meetforever/GRPO_CL huggingface dataset:
user: Chef has  $N$ boxes arranged in a line.Each box has some candies in it,say $C[i]$. Chef wants to distribute all the candies between of his friends: $A$ and $B$, in the following way:
$A$ starts eating candies kept in the leftmost box(box at $1$st place) and $B$ starts eating candies kept in the rightmost box(box at $N$th place). $A$ eats  candies $X$ times faster than $B$ i.e. $A$ eats $X$ candies when $B$ eats only $1$. Candies in each box can be eaten by only the person who reaches that box first. If both reach a box at the same time, then the one who has eaten from more number of BOXES till now will eat the candies in that box. If both have eaten from the same number of boxes till now ,then $A$ will eat the candies in that box.
Find the number of boxes finished by both $A$ and $B$.
NOTE:- We assume that it does not take any time to switch from one box to another.

-----Input:-----
- First line will contain $T$, number of testcases. Then the testcases follow. 
- Each testcase contains three lines of input.
The first line of each test case contains $N$, the number of boxes.
- The second line of each test case contains a sequence,$C_1$ ,$C_2$ ,$C_3$ . . . $C_N$ where $C_i$ denotes the number of candies in the i-th box.  
- The third line of each test case contains an integer $X$ .

-----Output:-----
For each testcase, print two space separated integers in a new line - the number of boxes eaten by $A$  and  $B$ respectively. 

-----Constraints-----
- $1 \leq T \leq 100$
- $1 \leq N \leq 200000$
- $1 \leq C_i \leq 1000000$
- $1 \leq X \leq 10$
- Sum of $N$ over all test cases does not exceed $300000$

-----Subtasks-----
Subtask 1(24 points):
- $1 \leq T \leq 10$
- $1 \leq N \leq 1000$
- $1 \leq C_i \leq 1000$
- $1 \leq X \leq 10$
Subtask 2(51 points): original constraints

-----Sample Input:-----
1
5
2 8 8 2 9
2

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

-----EXPLANATION:-----
$A$ will start eating candies in the 1st box(leftmost box having 2 candies) . $B$ will start eating candies in the  5th box(rightmost box having 9 candies) .As $A's$ speed is 2 times as that of $B's$, $A$ will start eating candies in the  2nd box while $B$ would still be eating candies in the 5th box.$A$ will now start eating candies from the 3rd box while $B$ would still be eating candies in the 5th box.Now both $A$ and $B$ will finish candies in their respective boxes at the same time($A$ from the 3rd box and $B$ from 5th box). Since $A$ has eaten more number of boxes($A$ has eaten 3 boxes while $B$ has eaten 1 box) till now,so $A$ will be eating candies in the 4th box.
Hence $A$ has eaten 4 boxes and $B$ has eaten 1 box.
user: You have a sequence $a$ with length $N$ created by removing some elements (possibly zero) from a permutation of numbers $(1, 2, \dots, N)$. When an element is removed, the length of the sequence doesn't change, but there is an empty spot left where the removed element was. You also have an integer $K$.
Let's call a permutation $p_1, p_2, \dots, p_N$ good if:
- it is possible replace empty spots in $a$ by numbers in such a way that we obtain the permutation $p$
- the number of positions $i$ ($1 < i \le N$) such that $p_i > p_{i-1}$ is equal to $K$
Your task is to find the number of good permutations.

-----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 first line of each test case contains two space-separated integers $N$ and $K$.
- The second line contains $N$ space-separated integers $a_1, a_2, \dots, a_N$. Each element of this sequence is either $0$ (indicating an empty spot previously occupied by a removed element) or an integer between $1$ and $N$ inclusive.

-----Output-----
For each test case, print a single line containing one integer — the number of good permutations.

-----Constraints-----
- $1 \le T \le 300$
- $0 \le K < N \le 8$
- each integer between $1$ and $N$ inclusive appears in $a$ at most once

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

-----Example Output-----
2

-----Explanation-----
Example case 1: The two possible good permutations are $(2,3,1)$ and $(2,1,3)$.
user: $Harshad$ $Mehta$ is planning  a new scam with the stocks he is given a stock of  integer price S and a number K . $harshad$ has got the power to change the number $S$ at most $K$ times
In order to raise the price of stock and now cash it for his benefits
Find the largest price at which $harshad$ can sell the stock in order to maximize his profit 

-----Input:-----
- First line will contain $S$ and  $K$ , the price of the stock and the number K 

-----Output:-----
Print the largest profit  he can make in a single line.

