meetforever/GRPO_CL huggingface dataset:
user: In Chef's house there are N apples lying in a row on the floor. These apples are numbered from 1 (left most one) to N (right most one). The types of apples are also numbered by positive integers, and the type of apple i is Ti.
Chef has recently brought two trained dogs. Both of the dogs are too intelligent to know the smell of each type of apple. If Chef gives a dog an integer x, and releases it at one end of the row of apples, then the dog smells each apple one by one. Once the dog find an apple of type x, the dog picks the apple and back to Chef's room immidiately. If there is no apple of type x, then the dog will back without any apples.
Now Chef wants to eat two apples as soon as possible. Here the apples must have distinct types, and the sum of the types must be equal to K. Chef can release the dogs from either of the ends, namely, he can leave (both at left end) or (both at right end) or (one at left end and one at right end) and he can release them at the same time. The dogs take one second to smell each apple. However the dogs can run rapidly, so the time for moving can be ignored. What is the minimum time (in seconds) to get the desired apples from his dogs?

-----Input-----
The first line of input contains two space-separated integers N and K, denoting the number of apples and the required sum respectively. Then the next line contains N space-separated integers T1, T2, ..., TN, denoting the types of the apples.

-----Output-----
Print one integer describing the minimum number of seconds that Chef needs to wait till he gets the desired apples. If Chef cannot get the desired apples, then output "-1" without quotes.

-----Constraints-----
- 2 ≤ N ≤ 500000 (5 × 105)
- 1 ≤ K ≤ 1000000 (106)
- 1 ≤ Ti ≤ 1000000 (106)

-----Example-----
Sample Input 1:
5 5
2 4 3 2 1

Sample Output 1:
2

Sample Input 2:
5 5
2 4 9 2 5

Sample Output 2:
-1

-----Explanation-----
In the first example, if Chef leaves the first dog from left and gives it integer 4, and the second dog from right and gives it integer 1, then the first dog takes 2 seconds and the second dog takes 1 second to get the apples. Thus Chef needs to wait 2 seconds. In any other way, Chef can't get the desired apples in less than 2 seconds.
In the second example, Chef cannot get two apples such that the sum of their types is 5 so the answer is "-1".
user: Binod and his family live in Codingland. They have a festival called N-Halloween.
The festival is celebrated for N  consecutive days. On each day Binod gets some candies from his mother. He may or may not take them. On a given day ,  Binod will be sad if he collected candies on that day and he does not have at least X   candies remaining  from the candies he collected that day at the end of that day . His friend Pelu who is very fond of candies asks for X  candies from Binod on a day if Binod collects any candy on that day. He does so immediately after Binod collects them. Binod being a good friend never denies him.  

Given a list a   where ai   denotes the number of candies Binod may take on the ith   day and  Q  queries having a number X , find the maximum number of candies Binod can collect so that he won't be sad after the festival ends.
Input format: 

First-line contains two integers N and Q denoting the number of festival days and number of queries respectively.

The second line is the array whose ith   element is the maximum number of candies Binod may
collect on that day.

Each of the next Q lines contains the number X i.e the minimum number of candies Binod wants to have at the end of every day on which he collects any candy.
Output format: 

For every query output, a single integer denoting the max number of candies Binod may
collect (for the given X ) to be happy after the festival ends.
Constraints:  

1<=N,Q<=105  

1<=Q<=105  

0<=ai<=109  

0<=X<=109  

Sample Input : 

5 2

4 6 5 8 7

1

2

Sample Output : 

30

30

Sample Input:  

6 3 

20 10 12 3 30 5 

2 

6 

13 

Sample Output  

77 

62 

30 

Explanation: 

In the first query of sample input 1, Binod can collect the maximum number of given chocolates for a given day each day as after the end of every day Binod will have a number of collected
chocolates on that day greater than equal to 1 even after giving 1 chocolate to Pelu. So the
the answer is 4+6+5+8+7=30.
user: Devu has an array A consisting of N positive integers. He would like to perform following operation on array.

- Pick some two elements a, b in the array (a could be same as b, but their corresponding indices in the array should not be same).
Remove both the elements a and b and instead add a number x such that x lies between min(a, b) and max(a, b), both inclusive, (i.e. min(a, b) ≤ x ≤ max(a, b)).

Now, as you know after applying the above operation N - 1 times, Devu will end up with a single number in the array. He is wondering whether it is possible to do the operations in such a way that he ends up a number t. 

He asks your help in answering Q such queries, each of them will contain an integer t and you have to tell whether it is possible to end up t. 

