meetforever/GRPO_CL huggingface dataset:
user: Tic-Tac-Toe used to be Chef's favourite game during his childhood. Reminiscing in his childhood memories, he decided to create his own "Tic-Tac-Toe", with rules being similar to the original Tic-Tac-Toe, other than the fact that it is played on an NxN board.

The game is played between two players taking turns. First player puts an 'X' in an empty cell of the board, then the second player puts an 'O' in some other free cell. If the first player has K continuous X's or the second player has K continuous O's in row, column or diagonal, then he wins.

Chef started playing this new "Tic-Tac-Toe" with his assistant, beginning as the first player himself (that is, Chef plays 'X's). Currently, the game is ongoign, and it's Chef's turn. However, he needs to leave soon to begin tonight's dinner preparations, and has time to play only one more move. If he can win in one move, output "YES", otherwise output "NO" (without quotes). It is guaranteed that no player has already completed the winning criterion before this turn, and that it's a valid "Tic-Tac-Toe" game.

-----Input-----
The first line of input contains one integer T denoting the number of testcases. First line of each testcase contains two integers N and K, next N lines contains N characters each. Each character is either an 'X' denoting that the first player used this cell, an 'O' meaning that the second player used this cell, or a '.' (a period) representing a free cell.

-----Output-----
For each testcase, output, in a single line, "YES" if Chef can win in one move, or "NO" otherwise.

-----Constraints-----
- 1 ≤ T ≤ 100
- 3 ≤ N ≤ 20
- 1 ≤ K ≤ N

-----Example-----
Input:
3
3 3
XOX
O.O
XOX
3 1
...
...
...
3 2
...
...
...

Output:
YES
YES
NO

Input:
1
4 4
XOXO
OX..
XO..
OXOX

Output:
YES

-----Subtasks-----
- Subtask 1:  K  = 1. Points - 10
- Subtask 2:  N  =  K  = 3. Points - 30
- Subtask 3: Original constraints. Points - 60

-----Explanation-----
Test #1:

In first testcase, put 'X' in (2, 2), in second we can put 'X' in any cell and win. 
Test #2:

If you put an 'X' in (3, 3), there will be four 'X's on the main diagonal (1, 1) - (2, 2) - (3, 3) - (4, 4).
user: As we all know, a palindrome is a word that equals its reverse. Here are some examples of palindromes: malayalam, gag, appa, amma.
We consider any sequence consisting of the letters of the English alphabet to be a word. So axxb,abbba and bbbccddx are words for our purpose. And aaabbaaa, abbba and bbb are examples of palindromes.
By a subword of a word, we mean a contiguous subsequence of the word. For example the subwords of the word abbba are a, b, ab, bb, ba, abb, bbb, bba, abbb, bbba and abbba.
In this task you will given a word and you must find the longest subword of this word that is also a palindrome.
For example if the given word is abbba then the answer is abbba. If the given word is abcbcabbacba then the answer is bcabbacb.

-----Input:-----
The first line of the input contains a single integer $N$ indicating the length of the word. The following line contains a single word of length $N$, made up of the letters a,b,…, z.

-----Output:-----
The first line of the output must contain a single integer indicating the length of the longest subword of the given word that is a palindrome. The second line must contain a subword that is a palindrome and which of maximum length. If there is more than one subword palindrome of maximum length, it suffices to print out any one.

-----Constraints:-----
- $1 \leq N \leq 5000$. 
- You may assume that in $30 \%$ of the inputs $1 \leq N \leq 300$.

-----Sample Input 1:-----
5
abbba

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

-----Sample Input 2:-----
12
abcbcabbacba

-----Sample Output 2:-----
8
bcabbacb
user: You are given a string S  of numbers. Dr. Dragoon has eaten up some numbers of the string. You decide to fix the string by putting the numbers 0 and 1 in the empty spaces. 
The base cost for putting the ‘0’  is x  and putting ‘1’  is y . The cost of putting a number is the base cost multiplied by the number of times you use the letter till  that position (including   the position ).  The local mayor is happy with your work and commissions you for every number you put. 

