Split (3)

train · 6.33k rows

contest_id int32 1 2.13k	index stringclasses 62 values	problem_id stringlengths 2 6	title stringlengths 0 67	rating int32 0 3.5k	tags stringlengths 0 139	statement stringlengths 0 6.96k	input_spec stringlengths 0 2.32k	output_spec stringlengths 0 1.52k	note stringlengths 0 5.06k	sample_tests stringlengths 0 1.02k	difficulty_category stringclasses 6 values	tag_count int8 0 11	statement_length int32 0 6.96k	input_spec_length int16 0 2.32k	output_spec_length int16 0 1.52k	contest_year int16 0 21
712	E	712E	E. Memory and Casinos	2,500	data structures; math; probabilities	There are n casinos lined in a row. If Memory plays at casino i, he has probability pi to win and move to the casino on the right (i + 1) or exit the row (if i = n), and a probability 1 - pi to lose and move to the casino on the left (i - 1) or also exit the row (if i = 1). We say that Memory dominates on the interval ...	The first line of the input contains two integers n and q(1 ≤ n, q ≤ 100 000), — number of casinos and number of requests respectively.The next n lines each contain integers ai and bi (1 ≤ ai < bi ≤ 109) — is the probability pi of winning in casino i.The next q lines each contain queries of one of the types specified a...	Print a real number for every request of type 2 — the probability that boy will ""dominate"" on that interval. Your answer will be considered correct if its absolute error does not exceed 10 - 4.Namely: let's assume that one of your answers is a, and the corresponding answer of the jury is b. The checker program will c...		Input: 3 131 31 22 32 1 12 1 22 1 32 2 22 2 32 3 31 2 2 32 1 12 1 22 1 32 2 22 2 32 3 3 \| Output: 0.33333333330.20000000000.16666666670.50000000000.40000000000.66666666670.33333333330.25000000000.22222222220.66666666670.57142857140.6666666667	Expert	3	1,031	552	368	7
1,830	D	1830D	D. Mex Tree	2,800	brute force; dp; trees	You are given a tree with $n$ nodes. For each node, you either color it in $0$ or $1$.The value of a path $(u,v)$ is equal to the MEX$^\dagger$ of the colors of the nodes from the shortest path between $u$ and $v$.The value of a coloring is equal to the sum of values of all paths $(u,v)$ such that \(1 \...	Each test contains multiple test cases. The first line of input contains a single integer $t$ ($1 \le t \le 10^4$) — the number of test cases. The description of test cases follows.The first line of each test case contains a single integer $n$ ($1 \le n \le 2 \cdot 10^5$) — the number of nodes in the tree.The f...	For each test case, print the maximum possible value of any coloring of the tree.	In the first sample, we will color vertex $2$ in $1$ and vertices $1,3$ in $0$. After this, we consider all paths: $(1,1)$ with value $1$ $(1,2)$ with value $2$ $(1,3)$ with value $2$ $(2,2)$ with value $0$ $(2,3)$ with value $2$ $(3,3)$ with value $1$ We notice the sum of values is \(8\...	Input: 431 22 341 21 31 4101 21 33 43 51 65 72 86 96 101 \| Output: 8 15 96 1	Master	3	835	651	81	18
1,278	C	1278C	C. Berry Jam	1,700	data structures; dp; greedy; implementation	Karlsson has recently discovered a huge stock of berry jam jars in the basement of the house. More specifically, there were $2n$ jars of strawberry and blueberry jam.All the $2n$ jars are arranged in a row. The stairs to the basement are exactly in the middle of that row. So when Karlsson enters the basement, he se...	The first line contains one integer $t$ ($1 \le t \le 1000$) — the number of test cases.The first line of each test case contains a single integer $n$ ($1 \le n \le 10^5$).The second line of each test case contains $2n$ integers $a_1, a_2, \dots, a_{2n}$ ($1 \le a_i \le 2$) — $a_i=1$ means that the \(i\...	For each test case print the answer to it — the minimum number of jars Karlsson is required to empty so that an equal number of full strawberry and blueberry jam jars is left.	The picture from the statement describes the first test case.In the second test case the number of strawberry and blueberry jam jars is already equal.In the third test case Karlsson is required to eat all $6$ jars so that there remain $0$ jars of both jams.In the fourth test case Karlsson can empty either the secon...	Input: 4 6 1 1 1 2 2 1 2 1 2 1 1 2 2 1 2 1 2 3 1 1 1 1 1 1 2 2 1 1 1 \| Output: 6 0 6 2	Medium	4	1,239	502	175	12
1,415	C	1415C	C. Bouncing Ball	1,400	brute force; dp; implementation	You're creating a game level for some mobile game. The level should contain some number of cells aligned in a row from left to right and numbered with consecutive integers starting from $1$, and in each cell you can either put a platform or leave it empty.In order to pass a level, a player must throw a ball from the ...	The first line contains the number of test cases $t$ ($1 \le t \le 100$). Description of test cases follows.The first line of each test case contains three integers $n$, $p$, and $k$ ($1 \le p \le n \le 10^5$, $1 \le k \le n$) — the number of cells you have, the first cell that should contain a platform, ...	For each test case output a single integer — the minimum number of seconds you need to modify the level accordingly.It can be shown that it is always possible to make the level passable.	In the first test case it's best to just remove the first cell, after that all required platforms are in their places: 0101010101. The stroked out digit is removed, the bold ones are where platforms should be located. The time required is $y = 2$.In the second test case it's best to add a platform to both cells $4$...	Input: 3 10 3 2 0101010101 2 2 5 4 1 00000 2 10 11 2 3 10110011000 4 3 \| Output: 2 4 10	Easy	3	1,436	751	186	14
178	F2	178F2	F2. Representative Sampling	2,200	dp; sortings; strings	The Smart Beaver from ABBYY has a long history of cooperating with the ""Institute of Cytology and Genetics"". Recently, the Institute staff challenged the Beaver with a new problem. The problem is as follows.There is a collection of n proteins (not necessarily distinct). Each protein is a string consisting of lowercas...	The first input line contains two integers n and k (1 ≤ k ≤ n), separated by a single space. The following n lines contain the descriptions of proteins, one per line. Each protein is a non-empty string of no more than 500 characters consisting of only lowercase Latin letters (a...z). Some of the strings may be equal.Th...	Print a single number denoting the largest possible value of representativity that a subcollection of size k of the given collection of proteins can have.		Input: 3 2ababzdabq \| Output: 2	Hard	3	1,476	501	154	1
1,174	A	1174A	A. Ehab Fails to Be Thanos	1,000	constructive algorithms; greedy; sortings	You're given an array $a$ of length $2n$. Is it possible to reorder it in such way so that the sum of the first $n$ elements isn't equal to the sum of the last $n$ elements?	The first line contains an integer $n$ ($1 \le n \le 1000$), where $2n$ is the number of elements in the array $a$.The second line contains $2n$ space-separated integers $a_1$, $a_2$, $\ldots$, $a_{2n}$ ($1 \le a_i \le 10^6$) — the elements of the array $a$.	If there's no solution, print ""-1"" (without quotes). Otherwise, print a single line containing $2n$ space-separated integers. They must form a reordering of $a$. You are allowed to not change the order.	In the first example, the first $n$ elements have sum $2+1+3=6$ while the last $n$ elements have sum $1+1+2=4$. The sums aren't equal.In the second example, there's no solution.	Input: 3 1 2 2 1 3 1 \| Output: 2 1 3 1 1 2	Beginner	3	181	280	208	11
1,430	C	1430C	C. Numbers on Whiteboard	1,000	constructive algorithms; data structures; greedy; implementation; math	Numbers $1, 2, 3, \dots n$ (each integer from $1$ to $n$ once) are written on a board. In one operation you can erase any two numbers $a$ and $b$ from the board and write one integer $\frac{a + b}{2}$ rounded up instead.You should perform the given operation $n - 1$ times and make the resulting number tha...	The first line contains one integer $t$ ($1 \le t \le 1000$) — the number of test cases.The only line of each test case contains one integer $n$ ($2 \le n \le 2 \cdot 10^5$) — the number of integers written on the board initially.It's guaranteed that the total sum of $n$ over test cases doesn't exceed \(2 \cd...	For each test case, in the first line, print the minimum possible number left on the board after $n - 1$ operations. Each of the next $n - 1$ lines should contain two integers — numbers $a$ and $b$ chosen and erased in each operation.		Input: 1 4 \| Output: 2 2 4 3 3 3 1	Beginner	5	854	330	242	14
2,120	B	2120B	B. Square Pool	1,000	geometry	Aryan and Harshith are playing pool in universe AX120 on a fixed square pool table of side $s$ with pockets at its $4$ corners. The corners are situated at $(0,0)$, $(0,s)$, $(s,0)$, and $(s,s)$. In this game variation, $n$ identical balls are placed on the table with integral coordinates such that no bal...	Each test contains multiple test cases. The first line contains the number of test cases $t$ ($1 \le t \le 1000$). The description of the test cases follows. The first line of each test case contains two integers $n$ and $s$ ($1 \le n \le 10^3$, $2 \le s\le 10^9$) — the number of balls placed on the table a...	For each test case, print a single integer — the number of balls potted in that game.	In the first test case, there is a single ball and it's shot directly towards the pocket at $(2, 2)$, thus potted.In the second test case, the state progresses as $\rightarrow$ $\rightarrow$ $\rightarrow$ $\rightarrow$	Input: 21 21 1 1 15 41 -1 1 11 -1 2 2-1 1 2 31 -1 1 3-1 1 3 1 \| Output: 1 3	Beginner	1	936	829	85	21
662	B	662B	B. Graph Coloring	2,200	dfs and similar; graphs	You are given an undirected graph that consists of n vertices and m edges. Initially, each edge is colored either red or blue. Each turn a player picks a single vertex and switches the color of all edges incident to it. That is, all red edges with an endpoint in this vertex change the color to blue, while all blue edge...	The first line of the input contains two integers n and m (1 ≤ n, m ≤ 100 000) — the number of vertices and edges, respectively.The following m lines provide the description of the edges, as the i-th of them contains two integers ui and vi (1 ≤ ui, vi ≤ n, ui ≠ vi) — the indices of the vertices connected by the i-th ed...	If there is no way to make the colors of all edges equal output - 1 in the only line of the output. Otherwise first output k — the minimum number of moves required to achieve the goal, then output k integers a1, a2, ..., ak, where ai is equal to the index of the vertex that should be used at the i-th move.If there are ...		Input: 3 31 2 B3 1 R3 2 B \| Output: 12	Hard	2	467	582	376	6
1,436	C	1436C	C. Binary Search	1,500	binary search; combinatorics	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 ...	The only line of input contains integers $n$, $x$ and $pos$ ($1 \le x \le n \le 1000$, $0 \le pos \le n - 1$) — the required length of the permutation, the number to search, and the required position of that number, respectively.	Print a single number — the remainder of the division of the number of valid permutations by $10^9+7$.	All possible permutations in the first test case: $(2, 3, 1, 4)$, $(2, 4, 1, 3)$, $(3, 2, 1, 4)$, $(3, 4, 1, 2)$, $(4, 2, 1, 3)$, $(4, 3, 1, 2)$.	Input: 4 1 2 \| Output: 6	Medium	2	1,239	239	104	14
300	B	300B	B. Coach	1,500	brute force; dfs and similar; graphs	A programming coach has n students to teach. We know that n is divisible by 3. Let's assume that all students are numbered from 1 to n, inclusive.Before the university programming championship the coach wants to split all students into groups of three. For some pairs of students we know that they want to be on the same...	The first line of the input contains integers n and m (3 ≤ n ≤ 48, . Then follow m lines, each contains a pair of integers ai, bi (1 ≤ ai < bi ≤ n) — the pair ai, bi means that students with numbers ai and bi want to be on the same team.It is guaranteed that n is divisible by 3. It is guaranteed that each pair ai, bi o...	If the required division into teams doesn't exist, print number -1. Otherwise, print lines. In each line print three integers xi, yi, zi (1 ≤ xi, yi, zi ≤ n) — the i-th team. If there are multiple answers, you are allowed to print any of them.		Input: 3 0 \| Output: 3 2 1	Medium	3	812	352	243	3