-----Input-----
There is only one test case per test file.
First line of the input contains two space separated integers N, Q denoting number of elements in A and number of queries for which Devu asks your help, respectively
Second line contains N space separated integers denoting the content of array A.

Each of the next Q lines, will contain a single integer t corresponding to the query.

-----Output-----
Output Q lines, each containing "Yes" or "No" (both without quotes) corresponding to the answer of corresponding query.

-----Constraints-----
- 1 ≤ N, Q ≤ 105
- 0 ≤ t ≤ 109

-----Subtasks-----
Subtask #1 : 30 points
- 1 ≤ Ai ≤ 2

Subtask #2 : 70 points
- 1 ≤ Ai ≤ 109

-----Example-----
Input 1:
1 2
1
1
2

Output:
Yes
No

Input 2:
2 4
1 3
1
2
3
4

Output:
Yes
Yes
Yes
No

-----Explanation-----
In the first example, Devu can't apply any operation. So the final element in the array will be 1 itself. 

In the second example,
Devu can replace 1 and 3 with any of the numbers among 1, 2, 3. Hence final element of the array could be 1, 2 or 3.
user: Uppal-balu is busy in extraction of gold from ores. He got an assignment from his favorite professor MH sir, but he got stuck in a problem. Can you help Uppal-balu to solve the problem.
You are given an array $a_1$, $a_2$, $\dots$, $a_n$ of length $n$. You can perform the following operations on it:
- Choose an index $i$ ($1 \leq i \leq n$), and replace $a_i$ by $a_{i} + 1$ or $a_{i} - 1$, which means add or subtract one to the element at index $i$.
Beauty of the array is defined as maximum length of a subarray containing numbers which give same remainder upon dividing it by $k$ (that is, ($a_l$ mod $k$) = ($a_{l+1}$ mod $k$) = $\dots$ = ($a_r$ mod $k$) for some $1 \leq l \leq r \leq n$).
You need to calculate the beauty of the array $a_1$, $a_2$, $\dots$, $a_n$ after applying at most $m$ operations.
NOTE:
- The subarray of a is a contiguous part of the array $a$, i. e. the array $a_l$, $a_{l+1}$, $\dots$, $a_r$ for some $1 \leq l \leq r \leq n$.
- $x$ mod $y$ means the remainder of $x$ after dividing it by $y$.

-----Input:-----
- First line of input contains 3 integers $n$, $m$ and $k$.   
- The second line contains $n$ integers $a_1$, $a_2$, $\dots$, $a_n$.

-----Output:-----
Output in a single line the beauty of the array after applying at most m operations.

-----Constraints-----
- $1 \leq n,m \leq 2\cdot10^{5}$
- $1 \leq k \leq 7$
- $1 \leq a_i \leq 10^9$

-----Sample Input 1:-----
7 3 4

8 2 3 7 8 1 1    

-----Sample Output 1:-----
5

-----Sample Input 2:-----
8 3 5

7 2 1 3 6 5 6 2   

-----Sample Output 2:-----
5
user: Jack and Jill got into a serious fight. Jack didn't not belive Jill when she said that her memory was far better than the others. He asked her to prove it as follows :- 

-  Jack would dictate a long list of numbers to her. At any point after he has dictated  at least "k" numbers, he can ask her what is the k-th minimum number (the k-th number if the numbers are arranged in increasing order) in the list so far. 
-  She succeeds in proving herself if she can tell the k-th minimum number every time he asks. 
-  The number of queries (dictate a new number or ask her the k-th minimum of the numbers given till then) has to be pre-decided before he starts asking. 

Jill succeeded in proving herself by convincing Jack quite a few times. Now, Jill remembered that Jack had claimed that he was good at programming. It's her turn to ask him to prove his skill. Jack doesn't want to lose to her and comes to you for help. He asks you to make the program for him. 

-----Input-----
Jill has agreed to let Jack decide the format of the input and here's what he has decided. First line of the input contains n, the number of queries. Next line contains k. Next n lines contain a query each, say q. If  q >= 0  then the number is being 'dictated' to the system and needs to be remembered. If q = -1, then your program should return the k-th minimum number presented so far . It is given that 'q' can be -1 only if at least k numbers have already been given.

-----Output-----
For every q = -1, you have to output the k-th minimum number given as input so far (not counting -1 as an input)

-----Example-----
Input1:
6
2
3
2
-1
-1
1
-1

Output1:
3
3
2

Input2:
10
5
3
6
1
4
2
9
3
1
0
-1

Output2:
3
user: Given an array A of n non-negative integers. Find the number of ways to partition/divide the array into subarrays, such that  mex in each subarray is not more than k. For example, mex of the arrays [1, 2] will be 0, and that of [0, 2] will be 1, and that of [0, 1, 2] will be 3. Due to the fact that the answer can turn out to be quite large, calculate it modulo 109 + 7.