-----Constraints-----
- S can take value upto 10^18
NOTE: use 64 int number to fit range
- K can take value from [0.. 9]

-----Sample Input:-----
4483 2

-----Sample Output:-----
9983

-----EXPLANATION:-----
First two digits of the number are changed to get the required number.
user: Rahul is a serial killer. Rahul has been betrayed by his lover in the past and now he want to eliminate entire Universe.He has already Eliminated majority of the population and now only a handful number of people are left. Like other Serial killers, he has an interesting pattern of killing people. 
He either kill one individual at a time or if he find two individuals of different heights,he eliminates both of them simultaneously. Now Rahul wants to eliminate them as quickly as he can.
So given $N$ as the number of people left and an array containing height of those $N$ people,tell the minimum number of kills Rahul require to eliminate the entire universe.

-----Input:-----
- First line will contain $T$, number of testcases. Then the testcases follow. 
- Each test case constitutes of Two lines. 
- First line contains $N$, representing the number of people left in the universe
- The second line contains an array $a[i]$ of size $N$ containing heights of those $N$ people.

-----Output:-----
For each testcase, you have to output a Single line Containing the minimum number of kills required by Rahul to eliminate the Universe.

-----Constraints-----
- $1 \leq T \leq 50000$
- $1 \leq N \leq 50000$
- $100 \leq a[i] \leq 10^5$

-----Sample Input:-----
1
10
178 184 178 177 171 173 171 183 171 175

-----Sample Output:-----
5
user: Chef recently learned about ratios and proportions. He wrote some positive integers a, b, c, d on a paper. Chef wants to know whether he can shuffle these numbers so as to make some proportion? Formally, four numbers x, y, z, w are said to make a proportion if ratio of x : y is same as that of z : w.

-----Input-----
Only line of the input contains four space separated positive integers - a, b, c, d.

-----Output-----
Print "Possible" if it is possible to shuffle a, b, c, d to make proportion, otherwise "Impossible" (without quotes).

-----Constraints-----
- 1 ≤ a, b, c, d  ≤ 1000

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

Output:
Possible

-----Explanation-----
By swapping 4 and the second 2, we get 1 2 2 4. Note that 1 2 2 4 make proportion as 1 : 2 = 2 : 4. Hence answer is "Possible"
user: Devu is a disastrous oracle: his predictions about various events of your life are horrifying. Instead of providing good luck, he "blesses" you with bad luck. The secret behind his wickedness is a hidden omen which is a string of length m. On your visit to him, you can ask a lot of questions about your future, each of which should be a string of length m. In total you asked him n such questions, denoted by strings s1, s2, ... , sn of length m each. Each of the question strings is composed of the characters 'a' and 'b' only.

Amount of bad luck this visit will bring you is equal to the length of longest common subsequence (LCS) of all the question strings and the hidden omen string. Of course, as the omen string is hidden, you are wondering what could be the least value of bad luck you can get.

Can you find out what could be the least bad luck you can get? Find it fast, before Devu tells you any bad omens.

-----Input-----
The first line of the input contains an integer T denoting the number of test cases. The description of T test cases follows.
First line of each test case contains a single integer n denoting number of strings.
For each of next n lines, the ith line contains the string si.

-----Output-----
For each test case, output a single integer corresponding to the answer of the problem. 


-----Constraints-----
- All the strings (including the hidden omen) contain the characters 'a' and 'b' only.

Subtask #1: (40 points) 

- 1 ≤ T, n, m ≤ 14

Subtask #2: (60 points) 

- 1 ≤ T, n, m ≤ 100

-----Example-----
Input:3
2
ab
ba
2
aa
bb
3
aabb
abab
baab

Output:1
0
2

-----Explanation-----
In the first example, the minimum value of LCS of all the strings is 1, the string by oracle can be one of these {aa, ab, ba, bb}. 

In the second example, whatever string oracle has does not matter, LCS will always be zero.
user: Rohit has n empty boxes lying on the ground in a line. The size of the boxes is given in the form of an array $a$. The size of the ith box is denoted by $a[i]$. Since Rohit has a tiny room, there is a shortage of space. Therefore, he has to reduce the number of boxes on the ground by putting a box into another box that is at least twice the size of the current box i.e if we have to put the ith box into the jth box then $( 2*a[i] ) <= a[j]$.
Each box can contain a maximum of one box and the box which is kept in another box cannot
hold any box itself.
Find the minimum number of boxes that will remain on the ground after putting boxes into each other.