280	E	280E	E. Sequence Transformation	3,000	brute force; data structures; dp; implementation; math	You've got a non-decreasing sequence x1, x2, ..., xn (1 ≤ x1 ≤ x2 ≤ ... ≤ xn ≤ q). You've also got two integers a and b (a ≤ b; a·(n - 1) < q).Your task is to transform sequence x1, x2, ..., xn into some sequence y1, y2, ..., yn (1 ≤ yi ≤ q; a ≤ yi + 1 - yi ≤ b). The transformation price is the following sum: . Your ta...	The first line contains four integers n, q, a, b (2 ≤ n ≤ 6000; 1 ≤ q, a, b ≤ 109; a·(n - 1) < q; a ≤ b).The second line contains a non-decreasing integer sequence x1, x2, ..., xn (1 ≤ x1 ≤ x2 ≤ ... ≤ xn ≤ q).	In the first line print n real numbers — the sought sequence y1, y2, ..., yn (1 ≤ yi ≤ q; a ≤ yi + 1 - yi ≤ b). In the second line print the minimum transformation price, that is, .If there are multiple optimal answers you can print any of them.The answer will be considered correct if the absolute or relative error doe...		Input: 3 6 2 21 4 6 \| Output: 1.666667 3.666667 5.666667 0.666667	Master	5	402	209	339	2
1,934	A	1934A	A. Too Min Too Max	800	greedy; math	Given an array $a$ of $n$ elements, find the maximum value of the expression:$$$$\|a_i - a_j\| + \|a_j - a_k\| + \|a_k - a_l\| + \|a_l - a_i\|$$where $i$, $j$, $k$, and $l$ are four distinct indices of the array $a$, with $1 \le i, j, k, l \le n$.Here $\|x\|$ denotes the absolute value of $x$$$.	The first line contains one integer $t$ ($1 \le t \le 500$) — the number of test cases. The description of the test cases follows.The first line of each test case contains a single integer $n$ ($4 \le n \le 100$) — the length of the given array.The second line of each test case contains $n$ integers \(a_1, a_...	For each test case, print a single integer — the maximum value.	In the first test case, for any selection of $i$, $j$, $k$, $l$, the answer will be $0$. For example, $\|a_1 - a_2\| + \|a_2 - a_3\| + \|a_3 - a_4\| + \|a_4 - a_1\| = \|1 - 1\| + \|1 - 1\| + \|1 - 1\| + \|1 - 1\| = 0 + 0 + 0 + 0 = 0$.In the second test case, for $i = 1$, $j = 3$, $k = 2$, and $l = 5$, the answer wi...	Input: 541 1 1 151 1 2 2 385 1 3 2 -3 -1 10 343 3 1 141 2 2 -1 \| Output: 0 6 38 8 8	Beginner	2	308	366	63	19
886	A	886A	A. ACM ICPC	1,000	brute force	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 sco...	The single line contains six integers a1, ..., a6 (0 ≤ ai ≤ 1000) — scores of the participants	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"").	In the first sample, first team can be composed of 1st, 2nd and 6th participant, second — of 3rd, 4th and 5th: team scores are 1 + 3 + 1 = 2 + 1 + 2 = 5.In the second sample, score of participant number 6 is too high: his team score will be definitely greater.	Input: 1 3 2 1 2 1 \| Output: YES	Beginner	1	501	94	223	8
1,477	A	1477A	A. Nezzar and Board	1,800	constructive algorithms; math; number theory	$n$ distinct integers $x_1,x_2,\ldots,x_n$ are written on the board. Nezzar can perform the following operation multiple times. Select two integers $x,y$ (not necessarily distinct) on the board, and write down $2x-y$. Note that you don't remove selected numbers. Now, Nezzar wonders if it is possible to have his...	The first line contains a single integer $t$ ($1 \le t \le 10^5$) — the number of test cases. The first line of each test case contains two integers $n,k$ ($2 \le n \le 2 \cdot 10^5$, $-10^{18} \le k \le 10^{18}$).The second line of each test case contains $n$ distinct integers $x_1,x_2,\ldots,x_n$ (\(-10...	For each test case, print ""YES"" on a single line if it is possible to have $k$ on the board. Otherwise, print ""NO"".You can print each letter in any case (upper or lower).	In the first test case, the number $1$ is already on the board.In the second test case, Nezzar could perform the following operations to write down $k=0$ on the board: Select $x=3$ and $y=2$ and write down $4$ on the board. Select $x=4$ and $y=7$ and write down $1$ on the board. Select $x=1$ and \(y=2...	Input: 6 2 1 1 2 3 0 2 3 7 2 -1 31415926 27182818 2 1000000000000000000 1 1000000000000000000 2 -1000000000000000000 -1000000000000000000 123 6 80 -5 -20 13 -14 -2 -11 \| Output: YES YES NO YES YES NO	Medium	3	402	440	176	14
1,505	B	1505B	B. DMCA	1,600	*special; implementation; number theory	Many people are aware of DMCA – Digital Millennium Copyright Act. But another recently proposed DMCA – Digital Millennium Calculation Act – is much less known.In this problem you need to find a root of a number according to this new DMCA law.	The input contains a single integer $a$ ($1 \le a \le 1000000$).	Output the result – an integer number.		Input: 1 \| Output: 1	Medium	3	242	68	38	15
2,075	B	2075B	B. Array Recoloring	1,300	constructive algorithms; greedy	You are given an integer array $a$ of size $n$. Initially, all elements of the array are colored red.You have to choose exactly $k$ elements of the array and paint them blue. Then, while there is at least one red element, you have to select any red element with a blue neighbor and make it blue.The cost of paintin...	The first line contains a single integer $t$ ($1 \le t \le 10^3$) — the number of test cases.The first line of each test case contains two integers $n$ and $k$ ($2 \le n \le 5000$; $1 \le k < n$).The second line contains $n$ integers $a_1, a_2, \dots, a_n$ ($1 \le a_i \le 10^9$).Additional constraint ...	For each test case, print a single integer — the maximum possible cost of painting for the given array.	In the first example, you can initially color the $2$-nd element, and then color the elements in the order $1, 3$. Then the cost of painting is equal to $2+3=5$.In the second example, you can initially color the elements $1$ and $5$, and then color the elements in the order $2, 4, 3$. Then the cost of paint...	Input: 33 11 2 35 24 2 3 1 34 32 2 2 2 \| Output: 5 10 8	Easy	2	503	395	103	20
859	B	859B	B. Lazy Security Guard	1,000	brute force; geometry; math	Your security guard friend recently got a new job at a new security company. The company requires him to patrol an area of the city encompassing exactly N city blocks, but they let him choose which blocks. That is, your friend must walk the perimeter of a region whose area is exactly N blocks. Your friend is quite lazy...	Input will consist of a single integer N (1 ≤ N ≤ 106), the number of city blocks that must be enclosed by the route.	Print the minimum perimeter that can be achieved.	Here are some possible shapes for the examples:	Input: 4 \| Output: 8	Beginner	3	541	117	49	8
952	G	952G	G. Puzzling Language	2,200	special; special; *special; constructive algorithms	In this problem you will write a simple code generator for a 2D programming language derived from Brainfuck.The code in this language is a rectangular grid of characters '.' and 'X'. The code is converted to a Brainfuck program as follows: the characters are read in the usual order (top to bottom, left to right), and e...	The input consists of a single string of characters with ASCII codes between 33 ('!') and 122 ('z'), inclusive. The length of the string is between 1 and 10 characters, inclusive.	Output a program in the described language which, when executed, will print the given message.	The example corresponds to the following Brainfuck program: - >+< >+++< >+++++< >+++++++< >+++++++++< >+++++++++++<< >...The triangular block decrements the first memory cell and sets the value of the second memory cell to 36 - the ASCII code of '$' character. The next line after the triangular block moves the memory p...	Input: $$$ \| Output: .......X.............XXX...........XXXXX.........XXXXXXX.......XXXXXXXXX.....XXXXXXXXXXX...XXXXXXXXXXXXX................X.............XX..............X..............X..............	Hard	4	1,391	179	94	9
1,504	A	1504A	A. Déjà Vu	800	constructive algorithms; strings	A palindrome is a string that reads the same backward as forward. For example, the strings ""z"", ""aaa"", ""aba"", and ""abccba"" are palindromes, but ""codeforces"" and ""ab"" are not. You hate palindromes because they give you déjà vu.There is a string $s$. You must insert exactly one character 'a' somewhere in \(...	The first line contains a single integer $t$ ($1\le t\le 10^4$) — the number of test cases.The only line of each test case contains a string $s$ consisting of lowercase English letters.The total length of all strings does not exceed $3\cdot 10^5$.	For each test case, if there is no solution, output ""NO"".Otherwise, output ""YES"" followed by your constructed string of length $\|s\|+1$ on the next line. If there are multiple solutions, you may print any.You can print each letter of ""YES"" and ""NO"" in any case (upper or lower).	The first test case is described in the statement.In the second test case, we can make either ""aab"" or ""aba"". But ""aba"" is a palindrome, so ""aab"" is the only correct answer.In the third test case, ""zaza"" and ""zzaa"" are correct answers, but not ""azza"".In the fourth test case, ""baa"" is the only correct an...	Input: 6 cbabc ab zza ba a nutforajaroftuna \| Output: YES cbabac YES aab YES zaza YES baa NO YES nutforajarofatuna	Beginner	2	686	255	287	15
1,658	B	1658B	B. Marin and Anti-coprime Permutation	800	combinatorics; math; number theory	Marin wants you to count number of permutations that are beautiful. A beautiful permutation of length $n$ is a permutation that has the following property: $$$$ \gcd (1 \cdot p_1, \, 2 \cdot p_2, \, \dots, \, n \cdot p_n) > 1, $$ where $\gcd\( is the greatest common divisor.A permutation is an array consisting of...	The first line contains one integer $t$ ($1 \le t \le 10^3$) — the number of test cases.Each test case consists of one line containing one integer $n$ ($1 \le n \le 10^3$).	For each test case, print one integer — number of beautiful permutations. Because the answer can be very big, please print the answer modulo $998\,244\,353$.	In first test case, we only have one permutation which is $[1]$ but it is not beautiful because $\gcd(1 \cdot 1) = 1$.In second test case, we only have one beautiful permutation which is $[2, 1]$ because $\gcd(1 \cdot 2, 2 \cdot 1) = 2$.	Input: 71234561000 \| Output: 0 1 0 4 0 36 665702330	Beginner	3	590	180	159	16
1,002	B2	1002B2	B2. Distinguish GHZ state and W state	1,600	*special	You are given N qubits (2 ≤ N ≤ 8) which are guaranteed to be in one of the two states: state, or state. Your task is to perform necessary operations and measurements to figure out which state it was and to return 0 if it was GHZ state or 1 if it was W state. The state of the qubits after the operations does not matter...					Medium	1	624	0	0	10
282	E	282E	E. Sausage Maximization	2,200	bitmasks; data structures; trees	The Bitlandians are quite weird people. They have their own problems and their own solutions. They have their own thoughts and their own beliefs, they have their own values and their own merits. They have their own dishes and their own sausages!In Bitland a sausage is an array of integers! A sausage's deliciousness is ...	The first line contains an integer n (1 ≤ n ≤ 105).The next line contains n integers a1, a2, ..., an (0 ≤ ai ≤ 1012) — Mr. Bitkoch's sausage.Please, do not use the %lld specifier to read or write 64-bit integers in С++. It is preferred to use the cin, cout streams or the %I64d specifier.	Print a single integer — the maximum pleasure BitHaval and BitAryo can get from the dinner.		Input: 21 2 \| Output: 3	Hard	3	1,256	288	91	2
1,425	A	1425A	A. Arena of Greed	1,400	games; greedy	Lately, Mr. Chanek frequently plays the game Arena of Greed. As the name implies, the game's goal is to find the greediest of them all, who will then be crowned king of Compfestnesia.The game is played by two people taking turns, where Mr. Chanek takes the first turn. Initially, there is a treasure chest containing \(N...	The first line contains a single integer $T$ $(1 \le T \le 10^5)$ denotes the number of test cases.The next $T$ lines each contain a single integer $N$ $(1 \le N \le 10^{18})$.	$T$ lines, each line is the answer requested by Mr. Chanek.	For the first case, the game is as follows: Mr. Chanek takes one coin. The opponent takes two coins. Mr. Chanek takes one coin. The opponent takes one coin. For the second case, the game is as follows: Mr. Chanek takes three coins. The opponent takes one coin. Mr. Chanek takes one coin. The opponent takes one coin.	Input: 2 5 6 \| Output: 2 4	Easy	2	813	186	61	14
877	A	877A	A. Alex and broken contest	1,100	implementation; strings	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...	The only line contains string from lowercase and uppercase letters and ""_"" symbols of length, not more than 100 — the name of the problem.	Print ""YES"", if problem is from this contest, and ""NO"" otherwise.		Input: Alex_and_broken_contest \| Output: NO	Easy	2	555	140	69	8