-----Input-----
- The first line of the input contains two integers n, k denoting the number of elements and limit of mex.
- The second line contains n space-separated integers A1, A2, ... , An .

-----Output-----
- Output a single integer corresponding to the answer of the problem.

-----Constraints-----
- 1 ≤ n ≤ 5 * 105
- 0 ≤ k, A[i] ≤ 109

-----Example-----
Input:
3 1
0 1 2

Output:
2

Input:
10 3
0 1 2 3 4 0 1 2 5 3

Output:
379

-----Explanation-----
Example 1. The valid ways of partitioning will be [[0], [1, 2]] (mex of first subarray is 1, while that of the second is zero), and [[0], [1], [2]] (mex of first subarray is 1, and that of others is 0). There is no other way to partition the array such that mex is less than or equal to 1. For example, [[0, 1], [2]] is not a valid partitioning as mex of first subarray is 2 which is more than 1.
user: Ayush is learning how to decrease a number by one, but he does it wrong with a number consisting of two or more digits. Ayush subtracts one from a number by the following algorithm:
if the last digit of the number is non-zero, he decreases the number by one.
if the last digit of the number is zero, he divides the number by 10.
You are given an integer number n
Ayush will subtract one from it k times. Your task is to print the result after all k subtractions.
It is guaranteed that the result will be a positive integer number.
Input
The first line of the input contains two integers n and k (2 ≤ n ≤ 10^9, 1 ≤ k ≤ 50) -- the number from which Ayush will subtract and the number of subtractions respectively.
Output
Print one integer number — the result of the decreasing n by one k times.
It is guaranteed that the result will be a positive integer number.
EXAMPLE
Sample Input 1
512 4
Sample Output 1
50
Sample Input 2
1000000000 9
Sample Output 2
1
user: You think you can code?

 This problem will test you on various basic programming techniques.

 You are given two integers $N$ and $t$; and then an array $A$ of $N$ integers ($0$-based indexing).

 Based on the value of $t$, you will perform an action on $A$.

$t$

Action Needed

$1$

Print $7$, regardless of the content of $A$

$2$

Print “Bigger” if $A[0] > A[1]$, or 

Print “Equal” if $A[0] == A[1]$, or 

Print “Smaller” otherwise (without the quotes); 

Ignore other indices of $A$, if any

$3$

Print the median of three integers {$A[0]$, $A[1]$, and $A[2]$}; 

Ignore other indices of $A$, if any

$4$

Print the sum of all integers in $A$

$5$

Print the sum of all even integers in $A$

$6$

Apply modulo (%) $26$ to each integer in $A$, 

Map integer $0$/$1$/$\ldots $/$25$ to character ‘a’/‘b’/$\ldots $/‘z’, 

Finally, print the sequence of characters as a string (without the spaces)

$7$

a. Start from index $i = 0$; 

b. Jump to index $i = A[i]$; 

c. If the current index $i$ is outside the valid bound of [0..$N$-1], print “Out” and stop; 

d. Else if the current index $i$ is index $N$-$1$, print “Done” and stop; 

e1. Otherwise, repeat step b; 

e2. If doing this leads to an infinite loop, print “Cyclic” and stop; 

(all output are without the quotes)

-----Input-----
The first line of the input contains an integer $N$ and $t$ ($3 \leq N \leq 200000$; $1 \leq t \leq 7$).

 The second line of the input contains $N$ non-negative $32$-bit signed integers.

-----Output-----
For each test case, output the required answer based on the value of $t$.

-----Scoring-----
There are $20$ hidden test cases that test various requirements of this problem.

 All $20$ test cases will be tested.

 Each hidden test case worth $5$ points (the $7$ sample test cases below worth $0$ point).

-----Examples-----
Sample Input 1:
7 1
1 2 3 4 5 6 7
Sample Output 1:
7

Sample Input 2:
7 2
1 2 3 4 5 6 7
Sample Output 2:
Smaller

Sample Input 3:
7 3
1 2 3 4 5 6 7
Sample Output 3:
2

Sample Input 4:
7 4
1 2 3 4 5 6 7
Sample Output 4:
28

Sample Input 5:
7 5
1 2 3 4 5 6 7
Sample Output 5:
12

Sample Input 6:
10 6
7 4 11 37 14 22 40 17 11 3
Sample Output 6:
helloworld
user: In the country there are n cities and m bidirectional roads between them. Each city has an army. Army of the i-th city consists of a_{i} soldiers. Now soldiers roam. After roaming each soldier has to either stay in his city or to go to the one of neighboring cities by at moving along at most one road.