More specifically ,  if you put , say 0  in 5th position, the mayor will count the number of occurrences of 0  till 5th   position and pay you the same amount. You wonder what the minimum cost for fixing the string is. Note  – The answer can also be negative, they denote that you got an overall profit.

Input Format: 

The input consists of 2 lines. First-line consists of the string of numbers S. ‘?’  denotes an empty position. 

The second line consists of 2 integers x,y, the base cost of 0 and 1. 

Output Format:  

Output 1 integer, the minimum cost of fixing the string.

Constraints :  

1<=|S|<=100

1<=x,y<=100 

Sample Input:  

501?1?

6 5

Sample Output:  

6

Sample Input:  

1001?11?

5  23

Sample Output:  

8

Explanation  :  

Fill 0 in the first place, the net cost will be 6-2=4. In the second place fill, 1 the net cost will be 5-3=2 Hence total cost is 4+2=6. 

In second test case we will fill both spaces with zero , filling first zero costs  1*5-3=2 and filling the other zero costs  2*5  - 4 =6  , so total being 8.
user: Knights' tournaments were quite popular in the Middle Ages. A lot of boys were dreaming of becoming a knight, while a lot of girls were dreaming of marrying a knight on a white horse.

In this problem we consider one of these tournaments. 

Let's us call a tournament binary, if it runs according to the scheme described below:

- Exactly N knights take part in the tournament, N=2K for some integer K > 0.
		
- Each knight has a unique skill called strength, described as an integer from the interval [1, N].
		
- Initially, all the knights are standing in a line, waiting for a battle. Since all their strengths are unique, each initial configuration can be described as a permutation of numbers from 1 to N.
		
- There are exactly K rounds in the tournament, 2K - i + 1 knights take part in the i'th round. The K'th round is called the final.
		
- The i'th round runs in the following way: for each positive integer j ≤ 2K - i happens a battle between a knight on the 2∙j'th position and a knight on the 2∙j+1'th position. The strongest of two continues his tournament, taking the j'th position on the next round, while the weakest of two is forced to leave.
		
- The only knight, who has won K rounds, is the winner. The only knight, who has won K - 1 rounds, but lost the final, is the runner-up.   
	

As you can see from the scheme, the winner is always the same, an initial configuration doesn't change anything. So, your task is to determine chances of each knight to appear in the final.

Formally, for each knight you need to count the number of initial configurations, which will lead him to the final. Since the number can be extremly huge, you are asked to do all the calculations under modulo 109 + 9.

-----Input-----

The first line contains the only integer K, denoting the number of rounds of the tournament.

-----Output-----
Output should consist of 2K lines. The i'th line should contain the number of initial configurations, which lead the participant with strength equals to i to the final.

-----Constraints-----
1 ≤ K < 20


-----Examples-----
Input:
1

Output:
2
2

Input:
2

Output:
0
8
16
24

-----Explanation-----

In the first example we have N=2 knights. Let's consider each initial configuration that could appear and simulate the tournament.

(1, 2) -> (2)

(2, 1) -> (2)

In the second example we have N=4 knights. Let's consider some initial configurations that could appear and simulate the tournament.

(1, 2, 3, 4) -> (2, 4) -> (4)

(3, 2, 4, 1) -> (3, 4) -> (4)