367	A	367A	A. Sereja and Algorithm	1,500	data structures; implementation	Sereja loves all sorts of algorithms. He has recently come up with a new algorithm, which receives a string as an input. Let's represent the input string of the algorithm as q = q1q2... qk. The algorithm consists of two steps: Find any continuous subsequence (substring) of three characters of string q, which doesn't eq...	The first line contains non-empty string s, its length (n) doesn't exceed 105. It is guaranteed that string s only contains characters: 'x', 'y', 'z'.The second line contains integer m (1 ≤ m ≤ 105) — the number of tests. Next m lines contain the tests. The i-th line contains a pair of integers li, ri (1 ≤ li ≤ ri ≤ n)...	For each test, print ""YES"" (without the quotes) if the algorithm works correctly on the corresponding test and ""NO"" (without the quotes) otherwise.	In the first example, in test one and two the algorithm will always be terminated in one step. In the fourth test you can get string ""xzyx"" on which the algorithm will terminate. In all other tests the algorithm doesn't work correctly.	Input: zyxxxxxxyyz55 51 31 111 43 6 \| Output: YESYESNOYESNO	Medium	2	1,227	321	151	3
492	E	492E	E. Vanya and Field	2,000	math	Vanya decided to walk in the field of size n × n cells. The field contains m apple trees, the i-th apple tree is at the cell with coordinates (xi, yi). Vanya moves towards vector (dx, dy). That means that if Vanya is now at the cell (x, y), then in a second he will be at cell . The following condition is satisfied for ...	The first line contains integers n, m, dx, dy(1 ≤ n ≤ 106, 1 ≤ m ≤ 105, 1 ≤ dx, dy ≤ n) — the size of the field, the number of apple trees and the vector of Vanya's movement. Next m lines contain integers xi, yi (0 ≤ xi, yi ≤ n - 1) — the coordinates of apples. One cell may contain multiple apple trees.	Print two space-separated numbers — the coordinates of the cell from which you should start your path. If there are several answers you are allowed to print any of them.	In the first sample Vanya's path will look like: (1, 3) - (3, 1) - (0, 4) - (2, 2) - (4, 0) - (1, 3)In the second sample: (0, 0) - (1, 1) - (0, 0)	Input: 5 5 2 30 01 21 32 43 1 \| Output: 1 3	Hard	1	570	304	169	4
1,252	I	1252I	I. Mission Possible	3,000		Allen, a government secret service, has been assigned to infiltrate a mafia secret base to uncover crucial information regarding the mafia's operations.The secret base is a rectangular bounded by $(x_L,y_L)$, $(x_L,y_R)$, $(x_R,y_L)$, and $(x_R,y_R)$ in a Cartesian coordinate system where $x_L < x_R$ and \(y_...	Input begins with a line containing five integers: $N$ $x_L$ $y_L$ $x_R$ $y_R$ ($0 \le N \le 50$; $0 \le x_L < x_R \le 1000$; $0 \le y_L < y_R \le 1000$) representing the number of sensors and the secret base ($x_L$, $y_L$, $x_R$, $y_R$), respectively. The next line contains two integers: \(x_s\...	Output in a line an integer representing the size of a feasible $P$. The next $\|P\|$ lines each contains two real numbers (separated by a single space); the $j^{th}$ line contains $x_j$ $y_j$ representing the $j^{th}$ point in $P$. You may output any feasible $P$ with no more than $1000$ points.Due to ...	Explanation for the sample input/output #1The figure above shows the $P$ from the sample output. Note that there exists a feasible $P$ with only one point in this sample, although you are not required to find such $P$.	Input: 3 2 2 50 26 4 14 48 14 15 13 7 36 16 6 46 18 3 \| Output: 2 13.25 23.1234567 36.591003 7.1	Master	0	2,353	1,114	1,523	12
2,045	H	2045H	H. Missing Separators	2,200	dp; sortings; string suffix structures; strings	You have a dictionary, which is a list of distinct words sorted in alphabetical order. Each word consists of uppercase English letters.You want to print this dictionary. However, there is a bug with the printing system, and all words in the list are printed next to each other without any separators between words. Now, ...	A single line consisting of a string $S$ ($1 \leq \|S\| \leq 5000)$. String $S$ consists of only uppercase English letters.	First, output an integer in a single line representing the maximum number of the words in the reconstructed dictionary. Denote this number as $n$.Then, output $n$ lines, each containing a single string representing the word. The words must be distinct, and the list must be sorted alphabetically. The concatenation o...		Input: ABACUS \| Output: 4 A BA C US	Hard	4	795	127	465	20
2,041	A	2041A	A. The Bento Box Adventure	1,300	implementation; sortings	Image generated by ChatGPT 4o. Boxed meals in Taiwan are very common, offering convenient and affordable nutrition-balanced choices for students and office workers. These meals typically include a variety of vegetables, protein, and rice, providing a well-rounded diet. With numerous options available at local self-serv...	A single line of input containing four integers $a, b, c, d$, each between 1 and 5 (inclusive), representing the restaurant numbers you visited from Monday to Thursday, in order. $1\le a, b, c, d\le 5$ All four numbers will be different.	Output the restaurant number you should visit on Friday.		Input: 1 3 2 5 \| Output: 4	Easy	2	969	241	56	20
587	A	587A	A. Duff and Weight Lifting	1,500	greedy	Recently, Duff has been practicing weight lifting. As a hard practice, Malek gave her a task. He gave her a sequence of weights. Weight of i-th of them is 2wi pounds. In each step, Duff can lift some of the remaining weights and throw them away. She does this until there's no more weight left. Malek asked her to minimi...	The first line of input contains integer n (1 ≤ n ≤ 106), the number of weights.The second line contains n integers w1, ..., wn separated by spaces (0 ≤ wi ≤ 106 for each 1 ≤ i ≤ n), the powers of two forming the weights values.	Print the minimum number of steps in a single line.	In the first sample case: One optimal way would be to throw away the first three in the first step and the rest in the second step. Also, it's not possible to do it in one step because their sum is not a power of two.In the second sample case: The only optimal way is to throw away one weight in each step. It's not poss...	Input: 51 1 2 3 3 \| Output: 2	Medium	1	752	228	51	5
1,016	F	1016F	F. Road Projects	2,600	dfs and similar; dp; trees	There are $n$ cities in the country of Berland. Some of them are connected by bidirectional roads in such a way that there exists exactly one path, which visits each road no more than once, between every pair of cities. Each road has its own length. Cities are numbered from $1$ to $n$.The travelling time between ...	The first line contains two integers $n$ and $m$ ($3 \le n \le 3 \cdot 10^5$, $1 \le m \le 3 \cdot 10^5$) — the number of cities and the number of projects, respectively.Each of the next $n - 1$ lines contains three integers $v_i$, $u_i$ and $w_i$ ($1 \le v_i, u_i \le n$, $1 \le w_i \le 10^9$) — the...	Print $m$ lines, the $j$-th line should contain a single integer — the maximal possible travelling time between the most important cities for the $j$-th project.	The road network from the first example:You can build the road with length $1$ between cities $5$ and $6$ to get $83$ as the travelling time between $1$ and $7$ ($1 \rightarrow 2 \rightarrow 6 \rightarrow 5 \rightarrow 3 \rightarrow 4 \rightarrow 7$ $=$ $18 + 4 + 1 + 12 + 24 + 24 = 83$). Other possibl...	Input: 7 21 2 182 3 223 4 244 7 242 6 43 5 121100 \| Output: 8388	Expert	3	1,680	617	167	10
2,121	A	2121A	A. Letter Home	800	brute force; math	You are given an array of distinct integers $x_1, x_2, \ldots, x_n$ and an integer $s$. Initially, you are at position $pos = s$ on the $X$ axis. In one step, you can perform exactly one of the following two actions: Move from position $pos$ to position $pos + 1$. Move from position $pos$ to position \(po...	Each test consists of multiple test cases. The first line contains a single integer $t$ ($1 \leq t \leq 1000$) — the number of test cases. The description of the test cases follows.The first line of each test case contains two integers $n$ and $s$ ($1 \leq n \leq 10$, $1 \leq s \leq 100$) — the number of po...	For each test case, output the minimum number of steps in any successful sequence of steps.	In the first test case, no steps need to be taken, so the only visited position will be $1$. In the second test case, the following path can be taken: $2 \rightarrow 1$. The number of steps is $1$. In the third test case, the following path can be taken: $1 \rightarrow 2$. The number of steps is $1$.In the fi...	Input: 121 111 211 122 12 32 21 32 31 23 11 2 33 21 3 43 31 2 34 31 2 3 105 51 2 3 6 76 61 2 3 9 10 11 \| Output: 0 1 1 2 3 2 2 4 2 11 8 15	Beginner	2	636	557	91	21
1,036	E	1036E	E. Covered Points	2,400	fft; geometry; number theory	You are given $n$ segments on a Cartesian plane. Each segment's endpoints have integer coordinates. Segments can intersect with each other. No two segments lie on the same line.Count the number of distinct points with integer coordinates, which are covered by at least one segment.	The first line contains a single integer $n$ ($1 \le n \le 1000$) — the number of segments.Each of the next $n$ lines contains four integers $Ax_i, Ay_i, Bx_i, By_i$ ($-10^6 \le Ax_i, Ay_i, Bx_i, By_i \le 10^6$) — the coordinates of the endpoints $A$, $B$ ($A \ne B$) of the $i$-th segment.It is guaran...	Print a single integer — the number of distinct points with integer coordinates, which are covered by at least one segment.	The image for the first example: Several key points are marked blue, the answer contains some non-marked points as well.The image for the second example:	Input: 90 0 4 4-1 5 4 04 0 4 45 2 11 26 1 6 75 6 11 610 1 10 77 0 9 810 -1 11 -1 \| Output: 42	Expert	3	283	367	123	10
245	H	245H	H. Queries for Number of Palindromes	1,800	dp; hashing; strings	You've got a string s = s1s2... s\|s\| of length \|s\|, consisting of lowercase English letters. There also are q queries, each query is described by two integers li, ri (1 ≤ li ≤ ri ≤ \|s\|). The answer to the query is the number of substrings of string s[li... ri], which are palindromes.String s[l... r] = slsl + 1... sr (1...	The first line contains string s (1 ≤ \|s\| ≤ 5000). The second line contains a single integer q (1 ≤ q ≤ 106) — the number of queries. Next q lines contain the queries. The i-th of these lines contains two space-separated integers li, ri (1 ≤ li ≤ ri ≤ \|s\|) — the description of the i-th query.It is guaranteed that the g...	Print q integers — the answers to the queries. Print the answers in the order, in which the queries are given in the input. Separate the printed numbers by whitespaces.	Consider the fourth query in the first test case. String s[4... 6] = «aba». Its palindrome substrings are: «a», «b», «a», «aba».	Input: caaaba51 11 42 34 64 5 \| Output: 17342	Medium	3	526	375	168	2
1,682	B	1682B	B. AND Sorting	1,100	bitmasks; constructive algorithms; sortings	You are given a permutation $p$ of integers from $0$ to $n-1$ (each of them occurs exactly once). Initially, the permutation is not sorted (that is, $p_i>p_{i+1}$ for at least one $1 \le i \le n - 1$). The permutation is called $X$-sortable for some non-negative integer $X$ if it is possible to sort the p...	The input consists of multiple test cases. The first line contains a single integer $t$ $(1 \le t \le 10^4)$ — the number of test cases. Description of test cases follows.The first line of each test case contains a single integer $n$ $(2 \le n \le 2 \cdot 10^5)$ — the length of the permutation.The second line o...	For each test case output a single integer — the maximum value of $X$ such that $p$ is $X$-sortable.	In the first test case, the only $X$ for which the permutation is $X$-sortable are $X = 0$ and $X = 2$, maximum of which is $2$.Sorting using $X = 0$: Swap $p_1$ and $p_4$, $p = [2, 1, 3, 0]$. Swap $p_3$ and $p_4$, $p = [2, 1, 0, 3]$. Swap $p_1$ and $p_3$, $p = [0, 1, 2, 3]$. Sorting using...	Input: 440 1 3 221 070 1 2 3 5 6 450 3 2 1 4 \| Output: 2 0 4 1	Easy	3	719	588	106	16
194	A	194A	A. Exams	900	implementation; math	One day the Codeforces round author sat exams. He had n exams and he needed to get an integer from 2 to 5 for each exam. He will have to re-sit each failed exam, i.e. the exam that gets mark 2. The author would need to spend too much time and effort to make the sum of his marks strictly more than k. That could have spo...	The single input line contains space-separated integers n and k (1 ≤ n ≤ 50, 1 ≤ k ≤ 250) — the number of exams and the required sum of marks.It is guaranteed that there exists a way to pass n exams in the way that makes the sum of marks equal exactly k.	Print the single number — the minimum number of exams that the author will get a 2 for, considering that the sum of marks for all exams must equal k.	In the first sample the author has to get a 2 for all his exams.In the second sample he should get a 3 for two exams and a 2 for two more.In the third sample he should get a 3 for one exam.	Input: 4 8 \| Output: 4	Beginner	2	774	254	149	1
