{"nl": {"description": "Santa Claus is the first who came to the Christmas Olympiad, and he is going to be the first to take his place at a desk! In the classroom there are n lanes of m desks each, and there are two working places at each of the desks. The lanes are numbered from 1 to n from the left to the right, the desks in a lane are numbered from 1 to m starting from the blackboard. Note that the lanes go perpendicularly to the blackboard, not along it (see picture).The organizers numbered all the working places from 1 to 2nm. The places are numbered by lanes (i.\u00a0e. all the places of the first lane go first, then all the places of the second lane, and so on), in a lane the places are numbered starting from the nearest to the blackboard (i.\u00a0e. from the first desk in the lane), at each desk, the place on the left is numbered before the place on the right.    The picture illustrates the first and the second samples. Santa Clause knows that his place has number k. Help him to determine at which lane at which desk he should sit, and whether his place is on the left or on the right!", "input_spec": "The only line contains three integers n, m and k (1\u2009\u2264\u2009n,\u2009m\u2009\u2264\u200910\u2009000, 1\u2009\u2264\u2009k\u2009\u2264\u20092nm)\u00a0\u2014 the number of lanes, the number of desks in each lane and the number of Santa Claus' place.", "output_spec": "Print two integers: the number of lane r, the number of desk d, and a character s, which stands for the side of the desk Santa Claus. The character s should be \"L\", if Santa Clause should sit on the left, and \"R\" if his place is on the right.", "sample_inputs": ["4 3 9", "4 3 24", "2 4 4"], "sample_outputs": ["2 2 L", "4 3 R", "1 2 R"], "notes": "NoteThe first and the second samples are shown on the picture. The green place corresponds to Santa Claus' place in the first example, the blue place corresponds to Santa Claus' place in the second example.In the third sample there are two lanes with four desks in each, and Santa Claus has the fourth place. Thus, his place is in the first lane at the second desk on the right."}, "src_uid": "d6929926b44c2d5b1a8e6b7f965ca1bb"}
{"nl": {"description": "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": "There is a very secret base in Potatoland where potato mash is made according to a special recipe. The neighbours from Porridgia decided to seize this recipe and to sell it to Pilauland. For this mission they have been preparing special agent Pearlo for many years. When, finally, Pearlo learned all secrets of espionage, he penetrated into the Potatoland territory and reached the secret base.Now he is standing at the entrance, but to get inside he need to pass combination lock. Minute ago one of the workers entered the password on the terminal and opened the door. The terminal is a square digital keyboard 3\u2009\u00d7\u20093 with digits from 1 to 9.Pearlo knows that the password consists from distinct digits and is probably symmetric with respect to the central button of the terminal. He has heat sensor which allowed him to detect the digits which the worker pressed. Now he wants to check whether the password entered by the worker is symmetric with respect to the central button of the terminal. This fact can Help Pearlo to reduce the number of different possible password combinations.", "input_spec": "Input contains the matrix of three rows of three symbols each. Symbol \u00abX\u00bb means that the corresponding button was pressed, and \u00ab.\u00bb means that is was not pressed. The matrix may contain no \u00abX\u00bb, also it may contain no \u00ab.\u00bb.", "output_spec": "Print YES if the password is symmetric with respect to the central button of the terminal and NO otherwise.", "sample_inputs": ["XX.\n...\n.XX", "X.X\nX..\n..."], "sample_outputs": ["YES", "NO"], "notes": "NoteIf you are not familiar with the term \u00abcentral symmetry\u00bb, you may look into http://en.wikipedia.org/wiki/Central_symmetry"}, "src_uid": "6a5fe5fac8a4e3993dc3423180cdd6a9"}
{"nl": {"description": "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": "Since next season are coming, you'd like to form a team from two or three participants. There are $$$n$$$ candidates, the $$$i$$$-th candidate has rank $$$a_i$$$. But you have weird requirements for your teammates: if you have rank $$$v$$$ and have chosen the $$$i$$$-th and $$$j$$$-th candidate, then $$$GCD(v, a_i) = X$$$ and $$$LCM(v, a_j) = Y$$$ must be met.You are very experienced, so you can change your rank to any non-negative integer but $$$X$$$ and $$$Y$$$ are tied with your birthdate, so they are fixed.Now you want to know, how many are there pairs $$$(i, j)$$$ such that there exists an integer $$$v$$$ meeting the following constraints: $$$GCD(v, a_i) = X$$$ and $$$LCM(v, a_j) = Y$$$. It's possible that $$$i = j$$$ and you form a team of two.$$$GCD$$$ is the greatest common divisor of two number, $$$LCM$$$ \u2014 the least common multiple.", "input_spec": "First line contains three integers $$$n$$$, $$$X$$$ and $$$Y$$$ ($$$1 \\le n \\le 2 \\cdot 10^5$$$, $$$1 \\le X \\le Y \\le 10^{18}$$$) \u2014 the number of candidates and corresponding constants. Second line contains $$$n$$$ space separated integers $$$a_1, a_2, \\dots, a_n$$$ ($$$1 \\le a_i \\le 10^{18}$$$) \u2014 ranks of candidates.", "output_spec": "Print the only integer \u2014 the number of pairs $$$(i, j)$$$ such that there exists an integer $$$v$$$ meeting the following constraints: $$$GCD(v, a_i) = X$$$ and $$$LCM(v, a_j) = Y$$$. It's possible that $$$i = j$$$.", "sample_inputs": ["12 2 2\n1 2 3 4 5 6 7 8 9 10 11 12", "12 1 6\n1 3 5 7 9 11 12 10 8 6 4 2"], "sample_outputs": ["12", "30"], "notes": "NoteIn the first example next pairs are valid: $$$a_j = 1$$$ and $$$a_i = [2, 4, 6, 8, 10, 12]$$$ or $$$a_j = 2$$$ and $$$a_i = [2, 4, 6, 8, 10, 12]$$$. The $$$v$$$ in both cases can be equal to $$$2$$$.In the second example next pairs are valid:   $$$a_j = 1$$$ and $$$a_i = [1, 5, 7, 11]$$$;  $$$a_j = 2$$$ and $$$a_i = [1, 5, 7, 11, 10, 8, 4, 2]$$$;  $$$a_j = 3$$$ and $$$a_i = [1, 3, 5, 7, 9, 11]$$$;  $$$a_j = 6$$$ and $$$a_i = [1, 3, 5, 7, 9, 11, 12, 10, 8, 6, 4, 2]$$$. "}, "src_uid": "8d43a542d5bf79d15926c4a6a5ff608f"}
{"nl": {"description": "Polycarp has just invented a new binary protocol for data transmission. He is encoding positive integer decimal number to binary string using following algorithm:  Each digit is represented with number of '1' characters equal to the value of that digit (for 0 it is zero ones).  Digits are written one by one in order corresponding to number and separated by single '0' character. Though Polycarp learnt how to encode the numbers, he has no idea how to decode them back. Help him calculate the decoded number.", "input_spec": "The first line contains one integer number n (1\u2009\u2264\u2009n\u2009\u2264\u200989) \u2014 length of the string s. The second line contains string s \u2014 sequence of '0' and '1' characters, number in its encoded format. It is guaranteed that the number corresponding to the string is positive and doesn't exceed 109. The string always starts with '1'.", "output_spec": "Print the decoded number.", "sample_inputs": ["3\n111", "9\n110011101"], "sample_outputs": ["3", "2031"], "notes": null}, "src_uid": "a4b3da4cb9b6a7ed0a33a862e940cafa"}
{"nl": {"description": "The leader of some very secretive organization has decided to invite all other members to a meeting. All members of the organization live in the same town which can be represented as $$$n$$$ crossroads connected by $$$m$$$ two-directional streets. The meeting will be held in the leader's house near the crossroad $$$1$$$. There are $$$k$$$ members of the organization invited to the meeting; $$$i$$$-th of them lives near the crossroad $$$a_i$$$. All members of the organization receive the message about the meeting at the same moment and start moving to the location where the meeting is held. In the beginning of each minute each person is located at some crossroad. He or she can either wait a minute at this crossroad, or spend a minute to walk from the current crossroad along some street to another crossroad (obviously, it is possible to start walking along the street only if it begins or ends at the current crossroad). In the beginning of the first minute each person is at the crossroad where he or she lives. As soon as a person reaches the crossroad number $$$1$$$, he or she immediately comes to the leader's house and attends the meeting.Obviously, the leader wants all other members of the organization to come up as early as possible. But, since the organization is very secretive, the leader does not want to attract much attention. Let's denote the discontent of the leader as follows  initially the discontent is $$$0$$$;  whenever a person reaches the crossroad number $$$1$$$, the discontent of the leader increases by $$$c \\cdot x$$$, where $$$c$$$ is some fixed constant, and $$$x$$$ is the number of minutes it took the person to reach the crossroad number $$$1$$$;  whenever $$$x$$$ members of the organization walk along the same street at the same moment in the same direction, $$$dx^2$$$ is added to the discontent, where $$$d$$$ is some fixed constant. This is not cumulative: for example, if two persons are walking along the same street in the same direction at the same moment, then $$$4d$$$ is added to the discontent, not $$$5d$$$. Before sending a message about the meeting, the leader can tell each member of the organization which path they should choose and where they should wait. Help the leader to establish a plan for every member of the organization so they all reach the crossroad $$$1$$$, and the discontent is minimized.", "input_spec": "The first line of the input contains five integer numbers $$$n$$$, $$$m$$$, $$$k$$$, $$$c$$$ and $$$d$$$ ($$$2 \\le n \\le 50$$$, $$$n - 1 \\le m \\le 50$$$, $$$1 \\le k, c, d \\le 50$$$) \u2014 the number of crossroads, the number of streets, the number of persons invited to the meeting and the constants affecting the discontent, respectively. The second line contains $$$k$$$ numbers $$$a_1$$$, $$$a_2$$$, ..., $$$a_k$$$ ($$$2 \\le a_i \\le n$$$) \u2014 the crossroads where the members of the organization live. Then $$$m$$$ lines follow, each denoting a bidirectional street. Each line contains two integers $$$x_i$$$ and $$$y_i$$$ ($$$1 \\le x_i, y_i \\le n$$$, $$$x_i \\ne y_i$$$) denoting a street connecting crossroads $$$x_i$$$ and $$$y_i$$$. There may be multiple streets connecting the same pair of crossroads. It is guaranteed that every crossroad can be reached from every other crossroad using the given streets. ", "output_spec": "Print one integer: the minimum discontent of the leader after everyone reaches crossroad $$$1$$$.", "sample_inputs": ["3 2 4 2 3\n3 3 3 3\n1 2\n2 3", "3 3 4 2 3\n3 2 2 3\n1 2\n2 3\n2 3"], "sample_outputs": ["52", "38"], "notes": "NoteThe best course of action in the first test is the following:  the first person goes along the street $$$2$$$ to the crossroad $$$2$$$, then goes along the street $$$1$$$ to the crossroad $$$1$$$ and attends the meeting;  the second person waits one minute on the crossroad $$$3$$$, then goes along the street $$$2$$$ to the crossroad $$$2$$$, then goes along the street $$$1$$$ to the crossroad $$$1$$$ and attends the meeting;  the third person waits two minutes on the crossroad $$$3$$$, then goes along the street $$$2$$$ to the crossroad $$$2$$$, then goes along the street $$$1$$$ to the crossroad $$$1$$$ and attends the meeting;  the fourth person waits three minutes on the crossroad $$$3$$$, then goes along the street $$$2$$$ to the crossroad $$$2$$$, then goes along the street $$$1$$$ to the crossroad $$$1$$$ and attends the meeting. "}, "src_uid": "2d0aa75f2e63c4fb8c98742ac8cd821c"}
{"nl": {"description": "Little girl Alyona is in a shop to buy some copybooks for school. She study four subjects so she wants to have equal number of copybooks for each of the subjects. There are three types of copybook's packs in the shop: it is possible to buy one copybook for a rubles, a pack of two copybooks for b rubles, and a pack of three copybooks for c rubles. Alyona already has n copybooks.What is the minimum amount of rubles she should pay to buy such number of copybooks k that n\u2009+\u2009k is divisible by 4? There are infinitely many packs of any type in the shop. Alyona can buy packs of different type in the same purchase.", "input_spec": "The only line contains 4 integers n, a, b, c (1\u2009\u2264\u2009n,\u2009a,\u2009b,\u2009c\u2009\u2264\u2009109).", "output_spec": "Print the minimum amount of rubles she should pay to buy such number of copybooks k that n\u2009+\u2009k is divisible by 4.", "sample_inputs": ["1 1 3 4", "6 2 1 1", "4 4 4 4", "999999999 1000000000 1000000000 1000000000"], "sample_outputs": ["3", "1", "0", "1000000000"], "notes": "NoteIn the first example Alyona can buy 3 packs of 1 copybook for 3a\u2009=\u20093 rubles in total. After that she will have 4 copybooks which she can split between the subjects equally. In the second example Alyuna can buy a pack of 2 copybooks for b\u2009=\u20091 ruble. She will have 8 copybooks in total.In the third example Alyona can split the copybooks she already has between the 4 subject equally, so she doesn't need to buy anything.In the fourth example Alyona should buy one pack of one copybook."}, "src_uid": "c74537b7e2032c1d928717dfe15ccfb8"}
{"nl": {"description": "You are given a 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": "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": "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": "Manao is trying to open a rather challenging lock. The lock has n buttons on it and to open it, you should press the buttons in a certain order to open the lock. When you push some button, it either stays pressed into the lock (that means that you've guessed correctly and pushed the button that goes next in the sequence), or all pressed buttons return to the initial position. When all buttons are pressed into the lock at once, the lock opens.Consider an example with three buttons. Let's say that the opening sequence is: {2, 3, 1}. If you first press buttons 1 or 3, the buttons unpress immediately. If you first press button 2, it stays pressed. If you press 1 after 2, all buttons unpress. If you press 3 after 2, buttons 3 and 2 stay pressed. As soon as you've got two pressed buttons, you only need to press button 1 to open the lock.Manao doesn't know the opening sequence. But he is really smart and he is going to act in the optimal way. Calculate the number of times he's got to push a button in order to open the lock in the worst-case scenario.", "input_spec": "A single line contains integer n (1\u2009\u2264\u2009n\u2009\u2264\u20092000) \u2014 the number of buttons the lock has.", "output_spec": "In a single line print the number of times Manao has to push a button in the worst-case scenario.", "sample_inputs": ["2", "3"], "sample_outputs": ["3", "7"], "notes": "NoteConsider the first test sample. Manao can fail his first push and push the wrong button. In this case he will already be able to guess the right one with his second push. And his third push will push the second right button. Thus, in the worst-case scenario he will only need 3 pushes."}, "src_uid": "6df251ac8bf27427a24bc23d64cb9884"}
{"nl": {"description": "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": "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": "Mishka got a six-faced dice. It has integer numbers from $$$2$$$ to $$$7$$$ written on its faces (all numbers on faces are different, so this is an almost usual dice).Mishka wants to get exactly $$$x$$$ points by rolling his dice. The number of points is just a sum of numbers written at the topmost face of the dice for all the rolls Mishka makes.Mishka doesn't really care about the number of rolls, so he just wants to know any number of rolls he can make to be able to get exactly $$$x$$$ points for them. Mishka is very lucky, so if the probability to get $$$x$$$ points with chosen number of rolls is non-zero, he will be able to roll the dice in such a way. Your task is to print this number. It is guaranteed that at least one answer exists.Mishka is also very curious about different number of points to score so you have to answer $$$t$$$ independent queries.", "input_spec": "The first line of the input contains one integer $$$t$$$ ($$$1 \\le t \\le 100$$$) \u2014 the number of queries. Each of the next $$$t$$$ lines contains one integer each. The $$$i$$$-th line contains one integer $$$x_i$$$ ($$$2 \\le x_i \\le 100$$$) \u2014 the number of points Mishka wants to get.", "output_spec": "Print $$$t$$$ lines. In the $$$i$$$-th line print the answer to the $$$i$$$-th query (i.e. any number of rolls Mishka can make to be able to get exactly $$$x_i$$$ points for them). It is guaranteed that at least one answer exists.", "sample_inputs": ["4\n2\n13\n37\n100"], "sample_outputs": ["1\n3\n8\n27"], "notes": "NoteIn the first query Mishka can roll a dice once and get $$$2$$$ points.In the second query Mishka can roll a dice $$$3$$$ times and get points $$$5$$$, $$$5$$$ and $$$3$$$ (for example).In the third query Mishka can roll a dice $$$8$$$ times and get $$$5$$$ points $$$7$$$ times and $$$2$$$ points with the remaining roll.In the fourth query Mishka can roll a dice $$$27$$$ times and get $$$2$$$ points $$$11$$$ times, $$$3$$$ points $$$6$$$ times and $$$6$$$ points $$$10$$$ times."}, "src_uid": "a661b6ce166fe4b2bbfd0ace56a7dc2c"}
{"nl": {"description": "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": "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": "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": "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": "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": "Two little greedy bears have found two pieces of cheese in the forest of weight a and b grams, correspondingly. The bears are so greedy that they are ready to fight for the larger piece. That's where the fox comes in and starts the dialog: \"Little bears, wait a little, I want to make your pieces equal\" \"Come off it fox, how are you going to do that?\", the curious bears asked. \"It's easy\", said the fox. \"If the mass of a certain piece is divisible by two, then I can eat exactly a half of the piece. If the mass of a certain piece is divisible by three, then I can eat exactly two-thirds, and if the mass is divisible by five, then I can eat four-fifths. I'll eat a little here and there and make the pieces equal\". The little bears realize that the fox's proposal contains a catch. But at the same time they realize that they can not make the two pieces equal themselves. So they agreed to her proposal, but on one condition: the fox should make the pieces equal as quickly as possible. Find the minimum number of operations the fox needs to make pieces equal.", "input_spec": "The first line contains two space-separated integers a and b (1\u2009\u2264\u2009a,\u2009b\u2009\u2264\u2009109). ", "output_spec": "If the fox is lying to the little bears and it is impossible to make the pieces equal, print -1. Otherwise, print the required minimum number of operations. If the pieces of the cheese are initially equal, the required number is 0.", "sample_inputs": ["15 20", "14 8", "6 6"], "sample_outputs": ["3", "-1", "0"], "notes": null}, "src_uid": "75a97f4d85d50ea0e1af0d46f7565b49"}
{"nl": {"description": "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": "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": "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": "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": "Hasan loves playing games and has recently discovered a game called TopScore. In this soccer-like game there are $$$p$$$ players doing penalty shoot-outs. Winner is the one who scores the most. In case of ties, one of the top-scorers will be declared as the winner randomly with equal probability.They have just finished the game and now are waiting for the result. But there's a tiny problem! The judges have lost the paper of scores! Fortunately they have calculated sum of the scores before they get lost and also for some of the players they have remembered a lower bound on how much they scored. However, the information about the bounds is private, so Hasan only got to know his bound.According to the available data, he knows that his score is at least $$$r$$$ and sum of the scores is $$$s$$$.Thus the final state of the game can be represented in form of sequence of $$$p$$$ integers $$$a_1, a_2, \\dots, a_p$$$ ($$$0 \\le a_i$$$) \u2014 player's scores. Hasan is player number $$$1$$$, so $$$a_1 \\ge r$$$. Also $$$a_1 + a_2 + \\dots + a_p = s$$$. Two states are considered different if there exists some position $$$i$$$ such that the value of $$$a_i$$$ differs in these states. Once again, Hasan doesn't know the exact scores (he doesn't know his exact score as well). So he considers each of the final states to be equally probable to achieve.Help Hasan find the probability of him winning.It can be shown that it is in the form of $$$\\frac{P}{Q}$$$ where $$$P$$$ and $$$Q$$$ are non-negative integers and $$$Q \\ne 0$$$, $$$P \\le Q$$$. Report the value of $$$P \\cdot Q^{-1} \\pmod {998244353}$$$.", "input_spec": "The only line contains three integers $$$p$$$, $$$s$$$ and $$$r$$$ ($$$1 \\le p \\le 100$$$, $$$0 \\le r \\le s \\le 5000$$$) \u2014 the number of players, the sum of scores of all players and Hasan's score, respectively.", "output_spec": "Print a single integer \u2014 the probability of Hasan winning. It can be shown that it is in the form of $$$\\frac{P}{Q}$$$ where $$$P$$$ and $$$Q$$$ are non-negative integers and $$$Q \\ne 0$$$, $$$P \\le Q$$$. Report the value of $$$P \\cdot Q^{-1} \\pmod {998244353}$$$.", "sample_inputs": ["2 6 3", "5 20 11", "10 30 10"], "sample_outputs": ["124780545", "1", "85932500"], "notes": "NoteIn the first example Hasan can score $$$3$$$, $$$4$$$, $$$5$$$ or $$$6$$$ goals. If he scores $$$4$$$ goals or more than he scores strictly more than his only opponent. If he scores $$$3$$$ then his opponent also scores $$$3$$$ and Hasan has a probability of $$$\\frac 1 2$$$ to win the game. Thus, overall he has the probability of $$$\\frac 7 8$$$ to win.In the second example even Hasan's lower bound on goal implies him scoring more than any of his opponents. Thus, the resulting probability is $$$1$$$."}, "src_uid": "609195ef4a970c62a8210dafe118580e"}
{"nl": {"description": "Maksim walks on a Cartesian plane. Initially, he stands at the point $$$(0, 0)$$$ and in one move he can go to any of four adjacent points (left, right, up, down). For example, if Maksim is currently at the point $$$(0, 0)$$$, he can go to any of the following points in one move:   $$$(1, 0)$$$;  $$$(0, 1)$$$;  $$$(-1, 0)$$$;  $$$(0, -1)$$$. There are also $$$n$$$ distinct key points at this plane. The $$$i$$$-th point is $$$p_i = (x_i, y_i)$$$. It is guaranteed that $$$0 \\le x_i$$$ and $$$0 \\le y_i$$$ and there is no key point $$$(0, 0)$$$.Let the first level points be such points that $$$max(x_i, y_i) = 1$$$, the second level points be such points that $$$max(x_i, y_i) = 2$$$ and so on. Maksim wants to visit all the key points. But he shouldn't visit points of level $$$i + 1$$$ if he does not visit all the points of level $$$i$$$. He starts visiting the points from the minimum level of point from the given set.The distance between two points $$$(x_1, y_1)$$$ and $$$(x_2, y_2)$$$ is $$$|x_1 - x_2| + |y_1 - y_2|$$$ where $$$|v|$$$ is the absolute value of $$$v$$$.Maksim wants to visit all the key points in such a way that the total distance he walks will be minimum possible. Your task is to find this distance.If you are Python programmer, consider using PyPy instead of Python when you submit your code.", "input_spec": "The first line of the input contains one integer $$$n$$$ ($$$1 \\le n \\le 2 \\cdot 10^5$$$) \u2014 the number of key points. Each of the next $$$n$$$ lines contains two integers $$$x_i$$$, $$$y_i$$$ ($$$0 \\le x_i, y_i \\le 10^9$$$) \u2014 $$$x$$$-coordinate of the key point $$$p_i$$$ and $$$y$$$-coordinate of the key point $$$p_i$$$. It is guaranteed that all the points are distinct and the point $$$(0, 0)$$$ is not in this set.", "output_spec": "Print one integer \u2014 the minimum possible total distance Maksim has to travel if he needs to visit all key points in a way described above.", "sample_inputs": ["8\n2 2\n1 4\n2 3\n3 1\n3 4\n1 1\n4 3\n1 2", "5\n2 1\n1 0\n2 0\n3 2\n0 3"], "sample_outputs": ["15", "9"], "notes": "NoteThe picture corresponding to the first example: There is one of the possible answers of length $$$15$$$.The picture corresponding to the second example: There is one of the possible answers of length $$$9$$$."}, "src_uid": "06646a9bdce2d65e92e525e97b2c975d"}
{"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": "Each evening after the dinner the SIS's students gather together to play the game of Sport Mafia. For the tournament, Alya puts candies into the box, which will serve as a prize for a winner. To do that, she performs $$$n$$$ actions. The first action performed is to put a single candy into the box. For each of the remaining moves she can choose from two options:  the first option, in case the box contains at least one candy, is to take exactly one candy out and eat it. This way the number of candies in the box decreased by $$$1$$$;  the second option is to put candies in the box. In this case, Alya will put $$$1$$$ more candy, than she put in the previous time. Thus, if the box is empty, then it can only use the second option.For example, one possible sequence of Alya's actions look as follows:  put one candy into the box;  put two candies into the box;  eat one candy from the box;  eat one candy from the box;  put three candies into the box;  eat one candy from the box;  put four candies into the box;  eat one candy from the box;  put five candies into the box; This way she will perform $$$9$$$ actions, the number of candies at the end will be $$$11$$$, while Alya will eat $$$4$$$ candies in total.You know the total number of actions $$$n$$$ and the number of candies at the end $$$k$$$. You need to find the total number of sweets Alya ate. That is the number of moves of the first option. It's guaranteed, that for the given $$$n$$$ and $$$k$$$ the answer always exists.Please note, that during an action of the first option, Alya takes out and eats exactly one candy.", "input_spec": "The first line contains two integers $$$n$$$ and $$$k$$$ ($$$1 \\le n \\le 10^9$$$; $$$0 \\le k \\le 10^9$$$)\u00a0\u2014 the total number of moves and the number of candies in the box at the end.  It's guaranteed, that for the given $$$n$$$ and $$$k$$$ the answer exists.", "output_spec": "Print a single integer\u00a0\u2014 the number of candies, which Alya ate. Please note, that in this problem there aren't multiple possible answers\u00a0\u2014 the answer is unique for any input data. ", "sample_inputs": ["1 1", "9 11", "5 0", "3 2"], "sample_outputs": ["0", "4", "3", "1"], "notes": "NoteIn the first example, Alya has made one move only. According to the statement, the first move is always putting one candy in the box. Hence Alya ate $$$0$$$ candies.In the second example the possible sequence of Alya's actions looks as follows:   put $$$1$$$ candy,  put $$$2$$$ candies,  eat a candy,  eat a candy,  put $$$3$$$ candies,  eat a candy,  put $$$4$$$ candies,  eat a candy,  put $$$5$$$ candies.  This way, she will make exactly $$$n=9$$$ actions and in the end the box will contain $$$1+2-1-1+3-1+4-1+5=11$$$ candies. The answer is $$$4$$$, since she ate $$$4$$$ candies in total."}, "src_uid": "17b5ec1c6263ef63c668c2b903db1d77"}
{"nl": {"description": "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": "We've got no test cases. A big olympiad is coming up. But the problemsetters' number one priority should be adding another problem to the round. The diameter of a multiset of points on the line is the largest distance between two points from this set. For example, the diameter of the multiset {1,\u20093,\u20092,\u20091} is 2.Diameter of multiset consisting of one point is 0.You are given n points on the line. What is the minimum number of points you have to remove, so that the diameter of the multiset of the remaining points will not exceed d?", "input_spec": "The first line contains two integers n and d (1\u2009\u2264\u2009n\u2009\u2264\u2009100,\u20090\u2009\u2264\u2009d\u2009\u2264\u2009100)\u00a0\u2014 the amount of points and the maximum allowed diameter respectively. The second line contains n space separated integers (1\u2009\u2264\u2009xi\u2009\u2264\u2009100)\u00a0\u2014 the coordinates of the points.", "output_spec": "Output a single integer\u00a0\u2014 the minimum number of points you have to remove.", "sample_inputs": ["3 1\n2 1 4", "3 0\n7 7 7", "6 3\n1 3 4 6 9 10"], "sample_outputs": ["1", "0", "3"], "notes": "NoteIn the first test case the optimal strategy is to remove the point with coordinate 4. The remaining points will have coordinates 1 and 2, so the diameter will be equal to 2\u2009-\u20091\u2009=\u20091.In the second test case the diameter is equal to 0, so its is unnecessary to remove any points. In the third test case the optimal strategy is to remove points with coordinates 1, 9 and 10. The remaining points will have coordinates 3, 4 and 6, so the diameter will be equal to 6\u2009-\u20093\u2009=\u20093."}, "src_uid": "6bcb324c072f796f4d50bafea5f624b2"}
{"nl": {"description": "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": "Limak is a little polar bear. Polar bears hate long strings and thus they like to compress them. You should also know that Limak is so young that he knows only first six letters of the English alphabet: 'a', 'b', 'c', 'd', 'e' and 'f'.You are given a set of q possible operations. Limak can perform them in any order, any operation may be applied any number of times. The i-th operation is described by a string ai of length two and a string bi of length one. No two of q possible operations have the same string ai.When Limak has a string s he can perform the i-th operation on s if the first two letters of s match a two-letter string ai. Performing the i-th operation removes first two letters of s and inserts there a string bi. See the notes section for further clarification.You may note that performing an operation decreases the length of a string s exactly by 1. Also, for some sets of operations there may be a string that cannot be compressed any further, because the first two letters don't match any ai.Limak wants to start with a string of length n and perform n\u2009-\u20091 operations to finally get a one-letter string \"a\". In how many ways can he choose the starting string to be able to get \"a\"? Remember that Limak can use only letters he knows.", "input_spec": "The first line contains two integers n and q (2\u2009\u2264\u2009n\u2009\u2264\u20096, 1\u2009\u2264\u2009q\u2009\u2264\u200936)\u00a0\u2014 the length of the initial string and the number of available operations. The next q lines describe the possible operations. The i-th of them contains two strings ai and bi (|ai|\u2009=\u20092,\u2009|bi|\u2009=\u20091). It's guaranteed that ai\u2009\u2260\u2009aj for i\u2009\u2260\u2009j and that all ai and bi consist of only first six lowercase English letters.", "output_spec": "Print the number of strings of length n that Limak will be able to transform to string \"a\" by applying only operations given in the input.", "sample_inputs": ["3 5\nab a\ncc c\nca a\nee c\nff d", "2 8\naf e\ndc d\ncc f\nbc b\nda b\neb a\nbb b\nff c", "6 2\nbb a\nba a"], "sample_outputs": ["4", "1", "0"], "notes": "NoteIn the first sample, we count initial strings of length 3 from which Limak can get a required string \"a\". There are 4 such strings: \"abb\", \"cab\", \"cca\", \"eea\". The first one Limak can compress using operation 1 two times (changing \"ab\" to a single \"a\"). The first operation would change \"abb\" to \"ab\" and the second operation would change \"ab\" to \"a\".Other three strings may be compressed as follows:   \"cab\"  \"ab\"  \"a\"  \"cca\"  \"ca\"  \"a\"  \"eea\"  \"ca\"  \"a\" In the second sample, the only correct initial string is \"eb\" because it can be immediately compressed to \"a\"."}, "src_uid": "c42abec29bfd17de3f43385fa6bea534"}
{"nl": {"description": "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": "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": "You have a set of $$$n$$$ weights. You know that their masses are $$$a_1$$$, $$$a_2$$$, ..., $$$a_n$$$ grams, but you don't know which of them has which mass. You can't distinguish the weights.However, your friend does know the mass of each weight. You can ask your friend to give you exactly $$$k$$$ weights with the total mass $$$m$$$ (both parameters $$$k$$$ and $$$m$$$ are chosen by you), and your friend will point to any valid subset of weights, if it is possible.You are allowed to make this query only once. Find the maximum possible number of weights you can reveal after this query.", "input_spec": "The first line contains a single integer $$$n$$$ ($$$1 \\le n \\le 100$$$)\u00a0\u2014 the number of weights. The second line contains $$$n$$$ integers $$$a_1, a_2, \\ldots, a_n$$$ ($$$1 \\le a_i \\le 100$$$)\u00a0\u2014 the masses of the weights.", "output_spec": "Print the maximum number of weights you can learn the masses for after making a single query.", "sample_inputs": ["4\n1 4 2 2", "6\n1 2 4 4 4 9"], "sample_outputs": ["2", "2"], "notes": "NoteIn the first example we can ask for a subset of two weights with total mass being equal to $$$4$$$, and the only option is to get $$$\\{2, 2\\}$$$.Another way to obtain the same result is to ask for a subset of two weights with the total mass of $$$5$$$ and get $$$\\{1, 4\\}$$$. It is easy to see that the two remaining weights have mass of $$$2$$$ grams each.In the second example we can ask for a subset of two weights with total mass being $$$8$$$, and the only answer is $$$\\{4, 4\\}$$$. We can prove it is not possible to learn masses for three weights in one query, but we won't put the proof here."}, "src_uid": "ccc4b27889598266e8efe73b8aa3666c"}
{"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": "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": "Overlooking the captivating blend of myriads of vernal hues, Arkady the painter lays out a long, long canvas.Arkady has a sufficiently large amount of paint of three colours: cyan, magenta, and yellow. On the one-dimensional canvas split into n consecutive segments, each segment needs to be painted in one of the colours.Arkady has already painted some (possibly none or all) segments and passes the paintbrush to you. You are to determine whether there are at least two ways of colouring all the unpainted segments so that no two adjacent segments are of the same colour. Two ways are considered different if and only if a segment is painted in different colours in them.", "input_spec": "The first line contains a single positive integer n (1\u2009\u2264\u2009n\u2009\u2264\u2009100)\u00a0\u2014 the length of the canvas. The second line contains a string s of n characters, the i-th of which is either 'C' (denoting a segment painted in cyan), 'M' (denoting one painted in magenta), 'Y' (one painted in yellow), or '?' (an unpainted one).", "output_spec": "If there are at least two different ways of painting, output \"Yes\"; otherwise output \"No\" (both without quotes). You can print each character in any case (upper or lower).", "sample_inputs": ["5\nCY??Y", "5\nC?C?Y", "5\n?CYC?", "5\nC??MM", "3\nMMY"], "sample_outputs": ["Yes", "Yes", "Yes", "No", "No"], "notes": "NoteFor the first example, there are exactly two different ways of colouring: CYCMY and CYMCY.For the second example, there are also exactly two different ways of colouring: CMCMY and CYCMY.For the third example, there are four ways of colouring: MCYCM, MCYCY, YCYCM, and YCYCY.For the fourth example, no matter how the unpainted segments are coloured, the existing magenta segments will prevent the painting from satisfying the requirements. The similar is true for the fifth example."}, "src_uid": "f8adfa0dde7ac1363f269dbdf00212c3"}
{"nl": {"description": "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": "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": "After finishing eating her bun, Alyona came up with two integers n and m. She decided to write down two columns of integers\u00a0\u2014 the first column containing integers from 1 to n and the second containing integers from 1 to m. Now the girl wants to count how many pairs of integers she can choose, one from the first column and the other from the second column, such that their sum is divisible by 5.Formally, Alyona wants to count the number of pairs of integers (x,\u2009y) such that 1\u2009\u2264\u2009x\u2009\u2264\u2009n, 1\u2009\u2264\u2009y\u2009\u2264\u2009m and  equals 0.As usual, Alyona has some troubles and asks you to help.", "input_spec": "The only line of the input contains two integers n and m (1\u2009\u2264\u2009n,\u2009m\u2009\u2264\u20091\u2009000\u2009000).", "output_spec": "Print the only integer\u00a0\u2014 the number of pairs of integers (x,\u2009y) such that 1\u2009\u2264\u2009x\u2009\u2264\u2009n, 1\u2009\u2264\u2009y\u2009\u2264\u2009m and (x\u2009+\u2009y) is divisible by 5.", "sample_inputs": ["6 12", "11 14", "1 5", "3 8", "5 7", "21 21"], "sample_outputs": ["14", "31", "1", "5", "7", "88"], "notes": "NoteFollowing pairs are suitable in the first sample case:   for x\u2009=\u20091 fits y equal to 4 or 9;  for x\u2009=\u20092 fits y equal to 3 or 8;  for x\u2009=\u20093 fits y equal to 2, 7 or 12;  for x\u2009=\u20094 fits y equal to 1, 6 or 11;  for x\u2009=\u20095 fits y equal to 5 or 10;  for x\u2009=\u20096 fits y equal to 4 or 9. Only the pair (1,\u20094) is suitable in the third sample case."}, "src_uid": "df0879635b59e141c839d9599abd77d2"}
{"nl": {"description": "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": " When the curtains are opened, a canvas unfolds outside. Kanno marvels at all the blonde colours along the riverside\u00a0\u2014 not tangerines, but blossoms instead.\"What a pity it's already late spring,\" sighs Mino with regret, \"one more drizzling night and they'd be gone.\"\"But these blends are at their best, aren't they?\" Absorbed in the landscape, Kanno remains optimistic. The landscape can be expressed as a row of consecutive cells, each of which either contains a flower of colour amber or buff or canary yellow, or is empty.When a flower withers, it disappears from the cell that it originally belonged to, and it spreads petals of its colour in its two neighbouring cells (or outside the field if the cell is on the side of the landscape). In case petals fall outside the given cells, they simply become invisible.You are to help Kanno determine whether it's possible that after some (possibly none or all) flowers shed their petals, at least one of the cells contains all three colours, considering both petals and flowers. Note that flowers can wither in arbitrary order.", "input_spec": "The first and only line of input contains a non-empty string $$$s$$$ consisting of uppercase English letters 'A', 'B', 'C' and characters '.' (dots) only ($$$\\lvert s \\rvert \\leq 100$$$)\u00a0\u2014 denoting cells containing an amber flower, a buff one, a canary yellow one, and no flowers, respectively.", "output_spec": "Output \"Yes\" if it's possible that all three colours appear in some cell, and \"No\" otherwise. You can print each letter in any case (upper or lower).", "sample_inputs": [".BAC.", "AA..CB"], "sample_outputs": ["Yes", "No"], "notes": "NoteIn the first example, the buff and canary yellow flowers can leave their petals in the central cell, blending all three colours in it.In the second example, it's impossible to satisfy the requirement because there is no way that amber and buff meet in any cell."}, "src_uid": "ba6ff507384570152118e2ab322dd11f"}
{"nl": {"description": "Polycarp 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": "Kolya is very absent-minded. Today his math teacher asked him to solve a simple problem with the equation $$$a + 1 = b$$$ with positive integers $$$a$$$ and $$$b$$$, but Kolya forgot the numbers $$$a$$$ and $$$b$$$. He does, however, remember that the first (leftmost) digit of $$$a$$$ was $$$d_a$$$, and the first (leftmost) digit of $$$b$$$ was $$$d_b$$$.Can you reconstruct any equation $$$a + 1 = b$$$ that satisfies this property? It may be possible that Kolya misremembers the digits, and there is no suitable equation, in which case report so.", "input_spec": "The only line contains two space-separated digits $$$d_a$$$ and $$$d_b$$$ ($$$1 \\leq d_a, d_b \\leq 9$$$).", "output_spec": "If there is no equation $$$a + 1 = b$$$ with positive integers $$$a$$$ and $$$b$$$ such that the first digit of $$$a$$$ is $$$d_a$$$, and the first digit of $$$b$$$ is $$$d_b$$$, print a single number $$$-1$$$. Otherwise, print any suitable $$$a$$$ and $$$b$$$ that both are positive and do not exceed $$$10^9$$$. It is guaranteed that if a solution exists, there also exists a solution with both numbers not exceeding $$$10^9$$$.", "sample_inputs": ["1 2", "4 4", "5 7", "6 2"], "sample_outputs": ["199 200", "412 413", "-1", "-1"], "notes": null}, "src_uid": "3eff6f044c028146bea5f0dfd2870d23"}
{"nl": {"description": "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": "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": "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": "Today an outstanding event is going to happen in the forest\u00a0\u2014 hedgehog Filya will come to his old fried Sonya!Sonya is an owl and she sleeps during the day and stay awake from minute l1 to minute r1 inclusive. Also, during the minute k she prinks and is unavailable for Filya.Filya works a lot and he plans to visit Sonya from minute l2 to minute r2 inclusive.Calculate the number of minutes they will be able to spend together.", "input_spec": "The only line of the input contains integers l1, r1, l2, r2 and k (1\u2009\u2264\u2009l1,\u2009r1,\u2009l2,\u2009r2,\u2009k\u2009\u2264\u20091018, l1\u2009\u2264\u2009r1, l2\u2009\u2264\u2009r2), providing the segments of time for Sonya and Filya and the moment of time when Sonya prinks.", "output_spec": "Print one integer\u00a0\u2014 the number of minutes Sonya and Filya will be able to spend together.", "sample_inputs": ["1 10 9 20 1", "1 100 50 200 75"], "sample_outputs": ["2", "50"], "notes": "NoteIn the first sample, they will be together during minutes 9 and 10.In the second sample, they will be together from minute 50 to minute 74 and from minute 76 to minute 100."}, "src_uid": "9a74b3b0e9f3a351f2136842e9565a82"}
{"nl": {"description": "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": "Polycarpus has recently got interested in sequences of pseudorandom numbers. He learned that many programming languages generate such sequences in a similar way:  (for i\u2009\u2265\u20091). Here a, b, m are constants, fixed for the given realization of the pseudorandom numbers generator, r0 is the so-called randseed (this value can be set from the program using functions like RandSeed(r) or srand(n)), and  denotes the operation of taking the remainder of division.For example, if a\u2009=\u20092,\u2009b\u2009=\u20096,\u2009m\u2009=\u200912,\u2009r0\u2009=\u200911, the generated sequence will be: 4,\u20092,\u200910,\u20092,\u200910,\u20092,\u200910,\u20092,\u200910,\u20092,\u200910,\u2009....Polycarpus realized that any such sequence will sooner or later form a cycle, but the cycle may occur not in the beginning, so there exist a preperiod and a period. The example above shows a preperiod equal to 1 and a period equal to 2.Your task is to find the period of a sequence defined by the given values of a,\u2009b,\u2009m and r0. Formally, you have to find such minimum positive integer t, for which exists such positive integer k, that for any i\u2009\u2265\u2009k: ri\u2009=\u2009ri\u2009+\u2009t.", "input_spec": "The single line of the input contains four integers a, b, m and r0 (1\u2009\u2264\u2009m\u2009\u2264\u2009105,\u20090\u2009\u2264\u2009a,\u2009b\u2009\u2264\u20091000,\u20090\u2009\u2264\u2009r0\u2009<\u2009m), separated by single spaces.", "output_spec": "Print a single integer \u2014 the period of the sequence.", "sample_inputs": ["2 6 12 11", "2 3 5 1", "3 6 81 9"], "sample_outputs": ["2", "4", "1"], "notes": "NoteThe first sample is described above. In the second sample the sequence is (starting from the first element): 0,\u20093,\u20094,\u20091,\u20090,\u20093,\u20094,\u20091,\u20090,\u2009...In the third sample the sequence is (starting from the first element): 33,\u200924,\u200978,\u200978,\u200978,\u200978,\u2009..."}, "src_uid": "9137197ee1b781cd5cc77c46f50b9012"}
{"nl": {"description": "Furik loves math lessons very much, so he doesn't attend them, unlike Rubik. But now Furik wants to get a good mark for math. For that Ms. Ivanova, his math teacher, gave him a new task. Furik solved the task immediately. Can you?You are given a system of equations:   You should count, how many there are pairs of integers (a,\u2009b) (0\u2009\u2264\u2009a,\u2009b) which satisfy the system.", "input_spec": "A single line contains two integers n,\u2009m (1\u2009\u2264\u2009n,\u2009m\u2009\u2264\u20091000) \u2014 the parameters of the system. The numbers on the line are separated by a space.", "output_spec": "On a single line print the answer to the problem.", "sample_inputs": ["9 3", "14 28", "4 20"], "sample_outputs": ["1", "1", "0"], "notes": "NoteIn the first sample the suitable pair is integers (3,\u20090). In the second sample the suitable pair is integers (3,\u20095). In the third sample there is no suitable pair."}, "src_uid": "03caf4ddf07c1783e42e9f9085cc6efd"}