(4, 1, 3, 2) -> (4, 3) -> (4)
user: We consider permutations of the numbers $1,..., N$ for some $N$. By permutation we mean a rearrangment of the number $1,...,N$. For example
24517638245176382 \quad 4 \quad 5 \quad 1 \quad 7 \quad 6 \quad 3 \quad 8
is a permutation of $1,2,...,8$. Of course,
12345678123456781 \quad 2 \quad 3 \quad 4 \quad 5 \quad 6 \quad 7 \quad 8
is also a permutation of $1,2,...,8$.
We can "walk around" a permutation in a interesting way and here is how it is done for the permutation above:
Start at position $1$. At position $1$ we have $2$ and so we go to position $2$. Here we find $4$ and so we go to position $4$. Here we find $1$, which is a position that we have already visited. This completes the first part of our walk and we denote this walk by  ($1$ $2$ $4$ $1$). Such a walk is called a cycle. An interesting property of such walks, that you may take for granted, is that the position we revisit will always be the one we started from!
We continue our walk by jumping to first unvisited position, in this case position $3$ and continue in the same manner. This time we find $5$ at position $3$ and so we go to position $5$ and find $7$ and we go to position $7$ and find $3$ and thus we get the cycle ($3$ $5$ $7$ $3$). Next we start at position $6$ and get ($6$ $6$), and finally we start at position $8$ and get the cycle ($8$ $8$). We have exhausted all the positions. Our walk through this permutation consists of $4$ cycles.
One can carry out this walk through any permutation and obtain a set of cycles as the result. Your task is to print out the cycles that result from walking through a given permutation.

-----Input:-----
The first line of the input is a positive integer $N$ indicating the length of the permutation. The next line contains $N$ integers and is a permutation of $1,2,...,N$.

-----Output:-----
The first line of the output must contain a single integer $k$ denoting the number of cycles in the permutation. Line $2$ should describe the first cycle, line $3$ the second cycle and so on and line $k+1$ should describe the $k^{th}$ cycle.

-----Constraints:-----
- $1 \leq N \leq 1000$.

-----Sample input 1:-----
8
2 4 5 1 7 6 3 8

-----Sample output 1:-----
4
1 2 4 1
3 5 7 3
6 6
8 8 

-----Sample input 2:-----
8
1 2 3 4 5 6 7 8

-----Sample output 2:-----
8
1 1
2 2
3 3
4 4
5 5
6 6
7 7
8 8
user: $Riggi$   is a spy of $KBI$ and he is on a secret mission, he is spying an Underworld Don  $Anit$.
$Riggi$  is spying him since 5 years and he is not able to find  any evidence against $Anit$. 
$KBI$ told $Riggi$ they will send him a code string in a special format that will inform him whether he  has continue or return back from mission.
According to $KBI$  firstly  he  has to find what is the original string and then he has to check string is palindrome or not .
If its a palindrome then he has to leave the mission and return back else continue spying $Anit$. 
Rules to find original string :
1:-If in Code string any integer(N) followed by a string of alphabets that starts with '+' and  ends with '-' then he has to repeat that string N times  , like 3+acg- = acgacgacg.
2:-If there is no integer present before string then print the string is repeated 1 time.
like bc=bc.
Example of conversion from  Code string  to original string  : 2+ac-3+kb-j=acackbkbkbj  

-----Input:-----
- Code string $S$ is taken as input  .

-----Output:-----
- Print  string $Continue$ if code string $S$ is not a palindrome else print $Return$ .

-----Constraints-----
- $1 \leq S \leq 1000$
- $1 \leq N \leq 1000$

-----Sample Input 1:-----
3+xy-bb3+yx-

-----Sample Output 1:-----
Return

-----Sample Input 2:-----
3+xy-bb3+xy-

-----Sample Output 2:-----
Continue

-----EXPLANATION:-----
Sample 1:- original string will be xyxyxybbyxyxyx which is  a palindrome hence print $Return$.
Sample 2:- original string will be xyxyxybbxyxyxy which is not a palindrome hence print 
$Continue$.
user: Alisha has a string of length n. Each character is either 'a', 'b' or 'c'. She has to select two characters s[i] and s[j] such that s[i] != s[j] and i,j are valid indexes. She has to find the maximum value of the absolute difference between i and j i.e abs(i-j) .
Since Alisha is busy with her Semester exams help her find the maximum distance where distance is the maximum value of absolute difference between i and j  i.e abs(i-j) .

-----Input:-----
- The first and the only line contains the string s with each character either 'a', 'b', or 'c'. 