209	C	209C	C. Trails and Glades	2,400	constructive algorithms; dsu; graphs; greedy	Vasya went for a walk in the park. The park has n glades, numbered from 1 to n. There are m trails between the glades. The trails are numbered from 1 to m, where the i-th trail connects glades xi and yi. The numbers of the connected glades may be the same (xi = yi), which means that a trail connects a glade to itself. ...	The first line contains two integers n and m (1 ≤ n ≤ 106; 0 ≤ m ≤ 106) — the number of glades in the park and the number of trails in the park, respectively. Next m lines specify the trails. The i-th line specifies the i-th trail as two space-separated numbers, xi, yi (1 ≤ xi, yi ≤ n) — the numbers of the glades conne...	Print the single integer — the answer to the problem. If Vasya's walk is possible without adding extra trails, print 0, otherwise print the minimum number of trails the authorities need to add to the park in order to make Vasya's walk possible.	In the first test case the described walk is possible without building extra trails. For example, let's first go on the first trail, then on the second one, and finally on the third one.In the second test case the described walk is impossible without adding extra trails. To make the walk possible, it is enough to add o...	Input: 3 31 22 33 1 \| Output: 0	Expert	4	1,023	339	244	2
883	J	883J	J. Renovation	2,400	constructive algorithms; greedy; sortings	The mayor of the Berland city S sees the beauty differently than other city-dwellers. In particular, he does not understand at all, how antique houses can be nice-looking. So the mayor wants to demolish all ancient buildings in the city.The city S is going to host the football championship very soon. In order to make t...	The first line of the input contains two integers n and m (1 ≤ n, m ≤ 100 000) — the number of months before the championship and the number of ancient buildings in the city S.The second line contains n integers a1, a2, ..., an (1 ≤ ai ≤ 109), where ai is the tranche of the i-th month.The third line contains m integers...	Output single integer — the maximal number of buildings the mayor can demolish.	In the third example the mayor acts as follows.In the first month he obtains 6 burles tranche and demolishes buildings #2 (renovation cost 6, demolishing cost 4) and #4 (renovation cost 5, demolishing cost 2). He spends all the money on it.After getting the second month tranche of 3 burles, the mayor selects only build...	Input: 2 32 46 2 31 3 2 \| Output: 2	Expert	3	1,843	524	79	8
1,517	E	1517E	E. Group Photo	2,500	binary search; data structures; implementation; two pointers	In the 2050 Conference, some people from the competitive programming community meet together and are going to take a photo. The $n$ people form a line. They are numbered from $1$ to $n$ from left to right. Each of them either holds a cardboard with the letter 'C' or a cardboard with the letter 'P'.Let \(C=\{c_1,c...	Each test contains multiple test cases. The first line contains the number of test cases $t$ ($1 \le t \le 200\,000$). Description of the test cases follows.The first line of each test case contains a single integer $n$ ($1\leq n\leq 200\,000$).The second line contains $n$ integers $a_1, a_2, \ldots, a_n$ (...	For each test case, output the answer modulo $998\,244\,353$ in a separate line.	For the first test case, there are $10$ possible good photos satisfying the condition: PPPPP, CPPPP, PCPPP, CCPPP, PCCPP, PCPCP, PPPPC, CPPPC, PCPPC, PPPCC.For the second test case, there are $7$ possible good photos satisfying the condition: PPPP, PCPP, PCCP, PPPC, PCPC, PPCC, PCCC.	Input: 3 5 2 1 2 1 1 4 9 2 2 2 1 998244353 \| Output: 10 7 1	Expert	4	1,122	432	82	15
1,989	E	1989E	E. Distance to Different	2,300	combinatorics; dp; math	Consider an array $a$ of $n$ integers, where every element is from $1$ to $k$, and every integer from $1$ to $k$ appears at least once.Let the array $b$ be constructed as follows: for the $i$-th element of $a$, $b_i$ is the distance to the closest element in $a$ which is not equal to $a_i$. In o...	The only line of the input contains two integers $n$ and $k$ ($2 \le n \le 2 \cdot 10^5$; $2 \le k \le \min(n, 10)$).	Print one integer — the number of different arrays $b$ you can obtain, taken modulo $998244353$.		Input: 2 2 \| Output: 1	Expert	3	618	125	100	19
2,127	D	2127D	D. Root was Built by Love, Broken by Destiny	1,800	combinatorics; dfs and similar; graphs; trees	Heartfall River runs horizontally through Destinyland and divides it into the northern and southern sides.Engineer Root wants to build $n$ houses along the river, numbered from $1$ to $n$. All houses on the northern side and all houses on the southern side must lie along straight lines parallel to Heartfall River...	Each test contains multiple test cases. The first line contains the number of test cases $t$ ($1 \le t \le 10^4$). The description of the test cases follows. The first line of each test case contains two integers $n$ and $m$ ($2 \leq n \leq 2 \cdot 10^5$, \(n-1 \leq m \leq \min\left(\frac{n(n-1)}{2}, 2 \cdot ...	For each test case, output a single integer — the number of ways to arrange the $n$ houses along the river, modulo $10^9+7$.	In the first test case, either house $1$ should be built on the northern side and house $2$ on the southern side, or vice versa.In the second test case, at least two houses must be built on the same side of the river. But every pair of houses is connected by a bridge. So in every arrangement, at least one bridge wi...	Input: 42 11 23 31 21 32 35 41 21 33 43 54 31 21 31 4 \| Output: 2 0 8 12	Medium	4	1,544	870	128	21
1,271	F	1271F	F. Divide The Students	2,700	brute force	Recently a lot of students were enrolled in Berland State University. All students were divided into groups according to their education program. Some groups turned out to be too large to attend lessons in the same auditorium, so these groups should be divided into two subgroups. Your task is to help divide the first-y...	The first line contains one integer $t$ ($1 \le t \le 300$) — the number of groups.Then the descriptions of groups follow. The description of the $i$-th group consists of three lines: the first line contains three integers $a_{i, 1}$, $b_{i, 1}$ and $c_{i, 1}$ (\(1 \le a_{i, 1}, b_{i, 1}, c_{i, 1} \le 3000\...	For each group, print the result of its division as follows: if it is impossible to divide the group, print one integer $-1$; otherwise print seven integers $f_{i, 1}$, $f_{i, 2}$, ..., $f_{i, 7}$ ($0 \le f_{i, j} \le d_{i, j}$) — the number of students the first, second, ..., seventh type in the first subgro...		Input: 3 9 4 13 1 10 3 1 2 3 4 5 6 7 9 4 13 1 10 3 2 1 3 4 5 6 7 1 2 3 4 5 6 0 0 0 0 0 0 0 \| Output: 1 1 3 4 2 0 7 -1 0 0 0 0 0 0 0	Master	1	2,583	1,128	456	12
873	E	873E	E. Awards For Contestants	2,300	brute force; data structures; dp	Alexey recently held a programming contest for students from Berland. n students participated in a contest, i-th of them solved ai problems. Now he wants to award some contestants. Alexey can award the students with diplomas of three different degrees. Each student either will receive one diploma of some degree, or won...	The first line contains one integer number n (3 ≤ n ≤ 3000).The second line contains n integer numbers a1, a2, ..., an (1 ≤ ai ≤ 5000).	Output n numbers. i-th number must be equal to the degree of diploma i-th contestant will receive (or - 1 if he doesn't receive any diploma).If there are multiple optimal solutions, print any of them. It is guaranteed that the answer always exists.		Input: 41 2 3 4 \| Output: 3 3 2 1	Expert	3	1,685	135	248	8
1,707	E	1707E	E. Replace	3,500	binary search; data structures	You are given an integer array $a_1,\ldots, a_n$, where $1\le a_i \le n$ for all $i$.There's a ""replace"" function $f$ which takes a pair of integers $(l, r)$, where $l \le r$, as input and outputs the pair $$$\(f\big( (l, r) \big)=\left(\min\{a_l,a_{l+1},\ldots,a_r\},\, \max\{a_l,a_{l+1},\ldots,a_r\}\righ...	The first line contains two positive integers $n$, $q$ ($1\le n,q\le 10^5$) — the length of the sequence $a$ and the number of the queries.The second line contains $n$ positive integers $a_1,a_2,\ldots,a_n$ ($1\le a_i\le n$) — the sequence $a$.Each line of the following $q$ lines contains two integers...	For each query, output the required number of times, or $-1$ if it is impossible.	In the first example, $n=5$ and $a=[2,5,4,1,3]$.For the first query: $(4,4)\to(1,1)\to(2,2)\to(5,5)\to(3,3)\to(4,4)\to\ldots$, so it's impossible to get $(1,5)$.For the second query, you already have $(1,5)$.For the third query: $(1,4)\to(1,5)$.For the fourth query: $(3,5)\to(1,4)\to(1,5)$.For the fifth q...	Input: 5 6 2 5 4 1 3 4 4 1 5 1 4 3 5 4 5 2 3 \| Output: -1 0 1 2 3 4	Master	2	832	379	83	17
858	B	858B	B. Which floor?	1,500	brute force; implementation	In a building where Polycarp lives there are equal number of flats on each floor. Unfortunately, Polycarp don't remember how many flats are on each floor, but he remembers that the flats are numbered from 1 from lower to upper floors. That is, the first several flats are on the first floor, the next several flats are o...	The first line contains two integers n and m (1 ≤ n ≤ 100, 0 ≤ m ≤ 100), where n is the number of the flat you need to restore floor for, and m is the number of flats in Polycarp's memory.m lines follow, describing the Polycarp's memory: each of these lines contains a pair of integers ki, fi (1 ≤ ki ≤ 100, 1 ≤ fi ≤ 100...	Print the number of the floor in which the n-th flat is located, if it is possible to determine it in a unique way. Print -1 if it is not possible to uniquely restore this floor.	In the first example the 6-th flat is on the 2-nd floor, while the 7-th flat is on the 3-rd, so, the 6-th flat is the last on its floor and there are 3 flats on each floor. Thus, the 10-th flat is on the 4-th floor.In the second example there can be 3 or 4 flats on each floor, so we can't restore the floor for the 8-th...	Input: 10 36 22 17 3 \| Output: 4	Medium	2	908	472	178	8
1,368	H1	1368H1	H1. Breadboard Capacity (easy version)	3,300	dp; flows; greedy	This is an easier version of the problem H without modification queries.Lester and Delbert work at an electronics company. They are currently working on a microchip component serving to connect two independent parts of a large supercomputer.The component is built on top of a breadboard — a grid-like base for a microchi...	The first line contains three integers $n, m, q$ ($1 \leq n, m \leq 10^5$, $\pmb{q = 0}$). $n$ and $m$ are the number of rows and columns of the breadboard respectively. In this version $q$ is always zero, and is only present for consistency with the harder version.The next four lines describe initial color...	Print a single integer — the given breadboard capacity.		Input: 4 5 0 BBRR RBBR BBBBB RRRRR \| Output: 7	Master	3	1,649	705	55	13
493	D	493D	D. Vasya and Chess	1,700	constructive algorithms; games; math	Vasya decided to learn to play chess. Classic chess doesn't seem interesting to him, so he plays his own sort of chess.The queen is the piece that captures all squares on its vertical, horizontal and diagonal lines. If the cell is located on the same vertical, horizontal or diagonal line with queen, and the cell contai...	The input contains a single number n (2 ≤ n ≤ 109) — the size of the board.	On the first line print the answer to problem — string ""white"" or string ""black"", depending on who wins if the both players play optimally. If the answer is ""white"", then you should also print two integers r and c representing the cell (r, c), where the first player should make his first move to win. If there are...	In the first sample test the white queen can capture the black queen at the first move, so the white player wins.In the second test from the statement if the white queen captures the green pawn located on the central vertical line, then it will be captured by the black queen during the next move. So the only move for t...	Input: 2 \| Output: white1 2	Medium	3	1,323	75	446	4
146	A	146A	A. Lucky Ticket	800	implementation	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 ...	The first line contains an even integer n (2 ≤ n ≤ 50) — the length of the ticket number that needs to be checked. The second line contains an integer whose length equals exactly n — the ticket number. The number may contain leading zeros.	On the first line print ""YES"" if the given ticket number is lucky. Otherwise, print ""NO"" (without the quotes).	In the first sample the sum of digits in the first half does not equal the sum of digits in the second half (4 ≠ 7).In the second sample the ticket number is not the lucky number.	Input: 247 \| Output: NO	Beginner	1	615	239	114	1
