meetforever/GRPO_CL huggingface dataset:
user: The chef has a recipe he wishes to use for his guests,
but the recipe will make far more food than he can serve to the guests.
The chef therefore would like to make a reduced version of the recipe which has the same ratios of ingredients, but makes less food.
The chef, however, does not like fractions.
The original recipe contains only whole numbers of ingredients,
and the chef wants the reduced recipe to only contain whole numbers of ingredients as well.
Help the chef determine how much of each ingredient to use in order to make as little food as possible.

-----Input-----
Input will begin with an integer T, the number of test cases.
Each test case consists of a single line.
The line begins with a positive integer N, the number of ingredients.
N integers follow, each indicating the quantity of a particular ingredient that is used.

-----Output-----
For each test case, output exactly N space-separated integers on a line,
giving the quantity of each ingredient that the chef should use in order to make as little food as possible.

-----Sample Input-----
3
2 4 4
3 2 3 4
4 3 15 9 6

-----Sample Output-----
1 1
2 3 4
1 5 3 2

-----Constraints-----
T≤100

2≤N≤50

All ingredient quantities are between 1 and 1000, inclusive.
user: Today is Chef's birthday. His mom has surprised him with truly fruity gifts: 2 fruit baskets. The first basket contains N apples, and the second one contains M oranges. Chef likes apples and oranges very much but he likes them equally, and therefore, wants to have the minimum possible difference between the number of apples and oranges he has. To do so, he can purchase 1 apple or 1 orange by paying exactly 1 gold coin (that's some expensive fruit, eh?). Chef can purchase fruits at most K times (as he has only K gold coins in his pocket) to make the difference the minimum possible.
Our little Chef is busy in celebrating his birthday to the fullest, and therefore, he has handed this job to his best friend — you. Can you help him by finding the minimum possible difference he can achieve between the number of apples and orange he owns?

-----Input-----
The first line of input contains a single integer T denoting the number of test cases. The first and only line of each test case contains 3 space separated integers — N, M and K — denoting the number of apples, number of oranges, and number of gold coins our little Chef has.

-----Output-----
For each test case, output the minimum possible difference between the number of apples and oranges that Chef can achieve.

-----Constraints-----
- 1 ≤ T ≤ 100
- 1 ≤ N, M, K ≤ 100

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

Output
0
2
0

-----Explanation-----
- Test 1: Chef will buy 1 apple by paying 1 gold coin and will have equal number of apples and oranges. 
- Test 2: Chef will buy 1 orange by paying 1 gold coin and will have 5 apples and 3 oranges.
user: After acquiring an extraordinary amount of knowledge through programming contests, Malvika decided to harness her expertise to train the next generation of Indian programmers. So, she decided to hold a programming camp. In the camp, she held a discussion session for n members (n-1 students, and herself). They are sitting in a line from left to right numbered through 1 to n.

Malvika is sitting in the nth spot. She wants to teach m topics of competitive programming to the students. As the people taking part in the camp are all newbies, they know none of the topics being taught, i.e., initially, the first n - 1 people in the line know none of the topics, while the nth knows all of them.

It takes one hour for a person to learn a topic from his neighbour. Obviously, one person cannot both teach a topic as well as learn one during the same hour. That is, in any particular hour, a person can either teach a topic that he knows to one of his neighbors, or he can learn a topic from one of his neighbors, or he can sit idly. It is also obvious that if person x is learning from person y at a particular hour, then person y must be teaching person x at that hour.

Also, note that people can work parallely too, i.e., in the same hour when the 4th person is teaching the 3rd person, the 1st person can also teach the 2nd or learn from 2nd.

Find out the minimum number of hours needed so that each person learns all the m topics.

-----Input-----
- The first line of input contains a single integer T denoting number of test cases.
- The only line of each test case contains two space separated integers n, m as defined in the statement.

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

-----Constraints-----
- 1 ≤ T, n, m ≤ 100

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

Output:
1
4

-----Explanation-----
In the first example, there are two people. Second person is Malvika and she has to teach only one topic to the first person. It will take only one hour to do so.

In the second example, there are three people. The 3rd person is Malvika and she has to teach only two topics to 1st and 2nd person. In the 1st hour, she teaches the 1st topic to the 2nd person. Now, in the 2nd hour, the 2nd person will teach the 1st topic to the 1st person. In the 3rd hour, Malvika will teach the 2nd topic to the 2nd person. Now the 2nd person will teach that topic to the 1st in the 4th hour. So, it takes a total of 4 hours for all the people to know all the topics.
user: Find out the maximum sub-array of non negative numbers from an array. 