Check if is it possible that after roaming there will be exactly b_{i} soldiers in the i-th city.


-----Input-----

First line of input consists of two integers n and m (1 ≤ n ≤ 100, 0 ≤ m ≤ 200).

Next line contains n integers a_1, a_2, ..., a_{n} (0 ≤ a_{i} ≤ 100).

Next line contains n integers b_1, b_2, ..., b_{n} (0 ≤ b_{i} ≤ 100).

Then m lines follow, each of them consists of two integers p and q (1 ≤ p, q ≤ n, p ≠ q) denoting that there is an undirected road between cities p and q. 

It is guaranteed that there is at most one road between each pair of cities.


-----Output-----

If the conditions can not be met output single word "NO".

Otherwise output word "YES" and then n lines, each of them consisting of n integers. Number in the i-th line in the j-th column should denote how many soldiers should road from city i to city j (if i ≠ j) or how many soldiers should stay in city i (if i = j).

If there are several possible answers you may output any of them.


-----Examples-----
Input
4 4
1 2 6 3
3 5 3 1
1 2
2 3
3 4
4 2

Output
YES
1 0 0 0 
2 0 0 0 
0 5 1 0 
0 0 2 1 

Input
2 0
1 2
2 1

Output
NO
user: While exploring the old caves, researchers found a book, or more precisely, a stash of mixed pages from a book. Luckily, all of the original pages are present and each page contains its number. Therefore, the researchers can reconstruct the book.

After taking a deeper look into the contents of these pages, linguists think that this may be some kind of dictionary. What's interesting is that this ancient civilization used an alphabet which is a subset of the English alphabet, however, the order of these letters in the alphabet is not like the one in the English language.

Given the contents of pages that researchers have found, your task is to reconstruct the alphabet of this ancient civilization using the provided pages from the dictionary.


-----Input-----

First-line contains two integers: $n$ and $k$ ($1 \le n, k \le 10^3$) — the number of pages that scientists have found and the number of words present at each page. Following $n$ groups contain a line with a single integer $p_i$ ($0 \le n \lt 10^3$) — the number of $i$-th page, as well as $k$ lines, each line containing one of the strings (up to $100$ characters) written on the page numbered $p_i$.


-----Output-----

Output a string representing the reconstructed alphabet of this ancient civilization. If the book found is not a dictionary, output "IMPOSSIBLE" without quotes. In case there are multiple solutions, output any of them.


-----Example-----
Input
3 3
2
b
b
bbac
0
a
aca
acba
1
ab
c
ccb

Output
acb
user: Yura is tasked to build a closed fence in shape of an arbitrary non-degenerate simple quadrilateral. He's already got three straight fence segments with known lengths $a$, $b$, and $c$. Now he needs to find out some possible integer length $d$ of the fourth straight fence segment so that he can build the fence using these four segments. In other words, the fence should have a quadrilateral shape with side lengths equal to $a$, $b$, $c$, and $d$. Help Yura, find any possible length of the fourth side.

A non-degenerate simple quadrilateral is such a quadrilateral that no three of its corners lie on the same line, and it does not cross itself.


-----Input-----

The first line contains a single integer $t$ — the number of test cases ($1 \le t \le 1000$). The next $t$ lines describe the test cases.

Each line contains three integers $a$, $b$, and $c$ — the lengths of the three fence segments ($1 \le a, b, c \le 10^9$).


-----Output-----

For each test case print a single integer $d$ — the length of the fourth fence segment that is suitable for building the fence. If there are multiple answers, print any. We can show that an answer always exists.


-----Example-----
Input
2
1 2 3
12 34 56

Output
4
42



-----Note-----

We can build a quadrilateral with sides $1$, $2$, $3$, $4$.

We can build a quadrilateral with sides $12$, $34$, $56$, $42$.
user: The gaming company Sandstorm is developing an online two player game. You have been asked to implement the ranking system. All players have a rank determining their playing strength which gets updated after every game played. There are $25$ regular ranks, and an extra rank, “Legend”, above that. The ranks are numbered in decreasing order, $25$ being the lowest rank, $1$ the second highest rank, and Legend the highest rank. 

Each rank has a certain number of “stars” that one needs to gain before advancing to the next rank. If a player wins a game, she gains a star. If before the game the player was on rank $6$-$25$, and this was the third or more consecutive win, she gains an additional bonus star for that win. When she has all the stars for her rank (see list below) and gains another star, she will instead gain one rank and have one star on the new rank.