{"nl": {"description": "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": "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": "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": "Statistics claims that students sleep no more than three hours a day. But even in the world of their dreams, while they are snoring peacefully, the sense of impending doom is still upon them.A poor student is dreaming that he is sitting the mathematical analysis exam. And he is examined by the most formidable professor of all times, a three times Soviet Union Hero, a Noble Prize laureate in student expulsion, venerable Petr Palych.The poor student couldn't answer a single question. Thus, instead of a large spacious office he is going to apply for a job to thorium mines. But wait a minute! Petr Palych decided to give the student the last chance! Yes, that is possible only in dreams. So the professor began: \"Once a Venusian girl and a Marsian boy met on the Earth and decided to take a walk holding hands. But the problem is the girl has al fingers on her left hand and ar fingers on the right one. The boy correspondingly has bl and br fingers. They can only feel comfortable when holding hands, when no pair of the girl's fingers will touch each other. That is, they are comfortable when between any two girl's fingers there is a boy's finger. And in addition, no three fingers of the boy should touch each other. Determine if they can hold hands so that the both were comfortable.\"The boy any the girl don't care who goes to the left and who goes to the right. The difference is only that if the boy goes to the left of the girl, he will take her left hand with his right one, and if he goes to the right of the girl, then it is vice versa.", "input_spec": "The first line contains two positive integers not exceeding 100. They are the number of fingers on the Venusian girl's left and right hand correspondingly. The second line contains two integers not exceeding 100. They are the number of fingers on the Marsian boy's left and right hands correspondingly.", "output_spec": "Print YES or NO, that is, the answer to Petr Palych's question.", "sample_inputs": ["5 1\n10 5", "4 5\n3 3", "1 2\n11 6"], "sample_outputs": ["YES", "YES", "NO"], "notes": "NoteThe boy and the girl don't really care who goes to the left."}, "src_uid": "36b7478e162be6e985613b2dad0974dd"}
{"nl": {"description": "You have 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": "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 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": "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": "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": "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$$$."}, "src_uid": "783c4b3179c558369f94f4a16ac562d4"}
{"nl": {"description": "There is a straight line colored in white. n black segments are added on it one by one.After each segment is added, determine the number of connected components of black segments (i.\u00a0e. the number of black segments in the union of the black segments). In particular, if one segment ends in a point x, and another segment starts in the point x, these two segments belong to the same connected component.", "input_spec": "The first line contains a single integer n (1\u2009\u2264\u2009n\u2009\u2264\u2009200\u2009000) \u2014 the number of segments. The i-th of the next n lines contains two integers li and ri (1\u2009\u2264\u2009li\u2009<\u2009ri\u2009\u2264\u2009109) \u2014 the coordinates of the left and the right ends of the i-th segment. The segments are listed in the order they are added on the white line.", "output_spec": "Print n integers \u2014 the number of connected components of black segments after each segment is added. ", "sample_inputs": ["3\n1 3\n4 5\n2 4", "9\n10 20\n50 60\n30 40\n70 80\n90 100\n60 70\n10 40\n40 50\n80 90"], "sample_outputs": ["1 2 1", "1 2 3 4 5 4 3 2 1"], "notes": "NoteIn the first example there are two components after the addition of the first two segments, because these segments do not intersect. The third added segment intersects the left segment and touches the right segment at the point 4 (these segments belong to the same component, according to the statements). Thus the number of connected components of black segments is equal to 1 after that."}, "src_uid": "3979abbe7bad0f3b5cab15c1cba19f6b"}
{"nl": {"description": "Consider the following experiment. You have a deck of $$$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$$$).", "sample_inputs": ["1 1 1", "1 1 5000", "2 2 2", "998244352 1337 5000"], "sample_outputs": ["1", "1", "499122178", "326459680"], "notes": null}, "src_uid": "e6b3e559b5fd4e05adf9f1cd1b22126b"}
{"nl": {"description": "This is the easy version of the problem. The only difference between the easy version and the hard version is the constraints on $$$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]$$$. "}, "src_uid": "ae0320a57d73fab1d05f5d10fbdb9e1a"}
{"nl": {"description": "This morning, Roman woke up and opened the browser with $$$n$$$ opened tabs numbered from $$$1$$$ to $$$n$$$. There are two kinds of tabs: those with the information required for the test and those with social network sites. Roman decided that there are too many tabs open so he wants to close some of them.He decided to accomplish this by closing every $$$k$$$-th ($$$2 \\leq k \\leq n - 1$$$) tab. Only then he will decide whether he wants to study for the test or to chat on the social networks. Formally, Roman will choose one tab (let its number be $$$b$$$) and then close all tabs with numbers $$$c = b + i \\cdot k$$$ that satisfy the following condition: $$$1 \\leq c \\leq n$$$ and $$$i$$$ is an integer (it may be positive, negative or zero).For example, if $$$k = 3$$$, $$$n = 14$$$ and Roman chooses $$$b = 8$$$, then he will close tabs with numbers $$$2$$$, $$$5$$$, $$$8$$$, $$$11$$$ and $$$14$$$.After closing the tabs Roman will calculate the amount of remaining tabs with the information for the test (let's denote it $$$e$$$) and the amount of remaining social network tabs ($$$s$$$). Help Roman to calculate the maximal absolute value of the difference of those values $$$|e - s|$$$ so that it would be easy to decide what to do next.", "input_spec": "The first line contains two integers $$$n$$$ and $$$k$$$ ($$$2 \\leq k < n \\leq 100$$$) \u2014 the amount of tabs opened currently and the distance between the tabs closed. The second line consists of $$$n$$$ integers, each of them equal either to $$$1$$$ or to $$$-1$$$. The $$$i$$$-th integer denotes the type of the $$$i$$$-th tab: if it is equal to $$$1$$$, this tab contains information for the test, and if it is equal to $$$-1$$$, it's a social network tab.", "output_spec": "Output a single integer \u2014 the maximum absolute difference between the amounts of remaining tabs of different types $$$|e - s|$$$.", "sample_inputs": ["4 2\n1 1 -1 1", "14 3\n-1 1 -1 -1 1 -1 -1 1 -1 -1 1 -1 -1 1"], "sample_outputs": ["2", "9"], "notes": "NoteIn the first example we can choose $$$b = 1$$$ or $$$b = 3$$$. We will delete then one tab of each type and the remaining tabs are then all contain test information. Thus, $$$e = 2$$$ and $$$s = 0$$$ and $$$|e - s| = 2$$$.In the second example, on the contrary, we can leave opened only tabs that have social networks opened in them."}, "src_uid": "6119258322e06fa6146e592c63313df3"}
{"nl": {"description": "Right now she actually isn't. But she will be, if you don't solve this problem.You are given integers n, k, A and B. There is a number x, which is initially equal to n. You are allowed to perform two types of operations:   Subtract 1 from x. This operation costs you A coins.  Divide x by k. Can be performed only if x is divisible by k. This operation costs you B coins.  What is the minimum amount of coins you have to pay to make x equal to 1?", "input_spec": "The first line contains a single integer n (1\u2009\u2264\u2009n\u2009\u2264\u20092\u00b7109). The second line contains a single integer k (1\u2009\u2264\u2009k\u2009\u2264\u20092\u00b7109). The third line contains a single integer A (1\u2009\u2264\u2009A\u2009\u2264\u20092\u00b7109). The fourth line contains a single integer B (1\u2009\u2264\u2009B\u2009\u2264\u20092\u00b7109).", "output_spec": "Output a single integer\u00a0\u2014 the minimum amount of coins you have to pay to make x equal to 1.", "sample_inputs": ["9\n2\n3\n1", "5\n5\n2\n20", "19\n3\n4\n2"], "sample_outputs": ["6", "8", "12"], "notes": "NoteIn the first testcase, the optimal strategy is as follows:   Subtract 1 from x (9\u2009\u2192\u20098) paying 3 coins.  Divide x by 2 (8\u2009\u2192\u20094) paying 1 coin.  Divide x by 2 (4\u2009\u2192\u20092) paying 1 coin.  Divide x by 2 (2\u2009\u2192\u20091) paying 1 coin. The total cost is 6 coins.In the second test case the optimal strategy is to subtract 1 from x 4 times paying 8 coins in total."}, "src_uid": "f838fae7c98bf51cfa0b9bd158650b10"}
{"nl": {"description": "Let's call a fraction $$$\\frac{x}{y}$$$ good if there exists at least one another fraction $$$\\frac{x'}{y'}$$$ such that $$$\\frac{x}{y} = \\frac{x'}{y'}$$$, $$$1 \\le x', y' \\le 9$$$, the digit denoting $$$x'$$$ is contained in the decimal representation of $$$x$$$, and the digit denoting $$$y'$$$ is contained in the decimal representation of $$$y$$$. For example, $$$\\frac{26}{13}$$$ is a good fraction, because $$$\\frac{26}{13} = \\frac{2}{1}$$$.You are given an integer number $$$n$$$. Please calculate the number of good fractions $$$\\frac{x}{y}$$$ such that $$$1 \\le x \\le n$$$ and $$$1 \\le y \\le n$$$. The answer may be really large, so print it modulo $$$998244353$$$.", "input_spec": "The only line of the input contains one integer $$$n$$$ ($$$1 \\le n < 10^{100}$$$).", "output_spec": "Print the number of good fractions $$$\\frac{x}{y}$$$ such that $$$1 \\le x \\le n$$$ and $$$1 \\le y \\le n$$$. The answer may be really large, so print it modulo $$$998244353$$$.", "sample_inputs": ["42", "3141592653589793238462643383279"], "sample_outputs": ["150", "459925407"], "notes": null}, "src_uid": "b6f2061e2ca174c2385bf4520d232aaf"}
{"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": "Petya started to attend programming lessons. On the first lesson his task was to write a simple program. The program was supposed to do the following: in the given string, consisting if uppercase and lowercase Latin letters, it:   deletes all the vowels,  inserts a character \".\" before each consonant,  replaces all uppercase consonants with corresponding lowercase ones. Vowels are letters \"A\", \"O\", \"Y\", \"E\", \"U\", \"I\", and the rest are consonants. The program's input is exactly one string, it should return the output as a single string, resulting after the program's processing the initial string.Help Petya cope with this easy task.", "input_spec": "The first line represents input string of Petya's program. This string only consists of uppercase and lowercase Latin letters and its length is from 1 to 100, inclusive.", "output_spec": "Print the resulting string. It is guaranteed that this string is not empty.", "sample_inputs": ["tour", "Codeforces", "aBAcAba"], "sample_outputs": [".t.r", ".c.d.f.r.c.s", ".b.c.b"], "notes": null}, "src_uid": "db9520e85b3e9186dd3a09ff8d1e8c1b"}
{"nl": {"description": "Our good friend Mole is trying to code a big message. He is typing on an unusual keyboard with characters arranged in following way:qwertyuiopasdfghjkl;zxcvbnm,./Unfortunately Mole is blind, so sometimes it is problem for him to put his hands accurately. He accidentally moved both his hands with one position to the left or to the right. That means that now he presses not a button he wants, but one neighboring button (left or right, as specified in input).We have a sequence of characters he has typed and we want to find the original message.", "input_spec": "First line of the input contains one letter describing direction of shifting ('L' or 'R' respectively for left or right). Second line contains a sequence of characters written by Mole. The size of this sequence will be no more than 100. Sequence contains only symbols that appear on Mole's keyboard. It doesn't contain spaces as there is no space on Mole's keyboard. It is guaranteed that even though Mole hands are moved, he is still pressing buttons on keyboard and not hitting outside it.", "output_spec": "Print a line that contains the original message.", "sample_inputs": ["R\ns;;upimrrfod;pbr"], "sample_outputs": ["allyouneedislove"], "notes": null}, "src_uid": "df49c0c257903516767fdb8ac9c2bfd6"}
{"nl": {"description": "A string $$$s$$$ of length $$$n$$$ can be encrypted by the following algorithm:  iterate over all divisors of $$$n$$$ in decreasing order (i.e. from $$$n$$$ to $$$1$$$),  for each divisor $$$d$$$, reverse the substring $$$s[1 \\dots d]$$$ (i.e. the substring which starts at position $$$1$$$ and ends at position $$$d$$$). For example, the above algorithm applied to the string $$$s$$$=\"codeforces\" leads to the following changes: \"codeforces\" $$$\\to$$$ \"secrofedoc\" $$$\\to$$$ \"orcesfedoc\" $$$\\to$$$ \"rocesfedoc\" $$$\\to$$$ \"rocesfedoc\" (obviously, the last reverse operation doesn't change the string because $$$d=1$$$).You are given the encrypted string $$$t$$$. Your task is to decrypt this string, i.e., to find a string $$$s$$$ such that the above algorithm results in string $$$t$$$. It can be proven that this string $$$s$$$ always exists and is unique.", "input_spec": "The first line of input consists of a single integer $$$n$$$ ($$$1 \\le n \\le 100$$$) \u2014 the length of the string $$$t$$$. The second line of input consists of the string $$$t$$$. The length of $$$t$$$ is $$$n$$$, and it consists only of lowercase Latin letters.", "output_spec": "Print a string $$$s$$$ such that the above algorithm results in $$$t$$$.", "sample_inputs": ["10\nrocesfedoc", "16\nplmaetwoxesisiht", "1\nz"], "sample_outputs": ["codeforces", "thisisexampletwo", "z"], "notes": "NoteThe first example is described in the problem statement."}, "src_uid": "1b0b2ee44c63cb0634cb63f2ad65cdd3"}
{"nl": {"description": "The only difference between easy and hard versions is constraints.Polycarp loves to listen to music, so he never leaves the player, even on the way home from the university. Polycarp overcomes the distance from the university to the house in exactly $$$T$$$ minutes.In the player, Polycarp stores $$$n$$$ songs, each of which is characterized by two parameters: $$$t_i$$$ and $$$g_i$$$, where $$$t_i$$$ is the length of the song in minutes ($$$1 \\le t_i \\le 15$$$), $$$g_i$$$ is its genre ($$$1 \\le g_i \\le 3$$$).Polycarp wants to create such a playlist so that he can listen to music all the time on the way from the university to his home, and at the time of his arrival home, the playlist is over. Polycarp never interrupts songs and always listens to them from beginning to end. Thus, if he started listening to the $$$i$$$-th song, he would spend exactly $$$t_i$$$ minutes on its listening. Polycarp also does not like when two songs of the same genre play in a row (i.e. successively/adjacently) or when the songs in his playlist are repeated.Help Polycarpus count the number of different sequences of songs (their order matters), the total duration is exactly $$$T$$$, such that there are no two consecutive songs of the same genre in them and all the songs in the playlist are different.", "input_spec": "The first line of the input contains two integers $$$n$$$ and $$$T$$$ ($$$1 \\le n \\le 15, 1 \\le T \\le 225$$$) \u2014 the number of songs in the player and the required total duration, respectively. Next, the $$$n$$$ lines contain descriptions of songs: the $$$i$$$-th line contains two integers $$$t_i$$$ and $$$g_i$$$ ($$$1 \\le t_i \\le 15, 1 \\le g_i \\le 3$$$) \u2014 the duration of the $$$i$$$-th song and its genre, respectively.", "output_spec": "Output one integer \u2014 the number of different sequences of songs, the total length of exactly $$$T$$$, such that there are no two consecutive songs of the same genre in them and all the songs in the playlist are different. Since the answer may be huge, output it modulo $$$10^9 + 7$$$ (that is, the remainder when dividing the quantity by $$$10^9 + 7$$$).", "sample_inputs": ["3 3\n1 1\n1 2\n1 3", "3 3\n1 1\n1 1\n1 3", "4 10\n5 3\n2 1\n3 2\n5 1"], "sample_outputs": ["6", "2", "10"], "notes": "NoteIn the first example, Polycarp can make any of the $$$6$$$ possible playlist by rearranging the available songs: $$$[1, 2, 3]$$$, $$$[1, 3, 2]$$$, $$$[2, 1, 3]$$$, $$$[2, 3, 1]$$$, $$$[3, 1, 2]$$$ and $$$[3, 2, 1]$$$ (indices of the songs are given).In the second example, the first and second songs cannot go in succession (since they have the same genre). Thus, Polycarp can create a playlist in one of $$$2$$$ possible ways: $$$[1, 3, 2]$$$ and $$$[2, 3, 1]$$$ (indices of the songs are given).In the third example, Polycarp can make the following playlists: $$$[1, 2, 3]$$$, $$$[1, 3, 2]$$$, $$$[2, 1, 3]$$$, $$$[2, 3, 1]$$$, $$$[3, 1, 2]$$$, $$$[3, 2, 1]$$$, $$$[1, 4]$$$, $$$[4, 1]$$$, $$$[2, 3, 4]$$$ and $$$[4, 3, 2]$$$ (indices of the songs are given)."}, "src_uid": "ac2a37ff4c7e89a345b189e4891bbf56"}
{"nl": {"description": "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": "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": "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": "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": "On the way to Rio de Janeiro Ostap kills time playing with a grasshopper he took with him in a special box. Ostap builds a line of length n such that some cells of this line are empty and some contain obstacles. Then, he places his grasshopper to one of the empty cells and a small insect in another empty cell. The grasshopper wants to eat the insect.Ostap knows that grasshopper is able to jump to any empty cell that is exactly k cells away from the current (to the left or to the right). Note that it doesn't matter whether intermediate cells are empty or not as the grasshopper makes a jump over them. For example, if k\u2009=\u20091 the grasshopper can jump to a neighboring cell only, and if k\u2009=\u20092 the grasshopper can jump over a single cell.Your goal is to determine whether there is a sequence of jumps such that grasshopper will get from his initial position to the cell with an insect.", "input_spec": "The first line of the input contains two integers n and k (2\u2009\u2264\u2009n\u2009\u2264\u2009100, 1\u2009\u2264\u2009k\u2009\u2264\u2009n\u2009-\u20091)\u00a0\u2014 the number of cells in the line and the length of one grasshopper's jump. The second line contains a string of length n consisting of characters '.', '#', 'G' and 'T'. Character '.' means that the corresponding cell is empty, character '#' means that the corresponding cell contains an obstacle and grasshopper can't jump there. Character 'G' means that the grasshopper starts at this position and, finally, 'T' means that the target insect is located at this cell. It's guaranteed that characters 'G' and 'T' appear in this line exactly once.", "output_spec": "If there exists a sequence of jumps (each jump of length k), such that the grasshopper can get from his initial position to the cell with the insect, print \"YES\" (without quotes) in the only line of the input. Otherwise, print \"NO\" (without quotes).", "sample_inputs": ["5 2\n#G#T#", "6 1\nT....G", "7 3\nT..#..G", "6 2\n..GT.."], "sample_outputs": ["YES", "YES", "NO", "NO"], "notes": "NoteIn the first sample, the grasshopper can make one jump to the right in order to get from cell 2 to cell 4.In the second sample, the grasshopper is only able to jump to neighboring cells but the way to the insect is free\u00a0\u2014 he can get there by jumping left 5 times.In the third sample, the grasshopper can't make a single jump.In the fourth sample, the grasshopper can only jump to the cells with odd indices, thus he won't be able to reach the insect."}, "src_uid": "189a9b5ce669bdb04b9d371d74a5dd41"}
{"nl": {"description": "Let's introduce some definitions that will be needed later.Let $$$prime(x)$$$ be the set of prime divisors of $$$x$$$. For example, $$$prime(140) = \\{ 2, 5, 7 \\}$$$, $$$prime(169) = \\{ 13 \\}$$$.Let $$$g(x, p)$$$ be the maximum possible integer $$$p^k$$$ where $$$k$$$ is an integer such that $$$x$$$ is divisible by $$$p^k$$$. For example:  $$$g(45, 3) = 9$$$ ($$$45$$$ is divisible by $$$3^2=9$$$ but not divisible by $$$3^3=27$$$),  $$$g(63, 7) = 7$$$ ($$$63$$$ is divisible by $$$7^1=7$$$ but not divisible by $$$7^2=49$$$). Let $$$f(x, y)$$$ be the product of $$$g(y, p)$$$ for all $$$p$$$ in $$$prime(x)$$$. For example:  $$$f(30, 70) = g(70, 2) \\cdot g(70, 3) \\cdot g(70, 5) = 2^1 \\cdot 3^0 \\cdot 5^1 = 10$$$,  $$$f(525, 63) = g(63, 3) \\cdot g(63, 5) \\cdot g(63, 7) = 3^2 \\cdot 5^0 \\cdot 7^1 = 63$$$. You have integers $$$x$$$ and $$$n$$$. Calculate $$$f(x, 1) \\cdot f(x, 2) \\cdot \\ldots \\cdot f(x, n) \\bmod{(10^{9} + 7)}$$$.", "input_spec": "The only line contains integers $$$x$$$ and $$$n$$$ ($$$2 \\le x \\le 10^{9}$$$, $$$1 \\le n \\le 10^{18}$$$)\u00a0\u2014 the numbers used in formula.", "output_spec": "Print the answer.", "sample_inputs": ["10 2", "20190929 1605", "947 987654321987654321"], "sample_outputs": ["2", "363165664", "593574252"], "notes": "NoteIn the first example, $$$f(10, 1) = g(1, 2) \\cdot g(1, 5) = 1$$$, $$$f(10, 2) = g(2, 2) \\cdot g(2, 5) = 2$$$.In the second example, actual value of formula is approximately $$$1.597 \\cdot 10^{171}$$$. Make sure you print the answer modulo $$$(10^{9} + 7)$$$.In the third example, be careful about overflow issue."}, "src_uid": "04610fbaa746c083dda30e21fa6e1a0c"}
{"nl": {"description": "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": "You are given a rooted tree. Let's denote d(x) as depth of node x: depth of the root is 1, depth of any other node x is d(y)\u2009+\u20091, where y is a parent of x.The tree has the following property: every node x with d(x)\u2009=\u2009i has exactly ai children. Maximum possible depth of a node is n, and an\u2009=\u20090.We define fk as the number of unordered pairs of vertices in the tree such that the number of edges on the simple path between them is equal to k.Calculate fk modulo 109\u2009+\u20097 for every 1\u2009\u2264\u2009k\u2009\u2264\u20092n\u2009-\u20092.", "input_spec": "The first line of input contains an integer n (2\u2009\u2009\u2264\u2009\u2009n\u2009\u2009\u2264\u2009\u20095\u2009000) \u2014 the maximum depth of a node. The second line of input contains n\u2009-\u20091 integers a1,\u2009\u2009a2,\u2009\u2009...,\u2009\u2009an\u2009-\u20091 (2\u2009\u2264\u2009\u2009ai\u2009\u2009\u2264\u2009109), where ai is the number of children of every node x such that d(x)\u2009=\u2009i. Since an\u2009=\u20090, it is not given in the input.", "output_spec": "Print 2n\u2009-\u20092 numbers. The k-th of these numbers must be equal to fk modulo 109\u2009+\u20097.", "sample_inputs": ["4\n2 2 2", "3\n2 3"], "sample_outputs": ["14 19 20 20 16 16", "8 13 6 9"], "notes": "NoteThis the tree from the first sample:   "}, "src_uid": "3b86dfd0d077bc857ae3de70f026a409"}
{"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": "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$$$-th order rhombus.", "sample_inputs": ["1", "2", "3"], "sample_outputs": ["1", "5", "13"], "notes": "NoteImages of rhombus corresponding to the examples are given in the statement."}, "src_uid": "758d342c1badde6d0b4db81285be780c"}
{"nl": {"description": "Eighth-grader Vova is on duty today in the class. After classes, he went into the office to wash the board, and found on it the number n. He asked what is this number and the teacher of mathematics Inna Petrovna answered Vova that n is the answer to the arithmetic task for first-graders. In the textbook, a certain positive integer x was given. The task was to add x to the sum of the digits of the number x written in decimal numeral system.Since the number n on the board was small, Vova quickly guessed which x could be in the textbook. Now he wants to get a program which will search for arbitrary values of the number n for all suitable values of x or determine that such x does not exist. Write such a program for Vova.", "input_spec": "The first line contains integer n (1\u2009\u2264\u2009n\u2009\u2264\u2009109).", "output_spec": "In the first line print one integer k\u00a0\u2014 number of different values of x satisfying the condition.  In next k lines print these values in ascending order.", "sample_inputs": ["21", "20"], "sample_outputs": ["1\n15", "0"], "notes": "NoteIn the first test case x\u2009=\u200915 there is only one variant: 15\u2009+\u20091\u2009+\u20095\u2009=\u200921.In the second test case there are no such x."}, "src_uid": "ae20ae2a16273a0d379932d6e973f878"}
{"nl": {"description": "You are given two positive integers $$$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$$$ and NO if you can't.", "sample_inputs": ["3 3", "7 4", "2 8", "34 69", "8935891487501725 71487131900013807"], "sample_outputs": ["YES", "NO", "NO", "YES", "YES"], "notes": "NoteIn the first example, you don't even need to do anything.The fourth example is described in the statement."}, "src_uid": "9f39a3c160087beb0efab2e3cb510e89"}
{"nl": {"description": "The final match of the Berland Football Cup has been held recently. The referee has shown $$$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": "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": "Polycarp invited all his friends to the tea party to celebrate the holiday. He has n cups, one for each of his n friends, with volumes a1,\u2009a2,\u2009...,\u2009an. His teapot stores w milliliters of tea (w\u2009\u2264\u2009a1\u2009+\u2009a2\u2009+\u2009...\u2009+\u2009an). Polycarp wants to pour tea in cups in such a way that:  Every cup will contain tea for at least half of its volume  Every cup will contain integer number of milliliters of tea  All the tea from the teapot will be poured into cups  All friends will be satisfied. Friend with cup i won't be satisfied, if there exists such cup j that cup i contains less tea than cup j but ai\u2009>\u2009aj.For each cup output how many milliliters of tea should be poured in it. If it's impossible to pour all the tea and satisfy all conditions then output -1.", "input_spec": "The first line contains two integer numbers n and w (1\u2009\u2264\u2009n\u2009\u2264\u2009100, ). The second line contains n numbers a1,\u2009a2,\u2009...,\u2009an (1\u2009\u2264\u2009ai\u2009\u2264\u2009100).", "output_spec": "Output how many milliliters of tea every cup should contain. If there are multiple answers, print any of them. If it's impossible to pour all the tea and satisfy all conditions then output -1.", "sample_inputs": ["2 10\n8 7", "4 4\n1 1 1 1", "3 10\n9 8 10"], "sample_outputs": ["6 4", "1 1 1 1", "-1"], "notes": "NoteIn the third example you should pour to the first cup at least 5 milliliters, to the second one at least 4, to the third one at least 5. It sums up to 14, which is greater than 10 milliliters available."}, "src_uid": "5d3bb9e03f4c5c8ecb6233bd5f90f3a3"}
{"nl": {"description": "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$$$ bourles after the evening.In the second example test, it's optimal not to take any action."}, "src_uid": "42f25d492bddc12d3d89d39315d63cb9"}
{"nl": {"description": "Bob is decorating his kitchen, more precisely, the floor. He has found a prime candidate for the tiles he will use. They come in a simple form factor\u00a0\u2014\u00a0a square tile that is diagonally split into white and black part as depicted in the figure below.  The dimension of this tile is perfect for this kitchen, as he will need exactly $$$w \\times h$$$ tiles without any scraps. That is, the width of the kitchen is $$$w$$$ tiles, and the height is $$$h$$$ tiles. As each tile can be rotated in one of four ways, he still needs to decide on how exactly he will tile the floor. There is a single aesthetic criterion that he wants to fulfil: two adjacent tiles must not share a colour on the edge\u00a0\u2014\u00a0i.e. one of the tiles must have a white colour on the shared border, and the second one must be black.    The picture on the left shows one valid tiling of a $$$3 \\times 2$$$ kitchen. The picture on the right shows an invalid arrangement, as the bottom two tiles touch with their white parts. Find the number of possible tilings. As this number may be large, output its remainder when divided by $$$998244353$$$ (a prime number). ", "input_spec": "The only line contains two space separated integers $$$w$$$, $$$h$$$\u00a0($$$1 \\leq w,h \\leq 1\\,000$$$)\u00a0\u2014\u00a0the width and height of the kitchen, measured in tiles.", "output_spec": "Output a single integer $$$n$$$\u00a0\u2014\u00a0the remainder of the number of tilings when divided by $$$998244353$$$.", "sample_inputs": ["2 2", "2 4"], "sample_outputs": ["16", "64"], "notes": null}, "src_uid": "8b2a9ae21740c89079a6011a30cd6aee"}
{"nl": {"description": "zscoder wants to generate an input file for some programming competition problem.His input is a string consisting of n letters 'a'. He is too lazy to write a generator so he will manually generate the input in a text editor.Initially, the text editor is empty. It takes him x seconds to insert or delete a letter 'a' from the text file and y seconds to copy the contents of the entire text file, and duplicate it.zscoder wants to find the minimum amount of time needed for him to create the input file of exactly n letters 'a'. Help him to determine the amount of time needed to generate the input.", "input_spec": "The only line contains three integers n, x and y (1\u2009\u2264\u2009n\u2009\u2264\u2009107, 1\u2009\u2264\u2009x,\u2009y\u2009\u2264\u2009109) \u2014 the number of letters 'a' in the input file and the parameters from the problem statement.", "output_spec": "Print the only integer t \u2014 the minimum amount of time needed to generate the input file.", "sample_inputs": ["8 1 1", "8 1 10"], "sample_outputs": ["4", "8"], "notes": null}, "src_uid": "0f270af00be2a523515d5e7bd66800f6"}
{"nl": {"description": "Given an integer $$$x$$$, find 2 integers $$$a$$$ and $$$b$$$ such that:   $$$1 \\le a,b \\le x$$$  $$$b$$$ divides $$$a$$$ ($$$a$$$ is divisible by $$$b$$$).  $$$a \\cdot b>x$$$.  $$$\\frac{a}{b}<x$$$. ", "input_spec": "The only line contains the integer $$$x$$$ $$$(1 \\le x \\le 100)$$$.", "output_spec": "You should output two integers $$$a$$$ and $$$b$$$, satisfying the given conditions, separated by a space. If no pair of integers satisfy the conditions above, print \"-1\" (without quotes).", "sample_inputs": ["10", "1"], "sample_outputs": ["6 3", "-1"], "notes": null}, "src_uid": "883f67177474d23d7a320d9dbfa70dd3"}
{"nl": {"description": "Alice has a lovely piece of cloth. It has the shape of a square with a side of length $$$a$$$ centimeters. Bob also wants such piece of cloth. He would prefer a square with a side of length $$$b$$$ centimeters (where $$$b < a$$$). Alice wanted to make Bob happy, so she cut the needed square out of the corner of her piece and gave it to Bob. Now she is left with an ugly L shaped cloth (see pictures below).Alice would like to know whether the area of her cloth expressed in square centimeters is prime. Could you help her to determine it?", "input_spec": "The first line contains a number $$$t$$$\u00a0($$$1 \\leq t \\leq 5$$$)\u00a0\u2014 the number of test cases. Each of the next $$$t$$$ lines describes the $$$i$$$-th test case. It contains two integers $$$a$$$ and $$$b~(1 \\leq b < a \\leq 10^{11})$$$\u00a0\u2014 the side length of Alice's square and the side length of the square that Bob wants.", "output_spec": "Print $$$t$$$ lines, where the $$$i$$$-th line is the answer to the $$$i$$$-th test case. Print \"YES\" (without quotes) if the area of the remaining piece of cloth is prime, otherwise print \"NO\". You can print each letter in an arbitrary case (upper or lower).", "sample_inputs": ["4\n6 5\n16 13\n61690850361 24777622630\n34 33"], "sample_outputs": ["YES\nNO\nNO\nYES"], "notes": "NoteThe figure below depicts the first test case. The blue part corresponds to the piece which belongs to Bob, and the red part is the piece that Alice keeps for herself. The area of the red part is $$$6^2 - 5^2 = 36 - 25 = 11$$$, which is prime, so the answer is \"YES\".  In the second case, the area is $$$16^2 - 13^2 = 87$$$, which is divisible by $$$3$$$.  In the third case, the area of the remaining piece is $$$61690850361^2 - 24777622630^2 = 3191830435068605713421$$$. This number is not prime because $$$3191830435068605713421 = 36913227731 \\cdot 86468472991 $$$.In the last case, the area is $$$34^2 - 33^2 = 67$$$."}, "src_uid": "5a052e4e6c64333d94c83df890b1183c"}
{"nl": {"description": "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": "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": "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": "The king is left alone on the chessboard. In spite of this loneliness, he doesn't lose heart, because he has business of national importance. For example, he has to pay an official visit to square t. As the king is not in habit of wasting his time, he wants to get from his current position s to square t in the least number of moves. Help him to do this.  In one move the king can get to the square that has a common side or a common vertex with the square the king is currently in (generally there are 8 different squares he can move to).", "input_spec": "The first line contains the chessboard coordinates of square s, the second line \u2014 of square t. Chessboard coordinates consist of two characters, the first one is a lowercase Latin letter (from a to h), the second one is a digit from 1 to 8.", "output_spec": "In the first line print n \u2014 minimum number of the king's moves. Then in n lines print the moves themselves. Each move is described with one of the 8: L, R, U, D, LU, LD, RU or RD.  L, R, U, D stand respectively for moves left, right, up and down (according to the picture), and 2-letter combinations stand for diagonal moves. If the answer is not unique, print any of them. ", "sample_inputs": ["a8\nh1"], "sample_outputs": ["7\nRD\nRD\nRD\nRD\nRD\nRD\nRD"], "notes": null}, "src_uid": "d25d454702b7755297a7a8e1f6f36ab9"}
{"nl": {"description": "Dreamoon is standing at the position 0 on a number line. Drazil is sending a list of commands through Wi-Fi to Dreamoon's smartphone and Dreamoon follows them.Each command is one of the following two types:   Go 1 unit towards the positive direction, denoted as '+'  Go 1 unit towards the negative direction, denoted as '-' But the Wi-Fi condition is so poor that Dreamoon's smartphone reports some of the commands can't be recognized and Dreamoon knows that some of them might even be wrong though successfully recognized. Dreamoon decides to follow every recognized command and toss a fair coin to decide those unrecognized ones (that means, he moves to the 1 unit to the negative or positive direction with the same probability 0.5). You are given an original list of commands sent by Drazil and list received by Dreamoon. What is the probability that Dreamoon ends in the position originally supposed to be final by Drazil's commands?", "input_spec": "The first line contains a string s1 \u2014 the commands Drazil sends to Dreamoon, this string consists of only the characters in the set {'+', '-'}.  The second line contains a string s2 \u2014 the commands Dreamoon's smartphone recognizes, this string consists of only the characters in the set {'+', '-', '?'}. '?' denotes an unrecognized command. Lengths of two strings are equal and do not exceed 10.", "output_spec": "Output a single real number corresponding to the probability. The answer will be considered correct if its relative or absolute error doesn't exceed 10\u2009-\u20099.", "sample_inputs": ["++-+-\n+-+-+", "+-+-\n+-??", "+++\n??-"], "sample_outputs": ["1.000000000000", "0.500000000000", "0.000000000000"], "notes": "NoteFor the first sample, both s1 and s2 will lead Dreamoon to finish at the same position \u2009+\u20091. For the second sample, s1 will lead Dreamoon to finish at position 0, while there are four possibilites for s2: {\"+-++\", \"+-+-\", \"+--+\", \"+---\"} with ending position {+2, 0, 0, -2} respectively. So there are 2 correct cases out of 4, so the probability of finishing at the correct position is 0.5. For the third sample, s2 could only lead us to finish at positions {+1, -1, -3}, so the probability to finish at the correct position \u2009+\u20093 is 0."}, "src_uid": "f7f68a15cfd33f641132fac265bc5299"}
{"nl": {"description": "There is a sequence of colorful stones. The color of each stone is one of red, green, or blue. You are given a string s. The i-th (1-based) character of s represents the color of the i-th stone. If the character is \"R\", \"G\", or \"B\", the color of the corresponding stone is red, green, or blue, respectively.Initially Squirrel Liss is standing on the first stone. You perform instructions one or more times.Each instruction is one of the three types: \"RED\", \"GREEN\", or \"BLUE\". After an instruction c, if Liss is standing on a stone whose colors is c, Liss will move one stone forward, else she will not move.You are given a string t. The number of instructions is equal to the length of t, and the i-th character of t represents the i-th instruction.Calculate the final position of Liss (the number of the stone she is going to stand on in the end) after performing all the instructions, and print its 1-based position. It is guaranteed that Liss don't move out of the sequence.", "input_spec": "The input contains two lines. The first line contains the string s (1\u2009\u2264\u2009|s|\u2009\u2264\u200950). The second line contains the string t (1\u2009\u2264\u2009|t|\u2009\u2264\u200950). The characters of each string will be one of \"R\", \"G\", or \"B\". It is guaranteed that Liss don't move out of the sequence.", "output_spec": "Print the final 1-based position of Liss in a single line.", "sample_inputs": ["RGB\nRRR", "RRRBGBRBBB\nBBBRR", "BRRBGBRGRBGRGRRGGBGBGBRGBRGRGGGRBRRRBRBBBGRRRGGBBB\nBBRBGGRGRGBBBRBGRBRBBBBRBRRRBGBBGBBRRBBGGRBRRBRGRB"], "sample_outputs": ["2", "3", "15"], "notes": null}, "src_uid": "f5a907d6d35390b1fb11c8ce247d0252"}
{"nl": {"description": "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": "Nicholas has an array a that contains n distinct integers from 1 to n. In other words, Nicholas has a permutation of size n.Nicholas want the minimum element (integer 1) and the maximum element (integer n) to be as far as possible from each other. He wants to perform exactly one swap in order to maximize the distance between the minimum and the maximum elements. The distance between two elements is considered to be equal to the absolute difference between their positions.", "input_spec": "The first line of the input contains a single integer n (2\u2009\u2264\u2009n\u2009\u2264\u2009100)\u00a0\u2014 the size of the permutation. The second line of the input contains n distinct integers a1,\u2009a2,\u2009...,\u2009an (1\u2009\u2264\u2009ai\u2009\u2264\u2009n), where ai is equal to the element at the i-th position.", "output_spec": "Print a single integer\u00a0\u2014 the maximum possible distance between the minimum and the maximum elements Nicholas can achieve by performing exactly one swap.", "sample_inputs": ["5\n4 5 1 3 2", "7\n1 6 5 3 4 7 2", "6\n6 5 4 3 2 1"], "sample_outputs": ["3", "6", "5"], "notes": "NoteIn the first sample, one may obtain the optimal answer by swapping elements 1 and 2.In the second sample, the minimum and the maximum elements will be located in the opposite ends of the array if we swap 7 and 2.In the third sample, the distance between the minimum and the maximum elements is already maximum possible, so we just perform some unnecessary swap, for example, one can swap 5 and 2."}, "src_uid": "1d2b81ce842f8c97656d96bddff4e8b4"}
{"nl": {"description": "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": "Vasya likes everything infinite. Now he is studying the properties of a sequence s, such that its first element is equal to a (s1\u2009=\u2009a), and the difference between any two neighbouring elements is equal to c (si\u2009-\u2009si\u2009-\u20091\u2009=\u2009c). In particular, Vasya wonders if his favourite integer b appears in this sequence, that is, there exists a positive integer i, such that si\u2009=\u2009b. Of course, you are the person he asks for a help.", "input_spec": "The first line of the input contain three integers a, b and c (\u2009-\u2009109\u2009\u2264\u2009a,\u2009b,\u2009c\u2009\u2264\u2009109)\u00a0\u2014 the first element of the sequence, Vasya's favorite number and the difference between any two neighbouring elements of the sequence, respectively.", "output_spec": "If b appears in the sequence s print \"YES\" (without quotes), otherwise print \"NO\" (without quotes).", "sample_inputs": ["1 7 3", "10 10 0", "1 -4 5", "0 60 50"], "sample_outputs": ["YES", "YES", "NO", "NO"], "notes": "NoteIn the first sample, the sequence starts from integers 1, 4, 7, so 7 is its element.In the second sample, the favorite integer of Vasya is equal to the first element of the sequence.In the third sample all elements of the sequence are greater than Vasya's favorite integer.In the fourth sample, the sequence starts from 0, 50, 100, and all the following elements are greater than Vasya's favorite integer."}, "src_uid": "9edf42c20ddf22a251b84553d7305a7d"}
{"nl": {"description": "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": "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": "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": "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$$$. If there are several possible such pairs, you can print any.", "sample_inputs": ["2", "6", "4", "1"], "sample_outputs": ["1 2", "2 3", "1 4", "1 1"], "notes": null}, "src_uid": "e504a04cefef3da093573f9df711bcea"}
{"nl": {"description": "Let's consider a table consisting of n rows and n columns. The cell located at the intersection of i-th row and j-th column contains number i\u2009\u00d7\u2009j. The rows and columns are numbered starting from 1.You are given a positive integer x. Your task is to count the number of cells in a table that contain number x.", "input_spec": "The single line contains numbers n and x (1\u2009\u2264\u2009n\u2009\u2264\u2009105, 1\u2009\u2264\u2009x\u2009\u2264\u2009109) \u2014 the size of the table and the number that we are looking for in the table.", "output_spec": "Print a single number: the number of times x occurs in the table.", "sample_inputs": ["10 5", "6 12", "5 13"], "sample_outputs": ["2", "4", "0"], "notes": "NoteA table for the second sample test is given below. The occurrences of number 12 are marked bold.   "}, "src_uid": "c4b139eadca94201596f1305b2f76496"}
{"nl": {"description": "Let's define a function $$$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$$$."}, "src_uid": "b2d59b1279d891dba9372a52364bced2"}
{"nl": {"description": "During the break the schoolchildren, boys and girls, formed a queue of n people in the canteen. Initially the children stood in the order they entered the canteen. However, after a while the boys started feeling awkward for standing in front of the girls in the queue and they started letting the girls move forward each second. Let's describe the process more precisely. Let's say that the positions in the queue are sequentially numbered by integers from 1 to n, at that the person in the position number 1 is served first. Then, if at time x a boy stands on the i-th position and a girl stands on the (i\u2009+\u20091)-th position, then at time x\u2009+\u20091 the i-th position will have a girl and the (i\u2009+\u20091)-th position will have a boy. The time is given in seconds.You've got the initial position of the children, at the initial moment of time. Determine the way the queue is going to look after t seconds.", "input_spec": "The first line contains two integers n and t (1\u2009\u2264\u2009n,\u2009t\u2009\u2264\u200950), which represent the number of children in the queue and the time after which the queue will transform into the arrangement you need to find.  The next line contains string s, which represents the schoolchildren's initial arrangement. If the i-th position in the queue contains a boy, then the i-th character of string s equals \"B\", otherwise the i-th character equals \"G\".", "output_spec": "Print string a, which describes the arrangement after t seconds. If the i-th position has a boy after the needed time, then the i-th character a must equal \"B\", otherwise it must equal \"G\".", "sample_inputs": ["5 1\nBGGBG", "5 2\nBGGBG", "4 1\nGGGB"], "sample_outputs": ["GBGGB", "GGBGB", "GGGB"], "notes": null}, "src_uid": "964ed316c6e6715120039b0219cc653a"}
{"nl": {"description": "Kavi has $$$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$$$.", "sample_inputs": ["1", "2", "3", "100"], "sample_outputs": ["1", "3", "6", "688750769"], "notes": "NoteThe good pairings for the second example are:   In the third example, the good pairings are:   "}, "src_uid": "09be46206a151c237dc9912df7e0f057"}
{"nl": {"description": "Recently a Golden Circle of Beetlovers was found in Byteland. It is a circle route going through $$$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$$$."}, "src_uid": "5bb4adff1b332f43144047955eefba0c"}