964	B	964B	B. Messages	1,300	math	There are n incoming messages for Vasya. The i-th message is going to be received after ti minutes. Each message has a cost, which equals to A initially. After being received, the cost of a message decreases by B each minute (it can become negative). Vasya can read any message after receiving it at any moment of time. ...	The first line contains five integers n, A, B, C and T (1 ≤ n, A, B, C, T ≤ 1000).The second string contains n integers ti (1 ≤ ti ≤ T).	Output one integer — the answer to the problem.	In the first sample the messages must be read immediately after receiving, Vasya receives A points for each message, n·A = 20 in total.In the second sample the messages can be read at any integer moment.In the third sample messages must be read at the moment T. This way Vasya has 1, 2, 3, 4 and 0 unread messages at the...	Input: 4 5 5 3 51 5 5 4 \| Output: 20	Easy	1	757	136	47	9
2,008	B	2008B	B. Square or Not	800	brute force; math; strings	A beautiful binary matrix is a matrix that has ones on its edges and zeros inside. Examples of four beautiful binary matrices. Today, Sakurako was playing with a beautiful binary matrix of size $r \times c$ and created a binary string $s$ by writing down all the rows of the matrix, starting from the first and endin...	The first line contains a single integer $t$ ($1 \le t \le 10^4$) — the number of test cases.The first line of each test case contains a single integer $n$ ($2 \le n \le 2 \cdot 10^5$) — the length of the string.The second line of each test case contains the string $s$ of length $n$. The string is always th...	Print ""Yes"", if the original matrix could have been square, and ""No"" otherwise.	For the second test case, string 1111 can be obtained from the matrix: $1$$1$$1$$1$ For the third test case, string 111101111 can be obtained from the matrix: $1$$1$$1$$1$$0$$1$$1$$1$$1$ There is no square matrix in the fourth case, such that the string can be obtained from it.	Input: 5211411119111101111911111111112111110011111 \| Output: No Yes Yes No No	Beginner	3	735	472	83	20
1,743	F	1743F	F. Intersection and Union	2,300	data structures; dp; matrices; probabilities	You are given $n$ segments on the coordinate axis. The $i$-th segment is $[l_i, r_i]$. Let's denote the set of all integer points belonging to the $i$-th segment as $S_i$.Let $A \cup B$ be the union of two sets $A$ and $B$, $A \cap B$ be the intersection of two sets $A$ and $B$, and $A \oplus B$...	The first line contains one integer $n$ ($2 \le n \le 3 \cdot 10^5$).Then, $n$ lines follow. The $i$-th of them contains two integers $l_i$ and $r_i$ ($0 \le l_i \le r_i \le 3 \cdot 10^5$).	Print one integer — the sum of $\|(((S_1\ \mathbin{op}_1\ S_2)\ \mathbin{op}_2\ S_3)\ \mathbin{op}_3\ S_4)\ \dots\ \mathbin{op}_{n-1}\ S_n\|$ over all possible ways to choose $[\mathbin{op}_1, \mathbin{op}_2, \dots, \mathbin{op}_{n-1}]$. Since the answer can be huge, print it modulo $998244353$.		Input: 4 3 5 4 8 2 2 1 9 \| Output: 162	Expert	4	897	203	300	17
1,533	C	1533C	C. Sweets	0	*special; data structures; implementation	Anya came to her friend's birthday party. There are $n$ delicious sweets on a circle table (for convenience, we will number them from $1$ to $n$ in clockwise direction). For each of the sweets, it is known whether Anya likes it or not. Anya decided that she should eat all the sweets that are on the table, and she...	The first line contains a single integer $t$ ($1 \le t \le 5000$) — the number of test cases.The first line of each test case contains two integers $n$ and $k$ ($1 \le k \le n \le 5000$) — the number of sweets and the parameter $k$.The next line contains the string $s$, where $s_i = 1$ if Anya likes \(i...	For each test case, print one integer — the number of sweets that Anya will eat.	The first test case of the example is described in the statement.	Input: 4 6 4 000111 7 3 0000100 3 2 000 5 1 10011 \| Output: 4 4 0 5	Beginner	3	2,172	443	80	15
302	B	302B	B. Eugeny and Play List	1,200	binary search; implementation; two pointers	Eugeny loves listening to music. He has n songs in his play list. We know that song number i has the duration of ti minutes. Eugeny listens to each song, perhaps more than once. He listens to song number i ci times. Eugeny's play list is organized as follows: first song number 1 plays c1 times, then song number 2 plays...	The first line contains two integers n, m (1 ≤ n, m ≤ 105). The next n lines contain pairs of integers. The i-th line contains integers ci, ti (1 ≤ ci, ti ≤ 109) — the description of the play list. It is guaranteed that the play list's total duration doesn't exceed 109 .The next line contains m positive integers v1, v2...	Print m integers — the i-th number must equal the number of the song that was playing during the vi-th minute after Eugeny started listening to the play list.		Input: 1 22 81 16 \| Output: 11	Easy	3	737	666	158	3
1,884	C	1884C	C. Medium Design	1,700	brute force; data structures; dp; greedy; sortings	The array $a_1, a_2, \ldots, a_m$ is initially filled with zeroes. You are given $n$ pairwise distinct segments $1 \le l_i \le r_i \le m$. You have to select an arbitrary subset of these segments (in particular, you may select an empty set). Next, you do the following: For each $i = 1, 2, \ldots, n$, if the seg...	Each test contains multiple test cases. The first line contains the number of test cases $t$ ($1 \le t \le 10^4$). The description of the test cases follows.The first line of each test case contains two integers $n$ and $m$ ($1 \le n \le 10^5$, $1 \le m \le 10^9$) — the number of segments and the length of ...	For each test case, output the maximum cost among all subsets of the given set of segments.	In the first test case, there is only one segment available. If we do not select it, then the array will be $a = [0, 0, 0]$, and the cost of such (empty) subset of segments will be $0$. If, however, we select the only segment, the array will be $a = [0, 1, 0]$, and the cost will be $1 - 0 = 1$.In the second tes...	Input: 61 32 23 82 43 54 66 31 11 21 32 22 33 37 62 21 61 25 61 54 43 66 276 265 172 320 211 2212 244 10000000002 9999999993 1000000000123456789 9876543219274 123456789 \| Output: 1 3 2 3 4 4	Medium	5	911	647	91	18
1,338	D	1338D	D. Nested Rubber Bands	2,700	constructive algorithms; dfs and similar; dp; math; trees	You have a tree of $n$ vertices. You are going to convert this tree into $n$ rubber bands on infinitely large plane. Conversion rule follows: For every pair of vertices $a$ and $b$, rubber bands $a$ and $b$ should intersect if and only if there is an edge exists between $a$ and $b$ in the tree. Shape of...	The first line contains integer $n$ ($3 \le n \le 10^{5}$) — the number of vertices in tree.The $i$-th of the next $n-1$ lines contains two integers $a_{i}$ and $b_{i}$ ($1 \le a_{i} \lt b_{i} \le n$) — it means there is an edge between $a_{i}$ and $b_{i}$. It is guaranteed that given graph forms tree...	Print the answer.	In the first sample, you can obtain a nested sequence of $4$ rubber bands($1$, $2$, $5$, and $6$) by the conversion shown below. Of course, there are other conversions exist to make a nested sequence of $4$ rubber bands. However, you cannot make sequence of $5$ or more nested rubber bands with given tree....	Input: 6 1 3 2 3 3 4 4 5 4 6 \| Output: 4	Master	5	1,089	339	17	13
2,033	F	2033F	F. Kosuke's Sloth	1,800	brute force; math; number theory	Kosuke is too lazy. He will not give you any legend, just the task:Fibonacci numbers are defined as follows: $f(1)=f(2)=1$. $f(n)=f(n-1)+f(n-2)$ $(3\le n)$ We denote $G(n,k)$ as an index of the $n$-th Fibonacci number that is divisible by $k$. For given $n$ and $k$, compute $G(n,k)$.As this number can...	The first line of the input data contains a single integer $t$ ($1 \le t \le 10^4$) — the number of test cases.The first and only line contains two integers $n$ and $k$ ($1 \le n \le 10^{18}$, $1 \le k \le 10^5$).It is guaranteed that the sum of $k$ across all test cases does not exceed $10^6$.	For each test case, output the only number: the value $G(n,k)$ taken by modulo $10^9+7$.		Input: 33 2100 11000000000000 1377 \| Output: 9 100 999244007	Medium	3	520	311	92	20
39	J	39J	J. Spelling Check	1,500	hashing; implementation; strings	Petya has noticed that when he types using a keyboard, he often presses extra buttons and adds extra letters to the words. Of course, the spell-checking system underlines the words for him and he has to click every word and choose the right variant. Petya got fed up with correcting his mistakes himself, that’s why he d...	The input data contains two strings, consisting of lower-case Latin letters. The length of each string is from 1 to 106 symbols inclusive, the first string contains exactly 1 symbol more than the second one.	In the first line output the number of positions of the symbols in the first string, after the deleting of which the first string becomes identical to the second one. In the second line output space-separated positions of these symbols in increasing order. The positions are numbered starting from 1. If it is impossible...		Input: abdrakadabraabrakadabra \| Output: 13	Medium	3	806	207	421	0
1,898	E	1898E	E. Sofia and Strings	2,200	data structures; greedy; sortings; strings; two pointers	Sofia has a string $s$ of length $n$, consisting only of lowercase English letters. She can perform operations of the following types with this string. Select an index $1 \le i \le \|s\|$ and remove the character $s_i$ from the string. Select a pair of indices $(l, r)$ ($1 \le l \le r \le \|s\|$) and sort the s...	The first line contains one integer $t$ ($1 \leq t \leq 10\,000$) — the number of test cases.The first line of each test case contains two integers $n$, $m$ ($1\leq m \leq n \leq 2\cdot 10^5$) — the lengths of string $s$ and $t$, respectively.The second line of each test case contains the string $s$ of ...	For each test case, output ""YES"" if Sofia can obtain the string $t$ from $s$ using the operations above. Otherwise, output ""NO"".You can output the answer in any case (upper or lower). For example, the strings ""yEs"", ""yes"", ""Yes"", and ""YES"" will be recognized as positive responses.	In the first test case, Sofia can perform the following operation: operation of the second type with $l=1$ and $r=5$: string $s$ becomes $\mathtt{afios}$ after it. In the second test case, Sofia can perform the following operations: operation of the second type with $l=1$ and $r=2$: string $s$ becomes \(\...	Input: 85 5sofiaafios3 2cbabc5 1sofiae15 7anavolimilovanaaamanan26 4abcdefghijklmnopqrstuvwxyznope26 4zyxwvutsrqponmlkjihgfedcbanope7 3apricotcat3 3cbaacb \| Output: YES YES NO YES NO YES NO YES	Hard	5	940	591	297	18
617	D	617D	D. Polyline	1,700	constructive algorithms; implementation	There are three points marked on the coordinate plane. The goal is to make a simple polyline, without self-intersections and self-touches, such that it passes through all these points. Also, the polyline must consist of only segments parallel to the coordinate axes. You are to find the minimum number of segments this p...	Each of the three lines of the input contains two integers. The i-th line contains integers xi and yi ( - 109 ≤ xi, yi ≤ 109) — the coordinates of the i-th point. It is guaranteed that all points are distinct.	Print a single number — the minimum possible number of segments of the polyline.	The variant of the polyline in the first sample: The variant of the polyline in the second sample: The variant of the polyline in the third sample:	Input: 1 -11 11 2 \| Output: 1	Medium	2	343	209	80	6
1,296	B	1296B	B. Food Buying	900	math	Mishka wants to buy some food in the nearby shop. Initially, he has $s$ burles on his card. Mishka can perform the following operation any number of times (possibly, zero): choose some positive integer number $1 \le x \le s$, buy food that costs exactly $x$ burles and obtain $\lfloor\frac{x}{10}\rfloor$ burles ...	The first line of the input contains one integer $t$ ($1 \le t \le 10^4$) — the number of test cases.The next $t$ lines describe test cases. Each test case is given on a separate line and consists of one integer $s$ ($1 \le s \le 10^9$) — the number of burles Mishka initially has.	For each test case print the answer on it — the maximum number of burles Mishka can spend if he buys food optimally.		Input: 6 1 10 19 9876 12345 1000000000 \| Output: 1 11 21 10973 13716 1111111111	Beginner	1	1,036	291	116	12