For instance, if before a winning game the player had all the stars on her current rank, she will after the game have gained one rank and have $1$ or $2$ stars (depending on whether she got a bonus star) on the new rank. If on the other hand she had all stars except one on a rank, and won a game that also gave her a bonus star, she would gain one rank and have $1$ star on the new rank.

If a player on rank $1$-$20$ loses a game, she loses a star. If a player has zero stars on a rank and loses a star, she will lose a rank and have all stars minus one on the rank below. However, one can never drop below rank $20$ (losing a game at rank $20$ with no stars will have no effect).

If a player reaches the Legend rank, she will stay legend no matter how many losses she incurs afterwards.

The number of stars on each rank are as follows:
 - Rank $25$-$21$: $2$ stars
 - Rank $20$-$16$: $3$ stars
 - Rank $15$-$11$: $4$ stars
 - Rank $10$-$1$: $5$ stars

A player starts at rank $25$ with no stars. Given the match history of a player, what is her rank at the end of the sequence of matches?

-----Input-----
The input consists of a single line describing the sequence of matches. Each character corresponds to one game; ‘W’ represents a win and ‘L’ a loss. The length of the line is between $1$ and $10000$ characters (inclusive).

-----Output-----
Output a single line containing a rank after having played the given sequence of games; either an integer between $1$ and $25$ or “Legend”.

-----Examples-----
Sample Input 1:
WW
Sample Output 1:
25

Sample Input 2:
WWW
Sample Output 2:
24

Sample Input 3:
WWWW
Sample Output 3:
23

Sample Input 4:
WLWLWLWL
Sample Output 4:
24

Sample Input 5:
WWWWWWWWWLLWW
Sample Output 5:
19
user: You are given an undirected unweighted graph consisting of $n$ vertices and $m$ edges.

You have to write a number on each vertex of the graph. Each number should be $1$, $2$ or $3$. The graph becomes beautiful if for each edge the sum of numbers on vertices connected by this edge is odd.

Calculate the number of possible ways to write numbers $1$, $2$ and $3$ on vertices so the graph becomes beautiful. Since this number may be large, print it modulo $998244353$.

Note that you have to write exactly one number on each vertex.

The graph does not have any self-loops or multiple edges.


-----Input-----

The first line contains one integer $t$ ($1 \le t \le 3 \cdot 10^5$) — the number of tests in the input.

The first line of each test contains two integers $n$ and $m$ ($1 \le n \le 3 \cdot 10^5, 0 \le m \le 3 \cdot 10^5$) — the number of vertices and the number of edges, respectively. Next $m$ lines describe edges: $i$-th line contains two integers $u_i$, $ v_i$ ($1 \le u_i, v_i \le n; u_i \neq v_i$) — indices of vertices connected by $i$-th edge.

It is guaranteed that $\sum\limits_{i=1}^{t} n \le 3 \cdot 10^5$ and $\sum\limits_{i=1}^{t} m \le 3 \cdot 10^5$.


-----Output-----

For each test print one line, containing one integer — the number of possible ways to write numbers $1$, $2$, $3$ on the vertices of given graph so it becomes beautiful. Since answers may be large, print them modulo $998244353$.


-----Example-----
Input
2
2 1
1 2
4 6
1 2
1 3
1 4
2 3
2 4
3 4

Output
4
0



-----Note-----

Possible ways to distribute numbers in the first test:   the vertex $1$ should contain $1$, and $2$ should contain $2$;  the vertex $1$ should contain $3$, and $2$ should contain $2$;  the vertex $1$ should contain $2$, and $2$ should contain $1$;  the vertex $1$ should contain $2$, and $2$ should contain $3$. 

In the second test there is no way to distribute numbers.
user: We have a sequence of length N consisting of non-negative integers. Consider performing the following operation on this sequence until the largest element in this sequence becomes N-1 or smaller.
 - Determine the largest element in the sequence (if there is more than one, choose one). Decrease the value of this element by N, and increase each of the other elements by 1.
It can be proved that the largest element in the sequence becomes N-1 or smaller after a finite number of operations.
You are given an integer K. Find an integer sequence a_i such that the number of times we will perform the above operation is exactly K. It can be shown that there is always such a sequence under the constraints on input and output in this problem.

-----Constraints-----
 - 0 ≤ K ≤ 50 \times 10^{16}

-----Input-----
Input is given from Standard Input in the following format:
K

-----Output-----
Print a solution in the following format:
N
a_1 a_2 ... a_N

Here, 2 ≤ N ≤ 50 and 0 ≤ a_i ≤ 10^{16} + 1000 must hold.

-----Sample Input-----
0

-----Sample Output-----
4
3 3 3 3