{"nl": {"description": "In order to make the \"Sea Battle\" game more interesting, Boris decided to add a new ship type to it. The ship consists of two rectangles. The first rectangle has a width of $$$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": "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": "Buses run between the cities A and B, the first one is at 05:00 AM and the last one departs not later than at 11:59 PM. A bus from the city A departs every a minutes and arrives to the city B in a ta minutes, and a bus from the city B departs every b minutes and arrives to the city A in a tb minutes.The driver Simion wants to make his job diverse, so he counts the buses going towards him. Simion doesn't count the buses he meet at the start and finish.You know the time when Simion departed from the city A to the city B. Calculate the number of buses Simion will meet to be sure in his counting.", "input_spec": "The first line contains two integers a,\u2009ta (1\u2009\u2264\u2009a,\u2009ta\u2009\u2264\u2009120) \u2014 the frequency of the buses from the city A to the city B and the travel time. Both values are given in minutes. The second line contains two integers b,\u2009tb (1\u2009\u2264\u2009b,\u2009tb\u2009\u2264\u2009120) \u2014 the frequency of the buses from the city B to the city A and the travel time. Both values are given in minutes. The last line contains the departure time of Simion from the city A in the format hh:mm. It is guaranteed that there are a bus from the city A at that time. Note that the hours and the minutes are given with exactly two digits.", "output_spec": "Print the only integer z \u2014 the number of buses Simion will meet on the way. Note that you should not count the encounters in cities A and B.", "sample_inputs": ["10 30\n10 35\n05:20", "60 120\n24 100\n13:00"], "sample_outputs": ["5", "9"], "notes": "NoteIn the first example Simion departs form the city A at 05:20 AM and arrives to the city B at 05:50 AM. He will meet the first 5 buses from the city B that departed in the period [05:00 AM - 05:40 AM]. Also Simion will meet a bus in the city B at 05:50 AM, but he will not count it.Also note that the first encounter will be between 05:26 AM and 05:27 AM (if we suggest that the buses are go with the sustained speed)."}, "src_uid": "1c4cf1c3cb464a483511a8a61f8685a7"}
{"nl": {"description": "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": "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": "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": "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": "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": "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": "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": "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": "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": "There are n stones on the table in a row, each of them can be red, green or blue. Count the minimum number of stones to take from the table so that any two neighboring stones had different colors. Stones in a row are considered neighboring if there are no other stones between them.", "input_spec": "The first line contains integer n (1\u2009\u2264\u2009n\u2009\u2264\u200950) \u2014 the number of stones on the table.  The next line contains string s, which represents the colors of the stones. We'll consider the stones in the row numbered from 1 to n from left to right. Then the i-th character s equals \"R\", if the i-th stone is red, \"G\", if it's green and \"B\", if it's blue.", "output_spec": "Print a single integer \u2014 the answer to the problem.", "sample_inputs": ["3\nRRG", "5\nRRRRR", "4\nBRBG"], "sample_outputs": ["1", "4", "0"], "notes": null}, "src_uid": "d561436e2ddc9074b98ebbe49b9e27b8"}
{"nl": {"description": "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": "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": "One rainy gloomy evening when all modules hid in the nearby cafes to drink hot energetic cocktails, the Hexadecimal virus decided to fly over the Mainframe to look for a Great Idea. And she has found one!Why not make her own Codeforces, with blackjack and other really cool stuff? Many people will surely be willing to visit this splendid shrine of high culture.In Mainframe a standard pack of 52 cards is used to play blackjack. The pack contains cards of 13 values: 2, 3, 4, 5, 6, 7, 8, 9, 10, jacks, queens, kings and aces. Each value also exists in one of four suits: hearts, diamonds, clubs and spades. Also, each card earns some value in points assigned to it: cards with value from two to ten earn from 2 to 10 points, correspondingly. An ace can either earn 1 or 11, whatever the player wishes. The picture cards (king, queen and jack) earn 10 points. The number of points a card earns does not depend on the suit. The rules of the game are very simple. The player gets two cards, if the sum of points of those cards equals n, then the player wins, otherwise the player loses.The player has already got the first card, it's the queen of spades. To evaluate chances for victory, you should determine how many ways there are to get the second card so that the sum of points exactly equals n.", "input_spec": "The only line contains n (1\u2009\u2264\u2009n\u2009\u2264\u200925) \u2014 the required sum of points.", "output_spec": "Print the numbers of ways to get the second card in the required way if the first card is the queen of spades.", "sample_inputs": ["12", "20", "10"], "sample_outputs": ["4", "15", "0"], "notes": "NoteIn the first sample only four two's of different suits can earn the required sum of points.In the second sample we can use all tens, jacks, queens and kings; overall it's 15 cards, as the queen of spades (as any other card) is only present once in the pack of cards and it's already in use.In the third sample there is no card, that would add a zero to the current ten points."}, "src_uid": "5802f52caff6015f21b80872274ab16c"}
{"nl": {"description": "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": "HQ9+ is a joke programming language which has only four one-character instructions: \"H\" prints \"Hello, World!\", \"Q\" prints the source code of the program itself, \"9\" prints the lyrics of \"99 Bottles of Beer\" song,  \"+\" increments the value stored in the internal accumulator.Instructions \"H\" and \"Q\" are case-sensitive and must be uppercase. The characters of the program which are not instructions are ignored.You are given a program written in HQ9+. You have to figure out whether executing this program will produce any output.", "input_spec": "The input will consist of a single line p which will give a program in HQ9+. String p will contain between 1 and 100 characters, inclusive. ASCII-code of each character of p will be between 33 (exclamation mark) and 126 (tilde), inclusive.", "output_spec": "Output \"YES\", if executing the program will produce any output, and \"NO\" otherwise.", "sample_inputs": ["Hi!", "Codeforces"], "sample_outputs": ["YES", "NO"], "notes": "NoteIn the first case the program contains only one instruction \u2014 \"H\", which prints \"Hello, World!\".In the second case none of the program characters are language instructions."}, "src_uid": "1baf894c1c7d5aeea01129c7900d3c12"}
{"nl": {"description": "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": "Polycarp has $$$n$$$ coins, the value of the $$$i$$$-th coin is $$$a_i$$$. Polycarp wants to distribute all the coins between his pockets, but he cannot put two coins with the same value into the same pocket.For example, if Polycarp has got six coins represented as an array $$$a = [1, 2, 4, 3, 3, 2]$$$, he can distribute the coins into two pockets as follows: $$$[1, 2, 3], [2, 3, 4]$$$.Polycarp wants to distribute all the coins with the minimum number of used pockets. Help him to do that.", "input_spec": "The first line of the input contains one integer $$$n$$$ ($$$1 \\le n \\le 100$$$) \u2014 the number of coins. The second line of the input contains $$$n$$$ integers $$$a_1, a_2, \\dots, a_n$$$ ($$$1 \\le a_i \\le 100$$$) \u2014 values of coins.", "output_spec": "Print only one integer \u2014 the minimum number of pockets Polycarp needs to distribute all the coins so no two coins with the same value are put into the same pocket.", "sample_inputs": ["6\n1 2 4 3 3 2", "1\n100"], "sample_outputs": ["2", "1"], "notes": null}, "src_uid": "f30329023e84b4c50b1b118dc98ae73c"}
{"nl": {"description": "Petr wants to make a calendar for current month. For this purpose he draws a table in which columns correspond to weeks (a week is seven consequent days from Monday to Sunday), rows correspond to weekdays, and cells contain dates. For example, a calendar for January 2017 should look like on the picture:  Petr wants to know how many columns his table should have given the month and the weekday of the first date of that month? Assume that the year is non-leap.", "input_spec": "The only line contain two integers m and d (1\u2009\u2264\u2009m\u2009\u2264\u200912, 1\u2009\u2264\u2009d\u2009\u2264\u20097)\u00a0\u2014 the number of month (January is the first month, December is the twelfth) and the weekday of the first date of this month (1 is Monday, 7 is Sunday).", "output_spec": "Print single integer: the number of columns the table should have.", "sample_inputs": ["1 7", "1 1", "11 6"], "sample_outputs": ["6", "5", "5"], "notes": "NoteThe first example corresponds to the January 2017 shown on the picture in the statements.In the second example 1-st January is Monday, so the whole month fits into 5 columns.In the third example 1-st November is Saturday and 5 columns is enough."}, "src_uid": "5b969b6f564df6f71e23d4adfb2ded74"}
{"nl": {"description": "Dawid has four bags of candies. The $$$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": "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": "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": "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": "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": "Madoka wants to enter to \"Novosibirsk State University\", but in the entrance exam she came across a very difficult task:Given an integer $$$n$$$, it is required to calculate $$$\\sum{\\operatorname{lcm}(c, \\gcd(a, b))}$$$, for all triples of positive integers $$$(a, b, c)$$$, where $$$a + b + c = n$$$.In this problem $$$\\gcd(x, y)$$$ denotes the greatest common divisor of $$$x$$$ and $$$y$$$, and $$$\\operatorname{lcm}(x, y)$$$ denotes the least common multiple of $$$x$$$ and $$$y$$$.Solve this problem for Madoka and help her to enter to the best university!", "input_spec": "The first and the only line contains a single integer $$$n$$$ ($$$3 \\le n \\le 10^5$$$).", "output_spec": "Print exactly one interger\u00a0\u2014 $$$\\sum{\\operatorname{lcm}(c, \\gcd(a, b))}$$$. Since the answer can be very large, then output it modulo $$$10^9 + 7$$$.", "sample_inputs": ["3", "5", "69228"], "sample_outputs": ["1", "11", "778304278"], "notes": "NoteIn the first example, there is only one suitable triple $$$(1, 1, 1)$$$. So the answer is $$$\\operatorname{lcm}(1, \\gcd(1, 1)) = \\operatorname{lcm}(1, 1) = 1$$$.In the second example, $$$\\operatorname{lcm}(1, \\gcd(3, 1)) + \\operatorname{lcm}(1, \\gcd(2, 2)) + \\operatorname{lcm}(1, \\gcd(1, 3)) + \\operatorname{lcm}(2, \\gcd(2, 1)) + \\operatorname{lcm}(2, \\gcd(1, 2)) + \\operatorname{lcm}(3, \\gcd(1, 1)) = \\operatorname{lcm}(1, 1) + \\operatorname{lcm}(1, 2) + \\operatorname{lcm}(1, 1) + \\operatorname{lcm}(2, 1) + \\operatorname{lcm}(2, 1) + \\operatorname{lcm}(3, 1) = 1 + 2 + 1 + 2 + 2 + 3 = 11$$$"}, "src_uid": "c3694a6ff95c64bef8cbe8834c3fd6cb"}
{"nl": {"description": "You are given a sequence $$$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$$$, print -1.", "sample_inputs": ["6\n1 4 4 7 4 1", "5\n2 2 5 2 5", "4\n1 3 3 7", "2\n2 8"], "sample_outputs": ["3", "3", "-1", "3"], "notes": null}, "src_uid": "d486a88939c132848a7efdf257b9b066"}
{"nl": {"description": "THE SxPLAY & KIV\u039b - \u6f02\u6d41 KIV\u039b & Nikki Simmons - PerspectivesWith a new body, our idol Aroma White (or should we call her Kaori Minamiya?) begins to uncover her lost past through the OS space.The space can be considered a 2D plane, with an infinite number of data nodes, indexed from $$$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": "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": "Manao is working for a construction company. Recently, an order came to build wall bars in a children's park. Manao was commissioned to develop a plan of construction, which will enable the company to save the most money.After reviewing the formal specifications for the wall bars, Manao discovered a number of controversial requirements and decided to treat them to the company's advantage. His resulting design can be described as follows:  Let's introduce some unit of length. The construction center is a pole of height n.  At heights 1,\u20092,\u2009...,\u2009n exactly one horizontal bar sticks out from the pole. Each bar sticks in one of four pre-fixed directions.  A child can move from one bar to another if the distance between them does not exceed h and they stick in the same direction. If a child is on the ground, he can climb onto any of the bars at height between 1 and h. In Manao's construction a child should be able to reach at least one of the bars at heights n\u2009-\u2009h\u2009+\u20091,\u2009n\u2009-\u2009h\u2009+\u20092,\u2009...,\u2009n if he begins at the ground.   The figure to the left shows what a common set of wall bars looks like. The figure to the right shows Manao's construction Manao is wondering how many distinct construction designs that satisfy his requirements exist. As this number can be rather large, print the remainder after dividing it by 1000000009\u00a0(109\u2009+\u20099). Two designs are considered distinct if there is such height i, that the bars on the height i in these designs don't stick out in the same direction.", "input_spec": "A single line contains two space-separated integers, n and h (1\u2009\u2264\u2009n\u2009\u2264\u20091000, 1\u2009\u2264\u2009h\u2009\u2264\u2009min(n,\u200930)).", "output_spec": "In a single line print the remainder after dividing the number of designs by 1000000009\u00a0(109\u2009+\u20099).", "sample_inputs": ["5 1", "4 2", "4 3", "5 2"], "sample_outputs": ["4", "148", "256", "376"], "notes": "NoteConsider several designs for h\u2009=\u20092. A design with the first bar sticked out in direction d1, the second \u2014 in direction d2 and so on (1\u2009\u2264\u2009di\u2009\u2264\u20094) is denoted as string d1d2...dn.Design \"1231\" (the first three bars are sticked out in different directions, the last one \u2014 in the same as first). A child can reach neither the bar at height 3 nor the bar at height 4.Design \"414141\". A child can reach the bar at height 5. To do this, he should first climb at the first bar, then at the third and then at the fifth one. He can also reach bar at height 6 by the route second \u2009\u2192\u2009 fourth \u2009\u2192\u2009 sixth bars.Design \"123333\". The child can't reach the upper two bars.Design \"323323\". The bar at height 6 can be reached by the following route: first \u2009\u2192\u2009 third \u2009\u2192\u2009 fourth \u2009\u2192\u2009 sixth bars."}, "src_uid": "9fe9658db35076c0bddc8b7ddce11013"}
{"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": "Every summer Vitya comes to visit his grandmother in the countryside. This summer, he got a huge wart. Every grandma knows that one should treat warts when the moon goes down. Thus, Vitya has to catch the moment when the moon is down.Moon cycle lasts 30 days. The size of the visible part of the moon (in Vitya's units) for each day is 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, and then cycle repeats, thus after the second 1 again goes 0.As there is no internet in the countryside, Vitya has been watching the moon for n consecutive days and for each of these days he wrote down the size of the visible part of the moon. Help him find out whether the moon will be up or down next day, or this cannot be determined by the data he has.", "input_spec": "The first line of the input contains a single integer n (1\u2009\u2264\u2009n\u2009\u2264\u200992)\u00a0\u2014 the number of consecutive days Vitya was watching the size of the visible part of the moon.  The second line contains n integers ai (0\u2009\u2264\u2009ai\u2009\u2264\u200915)\u00a0\u2014 Vitya's records. It's guaranteed that the input data is consistent.", "output_spec": "If Vitya can be sure that the size of visible part of the moon on day n\u2009+\u20091 will be less than the size of the visible part on day n, then print \"DOWN\" at the only line of the output. If he might be sure that the size of the visible part will increase, then print \"UP\". If it's impossible to determine what exactly will happen with the moon, print -1.", "sample_inputs": ["5\n3 4 5 6 7", "7\n12 13 14 15 14 13 12", "1\n8"], "sample_outputs": ["UP", "DOWN", "-1"], "notes": "NoteIn the first sample, the size of the moon on the next day will be equal to 8, thus the answer is \"UP\".In the second sample, the size of the moon on the next day will be 11, thus the answer is \"DOWN\".In the third sample, there is no way to determine whether the size of the moon on the next day will be 7 or 9, thus the answer is -1."}, "src_uid": "8330d9fea8d50a79741507b878da0a75"}
{"nl": {"description": "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": "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": "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": "The cows have just learned what a primitive root is! Given a prime p, a primitive root  is an integer x (1\u2009\u2264\u2009x\u2009<\u2009p) such that none of integers x\u2009-\u20091,\u2009x2\u2009-\u20091,\u2009...,\u2009xp\u2009-\u20092\u2009-\u20091 are divisible by p, but xp\u2009-\u20091\u2009-\u20091 is. Unfortunately, computing primitive roots can be time consuming, so the cows need your help. Given a prime p, help the cows find the number of primitive roots .", "input_spec": "The input contains a single line containing an integer p (2\u2009\u2264\u2009p\u2009<\u20092000). It is guaranteed that p is a prime.", "output_spec": "Output on a single line the number of primitive roots .", "sample_inputs": ["3", "5"], "sample_outputs": ["1", "2"], "notes": "NoteThe only primitive root  is 2.The primitive roots  are 2 and 3."}, "src_uid": "3bed682b6813f1ddb54410218c233cff"}
{"nl": {"description": "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": "\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$$$)\u00a0\u2014 \u044d\u043b\u0435\u043c\u0435\u043d\u0442\u044b \u043f\u0435\u0440\u0435\u0441\u0442\u0430\u043d\u043e\u0432\u043a\u0438. \u0415\u0441\u043b\u0438 \u0441\u0443\u0449\u0435\u0441\u0442\u0432\u0443\u0435\u0442 \u043d\u0435\u0441\u043a\u043e\u043b\u044c\u043a\u043e \u0432\u0430\u0440\u0438\u0430\u043d\u0442\u043e\u0432 \u043e\u0442\u0432\u0435\u0442\u0430, \u0432\u044b\u0432\u0435\u0434\u0438\u0442\u0435 \u043b\u044e\u0431\u043e\u0439 \u0438\u0437 \u043d\u0438\u0445.", "sample_inputs": ["00000000000000000000000000000000", "11111111111111111111111111111111", "101011010001100100011011001111011000011110010"], "sample_outputs": ["16\n1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16", "16\n16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1", "16\n13 6 1 7 12 5 4 15 14 16 10 11 3 8 9 2"], "notes": null}, "src_uid": "b2ee84d23d73947fa84faaaebfde85c8"}
{"nl": {"description": "You stumbled upon a new kind of chess puzzles. The chessboard you are given is not necesserily $$$8 \\times 8$$$, but it still is $$$N \\times N$$$. Each square has some number written on it, all the numbers are from $$$1$$$ to $$$N^2$$$ and all the numbers are pairwise distinct. The $$$j$$$-th square in the $$$i$$$-th row has a number $$$A_{ij}$$$ written on it.In your chess set you have only three pieces: a knight, a bishop and a rook. At first, you put one of them on the square with the number $$$1$$$ (you can choose which one). Then you want to reach square $$$2$$$ (possibly passing through some other squares in process), then square $$$3$$$ and so on until you reach square $$$N^2$$$. In one step you are allowed to either make a valid move with the current piece or replace it with some other piece. Each square can be visited arbitrary number of times.A knight can move to a square that is two squares away horizontally and one square vertically, or two squares vertically and one square horizontally. A bishop moves diagonally. A rook moves horizontally or vertically. The move should be performed to a different square from the one a piece is currently standing on.You want to minimize the number of steps of the whole traversal. Among all the paths to have the same number of steps you want to choose the one with the lowest number of piece replacements.What is the path you should take to satisfy all conditions?", "input_spec": "The first line contains a single integer $$$N$$$ ($$$3 \\le N \\le 10$$$) \u2014 the size of the chessboard. Each of the next $$$N$$$ lines contains $$$N$$$ integers $$$A_{i1}, A_{i2}, \\dots, A_{iN}$$$ ($$$1 \\le A_{ij} \\le N^2$$$) \u2014 the numbers written on the squares of the $$$i$$$-th row of the board. It is guaranteed that all $$$A_{ij}$$$ are pairwise distinct.", "output_spec": "The only line should contain two integers \u2014 the number of steps in the best answer and the number of replacement moves in it.", "sample_inputs": ["3\n1 9 3\n8 6 7\n4 2 5"], "sample_outputs": ["12 1"], "notes": "NoteHere are the steps for the first example (the starting piece is a knight):  Move to $$$(3, 2)$$$  Move to $$$(1, 3)$$$  Move to $$$(3, 2)$$$  Replace the knight with a rook  Move to $$$(3, 1)$$$  Move to $$$(3, 3)$$$  Move to $$$(3, 2)$$$  Move to $$$(2, 2)$$$  Move to $$$(2, 3)$$$  Move to $$$(2, 1)$$$  Move to $$$(1, 1)$$$  Move to $$$(1, 2)$$$ "}, "src_uid": "5fe44b6cd804e0766a0e993eca1846cd"}
{"nl": {"description": "A mouse encountered a nice big cake and decided to take a walk across it, eating the berries on top of the cake on its way. The cake is rectangular, neatly divided into squares; some of the squares have a berry in them, and some don't.The mouse is in a bit of a hurry, though, so once she enters the cake from its northwest corner (the top left cell in the input data), she will only go east (right) or south (down), until she reaches the southeast corner (the bottom right cell). She will eat every berry in the squares she passes through, but not in the other squares.The mouse tries to choose her path so as to maximize the number of berries consumed. However, her haste and hunger might be clouding her judgement, leading her to suboptimal decisions...", "input_spec": "The first line of input contains two integers $$$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": "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": "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": "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": "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": "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": "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": "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 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": "Princess Twilight went to Celestia and Luna's old castle to research the chest from the Elements of Harmony.  A sequence of positive integers bi is harmony if and only if for every two elements of the sequence their greatest common divisor equals 1. According to an ancient book, the key of the chest is a harmony sequence bi which minimizes the following expression:You are given sequence ai, help Princess Twilight to find the key.", "input_spec": "The first line contains an integer n (1\u2009\u2264\u2009n\u2009\u2264\u2009100) \u2014 the number of elements of the sequences a and b. The next line contains n integers a1,\u2009a2,\u2009...,\u2009an (1\u2009\u2264\u2009ai\u2009\u2264\u200930).", "output_spec": "Output the key \u2014 sequence bi that minimizes the sum described above. If there are multiple optimal sequences, you can output any of them.", "sample_inputs": ["5\n1 1 1 1 1", "5\n1 6 4 2 8"], "sample_outputs": ["1 1 1 1 1", "1 5 3 1 8"], "notes": null}, "src_uid": "f26c74f27bbc723efd69c38ad0e523c6"}
{"nl": {"description": "A few years ago, Hitagi encountered a giant crab, who stole the whole of her body weight. Ever since, she tried to avoid contact with others, for fear that this secret might be noticed.To get rid of the oddity and recover her weight, a special integer sequence is needed. Hitagi's sequence has been broken for a long time, but now Kaiki provides an opportunity.Hitagi's sequence a has a length of n. Lost elements in it are denoted by zeros. Kaiki provides another sequence b, whose length k equals the number of lost elements in a (i.e. the number of zeros). Hitagi is to replace each zero in a with an element from b so that each element in b should be used exactly once. Hitagi knows, however, that, apart from 0, no integer occurs in a and b more than once in total.If the resulting sequence is not an increasing sequence, then it has the power to recover Hitagi from the oddity. You are to determine whether this is possible, or Kaiki's sequence is just another fake. In other words, you should detect whether it is possible to replace each zero in a with an integer from b so that each integer from b is used exactly once, and the resulting sequence is not increasing.", "input_spec": "The first line of input contains two space-separated positive integers n (2\u2009\u2264\u2009n\u2009\u2264\u2009100) and k (1\u2009\u2264\u2009k\u2009\u2264\u2009n) \u2014 the lengths of sequence a and b respectively. The second line contains n space-separated integers a1,\u2009a2,\u2009...,\u2009an (0\u2009\u2264\u2009ai\u2009\u2264\u2009200) \u2014 Hitagi's broken sequence with exactly k zero elements. The third line contains k space-separated integers b1,\u2009b2,\u2009...,\u2009bk (1\u2009\u2264\u2009bi\u2009\u2264\u2009200) \u2014 the elements to fill into Hitagi's sequence. Input guarantees that apart from 0, no integer occurs in a and b more than once in total.", "output_spec": "Output \"Yes\" if it's possible to replace zeros in a with elements in b and make the resulting sequence not increasing, and \"No\" otherwise.", "sample_inputs": ["4 2\n11 0 0 14\n5 4", "6 1\n2 3 0 8 9 10\n5", "4 1\n8 94 0 4\n89", "7 7\n0 0 0 0 0 0 0\n1 2 3 4 5 6 7"], "sample_outputs": ["Yes", "No", "Yes", "Yes"], "notes": "NoteIn the first sample:   Sequence a is 11,\u20090,\u20090,\u200914.  Two of the elements are lost, and the candidates in b are 5 and 4.  There are two possible resulting sequences: 11,\u20095,\u20094,\u200914 and 11,\u20094,\u20095,\u200914, both of which fulfill the requirements. Thus the answer is \"Yes\". In the second sample, the only possible resulting sequence is 2,\u20093,\u20095,\u20098,\u20099,\u200910, which is an increasing sequence and therefore invalid."}, "src_uid": "40264e84c041fcfb4f8c0af784df102a"}
{"nl": {"description": "Once upon a time in the Kingdom of Far Far Away lived Sam the Farmer. Sam had a cow named Dawn and he was deeply attached to her. Sam would spend the whole summer stocking hay to feed Dawn in winter. Sam scythed hay and put it into haystack. As Sam was a bright farmer, he tried to make the process of storing hay simpler and more convenient to use. He collected the hay into cubical hay blocks of the same size. Then he stored the blocks in his barn. After a summer spent in hard toil Sam stored A\u00b7B\u00b7C hay blocks and stored them in a barn as a rectangular parallelepiped A layers high. Each layer had B rows and each row had C blocks.At the end of the autumn Sam came into the barn to admire one more time the hay he'd been stacking during this hard summer. Unfortunately, Sam was horrified to see that the hay blocks had been carelessly scattered around the barn. The place was a complete mess. As it turned out, thieves had sneaked into the barn. They completely dissembled and took away a layer of blocks from the parallelepiped's front, back, top and sides. As a result, the barn only had a parallelepiped containing (A\u2009-\u20091)\u2009\u00d7\u2009(B\u2009-\u20092)\u2009\u00d7\u2009(C\u2009-\u20092) hay blocks. To hide the evidence of the crime, the thieves had dissembled the parallelepiped into single 1\u2009\u00d7\u20091\u2009\u00d7\u20091 blocks and scattered them around the barn. After the theft Sam counted n hay blocks in the barn but he forgot numbers A, B \u0438 C.Given number n, find the minimally possible and maximally possible number of stolen hay blocks.", "input_spec": "The only line contains integer n from the problem's statement (1\u2009\u2264\u2009n\u2009\u2264\u2009109).", "output_spec": "Print space-separated minimum and maximum number of hay blocks that could have been stolen by the thieves. Note that the answer to the problem can be large enough, so you must use the 64-bit integer type for calculations. Please, do not use the %lld specificator to read or write 64-bit integers in \u0421++. It is preferred to use cin, cout streams or the %I64d specificator.", "sample_inputs": ["4", "7", "12"], "sample_outputs": ["28 41", "47 65", "48 105"], "notes": "NoteLet's consider the first sample test. If initially Sam has a parallelepiped consisting of 32\u2009=\u20092\u2009\u00d7\u20094\u2009\u00d7\u20094 hay blocks in his barn, then after the theft the barn has 4\u2009=\u2009(2\u2009-\u20091)\u2009\u00d7\u2009(4\u2009-\u20092)\u2009\u00d7\u2009(4\u2009-\u20092) hay blocks left. Thus, the thieves could have stolen 32\u2009-\u20094\u2009=\u200928 hay blocks. If Sam initially had a parallelepiped consisting of 45\u2009=\u20095\u2009\u00d7\u20093\u2009\u00d7\u20093 hay blocks in his barn, then after the theft the barn has 4\u2009=\u2009(5\u2009-\u20091)\u2009\u00d7\u2009(3\u2009-\u20092)\u2009\u00d7\u2009(3\u2009-\u20092) hay blocks left. Thus, the thieves could have stolen 45\u2009-\u20094\u2009=\u200941 hay blocks. No other variants of the blocks' initial arrangement (that leave Sam with exactly 4 blocks after the theft) can permit the thieves to steal less than 28 or more than 41 blocks."}, "src_uid": "2468eead8acc5b8f5ddc51bfa2bd4fb7"}
{"nl": {"description": "Dima and his friends have been playing hide and seek at Dima's place all night. As a result, Dima's place got messy. In the morning they decided that they need to clean the place.To decide who exactly would clean the apartment, the friends want to play a counting-out game. First, all the guys stand in a circle, and then each of them shows some number of fingers on one hand (one to five), and then the boys count in a circle, starting from Dima, the number of people, respective to the total number of fingers shown. The person on who the countdown stops will clean the apartment.For example, if Dima and one of his friends played hide and seek, and 7 fingers were shown during the counting-out, then Dima would clean the place. If there were 2 or say, 8 fingers shown, then his friend would clean the place.Dima knows how many fingers each of his friends will show during the counting-out. Now he is interested in the number of ways to show some number of fingers on one hand (one to five), so that he did not have to clean the place. Help Dima.", "input_spec": "The first line contains integer n (1\u2009\u2264\u2009n\u2009\u2264\u2009100) \u2014 the number of Dima's friends. Dima himself isn't considered to be his own friend. The second line contains n positive integers, not exceeding 5, representing, how many fingers the Dima's friends will show.  The numbers in the lines are separated by a single space.", "output_spec": "In a single line print the answer to the problem.", "sample_inputs": ["1\n1", "1\n2", "2\n3 5"], "sample_outputs": ["3", "2", "3"], "notes": "NoteIn the first sample Dima can show 1, 3 or 5 fingers. If Dima shows 3 fingers, then the counting-out will go like that: Dima, his friend, Dima, his friend.In the second sample Dima can show 2 or 4 fingers."}, "src_uid": "ff6b3fd358c758324c19a26283ab96a4"}
{"nl": {"description": "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": "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": "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": "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]$$$ "}, "src_uid": "4f0e0d1deef0761a46b64de3eb98e774"}
{"nl": {"description": "Given 2 integers $$$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$$$. There is no valid array of smaller length.Notice that in the fourth sample the array is empty."}, "src_uid": "490f23ced6c43f9e12f1bcbecbb14904"}
{"nl": {"description": "Alice and Bob play a game. Alice has got $$$n$$$ treasure chests (the $$$i$$$-th of which contains $$$a_i$$$ coins) and $$$m$$$ keys (the $$$j$$$-th of which she can sell Bob for $$$b_j$$$ coins).Firstly, Alice puts some locks on the chests. There are $$$m$$$ types of locks, the locks of the $$$j$$$-th type can only be opened with the $$$j$$$-th key. To put a lock of type $$$j$$$ on the $$$i$$$-th chest, Alice has to pay $$$c_{i,j}$$$ dollars. Alice can put any number of different types of locks on each chest (possibly, zero).Then, Bob buys some of the keys from Alice (possibly none, possibly all of them) and opens each chest he can (he can open a chest if he has the keys for all of the locks on this chest). Bob's profit is the difference between the total number of coins in the opened chests and the total number of coins he spends buying keys from Alice. If Bob's profit is strictly positive (greater than zero), he wins the game. Otherwise, Alice wins the game.Alice wants to put some locks on some chests so no matter which keys Bob buys, she always wins (Bob cannot get positive profit). Of course, she wants to spend the minimum possible number of dollars on buying the locks. Help her to determine whether she can win the game at all, and if she can, how many dollars she has to spend on the locks.", "input_spec": "The first line contains two integers $$$n$$$ and $$$m$$$ ($$$1 \\le n, m \\le 6$$$)\u00a0\u2014 the number of chests and the number of keys, respectively. The second line contains $$$n$$$ integers $$$a_1, a_2, \\dots, a_n$$$ ($$$1 \\le a_i \\le 4$$$), where $$$a_i$$$ is the number of coins in the $$$i$$$-th chest. The third line contains $$$m$$$ integers $$$b_1, b_2, \\dots, b_m$$$ ($$$1 \\le b_j \\le 4$$$), where $$$b_j$$$ is the number of coins Bob has to spend to buy the $$$j$$$-th key from Alice. Then $$$n$$$ lines follow. The $$$i$$$-th of them contains $$$m$$$ integers $$$c_{i,1}, c_{i,2}, \\dots, c_{i,m}$$$ ($$$1 \\le c_{i,j} \\le 10^7$$$), where $$$c_{i,j}$$$ is the number of dollars Alice has to spend to put a lock of the $$$j$$$-th type on the $$$i$$$-th chest.", "output_spec": "If Alice cannot ensure her victory (no matter which locks she puts on which chests, Bob always has a way to gain positive profit), print $$$-1$$$. Otherwise, print one integer\u00a0\u2014 the minimum number of dollars Alice has to spend to win the game regardless of Bob's actions.", "sample_inputs": ["2 3\n3 3\n1 1 4\n10 20 100\n20 15 80", "2 3\n3 3\n2 1 4\n10 20 100\n20 15 80", "2 3\n3 4\n1 1 4\n10 20 100\n20 15 80"], "sample_outputs": ["205", "110", "-1"], "notes": "NoteIn the first example, Alice should put locks of types $$$1$$$ and $$$3$$$ on the first chest, and locks of type $$$2$$$ and $$$3$$$ on the second chest.In the second example, Alice should put locks of types $$$1$$$ and $$$2$$$ on the first chest, and a lock of type $$$3$$$ on the second chest."}, "src_uid": "4dc5dc78bda59c1ec6dd8acd6f1d7333"}
{"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": "In one very old text file there was written Great Wisdom. This Wisdom was so Great that nobody could decipher it, even Phong \u2014 the oldest among the inhabitants of Mainframe. But still he managed to get some information from there. For example, he managed to learn that User launches games for pleasure \u2014 and then terrible Game Cubes fall down on the city, bringing death to those modules, who cannot win the game...For sure, as guard Bob appeared in Mainframe many modules stopped fearing Game Cubes. Because Bob (as he is alive yet) has never been defeated by User, and he always meddles with Game Cubes, because he is programmed to this.However, unpleasant situations can happen, when a Game Cube falls down on Lost Angles. Because there lives a nasty virus \u2014 Hexadecimal, who is... mmm... very strange. And she likes to play very much. So, willy-nilly, Bob has to play with her first, and then with User.This time Hexadecimal invented the following entertainment: Bob has to leap over binary search trees with n nodes. We should remind you that a binary search tree is a binary tree, each node has a distinct key, for each node the following is true: the left sub-tree of a node contains only nodes with keys less than the node's key, the right sub-tree of a node contains only nodes with keys greater than the node's key. All the keys are different positive integer numbers from 1 to n. Each node of such a tree can have up to two children, or have no children at all (in the case when a node is a leaf).In Hexadecimal's game all the trees are different, but the height of each is not lower than h. In this problem \u00abheight\u00bb stands for the maximum amount of nodes on the way from the root to the remotest leaf, the root node and the leaf itself included. When Bob leaps over a tree, it disappears. Bob gets the access to a Cube, when there are no trees left. He knows how many trees he will have to leap over in the worst case. And you?", "input_spec": "The input data contains two space-separated positive integer numbers n and h (n\u2009\u2264\u200935, h\u2009\u2264\u2009n).", "output_spec": "Output one number \u2014 the answer to the problem. It is guaranteed that it does not exceed 9\u00b71018.", "sample_inputs": ["3 2", "3 3"], "sample_outputs": ["5", "4"], "notes": null}, "src_uid": "faf12a603d0c27f8be6bf6b02531a931"}
{"nl": {"description": "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$$$, and you will be able to watch shows for the last eight days."}, "src_uid": "56da4ec7cd849c4330d188d8c9bd6094"}
{"nl": {"description": "There are $$$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": "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": "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": "n children are standing in a circle and playing a game. Children's numbers in clockwise order form a permutation a1,\u2009a2,\u2009...,\u2009an of length n. It is an integer sequence such that each integer from 1 to n appears exactly once in it.The game consists of m steps. On each step the current leader with index i counts out ai people in clockwise order, starting from the next person. The last one to be pointed at by the leader becomes the new leader.You are given numbers l1,\u2009l2,\u2009...,\u2009lm \u2014 indices of leaders in the beginning of each step. Child with number l1 is the first leader in the game. Write a program which will restore a possible permutation a1,\u2009a2,\u2009...,\u2009an. If there are multiple solutions then print any of them. If there is no solution then print -1.", "input_spec": "The first line contains two integer numbers n, m (1\u2009\u2264\u2009n,\u2009m\u2009\u2264\u2009100). The second line contains m integer numbers l1,\u2009l2,\u2009...,\u2009lm (1\u2009\u2264\u2009li\u2009\u2264\u2009n) \u2014 indices of leaders in the beginning of each step.", "output_spec": "Print such permutation of n numbers a1,\u2009a2,\u2009...,\u2009an that leaders in the game will be exactly l1,\u2009l2,\u2009...,\u2009lm if all the rules are followed. If there are multiple solutions print any of them.  If there is no permutation which satisfies all described conditions print -1.", "sample_inputs": ["4 5\n2 3 1 4 4", "3 3\n3 1 2"], "sample_outputs": ["3 1 2 4", "-1"], "notes": "NoteLet's follow leadership in the first example:   Child 2 starts.  Leadership goes from 2 to 2\u2009+\u2009a2\u2009=\u20093.  Leadership goes from 3 to 3\u2009+\u2009a3\u2009=\u20095. As it's greater than 4, it's going in a circle to 1.  Leadership goes from 1 to 1\u2009+\u2009a1\u2009=\u20094.  Leadership goes from 4 to 4\u2009+\u2009a4\u2009=\u20098. Thus in circle it still remains at 4. "}, "src_uid": "4a7c959ca279d0a9bd9bbf0ce88cf72b"}
{"nl": {"description": "Let's introduce a number system which is based on a roman digits. There are digits I, V, X, L which correspond to the numbers $$$1$$$, $$$5$$$, $$$10$$$ and $$$50$$$ respectively. The use of other roman digits is not allowed.Numbers in this system are written as a sequence of one or more digits. We define the value of the sequence simply as the sum of digits in it.For example, the number XXXV evaluates to $$$35$$$ and the number IXI\u00a0\u2014 to $$$12$$$.Pay attention to the difference to the traditional roman system\u00a0\u2014 in our system any sequence of digits is valid, moreover the order of digits doesn't matter, for example IX means $$$11$$$, not $$$9$$$.One can notice that this system is ambiguous, and some numbers can be written in many different ways. Your goal is to determine how many distinct integers can be represented by exactly $$$n$$$ roman digits I, V, X, L.", "input_spec": "The only line of the input file contains a single integer $$$n$$$ ($$$1 \\le n \\le 10^9$$$)\u00a0\u2014 the number of roman digits to use.", "output_spec": "Output a single integer\u00a0\u2014 the number of distinct integers which can be represented using $$$n$$$ roman digits exactly.", "sample_inputs": ["1", "2", "10"], "sample_outputs": ["4", "10", "244"], "notes": "NoteIn the first sample there are exactly $$$4$$$ integers which can be represented\u00a0\u2014 I, V, X and L.In the second sample it is possible to represent integers $$$2$$$ (II), $$$6$$$ (VI), $$$10$$$ (VV), $$$11$$$ (XI), $$$15$$$ (XV), $$$20$$$ (XX), $$$51$$$ (IL), $$$55$$$ (VL), $$$60$$$ (XL) and $$$100$$$ (LL)."}, "src_uid": "75ec99318736a8a1b62a8d51efd95355"}
{"nl": {"description": "When new students come to the Specialized Educational and Scientific Centre (SESC) they need to start many things from the beginning. Sometimes the teachers say (not always unfairly) that we cannot even count. So our teachers decided to teach us arithmetics from the start. And what is the best way to teach students add and subtract? \u2014 That's right, using counting sticks! An here's our new task: An expression of counting sticks is an expression of type:[ A sticks][sign +][B sticks][sign =][C sticks] (1\u2009\u2264\u2009A,\u2009B,\u2009C).  Sign + consists of two crossed sticks: one vertical and one horizontal. Sign = consists of two horizontal sticks. The expression is arithmetically correct if A\u2009+\u2009B\u2009=\u2009C.We've got an expression that looks like A\u2009+\u2009B\u2009=\u2009C given by counting sticks. Our task is to shift at most one stick (or we can shift nothing) so that the expression became arithmetically correct. Note that we cannot remove the sticks from the expression, also we cannot shift the sticks from the signs + and =.We really aren't fabulous at arithmetics. Can you help us?", "input_spec": "The single line contains the initial expression. It is guaranteed that the expression looks like A\u2009+\u2009B\u2009=\u2009C, where 1\u2009\u2264\u2009A,\u2009B,\u2009C\u2009\u2264\u2009100.", "output_spec": "If there isn't a way to shift the stick so the expression becomes correct, print on a single line \"Impossible\" (without the quotes). If there is a way, print the resulting expression. Follow the format of the output from the test samples. Don't print extra space characters. If there are multiple correct answers, print any of them. For clarifications, you are recommended to see the test samples.", "sample_inputs": ["||+|=|||||", "|||||+||=||", "|+|=||||||", "||||+||=||||||"], "sample_outputs": ["|||+|=||||", "Impossible", "Impossible", "||||+||=||||||"], "notes": "NoteIn the first sample we can shift stick from the third group of sticks to the first one.In the second sample we cannot shift vertical stick from + sign to the second group of sticks. So we cannot make a - sign.There is no answer in the third sample because we cannot remove sticks from the expression.In the forth sample the initial expression is already arithmetically correct and that is why we don't have to shift sticks."}, "src_uid": "ee0aaa7acf127e9f3a9edafc58f4e2d6"}
{"nl": {"description": "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": "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": "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$$$ characters '(' and ')'.", "output_spec": "Print one line \u2014 the shortest regular bracket sequence that contains both given bracket sequences as subsequences (not necessarily contiguous). If there are several answers, you can print any.", "sample_inputs": ["(())(()\n()))()", ")\n((", ")\n)))", "())\n(()(()(()("], "sample_outputs": ["(())()()", "(())", "((()))", "(()()()(()()))"], "notes": null}, "src_uid": "cc222aab45b3ad3d0e71227592c883f1"}
{"nl": {"description": "Monocarp is playing a video game. In the game, he controls a spaceship and has to destroy an enemy spaceship.Monocarp has two lasers installed on his spaceship. Both lasers $$$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$$$ damage each time."}, "src_uid": "ca9d48e48e69b931236907a9ac262433"}