-----Output:-----
Print a single integer the maximum absolute difference between i and j. 

-----Constraints-----
- $1 \leq n \leq 10^5$
- s[i] can either be 'a', 'b' or 'c'.

-----Subtasks-----
- 40 points : $1 \leq n \leq 100$
- 60 points : $1 \leq n \leq 10^5$

-----Sample Input1:-----
aabcaaa

-----Sample Output1:-----
4

-----Sample Input2:-----
aba

-----Sample Output2:-----
1
user: Tim buy a string of  length N from his friend which consist of  ‘d’ and ‘u’ letters only
,but now Tim wants to sell the string at maximum cost.  
The maximum cost of string is defined as the maximum length of a Substring (consecutive subsequence) consisting of equal letters.
Tim can change at most P characters of string (‘d’ to ‘u’   and   ‘u’ to ‘d’) you have to find out the maximum cost of string?

-----Input:-----
- First line will contain $N$ and $P$ .
- Second line will contain the String $S$.

-----Output:-----
Maximum cost of string S.

-----Constraints-----
- $1 \leq N\leq 10^5$
- $0 \leq P \leq N$

-----Sample Input 1:-----
4  2
$duud$

-----Sample Output 1:-----
4

-----Sample Input 2 :-----
10 1
$dduddudddu$

-----Sample Output 2:-----
6

-----EXPLANATION:-----
In the first sample input , We can obtain both strings $dddd$ and $uuuu$ .
In the second sample, the optimal answer is obtained with the string $dddddudd$ or with the string $dduddddd$
user: Chef is baking delicious cookies today! Since Chef is super hungry, he wants to eat at least $N$ cookies.
Since Chef is a messy eater, he drops a lot of crumbs. Crumbs of $B$ cookies can be put together to make a new cookie! 
Given $N$ and $B$, help Chef find out the minimum number of cookies he must initially bake, $A$, to satisfy his hunger.

-----Input:-----
- First line will contain $T$, number of testcases. Then the testcases follow. 
- Each testcase contains of  two space separated integers $N, B$. 

-----Output:-----
For each test case, print a single integer $A$, the minimum number of cookies Chef must bake initially.

-----Constraints-----
- $1 \leq T \leq 1000$
- $1 \leq N \leq 1000000000$
- $2 \leq B \leq 1000000000$

-----Sample Input 1:-----
1
3 2

-----Sample Output 1:-----
2

-----Sample Input 2:-----
1
11 2

-----Sample Output 2:-----
6

-----Explanation 2:-----
Chef initially make 6 cookies. From the crumbs, Chef makes 3 new cookies with no crumbs left over. From the crumbs of the new cookies, Chef makes 1 new cookie and have crumbs left from one cookie. From the new cookie, Chef gets more crumbs. He adds the crumbs and gets one last cookie. After eating that, there are not enough crumbs left to make a new cookie. So a total of 11 cookies are consumed!
user: This is a rather simple problem to describe. You will be given three numbers $S, P$ and $k$. Your task is to find if there are integers $n_1, n_2,...,n_k$ such that $n_1 + n_2 +...+ n_k = S$, $n_1 \cdot n_2 \cdot ... \cdot n_k = P$. If such integers exist, print them out. If no such sequence of integers exist, then print "NO".
For example if $S=11, P=48$ and $k=3$ then $3, 4$ and $4$ is a solution. On the other hand, if $S=11, P=100$ and $k=3$, there is no solution and you should print "NO".

-----Input:-----
A single line with three integers $S, P$ and $k$.

-----Output:-----
A single word "NO" or a seqence of $k$ integers $n_1, n_2,..., n_k$ on a single line. (The $n_i$'s must add up to $S$ and their product must be $P$).

-----Constraints:-----
- $1 \leq k \leq 4$.
- $1 \leq S \leq 1000$.
- $1 \leq P \leq 1000$.