-----Input:-----
- The first line contains a single integer n.
- The next n lines contain the integer a[i] - the size of the i-th box.

-----Output:-----
Output a single integer denoting the minimum number of boxes remaining on the ground.

-----Constraints-----
- $1 \leq n \leq 5*10^5$
- $1 \leq a[i] \leq 10^5$

-----Subtasks-----
- 30 points : $1 \leq n \leq 10^2$
- 70 points : $1 \leq n \leq 5*10^5$

-----Sample Input:-----
5
16
1
4
8
2

-----Sample Output:-----
3
user: After completing some serious investigation, Watson and Holmes are now chilling themselves in the Shimla hills. Very soon Holmes became bored. Holmes lived entirely for his profession. We know he is a workaholic. So Holmes wants to stop his vacation and get back to work. But after a tiresome season, Watson is in no mood to return soon. So to keep Holmes engaged, he decided to give Holmes one math problem. And Holmes agreed to solve the problem and said as soon as he solves the problem, they should return back to work. Watson too agreed. 
The problem was as follows. Watson knows Holmes’ favorite numbers are 6 and 5. So he decided to give Holmes N  single digit numbers. Watson asked Holmes to form a new number with the given N numbers in such a way that the newly formed number should be completely divisible by 5 and 6. Watson told Holmes that he should also form the number from these digits in such a way that the formed number is maximum. He may or may not use all the given numbers. But he is not allowed to use leading zeros. Though he is allowed to leave out some of the numbers, he is not allowed to add any extra numbers, which means the maximum count of each digit in the newly formed number, is the same as the number of times that number is present in those given N digits.

-----Input-----
The first line of input contains one integers T denoting the number of test cases.
Each test case consists of one integer N, number of numbers.
Next line contains contains N single digit integers 

-----Output-----
For each test case output a single number, where the above said conditions are satisfied. If it is not possible to create such a number with the given constraints print -1.If there exists a solution, the maximised number should be greater than or equal to 0. 

-----Constraints-----
- 1 ≤ T ≤ 100
- 1 ≤ N ≤ 10000
- 0 ≤ Each digit ≤ 9

-----Subtasks-----
Subtask #1 : (90 points)
- 1 ≤ T ≤ 100
- 1 ≤ N ≤ 10000

Subtask 2 : (10 points) 

- 1 ≤ T ≤ 10
- 1 ≤ N≤ 10

-----Example-----
Input:
2
12
3 1 2 3 2 0 2 2 2 0 2 3
11
3 9 9 6 4 3 6 4 9 6 0

Output:
33322222200
999666330
user: Chef has a nice complete binary tree in his garden. Complete means that each node has exactly two sons, so the tree is infinite. Yesterday he had enumerated the nodes of the tree in such a way: 
- Let's call the nodes' level a number of nodes that occur on the way to this node from the root, including this node. This way, only the root has the level equal to 1, while only its two sons has the level equal to 2.
- Then, let's take all the nodes with the odd level and enumerate them with consecutive odd numbers, starting from the smallest levels and the leftmost nodes, going to the rightmost nodes and the highest levels.
- Then, let's take all the nodes with the even level and enumerate them with consecutive even numbers, starting from the smallest levels and the leftmost nodes, going to the rightmost nodes and the highest levels.
- For the better understanding there is an example: 
1
/           \
2                   4
/   \                /       \
3       5           7        9
/ \      /  \          /  \       /  \
6  8 10 12      14 16   18 20 

Here you can see the visualization of the process. For example, in odd levels, the root was enumerated first, then, there were enumerated roots' left sons' sons and roots' right sons' sons.
You are given the string of symbols, let's call it S. Each symbol is either l or r. Naturally, this sequence denotes some path from the root, where l means going to the left son and r means going to the right son.
Please, help Chef to determine the number of the last node in this path.

-----Input-----
The first line contains single integer T number of test cases.
Each of next T lines contain a string S consisting only of the symbols l and r.

-----Output-----
Per each line output the number of the last node in the path, described by S, modulo 109+7.

-----Constraints-----
- 1 ≤ |T| ≤ 5
- 1 ≤ |S| ≤ 10^5
- Remember that the tree is infinite, so each path described by appropriate S is a correct one.