The sub-array should be continuous. That is, a sub-array created by choosing the second and fourth element and skipping the third element is invalid.

Maximum sub-array is defined in terms of the sum of the elements in the sub-array. Sub-array A is greater than sub-array B if sum(A) > sum(B).

NOTE 1 :If there is a tie, then compare with segment's length and return segment which has maximum length 

NOTE 2: If there is still a tie, then return the segment with minimum starting index.

-----Input-----

The first line contains the number of test cases. Each test cases contains an integer N. next line consists of N integers, the elements of the array.

-----Output-----

Print out the maximum sub-array as stated above.

-----Constraints-----
-  1  ≤  T  ≤  100 
-  1  ≤  N  ≤  105 
-  1  ≤  Ai  ≤  105 

-----Example-----
Input:

1
6
1 2 5 -7 2 3

Output:

1 2 5
user: Chef found a strange string yesterday - a string of signs s, where each sign is either a '<', '=' or a '>'. Let N be the length of this string. Chef wants to insert N + 1 positive integers into this sequence and make it valid. A valid sequence is a sequence where every sign is preceded and followed by an integer, and the signs are correct. That is, if a sign '<' is preceded by the integer a and followed by an integer b, then a should be less than b. Likewise for the other two signs as well. 
Chef can take some positive integers in the range [1, P] and use a number in the range as many times as he wants.
Help Chef find the minimum possible P with which he can create a valid sequence.

-----Input-----
The first line of the input contains an integer T denoting the number of test cases. The description of T test cases follows.
The only line of each test case contains the string of signs s, where each sign is either '<', '=' or a '>'. 

-----Output-----
For each test case, output a single line containing an integer corresponding to the minimum possible P. 

-----Constraints-----
- 1 ≤ T, |s| ≤ 105
- 1 ≤ Sum of |s| over all test cases in a single test file ≤ 106

-----Subtasks-----
Subtask #1 (30 points)
- 1 ≤ T, |s| ≤ 103
- 1 ≤ Sum of |s| over all test cases in a single test file ≤ 104

Subtask #2 (70 points)
- Original constraints

-----Example-----
Input:
4
<<<
<><
<=>
<=<

Output:
4
2
2
3

-----Explanation-----
Here are some possible valid sequences which can be formed with the minimum P for each of the test cases:
1 < 2 < 3 < 4
1 < 2 > 1 < 2
1 < 2 = 2 > 1
1 < 2 = 2 < 3
user: You came across this story while reading a book. Long a ago when the modern entertainment systems did not exist people used to go to watch plays in theaters, where people would perform live in front of an audience. There was a beautiful actress who had a disability she could not pronounce the character $'r'$. To win her favours which many have been denied in past, you decide to write a whole play without the character $'r'$. Now you have to get the script reviewed by the editor before presenting it to her.
The editor was flattered by the script and agreed to you to proceed. The editor will edit the script in this way to suit her style. For each word replace it with a sub-sequence of itself such that it contains the character 'a'. 
A subsequence is a sequence that can be derived from another sequence by deleting some or no elements without changing the order of the remaining elements Wikipedia 
Now given a script with $N$ words, for each word in the script you wish to know the number of subsequences with which it can be replaced. 

-----Input:-----
- First-line will contain $N$, the number of words in the script. Then next $N$ line with one test case each. 
- Each test case contains a single word $W_i$

-----Output:-----
For each test case, output in a single line number of subsequences with which it can be replaced. 

-----Constraints-----
- $1 \leq N \leq 1000$
- $1 \leq$ length of $W_i$  $\leq 20$
- $W_i$  on contains lowercase english alphabets and does not have the character 'r'

-----Sample Input 1:-----
2
abc
aba

-----Sample Output 1:-----
4
6

-----EXPLANATION:-----
This subsequences with which $abc$ can be replaed : ${a,ab,ac,abc}$. 
This subsequences with which $aba$ can be replaed : ${a,ab,aba,a,ba,a}$. 

-----Sample Input 2:-----
3
abcde
abcdea
xyz

-----Sample Output 2:-----
16
48
0
user: Not everyone probably knows that Chef has younder brother Jeff. Currently Jeff learns to read.
He knows some subset of the letter of Latin alphabet. In order to help Jeff to study, Chef gave him a book with the text consisting of N words. Jeff can read a word iff it consists only of the letters he knows.
Now Chef is curious about which words his brother will be able to read, and which are not. Please help him!