{"nl": {"description": "Carl is a beginner magician. He has a blue, b violet and c orange magic spheres. In one move he can transform two spheres of the same color into one sphere of any other color. To make a spell that has never been seen before, he needs at least x blue, y violet and z orange spheres. Can he get them (possible, in multiple actions)?", "input_spec": "The first line of the input contains three integers a, b and c (0\u2009\u2264\u2009a,\u2009b,\u2009c\u2009\u2264\u20091\u2009000\u2009000)\u00a0\u2014 the number of blue, violet and orange spheres that are in the magician's disposal. The second line of the input contains three integers, x, y and z (0\u2009\u2264\u2009x,\u2009y,\u2009z\u2009\u2264\u20091\u2009000\u2009000)\u00a0\u2014 the number of blue, violet and orange spheres that he needs to get.", "output_spec": "If the wizard is able to obtain the required numbers of spheres, print \"Yes\". Otherwise, print \"No\".", "sample_inputs": ["4 4 0\n2 1 2", "5 6 1\n2 7 2", "3 3 3\n2 2 2"], "sample_outputs": ["Yes", "No", "Yes"], "notes": "NoteIn the first sample the wizard has 4 blue and 4 violet spheres. In his first action he can turn two blue spheres into one violet one. After that he will have 2 blue and 5 violet spheres. Then he turns 4 violet spheres into 2 orange spheres and he ends up with 2 blue, 1 violet and 2 orange spheres, which is exactly what he needs."}, "src_uid": "1db4ba9dc1000e26532bb73336cf12c3"}
{"nl": {"description": "You are given an integer sequence $$$1, 2, \\dots, n$$$. You have to divide it into two sets $$$A$$$ and $$$B$$$ in such a way that each element belongs to exactly one set and $$$|sum(A) - sum(B)|$$$ is minimum possible.The value $$$|x|$$$ is the absolute value of $$$x$$$ and $$$sum(S)$$$ is the sum of elements of the set $$$S$$$.", "input_spec": "The first line of the input contains one integer $$$n$$$ ($$$1 \\le n \\le 2 \\cdot 10^9$$$).", "output_spec": "Print one integer \u2014 the minimum possible value of $$$|sum(A) - sum(B)|$$$ if you divide the initial sequence $$$1, 2, \\dots, n$$$ into two sets $$$A$$$ and $$$B$$$.", "sample_inputs": ["3", "5", "6"], "sample_outputs": ["0", "1", "1"], "notes": "NoteSome (not all) possible answers to examples:In the first example you can divide the initial sequence into sets $$$A = \\{1, 2\\}$$$ and $$$B = \\{3\\}$$$ so the answer is $$$0$$$.In the second example you can divide the initial sequence into sets $$$A = \\{1, 3, 4\\}$$$ and $$$B = \\{2, 5\\}$$$ so the answer is $$$1$$$.In the third example you can divide the initial sequence into sets $$$A = \\{1, 4, 5\\}$$$ and $$$B = \\{2, 3, 6\\}$$$ so the answer is $$$1$$$."}, "src_uid": "fa163c5b619d3892e33e1fb9c22043a9"}
{"nl": {"description": "Vadim loves decorating the Christmas tree, so he got a beautiful garland as a present. It consists of $$$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)$$$ are the pairs of adjacent bulbs that have different parity.In the second case, one of the correct answers is 1 7 3 5 6 4 2. "}, "src_uid": "90db6b6548512acfc3da162144169dba"}
{"nl": {"description": "There is a building consisting of $$$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": "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": "Today Tavas got his test result as an integer score and he wants to share it with his girlfriend, Nafas.His phone operating system is Tavdroid, and its keyboard doesn't have any digits! He wants to share his score with Nafas via text, so he has no choice but to send this number using words.  He ate coffee mix without water again, so right now he's really messed up and can't think.Your task is to help him by telling him what to type.", "input_spec": "The first and only line of input contains an integer s (0\u2009\u2264\u2009s\u2009\u2264\u200999), Tavas's score. ", "output_spec": "In the first and only line of output, print a single string consisting only from English lowercase letters and hyphens ('-'). Do not use spaces.", "sample_inputs": ["6", "99", "20"], "sample_outputs": ["six", "ninety-nine", "twenty"], "notes": "NoteYou can find all you need to know about English numerals in http://en.wikipedia.org/wiki/English_numerals ."}, "src_uid": "a49ca177b2f1f9d5341462a38a25d8b7"}
{"nl": {"description": "Luba has a ticket consisting of 6 digits. In one move she can choose digit in any position and replace it with arbitrary digit. She wants to know the minimum number of digits she needs to replace in order to make the ticket lucky.The ticket is considered lucky if the sum of first three digits equals to the sum of last three digits.", "input_spec": "You are given a string consisting of 6 characters (all characters are digits from 0 to 9) \u2014 this string denotes Luba's ticket. The ticket can start with the digit 0.", "output_spec": "Print one number \u2014 the minimum possible number of digits Luba needs to replace to make the ticket lucky.", "sample_inputs": ["000000", "123456", "111000"], "sample_outputs": ["0", "2", "1"], "notes": "NoteIn the first example the ticket is already lucky, so the answer is 0.In the second example Luba can replace 4 and 5 with zeroes, and the ticket will become lucky. It's easy to see that at least two replacements are required.In the third example Luba can replace any zero with 3. It's easy to see that at least one replacement is required."}, "src_uid": "09601fd1742ffdc9f822950f1d3e8494"}
{"nl": {"description": "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": "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$$$. "}, "src_uid": "cedcc3cee864bf8684148df93804d029"}
{"nl": {"description": "Pak Chanek plans to build a garage. He wants the garage to consist of a square and a right triangle that are arranged like the following illustration.  Define $$$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$$$."}, "src_uid": "d0a8604b78ba19ab769fd1ec90a72e4e"}
{"nl": {"description": "\u00c6sir - CHAOS \u00c6sir - V.\"Everything has been planned out. No more hidden concerns. The condition of Cytus is also perfect.The time right now...... 00:01:12......It's time.\"The emotion samples are now sufficient. After almost 3 years, it's time for Ivy to awake her bonded sister, Vanessa.The system inside A.R.C.'s Library core can be considered as an undirected graph with infinite number of processing nodes, numbered with all positive integers ($$$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": "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": "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": "You are given a figure on a grid representing stairs consisting of 7 steps. The width of the stair on height i is wi squares. Formally, the figure is created by consecutively joining rectangles of size wi\u2009\u00d7\u2009i so that the wi sides lie on one straight line. Thus, for example, if all wi\u2009=\u20091, the figure will look like that (different colors represent different rectangles):  And if w\u2009=\u2009{5,\u20091,\u20090,\u20093,\u20090,\u20090,\u20091}, then it looks like that:  Find the number of ways to color some borders of the figure's inner squares so that no square had all four borders colored. The borders of the squares lying on the border of the figure should be considered painted. The ways that differ with the figure's rotation should be considered distinct. ", "input_spec": "The single line of the input contains 7 numbers w1,\u2009w2,\u2009...,\u2009w7 (0\u2009\u2264\u2009wi\u2009\u2264\u2009105). It is guaranteed that at least one of the wi's isn't equal to zero.", "output_spec": "In the single line of the output display a single number \u2014 the answer to the problem modulo 109\u2009+\u20097.", "sample_inputs": ["0 1 0 0 0 0 0", "0 2 0 0 0 0 0", "1 1 1 0 0 0 0", "5 1 0 3 0 0 1"], "sample_outputs": ["1", "7", "9", "411199181"], "notes": "NoteAll the possible ways of painting the third sample are given below:  "}, "src_uid": "a4bda63b95dc14185c47a08652fe41bd"}
{"nl": {"description": "Dante is engaged in a fight with \"The Savior\". Before he can fight it with his sword, he needs to break its shields. He has two guns, Ebony and Ivory, each of them is able to perform any non-negative number of shots.For every bullet that hits the shield, Ebony deals a units of damage while Ivory deals b units of damage. In order to break the shield Dante has to deal exactly c units of damage. Find out if this is possible.", "input_spec": "The first line of the input contains three integers a, b, c (1\u2009\u2264\u2009a,\u2009b\u2009\u2264\u2009100,\u20091\u2009\u2264\u2009c\u2009\u2264\u200910\u2009000)\u00a0\u2014 the number of units of damage dealt by Ebony gun and Ivory gun, and the total number of damage required to break the shield, respectively.", "output_spec": "Print \"Yes\" (without quotes) if Dante can deal exactly c damage to the shield and \"No\" (without quotes) otherwise.", "sample_inputs": ["4 6 15", "3 2 7", "6 11 6"], "sample_outputs": ["No", "Yes", "Yes"], "notes": "NoteIn the second sample, Dante can fire 1 bullet from Ebony and 2 from Ivory to deal exactly 1\u00b73\u2009+\u20092\u00b72\u2009=\u20097 damage. In the third sample, Dante can fire 1 bullet from ebony and no bullets from ivory to do 1\u00b76\u2009+\u20090\u00b711\u2009=\u20096 damage. "}, "src_uid": "e66ecb0021a34042885442b336f3d911"}
{"nl": {"description": "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": "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": "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": "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": "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": "  ", "input_spec": "The input contains two integers a,\u2009b (1\u2009\u2264\u2009a\u2009\u2264\u200910,\u20090\u2009\u2264\u2009b\u2009\u2264\u200922\u00b7a\u2009-\u20091) separated by a single space.", "output_spec": "Output two integers separated by a single space.", "sample_inputs": ["1 0", "2 15", "4 160"], "sample_outputs": ["0 0", "3 0", "12 12"], "notes": null}, "src_uid": "879ac20ae5d3e7f1002afe907d9887df"}
{"nl": {"description": "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": "Count the number of distinct sequences a1,\u2009a2,\u2009...,\u2009an (1\u2009\u2264\u2009ai) consisting of positive integers such that gcd(a1,\u2009a2,\u2009...,\u2009an)\u2009=\u2009x and . As this number could be large, print the answer modulo 109\u2009+\u20097.gcd here means the greatest common divisor.", "input_spec": "The only line contains two positive integers x and y (1\u2009\u2264\u2009x,\u2009y\u2009\u2264\u2009109).", "output_spec": "Print the number of such sequences modulo 109\u2009+\u20097.", "sample_inputs": ["3 9", "5 8"], "sample_outputs": ["3", "0"], "notes": "NoteThere are three suitable sequences in the first test: (3,\u20093,\u20093), (3,\u20096), (6,\u20093).There are no suitable sequences in the second test."}, "src_uid": "de7731ce03735b962ee033613192f7bc"}
{"nl": {"description": "A word or a sentence in some language is called a pangram if all the characters of the alphabet of this language appear in it at least once. Pangrams are often used to demonstrate fonts in printing or test the output devices.You are given a string consisting of lowercase and uppercase Latin letters. Check whether this string is a pangram. We say that the string contains a letter of the Latin alphabet if this letter occurs in the string in uppercase or lowercase.", "input_spec": "The first line contains a single integer n (1\u2009\u2264\u2009n\u2009\u2264\u2009100)\u00a0\u2014 the number of characters in the string. The second line contains the string. The string consists only of uppercase and lowercase Latin letters.", "output_spec": "Output \"YES\", if the string is a pangram and \"NO\" otherwise.", "sample_inputs": ["12\ntoosmallword", "35\nTheQuickBrownFoxJumpsOverTheLazyDog"], "sample_outputs": ["NO", "YES"], "notes": null}, "src_uid": "f13eba0a0fb86e20495d218fc4ad532d"}
{"nl": {"description": "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": "Ayoub had an array $$$a$$$ of integers of size $$$n$$$ and this array had two interesting properties:   All the integers in the array were between $$$l$$$ and $$$r$$$ (inclusive).  The sum of all the elements was divisible by $$$3$$$. Unfortunately, Ayoub has lost his array, but he remembers the size of the array $$$n$$$ and the numbers $$$l$$$ and $$$r$$$, so he asked you to find the number of ways to restore the array. Since the answer could be very large, print it modulo $$$10^9 + 7$$$ (i.e. the remainder when dividing by $$$10^9 + 7$$$). In case there are no satisfying arrays (Ayoub has a wrong memory), print $$$0$$$.", "input_spec": "The first and only line contains three integers $$$n$$$, $$$l$$$ and $$$r$$$ ($$$1 \\le n \\le 2 \\cdot 10^5 , 1 \\le l \\le r \\le 10^9$$$)\u00a0\u2014 the size of the lost array and the range of numbers in the array.", "output_spec": "Print the remainder when dividing by $$$10^9 + 7$$$ the number of ways to restore the array.", "sample_inputs": ["2 1 3", "3 2 2", "9 9 99"], "sample_outputs": ["3", "1", "711426616"], "notes": "NoteIn the first example, the possible arrays are : $$$[1,2], [2,1], [3, 3]$$$.In the second example, the only possible array is $$$[2, 2, 2]$$$."}, "src_uid": "4c4852df62fccb0a19ad8bc41145de61"}
{"nl": {"description": "Alice and Bob are decorating a Christmas Tree. Alice wants only $$$3$$$ types of ornaments to be used on the Christmas Tree: yellow, blue and red. They have $$$y$$$ yellow ornaments, $$$b$$$ blue ornaments and $$$r$$$ red ornaments.In Bob's opinion, a Christmas Tree will be beautiful if:  the number of blue ornaments used is greater by exactly $$$1$$$ than the number of yellow ornaments, and  the number of red ornaments used is greater by exactly $$$1$$$ than the number of blue ornaments. That is, if they have $$$8$$$ yellow ornaments, $$$13$$$ blue ornaments and $$$9$$$ red ornaments, we can choose $$$4$$$ yellow, $$$5$$$ blue and $$$6$$$ red ornaments ($$$5=4+1$$$ and $$$6=5+1$$$).Alice wants to choose as many ornaments as possible, but she also wants the Christmas Tree to be beautiful according to Bob's opinion.In the example two paragraphs above, we would choose $$$7$$$ yellow, $$$8$$$ blue and $$$9$$$ red ornaments. If we do it, we will use $$$7+8+9=24$$$ ornaments. That is the maximum number.Since Alice and Bob are busy with preparing food to the New Year's Eve, they are asking you to find out the maximum number of ornaments that can be used in their beautiful Christmas Tree! It is guaranteed that it is possible to choose at least $$$6$$$ ($$$1+2+3=6$$$) ornaments.", "input_spec": "The only line contains three integers $$$y$$$, $$$b$$$, $$$r$$$ ($$$1 \\leq y \\leq 100$$$, $$$2 \\leq b \\leq 100$$$, $$$3 \\leq r \\leq 100$$$)\u00a0\u2014 the number of yellow, blue and red ornaments.  It is guaranteed that it is possible to choose at least $$$6$$$ ($$$1+2+3=6$$$) ornaments.", "output_spec": "Print one number\u00a0\u2014 the maximum number of ornaments that can be used. ", "sample_inputs": ["8 13 9", "13 3 6"], "sample_outputs": ["24", "9"], "notes": "NoteIn the first example, the answer is $$$7+8+9=24$$$.In the second example, the answer is $$$2+3+4=9$$$."}, "src_uid": "03ac8efe10de17590e1ae151a7bae1a5"}
{"nl": {"description": "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": "It seems like the year of 2013 came only yesterday. Do you know a curious fact? The year of 2013 is the first year after the old 1987 with only distinct digits.Now you are suggested to solve the following problem: given a year number, find the minimum year number which is strictly larger than the given one and has only distinct digits.", "input_spec": "The single line contains integer y (1000\u2009\u2264\u2009y\u2009\u2264\u20099000) \u2014 the year number.", "output_spec": "Print a single integer \u2014 the minimum year number that is strictly larger than y and all it's digits are distinct. It is guaranteed that the answer exists.", "sample_inputs": ["1987", "2013"], "sample_outputs": ["2013", "2014"], "notes": null}, "src_uid": "d62dabfbec52675b7ed7b582ad133acd"}
{"nl": {"description": "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": "Greatest common divisor GCD(a,\u2009b) of two positive integers a and b is equal to the biggest integer d such that both integers a and b are divisible by d. There are many efficient algorithms to find greatest common divisor GCD(a,\u2009b), for example, Euclid algorithm. Formally, find the biggest integer d, such that all integers a,\u2009a\u2009+\u20091,\u2009a\u2009+\u20092,\u2009...,\u2009b are divisible by d. To make the problem even more complicated we allow a and b to be up to googol, 10100\u00a0\u2014 such number do not fit even in 64-bit integer type!", "input_spec": "The only line of the input contains two integers a and b (1\u2009\u2264\u2009a\u2009\u2264\u2009b\u2009\u2264\u200910100).", "output_spec": "Output one integer\u00a0\u2014 greatest common divisor of all integers from a to b inclusive.", "sample_inputs": ["1 2", "61803398874989484820458683436563811772030917980576 61803398874989484820458683436563811772030917980576"], "sample_outputs": ["1", "61803398874989484820458683436563811772030917980576"], "notes": null}, "src_uid": "9c5b6d8a20414d160069010b2965b896"}
{"nl": {"description": "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": "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": "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": "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": "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": "You're given a string of lower-case Latin letters. Your task is to find the length of its longest substring that can be met in the string at least twice. These occurrences can overlap (see sample test 2).", "input_spec": "The first input line contains the string. It's guaranteed, that the string is non-empty, consists of lower-case Latin letters, and its length doesn't exceed 100.", "output_spec": "Output one number \u2014 length of the longest substring that can be met in the string at least twice.", "sample_inputs": ["abcd", "ababa", "zzz"], "sample_outputs": ["0", "3", "2"], "notes": null}, "src_uid": "13b5cf94f2fabd053375a5ccf3fd44c7"}
{"nl": {"description": "Petr has just bought a new car. He's just arrived at the most known Petersburg's petrol station to refuel it when he suddenly discovered that the petrol tank is secured with a combination lock! The lock has a scale of $$$360$$$ degrees and a pointer which initially points at zero:  Petr called his car dealer, who instructed him to rotate the lock's wheel exactly $$$n$$$ times. The $$$i$$$-th rotation should be $$$a_i$$$ degrees, either clockwise or counterclockwise, and after all $$$n$$$ rotations the pointer should again point at zero.This confused Petr a little bit as he isn't sure which rotations should be done clockwise and which should be done counterclockwise. As there are many possible ways of rotating the lock, help him and find out whether there exists at least one, such that after all $$$n$$$ rotations the pointer will point at zero again.", "input_spec": "The first line contains one integer $$$n$$$ ($$$1 \\leq n \\leq 15$$$) \u2014 the number of rotations. Each of the following $$$n$$$ lines contains one integer $$$a_i$$$ ($$$1 \\leq a_i \\leq 180$$$) \u2014 the angle of the $$$i$$$-th rotation in degrees.", "output_spec": "If it is possible to do all the rotations so that the pointer will point at zero after all of them are performed, print a single word \"YES\". Otherwise, print \"NO\". Petr will probably buy a new car in this case. You can print each letter in any case (upper or lower).", "sample_inputs": ["3\n10\n20\n30", "3\n10\n10\n10", "3\n120\n120\n120"], "sample_outputs": ["YES", "NO", "YES"], "notes": "NoteIn the first example, we can achieve our goal by applying the first and the second rotation clockwise, and performing the third rotation counterclockwise.In the second example, it's impossible to perform the rotations in order to make the pointer point at zero in the end.In the third example, Petr can do all three rotations clockwise. In this case, the whole wheel will be rotated by $$$360$$$ degrees clockwise and the pointer will point at zero again."}, "src_uid": "01b50fcba4185ceb1eb8e4ba04a0cc10"}
{"nl": {"description": "Quite recently a creative student Lesha had a lecture on trees. After the lecture Lesha was inspired and came up with the tree of his own which he called a k-tree.A k-tree is an infinite rooted tree where:  each vertex has exactly k children;  each edge has some weight;  if we look at the edges that goes from some vertex to its children (exactly k edges), then their weights will equal 1,\u20092,\u20093,\u2009...,\u2009k. The picture below shows a part of a 3-tree.      As soon as Dima, a good friend of Lesha, found out about the tree, he immediately wondered: \"How many paths of total weight n (the sum of all weights of the edges in the path) are there, starting from the root of a k-tree and also containing at least one edge of weight at least d?\".Help Dima find an answer to his question. As the number of ways can be rather large, print it modulo 1000000007 (109\u2009+\u20097). ", "input_spec": "A single line contains three space-separated integers: n, k and d (1\u2009\u2264\u2009n,\u2009k\u2009\u2264\u2009100; 1\u2009\u2264\u2009d\u2009\u2264\u2009k).", "output_spec": "Print a single integer \u2014 the answer to the problem modulo 1000000007 (109\u2009+\u20097). ", "sample_inputs": ["3 3 2", "3 3 3", "4 3 2", "4 5 2"], "sample_outputs": ["3", "1", "6", "7"], "notes": null}, "src_uid": "894a58c9bba5eba11b843c5c5ca0025d"}
{"nl": {"description": "You're given a row with $$$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": "Dima loves representing an odd number as the sum of multiple primes, and Lisa loves it when there are at most three primes. Help them to represent the given number as the sum of at most than three primes.More formally, you are given an odd numer n. Find a set of numbers pi (1\u2009\u2264\u2009i\u2009\u2264\u2009k), such that 1\u2009\u2264\u2009k\u2009\u2264\u20093 pi is a prime The numbers pi do not necessarily have to be distinct. It is guaranteed that at least one possible solution exists.", "input_spec": "The single line contains an odd number n (3\u2009\u2264\u2009n\u2009<\u2009109).", "output_spec": "In the first line print k (1\u2009\u2264\u2009k\u2009\u2264\u20093), showing how many numbers are in the representation you found. In the second line print numbers pi in any order. If there are multiple possible solutions, you can print any of them.", "sample_inputs": ["27"], "sample_outputs": ["3\n5 11 11"], "notes": "NoteA prime is an integer strictly larger than one that is divisible only by one and by itself."}, "src_uid": "f2aaa149ce81bf332d0b5d80b2a13bc3"}
{"nl": {"description": "Kolya got string s for his birthday, the string consists of small English letters. He immediately added k more characters to the right of the string.Then Borya came and said that the new string contained a tandem repeat of length l as a substring. How large could l be?See notes for definition of a tandem repeat.", "input_spec": "The first line contains s (1\u2009\u2264\u2009|s|\u2009\u2264\u2009200). This string contains only small English letters. The second line contains number k (1\u2009\u2264\u2009k\u2009\u2264\u2009200) \u2014 the number of the added characters.", "output_spec": "Print a single number \u2014 the maximum length of the tandem repeat that could have occurred in the new string.", "sample_inputs": ["aaba\n2", "aaabbbb\n2", "abracadabra\n10"], "sample_outputs": ["6", "6", "20"], "notes": "NoteA tandem repeat of length 2n is string s, where for any position i (1\u2009\u2264\u2009i\u2009\u2264\u2009n) the following condition fulfills: si\u2009=\u2009si\u2009+\u2009n.In the first sample Kolya could obtain a string aabaab, in the second \u2014 aaabbbbbb, in the third \u2014 abracadabrabracadabra."}, "src_uid": "bb65667b65ff069a9c0c9e8fe31da8ab"}
{"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": "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": "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": "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": "Awruk is taking part in elections in his school. It is the final round. He has only one opponent\u00a0\u2014 Elodreip. The are $$$n$$$ students in the school. Each student has exactly $$$k$$$ votes and is obligated to use all of them. So Awruk knows that if a person gives $$$a_i$$$ votes for Elodreip, than he will get exactly $$$k - a_i$$$ votes from this person. Of course $$$0 \\le k - a_i$$$ holds.Awruk knows that if he loses his life is over. He has been speaking a lot with his friends and now he knows $$$a_1, a_2, \\dots, a_n$$$ \u2014 how many votes for Elodreip each student wants to give. Now he wants to change the number $$$k$$$ to win the elections. Of course he knows that bigger $$$k$$$ means bigger chance that somebody may notice that he has changed something and then he will be disqualified.So, Awruk knows $$$a_1, a_2, \\dots, a_n$$$ \u2014 how many votes each student will give to his opponent. Help him select the smallest winning number $$$k$$$. In order to win, Awruk needs to get strictly more votes than Elodreip.", "input_spec": "The first line contains integer $$$n$$$ ($$$1 \\le n \\le 100$$$)\u00a0\u2014 the number of students in the school. The second line contains $$$n$$$ integers $$$a_1, a_2, \\ldots, a_n$$$ ($$$1 \\leq a_i \\leq 100$$$)\u00a0\u2014 the number of votes each student gives to Elodreip.", "output_spec": "Output the smallest integer $$$k$$$ ($$$k \\ge \\max a_i$$$) which gives Awruk the victory. In order to win, Awruk needs to get strictly more votes than Elodreip.", "sample_inputs": ["5\n1 1 1 5 1", "5\n2 2 3 2 2"], "sample_outputs": ["5", "5"], "notes": "NoteIn the first example, Elodreip gets $$$1 + 1 + 1 + 5 + 1 = 9$$$ votes. The smallest possible $$$k$$$ is $$$5$$$ (it surely can't be less due to the fourth person), and it leads to $$$4 + 4 + 4 + 0 + 4 = 16$$$ votes for Awruk, which is enough to win.In the second example, Elodreip gets $$$11$$$ votes. If $$$k = 4$$$, Awruk gets $$$9$$$ votes and loses to Elodreip."}, "src_uid": "d215b3541d6d728ad01b166aae64faa2"}
{"nl": {"description": "You are given three integers $$$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$$$ is any binary string satisfying conditions described above. It is guaranteed that the answer always exists.", "sample_inputs": ["2 2 1", "3 3 3", "5 3 6"], "sample_outputs": ["1100", "101100", "01010100"], "notes": "NoteAll possible answers for the first example:   1100;  0011. All possible answers for the second example:   110100;  101100;  110010;  100110;  011001;  001101;  010011;  001011. "}, "src_uid": "ef4123b8f3f3b511fde8b79ea9a6b20c"}
{"nl": {"description": "Olesya loves numbers consisting of n digits, and Rodion only likes numbers that are divisible by t. Find some number that satisfies both of them.Your task is: given the n and t print an integer strictly larger than zero consisting of n digits that is divisible by t. If such number doesn't exist, print \u2009-\u20091.", "input_spec": "The single line contains two numbers, n and t (1\u2009\u2264\u2009n\u2009\u2264\u2009100, 2\u2009\u2264\u2009t\u2009\u2264\u200910) \u2014 the length of the number and the number it should be divisible by.", "output_spec": "Print one such positive number without leading zeroes, \u2014 the answer to the problem, or \u2009-\u20091, if such number doesn't exist. If there are multiple possible answers, you are allowed to print any of them.", "sample_inputs": ["3 2"], "sample_outputs": ["712"], "notes": null}, "src_uid": "77ffc1e38c32087f98ab5b3cb11cd2ed"}
{"nl": {"description": "In Omkar's last class of math, he learned about the least common multiple, or $$$LCM$$$. $$$LCM(a, b)$$$ is the smallest positive integer $$$x$$$ which is divisible by both $$$a$$$ and $$$b$$$.Omkar, having a laudably curious mind, immediately thought of a problem involving the $$$LCM$$$ operation: given an integer $$$n$$$, find positive integers $$$a$$$ and $$$b$$$ such that $$$a + b = n$$$ and $$$LCM(a, b)$$$ is the minimum value possible.Can you help Omkar solve his ludicrously challenging math problem?", "input_spec": "Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \\leq t \\leq 10$$$). Description of the test cases follows. Each test case consists of a single integer $$$n$$$ ($$$2 \\leq n \\leq 10^{9}$$$).", "output_spec": "For each test case, output two positive integers $$$a$$$ and $$$b$$$, such that $$$a + b = n$$$ and $$$LCM(a, b)$$$ is the minimum possible.", "sample_inputs": ["3\n4\n6\n9"], "sample_outputs": ["2 2\n3 3\n3 6"], "notes": "NoteFor the first test case, the numbers we can choose are $$$1, 3$$$ or $$$2, 2$$$. $$$LCM(1, 3) = 3$$$ and $$$LCM(2, 2) = 2$$$, so we output $$$2 \\ 2$$$.For the second test case, the numbers we can choose are $$$1, 5$$$, $$$2, 4$$$, or $$$3, 3$$$. $$$LCM(1, 5) = 5$$$, $$$LCM(2, 4) = 4$$$, and $$$LCM(3, 3) = 3$$$, so we output $$$3 \\ 3$$$.For the third test case, $$$LCM(3, 6) = 6$$$. It can be shown that there are no other pairs of numbers which sum to $$$9$$$ that have a lower $$$LCM$$$."}, "src_uid": "3fd60db24b1873e906d6dee9c2508ac5"}
{"nl": {"description": "The year 2015 is almost over.Limak is a little polar bear. He has recently learnt about the binary system. He noticed that the passing year has exactly one zero in its representation in the binary system\u00a0\u2014 201510\u2009=\u2009111110111112. Note that he doesn't care about the number of zeros in the decimal representation.Limak chose some interval of years. He is going to count all years from this interval that have exactly one zero in the binary representation. Can you do it faster?Assume that all positive integers are always written without leading zeros.", "input_spec": "The only line of the input contains two integers a and b (1\u2009\u2264\u2009a\u2009\u2264\u2009b\u2009\u2264\u20091018)\u00a0\u2014 the first year and the last year in Limak's interval respectively.", "output_spec": "Print one integer\u00a0\u2013 the number of years Limak will count in his chosen interval.", "sample_inputs": ["5 10", "2015 2015", "100 105", "72057594000000000 72057595000000000"], "sample_outputs": ["2", "1", "0", "26"], "notes": "NoteIn the first sample Limak's interval contains numbers 510\u2009=\u20091012, 610\u2009=\u20091102, 710\u2009=\u20091112, 810\u2009=\u200910002, 910\u2009=\u200910012 and 1010\u2009=\u200910102. Two of them (1012 and 1102) have the described property."}, "src_uid": "581f61b1f50313bf4c75833cefd4d022"}
{"nl": {"description": "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": "In the city of Ultima Thule job applicants are often offered an IQ test. The test is as follows: the person gets a piece of squared paper with a 4\u2009\u00d7\u20094 square painted on it. Some of the square's cells are painted black and others are painted white. Your task is to repaint at most one cell the other color so that the picture has a 2\u2009\u00d7\u20092 square, completely consisting of cells of the same color. If the initial picture already has such a square, the person should just say so and the test will be completed. Your task is to write a program that determines whether it is possible to pass the test. You cannot pass the test if either repainting any cell or no action doesn't result in a 2\u2009\u00d7\u20092 square, consisting of cells of the same color.", "input_spec": "Four lines contain four characters each: the j-th character of the i-th line equals \".\" if the cell in the i-th row and the j-th column of the square is painted white, and \"#\", if the cell is black.", "output_spec": "Print \"YES\" (without the quotes), if the test can be passed and \"NO\" (without the quotes) otherwise.", "sample_inputs": ["####\n.#..\n####\n....", "####\n....\n####\n...."], "sample_outputs": ["YES", "NO"], "notes": "NoteIn the first test sample it is enough to repaint the first cell in the second row. After such repainting the required 2\u2009\u00d7\u20092 square is on the intersection of the 1-st and 2-nd row with the 1-st and 2-nd column."}, "src_uid": "01b145e798bbdf0ca2ecc383676d79f3"}
{"nl": {"description": "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": "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": "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": "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": "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": "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$$$ which makes it clearly impossible."}, "src_uid": "959d56affbe2ff5dd999a7e8729f60ce"}
{"nl": {"description": "You are given a string q. A sequence of k strings s1,\u2009s2,\u2009...,\u2009sk is called beautiful, if the concatenation of these strings is string q (formally, s1\u2009+\u2009s2\u2009+\u2009...\u2009+\u2009sk\u2009=\u2009q) and the first characters of these strings are distinct.Find any beautiful sequence of strings or determine that the beautiful sequence doesn't exist.", "input_spec": "The first line contains a positive integer k (1\u2009\u2264\u2009k\u2009\u2264\u200926) \u2014 the number of strings that should be in a beautiful sequence.  The second line contains string q, consisting of lowercase Latin letters. The length of the string is within range from 1 to 100, inclusive.", "output_spec": "If such sequence doesn't exist, then print in a single line \"NO\" (without the quotes). Otherwise, print in the first line \"YES\" (without the quotes) and in the next k lines print the beautiful sequence of strings s1,\u2009s2,\u2009...,\u2009sk. If there are multiple possible answers, print any of them.", "sample_inputs": ["1\nabca", "2\naaacas", "4\nabc"], "sample_outputs": ["YES\nabca", "YES\naaa\ncas", "NO"], "notes": "NoteIn the second sample there are two possible answers: {\"aaaca\",\u2009\"s\"} and {\"aaa\",\u2009\"cas\"}."}, "src_uid": "c1b071f09ef375f19031ce99d10e90ab"}
{"nl": {"description": "The king's birthday dinner was attended by $$$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": "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": "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": "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": "Have you ever tried to explain to the coordinator, why it is eight hours to the contest and not a single problem has been prepared yet? Misha had. And this time he has a really strong excuse: he faced a space-time paradox! Space and time replaced each other.The entire universe turned into an enormous clock face with three hands\u00a0\u2014 hour, minute, and second. Time froze, and clocks now show the time h hours, m minutes, s seconds.Last time Misha talked with the coordinator at t1 o'clock, so now he stands on the number t1 on the clock face. The contest should be ready by t2 o'clock. In the terms of paradox it means that Misha has to go to number t2 somehow. Note that he doesn't have to move forward only: in these circumstances time has no direction.Clock hands are very long, and Misha cannot get round them. He also cannot step over as it leads to the collapse of space-time. That is, if hour clock points 12 and Misha stands at 11 then he cannot move to 1 along the top arc. He has to follow all the way round the clock center (of course, if there are no other hands on his way).Given the hands' positions, t1, and t2, find if Misha can prepare the contest on time (or should we say on space?). That is, find if he can move from t1 to t2 by the clock face.", "input_spec": "Five integers h, m, s, t1, t2 (1\u2009\u2264\u2009h\u2009\u2264\u200912, 0\u2009\u2264\u2009m,\u2009s\u2009\u2264\u200959, 1\u2009\u2264\u2009t1,\u2009t2\u2009\u2264\u200912, t1\u2009\u2260\u2009t2). Misha's position and the target time do not coincide with the position of any hand.", "output_spec": "Print \"YES\" (quotes for clarity), if Misha can prepare the contest on time, and \"NO\" otherwise. You can print each character either upper- or lowercase (\"YeS\" and \"yes\" are valid when the answer is \"YES\").", "sample_inputs": ["12 30 45 3 11", "12 0 1 12 1", "3 47 0 4 9"], "sample_outputs": ["NO", "YES", "YES"], "notes": "NoteThe three examples are shown on the pictures below from left to right. The starting position of Misha is shown with green, the ending position is shown with pink. Note that the positions of the hands on the pictures are not exact, but are close to the exact and the answer is the same.  "}, "src_uid": "912c8f557a976bdedda728ba9f916c95"}
{"nl": {"description": "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": "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": "You are at a water bowling training. There are l people who play with their left hand, r people, who play with their right hand, and a ambidexters, who can play with left or right hand.The coach decided to form a team of even number of players, exactly half of the players should play with their right hand, and exactly half of the players should play with their left hand. One player should use only on of his hands.Ambidexters play as well with their right hand as with their left hand. In the team, an ambidexter can play with their left hand, or with their right hand.Please find the maximum possible size of the team, where equal number of players use their left and right hands, respectively.", "input_spec": "The only line contains three integers l, r and a (0\u2009\u2264\u2009l,\u2009r,\u2009a\u2009\u2264\u2009100) \u2014 the number of left-handers, the number of right-handers and the number of ambidexters at the training. ", "output_spec": "Print a single even integer\u00a0\u2014 the maximum number of players in the team. It is possible that the team can only have zero number of players.", "sample_inputs": ["1 4 2", "5 5 5", "0 2 0"], "sample_outputs": ["6", "14", "0"], "notes": "NoteIn the first example you can form a team of 6 players. You should take the only left-hander and two ambidexters to play with left hand, and three right-handers to play with right hand. The only person left can't be taken into the team.In the second example you can form a team of 14 people. You have to take all five left-handers, all five right-handers, two ambidexters to play with left hand and two ambidexters to play with right hand."}, "src_uid": "e8148140e61baffd0878376ac5f3857c"}
{"nl": {"description": "\"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": "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$$$ denotes that a suit for this dancer is still to be bought.", "output_spec": "If it is not possible to form a palindrome without swapping dancers and buying new suits for those who have one, then output -1. Otherwise, output the minimal price to get the desired visual effect.", "sample_inputs": ["5 100 1\n0 1 2 1 2", "3 10 12\n1 2 0", "3 12 1\n0 1 0"], "sample_outputs": ["101", "-1", "0"], "notes": "NoteIn the first sample, the cheapest way to obtain palindromic colors is to buy a black suit for the third from left dancer and a white suit for the rightmost dancer.In the second sample, the leftmost dancer's suit already differs from the rightmost dancer's suit so there is no way to obtain the desired coloring.In the third sample, all suits are already bought and their colors form a palindrome."}, "src_uid": "af07223819aeb5bd6ded4340c472b2b6"}
{"nl": {"description": "Translator's note: in Russia's most widespread grading system, there are four grades: 5, 4, 3, 2, the higher the better, roughly corresponding to A, B, C and F respectively in American grading system.The term is coming to an end and students start thinking about their grades. Today, a professor told his students that the grades for his course would be given out automatically \u00a0\u2014 he would calculate the simple average (arithmetic mean) of all grades given out for lab works this term and round to the nearest integer. The rounding would be done in favour of the student\u00a0\u2014 $$$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": "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": "Dima and Inna are doing so great! At the moment, Inna is sitting on the magic lawn playing with a pink pony. Dima wanted to play too. He brought an n\u2009\u00d7\u2009m chessboard, a very tasty candy and two numbers a and b.Dima put the chessboard in front of Inna and placed the candy in position (i,\u2009j) on the board. The boy said he would give the candy if it reaches one of the corner cells of the board. He's got one more condition. There can only be actions of the following types:  move the candy from position (x,\u2009y) on the board to position (x\u2009-\u2009a,\u2009y\u2009-\u2009b);  move the candy from position (x,\u2009y) on the board to position (x\u2009+\u2009a,\u2009y\u2009-\u2009b);  move the candy from position (x,\u2009y) on the board to position (x\u2009-\u2009a,\u2009y\u2009+\u2009b);  move the candy from position (x,\u2009y) on the board to position (x\u2009+\u2009a,\u2009y\u2009+\u2009b). Naturally, Dima doesn't allow to move the candy beyond the chessboard borders.Inna and the pony started shifting the candy around the board. They wonder what is the minimum number of allowed actions that they need to perform to move the candy from the initial position (i,\u2009j) to one of the chessboard corners. Help them cope with the task! ", "input_spec": "The first line of the input contains six integers n,\u2009m,\u2009i,\u2009j,\u2009a,\u2009b (1\u2009\u2264\u2009n,\u2009m\u2009\u2264\u2009106;\u00a01\u2009\u2264\u2009i\u2009\u2264\u2009n;\u00a01\u2009\u2264\u2009j\u2009\u2264\u2009m;\u00a01\u2009\u2264\u2009a,\u2009b\u2009\u2264\u2009106). You can assume that the chessboard rows are numbered from 1 to n from top to bottom and the columns are numbered from 1 to m from left to right. Position (i,\u2009j) in the statement is a chessboard cell on the intersection of the i-th row and the j-th column. You can consider that the corners are: (1,\u2009m), (n,\u20091), (n,\u2009m), (1,\u20091).", "output_spec": "In a single line print a single integer \u2014 the minimum number of moves needed to get the candy. If Inna and the pony cannot get the candy playing by Dima's rules, print on a single line \"Poor Inna and pony!\" without the quotes.", "sample_inputs": ["5 7 1 3 2 2", "5 5 2 3 1 1"], "sample_outputs": ["2", "Poor Inna and pony!"], "notes": "NoteNote to sample 1:Inna and the pony can move the candy to position (1\u2009+\u20092,\u20093\u2009+\u20092)\u2009=\u2009(3,\u20095), from there they can move it to positions (3\u2009-\u20092,\u20095\u2009+\u20092)\u2009=\u2009(1,\u20097) and (3\u2009+\u20092,\u20095\u2009+\u20092)\u2009=\u2009(5,\u20097). These positions correspond to the corner squares of the chess board. Thus, the answer to the test sample equals two."}, "src_uid": "51155e9bfa90e0ff29d049cedc3e1862"}
{"nl": {"description": "Everybody in Russia uses Gregorian calendar. In this calendar there are 31 days in January, 28 or 29 days in February (depending on whether the year is leap or not), 31 days in March, 30 days in April, 31 days in May, 30 in June, 31 in July, 31 in August, 30 in September, 31 in October, 30 in November, 31 in December.A year is leap in one of two cases: either its number is divisible by 4, but not divisible by 100, or is divisible by 400. For example, the following years are leap: 2000, 2004, but years 1900 and 2018 are not leap.In this problem you are given n (1\u2009\u2264\u2009n\u2009\u2264\u200924) integers a1,\u2009a2,\u2009...,\u2009an, and you have to check if these integers could be durations in days of n consecutive months, according to Gregorian calendar. Note that these months could belong to several consecutive years. In other words, check if there is a month in some year, such that its duration is a1 days, duration of the next month is a2 days, and so on.", "input_spec": "The first line contains single integer n (1\u2009\u2264\u2009n\u2009\u2264\u200924) \u2014 the number of integers. The second line contains n integers a1,\u2009a2,\u2009...,\u2009an (28\u2009\u2264\u2009ai\u2009\u2264\u200931) \u2014 the numbers you are to check.", "output_spec": "If there are several consecutive months that fit the sequence, print \"YES\" (without quotes). Otherwise, print \"NO\" (without quotes). You can print each letter in arbitrary case (small or large).", "sample_inputs": ["4\n31 31 30 31", "2\n30 30", "5\n29 31 30 31 30", "3\n31 28 30", "3\n31 31 28"], "sample_outputs": ["Yes", "No", "Yes", "No", "Yes"], "notes": "NoteIn the first example the integers can denote months July, August, September and October.In the second example the answer is no, because there are no two consecutive months each having 30 days.In the third example the months are: February (leap year) \u2014 March \u2014 April \u2013 May \u2014 June.In the fourth example the number of days in the second month is 28, so this is February. March follows February and has 31 days, but not 30, so the answer is NO.In the fifth example the months are: December \u2014 January \u2014 February (non-leap year)."}, "src_uid": "d60c8895cebcc5d0c6459238edbdb945"}
{"nl": {"description": "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$$$."}, "src_uid": "cb4de190ae26127df6eeb7a1a1db8a6d"}