-----Example-----
Input:
4
lrl
rll
r
lllr
Output:
10
14
4
13

-----Explanation-----
See the example in the statement for better understanding the samples.
user: Divya's watch of worth Rs10 cr is abducted by N thieves(1,2....i...N). The fight over the watch leads to a final decision that it should belong to the thief who wins a simple game. The rules of the game state that every thief  registers a time in the format HH:MM:SS . Accordingly the average A of three clockwise angles  between the hours , minutes and seconds hands is calculated . Thus the ith thief  with the maximum A wins the game and gets to keep the watch.

The thieves are poor in mathematics and will need your help . Given the number of thieves and their registered time resolves the conflict and help them in choosing the winner 

-----Input-----
First line of input contains T which denotes the number of test cases.

The first line of each test case consists of an integer which denotes the number of thieves thereby N line follow which give the time choosen by each thieve in the format HH:MM:SS.

-----Output:-----
Output single integer i which denotes the ith thief.

-----Constraints:-----

1<=T<=100

1<=N<=50

01<=HH<=12

00<=MM<=60

00<=SS<=60

-----Example:-----
Input:
2
3
12:28:26
07:26:04
11:23:17
2
07:43:25
06:23:34

Output:
3
1
user: Ash is on his way to becoming the Pokemon Master. His pokemon can perform the following moves:  
- Tackle - Deal damage worth $X$ points  
- Grow - Increase damage by $Y$ points i.e. $X$ = $X$ + $Y$ 
But, it can only perform Grow first (0 or more times) and then tackle (0 or more) times after which it cannot perform Grow again.

That is, it cannot perform the Grow operation once it has performed the tackle operation.  
A pokemon can be caught only if it’s health is exactly 1. A wild pokemon has appeared and has health worth $H$ points. Find the minimum number of moves required to catch it or say that it is not possible.  

-----Input:-----
- 
The first line of the input consists of a single integer $T$ denoting the number of test cases.
- 
Each test case consists of 3 space-separated integers $H$, $X$ and $Y$.

-----Output:-----
- For each test case, print a single line containing one integer - the minimum number of moves required to catch the pokemon if it is possible to catch it else print -1.

-----Constraints-----
- 
1 <= $T$ <= 103
- 
1 <=  $X$, $Y$ < $H$ <= 109

-----Subtasks-----
Subtask #1 (30 points):
- 1 <=  $X$, $Y$ < $H$ <= 1000
Subtask #2 (70 points):
- Original Constraints

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

101 10 10

11 3 3  

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

-1  

-----EXPLANATION:-----
- 
Example Case 1:

Ash can make use of Grow once. So $X$ = 10 + 10 = 20

Then he can do Tackle 5 times to decrease $H$ to 1.

OR

Ash can make use of Grow 4 times. So $X$ = 10 + 4*10 = 50

Then he can do Tackle 2 times to decrease $H$ to 1.

Hence, a total of 6 moves are required either way which is minimum.  
- 
Example Case 2:

No matter how many times Ash uses Grow or Tackle, pokemon can never be caught.
user: Given $N *M$ matrix containing elements either $1$ or $0$ and string S of length $N+M-1$ containing characters $0$ or $1$. Your task is to make all the  paths from top left corner to the  bottom right corner of the matrix same as the  given string .You can perform two types of operations any time .Path means you can only allow it to take right or down. 
Operations :
- Changing the matrix elements from $1$ to $0$ or vice versa  will cost P rupees per element.
- Changing the character of string  from $1$ to $0$ or vice versa  will cost Q rupees per character.
You have to  minimize the cost, (possibly 0) .

-----Input:-----
- First line of input contains the total no. of test cases $T$. 
- For every test case, first line of input contains two spaced positive integers, $N$ and $M$.
- Next $N$ lines contains $M$-spaced integers which can be only $0$ or $1$.
- Next line of input contains a string $S$ of length $N+M-1$.
- Last line of input contains two spaced integers, $P$ and $Q$.

-----Output:-----
- $You$ $have$ $to$ $print$ $the$ $minimum$ $cost .$

-----Constraints-----
- $1 \leq T \leq 20$
- $1 \leq N, M \leq 1000$
- $|S| = N+M-1$
- $0 \leq P, Q \leq 1000$The input/output is quite large, please use fast reading and writing methods.

-----Sample Input-----
2
3 3
1 0 1
0 1 1
1 1 0
10111
10 5
3 3 
0 0 1
0 1 1
0 1 1
00011
2 9

-----Sample Output-----
5
4

-----Explanation-----
- You can  change the last element of the matrix and also can change the last element of string but the minimum cost will produce by changing string element , therefore it will cost 5 rupees.
user: A valid parentheses sequence is a non-empty string where each character is either '(' or ')', which satisfies the following constraint:

You can find a way to repeat erasing adjacent pairs of parentheses '()' until it becomes empty.