1,202	C	1202C	C. You Are Given a WASD-string...	2,100	brute force; data structures; dp; greedy; implementation; math; strings	You have a string $s$ — a sequence of commands for your toy robot. The robot is placed in some cell of a rectangular grid. He can perform four commands: 'W' — move one cell up; 'S' — move one cell down; 'A' — move one cell left; 'D' — move one cell right. Let $Grid(s)$ be the grid of minimum possible area such that...	The first line contains one integer $T$ ($1 \le T \le 1000$) — the number of queries.Next $T$ lines contain queries: one per line. This line contains single string $s$ ($1 \le \|s\| \le 2 \cdot 10^5$, $s_i \in \{\text{W}, \text{A}, \text{S}, \text{D}\}$) — the sequence of commands.It's guaranteed that the tot...	Print $T$ integers: one per query. For each query print the minimum area of $Grid(s)$ you can achieve.	In the first query you have to get string $\text{DSAWW}\underline{D}\text{AW}$.In second and third queries you can not decrease the area of $Grid(s)$.	Input: 3 DSAWWAW D WA \| Output: 8 2 4	Hard	7	1,273	388	106	12
254	D	254D	D. Rats	2,300	brute force; dfs and similar; graphs; implementation; shortest paths	Rats have bred to hundreds and hundreds in the basement of the store, owned by Vasily Petrovich. Vasily Petrovich may have not noticed their presence, but they got into the habit of sneaking into the warehouse and stealing food from there. Vasily Petrovich cannot put up with it anymore, he has to destroy the rats in th...	The first line contains three integers n, m and d, separated by single spaces (4 ≤ n, m ≤ 1000, 1 ≤ d ≤ 8). Next n lines contain the table that represents the basement plan. Each row of the table consists of m characters. Character ""X"" means that the corresponding cell is occupied by the wall, character ""."" represe...	If it is impossible to blow up all cells with sleeping rats, print a single integer -1. Otherwise, print four space-separated integers r1, c1, r2, c2, that mean that one grenade should go off in cell (r1, c1), and the other one — in cell (r2, c2). Consider the table rows numbered from top to bottom from 1 to n and the ...		Input: 4 4 1XXXXXR.XX.RXXXXX \| Output: 2 2 2 3	Expert	5	1,912	603	725	2
414	C	414C	C. Mashmokh and Reverse Operation	2,100	combinatorics; divide and conquer	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 prog...	The first line of input contains a single integer n (0 ≤ n ≤ 20). The second line of input contains 2n space-separated integers a[1], a[2], ..., a[2n] (1 ≤ a[i] ≤ 109), the initial array.The third line of input contains a single integer m (1 ≤ m ≤ 106). The fourth line of input contains m space-separated integers q1, q...	Output m lines. In the i-th line print the answer (the number of inversions) for the i-th query.	If we reverse an array x[1], x[2], ..., x[n] it becomes new array y[1], y[2], ..., y[n], where y[i] = x[n - i + 1] for each i.The number of inversions of an array x[1], x[2], ..., x[n] is the number of pairs of indices i, j such that: i < j and x[i] > x[j].	Input: 22 1 4 341 2 0 2 \| Output: 0660	Hard	2	1,161	542	96	4
248	E	248E	E. Piglet's Birthday	2,600	dp; math; probabilities	Piglet has got a birthday today. His friend Winnie the Pooh wants to make the best present for him — a honey pot. Of course Winnie realizes that he won't manage to get the full pot to Piglet. In fact, he is likely to eat all the honey from the pot. And as soon as Winnie planned a snack on is way, the pot should initial...	The first line of the input contains a single number n (1 ≤ n ≤ 105) — the number of shelves at Winnie's place. The second line contains n integers ai (1 ≤ i ≤ n, 0 ≤ ai ≤ 100) — the number of honey pots on a shelf number i. The next line contains integer q (1 ≤ q ≤ 105) — the number of actions Winnie did the day befor...	For each Winnie's action print the value of the mathematical expectation m by the moment when this action is performed. The relative or absolute error of each value mustn't exceed 10 - 9.		Input: 32 2 351 2 12 1 21 2 23 1 13 2 2 \| Output: 0.0000000000000.3333333333331.0000000000001.0000000000002.000000000000	Expert	3	1,279	843	187	2
627	E	627E	E. Orchestra	3,000	two pointers	Paul is at the orchestra. The string section is arranged in an r × c rectangular grid and is filled with violinists with the exception of n violists. Paul really likes violas, so he would like to take a picture including at least k of them. Paul can take a picture of any axis-parallel rectangle in the orchestra. Count ...	The first line of input contains four space-separated integers r, c, n, k (1 ≤ r, c, n ≤ 3000, 1 ≤ k ≤ min(n, 10)) — the number of rows and columns of the string section, the total number of violas, and the minimum number of violas Paul would like in his photograph, respectively.The next n lines each contain two intege...	Print a single integer — the number of photographs Paul can take which include at least k violas.	We will use '' to denote violinists and '#' to denote violists.In the first sample, the orchestra looks as follows: #** Paul can take a photograph of just the viola, the 1 × 2 column containing the viola, the 2 × 1 row containing the viola, or the entire string section, for 4 pictures total.In the second sample, the ...	Input: 2 2 1 11 2 \| Output: 4	Master	1	476	461	97	6
714	A	714A	A. Meeting of Old Friends	1,100	implementation; math	Today an outstanding event is going to happen in the forest — hedgehog Filya will come to his old fried Sonya!Sonya is an owl and she sleeps during the day and stay awake from minute l1 to minute r1 inclusive. Also, during the minute k she prinks and is unavailable for Filya.Filya works a lot and he plans to visit Sony...	The only line of the input contains integers l1, r1, l2, r2 and k (1 ≤ l1, r1, l2, r2, k ≤ 1018, l1 ≤ r1, l2 ≤ r2), providing the segments of time for Sonya and Filya and the moment of time when Sonya prinks.	Print one integer — the number of minutes Sonya and Filya will be able to spend together.	In 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.	Input: 1 10 9 20 1 \| Output: 2	Easy	2	428	208	89	7
963	B	963B	B. Destruction of a Tree	2,000	constructive algorithms; dfs and similar; dp; greedy; trees	You are given a tree (a graph with n vertices and n - 1 edges in which it's possible to reach any vertex from any other vertex using only its edges).A vertex can be destroyed if this vertex has even degree. If you destroy a vertex, all edges connected to it are also deleted.Destroy all vertices in the given tree or det...	The first line contains integer n (1 ≤ n ≤ 2·105) — number of vertices in a tree.The second line contains n integers p1, p2, ..., pn (0 ≤ pi ≤ n). If pi ≠ 0 there is an edge between vertices i and pi. It is guaranteed that the given graph is a tree.	If it's possible to destroy all vertices, print ""YES"" (without quotes), otherwise print ""NO"" (without quotes).If it's possible to destroy all vertices, in the next n lines print the indices of the vertices in order you destroy them. If there are multiple correct answers, print any.	In the first example at first you have to remove the vertex with index 1 (after that, the edges (1, 2) and (1, 4) are removed), then the vertex with index 2 (and edges (2, 3) and (2, 5) are removed). After that there are no edges in the tree, so you can remove remaining vertices in any order.	Input: 50 1 2 1 2 \| Output: YES12354	Hard	5	349	249	286	9
1,425	I	1425I	I. Impressive Harvesting of The Orchard	2,800	data structures	Mr. Chanek has an orchard structured as a rooted ternary tree with $N$ vertices numbered from $1$ to $N$. The root of the tree is vertex $1$. $P_i$ denotes the parent of vertex $i$, for $(2 \le i \le N)$. Interestingly, the height of the tree is not greater than $10$. Height of a tree is defined to be t...	The first line contains two integers $N$ and $Q$ $(1 \le N,\ Q,\le 5 \cdot 10^4)$, which denotes the number of vertices and the number of days Mr. Chanek visits the orchard.The second line contains $N$ integers $A_i$ $(1 \le A_i \le 5 \cdot 10^4)$, which denotes the fruits growth speed on the bush at vertex...	Output $Q$ lines, line $i$ gives the sum of distances from the harvested bushes to $X_i$, and the number of harvested bushes.	For the first example: On day 1, Mr. Chanek starts at vertex $2$ and can harvest the bush at vertex 2. On day 2, Mr. Chanek starts at vertex $1$ and only harvest from bush $1$ (bush 2's fruit still has not grown yet). On day 3, Mr. Chanek starts at vertex $1$ and harvests the fruits on bush $1$ and $2$. The...	Input: 2 3 1 2 1 2 1 1 \| Output: 0 1 0 1 1 2	Master	1	1,239	837	131	14
337	C	337C	C. Quiz	1,600	binary search; greedy; math; matrices; number theory	Manao is taking part in a quiz. The quiz consists of n consecutive questions. A correct answer gives one point to the player. The game also has a counter of consecutive correct answers. When the player answers a question correctly, the number on this counter increases by 1. If the player answers a question incorrectly,...	The single line contains three space-separated integers n, m and k (2 ≤ k ≤ n ≤ 109; 0 ≤ m ≤ n).	Print a single integer — the remainder from division of Manao's minimum possible score in the quiz by 1000000009 (109 + 9).	Sample 1. Manao answered 3 questions out of 5, and his score would double for each two consecutive correct answers. If Manao had answered the first, third and fifth questions, he would have scored as much as 3 points.Sample 2. Now Manao answered 4 questions. The minimum possible score is obtained when the only wrong an...	Input: 5 3 2 \| Output: 3	Medium	5	1,004	96	123	3
923	E	923E	E. Perpetual Subtraction	3,100	fft; math; matrices	There is a number x initially written on a blackboard. You repeat the following action a fixed amount of times: take the number x currently written on a blackboard and erase it select an integer uniformly at random from the range [0, x] inclusive, and write it on the blackboard Determine the distribution of final numbe...	The first line contains two integers, N (1 ≤ N ≤ 105) — the maximum number written on the blackboard — and M (0 ≤ M ≤ 1018) — the number of steps to perform.The second line contains N + 1 integers P0, P1, ..., PN (0 ≤ Pi < 998244353), where Pi describes the probability that the starting number is i. We can express this...	Output a single line of N + 1 integers, where Ri is the probability that the final number after M steps is i. It can be proven that the probability may always be expressed as an irreducible fraction P / Q. You are asked to output .	In the first case, we start with number 2. After one step, it will be 0, 1 or 2 with probability 1/3 each.In the second case, the number will remain 2 with probability 1/9. With probability 1/9 it stays 2 in the first round and changes to 1 in the next, and with probability 1/6 changes to 1 in the first round and stays...	Input: 2 10 0 1 \| Output: 332748118 332748118 332748118	Master	3	387	440	231	9
429	E	429E	E. Points and Segments	3,000	graphs	Iahub isn't well prepared on geometry problems, but he heard that this year there will be a lot of geometry problems on the IOI selection camp. Scared, Iahub locked himself in the basement and started thinking of new problems of this kind. One of them is the following.Iahub wants to draw n distinct segments [li, ri] on...	The first line of input contains integer n (1 ≤ n ≤ 105) — the number of segments. The i-th of the next n lines contains two integers li and ri (0 ≤ li ≤ ri ≤ 109) — the borders of the i-th segment.It's guaranteed that all the segments are distinct.	If there is no good drawing for a given test, output a single integer -1. Otherwise output n integers; each integer must be 0 or 1. The i-th number denotes the color of the i-th segment (0 is red and 1 is blue).If there are multiple good drawings you can output any of them.		Input: 20 22 3 \| Output: 0 1	Master	1	833	249	274	4
1,939	D	1939D		0	*special; dp; games						Beginner	3	0	0	0	19
1,558	D	1558D	D. Top-Notch Insertions	2,600	combinatorics; data structures	Consider the insertion sort algorithm used to sort an integer sequence $[a_1, a_2, \ldots, a_n]$ of length $n$ in non-decreasing order.For each $i$ in order from $2$ to $n$, do the following. If $a_i \ge a_{i-1}$, do nothing and move on to the next value of $i$. Otherwise, find the smallest $j$ such tha...	Each test contains multiple test cases. The first line contains the number of test cases $t$ ($1 \le t \le 10^5$). Description of the test cases follows.The first line of each test case contains two integers $n$ and $m$ ($2 \le n \le 2 \cdot 10^5$; $0 \le m < n$) — the length of the sequence and the number ...	For each test case, print the number of sequences of length $n$ consisting of integers from $1$ to $n$ such that sorting them with the described algorithm produces the given sequence of insertions, modulo $998\,244\,353$.	In the first test case, the algorithm performs no insertions — therefore, the initial sequence is already sorted in non-decreasing order. There are $10$ such sequences: $[1, 1, 1], [1, 1, 2], [1, 1, 3], [1, 2, 2], [1, 2, 3], [1, 3, 3], [2, 2, 2], [2, 2, 3], [2, 3, 3], [3, 3, 3]$.In the second test case, the only se...	Input: 3 3 0 3 2 2 1 3 1 5 3 3 1 4 1 5 3 \| Output: 10 1 21	Expert	2	1,707	717	229	15
