, the second query is $$$$$$d'_2 = (1 + 2030) \\bmod 3 = 0$$$$$$ $$$$$$e'_2 = (1020 + 2030) \\bmod 2000 = 1050$$$$$$ Hence the weight of the edge $$$\\{1, 2\\}$$$ is changed to $$$1050$$$. This causes the pair $$$\\{1, 4\\}$$$ to be the pair with the greatest distance, namely $$$2080$$$.The third query is decoded as $$$$$$d'_3 = (1 + 2080) \\bmod 3 = 2$$$$$$ $$$$$$e'_3 = (890 + 2080) \\bmod 2000 = 970$$$$$$ As the weight of the edge $$$\\{2, 4\\}$$$ decreases to $$$970$$$, the most distant pair is suddenly $$$\\{1, 3\\}$$$ with $$$2050$$$."}, "src_uid": "2c7349bc99e56b86a5c11b8c683b2b6c"}
{"nl": {"description": "Polycarp loves lowercase letters and dislikes uppercase ones. Once he got a string s consisting only of lowercase and uppercase Latin letters.Let A be a set of positions in the string. Let's call it pretty if following conditions are met:  letters on positions from A in the string are all distinct and lowercase;  there are no uppercase letters in the string which are situated between positions from A (i.e. there is no such j that s[j] is an uppercase letter, and a1\u2009<\u2009j\u2009<\u2009a2 for some a1 and a2 from A). Write a program that will determine the maximum number of elements in a pretty set of positions.", "input_spec": "The first line contains a single integer n (1\u2009\u2264\u2009n\u2009\u2264\u2009200) \u2014 length of string s. The second line contains a string s consisting of lowercase and uppercase Latin letters.", "output_spec": "Print maximum number of elements in pretty set of positions for string s.", "sample_inputs": ["11\naaaaBaabAbA", "12\nzACaAbbaazzC", "3\nABC"], "sample_outputs": ["2", "3", "0"], "notes": "NoteIn the first example the desired positions might be 6 and 8 or 7 and 8. Positions 6 and 7 contain letters 'a', position 8 contains letter 'b'. The pair of positions 1 and 8 is not suitable because there is an uppercase letter 'B' between these position.In the second example desired positions can be 7, 8 and 11. There are other ways to choose pretty set consisting of three elements.In the third example the given string s does not contain any lowercase letters, so the answer is 0."}, "src_uid": "567ce65f87d2fb922b0f7e0957fbada3"}
{"nl": {"description": "You are given two strings $$$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": "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": "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": "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": "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": "One hot summer day Pete and his friend Billy decided to buy a watermelon. They chose the biggest and the ripest one, in their opinion. After that the watermelon was weighed, and the scales showed w kilos. They rushed home, dying of thirst, and decided to divide the berry, however they faced a hard problem.Pete and Billy are great fans of even numbers, that's why they want to divide the watermelon in such a way that each of the two parts weighs even number of kilos, at the same time it is not obligatory that the parts are equal. The boys are extremely tired and want to start their meal as soon as possible, that's why you should help them and find out, if they can divide the watermelon in the way they want. For sure, each of them should get a part of positive weight.", "input_spec": "The first (and the only) input line contains integer number w (1\u2009\u2264\u2009w\u2009\u2264\u2009100) \u2014 the weight of the watermelon bought by the boys.", "output_spec": "Print YES, if the boys can divide the watermelon into two parts, each of them weighing even number of kilos; and NO in the opposite case.", "sample_inputs": ["8"], "sample_outputs": ["YES"], "notes": "NoteFor example, the boys can divide the watermelon into two parts of 2 and 6 kilos respectively (another variant \u2014 two parts of 4 and 4 kilos)."}, "src_uid": "230a3c4d7090401e5fa3c6b9d994cdf2"}
{"nl": {"description": "A sequence of non-negative integers a1,\u2009a2,\u2009...,\u2009an of length n is called a wool sequence if and only if there exists two integers l and r (1\u2009\u2264\u2009l\u2009\u2264\u2009r\u2009\u2264\u2009n) such that . In other words each wool sequence contains a subsequence of consecutive elements with xor equal to 0.The expression  means applying the operation of a bitwise xor to numbers x and y. The given operation exists in all modern programming languages, for example, in languages C++ and Java it is marked as \"^\", in Pascal \u2014 as \"xor\".In this problem you are asked to compute the number of sequences made of n integers from 0 to 2m\u2009-\u20091 that are not a wool sequence. You should print this number modulo 1000000009 (109\u2009+\u20099).", "input_spec": "The only line of input contains two space-separated integers n and m (1\u2009\u2264\u2009n,\u2009m\u2009\u2264\u2009105).", "output_spec": "Print the required number of sequences modulo 1000000009 (109\u2009+\u20099) on the only line of output.", "sample_inputs": ["3 2"], "sample_outputs": ["6"], "notes": "NoteSequences of length 3 made of integers 0, 1, 2 and 3 that are not a wool sequence are (1, 3, 1), (1, 2, 1), (2, 1, 2), (2, 3, 2), (3, 1, 3) and (3, 2, 3)."}, "src_uid": "fef4d9c94a93fcf6d536f33503b1d4b8"}
{"nl": {"description": "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": "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$$$ Koa can't get to the island."}, "src_uid": "4941b0a365f86b2e2cf686cdf5d532f8"}
{"nl": {"description": "A string is called bracket sequence if it does not contain any characters other than \"(\" and \")\". A bracket sequence is called regular if it it is possible to obtain correct arithmetic expression by inserting characters \"+\" and \"1\" into this sequence. For example, \"\", \"(())\" and \"()()\" are regular bracket sequences; \"))\" and \")((\" are bracket sequences (but not regular ones), and \"(a)\" and \"(1)+(1)\" are not bracket sequences at all.You have a number of strings; each string is a bracket sequence of length $$$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$$$ otherwise.", "sample_inputs": ["3\n1\n4\n3", "0\n0\n0\n0", "1\n2\n3\n4"], "sample_outputs": ["1", "1", "0"], "notes": "NoteIn the first example it is possible to construct a string \"(())()(()((()()()())))\", which is a regular bracket sequence.In the second example it is possible to construct a string \"\", which is a regular bracket sequence."}, "src_uid": "b99578086043537297d374dc01eeb6f8"}
{"nl": {"description": "A permutation p of size n is an array such that every integer from 1 to n occurs exactly once in this array.Let's call a permutation an almost identity permutation iff there exist at least n\u2009-\u2009k indices i (1\u2009\u2264\u2009i\u2009\u2264\u2009n) such that pi\u2009=\u2009i.Your task is to count the number of almost identity permutations for given numbers n and k.", "input_spec": "The first line contains two integers n and k (4\u2009\u2264\u2009n\u2009\u2264\u20091000, 1\u2009\u2264\u2009k\u2009\u2264\u20094).", "output_spec": "Print the number of almost identity permutations for given n and k.", "sample_inputs": ["4 1", "4 2", "5 3", "5 4"], "sample_outputs": ["1", "7", "31", "76"], "notes": null}, "src_uid": "96d839dc2d038f8ae95fc47c217b2e2f"}
{"nl": {"description": "Nauuo is a girl who loves writing comments.One day, she posted a comment on Codeforces, wondering whether she would get upvotes or downvotes.It's known that there were $$$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": "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": "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": "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": "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": "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": "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"}