{"nl": {"description": "Moamen and Ezzat are playing a game. They create an array $$$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": "Sheldon, Leonard, Penny, Rajesh and Howard are in the queue for a \"Double Cola\" drink vending machine; there are no other people in the queue. The first one in the queue (Sheldon) buys a can, drinks it and doubles! The resulting two Sheldons go to the end of the queue. Then the next in the queue (Leonard) buys a can, drinks it and gets to the end of the queue as two Leonards, and so on. This process continues ad infinitum.For example, Penny drinks the third can of cola and the queue will look like this: Rajesh, Howard, Sheldon, Sheldon, Leonard, Leonard, Penny, Penny.Write a program that will print the name of a man who will drink the n-th can.Note that in the very beginning the queue looks like that: Sheldon, Leonard, Penny, Rajesh, Howard. The first person is Sheldon.", "input_spec": "The input data consist of a single integer n (1\u2009\u2264\u2009n\u2009\u2264\u2009109). It is guaranteed that the pretests check the spelling of all the five names, that is, that they contain all the five possible answers.", "output_spec": "Print the single line \u2014 the name of the person who drinks the n-th can of cola. The cans are numbered starting from 1. Please note that you should spell the names like this: \"Sheldon\", \"Leonard\", \"Penny\", \"Rajesh\", \"Howard\" (without the quotes). In that order precisely the friends are in the queue initially.", "sample_inputs": ["1", "6", "1802"], "sample_outputs": ["Sheldon", "Sheldon", "Penny"], "notes": null}, "src_uid": "023b169765e81d896cdc1184e5a82b22"}
{"nl": {"description": "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": "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$$$.In the second example, there is no way of building a majority, as both other parties are too large to become a coalition partner.In the third example, Alice already has the majority. The fourth example is described in the problem statement."}, "src_uid": "0a71fdaaf08c18396324ad762b7379d7"}
{"nl": {"description": "There are $$$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": "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": "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": "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": "Jon fought bravely to rescue the wildlings who were attacked by the white-walkers at Hardhome. On his arrival, Sam tells him that he wants to go to Oldtown to train at the Citadel to become a maester, so he can return and take the deceased Aemon's place as maester of Castle Black. Jon agrees to Sam's proposal and Sam sets off his journey to the Citadel. However becoming a trainee at the Citadel is not a cakewalk and hence the maesters at the Citadel gave Sam a problem to test his eligibility. Initially Sam has a list with a single element n. Then he has to perform certain operations on this list. In each operation Sam must remove any element x, such that x\u2009>\u20091, from the list and insert at the same position , ,  sequentially. He must continue with these operations until all the elements in the list are either 0 or 1.Now the masters want the total number of 1s in the range l to r (1-indexed). Sam wants to become a maester but unfortunately he cannot solve this problem. Can you help Sam to pass the eligibility test?", "input_spec": "The first line contains three integers n, l, r (0\u2009\u2264\u2009n\u2009<\u2009250, 0\u2009\u2264\u2009r\u2009-\u2009l\u2009\u2264\u2009105, r\u2009\u2265\u20091, l\u2009\u2265\u20091) \u2013 initial element and the range l to r. It is guaranteed that r is not greater than the length of the final list.", "output_spec": "Output the total number of 1s in the range l to r in the final sequence.", "sample_inputs": ["7 2 5", "10 3 10"], "sample_outputs": ["4", "5"], "notes": "NoteConsider first example:Elements on positions from 2-nd to 5-th in list is [1,\u20091,\u20091,\u20091]. The number of ones is 4.For the second example:Elements on positions from 3-rd to 10-th in list is [1,\u20091,\u20091,\u20090,\u20091,\u20090,\u20091,\u20090]. The number of ones is 5."}, "src_uid": "3ac61b1f8deee7911b1055c243f5eb6a"}
{"nl": {"description": "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": "Two players play a simple game. Each player is provided with a box with balls. First player's box contains exactly n1 balls and second player's box contains exactly n2 balls. In one move first player can take from 1 to k1 balls from his box and throw them away. Similarly, the second player can take from 1 to k2 balls from his box in his move. Players alternate turns and the first player starts the game. The one who can't make a move loses. Your task is to determine who wins if both players play optimally.", "input_spec": "The first line contains four integers n1,\u2009n2,\u2009k1,\u2009k2. All numbers in the input are from 1 to 50. This problem doesn't have subproblems. You will get 3 points for the correct submission.", "output_spec": "Output \"First\" if the first player wins and \"Second\" otherwise.", "sample_inputs": ["2 2 1 2", "2 1 1 1"], "sample_outputs": ["Second", "First"], "notes": "NoteConsider the first sample test. Each player has a box with 2 balls. The first player draws a single ball from his box in one move and the second player can either take 1 or 2 balls from his box in one move. No matter how the first player acts, the second player can always win if he plays wisely."}, "src_uid": "aed24ebab3ed9fd1741eea8e4200f86b"}
{"nl": {"description": "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": " \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": "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": "Alice has got addicted to a game called Sirtet recently.In Sirtet, player is given an $$$n \\times m$$$ grid. Initially $$$a_{i,j}$$$ cubes are stacked up in the cell $$$(i,j)$$$. Two cells are called adjacent if they share a side. Player can perform the following operations:   stack up one cube in two adjacent cells;  stack up two cubes in one cell. Cubes mentioned above are identical in height.Here is an illustration of the game. States on the right are obtained by performing one of the above operations on the state on the left, and grey cubes are added due to the operation.  Player's goal is to make the height of all cells the same (i.e. so that each cell has the same number of cubes in it) using above operations. Alice, however, has found out that on some starting grids she may never reach the goal no matter what strategy she uses. Thus, she is wondering the number of initial grids such that   $$$L \\le a_{i,j} \\le R$$$ for all $$$1 \\le i \\le n$$$, $$$1 \\le j \\le m$$$;  player can reach the goal using above operations. Please help Alice with it. Notice that the answer might be large, please output the desired value modulo $$$998,244,353$$$.", "input_spec": "The only line contains four integers $$$n$$$, $$$m$$$, $$$L$$$ and $$$R$$$ ($$$1\\le n,m,L,R \\le 10^9$$$, $$$L \\le R$$$, $$$n \\cdot m \\ge 2$$$).", "output_spec": "Output one integer, representing the desired answer modulo $$$998,244,353$$$.", "sample_inputs": ["2 2 1 1", "1 2 1 2"], "sample_outputs": ["1", "2"], "notes": "NoteIn the first sample, the only initial grid that satisfies the requirements is $$$a_{1,1}=a_{2,1}=a_{1,2}=a_{2,2}=1$$$. Thus the answer should be $$$1$$$.In the second sample, initial grids that satisfy the requirements are $$$a_{1,1}=a_{1,2}=1$$$ and $$$a_{1,1}=a_{1,2}=2$$$. Thus the answer should be $$$2$$$."}, "src_uid": "ded299fa1cd010822c60f2389a3ba1a3"}
{"nl": {"description": "To make a paper airplane, one has to use a rectangular piece of paper. From a sheet of standard size you can make $$$s$$$ airplanes.A group of $$$k$$$ people decided to make $$$n$$$ airplanes each. They are going to buy several packs of paper, each of them containing $$$p$$$ sheets, and then distribute the sheets between the people. Each person should have enough sheets to make $$$n$$$ airplanes. How many packs should they buy?", "input_spec": "The only line contains four integers $$$k$$$, $$$n$$$, $$$s$$$, $$$p$$$ ($$$1 \\le k, n, s, p \\le 10^4$$$)\u00a0\u2014 the number of people, the number of airplanes each should make, the number of airplanes that can be made using one sheet and the number of sheets in one pack, respectively.", "output_spec": "Print a single integer\u00a0\u2014 the minimum number of packs they should buy.", "sample_inputs": ["5 3 2 3", "5 3 100 1"], "sample_outputs": ["4", "5"], "notes": "NoteIn the first sample they have to buy $$$4$$$ packs of paper: there will be $$$12$$$ sheets in total, and giving $$$2$$$ sheets to each person is enough to suit everyone's needs.In the second sample they have to buy a pack for each person as they can't share sheets."}, "src_uid": "73f0c7cfc06a9b04e4766d6aa61fc780"}
{"nl": {"description": "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": "If an integer a is divisible by another integer b, then b is called the divisor of a.For example: 12 has positive 6 divisors. They are 1, 2, 3, 4, 6 and 12.Let\u2019s define a function D(n) \u2014 number of integers between 1 and n (inclusive) which has exactly four positive divisors.Between 1 and 10 only the integers 6, 8 and 10 has exactly four positive divisors. So, D(10)\u2009=\u20093.You are given an integer n. You have to calculate D(n).", "input_spec": "The only line contains integer n (1\u2009\u2264\u2009n\u2009\u2264\u20091011) \u2014 the parameter from the problem statement.", "output_spec": "Print the only integer c \u2014 the number of integers between 1 and n with exactly four divisors.", "sample_inputs": ["10", "20"], "sample_outputs": ["3", "5"], "notes": null}, "src_uid": "ffb7762f1d60dc3f16e9b27ea0ecdd7d"}
{"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": "In a small but very proud high school it was decided to win ACM ICPC. This goal requires to compose as many teams of three as possible, but since there were only 6 students who wished to participate, the decision was to build exactly two teams.After practice competition, participant number i got a score of ai. Team score is defined as sum of scores of its participants. High school management is interested if it's possible to build two teams with equal scores. Your task is to answer that question.", "input_spec": "The single line contains six integers a1,\u2009...,\u2009a6 (0\u2009\u2264\u2009ai\u2009\u2264\u20091000) \u2014 scores of the participants", "output_spec": "Print \"YES\" (quotes for clarity), if it is possible to build teams with equal score, and \"NO\" otherwise. You can print each character either upper- or lowercase (\"YeS\" and \"yes\" are valid when the answer is \"YES\").", "sample_inputs": ["1 3 2 1 2 1", "1 1 1 1 1 99"], "sample_outputs": ["YES", "NO"], "notes": "NoteIn the first sample, first team can be composed of 1st, 2nd and 6th participant, second \u2014 of 3rd, 4th and 5th: team scores are 1\u2009+\u20093\u2009+\u20091\u2009=\u20092\u2009+\u20091\u2009+\u20092\u2009=\u20095.In the second sample, score of participant number 6 is too high: his team score will be definitely greater."}, "src_uid": "2acf686862a34c337d1d2cbc0ac3fd11"}
{"nl": {"description": "Kirill plays a new computer game. He came to the potion store where he can buy any potion. Each potion is characterized by two integers\u00a0\u2014 amount of experience and cost. The efficiency of a potion is the ratio of the amount of experience to the cost. Efficiency may be a non-integer number.For each two integer numbers a and b such that l\u2009\u2264\u2009a\u2009\u2264\u2009r and x\u2009\u2264\u2009b\u2009\u2264\u2009y there is a potion with experience a and cost b in the store (that is, there are (r\u2009-\u2009l\u2009+\u20091)\u00b7(y\u2009-\u2009x\u2009+\u20091) potions).Kirill wants to buy a potion which has efficiency k. Will he be able to do this?", "input_spec": "First string contains five integer numbers l, r, x, y, k (1\u2009\u2264\u2009l\u2009\u2264\u2009r\u2009\u2264\u2009107, 1\u2009\u2264\u2009x\u2009\u2264\u2009y\u2009\u2264\u2009107, 1\u2009\u2264\u2009k\u2009\u2264\u2009107).", "output_spec": "Print \"YES\" without quotes if a potion with efficiency exactly k can be bought in the store and \"NO\" without quotes otherwise. You can output each of the letters in any register.", "sample_inputs": ["1 10 1 10 1", "1 5 6 10 1"], "sample_outputs": ["YES", "NO"], "notes": null}, "src_uid": "1110d3671e9f77fd8d66dca6e74d2048"}
{"nl": {"description": "This is the easy version of this problem. The difference between easy and hard versions is the constraint on $$$k$$$ and the time limit. Also, in this version of the problem, you only need to calculate the answer when $$$n=k$$$. You can make hacks only if both versions of the problem are solved.Cirno is playing a war simulator game with $$$n$$$ towers (numbered from $$$1$$$ to $$$n$$$) and $$$n$$$ bots (numbered from $$$1$$$ to $$$n$$$). The $$$i$$$-th tower is initially occupied by the $$$i$$$-th bot for $$$1 \\le i \\le n$$$.Before the game, Cirno first chooses a permutation $$$p = [p_1, p_2, \\ldots, p_n]$$$ of length $$$n$$$ (A permutation of length $$$n$$$ is an array of length $$$n$$$ where each integer between $$$1$$$ and $$$n$$$ appears exactly once). After that, she can choose a sequence $$$a = [a_1, a_2, \\ldots, a_n]$$$ ($$$1 \\le a_i \\le n$$$ and $$$a_i \\ne i$$$ for all $$$1 \\le i \\le n$$$).The game has $$$n$$$ rounds of attacks. In the $$$i$$$-th round, if the $$$p_i$$$-th bot is still in the game, it will begin its attack, and as the result the $$$a_{p_i}$$$-th tower becomes occupied by the $$$p_i$$$-th bot; the bot that previously occupied the $$$a_{p_i}$$$-th tower will no longer occupy it. If the $$$p_i$$$-th bot is not in the game, nothing will happen in this round.After each round, if a bot doesn't occupy any towers, it will be eliminated and leave the game. Please note that no tower can be occupied by more than one bot, but one bot can occupy more than one tower during the game.At the end of the game, Cirno will record the result as a sequence $$$b = [b_1, b_2, \\ldots, b_n]$$$, where $$$b_i$$$ is the number of the bot that occupies the $$$i$$$-th tower at the end of the game.However, as a mathematics master, she wants you to solve the following counting problem instead of playing games:Count the number of different pairs of sequences $$$a$$$ and $$$b$$$ that we can get from all possible choices of sequence $$$a$$$ and permutation $$$p$$$.Since this number may be large, output it modulo $$$M$$$.", "input_spec": "The only line contains two positive integers $$$k$$$ and $$$M$$$ ($$$1\\le k\\le 5000$$$, $$$2\\le M\\le 10^9$$$ ). It is guaranteed that $$$2^{18}$$$ is a divisor of $$$M-1$$$ and $$$M$$$ is a prime number. You need to calculate the answer for $$$n=k$$$.", "output_spec": "Output a single integer \u2014 the number of different pairs of sequences for $$$n=k$$$ modulo $$$M$$$.", "sample_inputs": ["1 998244353", "2 998244353", "3 998244353", "8 998244353"], "sample_outputs": ["0", "2", "24", "123391016"], "notes": "NoteFor $$$n=1$$$, no valid sequence $$$a$$$ exists. We regard the answer as $$$0$$$.For $$$n=2$$$, there is only one possible array $$$a$$$: $$$[2, 1]$$$.   For array $$$a$$$ is $$$[2, 1]$$$ and permutation $$$p$$$ is $$$[1, 2]$$$, the sequence $$$b$$$ will be $$$[1, 1]$$$ after all rounds have finished. The details for each rounds:   In the first round, the first bot will begin its attack and successfully capture the tower $$$2$$$. After this round, the second bot will be eliminated and leave the game as all of its towers are occupied by other bots.  In the second round, the second bot is not in the game.   For array $$$a$$$ is $$$[2, 1]$$$ and permutation $$$p$$$ is $$$[2, 1]$$$, the sequence $$$b$$$ will be $$$[2, 2]$$$ after all rounds have finished. The details for each rounds:   In the first round, the second bot will begin its attack and successfully capture the tower $$$1$$$. After this round, the first bot will be eliminated and leave the game as all of its towers are occupied by other bots.  In the second round, the first bot is not in the game.  So the number of different pairs of sequences $$$(a,b)$$$ is $$$2$$$ ($$$[2, 1]$$$, $$$[1, 1]$$$ and $$$[2, 1]$$$, $$$[2, 2]$$$) for $$$n=2$$$."}, "src_uid": "2d5a5055aaf34f4d300cfdf7c21748c3"}
{"nl": {"description": "Two chess pieces, a rook and a knight, stand on a standard chessboard 8\u2009\u00d7\u20098 in size. The positions in which they are situated are known. It is guaranteed that none of them beats the other one.Your task is to find the number of ways to place another knight on the board so that none of the three pieces on the board beat another one. A new piece can only be placed on an empty square.", "input_spec": "The first input line contains the description of the rook's position on the board. This description is a line which is 2 in length. Its first symbol is a lower-case Latin letter from a to h, and its second symbol is a number from 1 to 8. The second line contains the description of the knight's position in a similar way. It is guaranteed that their positions do not coincide.", "output_spec": "Print a single number which is the required number of ways.", "sample_inputs": ["a1\nb2", "a8\nd4"], "sample_outputs": ["44", "38"], "notes": null}, "src_uid": "073023c6b72ce923df2afd6130719cfc"}
{"nl": {"description": "You have $$$n$$$ coins, each of the same value of $$$1$$$.Distribute them into packets such that any amount $$$x$$$ ($$$1 \\leq x \\leq n$$$) can be formed using some (possibly one or all) number of these packets.Each packet may only be used entirely or not used at all. No packet may be used more than once in the formation of the single $$$x$$$, however it may be reused for the formation of other $$$x$$$'s.Find the minimum number of packets in such a distribution.", "input_spec": "The only line contains a single integer $$$n$$$ ($$$1 \\leq n \\leq 10^9$$$)\u00a0\u2014 the number of coins you have.", "output_spec": "Output a single integer\u00a0\u2014 the minimum possible number of packets, satisfying the condition above.", "sample_inputs": ["6", "2"], "sample_outputs": ["3", "2"], "notes": "NoteIn the first example, three packets with $$$1$$$, $$$2$$$ and $$$3$$$ coins can be made to get any amount $$$x$$$ ($$$1\\leq x\\leq 6$$$).  To get $$$1$$$ use the packet with $$$1$$$ coin.  To get $$$2$$$ use the packet with $$$2$$$ coins.  To get $$$3$$$ use the packet with $$$3$$$ coins.  To get $$$4$$$ use packets with $$$1$$$ and $$$3$$$ coins.  To get $$$5$$$ use packets with $$$2$$$ and $$$3$$$ coins  To get $$$6$$$ use all packets. In the second example, two packets with $$$1$$$ and $$$1$$$ coins can be made to get any amount $$$x$$$ ($$$1\\leq x\\leq 2$$$)."}, "src_uid": "95cb79597443461085e62d974d67a9a0"}
{"nl": {"description": "InputThe input contains a single integer a (10\u2009\u2264\u2009a\u2009\u2264\u2009999).OutputOutput 0 or 1.ExamplesInput13Output1Input927Output1Input48Output0", "input_spec": "The input contains a single integer a (10\u2009\u2264\u2009a\u2009\u2264\u2009999).", "output_spec": "Output 0 or 1.", "sample_inputs": ["13", "927", "48"], "sample_outputs": ["1", "1", "0"], "notes": null}, "src_uid": "78e64fdbf59c5ce89d0f0a1d0591f795"}
{"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": "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": "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": "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": "PolandBall is a young, clever Ball. He is interested in prime numbers. He has stated a following hypothesis: \"There exists such a positive integer n that for each positive integer m number n\u00b7m\u2009+\u20091 is a prime number\".Unfortunately, PolandBall is not experienced yet and doesn't know that his hypothesis is incorrect. Could you prove it wrong? Write a program that finds a counterexample for any n.", "input_spec": "The only number in the input is n (1\u2009\u2264\u2009n\u2009\u2264\u20091000)\u00a0\u2014 number from the PolandBall's hypothesis. ", "output_spec": "Output such m that n\u00b7m\u2009+\u20091 is not a prime number. Your answer will be considered correct if you output any suitable m such that 1\u2009\u2264\u2009m\u2009\u2264\u2009103. It is guaranteed the the answer exists.", "sample_inputs": ["3", "4"], "sample_outputs": ["1", "2"], "notes": "NoteA prime number (or a prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself.For the first sample testcase, 3\u00b71\u2009+\u20091\u2009=\u20094. We can output 1.In the second sample testcase, 4\u00b71\u2009+\u20091\u2009=\u20095. We cannot output 1 because 5 is prime. However, m\u2009=\u20092 is okay since 4\u00b72\u2009+\u20091\u2009=\u20099, which is not a prime number."}, "src_uid": "5c68e20ac6ecb7c289601ce8351f4e97"}
{"nl": {"description": "The only difference between easy and hard versions is the constraints.Polycarp has to write a coursework. The coursework consists of $$$m$$$ pages.Polycarp also has $$$n$$$ cups of coffee. The coffee in the $$$i$$$-th cup has $$$a_i$$$ caffeine in it. Polycarp can drink some cups of coffee (each one no more than once). He can drink cups in any order. Polycarp drinks each cup instantly and completely (i.e. he cannot split any cup into several days).Surely, courseworks are not usually being written in a single day (in a perfect world of Berland, at least). Some of them require multiple days of hard work.Let's consider some day of Polycarp's work. Consider Polycarp drinks $$$k$$$ cups of coffee during this day and caffeine dosages of cups Polycarp drink during this day are $$$a_{i_1}, a_{i_2}, \\dots, a_{i_k}$$$. Then the first cup he drinks gives him energy to write $$$a_{i_1}$$$ pages of coursework, the second cup gives him energy to write $$$max(0, a_{i_2} - 1)$$$ pages, the third cup gives him energy to write $$$max(0, a_{i_3} - 2)$$$ pages, ..., the $$$k$$$-th cup gives him energy to write $$$max(0, a_{i_k} - k + 1)$$$ pages.If Polycarp doesn't drink coffee during some day, he cannot write coursework at all that day.Polycarp has to finish his coursework as soon as possible (spend the minimum number of days to do it). Your task is to find out this number of days or say that it is impossible.", "input_spec": "The first line of the input contains two integers $$$n$$$ and $$$m$$$ ($$$1 \\le n \\le 100$$$, $$$1 \\le m \\le 10^4$$$) \u2014 the number of cups of coffee and the number of pages in the coursework. The second line of the input contains $$$n$$$ integers $$$a_1, a_2, \\dots, a_n$$$ ($$$1 \\le a_i \\le 100$$$), where $$$a_i$$$ is the caffeine dosage of coffee in the $$$i$$$-th cup.", "output_spec": "If it is impossible to write the coursework, print -1. Otherwise print the minimum number of days Polycarp needs to do it.", "sample_inputs": ["5 8\n2 3 1 1 2", "7 10\n1 3 4 2 1 4 2", "5 15\n5 5 5 5 5", "5 16\n5 5 5 5 5", "5 26\n5 5 5 5 5"], "sample_outputs": ["4", "2", "1", "2", "-1"], "notes": "NoteIn the first example Polycarp can drink fourth cup during first day (and write $$$1$$$ page), first and second cups during second day (and write $$$2 + (3 - 1) = 4$$$ pages), fifth cup during the third day (and write $$$2$$$ pages) and third cup during the fourth day (and write $$$1$$$ page) so the answer is $$$4$$$. It is obvious that there is no way to write the coursework in three or less days in this test.In the second example Polycarp can drink third, fourth and second cups during first day (and write $$$4 + (2 - 1) + (3 - 2) = 6$$$ pages) and sixth cup during second day (and write $$$4$$$ pages) so the answer is $$$2$$$. It is obvious that Polycarp cannot write the whole coursework in one day in this test.In the third example Polycarp can drink all cups of coffee during first day and write $$$5 + (5 - 1) + (5 - 2) + (5 - 3) + (5 - 4) = 15$$$ pages of coursework.In the fourth example Polycarp cannot drink all cups during first day and should drink one of them during the second day. So during first day he will write $$$5 + (5 - 1) + (5 - 2) + (5 - 3) = 14$$$ pages of coursework and during second day he will write $$$5$$$ pages of coursework. This is enough to complete it.In the fifth example Polycarp cannot write the whole coursework at all, even if he will drink one cup of coffee during each day, so the answer is -1."}, "src_uid": "acb8a57c8cfdb849a55fa65aff86628d"}
{"nl": {"description": "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": "Little Dima misbehaved during a math lesson a lot and the nasty teacher Mr. Pickles gave him the following problem as a punishment. Find all integer solutions x (0\u2009<\u2009x\u2009<\u2009109) of the equation:x\u2009=\u2009b\u00b7s(x)a\u2009+\u2009c,\u2009 where a, b, c are some predetermined constant values and function s(x) determines the sum of all digits in the decimal representation of number x.The teacher gives this problem to Dima for each lesson. He changes only the parameters of the equation: a, b, c. Dima got sick of getting bad marks and he asks you to help him solve this challenging problem.", "input_spec": "The first line contains three space-separated integers: a,\u2009b,\u2009c (1\u2009\u2264\u2009a\u2009\u2264\u20095;\u00a01\u2009\u2264\u2009b\u2009\u2264\u200910000;\u00a0\u2009-\u200910000\u2009\u2264\u2009c\u2009\u2264\u200910000).", "output_spec": "Print integer n \u2014 the number of the solutions that you've found. Next print n integers in the increasing order \u2014 the solutions of the given equation. Print only integer solutions that are larger than zero and strictly less than 109.", "sample_inputs": ["3 2 8", "1 2 -18", "2 2 -1"], "sample_outputs": ["3\n10 2008 13726", "0", "4\n1 31 337 967"], "notes": null}, "src_uid": "e477185b94f93006d7ae84c8f0817009"}
{"nl": {"description": "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": "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": "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$$$, so the answer is -1."}, "src_uid": "fa4b1de79708329bb85437e1413e13df"}
{"nl": {"description": "As behooves any intelligent schoolboy, Kevin Sun is studying psycowlogy, cowculus, and cryptcowgraphy at the Bovinia State University (BGU) under Farmer Ivan. During his Mathematics of Olympiads (MoO) class, Kevin was confronted with a weird functional equation and needs your help. For two fixed integers k and p, where p is an odd prime number, the functional equation states that  for some function . (This equation should hold for any integer x in the range 0 to p\u2009-\u20091, inclusive.)It turns out that f can actually be many different functions. Instead of finding a solution, Kevin wants you to count the number of distinct functions f that satisfy this equation. Since the answer may be very large, you should print your result modulo 109\u2009+\u20097.", "input_spec": "The input consists of two space-separated integers p and k (3\u2009\u2264\u2009p\u2009\u2264\u20091\u2009000\u2009000, 0\u2009\u2264\u2009k\u2009\u2264\u2009p\u2009-\u20091) on a single line. It is guaranteed that p is an odd prime number.", "output_spec": "Print a single integer, the number of distinct functions f modulo 109\u2009+\u20097.", "sample_inputs": ["3 2", "5 4"], "sample_outputs": ["3", "25"], "notes": "NoteIn the first sample, p\u2009=\u20093 and k\u2009=\u20092. The following functions work:   f(0)\u2009=\u20090, f(1)\u2009=\u20091, f(2)\u2009=\u20092.  f(0)\u2009=\u20090, f(1)\u2009=\u20092, f(2)\u2009=\u20091.  f(0)\u2009=\u2009f(1)\u2009=\u2009f(2)\u2009=\u20090. "}, "src_uid": "580bf65af24fb7f08250ddbc4ca67e0e"}
{"nl": {"description": "Recently you have received two positive integer numbers $$$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": "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": "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": "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": "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$$$ blue notebooks."}, "src_uid": "d259a3a5c38af34b2a15d61157cc0a39"}
{"nl": {"description": "Array of integers is unimodal, if:  it is strictly increasing in the beginning;  after that it is constant;  after that it is strictly decreasing. The first block (increasing) and the last block (decreasing) may be absent. It is allowed that both of this blocks are absent.For example, the following three arrays are unimodal: [5,\u20097,\u200911,\u200911,\u20092,\u20091], [4,\u20094,\u20092], [7], but the following three are not unimodal: [5,\u20095,\u20096,\u20096,\u20091], [1,\u20092,\u20091,\u20092], [4,\u20095,\u20095,\u20096].Write a program that checks if an array is unimodal.", "input_spec": "The first line contains integer n (1\u2009\u2264\u2009n\u2009\u2264\u2009100) \u2014 the number of elements in the array. The second line contains n integers a1,\u2009a2,\u2009...,\u2009an (1\u2009\u2264\u2009ai\u2009\u2264\u20091\u2009000) \u2014 the elements of the array.", "output_spec": "Print \"YES\" if the given array is unimodal. Otherwise, print \"NO\". You can output each letter in any case (upper or lower).", "sample_inputs": ["6\n1 5 5 5 4 2", "5\n10 20 30 20 10", "4\n1 2 1 2", "7\n3 3 3 3 3 3 3"], "sample_outputs": ["YES", "YES", "NO", "YES"], "notes": "NoteIn the first example the array is unimodal, because it is strictly increasing in the beginning (from position 1 to position 2, inclusively), that it is constant (from position 2 to position 4, inclusively) and then it is strictly decreasing (from position 4 to position 6, inclusively)."}, "src_uid": "5482ed8ad02ac32d28c3888299bf3658"}
{"nl": {"description": "The only difference between this problem and D2 is that you don't have to provide the way to construct the answer in this problem, but you have to do it in D2.There's a table of $$$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": "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": "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$$$.The third example is explained in the statements."}, "src_uid": "d8ca1c83b431466eff6054d3b422ab47"}
{"nl": {"description": "The only difference between easy and hard versions is constraints.Ivan plays a computer game that contains some microtransactions to make characters look cooler. Since Ivan wants his character to be really cool, he wants to use some of these microtransactions \u2014 and he won't start playing until he gets all of them.Each day (during the morning) Ivan earns exactly one burle.There are $$$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$$$-th day.", "output_spec": "Print one integer \u2014 the minimum day when Ivan can order all microtransactions he wants and actually start playing.", "sample_inputs": ["5 6\n1 2 0 2 0\n2 4\n3 3\n1 5\n1 2\n1 5\n2 3", "5 3\n4 2 1 3 2\n3 5\n4 2\n2 5"], "sample_outputs": ["8", "20"], "notes": null}, "src_uid": "2eb101dcfcc487fe6e44c9b4c0e4024d"}
{"nl": {"description": "During the breaks between competitions, top-model Izabella tries to develop herself and not to be bored. For example, now she tries to solve Rubik's cube 2x2x2.It's too hard to learn to solve Rubik's cube instantly, so she learns to understand if it's possible to solve the cube in some state using 90-degrees rotation of one face of the cube in any direction.To check her answers she wants to use a program which will for some state of cube tell if it's possible to solve it using one rotation, described above.Cube is called solved if for each face of cube all squares on it has the same color.https://en.wikipedia.org/wiki/Rubik's_Cube", "input_spec": "In first line given a sequence of 24 integers ai (1\u2009\u2264\u2009ai\u2009\u2264\u20096), where ai denotes color of i-th square. There are exactly 4 occurrences of all colors in this sequence.", "output_spec": "Print \u00abYES\u00bb (without quotes) if it's possible to solve cube using one rotation and \u00abNO\u00bb (without quotes) otherwise.", "sample_inputs": ["2 5 4 6 1 3 6 2 5 5 1 2 3 5 3 1 1 2 4 6 6 4 3 4", "5 3 5 3 2 5 2 5 6 2 6 2 4 4 4 4 1 1 1 1 6 3 6 3"], "sample_outputs": ["NO", "YES"], "notes": "NoteIn first test case cube looks like this:  In second test case cube looks like this:   It's possible to solve cube by rotating face with squares with numbers 13, 14, 15, 16."}, "src_uid": "881a820aa8184d9553278a0002a3b7c4"}
{"nl": {"description": "Petya has an array $$$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$$$."}, "src_uid": "1b9d3dfcc2353eac20b84c75c27fab5a"}
{"nl": {"description": "Let's call a string a phone number if it has length 11 and fits the pattern \"8xxxxxxxxxx\", where each \"x\" is replaced by a digit.For example, \"80123456789\" and \"80000000000\" are phone numbers, while \"8012345678\" and \"79000000000\" are not.You have $$$n$$$ cards with digits, and you want to use them to make as many phone numbers as possible. Each card must be used in at most one phone number, and you don't have to use all cards. The phone numbers do not necessarily have to be distinct.", "input_spec": "The first line contains an integer $$$n$$$\u00a0\u2014 the number of cards with digits that you have ($$$1 \\leq n \\leq 100$$$). The second line contains a string of $$$n$$$ digits (characters \"0\", \"1\", ..., \"9\") $$$s_1, s_2, \\ldots, s_n$$$. The string will not contain any other characters, such as leading or trailing spaces.", "output_spec": "If at least one phone number can be made from these cards, output the maximum number of phone numbers that can be made. Otherwise, output 0.", "sample_inputs": ["11\n00000000008", "22\n0011223344556677889988", "11\n31415926535"], "sample_outputs": ["1", "2", "0"], "notes": "NoteIn the first example, one phone number, \"8000000000\", can be made from these cards.In the second example, you can make two phone numbers from the cards, for example, \"80123456789\" and \"80123456789\".In the third example you can't make any phone number from the given cards."}, "src_uid": "259d01b81bef5536b969247ff2c2d776"}
{"nl": {"description": "You have r red, g green and b blue balloons. To decorate a single table for the banquet you need exactly three balloons. Three balloons attached to some table shouldn't have the same color. What maximum number t of tables can be decorated if we know number of balloons of each color?Your task is to write a program that for given values r, g and b will find the maximum number t of tables, that can be decorated in the required manner.", "input_spec": "The single line contains three integers r, g and b (0\u2009\u2264\u2009r,\u2009g,\u2009b\u2009\u2264\u20092\u00b7109) \u2014 the number of red, green and blue baloons respectively. The numbers are separated by exactly one space.", "output_spec": "Print a single integer t \u2014 the maximum number of tables that can be decorated in the required manner.", "sample_inputs": ["5 4 3", "1 1 1", "2 3 3"], "sample_outputs": ["4", "1", "2"], "notes": "NoteIn the first sample you can decorate the tables with the following balloon sets: \"rgg\", \"gbb\", \"brr\", \"rrg\", where \"r\", \"g\" and \"b\" represent the red, green and blue balls, respectively."}, "src_uid": "bae7cbcde19114451b8712d6361d2b01"}
{"nl": {"description": "Like any unknown mathematician, Yuri has favourite numbers: $$$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$$$."}, "src_uid": "4f92791b9ec658829f667fcea1faee01"}
{"nl": {"description": "Vitya has just started learning Berlanese language. It is known that Berlanese uses the Latin alphabet. Vowel letters are \"a\", \"o\", \"u\", \"i\", and \"e\". Other letters are consonant.In Berlanese, there has to be a vowel after every consonant, but there can be any letter after any vowel. The only exception is a consonant \"n\"; after this letter, there can be any letter (not only a vowel) or there can be no letter at all. For example, the words \"harakiri\", \"yupie\", \"man\", and \"nbo\" are Berlanese while the words \"horse\", \"king\", \"my\", and \"nz\" are not.Help Vitya find out if a word $$$s$$$ is Berlanese.", "input_spec": "The first line of the input contains the string $$$s$$$ consisting of $$$|s|$$$ ($$$1\\leq |s|\\leq 100$$$) lowercase Latin letters.", "output_spec": "Print \"YES\" (without quotes) if there is a vowel after every consonant except \"n\", otherwise print \"NO\". You can print each letter in any case (upper or lower).", "sample_inputs": ["sumimasen", "ninja", "codeforces"], "sample_outputs": ["YES", "YES", "NO"], "notes": "NoteIn the first and second samples, a vowel goes after each consonant except \"n\", so the word is Berlanese.In the third sample, the consonant \"c\" goes after the consonant \"r\", and the consonant \"s\" stands on the end, so the word is not Berlanese."}, "src_uid": "a83144ba7d4906b7692456f27b0ef7d4"}
{"nl": {"description": "It is the easy version of the problem. The difference is that in this version, there are no nodes with already chosen colors.Theofanis is starving, and he wants to eat his favorite food, sheftalia. However, he should first finish his homework. Can you help him with this problem?You have a perfect binary tree of $$$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$$$.", "sample_inputs": ["3", "14"], "sample_outputs": ["24576", "934234"], "notes": "NoteIn the picture below, you can see one of the correct colorings of the first example.  "}, "src_uid": "5144b9b281ea4087d8334d91c3c8bda4"}
{"nl": {"description": "Polycarp decided to relax on his weekend and visited to the performance of famous ropewalkers: Agafon, Boniface and Konrad.The rope is straight and infinite in both directions. At the beginning of the performance, Agafon, Boniface and Konrad are located in positions $$$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$$$, so the performance could be finished within 2 seconds."}, "src_uid": "47c07e46517dbc937e2e779ec0d74eb3"}
{"nl": {"description": "Recently Ivan the Fool decided to become smarter and study the probability theory. He thinks that he understands the subject fairly well, and so he began to behave like he already got PhD in that area.To prove his skills, Ivan decided to demonstrate his friends a concept of random picture. A picture is a field of $$$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": "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": "Luba is surfing the Internet. She currently has n opened tabs in her browser, indexed from 1 to n from left to right. The mouse cursor is currently located at the pos-th tab. Luba needs to use the tabs with indices from l to r (inclusive) for her studies, and she wants to close all the tabs that don't belong to this segment as fast as possible.Each second Luba can either try moving the cursor to the left or to the right (if the cursor is currently at the tab i, then she can move it to the tab max(i\u2009-\u20091,\u2009a) or to the tab min(i\u2009+\u20091,\u2009b)) or try closing all the tabs to the left or to the right of the cursor (if the cursor is currently at the tab i, she can close all the tabs with indices from segment [a,\u2009i\u2009-\u20091] or from segment [i\u2009+\u20091,\u2009b]). In the aforementioned expressions a and b denote the minimum and maximum index of an unclosed tab, respectively. For example, if there were 7 tabs initially and tabs 1, 2 and 7 are closed, then a\u2009=\u20093, b\u2009=\u20096.What is the minimum number of seconds Luba has to spend in order to leave only the tabs with initial indices from l to r inclusive opened?", "input_spec": "The only line of input contains four integer numbers n, pos, l, r (1\u2009\u2264\u2009n\u2009\u2264\u2009100, 1\u2009\u2264\u2009pos\u2009\u2264\u2009n, 1\u2009\u2264\u2009l\u2009\u2264\u2009r\u2009\u2264\u2009n) \u2014 the number of the tabs, the cursor position and the segment which Luba needs to leave opened.", "output_spec": "Print one integer equal to the minimum number of seconds required to close all the tabs outside the segment [l,\u2009r].", "sample_inputs": ["6 3 2 4", "6 3 1 3", "5 2 1 5"], "sample_outputs": ["5", "1", "0"], "notes": "NoteIn the first test Luba can do the following operations: shift the mouse cursor to the tab 2, close all the tabs to the left of it, shift the mouse cursor to the tab 3, then to the tab 4, and then close all the tabs to the right of it.In the second test she only needs to close all the tabs to the right of the current position of the cursor.In the third test Luba doesn't need to do anything."}, "src_uid": "5deaac7bd3afedee9b10e61997940f78"}
{"nl": {"description": "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": "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": "Some country is populated by wizards. They want to organize a demonstration.There are n people living in the city, x of them are the wizards who will surely go to the demonstration. Other city people (n\u2009-\u2009x people) do not support the wizards and aren't going to go to the demonstration. We know that the city administration will react only to the demonstration involving at least y percent of the city people. Having considered the matter, the wizards decided to create clone puppets which can substitute the city people on the demonstration. So all in all, the demonstration will involve only the wizards and their puppets. The city administration cannot tell the difference between a puppet and a person, so, as they calculate the percentage, the administration will consider the city to be consisting of only n people and not containing any clone puppets. Help the wizards and find the minimum number of clones to create to that the demonstration had no less than y percent of the city people.", "input_spec": "The first line contains three space-separated integers, n, x, y (1\u2009\u2264\u2009n,\u2009x,\u2009y\u2009\u2264\u2009104,\u2009x\u2009\u2264\u2009n) \u2014 the number of citizens in the city, the number of wizards and the percentage the administration needs, correspondingly. Please note that y can exceed 100 percent, that is, the administration wants to see on a demonstration more people that actually live in the city (\u2009>\u2009n).", "output_spec": "Print a single integer \u2014 the answer to the problem, the minimum number of clones to create, so that the demonstration involved no less than y percent of n (the real total city population). ", "sample_inputs": ["10 1 14", "20 10 50", "1000 352 146"], "sample_outputs": ["1", "0", "1108"], "notes": "NoteIn the first sample it is necessary that at least 14% of 10 people came to the demonstration. As the number of people should be integer, then at least two people should come. There is only one wizard living in the city and he is going to come. That isn't enough, so he needs to create one clone. In the second sample 10 people should come to the demonstration. The city has 10 wizards. They will all come to the demonstration, so nobody has to create any clones."}, "src_uid": "7038d7b31e1900588da8b61b325e4299"}
{"nl": {"description": "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": "Stepan is a very experienced olympiad participant. He has n cups for Physics olympiads and m cups for Informatics olympiads. Each cup is characterized by two parameters \u2014 its significance ci and width wi.Stepan decided to expose some of his cups on a shelf with width d in such a way, that:  there is at least one Physics cup and at least one Informatics cup on the shelf,  the total width of the exposed cups does not exceed d,  from each subjects (Physics and Informatics) some of the most significant cups are exposed (i. e. if a cup for some subject with significance x is exposed, then all the cups for this subject with significance greater than x must be exposed too). Your task is to determine the maximum possible total significance, which Stepan can get when he exposes cups on the shelf with width d, considering all the rules described above. The total significance is the sum of significances of all the exposed cups.", "input_spec": "The first line contains three integers n, m and d (1\u2009\u2264\u2009n,\u2009m\u2009\u2264\u2009100\u2009000, 1\u2009\u2264\u2009d\u2009\u2264\u2009109) \u2014 the number of cups for Physics olympiads, the number of cups for Informatics olympiads and the width of the shelf. Each of the following n lines contains two integers ci and wi (1\u2009\u2264\u2009ci,\u2009wi\u2009\u2264\u2009109) \u2014 significance and width of the i-th cup for Physics olympiads. Each of the following m lines contains two integers cj and wj (1\u2009\u2264\u2009cj,\u2009wj\u2009\u2264\u2009109) \u2014 significance and width of the j-th cup for Informatics olympiads.", "output_spec": "Print the maximum possible total significance, which Stepan can get exposing cups on the shelf with width d, considering all the rules described in the statement. If there is no way to expose cups on the shelf, then print 0.", "sample_inputs": ["3 1 8\n4 2\n5 5\n4 2\n3 2", "4 3 12\n3 4\n2 4\n3 5\n3 4\n3 5\n5 2\n3 4", "2 2 2\n5 3\n6 3\n4 2\n8 1"], "sample_outputs": ["8", "11", "0"], "notes": "NoteIn the first example Stepan has only one Informatics cup which must be exposed on the shelf. Its significance equals 3 and width equals 2, so after Stepan exposes it, the width of free space on the shelf becomes equal to 6. Also, Stepan must expose the second Physics cup (which has width 5), because it is the most significant cup for Physics (its significance equals 5). After that Stepan can not expose more cups on the shelf, because there is no enough free space. Thus, the maximum total significance of exposed cups equals to 8."}, "src_uid": "da573a39459087ed7c42f70bc1d0e8ff"}
{"nl": {"description": "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$$$, written in Roman numerals. But he can not just send the file, because it name contains three letters \"x\" in a row. To send the file he needs to remove any one of this letters."}, "src_uid": "8de14db41d0acee116bd5d8079cb2b02"}