-----Sample input 1:-----
11 48 3

-----Sample output 1:-----
3 4 4 

-----Sample input 2:-----
11 100 3

-----Sample output 2:-----
NO
user: Gotham City is again under attack. This time Joker has given an open challenge to solve the following problem in order to save Gotham. Help Batman in protecting Gotham by solving the problem.
You are given two strings A and B composed of lowercase letters of Latin alphabet. B can be obtained by removing some characters from A(including 0). You are given an array containing any random permutation of numbers $1$ to $N$, where $N$ is the length of the string A. You have to remove the letters of A in the given order of indices. Note that after removing one letter, the indices of other letters do not change. Return the maximum number of indices you can remove in the given order such that B is still obtainable from A.

-----Input:-----
- First two lines contains the strings A and B respectively.
- The third line contains a random permutation of numbers from $1$ to $N$ representing some order of indices of string A.

-----Output:-----
Print a single number denoting the maximum number of indices you can remove in the given order such that B is still obtainable from A.

-----Constraints-----
- $1 \leq |B| \leq |A| \leq 200000$

-----Sample Input #1:-----
xxyxxy
xyy
1 5 4 6 3 2

-----Sample Output #1:-----
3

-----Sample Input #2:-----
jphokenixr
joker
2 9 3 7 8 1 6 5 4 10

-----Sample Output #2:-----
5

-----EXPLANATION:-----
For the first example removing characters in order,
xxyxxy => _xyxxy => _xyx_y => _xy__y.
If we remove any other element now then we can not obtain 'xxy'. So the ans is 3.
user: Every year the professor selects the top two students from his class and takes them on a fun filled field trip, this year Ali and Zafar were selected.
The professor took them to a place where there was a never-ending queue of solid metal cubes. The professor could see $n$ cubes at a time. On the day before, he had painted the first $n$ cubes from the left with various colours.
Ali was allowed to choose any painted cube to initially stand on (say $X$). Zafar was asked to stand on the last painted cube (the $n^{th}$ cube) with the professor.
The two students were given an activity each:
- Ali had to shout out the colour of the cube he is standing on.
- Zafar had to paint the adjacent cube on the right of him with that colour.
Both Ali and Zafar had to take one step to the right each time they performed their activity.
The Professor jumped along with Zafar, and never left his side. Throughout the activity he was looking leftwards keeping an eye on Ali. They were given a gold star and were allowed to go home when all the cubes that the professor could see at the time were painted with the same color.
Ali wanted to choose a position furthest from the professor and also wanted the gold star.
Can you help Ali to choose this position $X$?
The cubes are numbered from 1 starting from the first painted cube.
The colours are represented as integers.

-----Input:-----
- The first line contains one integer n, the number of cubes initially painted.
- The second line contains n space-separated integers: $a_1$, $a_2$, $\dots$, $a_n$, the colours the professor chose for the first $n$ cubes.

-----Output:-----
Print a single line containing one integer $X$, the position Ali should initially stand on.

-----Constraints-----
- $1 \leq n \leq 10^{6}$
- $0 \leq a_i \leq 999$

-----Sample Input 1:-----
4

3 3 8 8   

-----Sample Output 1:-----
3

-----Sample Input 2:-----
4

2 8 7 3

-----Sample Output 2:-----
4
user: A greek once sifted some numbers. And it did something wonderful!

-----Input:-----
- First line will contain an integer $N$

-----Output:-----
Output in a single line answer to the problem.

-----Constraints-----
- $1 \leq N \leq 10^5$

-----Sample Input 1:-----
10

-----Sample Output 1:-----
4

-----Sample Input 2:-----
20

-----Sample Output 2:-----
8
user: Chef loves cooking. Also, he is very hygienic. Hence, Chef grows his own vegetables in his mini kitchen garden. He has $M$ lanes in which he grows vegetables. The $ith$  lane has $Ai$ vegetables growing in it.