	For example, '(())' and '()((()()))' are valid parentheses sequences, but ')()(' and '(()' are not.

	Mike has a valid parentheses sequence. He really likes everything about his sequence, except the fact that it is quite long. So Mike has recently decided that he will replace his parentheses sequence with a new one in the near future. But not every valid parentheses sequence will satisfy him. To help you understand his requirements we'll introduce the pseudocode of function F(S):

	FUNCTION F( S - a valid parentheses sequence )
	BEGIN
		balance = 0
		max_balance = 0
		FOR index FROM 1 TO LENGTH(S)
		BEGIN
			if S[index] == '(' then balance = balance + 1
			if S[index] == ')' then balance = balance - 1
			max_balance = max( max_balance, balance )
		END
		RETURN max_balance
	END

	In other words, F(S) is equal to the maximal balance over all prefixes of S.

	Let's denote A as Mike's current parentheses sequence, and B as a candidate for a new one. Mike is willing to replace A with B if F(A) is equal to F(B). He would also like to choose B with the minimal possible length amongst ones satisfying the previous condition. If there are several such strings with the minimal possible length, then Mike will choose the least one lexicographically, considering '(' to be less than ')'.

	Help Mike!

-----Input-----

	The first line of the input contains one integer T denoting the number of testcases to process.

	The only line of each testcase contains one string A denoting Mike's parentheses sequence. It is guaranteed that A only consists of the characters '(' and ')'. It is also guaranteed that A is a valid parentheses sequence.

-----Output-----

	The output should contain exactly T lines, one line per each testcase in the order of their appearance. The only line of each testcase should contain one string B denoting the valid parentheses sequence that should be chosen by Mike to replace A.

-----Constraints-----
1 ≤ T ≤ 5;
1 ≤ |A| ≤ 100000(105).

-----Example-----
Input:
1
()((()()))

Output:
((()))
user: Given a Complete Binary Tree of ‘n’ depth, you can perform 4 types of mirror operation on the tree:-

Mirror on the right. The tree is mirrored to the right and rightmost node on every level is connected with the mirrored corresponding node.

Mirror on the left. The tree is mirrored to the left and leftmost node on every level is connected with the mirrored corresponding node.

Mirror on the top. The tree is mirrored to the top and topmost nodes are connected with corresponding nodes.

Mirror on the bottom. The tree is mirrored to the bottom and bottom most nodes are connected with the corresponding nodes.

See the image for details.   
Mirror Right:  

Mirror Bottom:   

You are given ‘q’ queries, each performing this type of operation or asking for the no of edges in the produced graph.

Queries are of the form “1 x” or “2” where x is 1 for right, 2 for left, 3 for top or 4 for bottom.

1 x:  Perform x operation on the result graph.

2:     Print the no of edges in the graph. Since it can be very large, print it modulo 1000000007.   

-----Input:-----
- First line will contain $n$, the depth of the initial tree and $q$, the number of queries.    
- Next $q$ lines contain queries of the form "1 $x$" or "2".

-----Output:-----
For each query of type "2", output a single line containing the no of edges in the graph modulo 1000000007.

-----Constraints-----
- $1 \leq n \leq 1000$
- $1 \leq q \leq 10^5$
- $1 \leq x \leq 4$

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

-----Sample Output:-----
38

-----EXPLANATION:-----
Initial no of edges = 6

After the operation 1 1, no of edges = 15

After the operation 1 4, no of edges = 38

At operation 2, we print the no of edges that is 38.
user: Your are given a string $S$ containing only lowercase letter and a array of character $arr$. Find whether the given string only contains characters from the given character array. 
Print $1$ if the string contains characters from the given array only else print $0$.
Note: string contains characters in lower case only.

-----Input:-----
- First line will contain $T$, number of testcases. Then the testcases follow. 
- Each testcase contains- 
a string $S$ of lowercase letter
a integer $n$ denoting length of character array $arr$
next line contains $n$ space separated characters.

-----Output:-----
For each testcase, Print $1$ if the string contains characters from the given array only else print $0$.

-----Constraints-----
- $1 \leq T \leq 1000$
- $0 \leq n \leq 10^5$

-----Sample Input:-----
3
abcd
4
a b c d
aabbbcccdddd
4
a b c d
acd
3
a b d

-----Sample Output:-----
1
1
0