{"nl": {"description": "Little girl Tanya is learning how to decrease a number by one, but she does it wrong with a number consisting of two or more digits. Tanya subtracts one from a number by the following algorithm:  if the last digit of the number is non-zero, she decreases the number by one;  if the last digit of the number is zero, she divides the number by 10 (i.e. removes the last digit). You are given an integer number $$$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": "Once upon a time in the Kingdom of Far Far Away lived Sir Lancelot, the chief Royal General. He was very proud of his men and he liked to invite the King to come and watch drill exercises which demonstrated the fighting techniques and tactics of the squad he was in charge of. But time went by and one day Sir Lancelot had a major argument with the Fairy Godmother (there were rumors that the argument occurred after the general spoke badly of the Godmother's flying techniques. That seemed to hurt the Fairy Godmother very deeply). As the result of the argument, the Godmother put a rather strange curse upon the general. It sounded all complicated and quite harmless: \"If the squared distance between some two soldiers equals to 5, then those soldiers will conflict with each other!\"The drill exercises are held on a rectangular n\u2009\u00d7\u2009m field, split into nm square 1\u2009\u00d7\u20091 segments for each soldier. Thus, the square of the distance between the soldiers that stand on squares (x1,\u2009y1) and (x2,\u2009y2) equals exactly (x1\u2009-\u2009x2)2\u2009+\u2009(y1\u2009-\u2009y2)2. Now not all nm squad soldiers can participate in the drill exercises as it was before the Fairy Godmother's curse. Unless, of course, the general wants the soldiers to fight with each other or even worse... For example, if he puts a soldier in the square (2,\u20092), then he cannot put soldiers in the squares (1,\u20094), (3,\u20094), (4,\u20091) and (4,\u20093) \u2014 each of them will conflict with the soldier in the square (2,\u20092).Your task is to help the general. You are given the size of the drill exercise field. You are asked to calculate the maximum number of soldiers that can be simultaneously positioned on this field, so that no two soldiers fall under the Fairy Godmother's curse.", "input_spec": "The single line contains space-separated integers n and m (1\u2009\u2264\u2009n,\u2009m\u2009\u2264\u20091000) that represent the size of the drill exercise field.", "output_spec": "Print the desired maximum number of warriors.", "sample_inputs": ["2 4", "3 4"], "sample_outputs": ["4", "6"], "notes": "NoteIn the first sample test Sir Lancelot can place his 4 soldiers on the 2\u2009\u00d7\u20094 court as follows (the soldiers' locations are marked with gray circles on the scheme):  In the second sample test he can place 6 soldiers on the 3\u2009\u00d7\u20094 site in the following manner:  "}, "src_uid": "e858e7f22d91aaadd7a48a174d7b2dc9"}
{"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": "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$$$ since that is the maximum number of characters that can remain.In the second example, we don't need to erase any characters."}, "src_uid": "84cb9ad2ae3ba7e912920d7feb4f6219"}
{"nl": {"description": "There are $$$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": "You are given a string s consisting of |s| small english letters.In one move you can replace any character of this string to the next character in alphabetical order (a will be replaced with b, s will be replaced with t, etc.). You cannot replace letter z with any other letter.Your target is to make some number of moves (not necessary minimal) to get string abcdefghijklmnopqrstuvwxyz (english alphabet) as a subsequence. Subsequence of the string is the string that is obtained by deleting characters at some positions. You need to print the string that will be obtained from the given string and will be contain english alphabet as a subsequence or say that it is impossible.", "input_spec": "The only one line of the input consisting of the string s consisting of |s| (1\u2009\u2264\u2009|s|\u2009\u2264\u2009105) small english letters.", "output_spec": "If you can get a string that can be obtained from the given string and will contain english alphabet as a subsequence, print it. Otherwise print \u00ab-1\u00bb (without quotes).", "sample_inputs": ["aacceeggiikkmmooqqssuuwwyy", "thereisnoanswer"], "sample_outputs": ["abcdefghijklmnopqrstuvwxyz", "-1"], "notes": null}, "src_uid": "f8ad543d499bcc0da0121a71a26db854"}
{"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": "Many people are aware of DMCA \u2013 Digital Millennium Copyright Act. But another recently proposed DMCA \u2013 Digital Millennium Calculation Act \u2013 is much less known.In this problem you need to find a root of a number according to this new DMCA law.", "input_spec": "The input contains a single integer $$$a$$$ ($$$1 \\le a \\le 1000000$$$).", "output_spec": "Output the result \u2013 an integer number.", "sample_inputs": ["1", "81"], "sample_outputs": ["1", "9"], "notes": null}, "src_uid": "477a67877367dc68b3bf5143120ff45d"}
{"nl": {"description": "The 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": "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": "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": "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": "From beginning till end, this message has been waiting to be conveyed.For a given unordered multiset of n lowercase English letters (\"multi\" means that a letter may appear more than once), we treat all letters as strings of length 1, and repeat the following operation n\u2009-\u20091 times:  Remove any two elements s and t from the set, and add their concatenation s\u2009+\u2009t to the set. The cost of such operation is defined to be , where f(s,\u2009c) denotes the number of times character c appears in string s.Given a non-negative integer k, construct any valid non-empty set of no more than 100\u2009000 letters, such that the minimum accumulative cost of the whole process is exactly k. It can be shown that a solution always exists.", "input_spec": "The first and only line of input contains a non-negative integer k (0\u2009\u2264\u2009k\u2009\u2264\u2009100\u2009000) \u2014 the required minimum cost.", "output_spec": "Output a non-empty string of no more than 100\u2009000 lowercase English letters \u2014 any multiset satisfying the requirements, concatenated to be a string. Note that the printed string doesn't need to be the final concatenated string. It only needs to represent an unordered multiset of letters.", "sample_inputs": ["12", "3"], "sample_outputs": ["abababab", "codeforces"], "notes": "NoteFor the multiset {'a', 'b', 'a', 'b', 'a', 'b', 'a', 'b'}, one of the ways to complete the process is as follows:  {\"ab\", \"a\", \"b\", \"a\", \"b\", \"a\", \"b\"}, with a cost of 0;  {\"aba\", \"b\", \"a\", \"b\", \"a\", \"b\"}, with a cost of 1;  {\"abab\", \"a\", \"b\", \"a\", \"b\"}, with a cost of 1;  {\"abab\", \"ab\", \"a\", \"b\"}, with a cost of 0;  {\"abab\", \"aba\", \"b\"}, with a cost of 1;  {\"abab\", \"abab\"}, with a cost of 1;  {\"abababab\"}, with a cost of 8. The total cost is 12, and it can be proved to be the minimum cost of the process."}, "src_uid": "b991c064562704b6106a6ff2a297e64a"}
{"nl": {"description": "You are given an integer array $$$a_0, a_1, \\dots, a_{n - 1}$$$, and an integer $$$k$$$. You perform the following code with it:long long ans = 0; // create a 64-bit signed variable which is initially equal to 0for(int i = 1; i <= k; i++){  int idx = rnd.next(0, n - 1); // generate a random integer between 0 and n - 1, both inclusive                                // each integer from 0 to n - 1 has the same probability of being chosen  ans += a[idx];  a[idx] -= (a[idx] % i);}Your task is to calculate the expected value of the variable ans after performing this code.Note that the input is generated according to special rules (see the input format section).", "input_spec": "The only line contains six integers $$$n$$$, $$$a_0$$$, $$$x$$$, $$$y$$$, $$$k$$$ and $$$M$$$ ($$$1 \\le n \\le 10^7$$$; $$$1 \\le a_0, x, y < M \\le 998244353$$$; $$$1 \\le k \\le 17$$$). The array $$$a$$$ in the input is constructed as follows:   $$$a_0$$$ is given in the input;  for every $$$i$$$ from $$$1$$$ to $$$n - 1$$$, the value of $$$a_i$$$ can be calculated as $$$a_i = (a_{i - 1} \\cdot x + y) \\bmod M$$$. ", "output_spec": "Let the expected value of the variable ans after performing the code be $$$E$$$. It can be shown that $$$E \\cdot n^k$$$ is an integer. You have to output this integer modulo $$$998244353$$$.", "sample_inputs": ["3 10 3 5 13 88", "2 15363 270880 34698 17 2357023"], "sample_outputs": ["382842030", "319392398"], "notes": "NoteThe array in the first example test is $$$[10, 35, 22]$$$. In the second example, it is $$$[15363, 1418543]$$$."}, "src_uid": "1d45491e28d24e2b318605cd328d6ecf"}
{"nl": {"description": "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": "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 Tower of Hanoi is a well-known mathematical puzzle. It consists of three rods, and a number of disks of different sizes which can slide onto any rod. The puzzle starts with the disks in a neat stack in ascending order of size on one rod, the smallest at the top, thus making a conical shape.The objective of the puzzle is to move the entire stack to another rod, obeying the following simple rules:   Only one disk can be moved at a time.  Each move consists of taking the upper disk from one of the stacks and placing it on top of another stack i.e. a disk can only be moved if it is the uppermost disk on a stack.  No disk may be placed on top of a smaller disk. With three disks, the puzzle can be solved in seven moves. The minimum number of moves required to solve a Tower of Hanoi puzzle is 2n\u2009-\u20091, where n is the number of disks. (c) Wikipedia.SmallY's puzzle is very similar to the famous Tower of Hanoi. In the Tower of Hanoi puzzle you need to solve a puzzle in minimum number of moves, in SmallY's puzzle each move costs some money and you need to solve the same puzzle but for minimal cost. At the beginning of SmallY's puzzle all n disks are on the first rod. Moving a disk from rod i to rod j (1\u2009\u2264\u2009i,\u2009j\u2009\u2264\u20093) costs tij units of money. The goal of the puzzle is to move all the disks to the third rod.In the problem you are given matrix t and an integer n. You need to count the minimal cost of solving SmallY's puzzle, consisting of n disks.", "input_spec": "Each of the first three lines contains three integers \u2014 matrix t. The j-th integer in the i-th line is tij (1\u2009\u2264\u2009tij\u2009\u2264\u200910000;\u00a0i\u2009\u2260\u2009j). The following line contains a single integer n (1\u2009\u2264\u2009n\u2009\u2264\u200940) \u2014 the number of disks. It is guaranteed that for all i (1\u2009\u2264\u2009i\u2009\u2264\u20093), tii\u2009=\u20090.", "output_spec": "Print a single integer \u2014 the minimum cost of solving SmallY's puzzle.", "sample_inputs": ["0 1 1\n1 0 1\n1 1 0\n3", "0 2 2\n1 0 100\n1 2 0\n3", "0 2 1\n1 0 100\n1 2 0\n5"], "sample_outputs": ["7", "19", "87"], "notes": null}, "src_uid": "c4c20228624365e39299d0a6e8fe7095"}
{"nl": {"description": "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": "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": "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": "JATC's math teacher always gives the class some interesting math problems so that they don't get bored. Today the problem is as follows. Given an integer $$$n$$$, you can perform the following operations zero or more times:  mul $$$x$$$: multiplies $$$n$$$ by $$$x$$$ (where $$$x$$$ is an arbitrary positive integer).  sqrt: replaces $$$n$$$ with $$$\\sqrt{n}$$$ (to apply this operation, $$$\\sqrt{n}$$$ must be an integer). You can perform these operations as many times as you like. What is the minimum value of $$$n$$$, that can be achieved and what is the minimum number of operations, to achieve that minimum value?Apparently, no one in the class knows the answer to this problem, maybe you can help them?", "input_spec": "The only line of the input contains a single integer $$$n$$$ ($$$1 \\le n \\le 10^6$$$)\u00a0\u2014 the initial number.", "output_spec": "Print two integers: the minimum integer $$$n$$$ that can be achieved using the described operations and the minimum number of operations required.", "sample_inputs": ["20", "5184"], "sample_outputs": ["10 2", "6 4"], "notes": "NoteIn the first example, you can apply the operation mul $$$5$$$ to get $$$100$$$ and then sqrt to get $$$10$$$.In the second example, you can first apply sqrt to get $$$72$$$, then mul $$$18$$$ to get $$$1296$$$ and finally two more sqrt and you get $$$6$$$.Note, that even if the initial value of $$$n$$$ is less or equal $$$10^6$$$, it can still become greater than $$$10^6$$$ after applying one or more operations."}, "src_uid": "212cda3d9d611cd45332bb10b80f0b56"}
{"nl": {"description": "Tavak and Seyyed are good friends. Seyyed is very funny and he told Tavak to solve the following problem instead of longest-path.You are given l and r. For all integers from l to r, inclusive, we wrote down all of their integer divisors except 1. Find the integer that we wrote down the maximum number of times.Solve the problem to show that it's not a NP problem.", "input_spec": "The first line contains two integers l and r (2\u2009\u2264\u2009l\u2009\u2264\u2009r\u2009\u2264\u2009109).", "output_spec": "Print single integer, the integer that appears maximum number of times in the divisors.  If there are multiple answers, print any of them.", "sample_inputs": ["19 29", "3 6"], "sample_outputs": ["2", "3"], "notes": "NoteDefinition of a divisor: https://www.mathsisfun.com/definitions/divisor-of-an-integer-.htmlThe first example: from 19 to 29 these numbers are divisible by 2: {20,\u200922,\u200924,\u200926,\u200928}.The second example: from 3 to 6 these numbers are divisible by 3: {3,\u20096}."}, "src_uid": "a8d992ab26a528f0be327c93fb499c15"}
{"nl": {"description": "A big company decided to launch a new series of rectangular displays, and decided that the display must have exactly n pixels. Your task is to determine the size of the rectangular display \u2014 the number of lines (rows) of pixels a and the number of columns of pixels b, so that:  there are exactly n pixels on the display;  the number of rows does not exceed the number of columns, it means a\u2009\u2264\u2009b;  the difference b\u2009-\u2009a is as small as possible. ", "input_spec": "The first line contains the positive integer n (1\u2009\u2264\u2009n\u2009\u2264\u2009106)\u00a0\u2014 the number of pixels display should have.", "output_spec": "Print two integers\u00a0\u2014 the number of rows and columns on the display. ", "sample_inputs": ["8", "64", "5", "999999"], "sample_outputs": ["2 4", "8 8", "1 5", "999 1001"], "notes": "NoteIn the first example the minimum possible difference equals 2, so on the display should be 2 rows of 4 pixels.In the second example the minimum possible difference equals 0, so on the display should be 8 rows of 8 pixels.In the third example the minimum possible difference equals 4, so on the display should be 1 row of 5 pixels."}, "src_uid": "f52af273954798a4ae38a1378bfbf77a"}
{"nl": {"description": "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": "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$$$ squares in the manner described above.", "sample_inputs": ["1", "2", "4"], "sample_outputs": ["2", "3", "4"], "notes": null}, "src_uid": "eb8212aec951f8f69b084446da73eaf7"}
{"nl": {"description": "Polycarp plays \"Game 23\". Initially he has a number $$$n$$$ and his goal is to transform it to $$$m$$$. In one move, he can multiply $$$n$$$ by $$$2$$$ or multiply $$$n$$$ by $$$3$$$. He can perform any number of moves.Print the number of moves needed to transform $$$n$$$ to $$$m$$$. Print -1 if it is impossible to do so.It is easy to prove that any way to transform $$$n$$$ to $$$m$$$ contains the same number of moves (i.e. number of moves doesn't depend on the way of transformation).", "input_spec": "The only line of the input contains two integers $$$n$$$ and $$$m$$$ ($$$1 \\le n \\le m \\le 5\\cdot10^8$$$).", "output_spec": "Print the number of moves to transform $$$n$$$ to $$$m$$$, or -1 if there is no solution.", "sample_inputs": ["120 51840", "42 42", "48 72"], "sample_outputs": ["7", "0", "-1"], "notes": "NoteIn the first example, the possible sequence of moves is: $$$120 \\rightarrow 240 \\rightarrow 720 \\rightarrow 1440 \\rightarrow 4320 \\rightarrow 12960 \\rightarrow 25920 \\rightarrow 51840.$$$ The are $$$7$$$ steps in total.In the second example, no moves are needed. Thus, the answer is $$$0$$$.In the third example, it is impossible to transform $$$48$$$ to $$$72$$$."}, "src_uid": "3f9980ad292185f63a80bce10705e806"}
{"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": "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": "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": "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$$$ otherwise.", "sample_inputs": ["3\n1\n4\n3", "0\n0\n0\n0", "1\n2\n3\n4"], "sample_outputs": ["1", "1", "0"], "notes": "NoteIn the first example it is possible to construct a string \"(())()(()((()()()())))\", which is a regular bracket sequence.In the second example it is possible to construct a string \"\", which is a regular bracket sequence."}, "src_uid": "b99578086043537297d374dc01eeb6f8"}
{"nl": {"description": "You are given a binary string s (each character of this string is either 0 or 1).Let's denote the cost of string t as the number of occurences of s in t. For example, if s is 11 and t is 111011, then the cost of t is 3.Let's also denote the Fibonacci strings sequence as follows: F(0) is 0; F(1) is 1; F(i)\u2009=\u2009F(i\u2009-\u20091)\u2009+\u2009F(i\u2009-\u20092) if i\u2009>\u20091, where \u2009+\u2009 means the concatenation of two strings.Your task is to calculate the sum of costs of all subsequences of the string F(x). Since answer may be large, calculate it modulo 109\u2009+\u20097.", "input_spec": "The first line contains two integers n and x (1\u2009\u2264\u2009n\u2009\u2264\u2009100, 0\u2009\u2264\u2009x\u2009\u2264\u2009100) \u2014 the length of s and the index of a Fibonacci string you are interested in, respectively. The second line contains s \u2014 a string consisting of n characters. Each of these characters is either 0 or 1.", "output_spec": "Print the only integer \u2014 the sum of costs of all subsequences of the string F(x), taken modulo 109\u2009+\u20097. ", "sample_inputs": ["2 4\n11", "10 100\n1010101010"], "sample_outputs": ["14", "553403224"], "notes": null}, "src_uid": "52c6aa73ff4460799402c646c6263630"}
{"nl": {"description": "This is an easy version of the problem. The actual problems are different, but the easy version is almost a subtask of the hard version. Note that the constraints and the output format are different.You are given a string $$$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$$$-th character is colored the first color and '1' otherwise).", "sample_inputs": ["9\nabacbecfd", "8\naaabbcbb", "7\nabcdedc", "5\nabcde"], "sample_outputs": ["YES\n001010101", "YES\n01011011", "NO", "YES\n00000"], "notes": null}, "src_uid": "9bd31827cda83eacfcf5e46cdeaabe2b"}
{"nl": {"description": "Mr. Chanek wants to knit a batik, a traditional cloth from Indonesia. The cloth forms a grid $$$a$$$ with size $$$n \\times m$$$. There are $$$k$$$ colors, and each cell in the grid can be one of the $$$k$$$ colors.Define a sub-rectangle as an ordered pair of two cells $$$((x_1, y_1), (x_2, y_2))$$$, denoting the top-left cell and bottom-right cell (inclusively) of a sub-rectangle in $$$a$$$. Two sub-rectangles $$$((x_1, y_1), (x_2, y_2))$$$ and $$$((x_3, y_3), (x_4, y_4))$$$ have the same pattern if and only if the following holds:   they have the same width ($$$x_2 - x_1 = x_4 - x_3$$$);  they have the same height ($$$y_2 - y_1 = y_4 - y_3$$$);  for every pair $$$(i, j)$$$ where $$$0 \\leq i \\leq x_2 - x_1$$$ and $$$0 \\leq j \\leq y_2 - y_1$$$, the color of cells $$$(x_1 + i, y_1 + j)$$$ and $$$(x_3 + i, y_3 + j)$$$ are equal. Count the number of possible batik color combinations, such that the subrectangles $$$((a_x, a_y),(a_x + r - 1, a_y + c - 1))$$$ and $$$((b_x, b_y),(b_x + r - 1, b_y + c - 1))$$$ have the same pattern.Output the answer modulo $$$10^9 + 7$$$.", "input_spec": "The first line contains five integers $$$n$$$, $$$m$$$, $$$k$$$, $$$r$$$, and $$$c$$$ ($$$1 \\leq n, m \\leq 10^9$$$, $$$1 \\leq k \\leq 10^9$$$, $$$1 \\leq r \\leq \\min(10^6, n)$$$, $$$1 \\leq c \\leq \\min(10^6, m)$$$) \u2014 the size of the batik, the number of colors, and size of the sub-rectangle. The second line contains four integers $$$a_x$$$, $$$a_y$$$, $$$b_x$$$, and $$$b_y$$$ ($$$1 \\leq a_x, b_x \\leq n$$$, $$$1 \\leq a_y, b_y \\leq m$$$) \u2014 the top-left corners of the first and second sub-rectangle. Both of the sub-rectangles given are inside the grid ($$$1 \\leq a_x + r - 1$$$, $$$b_x + r - 1 \\leq n$$$, $$$1 \\leq a_y + c - 1$$$, $$$b_y + c - 1 \\leq m$$$).", "output_spec": "Output an integer denoting the number of possible batik color combinations modulo $$$10^9 + 7$$$.", "sample_inputs": ["3 3 2 2 2\n1 1 2 2", "4 5 170845 2 2\n1 4 3 1"], "sample_outputs": ["32", "756680455"], "notes": "NoteThe following are all $$$32$$$ possible color combinations in the first example.  "}, "src_uid": "3478e6a4ff2415508fd517413d40c13a"}
{"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": "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": "Little Chris is bored during his physics lessons (too easy), so he has built a toy box to keep himself occupied. The box is special, since it has the ability to change gravity.There are n columns of toy cubes in the box arranged in a line. The i-th column contains ai cubes. At first, the gravity in the box is pulling the cubes downwards. When Chris switches the gravity, it begins to pull all the cubes to the right side of the box. The figure shows the initial and final configurations of the cubes in the box: the cubes that have changed their position are highlighted with orange.  Given the initial configuration of the toy cubes in the box, find the amounts of cubes in each of the n columns after the gravity switch!", "input_spec": "The first line of input contains an integer n (1\u2009\u2264\u2009n\u2009\u2264\u2009100), the number of the columns in the box. The next line contains n space-separated integer numbers. The i-th number ai (1\u2009\u2264\u2009ai\u2009\u2264\u2009100) denotes the number of cubes in the i-th column.", "output_spec": "Output n integer numbers separated by spaces, where the i-th number is the amount of cubes in the i-th column after the gravity switch.", "sample_inputs": ["4\n3 2 1 2", "3\n2 3 8"], "sample_outputs": ["1 2 2 3", "2 3 8"], "notes": "NoteThe first example case is shown on the figure. The top cube of the first column falls to the top of the last column; the top cube of the second column falls to the top of the third column; the middle cube of the first column falls to the top of the second column.In the second example case the gravity switch does not change the heights of the columns."}, "src_uid": "ae20712265d4adf293e75d016b4b82d8"}
{"nl": {"description": "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": "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": "The only difference between easy and hard versions is constraints.Polycarp loves to listen to music, so he never leaves the player, even on the way home from the university. Polycarp overcomes the distance from the university to the house in exactly $$$T$$$ minutes.In the player, Polycarp stores $$$n$$$ songs, each of which is characterized by two parameters: $$$t_i$$$ and $$$g_i$$$, where $$$t_i$$$ is the length of the song in minutes ($$$1 \\le t_i \\le 50$$$), $$$g_i$$$ is its genre ($$$1 \\le g_i \\le 3$$$).Polycarp wants to create such a playlist so that he can listen to music all the time on the way from the university to his home, and at the time of his arrival home, the playlist is over. Polycarp never interrupts songs and always listens to them from beginning to end. Thus, if he started listening to the $$$i$$$-th song, he would spend exactly $$$t_i$$$ minutes on its listening. Polycarp also does not like when two songs of the same genre play in a row (i.e. successively/adjacently) or when the songs in his playlist are repeated.Help Polycarpus count the number of different sequences of songs (their order matters), the total duration is exactly $$$T$$$, such that there are no two consecutive songs of the same genre in them and all the songs in the playlist are different.", "input_spec": "The first line of the input contains two integers $$$n$$$ and $$$T$$$ ($$$1 \\le n \\le 50, 1 \\le T \\le 2500$$$) \u2014 the number of songs in the player and the required total duration, respectively. Next, the $$$n$$$ lines contain descriptions of songs: the $$$i$$$-th line contains two integers $$$t_i$$$ and $$$g_i$$$ ($$$1 \\le t_i \\le 50, 1 \\le g_i \\le 3$$$) \u2014 the duration of the $$$i$$$-th song and its genre, respectively.", "output_spec": "Output one integer \u2014 the number of different sequences of songs, the total length of exactly $$$T$$$, such that there are no two consecutive songs of the same genre in them and all the songs in the playlist are different. Since the answer may be huge, output it modulo $$$10^9 + 7$$$ (that is, the remainder when dividing the quantity by $$$10^9 + 7$$$).", "sample_inputs": ["3 3\n1 1\n1 2\n1 3", "3 3\n1 1\n1 1\n1 3", "4 10\n5 3\n2 1\n3 2\n5 1"], "sample_outputs": ["6", "2", "10"], "notes": "NoteIn the first example, Polycarp can make any of the $$$6$$$ possible playlist by rearranging the available songs: $$$[1, 2, 3]$$$, $$$[1, 3, 2]$$$, $$$[2, 1, 3]$$$, $$$[2, 3, 1]$$$, $$$[3, 1, 2]$$$ and $$$[3, 2, 1]$$$ (indices of the songs are given).In the second example, the first and second songs cannot go in succession (since they have the same genre). Thus, Polycarp can create a playlist in one of $$$2$$$ possible ways: $$$[1, 3, 2]$$$ and $$$[2, 3, 1]$$$ (indices of the songs are given).In the third example, Polycarp can make the following playlists: $$$[1, 2, 3]$$$, $$$[1, 3, 2]$$$, $$$[2, 1, 3]$$$, $$$[2, 3, 1]$$$, $$$[3, 1, 2]$$$, $$$[3, 2, 1]$$$, $$$[1, 4]$$$, $$$[4, 1]$$$, $$$[2, 3, 4]$$$ and $$$[4, 3, 2]$$$ (indices of the songs are given)."}, "src_uid": "ed5f913afe829c65792b54233a256757"}
{"nl": {"description": "Masha has three sticks of length $$$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": "Simon and Antisimon play a game. Initially each player receives one fixed positive integer that doesn't change throughout the game. Simon receives number a and Antisimon receives number b. They also have a heap of n stones. The players take turns to make a move and Simon starts. During a move a player should take from the heap the number of stones equal to the greatest common divisor of the fixed number he has received and the number of stones left in the heap. A player loses when he cannot take the required number of stones (i. e. the heap has strictly less stones left than one needs to take). Your task is to determine by the given a, b and n who wins the game.", "input_spec": "The only string contains space-separated integers a, b and n (1\u2009\u2264\u2009a,\u2009b,\u2009n\u2009\u2264\u2009100) \u2014 the fixed numbers Simon and Antisimon have received correspondingly and the initial number of stones in the pile.", "output_spec": "If Simon wins, print \"0\" (without the quotes), otherwise print \"1\" (without the quotes).", "sample_inputs": ["3 5 9", "1 1 100"], "sample_outputs": ["0", "1"], "notes": "NoteThe greatest common divisor of two non-negative integers a and b is such maximum positive integer k, that a is divisible by k without remainder and similarly, b is divisible by k without remainder. Let gcd(a,\u2009b) represent the operation of calculating the greatest common divisor of numbers a and b. Specifically, gcd(x,\u20090)\u2009=\u2009gcd(0,\u2009x)\u2009=\u2009x.In the first sample the game will go like that: Simon should take gcd(3,\u20099)\u2009=\u20093 stones from the heap. After his move the heap has 6 stones left. Antisimon should take gcd(5,\u20096)\u2009=\u20091 stone from the heap. After his move the heap has 5 stones left. Simon should take gcd(3,\u20095)\u2009=\u20091 stone from the heap. After his move the heap has 4 stones left. Antisimon should take gcd(5,\u20094)\u2009=\u20091 stone from the heap. After his move the heap has 3 stones left. Simon should take gcd(3,\u20093)\u2009=\u20093 stones from the heap. After his move the heap has 0 stones left. Antisimon should take gcd(5,\u20090)\u2009=\u20095 stones from the heap. As 0\u2009<\u20095, it is impossible and Antisimon loses.In the second sample each player during each move takes one stone from the heap. As n is even, Antisimon takes the last stone and Simon can't make a move after that."}, "src_uid": "0bd6fbb6b0a2e7e5f080a70553149ac2"}
{"nl": {"description": "You 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": "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": "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": "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": "Little Artem got n stones on his birthday and now wants to give some of them to Masha. He knows that Masha cares more about the fact of receiving the present, rather than the value of that present, so he wants to give her stones as many times as possible. However, Masha remembers the last present she received, so Artem can't give her the same number of stones twice in a row. For example, he can give her 3 stones, then 1 stone, then again 3 stones, but he can't give her 3 stones and then again 3 stones right after that.How many times can Artem give presents to Masha?", "input_spec": "The only line of the input contains a single integer n (1\u2009\u2264\u2009n\u2009\u2264\u2009109)\u00a0\u2014 number of stones Artem received on his birthday.", "output_spec": "Print the maximum possible number of times Artem can give presents to Masha.", "sample_inputs": ["1", "2", "3", "4"], "sample_outputs": ["1", "1", "2", "3"], "notes": "NoteIn the first sample, Artem can only give 1 stone to Masha.In the second sample, Atrem can give Masha 1 or 2 stones, though he can't give her 1 stone two times.In the third sample, Atrem can first give Masha 2 stones, a then 1 more stone.In the fourth sample, Atrem can first give Masha 1 stone, then 2 stones, and finally 1 stone again."}, "src_uid": "a993069e35b35ae158d35d6fe166aaef"}
{"nl": {"description": "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": "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": "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$$$.Therefore, there are five ways in total."}, "src_uid": "a524aa54e83fd0223489a19531bf0e79"}
{"nl": {"description": "Finished her homework, Nastya decided to play computer games. Passing levels one by one, Nastya eventually faced a problem. Her mission is to leave a room, where a lot of monsters live, as quickly as possible.There are $$$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$$$ moves are required to win."}, "src_uid": "24b02afe8d86314ec5f75a00c72af514"}
{"nl": {"description": "Reziba has many magic gems. Each magic gem can be split into $$$M$$$ normal gems. The amount of space each magic (and normal) gem takes is $$$1$$$ unit. A normal gem cannot be split.Reziba wants to choose a set of magic gems and split some of them, so the total space occupied by the resulting set of gems is $$$N$$$ units. If a magic gem is chosen and split, it takes $$$M$$$ units of space (since it is split into $$$M$$$ gems); if a magic gem is not split, it takes $$$1$$$ unit.How many different configurations of the resulting set of gems can Reziba have, such that the total amount of space taken is $$$N$$$ units? Print the answer modulo $$$1000000007$$$ ($$$10^9+7$$$). Two configurations are considered different if the number of magic gems Reziba takes to form them differs, or the indices of gems Reziba has to split differ.", "input_spec": "The input contains a single line consisting of $$$2$$$ integers $$$N$$$ and $$$M$$$ ($$$1 \\le N \\le 10^{18}$$$, $$$2 \\le M \\le 100$$$).", "output_spec": "Print one integer, the total number of configurations of the resulting set of gems, given that the total amount of space taken is $$$N$$$ units. Print the answer modulo $$$1000000007$$$ ($$$10^9+7$$$).", "sample_inputs": ["4 2", "3 2"], "sample_outputs": ["5", "3"], "notes": "NoteIn the first example each magic gem can split into $$$2$$$ normal gems, and we know that the total amount of gems are $$$4$$$.Let $$$1$$$ denote a magic gem, and $$$0$$$ denote a normal gem.The total configurations you can have is:   $$$1 1 1 1$$$ (None of the gems split);  $$$0 0 1 1$$$ (First magic gem splits into $$$2$$$ normal gems);  $$$1 0 0 1$$$ (Second magic gem splits into $$$2$$$ normal gems);  $$$1 1 0 0$$$ (Third magic gem splits into $$$2$$$ normal gems);  $$$0 0 0 0$$$ (First and second magic gems split into total $$$4$$$ normal gems). Hence, answer is $$$5$$$."}, "src_uid": "e7b9eec21d950f5d963ff50619c6f119"}
{"nl": {"description": "There was once young lass called Mary,  Whose jokes were occasionally scary.  On this April's Fool  Fixed limerick rules  Allowed her to trip the unwary.Can she fill all the linesTo work at all times?On juggling the wordsRight around two-thirdsShe nearly ran out of rhymes.", "input_spec": "The input contains a single integer $$$a$$$ ($$$4 \\le a \\le 998$$$). Not every integer in the range is a valid input for the problem; you are guaranteed that the input will be a valid integer.", "output_spec": "Output a single number.", "sample_inputs": ["35", "57", "391"], "sample_outputs": ["57", "319", "1723"], "notes": null}, "src_uid": "7220f2da5081547a12118595bbeda4f6"}
{"nl": {"description": "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": "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": "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": "Attention: we lost all the test cases for this problem, so instead of solving the problem, we need you to generate test cases. We're going to give you the answer, and you need to print a test case that produces the given answer. The original problem is in the following paragraph.People don't use cash as often as they used to. Having a credit card solves some of the hassles of cash, such as having to receive change when you can't form the exact amount of money needed to purchase an item. Typically cashiers will give you as few coins as possible in change, but they don't have to. For example, if your change is 30 cents, a cashier could give you a 5 cent piece and a 25 cent piece, or they could give you three 10 cent pieces, or ten 1 cent pieces, two 5 cent pieces, and one 10 cent piece. Altogether there are 18 different ways to make 30 cents using only 1 cent pieces, 5 cent pieces, 10 cent pieces, and 25 cent pieces. Two ways are considered different if they contain a different number of at least one type of coin. Given the denominations of the coins and an amount of change to be made, how many different ways are there to make change?As we mentioned before, we lost all the test cases for this problem, so we're actually going to give you the number of ways, and want you to produce a test case for which the number of ways is the given number. There could be many ways to achieve this (we guarantee there's always at least one), so you can print any, as long as it meets the constraints described below.", "input_spec": "Input will consist of a single integer A (1\u2009\u2264\u2009A\u2009\u2264\u2009105), the desired number of ways.", "output_spec": "In the first line print integers N and M (1\u2009\u2264\u2009N\u2009\u2264\u2009106,\u20091\u2009\u2264\u2009M\u2009\u2264\u200910), the amount of change to be made, and the number of denominations, respectively. Then print M integers D1,\u2009D2,\u2009...,\u2009DM (1\u2009\u2264\u2009Di\u2009\u2264\u2009106), the denominations of the coins. All denominations must be distinct: for any i\u2009\u2260\u2009j we must have Di\u2009\u2260\u2009Dj. If there are multiple tests, print any of them. You can print denominations in atbitrary order.", "sample_inputs": ["18", "3", "314"], "sample_outputs": ["30 4\n1 5 10 25", "20 2\n5 2", "183 4\n6 5 2 139"], "notes": null}, "src_uid": "5c000b4c82a8ecef764f53fda8cee541"}
{"nl": {"description": "Alice has a string consisting of characters 'A', 'B' and 'C'. Bob can use the following transitions on any substring of our string in any order any number of times:   A  BC  B  AC  C  AB  AAA  empty string Note that a substring is one or more consecutive characters. For given queries, determine whether it is possible to obtain the target string from source.", "input_spec": "The first line contains a string S (1\u2009\u2264\u2009|S|\u2009\u2264\u2009105). The second line contains a string T (1\u2009\u2264\u2009|T|\u2009\u2264\u2009105), each of these strings consists only of uppercase English letters 'A', 'B' and 'C'. The third line contains the number of queries Q (1\u2009\u2264\u2009Q\u2009\u2264\u2009105). The following Q lines describe queries. The i-th of these lines contains four space separated integers ai, bi, ci, di. These represent the i-th query: is it possible to create T[ci..di] from S[ai..bi] by applying the above transitions finite amount of times? Here, U[x..y] is a substring of U that begins at index x (indexed from 1) and ends at index y. In particular, U[1..|U|] is the whole string U. It is guaranteed that 1\u2009\u2264\u2009a\u2009\u2264\u2009b\u2009\u2264\u2009|S| and 1\u2009\u2264\u2009c\u2009\u2264\u2009d\u2009\u2264\u2009|T|.", "output_spec": "Print a string of Q characters, where the i-th character is '1' if the answer to the i-th query is positive, and '0' otherwise.", "sample_inputs": ["AABCCBAAB\nABCB\n5\n1 3 1 2\n2 2 2 4\n7 9 1 1\n3 4 2 3\n4 5 1 3"], "sample_outputs": ["10011"], "notes": "NoteIn the first query we can achieve the result, for instance, by using transitions .The third query asks for changing AAB to A\u00a0\u2014 but in this case we are not able to get rid of the character 'B'."}, "src_uid": "98e3182f047a7e7b10be7f207b219267"}
{"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": "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": "You might have heard about the next game in Lara Croft series coming out this year. You also might have watched its trailer. Though you definitely missed the main idea about its plot, so let me lift the veil of secrecy.Lara is going to explore yet another dangerous dungeon. Game designers decided to use good old 2D environment. The dungeon can be represented as a rectangle matrix of n rows and m columns. Cell (x,\u2009y) is the cell in the x-th row in the y-th column. Lara can move between the neighbouring by side cells in all four directions.Moreover, she has even chosen the path for herself to avoid all the traps. She enters the dungeon in cell (1,\u20091), that is top left corner of the matrix. Then she goes down all the way to cell (n,\u20091) \u2014 the bottom left corner. Then she starts moving in the snake fashion \u2014 all the way to the right, one cell up, then to the left to the cell in 2-nd column, one cell up. She moves until she runs out of non-visited cells. n and m given are such that she always end up in cell (1,\u20092).Lara has already moved to a neighbouring cell k times. Can you determine her current position?", "input_spec": "The only line contains three integers n, m and k (2\u2009\u2264\u2009n,\u2009m\u2009\u2264\u2009109, n is always even, 0\u2009\u2264\u2009k\u2009<\u2009n\u00b7m). Note that k doesn't fit into 32-bit integer type!", "output_spec": "Print the cell (the row and the column where the cell is situated) where Lara ends up after she moves k times.", "sample_inputs": ["4 3 0", "4 3 11", "4 3 7"], "sample_outputs": ["1 1", "1 2", "3 2"], "notes": "NoteHere is her path on matrix 4 by 3:  "}, "src_uid": "e88bb7621c7124c54e75109a00f96301"}
{"nl": {"description": "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": "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": "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$$$-bit integer data type.", "sample_inputs": ["2", "4", "8", "20"], "sample_outputs": ["1", "3", "1260", "12164510040883200"], "notes": null}, "src_uid": "ad0985c56a207f76afa2ecd642f56728"}
{"nl": {"description": "Xenia the beginner mathematician is a third year student at elementary school. She is now learning the addition operation.The teacher has written down the sum of multiple numbers. Pupils should calculate the sum. To make the calculation easier, the sum only contains numbers 1, 2 and 3. Still, that isn't enough for Xenia. She is only beginning to count, so she can calculate a sum only if the summands follow in non-decreasing order. For example, she can't calculate sum 1+3+2+1 but she can calculate sums 1+1+2 and 3+3.You've got the sum that was written on the board. Rearrange the summans and print the sum in such a way that Xenia can calculate the sum.", "input_spec": "The first line contains a non-empty string s \u2014 the sum Xenia needs to count. String s contains no spaces. It only contains digits and characters \"+\". Besides, string s is a correct sum of numbers 1, 2 and 3. String s is at most 100 characters long.", "output_spec": "Print the new sum that Xenia can count.", "sample_inputs": ["3+2+1", "1+1+3+1+3", "2"], "sample_outputs": ["1+2+3", "1+1+1+3+3", "2"], "notes": null}, "src_uid": "76c7312733ef9d8278521cf09d3ccbc8"}
{"nl": {"description": "Consider a playoff tournament where $$$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": "On her way to programming school tiger Dasha faced her first test \u2014 a huge staircase!  The steps were numbered from one to infinity. As we know, tigers are very fond of all striped things, it is possible that it has something to do with their color. So on some interval of her way she calculated two values \u2014 the number of steps with even and odd numbers. You need to check whether there is an interval of steps from the l-th to the r-th (1\u2009\u2264\u2009l\u2009\u2264\u2009r), for which values that Dasha has found are correct.", "input_spec": "In the only line you are given two integers a, b (0\u2009\u2264\u2009a,\u2009b\u2009\u2264\u2009100) \u2014 the number of even and odd steps, accordingly.", "output_spec": "In the only line print \"YES\", if the interval of steps described above exists, and \"NO\" otherwise.", "sample_inputs": ["2 3", "3 1"], "sample_outputs": ["YES", "NO"], "notes": "NoteIn the first example one of suitable intervals is from 1 to 5. The interval contains two even steps\u00a0\u2014 2 and 4, and three odd: 1, 3 and 5."}, "src_uid": "ec5e3b3f5ee6a13eaf01b9a9a66ff037"}
{"nl": {"description": "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": "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": "Vasya the programmer lives in the middle of the Programming subway branch. He has two girlfriends: Dasha and Masha, who live at the different ends of the branch, each one is unaware of the other one's existence.When Vasya has some free time, he goes to one of his girlfriends. He descends into the subway at some time, waits the first train to come and rides on it to the end of the branch to the corresponding girl. However, the trains run with different frequencies: a train goes to Dasha's direction every a minutes, but a train goes to Masha's direction every b minutes. If two trains approach at the same time, Vasya goes toward the direction with the lower frequency of going trains, that is, to the girl, to whose directions the trains go less frequently (see the note to the third sample).We know that the trains begin to go simultaneously before Vasya appears. That is the train schedule is such that there exists a moment of time when the two trains arrive simultaneously.Help Vasya count to which girlfriend he will go more often.", "input_spec": "The first line contains two integers a and b (a\u2009\u2260\u2009b,\u20091\u2009\u2264\u2009a,\u2009b\u2009\u2264\u2009106).", "output_spec": "Print \"Dasha\" if Vasya will go to Dasha more frequently, \"Masha\" if he will go to Masha more frequently, or \"Equal\" if he will go to both girlfriends with the same frequency.", "sample_inputs": ["3 7", "5 3", "2 3"], "sample_outputs": ["Dasha", "Masha", "Equal"], "notes": "NoteLet's take a look at the third sample. Let the trains start to go at the zero moment of time. It is clear that the moments of the trains' arrival will be periodic with period 6. That's why it is enough to show that if Vasya descends to the subway at a moment of time inside the interval (0,\u20096], he will go to both girls equally often. If he descends to the subway at a moment of time from 0 to 2, he leaves for Dasha on the train that arrives by the second minute.If he descends to the subway at a moment of time from 2 to 3, he leaves for Masha on the train that arrives by the third minute.If he descends to the subway at a moment of time from 3 to 4, he leaves for Dasha on the train that arrives by the fourth minute.If he descends to the subway at a moment of time from 4 to 6, he waits for both trains to arrive by the sixth minute and goes to Masha as trains go less often in Masha's direction.In sum Masha and Dasha get equal time \u2014 three minutes for each one, thus, Vasya will go to both girlfriends equally often."}, "src_uid": "06eb66df61ff5d61d678bbb3bb6553cc"}
{"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": "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": "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 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$$$ is minimal.", "sample_inputs": ["432", "99", "237", "42"], "sample_outputs": ["435", "103", "237", "44"], "notes": null}, "src_uid": "bb6fb9516b2c55d1ee47a30d423562d7"}