765	C	765C	C. Table Tennis Game 2	1,200	math	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...	The first line contains three space-separated integers k, a and b (1 ≤ k ≤ 109, 0 ≤ a, b ≤ 109, a + b > 0).	If the situation is impossible, print a single number -1. Otherwise, print the maximum possible number of sets.	Note 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.	Input: 11 11 5 \| Output: 1	Easy	1	530	107	111	7
746	D	746D	D. Green and Black Tea	1,500	constructive algorithms; greedy; math	Innokentiy likes tea very much and today he wants to drink exactly n cups of tea. He would be happy to drink more but he had exactly n tea bags, a of them are green and b are black.Innokentiy doesn't like to drink the same tea (green or black) more than k times in a row. Your task is to determine the order of brewing t...	The first line contains four integers n, k, a and b (1 ≤ k ≤ n ≤ 105, 0 ≤ a, b ≤ n) — the number of cups of tea Innokentiy wants to drink, the maximum number of cups of same tea he can drink in a row, the number of tea bags of green and black tea. It is guaranteed that a + b = n.	If it is impossible to drink n cups of tea, print ""NO"" (without quotes).Otherwise, print the string of the length n, which consists of characters 'G' and 'B'. If some character equals 'G', then the corresponding cup of tea should be green. If some character equals 'B', then the corresponding cup of tea should be blac...		Input: 5 1 3 2 \| Output: GBGBG	Medium	3	519	280	371	7
1,375	D	1375D	D. Replace by MEX	1,900	brute force; constructive algorithms; sortings	You're given an array of $n$ integers between $0$ and $n$ inclusive.In one operation, you can choose any element of the array and replace it by the MEX of the elements of the array (which may change after the operation).For example, if the current array is $[0, 2, 2, 1, 4]$, you can choose the second element an...	The first line contains a single integer $t$ ($1 \le t \le 200$) — the number of test cases. The description of the test cases follows.The first line of each test case contains a single integer $n$ ($3 \le n \le 1000$) — length of the array.The second line of each test case contains $n$ integers \(a_1, \ldots...	For each test case, you must output two lines:The first line must contain a single integer $k$ ($0 \le k \le 2n$) — the number of operations you perform.The second line must contain $k$ integers $x_1, \ldots, x_k$ ($1 \le x_i \le n$), where $x_i$ is the index chosen for the $i$-th operation.If there are m...	In the first test case, the array is already non-decreasing ($2 \le 2 \le 3$).Explanation of the second test case (the element modified by each operation is colored in red): $a = [2, 1, 0]$ ; the initial MEX is $3$. $a = [2, 1, \color{red}{3}]$ ; the new MEX is $0$. $a = [\color{red}{0}, 1, 3]$ ; the new ME...	Input: 5 3 2 2 3 3 2 1 0 7 0 7 3 1 3 7 7 9 2 0 1 1 2 4 4 2 0 9 8 4 7 6 1 2 3 0 5 \| Output: 0 2 3 1 4 2 5 5 4 11 3 8 9 7 8 5 9 6 4 1 2 10 1 8 1 9 5 2 4 6 3 7	Hard	3	1,285	499	419	13
461	B	461B	B. Appleman and Tree	2,000	dfs and similar; dp; trees	Appleman has a tree with n vertices. Some of the vertices (at least one) are colored black and other vertices are colored white.Consider a set consisting of k (0 ≤ k < n) edges of Appleman's tree. If Appleman deletes these edges from the tree, then it will split into (k + 1) parts. Note, that each part will be a tree w...	The first line contains an integer n (2 ≤ n ≤ 105) — the number of tree vertices. The second line contains the description of the tree: n - 1 integers p0, p1, ..., pn - 2 (0 ≤ pi ≤ i). Where pi means that there is an edge connecting vertex (i + 1) of the tree and vertex pi. Consider tree vertices are numbered from 0 to...	Output a single integer — the number of ways to split the tree modulo 1000000007 (109 + 7).		Input: 30 00 1 1 \| Output: 2	Hard	3	529	537	91	4
471	E	471E	E. MUH and Lots and Lots of Segments	2,700	data structures; dsu	Polar bears Menshykov and Uslada from the zoo of St. Petersburg and elephant Horace from the zoo of Kiev decided to do some painting. As they were trying to create their first masterpiece, they made a draft on a piece of paper. The draft consists of n segments. Each segment was either horizontal or vertical. Now the fr...	The first line of the input contains integer n (1 ≤ n ≤ 2·105) — the number of segments on the draft. The next n lines contain four integers each: x1, y1, x2, y2 ( - 109 ≤ x1 ≤ x2 ≤ 109; - 109 ≤ y1 ≤ y2 ≤ 109) — the two startpoint and the two endpoint coordinates of a segment. All segments are non-degenerative and eith...	Print a single integer — the maximum sum of lengths for the remaining segments.	The shapes that you can get in the two given samples are: In the first sample you need to delete any segment as the two segments together do not form a single connected shape.In the second sample the initial segments form a cycle, there are four ways to break the cycle: delete the first, second or fourth segment altoge...	Input: 20 0 0 11 0 1 1 \| Output: 1	Master	2	1,331	461	79	4
1,180	A	1180A	A. Alex and a Rhombus	800	dp; implementation; math	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 comm...	The first and only input line contains integer $n$ ($1 \leq n \leq 100$) — order of a rhombus whose numbers of cells should be computed.	Print exactly one integer — the number of cells in a $n$-th order rhombus.	Images of rhombus corresponding to the examples are given in the statement.	Input: 1 \| Output: 1	Beginner	3	462	140	76	11
1,826	E	1826E	E. Walk the Runway	2,400	bitmasks; brute force; data structures; dp; graphs; implementation; sortings	A fashion tour consists of $m$ identical runway shows in different cities. There are $n$ models willing to participate in the tour, numbered from $1$ to $n$. People in different cities have different views on the fashion industry, so they rate each model differently. In particular, people in city $i$ rate mod...	The first line contains two integers $m$ and $n$ ($1 \leq m \leq 500$, $1 \leq n \leq 5000$) — the number of shows and the number of models willing to participate respectively.The second line contains $n$ integers $p_j$ ($1 \leq p_j \leq 10^9$) — the profit you get inviting the $j$-th model to the tour....	Output a single integer — the largest total amount of money you can get.	In the first example, there are $3$ invited models. The show consists of models in the order $[1, 3, 4]$.Then, the corresponding ratings in the cities are as follows: City $1$ — $[ 1, 3, 4 ]$. City $2$ — $[ 1, 2, 3 ]$. City $3$ — $[ 2, 4, 5 ]$. You can see that the ratings are increasing. So the total p...	Input: 3 5 10 10 10 10 10 1 2 3 4 5 1 5 2 3 4 2 3 4 5 1 \| Output: 30	Expert	7	1,098	492	72	18
83	E	83E	E. Two Subsequences	2,800	bitmasks; dp	On an IT lesson Valera studied data compression. The teacher told about a new method, which we shall now describe to you.Let {a1, a2, ..., an} be the given sequence of lines needed to be compressed. Here and below we shall assume that all lines are of the same length and consist only of the digits 0 and 1. Let's define...	The first line of input data contains an integer n — the number of strings (1 ≤ n ≤ 2·105). Then on n lines follow elements of the sequence — strings whose lengths are from 1 to 20 characters, consisting only of digits 0 and 1. The i + 1-th input line contains the i-th element of the sequence. Elements of the sequence ...	Print a single number — the minimum possible value of S.	Detailed answers to the tests: The best option is to make one of the subsequences empty, and the second one equal to the whole given sequence. \|f(01, 10, 01)\| = \|f(f(01, 10), 01)\| = \|f(010, 01)\| = \|0101\| = 4. The best option is: b = {000, 001}, c = {111, 110}. S = \|f(000, 001)\| + \|f(111, 110)\| = \|0001\| + \|1110\| = 8. Th...	Input: 3011001 \| Output: 4	Master	2	1,424	406	56	0
1,020	B	1020B	B. Badge	1,000	brute force; dfs and similar; graphs	In Summer Informatics School, if a student doesn't behave well, teachers make a hole in his badge. And today one of the teachers caught a group of $n$ students doing yet another trick. Let's assume that all these students are numbered from $1$ to $n$. The teacher came to student $a$ and put a hole in his badge....	The first line of the input contains the only integer $n$ ($1 \le n \le 1000$) — the number of the naughty students.The second line contains $n$ integers $p_1$, ..., $p_n$ ($1 \le p_i \le n$), where $p_i$ indicates the student who was reported to the teacher by student $i$.	For every student $a$ from $1$ to $n$ print which student would receive two holes in the badge, if $a$ was the first student caught by the teacher.	The picture corresponds to the first example test case. When $a = 1$, the teacher comes to students $1$, $2$, $3$, $2$, in this order, and the student $2$ is the one who receives a second hole in his badge.When $a = 2$, the teacher comes to students $2$, $3$, $2$, and the student $2$ gets a second...	Input: 32 3 2 \| Output: 2 2 3	Beginner	3	1,103	290	155	10
44	J	44J	J. Triminoes	2,000	constructive algorithms; greedy	There are many interesting tasks on domino tilings. For example, an interesting fact is known. Let us take a standard chessboard (8 × 8) and cut exactly two squares out of it. It turns out that the resulting board can always be tiled using dominoes 1 × 2, if the two cut out squares are of the same color, otherwise it i...	The first line contains two integers n and m (1 ≤ n, m ≤ 1000) — the board size. Next n lines contain m symbols each and represent the board description. If some position contains ""."", then the square in this position has been cut out. Symbol ""w"" stands for a white square, ""b"" stands for a black square. It is gua...	If at least one correct tiling exists, in the first line print ""YES"" (without quotes), and then — the tiling description. The description must contain n lines, m symbols in each. The cut out squares, as well as in the input data, are marked by ""."". To denote triminoes symbols ""a"", ""b"", ""c"", ""d"" can be used,...		Input: 6 10.w.wbw.wbwwbwbw.w.w.bw.wbwbwbww.wbw.wbwb...wbw.w.w..wbw.wbw. \| Output: YES.a.aaa.cccbaccc.c.a.ba.dddcbabb.aaa.cbab...bbb.b.b..ccc.ddd.	Hard	2	1,219	489	855	0
188	C	188C	C. LCM	1,400	*special; implementation; math	Least common multiple (LCM) of two numbers is the smallest positive integer which is divisible by both of them. You are given integers a and b. Calculate their LCM.	The input contains two integers a and b (1 ≤ a, b ≤ 103), separated by a single space.	Output LCM(a, b).		Input: 10 42 \| Output: 210	Easy	3	164	86	17	1
331	E1	331E1	E1. Deja Vu	2,900	constructive algorithms; graphs; implementation	Everybody knows that we have been living in the Matrix for a long time. And in the new seventh Matrix the world is ruled by beavers.So let's take beaver Neo. Neo has so-called ""deja vu"" outbursts when he gets visions of events in some places he's been at or is going to be at. Let's examine the phenomenon in more deta...	The first line contains integers n and m — the number of shops and the number of streets, correspondingly, 1 ≤ n ≤ 50, . Next m lines contain the descriptions of the streets in the following format: xi yi ki v1 v2 ... vk, where xi and yi (1 ≤ xi, yi ≤ n, xi ≠ yi) are indices of shops connected by a street, ki (0 ≤ ki ≤...	Subproblem E1. In the first line print an integer k (1 ≤ k ≤ 2·n) — the numbers of shops on Neo's path. In the next line print k integers — the number of shops in the order Neo passes them. If the graph doesn't have such paths or the length of the shortest path includes more than 2·n shops, print on a single line 0.Sub...	The input in both samples are the same. The first sample contains the answer to the first subproblem, the second sample contains the answer to the second subproblem.	Input: 6 61 2 2 1 22 3 1 33 4 2 4 54 5 05 3 1 36 1 1 6 \| Output: 46 1 2 3	Master	3	1,132	886	464	3
1,970	D3	1970D3	D3. Arithmancy (Hard)	3,100	interactive	The only difference between the versions of this problem is the maximum value of $n$.Professor Vector is preparing to teach her Arithmancy class. She needs to prepare $n$ distinct magic words for the class. Each magic word is a string consisting of characters X and O. A spell is a string created by concatenating tw...				Input: 2 2 15 11 \| Output: XOXO X 1 1 2 1	Master	1	1,458	0	0	19