-----Input-----
The first line of the input contains a lowercase Latin letter string S, consisting of the letters Jeff can read. Every letter will appear in S no more than once.
The second line of the input contains an integer N denoting the number of words in the book.
Each of the following N lines contains a single lowecase Latin letter string Wi, denoting the ith word in the book.

-----Output-----
For each of the words, output "Yes" (without quotes) in case Jeff can read it, and "No" (without quotes) otherwise.

-----Constraints-----
- 1 ≤ |S| ≤ 26
- 1 ≤ N ≤ 1000
- 1 ≤ |Wi| ≤ 12
- Each letter will appear in S no more than once.
- S, Wi consist only of lowercase Latin letters.

-----Subtasks-----
- Subtask #1 (31 point): |S| = 1, i.e. Jeff knows only one letter.
- Subtask #2 (69 point)	: no additional constraints

-----Example-----
Input:act
2
cat
dog

Output:Yes
No

-----Explanation-----
The first word can be read.
The second word contains the letters d, o and g that aren't known by Jeff.
user: Chef has a calculator which has two screens and two buttons. Initially, each screen shows the number zero. Pressing the first button increments the number on the first screen by 1, and each click of the first button consumes 1 unit of energy.
Pressing the second button increases the number on the second screen by the number which is currently appearing on the first screen. Each click of the second button consumes B units of energy.
Initially the calculator has N units of energy.
Now chef wonders what the maximum possible number is, that he gets on the second screen of the calculator, with the limited energy.

-----Input-----
The first line of the input contains an integer T denoting the number of test cases.
Each test case is described using a single line containing two integers, N and B.

-----Output-----
For each test case, output a single line containing the answer to this test case.

-----Constraints-----
- 1 ≤ T ≤ 10,000
- 1 ≤ N, B ≤ 1,000,000,000

-----Subtasks-----
- Subtask 1 (20 points): 1 ≤ N, B ≤ 1,000
- Subtask 2 (80 points): Original constraints

-----Example-----
Input:
3
10 2
8 5
6 1

Output:
12
3
9

-----Explanation-----
Example case 1. There are 10 units of energy available. Pressing second button takes 2 units of energy. Chef can achieve 12 on the second screen as follows.

- Press first button to get scores (1, 0). 9 units of energey is left.
- Press first button to get scores (2, 0). 8 units of energy remaining.
- Press first button to get scores (3, 0). 7 units of energy remaining.
- Press first button to get scores (4, 0). 6 units of energy remaining.
- Press second button to get scores (4, 4). 4 units of energy remaining.
- Press second button to get scores (4, 8). 2 units of energy remaining.
- Press second button to get scores (4, 12). 0 units of energy remaining.
user: Chef has a circular sequence $A$ of $N$ non-negative integers $A_1, A_2, \ldots, A_N$ where $A_i$ and $A_{i+1}$ are considered adjacent, and elements $A_1$ and $A_N$ are considered adjacent.
An operation on position $p$ in array $A$ is defined as replacing $A_p$ by the bitwise OR of elements adjacent to $A_p$. Formally, an operation is defined as:
- If $p = 1$, replace $A_1$ with $A_N | A_{2}$
- If $1 < p < N$, replace $A_p$ with $A_{p-1} | A_{p+1}$
- If $p = N$, replace $A_N$ with $A_{N-1} | A_1$
Here, '|' denotes the bitwise OR operation.
Now, Chef must apply operations at each position exactly once, but he may apply the operations in any order.
Being a friend of Chef, you are required to find a sequence of operations, such that after applying all the $N$ operations, the bitwise OR of the resulting array is $K$, or determine that no such sequence of operations exist.

-----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 $K$ denoting the number of elements, and the required bitwise OR after operations.
- The second line contains $N$ space-separated integers $A_1, A_2, \ldots, A_N$.

-----Output:-----
For each test case, if no valid sequence of operations exist, print -1.
Otherwise, print $N$ space-separated integers in which $i$-th integer denote the position chosen in the $i$-th operation. If there are multiple valid sequences of operations, you may print any valid sequence.