{"nl": {"description": "Alice got many presents these days. So she decided to pack them into boxes and send them to her friends.There are $$$n$$$ kinds of presents. Presents of one kind are identical (i.e. there is no way to distinguish two gifts of the same kind). Presents of different kinds are different (i.e. that is, two gifts of different kinds are distinguishable). The number of presents of each kind, that Alice has is very big, so we can consider Alice has an infinite number of gifts of each kind.Also, there are $$$m$$$ boxes. All of them are for different people, so they are pairwise distinct (consider that the names of $$$m$$$ friends are written on the boxes). For example, putting the first kind of present into the first box but not into the second box, is different from putting the first kind of present into the second box but not into the first box.Alice wants to pack presents with the following rules:  She won't pack more than one present of each kind into the same box, so each box should contain presents of different kinds (i.e. each box contains a subset of $$$n$$$ kinds, empty boxes are allowed);  For each kind at least one present should be packed into some box. Now Alice wants to know how many different ways to pack the presents exists. Please, help her and calculate this number. Since the answer can be huge, output it by modulo $$$10^9+7$$$.See examples and their notes for clarification.", "input_spec": "The first line contains two integers $$$n$$$ and $$$m$$$, separated by spaces ($$$1 \\leq n,m \\leq 10^9$$$)\u00a0\u2014 the number of kinds of presents and the number of boxes that Alice has.", "output_spec": "Print one integer \u00a0\u2014 the number of ways to pack the presents with Alice's rules, calculated by modulo $$$10^9+7$$$", "sample_inputs": ["1 3", "2 2"], "sample_outputs": ["7", "9"], "notes": "NoteIn the first example, there are seven ways to pack presents:$$$\\{1\\}\\{\\}\\{\\}$$$$$$\\{\\}\\{1\\}\\{\\}$$$$$$\\{\\}\\{\\}\\{1\\}$$$$$$\\{1\\}\\{1\\}\\{\\}$$$$$$\\{\\}\\{1\\}\\{1\\}$$$$$$\\{1\\}\\{\\}\\{1\\}$$$$$$\\{1\\}\\{1\\}\\{1\\}$$$In the second example there are nine ways to pack presents:$$$\\{\\}\\{1,2\\}$$$$$$\\{1\\}\\{2\\}$$$$$$\\{1\\}\\{1,2\\}$$$$$$\\{2\\}\\{1\\}$$$$$$\\{2\\}\\{1,2\\}$$$$$$\\{1,2\\}\\{\\}$$$$$$\\{1,2\\}\\{1\\}$$$$$$\\{1,2\\}\\{2\\}$$$$$$\\{1,2\\}\\{1,2\\}$$$For example, the way $$$\\{2\\}\\{2\\}$$$ is wrong, because presents of the first kind should be used in the least one box."}, "src_uid": "71029e5bf085b0f5f39d1835eb801891"}
{"nl": {"description": "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 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": "The girl Taylor has a beautiful calendar for the year y. In the calendar all days are given with their days of week: Monday, Tuesday, Wednesday, Thursday, Friday, Saturday and Sunday.The calendar is so beautiful that she wants to know what is the next year after y when the calendar will be exactly the same. Help Taylor to find that year.Note that leap years has 366 days. The year is leap if it is divisible by 400 or it is divisible by 4, but not by 100 (https://en.wikipedia.org/wiki/Leap_year).", "input_spec": "The only line contains integer y (1000\u2009\u2264\u2009y\u2009<\u2009100'000) \u2014 the year of the calendar.", "output_spec": "Print the only integer y' \u2014 the next year after y when the calendar will be the same. Note that you should find the first year after y with the same calendar.", "sample_inputs": ["2016", "2000", "50501"], "sample_outputs": ["2044", "2028", "50507"], "notes": "NoteToday is Monday, the 13th of June, 2016."}, "src_uid": "565bbd09f79eb7bfe2f2da46647af0f2"}
{"nl": {"description": "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": "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": "Katie, Kuro and Shiro are best friends. They have known each other since kindergarten. That's why they often share everything with each other and work together on some very hard problems.Today is Shiro's birthday. She really loves pizza so she wants to invite her friends to the pizza restaurant near her house to celebrate her birthday, including her best friends Katie and Kuro.She has ordered a very big round pizza, in order to serve her many friends. Exactly $$$n$$$ of Shiro's friends are here. That's why she has to divide the pizza into $$$n + 1$$$ slices (Shiro also needs to eat). She wants the slices to be exactly the same size and shape. If not, some of her friends will get mad and go home early, and the party will be over.Shiro is now hungry. She wants to cut the pizza with minimum of straight cuts. A cut is a straight segment, it might have ends inside or outside the pizza. But she is too lazy to pick up the calculator.As usual, she will ask Katie and Kuro for help. But they haven't come yet. Could you help Shiro with this problem?", "input_spec": "A single line contains one non-negative integer $$$n$$$ ($$$0 \\le n \\leq 10^{18}$$$)\u00a0\u2014 the number of Shiro's friends. The circular pizza has to be sliced into $$$n + 1$$$ pieces.", "output_spec": "A single integer\u00a0\u2014 the number of straight cuts Shiro needs.", "sample_inputs": ["3", "4"], "sample_outputs": ["2", "5"], "notes": "NoteTo cut the round pizza into quarters one has to make two cuts through the center with angle $$$90^{\\circ}$$$ between them.To cut the round pizza into five equal parts one has to make five cuts."}, "src_uid": "236177ff30dafe68295b5d33dc501828"}
{"nl": {"description": "Fafa owns a company that works on huge projects. There are n employees in Fafa's company. Whenever the company has a new project to start working on, Fafa has to divide the tasks of this project among all the employees.Fafa finds doing this every time is very tiring for him. So, he decided to choose the best l employees in his company as team leaders. Whenever there is a new project, Fafa will divide the tasks among only the team leaders and each team leader will be responsible of some positive number of employees to give them the tasks. To make this process fair for the team leaders, each one of them should be responsible for the same number of employees. Moreover, every employee, who is not a team leader, has to be under the responsibility of exactly one team leader, and no team leader is responsible for another team leader.Given the number of employees n, find in how many ways Fafa could choose the number of team leaders l in such a way that it is possible to divide employees between them evenly.", "input_spec": "The input consists of a single line containing a positive integer n (2\u2009\u2264\u2009n\u2009\u2264\u2009105) \u2014 the number of employees in Fafa's company.", "output_spec": "Print a single integer representing the answer to the problem.", "sample_inputs": ["2", "10"], "sample_outputs": ["1", "3"], "notes": "NoteIn the second sample Fafa has 3 ways:  choose only 1 employee as a team leader with 9 employees under his responsibility.  choose 2 employees as team leaders with 4 employees under the responsibility of each of them.  choose 5 employees as team leaders with 1 employee under the responsibility of each of them. "}, "src_uid": "89f6c1659e5addbf909eddedb785d894"}
{"nl": {"description": "A permutation of length $$$n$$$ is an array consisting of $$$n$$$ distinct integers from $$$1$$$ to $$$n$$$ in arbitrary order. For example, $$$[2,3,1,5,4]$$$ is a permutation, but $$$[1,2,2]$$$ is not a permutation ($$$2$$$ appears twice in the array) and $$$[1,3,4]$$$ is also not a permutation ($$$n=3$$$ but there is $$$4$$$ in the array).Consider a permutation $$$p$$$ of length $$$n$$$, we build a graph of size $$$n$$$ using it as follows:   For every $$$1 \\leq i \\leq n$$$, find the largest $$$j$$$ such that $$$1 \\leq j < i$$$ and $$$p_j > p_i$$$, and add an undirected edge between node $$$i$$$ and node $$$j$$$  For every $$$1 \\leq i \\leq n$$$, find the smallest $$$j$$$ such that $$$i < j \\leq n$$$ and $$$p_j > p_i$$$, and add an undirected edge between node $$$i$$$ and node $$$j$$$ In cases where no such $$$j$$$ exists, we make no edges. Also, note that we make edges between the corresponding indices, not the values at those indices.For clarity, consider as an example $$$n = 4$$$, and $$$p = [3,1,4,2]$$$; here, the edges of the graph are $$$(1,3),(2,1),(2,3),(4,3)$$$.A permutation $$$p$$$ is cyclic if the graph built using $$$p$$$ has at least one simple cycle. Given $$$n$$$, find the number of cyclic permutations of length $$$n$$$. Since the number may be very large, output it modulo $$$10^9+7$$$.Please refer to the Notes section for the formal definition of a simple cycle", "input_spec": "The first and only line contains a single integer $$$n$$$ ($$$3 \\le n \\le 10^6$$$).", "output_spec": "Output a single integer $$$0 \\leq x < 10^9+7$$$, the number of cyclic permutations of length $$$n$$$ modulo $$$10^9+7$$$.", "sample_inputs": ["4", "583291"], "sample_outputs": ["16", "135712853"], "notes": "NoteThere are $$$16$$$ cyclic permutations for $$$n = 4$$$. $$$[4,2,1,3]$$$ is one such permutation, having a cycle of length four: $$$4 \\rightarrow 3 \\rightarrow 2 \\rightarrow 1 \\rightarrow 4$$$.Nodes $$$v_1$$$, $$$v_2$$$, $$$\\ldots$$$, $$$v_k$$$ form a simple cycle if the following conditions hold:   $$$k \\geq 3$$$.  $$$v_i \\neq v_j$$$ for any pair of indices $$$i$$$ and $$$j$$$. ($$$1 \\leq i < j \\leq k$$$)  $$$v_i$$$ and $$$v_{i+1}$$$ share an edge for all $$$i$$$ ($$$1 \\leq i < k$$$), and $$$v_1$$$ and $$$v_k$$$ share an edge. "}, "src_uid": "3dc1ee09016a25421ae371fa8005fce1"}
{"nl": {"description": "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": "Anton likes to listen to fairy tales, especially when Danik, Anton's best friend, tells them. Right now Danik tells Anton a fairy tale:\"Once upon a time, there lived an emperor. He was very rich and had much grain. One day he ordered to build a huge barn to put there all his grain. Best builders were building that barn for three days and three nights. But they overlooked and there remained a little hole in the barn, from which every day sparrows came through. Here flew a sparrow, took a grain and flew away...\"More formally, the following takes place in the fairy tale. At the beginning of the first day the barn with the capacity of n grains was full. Then, every day (starting with the first day) the following happens:  m grains are brought to the barn. If m grains doesn't fit to the barn, the barn becomes full and the grains that doesn't fit are brought back (in this problem we can assume that the grains that doesn't fit to the barn are not taken into account).  Sparrows come and eat grain. In the i-th day i sparrows come, that is on the first day one sparrow come, on the second day two sparrows come and so on. Every sparrow eats one grain. If the barn is empty, a sparrow eats nothing. Anton is tired of listening how Danik describes every sparrow that eats grain from the barn. Anton doesn't know when the fairy tale ends, so he asked you to determine, by the end of which day the barn will become empty for the first time. Help Anton and write a program that will determine the number of that day!", "input_spec": "The only line of the input contains two integers n and m (1\u2009\u2264\u2009n,\u2009m\u2009\u2264\u20091018)\u00a0\u2014 the capacity of the barn and the number of grains that are brought every day.", "output_spec": "Output one integer\u00a0\u2014 the number of the day when the barn will become empty for the first time. Days are numbered starting with one.", "sample_inputs": ["5 2", "8 1"], "sample_outputs": ["4", "5"], "notes": "NoteIn the first sample the capacity of the barn is five grains and two grains are brought every day. The following happens:  At the beginning of the first day grain is brought to the barn. It's full, so nothing happens.  At the end of the first day one sparrow comes and eats one grain, so 5\u2009-\u20091\u2009=\u20094 grains remain.  At the beginning of the second day two grains are brought. The barn becomes full and one grain doesn't fit to it.  At the end of the second day two sparrows come. 5\u2009-\u20092\u2009=\u20093 grains remain.  At the beginning of the third day two grains are brought. The barn becomes full again.  At the end of the third day three sparrows come and eat grain. 5\u2009-\u20093\u2009=\u20092 grains remain.  At the beginning of the fourth day grain is brought again. 2\u2009+\u20092\u2009=\u20094 grains remain.  At the end of the fourth day four sparrows come and eat grain. 4\u2009-\u20094\u2009=\u20090 grains remain. The barn is empty. So the answer is 4, because by the end of the fourth day the barn becomes empty."}, "src_uid": "3b585ea852ffc41034ef6804b6aebbd8"}
{"nl": {"description": "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": "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": "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": "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": "So, the New Year holidays are over. Santa Claus and his colleagues can take a rest and have guests at last. When two \"New Year and Christmas Men\" meet, thear assistants cut out of cardboard the letters from the guest's name and the host's name in honor of this event. Then the hung the letters above the main entrance. One night, when everyone went to bed, someone took all the letters of our characters' names. Then he may have shuffled the letters and put them in one pile in front of the door.The next morning it was impossible to find the culprit who had made the disorder. But everybody wondered whether it is possible to restore the names of the host and his guests from the letters lying at the door? That is, we need to verify that there are no extra letters, and that nobody will need to cut more letters.Help the \"New Year and Christmas Men\" and their friends to cope with this problem. You are given both inscriptions that hung over the front door the previous night, and a pile of letters that were found at the front door next morning.", "input_spec": "The input file consists of three lines: the first line contains the guest's name, the second line contains the name of the residence host and the third line contains letters in a pile that were found at the door in the morning. All lines are not empty and contain only uppercase Latin letters. The length of each line does not exceed 100.", "output_spec": "Print \"YES\" without the quotes, if the letters in the pile could be permuted to make the names of the \"New Year and Christmas Men\". Otherwise, print \"NO\" without the quotes.", "sample_inputs": ["SANTACLAUS\nDEDMOROZ\nSANTAMOROZDEDCLAUS", "PAPAINOEL\nJOULUPUKKI\nJOULNAPAOILELUPUKKI", "BABBONATALE\nFATHERCHRISTMAS\nBABCHRISTMASBONATALLEFATHER"], "sample_outputs": ["YES", "NO", "NO"], "notes": "NoteIn the first sample the letters written in the last line can be used to write the names and there won't be any extra letters left.In the second sample letter \"P\" is missing from the pile and there's an extra letter \"L\".In the third sample there's an extra letter \"L\"."}, "src_uid": "b6456a39d38fabcd25267793ed94d90c"}
{"nl": {"description": "\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": "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": "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": "This is an easier version of the problem. In this version, $$$n \\le 500$$$.Vasya is an experienced developer of programming competitions' problems. As all great minds at some time, Vasya faced a creative crisis. To improve the situation, Petya gifted him a string consisting of opening and closing brackets only. Petya believes, that the beauty of the bracket string is a number of its cyclical shifts, which form a correct bracket sequence.To digress from his problems, Vasya decided to select two positions of the string (not necessarily distinct) and swap characters located at this positions with each other. Vasya will apply this operation exactly once. He is curious what is the maximum possible beauty he can achieve this way. Please help him.We remind that bracket sequence $$$s$$$ is called correct if:   $$$s$$$ is empty;  $$$s$$$ is equal to \"($$$t$$$)\", where $$$t$$$ is correct bracket sequence;  $$$s$$$ is equal to $$$t_1 t_2$$$, i.e. concatenation of $$$t_1$$$ and $$$t_2$$$, where $$$t_1$$$ and $$$t_2$$$ are correct bracket sequences. For example, \"(()())\", \"()\" are correct, while \")(\" and \"())\" are not.The cyclical shift of the string $$$s$$$ of length $$$n$$$ by $$$k$$$ ($$$0 \\leq k < n$$$) is a string formed by a concatenation of the last $$$k$$$ symbols of the string $$$s$$$ with the first $$$n - k$$$ symbols of string $$$s$$$. For example, the cyclical shift of string \"(())()\" by $$$2$$$ equals \"()(())\".Cyclical shifts $$$i$$$ and $$$j$$$ are considered different, if $$$i \\ne j$$$.", "input_spec": "The first line contains an integer $$$n$$$ ($$$1 \\le n \\le 500$$$), the length of the string. The second line contains a string, consisting of exactly $$$n$$$ characters, where each of the characters is either \"(\" or \")\".", "output_spec": "The first line should contain a single integer\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": "2d10668fcc2d8e90e102b043f5e0578d"}
{"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": "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": "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": "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": "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": "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": "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": "Meg the Rabbit decided to do something nice, specifically \u2014 to determine the shortest distance between two points on the surface of our planet. But Meg... what can you say, she wants everything simple. So, she already regards our planet as a two-dimensional circle. No, wait, it's even worse \u2014 as a square of side n. Thus, the task has been reduced to finding the shortest path between two dots on a square (the path should go through the square sides). To simplify the task let us consider the vertices of the square to lie at points whose coordinates are: (0,\u20090), (n,\u20090), (0,\u2009n) and (n,\u2009n).", "input_spec": "The single line contains 5 space-separated integers: n,\u2009x1,\u2009y1,\u2009x2,\u2009y2 (1\u2009\u2264\u2009n\u2009\u2264\u20091000,\u20090\u2009\u2264\u2009x1,\u2009y1,\u2009x2,\u2009y2\u2009\u2264\u2009n) which correspondingly represent a side of the square, the coordinates of the first point and the coordinates of the second point. It is guaranteed that the points lie on the sides of the square.", "output_spec": "You must print on a single line the shortest distance between the points.", "sample_inputs": ["2 0 0 1 0", "2 0 1 2 1", "100 0 0 100 100"], "sample_outputs": ["1", "4", "200"], "notes": null}, "src_uid": "685fe16c217b5b71eafdb4198822250e"}
{"nl": {"description": "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": "\"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": "You are given a positive integer n. Let's build a graph on vertices 1,\u20092,\u2009...,\u2009n in such a way that there is an edge between vertices u and v if and only if . Let d(u,\u2009v) be the shortest distance between u and v, or 0 if there is no path between them. Compute the sum of values d(u,\u2009v) over all 1\u2009\u2264\u2009u\u2009<\u2009v\u2009\u2264\u2009n.The gcd (greatest common divisor) of two positive integers is the maximum positive integer that divides both of the integers.", "input_spec": "Single integer n (1\u2009\u2264\u2009n\u2009\u2264\u2009107).", "output_spec": "Print the sum of d(u,\u2009v) over all 1\u2009\u2264\u2009u\u2009<\u2009v\u2009\u2264\u2009n.", "sample_inputs": ["6", "10"], "sample_outputs": ["8", "44"], "notes": "NoteAll shortest paths in the first example:              There are no paths between other pairs of vertices.The total distance is 2\u2009+\u20091\u2009+\u20091\u2009+\u20092\u2009+\u20091\u2009+\u20091\u2009=\u20098."}, "src_uid": "bb1bd5d8bab7d79e514281230d484996"}
{"nl": {"description": "You are given two squares, one with sides parallel to the coordinate axes, and another one with sides at 45 degrees to the coordinate axes. Find whether the two squares intersect.The interior of the square is considered to be part of the square, i.e. if one square is completely inside another, they intersect. If the two squares only share one common point, they are also considered to intersect.", "input_spec": "The input data consists of two lines, one for each square, both containing 4 pairs of integers. Each pair represents coordinates of one vertex of the square. Coordinates within each line are either in clockwise or counterclockwise order. The first line contains the coordinates of the square with sides parallel to the coordinate axes, the second line contains the coordinates of the square at 45 degrees. All the values are integer and between $$$-100$$$ and $$$100$$$.", "output_spec": "Print \"Yes\" if squares intersect, otherwise print \"No\". You can print each letter in any case (upper or lower).", "sample_inputs": ["0 0 6 0 6 6 0 6\n1 3 3 5 5 3 3 1", "0 0 6 0 6 6 0 6\n7 3 9 5 11 3 9 1", "6 0 6 6 0 6 0 0\n7 4 4 7 7 10 10 7"], "sample_outputs": ["YES", "NO", "YES"], "notes": "NoteIn the first example the second square lies entirely within the first square, so they do intersect.In the second sample squares do not have any points in common.Here are images corresponding to the samples:      "}, "src_uid": "f6a3dd8b3bab58ff66055c61ddfdf06a"}
{"nl": {"description": "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": "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": "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": "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": "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": "A girl named Sonya is studying in the scientific lyceum of the Kingdom of Kremland. The teacher of computer science (Sonya's favorite subject!) invented a task for her.Given an array $$$a$$$ of length $$$n$$$, consisting only of the numbers $$$0$$$ and $$$1$$$, and the number $$$k$$$. Exactly $$$k$$$ times the following happens:   Two numbers $$$i$$$ and $$$j$$$ are chosen equiprobable such that ($$$1 \\leq i < j \\leq n$$$).  The numbers in the $$$i$$$ and $$$j$$$ positions are swapped. Sonya's task is to find the probability that after all the operations are completed, the $$$a$$$ array will be sorted in non-decreasing order. She turned to you for help. Help Sonya solve this problem.It can be shown that the desired probability is either $$$0$$$ or it can be represented as $$$\\dfrac{P}{Q}$$$, where $$$P$$$ and $$$Q$$$ are coprime integers and $$$Q \\not\\equiv 0~\\pmod {10^9+7}$$$.", "input_spec": "The first line contains two integers $$$n$$$ and $$$k$$$ ($$$2 \\leq n \\leq 100, 1 \\leq k \\leq 10^9$$$)\u00a0\u2014 the length of the array $$$a$$$ and the number of operations. The second line contains $$$n$$$ integers $$$a_1, a_2, \\ldots, a_n$$$ ($$$0 \\le a_i \\le 1$$$)\u00a0\u2014 the description of the array $$$a$$$.", "output_spec": "If the desired probability is $$$0$$$, print $$$0$$$, otherwise print the value $$$P \\cdot Q^{-1}$$$ $$$\\pmod {10^9+7}$$$, where $$$P$$$ and $$$Q$$$ are defined above.", "sample_inputs": ["3 2\n0 1 0", "5 1\n1 1 1 0 0", "6 4\n1 0 0 1 1 0"], "sample_outputs": ["333333336", "0", "968493834"], "notes": "NoteIn the first example, all possible variants of the final array $$$a$$$, after applying exactly two operations: $$$(0, 1, 0)$$$, $$$(0, 0, 1)$$$, $$$(1, 0, 0)$$$, $$$(1, 0, 0)$$$, $$$(0, 1, 0)$$$, $$$(0, 0, 1)$$$, $$$(0, 0, 1)$$$, $$$(1, 0, 0)$$$, $$$(0, 1, 0)$$$. Therefore, the answer is $$$\\dfrac{3}{9}=\\dfrac{1}{3}$$$.In the second example, the array will not be sorted in non-decreasing order after one operation, therefore the answer is $$$0$$$."}, "src_uid": "77f28d155a632ceaabd9f5a9d846461a"}
{"nl": {"description": "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": "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": "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": "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": "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": "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": "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": "Bear Limak prepares problems for a programming competition. Of course, it would be unprofessional to mention the sponsor name in the statement. Limak takes it seriously and he is going to change some words. To make it still possible to read, he will try to modify each word as little as possible.Limak has a string s that consists of uppercase English letters. In one move he can swap two adjacent letters of the string. For example, he can transform a string \"ABBC\" into \"BABC\" or \"ABCB\" in one move.Limak wants to obtain a string without a substring \"VK\" (i.e. there should be no letter 'V' immediately followed by letter 'K'). It can be easily proved that it's possible for any initial string s.What is the minimum possible number of moves Limak can do?", "input_spec": "The first line of the input contains an integer n (1\u2009\u2264\u2009n\u2009\u2264\u200975)\u00a0\u2014 the length of the string. The second line contains a string s, consisting of uppercase English letters. The length of the string is equal to n.", "output_spec": "Print one integer, denoting the minimum possible number of moves Limak can do, in order to obtain a string without a substring \"VK\".", "sample_inputs": ["4\nVKVK", "5\nBVVKV", "7\nVVKEVKK", "20\nVKVKVVVKVOVKVQKKKVVK", "5\nLIMAK"], "sample_outputs": ["3", "2", "3", "8", "0"], "notes": "NoteIn the first sample, the initial string is \"VKVK\". The minimum possible number of moves is 3. One optimal sequence of moves is: Swap two last letters. The string becomes \"VKKV\". Swap first two letters. The string becomes \"KVKV\". Swap the second and the third letter. The string becomes \"KKVV\". Indeed, this string doesn't have a substring \"VK\".In the second sample, there are two optimal sequences of moves. One is \"BVVKV\"\u2009\u2009\u2192\u2009\u2009\"VBVKV\"\u2009\u2009\u2192\u2009\u2009\"VVBKV\". The other is \"BVVKV\"\u2009\u2009\u2192\u2009\u2009\"BVKVV\"\u2009\u2009\u2192\u2009\u2009\"BKVVV\".In the fifth sample, no swaps are necessary."}, "src_uid": "08444f9ab1718270b5ade46852b155d7"}
{"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": "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": "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": "Let's denote (yet again) the sequence of Fibonacci strings:$$$F(0) = $$$ 0, $$$F(1) = $$$ 1, $$$F(i) = F(i - 2) + F(i - 1)$$$, where the plus sign denotes the concatenation of two strings.Let's denote the lexicographically sorted sequence of suffixes of string $$$F(i)$$$ as $$$A(F(i))$$$. For example, $$$F(4)$$$ is 01101, and $$$A(F(4))$$$ is the following sequence: 01, 01101, 1, 101, 1101. Elements in this sequence are numbered from $$$1$$$.Your task is to print $$$m$$$ first characters of $$$k$$$-th element of $$$A(F(n))$$$. If there are less than $$$m$$$ characters in this suffix, then output the whole suffix.", "input_spec": "The only line of the input contains three numbers $$$n$$$, $$$k$$$ and $$$m$$$ ($$$1 \\le n, m \\le 200$$$, $$$1 \\le k \\le 10^{18}$$$) denoting the index of the Fibonacci string you have to consider, the index of the element of $$$A(F(n))$$$ and the number of characters you have to output, respectively. It is guaranteed that $$$k$$$ does not exceed the length of $$$F(n)$$$.", "output_spec": "Output $$$m$$$ first characters of $$$k$$$-th element of $$$A(F(n))$$$, or the whole element if its length is less than $$$m$$$.", "sample_inputs": ["4 5 3", "4 3 3"], "sample_outputs": ["110", "1"], "notes": null}, "src_uid": "7b4a057efee5264bfaaf60d50fccb92b"}
{"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": "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": "Bad news came to Mike's village, some thieves stole a bunch of chocolates from the local factory! Horrible! Aside from loving sweet things, thieves from this area are known to be very greedy. So after a thief takes his number of chocolates for himself, the next thief will take exactly k times more than the previous one. The value of k (k\u2009>\u20091) is a secret integer known only to them. It is also known that each thief's bag can carry at most n chocolates (if they intend to take more, the deal is cancelled) and that there were exactly four thieves involved. Sadly, only the thieves know the value of n, but rumours say that the numbers of ways they could have taken the chocolates (for a fixed n, but not fixed k) is m. Two ways are considered different if one of the thieves (they should be numbered in the order they take chocolates) took different number of chocolates in them.Mike want to track the thieves down, so he wants to know what their bags are and value of n will help him in that. Please find the smallest possible value of n or tell him that the rumors are false and there is no such n.", "input_spec": "The single line of input contains the integer m (1\u2009\u2264\u2009m\u2009\u2264\u20091015)\u00a0\u2014 the number of ways the thieves might steal the chocolates, as rumours say.", "output_spec": "Print the only integer n\u00a0\u2014 the maximum amount of chocolates that thieves' bags can carry. If there are more than one n satisfying the rumors, print the smallest one. If there is no such n for a false-rumoured m, print \u2009-\u20091.", "sample_inputs": ["1", "8", "10"], "sample_outputs": ["8", "54", "-1"], "notes": "NoteIn the first sample case the smallest n that leads to exactly one way of stealing chocolates is n\u2009=\u20098, whereas the amounts of stealed chocolates are (1,\u20092,\u20094,\u20098) (the number of chocolates stolen by each of the thieves).In the second sample case the smallest n that leads to exactly 8 ways is n\u2009=\u200954 with the possibilities: (1,\u20092,\u20094,\u20098),\u2009\u2002(1,\u20093,\u20099,\u200927),\u2009\u2002(2,\u20094,\u20098,\u200916),\u2009\u2002(2,\u20096,\u200918,\u200954),\u2009\u2002(3,\u20096,\u200912,\u200924),\u2009\u2002(4,\u20098,\u200916,\u200932),\u2009\u2002(5,\u200910,\u200920,\u200940),\u2009\u2002(6,\u200912,\u200924,\u200948).There is no n leading to exactly 10 ways of stealing chocolates in the third sample case."}, "src_uid": "602deaad5c66e264997249457d555129"}
{"nl": {"description": "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": "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": "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": "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": "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": "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": "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": "You have n problems. You have estimated the difficulty of the i-th one as integer ci. Now you want to prepare a problemset for a contest, using some of the problems you've made.A problemset for the contest must consist of at least two problems. You think that the total difficulty of the problems of the contest must be at least l and at most r. Also, you think that the difference between difficulties of the easiest and the hardest of the chosen problems must be at least x.Find the number of ways to choose a problemset for the contest.", "input_spec": "The first line contains four integers n, l, r, x (1\u2009\u2264\u2009n\u2009\u2264\u200915, 1\u2009\u2264\u2009l\u2009\u2264\u2009r\u2009\u2264\u2009109, 1\u2009\u2264\u2009x\u2009\u2264\u2009106) \u2014 the number of problems you have, the minimum and maximum value of total difficulty of the problemset and the minimum difference in difficulty between the hardest problem in the pack and the easiest one, respectively. The second line contains n integers c1,\u2009c2,\u2009...,\u2009cn (1\u2009\u2264\u2009ci\u2009\u2264\u2009106) \u2014 the difficulty of each problem.", "output_spec": "Print the number of ways to choose a suitable problemset for the contest. ", "sample_inputs": ["3 5 6 1\n1 2 3", "4 40 50 10\n10 20 30 25", "5 25 35 10\n10 10 20 10 20"], "sample_outputs": ["2", "2", "6"], "notes": "NoteIn the first example two sets are suitable, one consisting of the second and third problem, another one consisting of all three problems.In the second example, two sets of problems are suitable \u2014 the set of problems with difficulties 10 and 30 as well as the set of problems with difficulties 20 and 30.In the third example any set consisting of one problem of difficulty 10 and one problem of difficulty 20 is suitable."}, "src_uid": "0d43104a0de924cdcf8e4aced5aa825d"}
{"nl": {"description": "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": "Andrey thinks he is truly a successful developer, but in reality he didn't know about the binary search algorithm until recently. After reading some literature Andrey understood that this algorithm allows to quickly find a certain number $$$x$$$ in an array. For an array $$$a$$$ indexed from zero, and an integer $$$x$$$ the pseudocode of the algorithm is as follows:  Note that the elements of the array are indexed from zero, and the division is done in integers (rounding down).Andrey read that the algorithm only works if the array is sorted. However, he found this statement untrue, because there certainly exist unsorted arrays for which the algorithm find $$$x$$$!Andrey wants to write a letter to the book authors, but before doing that he must consider the permutations of size $$$n$$$ such that the algorithm finds $$$x$$$ in them. A permutation of size $$$n$$$ is an array consisting of $$$n$$$ distinct integers between $$$1$$$ and $$$n$$$ in arbitrary order.Help Andrey and find the number of permutations of size $$$n$$$ which contain $$$x$$$ at position $$$pos$$$ and for which the given implementation of the binary search algorithm finds $$$x$$$ (returns true). As the result may be extremely large, print the remainder of its division by $$$10^9+7$$$.", "input_spec": "The only line of input contains integers $$$n$$$, $$$x$$$ and $$$pos$$$ ($$$1 \\le x \\le n \\le 1000$$$, $$$0 \\le pos \\le n - 1$$$) \u2014 the required length of the permutation, the number to search, and the required position of that number, respectively.", "output_spec": "Print a single number\u00a0\u2014 the remainder of the division of the number of valid permutations by $$$10^9+7$$$.", "sample_inputs": ["4 1 2", "123 42 24"], "sample_outputs": ["6", "824071958"], "notes": "NoteAll possible permutations in the first test case: $$$(2, 3, 1, 4)$$$, $$$(2, 4, 1, 3)$$$, $$$(3, 2, 1, 4)$$$, $$$(3, 4, 1, 2)$$$, $$$(4, 2, 1, 3)$$$, $$$(4, 3, 1, 2)$$$."}, "src_uid": "24e2f10463f440affccc2755f4462d8a"}
{"nl": {"description": "In Berland prime numbers are fashionable \u2014 the respectable citizens dwell only on the floors with numbers that are prime numbers. The numismatists value particularly high the coins with prime nominal values. All the prime days are announced holidays!Yet even this is not enough to make the Berland people happy. On the main street of the capital stand n houses, numbered from 1 to n. The government decided to paint every house a color so that the sum of the numbers of the houses painted every color is a prime number.However it turned out that not all the citizens approve of this decision \u2014 many of them protest because they don't want many colored houses on the capital's main street. That's why it is decided to use the minimal possible number of colors. The houses don't have to be painted consecutively, but every one of n houses should be painted some color. The one-colored houses should not stand consecutively, any way of painting is acceptable.There are no more than 5 hours left before the start of painting, help the government find the way when the sum of house numbers for every color is a prime number and the number of used colors is minimal. ", "input_spec": "The single input line contains an integer n (2\u2009\u2264\u2009n\u2009\u2264\u20096000) \u2014 the number of houses on the main streets of the capital.", "output_spec": "Print the sequence of n numbers, where the i-th number stands for the number of color for house number i. Number the colors consecutively starting from 1. Any painting order is allowed. If there are several solutions to that problem, print any of them. If there's no such way of painting print the single number -1.", "sample_inputs": ["8"], "sample_outputs": ["1 2 2 1 1 1 1 2"], "notes": null}, "src_uid": "94ef0d901f21e1945849fd5bfc2d1449"}
{"nl": {"description": "Bishwock is a chess figure that consists of three squares resembling an \"L-bar\". This figure can be rotated by 90, 180 and 270 degrees so it can have four possible states: XX   XX   .X   X.X.   .X   XX   XX Bishwocks don't attack any squares and can even occupy on the adjacent squares as long as they don't occupy the same square. Vasya has a board with $$$2\\times n$$$ squares onto which he wants to put some bishwocks. To his dismay, several squares on this board are already occupied by pawns and Vasya can't put bishwocks there. However, pawns also don't attack bishwocks and they can occupy adjacent squares peacefully.Knowing the positions of pawns on the board, help Vasya to determine the maximum amount of bishwocks he can put onto the board so that they wouldn't occupy the same squares and wouldn't occupy squares with pawns.", "input_spec": "The input contains two nonempty strings that describe Vasya's board. Those strings contain only symbols \"0\" (zero) that denote the empty squares and symbols \"X\" (uppercase English letter) that denote the squares occupied by pawns. Strings are nonempty and are of the same length that does not exceed $$$100$$$.", "output_spec": "Output a single integer\u00a0\u2014 the maximum amount of bishwocks that can be placed onto the given board.", "sample_inputs": ["00\n00", "00X00X0XXX0\n0XXX0X00X00", "0X0X0\n0X0X0", "0XXX0\n00000"], "sample_outputs": ["1", "4", "0", "2"], "notes": null}, "src_uid": "e6b3e787919e96fc893a034eae233fc6"}
{"nl": {"description": "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": "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": "Little Joty has got a task to do. She has a line of n tiles indexed from 1 to n. She has to paint them in a strange pattern.An unpainted tile should be painted Red if it's index is divisible by a and an unpainted tile should be painted Blue if it's index is divisible by b. So the tile with the number divisible by a and b can be either painted Red or Blue.After her painting is done, she will get p chocolates for each tile that is painted Red and q chocolates for each tile that is painted Blue.Note that she can paint tiles in any order she wants.Given the required information, find the maximum\u00a0number of chocolates Joty can get.", "input_spec": "The only line contains five integers n, a, b, p and q (1\u2009\u2264\u2009n,\u2009a,\u2009b,\u2009p,\u2009q\u2009\u2264\u2009109).", "output_spec": "Print the only integer s \u2014 the maximum number of chocolates Joty can get. Note that the answer can be too large, so you should use 64-bit integer type to store it. In C++ you can use the long long integer type and in Java you can use long integer type.", "sample_inputs": ["5 2 3 12 15", "20 2 3 3 5"], "sample_outputs": ["39", "51"], "notes": null}, "src_uid": "35d8a9f0d5b5ab22929ec050b55ec769"}
{"nl": {"description": "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": "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": "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": "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": "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": "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": "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": "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": "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": "Mr. Santa asks all the great programmers of the world to solve a trivial problem. He gives them an integer m and asks for the number of positive integers n, such that the factorial of n ends with exactly m zeroes. Are you among those great programmers who can solve this problem?", "input_spec": "The only line of input contains an integer m (1\u2009\u2264\u2009m\u2009\u2264\u2009100\u2009000)\u00a0\u2014 the required number of trailing zeroes in factorial.", "output_spec": "First print k\u00a0\u2014 the number of values of n such that the factorial of n ends with m zeroes. Then print these k integers in increasing order.", "sample_inputs": ["1", "5"], "sample_outputs": ["5\n5 6 7 8 9", "0"], "notes": "NoteThe factorial of n is equal to the product of all integers from 1 to n inclusive, that is n!\u2009=\u20091\u00b72\u00b73\u00b7...\u00b7n.In the first sample, 5!\u2009=\u2009120, 6!\u2009=\u2009720, 7!\u2009=\u20095040, 8!\u2009=\u200940320 and 9!\u2009=\u2009362880."}, "src_uid": "c27ecc6e4755b21f95a6b1b657ef0744"}
{"nl": {"description": "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": "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": "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": "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": "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": "Arpa is taking a geometry exam. Here is the last problem of the exam.You are given three points a,\u2009b,\u2009c.Find a point and an angle such that if we rotate the page around the point by the angle, the new position of a is the same as the old position of b, and the new position of b is the same as the old position of c.Arpa is doubting if the problem has a solution or not (i.e. if there exists a point and an angle satisfying the condition). Help Arpa determine if the question has a solution or not.", "input_spec": "The only line contains six integers ax,\u2009ay,\u2009bx,\u2009by,\u2009cx,\u2009cy (|ax|,\u2009|ay|,\u2009|bx|,\u2009|by|,\u2009|cx|,\u2009|cy|\u2009\u2264\u2009109). It's guaranteed that the points are distinct.", "output_spec": "Print \"Yes\" if the problem has a solution, \"No\" otherwise. You can print each letter in any case (upper or lower).", "sample_inputs": ["0 1 1 1 1 0", "1 1 0 0 1000 1000"], "sample_outputs": ["Yes", "No"], "notes": "NoteIn the first sample test, rotate the page around (0.5,\u20090.5) by .In the second sample test, you can't find any solution."}, "src_uid": "05ec6ec3e9ffcc0e856dc0d461e6eeab"}
{"nl": {"description": "Nastya received a gift on New Year\u00a0\u2014 a magic wardrobe. It is magic because in the end of each month the number of dresses in it doubles (i.e. the number of dresses becomes twice as large as it is in the beginning of the month).Unfortunately, right after the doubling the wardrobe eats one of the dresses (if any) with the 50% probability. It happens every month except the last one in the year. Nastya owns x dresses now, so she became interested in the expected number of dresses she will have in one year. Nastya lives in Byteland, so the year lasts for k\u2009+\u20091 months.Nastya is really busy, so she wants you to solve this problem. You are the programmer, after all. Also, you should find the answer modulo 109\u2009+\u20097, because it is easy to see that it is always integer.", "input_spec": "The only line contains two integers x and k (0\u2009\u2264\u2009x,\u2009k\u2009\u2264\u20091018), where x is the initial number of dresses and k\u2009+\u20091 is the number of months in a year in Byteland.", "output_spec": "In the only line print a single integer\u00a0\u2014 the expected number of dresses Nastya will own one year later modulo 109\u2009+\u20097.", "sample_inputs": ["2 0", "2 1", "3 2"], "sample_outputs": ["4", "7", "21"], "notes": "NoteIn the first example a year consists on only one month, so the wardrobe does not eat dresses at all.In the second example after the first month there are 3 dresses with 50% probability and 4 dresses with 50% probability. Thus, in the end of the year there are 6 dresses with 50% probability and 8 dresses with 50% probability. This way the answer for this test is (6\u2009+\u20098)\u2009/\u20092\u2009=\u20097."}, "src_uid": "e0e017e8c8872fc1957242ace739464d"}
{"nl": {"description": "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": "Amr is a young coder who likes music a lot. He always wanted to learn how to play music but he was busy coding so he got an idea.Amr has n instruments, it takes ai days to learn i-th instrument. Being busy, Amr dedicated k days to learn how to play the maximum possible number of instruments.Amr asked for your help to distribute his free days between instruments so that he can achieve his goal.", "input_spec": "The first line contains two numbers n, k (1\u2009\u2264\u2009n\u2009\u2264\u2009100, 0\u2009\u2264\u2009k\u2009\u2264\u200910\u2009000), the number of instruments and number of days respectively. The second line contains n integers ai (1\u2009\u2264\u2009ai\u2009\u2264\u2009100), representing number of days required to learn the i-th instrument.", "output_spec": "In the first line output one integer m representing the maximum number of instruments Amr can learn. In the second line output m space-separated integers: the indices of instruments to be learnt. You may output indices in any order. if there are multiple optimal solutions output any. It is not necessary to use all days for studying.", "sample_inputs": ["4 10\n4 3 1 2", "5 6\n4 3 1 1 2", "1 3\n4"], "sample_outputs": ["4\n1 2 3 4", "3\n1 3 4", "0"], "notes": "NoteIn the first test Amr can learn all 4 instruments.In the second test other possible solutions are: {2,\u20093,\u20095} or {3,\u20094,\u20095}.In the third test Amr doesn't have enough time to learn the only presented instrument."}, "src_uid": "dbb164a8dd190e63cceba95a31690a7c"}