1,516	B	1516B	B. AGAGA XOOORRR	1,500	bitmasks; brute force; dp; greedy	Baby Ehab is known for his love for a certain operation. He has an array $a$ of length $n$, and he decided to keep doing the following operation on it: he picks $2$ adjacent elements; he then removes them and places a single integer in their place: their bitwise XOR. Note that the length of the array decreases by...	The first line contains an integer $t$ ($1 \le t \le 15$) — the number of test cases you need to solve.The first line of each test case contains an integers $n$ ($2 \le n \le 2000$) — the number of elements in the array $a$.The second line contains $n$ space-separated integers $a_1$, $a_2$, $\ldots$, ...	If Baby Ehab can make all elements equal while leaving at least $2$ elements standing, print ""YES"". Otherwise, print ""NO"".	In the first sample, he can remove the first $2$ elements, $0$ and $2$, and replace them by $0 \oplus 2=2$. The array will be $[2,2]$, so all the elements are equal.In the second sample, there's no way to make all the elements equal.	Input: 2 3 0 2 2 4 2 3 1 10 \| Output: YES NO	Medium	4	495	389	128	15
1,707	B	1707B	B. Difference Array	1,900	brute force; data structures; implementation; sortings	You are given an array $a$ consisting of $n$ non-negative integers. It is guaranteed that $a$ is sorted from small to large.For each operation, we generate a new array $b_i=a_{i+1}-a_{i}$ for $1 \le i < n$. Then we sort $b$ from small to large, replace $a$ with $b$, and decrease $n$ by $1$.After per...	The input consists of multiple test cases. The first line contains a single integer $t$ ($1\le t\le 10^4$) — the number of test cases. The description of the test cases follows.The first line of each test case contains one integer $n$ ($2\le n\le 10^5$) — the length of the array $a$.The second line contains \...	For each test case, output the answer on a new line.	To simplify the notes, let $\operatorname{sort}(a)$ denote the array you get by sorting $a$ from small to large.In the first test case, $a=[1,10,100]$ at first. After the first operation, $a=\operatorname{sort}([10-1,100-10])=[9,90]$. After the second operation, $a=\operatorname{sort}([90-9])=[81]$.In the sec...	Input: 531 10 10044 8 9 1350 0 0 8 1362 4 8 16 32 6470 0 0 0 0 0 0 \| Output: 81 3 1 2 0	Hard	4	465	591	52	17
1,332	D	1332D	D. Walk on Matrix	1,700	bitmasks; constructive algorithms; math	Bob is playing a game named ""Walk on Matrix"".In this game, player is given an $n \times m$ matrix $A=(a_{i,j})$, i.e. the element in the $i$-th row in the $j$-th column is $a_{i,j}$. Initially, player is located at position $(1,1)$ with score $a_{1,1}$. To reach the goal, position $(n,m)$, player can ...	The only line of the input contains one single integer $k$ ($0 \le k \le 10^5$).	Output two integers $n$, $m$ ($1 \le n,m \le 500$) in the first line, representing the size of the matrix. Then output $n$ lines with $m$ integers in each line, $a_{i,j}$ in the $(i+1)$-th row, $j$-th column.	In the first example, the maximum score Bob can achieve is $300000$, while the output of his algorithm is $300000$.In the second example, the maximum score Bob can achieve is $7\&3\&3\&3\&7\&3=3$, while the output of his algorithm is $2$.	Input: 0 \| Output: 1 1 300000	Medium	3	1,361	84	224	13
1,539	F	1539F	F. Strange Array	2,600	data structures; greedy; sortings	Vasya has an array of $n$ integers $a_1, a_2, \ldots, a_n$. Vasya thinks that all numbers in his array are strange for some reason. To calculate how strange the $i$-th number is, Vasya created the following algorithm.He chooses a subsegment $a_l, a_{l+1}, \ldots, a_r$, such that $1 \le l \le i \le r \le n$, s...	The first line contains a single integer $n$ ($1 \le n \le 200\,000$) — the size of the array.The second line contains $n$ integers $a_1, a_2, \ldots, a_n$ ($1 \le a_i \le n$) — Vasya's array.	Print a single line with $n$ numbers. The $i$-th of them must be equal to the strangeness of the $i$-th element of the array.	In the first example: For the first position we choose the segment from $1$ to $5$. After sorting, it looks like $[1, 2, 3, 4, 5]$, the center is $3$. The distance from the center to $5$ is $2$. For the second position we choose the segment from $2$ to $4$. For the third position we choose the segment f...	Input: 5 5 4 3 2 1 \| Output: 2 1 1 2 2	Expert	3	1,063	202	131	15
1,594	F	1594F	F. Ideal Farm	2,400	constructive algorithms; math	Theofanis decided to visit his uncle's farm. There are $s$ animals and $n$ animal pens on the farm. For utility purpose, animal pens are constructed in one row.Uncle told Theofanis that a farm is lucky if you can distribute all animals in all pens in such a way that there are no empty pens and there is at least one...	The first line contains a single integer $t$ ($1 \le t \le 10^5$) — the number of test cases.The first and only line of each test case contains three integers $s$, $n$, and $k$ ($1 \le s, n, k \le 10^{18}$; $n \le s$).	For each test case, print YES (case-insensitive), if the farm is ideal, or NO (case-insensitive) otherwise.	For the first and the second test case, the only possible combination is $[1]$ so there always will be a subsegment with $1$ animal but not with $2$ animals.	Input: 4 1 1 1 1 1 2 100 50 200 56220 47258 14497 \| Output: YES NO NO YES	Expert	2	572	232	107	15
827	A	827A	A. String Reconstruction	1,700	data structures; greedy; sortings; strings	Ivan had string s consisting of small English letters. However, his friend Julia decided to make fun of him and hid the string s. Ivan preferred making a new string to finding the old one. Ivan knows some information about the string s. Namely, he remembers, that string ti occurs in string s at least ki times or more, ...	The first line contains single integer n (1 ≤ n ≤ 105) — the number of strings Ivan remembers.The next n lines contain information about the strings. The i-th of these lines contains non-empty string ti, then positive integer ki, which equal to the number of times the string ti occurs in string s, and then ki distinct ...	Print lexicographically minimal string that fits all the information Ivan remembers.		Input: 3a 4 1 3 5 7ab 2 1 5ca 1 4 \| Output: abacaba	Medium	4	651	741	84	8
2,038	B	2038B	B. Make It Equal	2,100	binary search; brute force; greedy; math	You are given an integer array $a$ of size $n$. The elements of the array are numbered from $1$ to $n$.You can perform the following operation any number of times (possibly, zero): choose an index $i$ from $1$ to $n$; decrease $a_i$ by $2$ and increase $a_{(i \bmod n) + 1}$ by $1$.After you perfor...	The first line contains a single integer $t$ ($1 \le t \le 10^4$) — the number of test cases.The first line of each test case contains a single integer $n$ ($2 \le n \le 2 \cdot 10^5$).The second line of each test case contains $n$ integers $a_1, a_2, \dots, a_n$ ($1 \le a_i \le 10^9$).Additional constrai...	For each test case, print a single integer — the minimum number of operations you have to perform. If it is impossible to make all elements of the array equal, print -1.		Input: 321 131 3 242 1 2 6 \| Output: 0 -1 3	Hard	4	481	406	169	20
1,368	A	1368A	A. C+=	800	brute force; greedy; implementation; math	Leo has developed a new programming language C+=. In C+=, integer variables can only be changed with a ""+="" operation that adds the right-hand side value to the left-hand side variable. For example, performing ""a += b"" when a = $2$, b = $3$ changes the value of a to $5$ (the value of b does not change).In a p...	The first line contains a single integer $T$ ($1 \leq T \leq 100$) — the number of test cases.Each of the following $T$ lines describes a single test case, and contains three integers $a, b, n$ ($1 \leq a, b \leq n \leq 10^9$) — initial values of a and b, and the value one of the variables has to exceed, resp...	For each test case print a single integer — the smallest number of operations needed. Separate answers with line breaks.	In the first case we cannot make a variable exceed $3$ in one operation. One way of achieving this in two operations is to perform ""b += a"" twice.	Input: 2 1 2 3 5 4 100 \| Output: 2 7	Beginner	4	674	329	120	13
1,509	B	1509B	B. TMT Document	1,100	greedy	The student council has a shared document file. Every day, some members of the student council write the sequence TMT (short for Towa Maji Tenshi) in it.However, one day, the members somehow entered the sequence into the document at the same time, creating a jumbled mess. Therefore, it is Suguru Doujima's task to figur...	The first line contains an integer $t$ ($1 \le t \le 5000$) — the number of test cases.The first line of each test case contains an integer $n$ ($3 \le n < 10^5$), the number of characters in the string entered in the document. It is guaranteed that $n$ is divisible by $3$.The second line of each test case ...	For each test case, print a single line containing YES if the described partition exists, and a single line containing NO otherwise.	In the first test case, the string itself is already a sequence equal to TMT.In the third test case, we may partition the string into the subsequences TMTMTT. Both the bolded and the non-bolded subsequences are equal to TMT.	Input: 5 3 TMT 3 MTT 6 TMTMTT 6 TMTTTT 6 TTMMTT \| Output: YES NO YES NO YES	Easy	1	816	480	132	15
1,398	G	1398G	G. Running Competition	2,600	bitmasks; fft; math; number theory	A running competition is going to be held soon. The stadium where the competition will be held can be represented by several segments on the coordinate plane: two horizontal segments: one connecting the points $(0, 0)$ and $(x, 0)$, the other connecting the points $(0, y)$ and $(x, y)$; $n + 1$ vertical segme...	The first line contains three integers $n$, $x$ and $y$ ($1 \le n, x, y \le 2 \cdot 10^5$, $n \le x$).The second line contains $n + 1$ integers $a_0$, $a_1$, ..., $a_n$ ($0 = a_0 < a_1 < a_2 < \dots < a_{n - 1} < a_n = x$).The third line contains one integer $q$ ($1 \le q \le 2 \cdot 10^5$) — th...	Print $q$ numbers. The $i$-th number should be equal to the maximum possible length of a suitable lap for the $i$-th stage, or $-1$ if it is impossible to choose a lap for that stage.		Input: 3 10 5 0 3 5 10 6 24 30 14 16 18 10 \| Output: 24 30 14 16 -1 -1	Expert	4	1,592	468	191	13
528	D	528D	D. Fuzzy Search	2,500	bitmasks; brute force; fft	Leonid works for a small and promising start-up that works on decoding the human genome. His duties include solving complex problems of finding certain patterns in long strings consisting of letters 'A', 'T', 'G' and 'C'.Let's consider the following scenario. There is a fragment of a human DNA chain, recorded as a stri...	The first line contains three integers \|S\|, \|T\|, k (1 ≤ \|T\| ≤ \|S\| ≤ 200 000, 0 ≤ k ≤ 200 000) — the lengths of strings S and T and the error threshold.The second line contains string S.The third line contains string T.Both strings consist only of uppercase letters 'A', 'T', 'G' and 'C'.	Print a single number — the number of occurrences of T in S with the error threshold k by the given definition.	If you happen to know about the structure of the human genome a little more than the author of the problem, and you are not impressed with Leonid's original approach, do not take everything described above seriously.	Input: 10 4 1AGCAATTCATACAT \| Output: 3	Expert	3	1,443	287	111	5
21	A	21A	A. Jabber ID	1,900	implementation; strings	Jabber ID on the national Berland service «Babber» has a form <username>@<hostname>[/resource], where <username> — is a sequence of Latin letters (lowercase or uppercase), digits or underscores characters «_», the length of <username> is between 1 and 16, inclusive. <hostname> — is a sequence of word separated by perio...	The input contains of a single line. The line has the length between 1 and 100 characters, inclusive. Each characters has ASCII-code between 33 and 127, inclusive.	Print YES or NO.		Input: [email protected] \| Output: YES	Hard	2	942	163	16	0
903	F	903F	F. Clear The Matrix	2,200	bitmasks; dp	You are given a matrix f with 4 rows and n columns. Each element of the matrix is either an asterisk (*) or a dot (.).You may perform the following operation arbitrary number of times: choose a square submatrix of f with size k × k (where 1 ≤ k ≤ 4) and replace each element of the chosen submatrix with a dot. Choosing ...	The first line contains one integer n (4 ≤ n ≤ 1000) — the number of columns in f.The second line contains 4 integers a1, a2, a3, a4 (1 ≤ ai ≤ 1000) — the cost to replace the square submatrix of size 1 × 1, 2 × 2, 3 × 3 or 4 × 4, respectively.Then four lines follow, each containing n characters and denoting a row of ma...	Print one integer — the minimum number of coins to replace all asterisks with dots.	In the first example you can spend 8 coins to replace the submatrix 3 × 3 in the top-left corner, and 1 coin to replace the 1 × 1 submatrix in the bottom-right corner.In the second example the best option is to replace the 4 × 4 submatrix containing columns 2 – 5, and the 2 × 2 submatrix consisting of rows 2 – 3 and co...	Input: 41 10 8 20*..*.... \| Output: 9	Hard	2	448	374	83	9

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