-----Constraints-----
- $1 \le T \le 10^5$
- $3 \le N \le 2*10^5$
- $0 \le A_i, K \le 10^9$
- It's guaranteed that the total length of the arrays in one test file doesn't exceed $10^6$

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

-----Sample Output:-----
2 1 3
-1
-1
-1
2 3 1

-----Explanation:-----
In the first test case, initially, the sequence is {2, 1, 6}. 
- Chef applies the operation on the $2^{nd}$ index, so the sequence converts to {2, 6, 6}.
- Next, Chef applies the operation on the $1^{st}$ index, so the sequence converts to {6, 6, 6}.
- Next, Chef applies the operation on the $3^{rd}$ index, and this time sequence does not change.
The final sequence is {6, 6, 6}, and bitwise OR of this sequence is $6$ that is equal to given $K$.
user: The chef is trying to decode some pattern problems, Chef wants your help to code it. Chef has one number K(odd) to form a new pattern. Help the chef to code this pattern problem.

-----Input:-----
- First-line will contain $T$, the number of test cases. Then the test cases follow. 
- Each test case contains a single line of input, one integer $K$. 

-----Output:-----
For each test case, output as the pattern.

-----Constraints-----
- $1 \leq T \leq 100$
- $1 \leq K \leq 100$

-----Sample Input:-----
4
1
3
5
7

-----Sample Output:-----
1
111
111
111
11111
11 11
1 1 1
11 11
11111
1111111
11   11
1 1 1 1
1  1  1
1 1 1 1
11   11
1111111

-----EXPLANATION:-----
No need, else pattern can be decode easily.
user: Humpy, the little elephant, has his birthday coming up. He invited all his cousins but doesn’t know how many of them are really coming as some of them are having exams coming up. He will only get to know how many of them are coming on the day of his birthday.

He ordered sugarcane for his party, of length L.

Humpy’s mom decided that she will be dividing the sugarcane among Humty and his friends in a way such that they get the sugarcane in ratio of their ages.

Your task is to determine whether it is possible to serve sugarcane to everyone as integral multiples of their ages.

-----INPUT-----
First line of input contains an integer N, denoting the number of test cases.

Then N test cases follow.

The first line of each test case contains three integers K, L and E. K denoting the number of friends coming; L denoting the length of the sugarcane and E denoting the age of the little elephant. Next line has  K  space separated integers denoting the age of friends who came to the party.

-----OUTPUT-----

For each test case, output “YES” (without quotes) if everyone gets their part as integral multiples of their ages; otherwise output “NO”(without quotes).

-----CONSTRAINTS-----

- 1 <= T<=30
- 1 <= K<=1000
- 1 <= L<=1000000
- 1 <= E<=100000
- 1 <= Age of Cousins<=100000

-----Example-----
Input:
2
4 10 2
2 2 3 1
4 12 3
6 5 7 3

Output:
YES 
NO
user: You may have tried your level best to help Chef but Dr Doof has managed to come up with his masterplan in the meantime. Sadly, you have to help Chef once again. Dr Doof has designed a parenthesis-inator. It throws a stream of $N$ brackets at the target, $1$ bracket per second. The brackets can either be opening or closing. Chef appears in front of the stream at time $t$. If Chef faces an opening bracket, he gets hit. However, if he faces a closing bracket, he may choose to let it pass through him (Chef is immune to closing brackets). Chef gets a chance to counter attack Doof as soon as he finds a balanced non-empty bracket sequence. Help Chef by providing him the minimum time $x$ at which he will be able to launch his counter attack. If Chef is unable to counter attack, answer $-1$.
Formally, you are given a string $S$ of length $N$ consisting only of opening brackets $($ and closing brackets $)$. The substring of $S$ starting at index $L$ and ending at index $R$, i.e. $S_L S_{L+1} \ldots S_{R}$ is denoted by $S[L, R]$ . Consider $Q$ cases. In the $i^{\text{th}}$ case, Chef appears at time $t_i$ $(1 \leq t_i \leq N)$ and faces all characters from index $t_i$ to $N$. Find the minimum index $x$ $(t_i \leq x \leq N)$ such that the substring $S[t_i, x]$ contains a non-empty balanced bracket subsequence containing the same number of opening brackets as $S[t_i, x]$ (i.e., you cannot remove any opening bracket from the substring). If such an $x$ does not exist, print $-1$.
A string $X$ is called a subsequence of a string $Y$ if it is possible to obtain $X$ by erasing some (possibly zero) characters from $Y$ without changing the order of the remaining characters.
A balanced bracket sequence is defined as:  
- an empty string is a balanced bracket sequence.
- if $s$ is a balanced bracket sequence, then so is $(s)$.
- if $s$ and $t$ are balanced bracket sequences, then so is $st$.
$Note :-$ The input files are large. The use of Fast I/O is recommended.