{"nl": {"description": "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": "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": "You are given a bracket sequence $$$s$$$ (not necessarily a regular one). A bracket sequence is a string containing only characters '(' and ')'.A regular bracket sequence is a bracket sequence that can be transformed into a correct arithmetic expression by inserting characters '1' and '+' between the original characters of the sequence. For example, bracket sequences \"()()\" and \"(())\" are regular (the resulting expressions are: \"(1)+(1)\" and \"((1+1)+1)\"), and \")(\", \"(\" and \")\" are not.Your problem is to calculate the number of regular bracket sequences of length $$$2n$$$ containing the given bracket sequence $$$s$$$ as a substring (consecutive sequence of characters) modulo $$$10^9+7$$$ ($$$1000000007$$$).", "input_spec": "The first line of the input contains one integer $$$n$$$ ($$$1 \\le n \\le 100$$$) \u2014 the half-length of the resulting regular bracket sequences (the resulting sequences must have length equal to $$$2n$$$). The second line of the input contains one string $$$s$$$ ($$$1 \\le |s| \\le 200$$$) \u2014 the string $$$s$$$ that should be a substring in each of the resulting regular bracket sequences ($$$|s|$$$ is the length of $$$s$$$).", "output_spec": "Print only one integer \u2014 the number of regular bracket sequences containing the given bracket sequence $$$s$$$ as a substring. Since this number can be huge, print it modulo $$$10^9+7$$$ ($$$1000000007$$$).", "sample_inputs": ["5\n()))()", "3\n(()", "2\n((("], "sample_outputs": ["5", "4", "0"], "notes": "NoteAll regular bracket sequences satisfying the conditions above for the first example:   \"(((()))())\";  \"((()()))()\";  \"((()))()()\";  \"(()(()))()\";  \"()((()))()\". All regular bracket sequences satisfying the conditions above for the second example:   \"((()))\";  \"(()())\";  \"(())()\";  \"()(())\". And there is no regular bracket sequences of length $$$4$$$ containing \"(((\" as a substring in the third example."}, "src_uid": "590a49a7af0eb83376ed911ed488d7e5"}
{"nl": {"description": "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": "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": "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": "Petya and Vasya decided to play a little. They found n red cubes and m blue cubes. The game goes like that: the players take turns to choose a cube of some color (red or blue) and put it in a line from left to right (overall the line will have n\u2009+\u2009m cubes). Petya moves first. Petya's task is to get as many pairs of neighbouring cubes of the same color as possible. Vasya's task is to get as many pairs of neighbouring cubes of different colors as possible. The number of Petya's points in the game is the number of pairs of neighboring cubes of the same color in the line, the number of Vasya's points in the game is the number of neighbouring cubes of the different color in the line. Your task is to calculate the score at the end of the game (Petya's and Vasya's points, correspondingly), if both boys are playing optimally well. To \"play optimally well\" first of all means to maximize the number of one's points, and second \u2014 to minimize the number of the opponent's points.", "input_spec": "The only line contains two space-separated integers n and m (1\u2009\u2264\u2009n,\u2009m\u2009\u2264\u2009105) \u2014 the number of red and blue cubes, correspondingly.", "output_spec": "On a single line print two space-separated integers \u2014 the number of Petya's and Vasya's points correspondingly provided that both players play optimally well.", "sample_inputs": ["3 1", "2 4"], "sample_outputs": ["2 1", "3 2"], "notes": "NoteIn the first test sample the optimal strategy for Petya is to put the blue cube in the line. After that there will be only red cubes left, so by the end of the game the line of cubes from left to right will look as [blue, red, red, red]. So, Petya gets 2 points and Vasya gets 1 point. If Petya would choose the red cube during his first move, then, provided that both boys play optimally well, Petya would get 1 point and Vasya would get 2 points."}, "src_uid": "c8378e6fcaab30d15469a55419f38b39"}
{"nl": {"description": "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": "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": "Vladimir wants to modernize partitions in his office. To make the office more comfortable he decided to remove a partition and plant several bamboos in a row. He thinks it would be nice if there are n bamboos in a row, and the i-th from the left is ai meters high. Vladimir has just planted n bamboos in a row, each of which has height 0 meters right now, but they grow 1 meter each day. In order to make the partition nice Vladimir can cut each bamboo once at any height (no greater that the height of the bamboo), and then the bamboo will stop growing.Vladimir wants to check the bamboos each d days (i.e. d days after he planted, then after 2d days and so on), and cut the bamboos that reached the required height. Vladimir wants the total length of bamboo parts he will cut off to be no greater than k meters.What is the maximum value d he can choose so that he can achieve what he wants without cutting off more than k meters of bamboo?", "input_spec": "The first line contains two integers n and k (1\u2009\u2264\u2009n\u2009\u2264\u2009100, 1\u2009\u2264\u2009k\u2009\u2264\u20091011)\u00a0\u2014 the number of bamboos and the maximum total length of cut parts, in meters. The second line contains n integers a1,\u2009a2,\u2009...,\u2009an (1\u2009\u2264\u2009ai\u2009\u2264\u2009109)\u00a0\u2014 the required heights of bamboos, in meters.", "output_spec": "Print a single integer\u00a0\u2014 the maximum value of d such that Vladimir can reach his goal.", "sample_inputs": ["3 4\n1 3 5", "3 40\n10 30 50"], "sample_outputs": ["3", "32"], "notes": "NoteIn the first example Vladimir can check bamboos each 3 days. Then he will cut the first and the second bamboos after 3 days, and the third bamboo after 6 days. The total length of cut parts is 2\u2009+\u20090\u2009+\u20091\u2009=\u20093 meters."}, "src_uid": "2e1ab01d4d4440f33c840c4564a20a60"}
{"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": "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": "Little Johnny Bubbles enjoys spending hours in front of his computer playing video games. His favorite game is Bubble Strike, fast-paced bubble shooting online game for two players.Each game is set in one of the N maps, each having different terrain configuration. First phase of each game decides on which map the game will be played. The game system randomly selects three maps and shows them to the players. Each player must pick one of those three maps to be discarded. The game system then randomly selects one of the maps that were not picked by any of the players and starts the game.Johnny is deeply enthusiastic about the game and wants to spend some time studying maps, thus increasing chances to win games played on those maps. However, he also needs to do his homework, so he does not have time to study all the maps. That is why he asked himself the following question: \"What is the minimum number of maps I have to study, so that the probability to play one of those maps is at least $$$P$$$\"?Can you help Johnny find the answer for this question? You can assume Johnny's opponents do not know him, and they will randomly pick maps.", "input_spec": "The first line contains two integers $$$N$$$ ($$$3$$$ $$$\\leq$$$ $$$N$$$ $$$\\leq$$$ $$$10^{3}$$$) and $$$P$$$ ($$$0$$$ $$$\\leq$$$ $$$P$$$ $$$\\leq$$$ $$$1$$$) \u2013 total number of maps in the game and probability to play map Johnny has studied. $$$P$$$ will have at most four digits after the decimal point.", "output_spec": "Output contains one integer number \u2013 minimum number of maps Johnny has to study.", "sample_inputs": ["7 1.0000"], "sample_outputs": ["6"], "notes": null}, "src_uid": "788ed59a964264bd0e755e155a37e14d"}
{"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": "Little C loves number \u00ab3\u00bb very much. He loves all things about it.Now he is playing a game on a chessboard of size $$$n \\times m$$$. The cell in the $$$x$$$-th row and in the $$$y$$$-th column is called $$$(x,y)$$$. Initially, The chessboard is empty. Each time, he places two chessmen on two different empty cells, the Manhattan distance between which is exactly $$$3$$$. The Manhattan distance between two cells $$$(x_i,y_i)$$$ and $$$(x_j,y_j)$$$ is defined as $$$|x_i-x_j|+|y_i-y_j|$$$.He want to place as many chessmen as possible on the chessboard. Please help him find the maximum number of chessmen he can place.", "input_spec": "A single line contains two integers $$$n$$$ and $$$m$$$ ($$$1 \\leq n,m \\leq 10^9$$$) \u2014 the number of rows and the number of columns of the chessboard.", "output_spec": "Print one integer \u2014 the maximum number of chessmen Little C can place.", "sample_inputs": ["2 2", "3 3"], "sample_outputs": ["0", "8"], "notes": "NoteIn the first example, the Manhattan distance between any two cells is smaller than $$$3$$$, so the answer is $$$0$$$.In the second example, a possible solution is $$$(1,1)(3,2)$$$, $$$(1,2)(3,3)$$$, $$$(2,1)(1,3)$$$, $$$(3,1)(2,3)$$$."}, "src_uid": "02ce135a4b276d1e9ba6a4ce37f2fe70"}
{"nl": {"description": "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": "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": "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": "You have a set of items, each having some integer weight not greater than $$$8$$$. You denote that a subset of items is good if total weight of items in the subset does not exceed $$$W$$$.You want to calculate the maximum possible weight of a good subset of items. Note that you have to consider the empty set and the original set when calculating the answer.", "input_spec": "The first line contains one integer $$$W$$$ ($$$0 \\le W \\le 10^{18}$$$) \u2014 the maximum total weight of a good subset. The second line denotes the set of items you have. It contains $$$8$$$ integers $$$cnt_1$$$, $$$cnt_2$$$, ..., $$$cnt_8$$$ ($$$0 \\le cnt_i \\le 10^{16}$$$), where $$$cnt_i$$$ is the number of items having weight $$$i$$$ in the set.", "output_spec": "Print one integer \u2014 the maximum possible weight of a good subset of items.", "sample_inputs": ["10\n1 2 3 4 5 6 7 8", "0\n0 0 0 0 0 0 0 0", "3\n0 4 1 0 0 9 8 3"], "sample_outputs": ["10", "0", "3"], "notes": null}, "src_uid": "8097e10157320524c0faed56f2bc4880"}
{"nl": {"description": "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": "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": "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": "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": "You are given a sequence a consisting of n integers. You may partition this sequence into two sequences b and c in such a way that every element belongs exactly to one of these sequences. Let B be the sum of elements belonging to b, and C be the sum of elements belonging to c (if some of these sequences is empty, then its sum is 0). What is the maximum possible value of B\u2009-\u2009C?", "input_spec": "The first line contains one integer n (1\u2009\u2264\u2009n\u2009\u2264\u2009100) \u2014 the number of elements in a. The second line contains n integers a1, a2, ..., an (\u2009-\u2009100\u2009\u2264\u2009ai\u2009\u2264\u2009100) \u2014 the elements of sequence a.", "output_spec": "Print the maximum possible value of B\u2009-\u2009C, where B is the sum of elements of sequence b, and C is the sum of elements of sequence c.", "sample_inputs": ["3\n1 -2 0", "6\n16 23 16 15 42 8"], "sample_outputs": ["3", "120"], "notes": "NoteIn the first example we may choose b\u2009=\u2009{1,\u20090}, c\u2009=\u2009{\u2009-\u20092}. Then B\u2009=\u20091, C\u2009=\u2009\u2009-\u20092, B\u2009-\u2009C\u2009=\u20093.In the second example we choose b\u2009=\u2009{16,\u200923,\u200916,\u200915,\u200942,\u20098}, c\u2009=\u2009{} (an empty sequence). Then B\u2009=\u2009120, C\u2009=\u20090, B\u2009-\u2009C\u2009=\u2009120."}, "src_uid": "4b5d14833f9b51bfd336cc0e661243a5"}
{"nl": {"description": "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": "Valera has got n domino pieces in a row. Each piece consists of two halves \u2014 the upper one and the lower one. Each of the halves contains a number from 1 to 6. Valera loves even integers very much, so he wants the sum of the numbers on the upper halves and the sum of the numbers on the lower halves to be even.To do that, Valera can rotate the dominoes by 180 degrees. After the rotation the upper and the lower halves swap places. This action takes one second. Help Valera find out the minimum time he must spend rotating dominoes to make his wish come true.", "input_spec": "The first line contains integer n (1\u2009\u2264\u2009n\u2009\u2264\u2009100), denoting the number of dominoes Valera has. Next n lines contain two space-separated integers xi,\u2009yi (1\u2009\u2264\u2009xi,\u2009yi\u2009\u2264\u20096). Number xi is initially written on the upper half of the i-th domino, yi is initially written on the lower half.", "output_spec": "Print a single number \u2014 the minimum required number of seconds. If Valera can't do the task in any time, print \u2009-\u20091.", "sample_inputs": ["2\n4 2\n6 4", "1\n2 3", "3\n1 4\n2 3\n4 4"], "sample_outputs": ["0", "-1", "1"], "notes": "NoteIn the first test case the sum of the numbers on the upper halves equals 10 and the sum of the numbers on the lower halves equals 6. Both numbers are even, so Valera doesn't required to do anything.In the second sample Valera has only one piece of domino. It is written 3 on the one of its halves, therefore one of the sums will always be odd.In the third case Valera can rotate the first piece, and after that the sum on the upper halves will be equal to 10, and the sum on the lower halves will be equal to 8."}, "src_uid": "f9bc04aed2b84c7dd288749ac264bb43"}
{"nl": {"description": "Today is Wednesday, the third day of the week. What's more interesting is that tomorrow is the last day of the year 2015.Limak is a little polar bear. He enjoyed this year a lot. Now, he is so eager to the coming year 2016.Limak wants to prove how responsible a bear he is. He is going to regularly save candies for the entire year 2016! He considers various saving plans. He can save one candy either on some fixed day of the week or on some fixed day of the month.Limak chose one particular plan. He isn't sure how many candies he will save in the 2016 with his plan. Please, calculate it and tell him.", "input_spec": "The only line of the input is in one of the following two formats:    \"x of week\" where x (1\u2009\u2264\u2009x\u2009\u2264\u20097) denotes the day of the week. The 1-st day is Monday and the 7-th one is Sunday.  \"x of month\" where x (1\u2009\u2264\u2009x\u2009\u2264\u200931) denotes the day of the month. ", "output_spec": "Print one integer\u00a0\u2014 the number of candies Limak will save in the year 2016.", "sample_inputs": ["4 of week", "30 of month"], "sample_outputs": ["52", "11"], "notes": "NotePolar bears use the Gregorian calendar. It is the most common calendar and you likely use it too. You can read about it on Wikipedia if you want to \u2013 https://en.wikipedia.org/wiki/Gregorian_calendar. The week starts with Monday.In the first sample Limak wants to save one candy on each Thursday (the 4-th day of the week). There are 52 Thursdays in the 2016. Thus, he will save 52 candies in total.In the second sample Limak wants to save one candy on the 30-th day of each month. There is the 30-th day in exactly 11 months in the 2016\u00a0\u2014 all months but February. It means that Limak will save 11 candies in total."}, "src_uid": "9b8543c1ae3666e6c163d268fdbeef6b"}
{"nl": {"description": "The Duck songFor simplicity, we'll assume that there are only three types of grapes: green grapes, purple grapes and black grapes.Andrew, Dmitry and Michal are all grapes' lovers, however their preferences of grapes are different. To make all of them happy, the following should happen: Andrew, Dmitry and Michal should eat at least $$$x$$$, $$$y$$$ and $$$z$$$ grapes, respectively. Andrew has an extreme affinity for green grapes, thus he will eat green grapes and green grapes only. On the other hand, Dmitry is not a fan of black grapes\u00a0\u2014 any types of grapes except black would do for him. In other words, Dmitry can eat green and purple grapes. Michal has a common taste\u00a0\u2014 he enjoys grapes in general and will be pleased with any types of grapes, as long as the quantity is sufficient.Knowing that his friends are so fond of grapes, Aki decided to host a grape party with them. He has prepared a box with $$$a$$$ green grapes, $$$b$$$ purple grapes and $$$c$$$ black grapes.However, Aki isn't sure if the box he prepared contains enough grapes to make everyone happy. Can you please find out whether it's possible to distribute grapes so that everyone is happy or Aki has to buy some more grapes?It is not required to distribute all the grapes, so it's possible that some of them will remain unused.", "input_spec": "The first line contains three integers $$$x$$$, $$$y$$$ and $$$z$$$ ($$$1 \\le x, y, z \\le 10^5$$$)\u00a0\u2014 the number of grapes Andrew, Dmitry and Michal want to eat. The second line contains three integers $$$a$$$, $$$b$$$, $$$c$$$ ($$$1 \\le a, b, c \\le 10^5$$$)\u00a0\u2014 the number of green, purple and black grapes in the box.", "output_spec": "If there is a grape distribution that allows everyone to be happy, print \"YES\", otherwise print \"NO\".", "sample_inputs": ["1 6 2\n4 3 3", "5 1 1\n4 3 2"], "sample_outputs": ["YES", "NO"], "notes": "NoteIn the first example, there is only one possible distribution:Andrew should take $$$1$$$ green grape, Dmitry should take $$$3$$$ remaining green grapes and $$$3$$$ purple grapes, and Michal will take $$$2$$$ out of $$$3$$$ available black grapes.In the second test, there is no possible distribution, since Andrew is not be able to eat enough green grapes. :("}, "src_uid": "d54201591f7284da5e9ce18984439f4e"}
{"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": "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": "Those days, many boys use beautiful girls' photos as avatars in forums. So it is pretty hard to tell the gender of a user at the first glance. Last year, our hero went to a forum and had a nice chat with a beauty (he thought so). After that they talked very often and eventually they became a couple in the network. But yesterday, he came to see \"her\" in the real world and found out \"she\" is actually a very strong man! Our hero is very sad and he is too tired to love again now. So he came up with a way to recognize users' genders by their user names.This is his method: if the number of distinct characters in one's user name is odd, then he is a male, otherwise she is a female. You are given the string that denotes the user name, please help our hero to determine the gender of this user by his method.", "input_spec": "The first line contains a non-empty string, that contains only lowercase English letters \u2014 the user name. This string contains at most 100 letters.", "output_spec": "If it is a female by our hero's method, print \"CHAT WITH HER!\" (without the quotes), otherwise, print \"IGNORE HIM!\" (without the quotes).", "sample_inputs": ["wjmzbmr", "xiaodao", "sevenkplus"], "sample_outputs": ["CHAT WITH HER!", "IGNORE HIM!", "CHAT WITH HER!"], "notes": "NoteFor the first example. There are 6 distinct characters in \"wjmzbmr\". These characters are: \"w\", \"j\", \"m\", \"z\", \"b\", \"r\". So wjmzbmr is a female and you should print \"CHAT WITH HER!\"."}, "src_uid": "a8c14667b94b40da087501fd4bdd7818"}
{"nl": {"description": "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": "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": "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": "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": "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": "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": "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": "A + B is often used as an example of the easiest problem possible to show some contest platform. However, some scientists have observed that sometimes this problem is not so easy to get accepted. Want to try?", "input_spec": "The input contains two integers a and b (0\u2009\u2264\u2009a,\u2009b\u2009\u2264\u2009103), separated by a single space.", "output_spec": "Output the sum of the given integers.", "sample_inputs": ["5 14", "381 492"], "sample_outputs": ["19", "873"], "notes": null}, "src_uid": "b6e3f9c9b124ec3ec20eb8fcea075add"}
{"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": "So nearly half of the winter is over and Maria is dreaming about summer. She's fed up with skates and sleds, she was dreaming about Hopscotch all night long. It's a very popular children's game. The game field, the court, looks as is shown in the figure (all blocks are square and are numbered from bottom to top, blocks in the same row are numbered from left to right). Let us describe the hopscotch with numbers that denote the number of squares in the row, staring from the lowest one: 1-1-2-1-2-1-2-(1-2)..., where then the period is repeated (1-2).  The coordinate system is defined as shown in the figure. Side of all the squares are equal and have length a.Maria is a very smart and clever girl, and she is concerned with quite serious issues: if she throws a stone into a point with coordinates (x,\u2009y), then will she hit some square? If the answer is positive, you are also required to determine the number of the square.It is believed that the stone has fallen into the square if it is located strictly inside it. In other words a stone that has fallen on the square border is not considered a to hit a square.", "input_spec": "The only input line contains three integers: a, x, y, where a (1\u2009\u2264\u2009a\u2009\u2264\u2009100) is the side of the square, x and y (\u2009-\u2009106\u2009\u2264\u2009x\u2009\u2264\u2009106,\u20090\u2009\u2264\u2009y\u2009\u2264\u2009106) are coordinates of the stone.", "output_spec": "Print the number of the square, inside which the stone fell. If the stone is on a border of some stone or outside the court, print \"-1\" without the quotes.", "sample_inputs": ["1 0 0", "3 1 1", "3 0 10", "3 0 7", "3 4 0"], "sample_outputs": ["-1", "1", "5", "-1", "-1"], "notes": null}, "src_uid": "cf48ff6ba3e77ba5d4afccb8f775fb02"}
{"nl": {"description": "A number is called quasibinary if its decimal representation contains only digits 0 or 1. For example, numbers 0, 1, 101, 110011\u00a0\u2014 are quasibinary and numbers 2, 12, 900 are not.You are given a positive integer n. Represent it as a sum of minimum number of quasibinary numbers.", "input_spec": "The first line contains a single integer n (1\u2009\u2264\u2009n\u2009\u2264\u2009106).", "output_spec": "In the first line print a single integer k\u00a0\u2014 the minimum number of numbers in the representation of number n as a sum of quasibinary numbers. In the second line print k numbers \u2014 the elements of the sum. All these numbers should be quasibinary according to the definition above, their sum should equal n. Do not have to print the leading zeroes in the numbers. The order of numbers doesn't matter. If there are multiple possible representations, you are allowed to print any of them.", "sample_inputs": ["9", "32"], "sample_outputs": ["9\n1 1 1 1 1 1 1 1 1", "3\n10 11 11"], "notes": null}, "src_uid": "033068c5e16d25f09039e29c88474275"}
{"nl": {"description": "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": "In Pavlopolis University where Noora studies it was decided to hold beauty contest \"Miss Pavlopolis University\". Let's describe the process of choosing the most beautiful girl in the university in more detail.The contest is held in several stages. Suppose that exactly n girls participate in the competition initially. All the participants are divided into equal groups, x participants in each group. Furthermore the number x is chosen arbitrarily, i. e. on every stage number x can be different. Within each group the jury of the contest compares beauty of the girls in the format \"each with each\". In this way, if group consists of x girls, then  comparisons occur. Then, from each group, the most beautiful participant is selected. Selected girls enter the next stage of the competition. Thus if n girls were divided into groups, x participants in each group, then exactly  participants will enter the next stage. The contest continues until there is exactly one girl left who will be \"Miss Pavlopolis University\"But for the jury this contest is a very tedious task. They would like to divide the girls into groups in each stage so that the total number of pairwise comparisons of the girls is as few as possible. Let f(n) be the minimal total number of comparisons that should be made to select the most beautiful participant, if we admit n girls to the first stage.The organizers of the competition are insane. They give Noora three integers t, l and r and ask the poor girl to calculate the value of the following expression: t0\u00b7f(l)\u2009+\u2009t1\u00b7f(l\u2009+\u20091)\u2009+\u2009...\u2009+\u2009tr\u2009-\u2009l\u00b7f(r). However, since the value of this expression can be quite large the organizers ask her to calculate it modulo 109\u2009+\u20097. If Noora can calculate the value of this expression the organizers promise her to help during the beauty contest. But the poor girl is not strong in mathematics, so she turned for help to Leha and he turned to you.", "input_spec": "The first and single line contains three integers t, l and r (1\u2009\u2264\u2009t\u2009<\u2009109\u2009+\u20097,\u20092\u2009\u2264\u2009l\u2009\u2264\u2009r\u2009\u2264\u20095\u00b7106).", "output_spec": "In the first line print single integer \u2014 the value of the expression modulo 109\u2009+\u20097.", "sample_inputs": ["2 2 4"], "sample_outputs": ["19"], "notes": "NoteConsider the sample.It is necessary to find the value of .f(2)\u2009=\u20091. From two girls you can form only one group of two people, in which there will be one comparison.f(3)\u2009=\u20093. From three girls you can form only one group of three people, in which there will be three comparisons.f(4)\u2009=\u20093. From four girls you can form two groups of two girls each. Then at the first stage there will be two comparisons, one in each of the two groups. In the second stage there will be two girls and there will be one comparison between them. Total 2\u2009+\u20091\u2009=\u20093 comparisons. You can also leave all girls in same group in the first stage. Then  comparisons will occur. Obviously, it's better to split girls into groups in the first way.Then the value of the expression is ."}, "src_uid": "c9d45dac4a22f8f452d98d05eca2e79b"}
{"nl": {"description": "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": "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": "There are $$$n$$$ cities in the kingdom $$$X$$$, numbered from $$$1$$$ through $$$n$$$. People travel between cities by some one-way roads. As a passenger, JATC finds it weird that from any city $$$u$$$, he can't start a trip in it and then return back to it using the roads of the kingdom. That is, the kingdom can be viewed as an acyclic graph.Being annoyed by the traveling system, JATC decides to meet the king and ask him to do something. In response, the king says that he will upgrade some cities to make it easier to travel. Because of the budget, the king will only upgrade those cities that are important or semi-important. A city $$$u$$$ is called important if for every city $$$v \\neq u$$$, there is either a path from $$$u$$$ to $$$v$$$ or a path from $$$v$$$ to $$$u$$$. A city $$$u$$$ is called semi-important if it is not important and we can destroy exactly one city $$$v \\neq u$$$ so that $$$u$$$ becomes important.The king will start to act as soon as he finds out all those cities. Please help him to speed up the process.", "input_spec": "The first line of the input contains two integers $$$n$$$ and $$$m$$$ ($$$2 \\le n \\le 300\\,000$$$, $$$1 \\le m \\le 300\\,000$$$)\u00a0\u2014 the number of cities and the number of one-way roads. Next $$$m$$$ lines describe the road system of the kingdom. Each of them contains two integers $$$u_i$$$ and $$$v_i$$$ ($$$1 \\le u_i, v_i \\le n$$$, $$$u_i \\neq v_i$$$), denoting one-way road from $$$u_i$$$ to $$$v_i$$$. It is guaranteed, that the kingdoms' roads make an acyclic graph, which doesn't contain multiple edges and self-loops.", "output_spec": "Print a single integer\u00a0\u2014 the number of cities that the king has to upgrade.", "sample_inputs": ["7 7\n1 2\n2 3\n3 4\n4 7\n2 5\n5 4\n6 4", "6 7\n1 2\n2 3\n3 4\n1 5\n5 3\n2 6\n6 4"], "sample_outputs": ["4", "4"], "notes": "NoteIn the first example:      Starting at the city $$$1$$$ we can reach all the other cities, except for the city $$$6$$$. Also, from the city $$$6$$$ we cannot reach the city $$$1$$$. Therefore, if we destroy the city $$$6$$$ then the city $$$1$$$ will become important. So $$$1$$$ is a semi-important city.  For city $$$2$$$, the set of cities that cannot reach $$$2$$$ and cannot be reached by $$$2$$$ is $$$\\{6\\}$$$. Therefore, destroying city $$$6$$$ will make the city $$$2$$$ important. So city $$$2$$$ is also semi-important.  For city $$$3$$$, the set is $$$\\{5, 6\\}$$$. As you can see, destroying either city $$$5$$$ or $$$6$$$ will not make the city $$$3$$$ important. Therefore, it is neither important nor semi-important.  For city $$$4$$$, the set is empty. So $$$4$$$ is an important city.  The set for city $$$5$$$ is $$$\\{3, 6\\}$$$ and the set for city $$$6$$$ is $$$\\{3, 5\\}$$$. Similarly to city $$$3$$$, both of them are not important nor semi-important.  The city $$$7$$$ is important since we can reach it from all other cities.  So we have two important cities ($$$4$$$ and $$$7$$$) and two semi-important cities ($$$1$$$ and $$$2$$$).In the second example, the important cities are $$$1$$$ and $$$4$$$. The semi-important cities are $$$2$$$ and $$$3$$$."}, "src_uid": "be26e93ca7aef1235e96e10467a6417e"}
{"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": "Manao has a monitor. The screen of the monitor has horizontal to vertical length ratio a:b. Now he is going to watch a movie. The movie's frame has horizontal to vertical length ratio c:d. Manao adjusts the view in such a way that the movie preserves the original frame ratio, but also occupies as much space on the screen as possible and fits within it completely. Thus, he may have to zoom the movie in or out, but Manao will always change the frame proportionally in both dimensions.Calculate the ratio of empty screen (the part of the screen not occupied by the movie) to the total screen size. Print the answer as an irreducible fraction p\u2009/\u2009q.", "input_spec": "A single line contains four space-separated integers a, b, c, d (1\u2009\u2264\u2009a,\u2009b,\u2009c,\u2009d\u2009\u2264\u20091000).", "output_spec": "Print the answer to the problem as \"p/q\", where p is a non-negative integer, q is a positive integer and numbers p and q don't have a common divisor larger than 1.", "sample_inputs": ["1 1 3 2", "4 3 2 2"], "sample_outputs": ["1/3", "1/4"], "notes": "NoteSample 1. Manao's monitor has a square screen. The movie has 3:2 horizontal to vertical length ratio. Obviously, the movie occupies most of the screen if the width of the picture coincides with the width of the screen. In this case, only 2/3 of the monitor will project the movie in the horizontal dimension: Sample 2. This time the monitor's width is 4/3 times larger than its height and the movie's frame is square. In this case, the picture must take up the whole monitor in the vertical dimension and only 3/4 in the horizontal dimension: "}, "src_uid": "b0f435fc2f7334aee0d07524bc37cb1e"}
{"nl": {"description": "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": "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": "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": "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": "While swimming at the beach, Mike has accidentally dropped his cellphone into the water. There was no worry as he bought a cheap replacement phone with an old-fashioned keyboard. The keyboard has only ten digital equal-sized keys, located in the following way:  Together with his old phone, he lost all his contacts and now he can only remember the way his fingers moved when he put some number in. One can formally consider finger movements as a sequence of vectors connecting centers of keys pressed consecutively to put in a number. For example, the finger movements for number \"586\" are the same as finger movements for number \"253\":    Mike has already put in a number by his \"finger memory\" and started calling it, so he is now worrying, can he be sure that he is calling the correct number? In other words, is there any other number, that has the same finger movements?", "input_spec": "The first line of the input contains the only integer n (1\u2009\u2264\u2009n\u2009\u2264\u20099)\u00a0\u2014 the number of digits in the phone number that Mike put in. The second line contains the string consisting of n digits (characters from '0' to '9') representing the number that Mike put in.", "output_spec": "If there is no other phone number with the same finger movements and Mike can be sure he is calling the correct number, print \"YES\" (without quotes) in the only line. Otherwise print \"NO\" (without quotes) in the first line.", "sample_inputs": ["3\n586", "2\n09", "9\n123456789", "3\n911"], "sample_outputs": ["NO", "NO", "YES", "YES"], "notes": "NoteYou can find the picture clarifying the first sample case in the statement above."}, "src_uid": "d0f5174bb0bcca5a486db327b492bf33"}
{"nl": {"description": "Consider a linear function f(x)\u2009=\u2009Ax\u2009+\u2009B. Let's define g(0)(x)\u2009=\u2009x and g(n)(x)\u2009=\u2009f(g(n\u2009-\u20091)(x)) for n\u2009>\u20090. For the given integer values A, B, n and x find the value of g(n)(x) modulo 109\u2009+\u20097.", "input_spec": "The only line contains four integers A, B, n and x (1\u2009\u2264\u2009A,\u2009B,\u2009x\u2009\u2264\u2009109,\u20091\u2009\u2264\u2009n\u2009\u2264\u20091018) \u2014 the parameters from the problem statement. Note that the given value n can be too large, so you should use 64-bit integer type to store it. In C++ you can use the long long integer type and in Java you can use long integer type.", "output_spec": "Print the only integer s \u2014 the value g(n)(x) modulo 109\u2009+\u20097.", "sample_inputs": ["3 4 1 1", "3 4 2 1", "3 4 3 1"], "sample_outputs": ["7", "25", "79"], "notes": null}, "src_uid": "e22a1fc38c8b2a4cc30ce3b9f893028e"}
{"nl": {"description": "Little Lesha loves listening to music via his smartphone. But the smartphone doesn't have much memory, so Lesha listens to his favorite songs in a well-known social network InTalk.Unfortunately, internet is not that fast in the city of Ekaterinozavodsk and the song takes a lot of time to download. But Lesha is quite impatient. The song's duration is T seconds. Lesha downloads the first S seconds of the song and plays it. When the playback reaches the point that has not yet been downloaded, Lesha immediately plays the song from the start (the loaded part of the song stays in his phone, and the download is continued from the same place), and it happens until the song is downloaded completely and Lesha listens to it to the end. For q seconds of real time the Internet allows you to download q\u2009-\u20091 seconds of the track.Tell Lesha, for how many times he will start the song, including the very first start.", "input_spec": "The single line contains three integers T,\u2009S,\u2009q (2\u2009\u2264\u2009q\u2009\u2264\u2009104, 1\u2009\u2264\u2009S\u2009<\u2009T\u2009\u2264\u2009105).", "output_spec": "Print a single integer\u00a0\u2014 the number of times the song will be restarted.", "sample_inputs": ["5 2 2", "5 4 7", "6 2 3"], "sample_outputs": ["2", "1", "1"], "notes": "NoteIn the first test, the song is played twice faster than it is downloaded, which means that during four first seconds Lesha reaches the moment that has not been downloaded, and starts the song again. After another two seconds, the song is downloaded completely, and thus, Lesha starts the song twice.In the second test, the song is almost downloaded, and Lesha will start it only once.In the third sample test the download finishes and Lesha finishes listening at the same moment. Note that song isn't restarted in this case."}, "src_uid": "0d01bf286fb2c7950ce5d5fa59a17dd9"}
{"nl": {"description": "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": "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": "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 may know, MemSQL has American offices in both San Francisco and Seattle. Being a manager in the company, you travel a lot between the two cities, always by plane.You prefer flying from Seattle to San Francisco than in the other direction, because it's warmer in San Francisco. You are so busy that you don't remember the number of flights you have made in either direction. However, for each of the last n days you know whether you were in San Francisco office or in Seattle office. You always fly at nights, so you never were at both offices on the same day. Given this information, determine if you flew more times from Seattle to San Francisco during the last n days, or not.", "input_spec": "The first line of input contains single integer n (2\u2009\u2264\u2009n\u2009\u2264\u2009100)\u00a0\u2014 the number of days. The second line contains a string of length n consisting of only capital 'S' and 'F' letters. If the i-th letter is 'S', then you were in Seattle office on that day. Otherwise you were in San Francisco. The days are given in chronological order, i.e. today is the last day in this sequence.", "output_spec": "Print \"YES\" if you flew more times from Seattle to San Francisco, and \"NO\" otherwise. You can print each letter in any case (upper or lower).", "sample_inputs": ["4\nFSSF", "2\nSF", "10\nFFFFFFFFFF", "10\nSSFFSFFSFF"], "sample_outputs": ["NO", "YES", "NO", "YES"], "notes": "NoteIn the first example you were initially at San Francisco, then flew to Seattle, were there for two days and returned to San Francisco. You made one flight in each direction, so the answer is \"NO\".In the second example you just flew from Seattle to San Francisco, so the answer is \"YES\".In the third example you stayed the whole period in San Francisco, so the answer is \"NO\".In the fourth example if you replace 'S' with ones, and 'F' with zeros, you'll get the first few digits of \u03c0 in binary representation. Not very useful information though."}, "src_uid": "ab8a2070ea758d118b3c09ee165d9517"}
{"nl": {"description": "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": "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": "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": "It's New Year's Eve soon, so Ivan decided it's high time he started setting the table. Ivan has bought two cakes and cut them into pieces: the first cake has been cut into a pieces, and the second one \u2014 into b pieces.Ivan knows that there will be n people at the celebration (including himself), so Ivan has set n plates for the cakes. Now he is thinking about how to distribute the cakes between the plates. Ivan wants to do it in such a way that all following conditions are met:  Each piece of each cake is put on some plate;  Each plate contains at least one piece of cake;  No plate contains pieces of both cakes. To make his guests happy, Ivan wants to distribute the cakes in such a way that the minimum number of pieces on the plate is maximized. Formally, Ivan wants to know the maximum possible number x such that he can distribute the cakes according to the aforementioned conditions, and each plate will contain at least x pieces of cake.Help Ivan to calculate this number x!", "input_spec": "The first line contains three integers n, a and b (1\u2009\u2264\u2009a,\u2009b\u2009\u2264\u2009100, 2\u2009\u2264\u2009n\u2009\u2264\u2009a\u2009+\u2009b) \u2014 the number of plates, the number of pieces of the first cake, and the number of pieces of the second cake, respectively.", "output_spec": "Print the maximum possible number x such that Ivan can distribute the cake in such a way that each plate will contain at least x pieces of cake.", "sample_inputs": ["5 2 3", "4 7 10"], "sample_outputs": ["1", "3"], "notes": "NoteIn the first example there is only one way to distribute cakes to plates, all of them will have 1 cake on it.In the second example you can have two plates with 3 and 4 pieces of the first cake and two plates both with 5 pieces of the second cake. Minimal number of pieces is 3."}, "src_uid": "a254b1e3451c507cf7ce3e2496b3d69e"}
{"nl": {"description": "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": "In some game by Playrix it takes t minutes for an oven to bake k carrot cakes, all cakes are ready at the same moment t minutes after they started baking. Arkady needs at least n cakes to complete a task, but he currently don't have any. However, he has infinitely many ingredients and one oven. Moreover, Arkady can build one more similar oven to make the process faster, it would take d minutes to build the oven. While the new oven is being built, only old one can bake cakes, after the new oven is built, both ovens bake simultaneously. Arkady can't build more than one oven.Determine if it is reasonable to build the second oven, i.e. will it decrease the minimum time needed to get n cakes or not. If the time needed with the second oven is the same as with one oven, then it is unreasonable.", "input_spec": "The only line contains four integers n, t, k, d (1\u2009\u2264\u2009n,\u2009t,\u2009k,\u2009d\u2009\u2264\u20091\u2009000)\u00a0\u2014 the number of cakes needed, the time needed for one oven to bake k cakes, the number of cakes baked at the same time, the time needed to build the second oven. ", "output_spec": "If it is reasonable to build the second oven, print \"YES\". Otherwise print \"NO\".", "sample_inputs": ["8 6 4 5", "8 6 4 6", "10 3 11 4", "4 2 1 4"], "sample_outputs": ["YES", "NO", "NO", "YES"], "notes": "NoteIn the first example it is possible to get 8 cakes in 12 minutes using one oven. The second oven can be built in 5 minutes, so after 6 minutes the first oven bakes 4 cakes, the second oven bakes 4 more ovens after 11 minutes. Thus, it is reasonable to build the second oven. In the second example it doesn't matter whether we build the second oven or not, thus it takes 12 minutes to bake 8 cakes in both cases. Thus, it is unreasonable to build the second oven.In the third example the first oven bakes 11 cakes in 3 minutes, that is more than needed 10. It is unreasonable to build the second oven, because its building takes more time that baking the needed number of cakes using the only oven."}, "src_uid": "32c866d3d394e269724b4930df5e4407"}
{"nl": {"description": "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": "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": "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": "Find the minimum number with the given sum of digits $$$s$$$ such that all digits in it are distinct (i.e. all digits are unique).For example, if $$$s=20$$$, then the answer is $$$389$$$. This is the minimum number in which all digits are different and the sum of the digits is $$$20$$$ ($$$3+8+9=20$$$).For the given $$$s$$$ print the required number.", "input_spec": "The first line contains an integer $$$t$$$ ($$$1 \\le t \\le 45$$$) \u2014 the number of test cases. Each test case is specified by a line that contains the only integer $$$s$$$ ($$$1 \\le s \\le 45$$$).", "output_spec": "Print $$$t$$$ integers \u2014 the answers to the given test cases.", "sample_inputs": ["4\n\n20\n\n8\n\n45\n\n10"], "sample_outputs": ["389\n8\n123456789\n19"], "notes": null}, "src_uid": "fe126aaa93acaca8c8559bc9e7e27b9f"}
{"nl": {"description": "You have a plate and you want to add some gilding to it. The plate is a rectangle that we split into $$$w\\times h$$$ cells. There should be $$$k$$$ gilded rings, the first one should go along the edge of the plate, the second one\u00a0\u2014 $$$2$$$ cells away from the edge and so on. Each ring has a width of $$$1$$$ cell. Formally, the $$$i$$$-th of these rings should consist of all bordering cells on the inner rectangle of size $$$(w - 4(i - 1))\\times(h - 4(i - 1))$$$.  The picture corresponds to the third example. Your task is to compute the number of cells to be gilded.", "input_spec": "The only line contains three integers $$$w$$$, $$$h$$$ and $$$k$$$ ($$$3 \\le w, h \\le 100$$$, $$$1 \\le k \\le \\left\\lfloor \\frac{min(n, m) + 1}{4}\\right\\rfloor$$$, where $$$\\lfloor x \\rfloor$$$ denotes the number $$$x$$$ rounded down) \u2014 the number of rows, columns and the number of rings, respectively.", "output_spec": "Print a single positive integer\u00a0\u2014 the number of cells to be gilded.", "sample_inputs": ["3 3 1", "7 9 1", "7 9 2"], "sample_outputs": ["8", "28", "40"], "notes": "NoteThe first example is shown on the picture below.  The second example is shown on the picture below.  The third example is shown in the problem description."}, "src_uid": "2c98d59917337cb321d76f72a1b3c057"}
{"nl": {"description": "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": "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": "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": "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"}