Vegetables in $ith$ lane become edible on day $Di$ and day $Di+1$(that is, the vegetables are edible only on days $Di$ and $Di+1$,where $Di+1$ is the next day of $Di$).   For Example, if $Di$ is 2, then vegetable is edible on day 2 and day 3 only.   If not collected in these days, they cannot be cooked.

Also, Chef is a lone worker. Hence, with respect to his capacity, he can collect only $V$ vegetables per day.
But, Chef is a hard worker, and is willing to work every day, starting from day 1.

Chef is busy sowing the seeds. So, he assigns you the task to find out the maximum number of vegetables he can collect, provided that he collects optimally.

-----Input:-----
- First line contains of 2 space separated integers $M$ and $V$, number of lanes and capacity of Chef.
- Next $M$ lines follow
- Each $ith$ line contains 2 space separated integers, $Di$ and $Ai$, the day when the vegetable of the $ith$ lane become edible and the number of vegetables in that lane.

-----Output:-----
For each testcase, output in a single integer, that is the maximum number of vegetables that can be cooked

-----Constraints-----
- $1 \leq M,V \leq 3000$
- $1 \leq Di,Ai \leq 3000$

-----Subtasks-----
- 20 points : $1 \leq M \leq 100$
- 30 points : $1 \leq M \leq 1000$
- 50 points : $Original  Constraints$

-----Sample Input 1:-----
2 4
1 6
2 5

-----Sample Output 1:-----
11

-----Sample Input 2:-----
3 3
1 4
6 2
5 3

-----Sample Output 2:-----
9

-----EXPLANATION:-----
In the first sample, in order to obtain the optimal answer, you should do the following:-
- On day 1, collect 4 vegetables from lane 1
- On day 2, collect 2 vegetables from lane 1 and 2 vegetables from lane 2
- On day 3, collect 3 vegetables from lane 2
In the first sample, in order to obtain the optimal answer, you should do the following:-
- On day 1, collect 3 vegetables from lane 1
- On day 2, collect 1 vegetable from lane 1
- On day 5, collect 3 vegetables from lane 3
- On day 6, collect 2 vegetables from lane 2
user: Rashmi loves the festival of Diwali as she gets to spend time with family and enjoy the festival. Before she can fully enjoy the festival she needs to complete the homework assigned by her teacher. Since Rashmi is smart , she has solved all the problems but is struck at one tricky pattern question.
Your Task is to help Rashmi solve the problem so that she can enjoy the festival with her family.
The Problem she is struck on is defined like this:
Given an integer N you need to generate the pattern according to following example:
Example:

Input:

3  
Output:

1 4 10

2 5 11

4 10 22

3 6 12  

-----Input:-----
The first line of the input contains a single integer T denoting the number of test cases. The description of T test cases follows.
The next line of each contains T space separated integers N.

-----Output:-----
For each N print the required pattern.

-----Constraints:-----
$1 \leq T \leq 10^5$
$1 \leq N \leq 30$

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

-----Sample Output:-----
1 4 10

2 5 11

4 10 22

3 6 12

1 4 10 22 46

2 5 11 23 47

4 10 22 46 94

3 6 12 24 48  

-----Sample Input:-----
1

4  

-----Sample Output:-----
1 4 10 22

2 5 11 23

4 10 22 46

3 6 12 24
user: Chef likes inequalities. Please help him to solve next one.
Given four integers a, b, c, d. Find number of solutions x < y, where a ≤ x ≤ b and c ≤ y ≤ d and x, y integers.

-----Input-----
The first line contains an integer T denoting number of tests.
First line of each test case contains four positive integer numbers a, b, c and d.

-----Output-----
For each test case, output a single number each in separate line denoting number of integer solutions as asked in the problem.

-----Constraints-----
- 1 ≤ T ≤ 20 
- 1 ≤ a, b, c, d ≤ 106 

-----Subtasks-----
- Subtask #1: (30 points)  1 ≤ a, b, c, d ≤ 103.
- Subtask #2: (70 points)  Original constraints.

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

Output:3

Input:1
2 999999 1 1000000

Output:499998500001