-----Input-----
- The first line contains a single integer $T$ denoting the number of testcases.
- The first line of each test case contains the string $S$.
- The next line contains a single integer $Q$ denoting the number of cases to consider.
- The next line contains $Q$ space separated integers, each denoting $t_i$.

-----Output-----
For each query, print the minimum value of $x$ in a separate line. If no such $x$ exists, print $-1$.

-----Constraints-----
- $1 \leq T \leq 10^3$
- $1 \leq |S| \leq 10^7$
- $1 \leq Q \leq 10^6$
- $1 \leq t_i \leq N$
- Every character of $S$ is either $($ or $)$.
- Sum of $|S|$ and $Q$ over all testcases for a particular test file does not exceed $10^7$ and $10^6$ respectively.

-----Sample Input-----
1
)())((()
3
1 7 6

-----Sample Output-----
3
8
-1

-----Explanation-----
For the first query, Chef chooses to let $S_1$ pass through him, gets hit by $S_2$ and finally completes a balanced bracket sequence by adding $S_3$ to $S_2$ at time $x$ = $3$.
user: Let's call a sequence good if the sum of all its elements is $0$.
You have a sequence of integers $A_1, A_2, \ldots, A_N$. You may perform any number of operations on this sequence (including zero). In one operation, you should choose a valid index $i$ and decrease $A_i$ by $i$. Can you make the sequence good using these operations?

-----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 a single integer $N$.
- The second line contains $N$ space-separated integers $A_1, A_2, \ldots, A_N$.

-----Output-----
For each test case, print a single line containing the string "YES" if it is possible to make the given sequence good or "NO" if it is impossible.

-----Constraints-----
- $1 \le T \le 1,000$
- $1 \le N \le 10$
- $|A_i| \le 100$ for each valid $i$

-----Subtasks-----
Subtask #1 (10 points): $N = 1$
Subtask #2 (30 points): $N \le 2$
Subtask #3 (60 points): original constraints

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

-----Example Output-----
NO
YES

-----Explanation-----
Example case 2: We can perform two operations ― subtract $1$ from $A_1$ and $2$ from $A_2$.
user: Given a binary string $S$ consisting of only 1’s and 0’s where 1 represents a Square and 0 represents a Circle. The diameter of the circle and the side of the square must be any integer (obviously > 0) . You will have to perfectly inscribe (as shown in the example below) the respective geometric figure at $S$$i+1$ inside of $S$$i$ where $i$ $\epsilon$ $[0,N-2]$, if it is possible. Note that, it will not be possible to inscribe if the dimension of the geometric figure you are perfectly inscribing is not an integer and you will discard the rest of the string. Find the maximum number of circles we can inscribe in a square according to the given string.  
For a given binary string there can be only one geometric figure and this figure is concentric.  
For example : the string 1100 can be represented as the figure below, the first two squares have the same side length and the next two circles have the same diameter.  

Another example : the string 0001 can be represented as the one given below
Again here, we have 3 circles of the same diameter and one square inscribed in them.  

-----Input:-----
The first line contains $N$, the number of strings

Then each of the next $N$ lines contains a binary string $S$.  

-----Output:-----
The $N$ lines of output should have $N$ integers in separate lines, the maximum number of circles we can inscribe in a square according to the given string $S$ .  

-----Constraints-----
- 1 $\leq$ $N$ $\leq$ 103
- 1 $\leq$ length of string $S$ $\leq$ 104

-----Sample Input:-----
3

1110

0010

1001000  

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

0

2  

-----Explanation:-----
In  the first case, we can inscribe the string 1110 as :  three squares of side length 4 units (on top of each other) and then  we can inscribe one circle of diameter 4 units.
The answer is 1 since, there is 1 circle inscribed in a square.

In the second case 0010, Let the first two circles be of some diameter 10, we can see that we cannot inscribe another square of any integer dimension inside them.

So, the answer is 0.

In the third case 1001000, we can take the first square of size 10, then inscribe two circles of diameter 5, then we cannot inscribe another square in this since, it will not be of any possible integer dimension and we discard the rest of the string.