meetforever/GRPO_CL huggingface dataset:
user: Ted$Ted$ loves prime numbers. One day he is playing a game called legendary$legendary$ with his girlfriend Robin$Robin$. Ted$Ted$ writes a number N$N$ on a table and the number is in the form of :
N = P1A1 *  P2A2 * ……….. * PnAn
Ted$Ted$ asks Robin$Robin$ to find the sum of all the numbers which are less than or equal to N$N$ and also contains all the primes whose minimum power in the number is given by an array B$B$.  
As Robin$Robin$ is bad with maths she asks your help to answer this question.

-----Input:-----
- The first line of the input contains a single integer T$T$ denoting the number of test cases. The description of T$T$ test cases follows.  
- The first line of each test case contains a single integer n$n$, represents a number of distinct prime numbers.
- The second line of each test case contains n$n$ space separated distinct prime numbers which represents an array P$P$.
- The third line of each test case contains n$n$ space separated integers which represents an array A$A$.
- The fourth line of each test case contains n$n$ space separated integers which represents an array B$B$ 

-----Output:-----
For each test case, output the Answer Modulo 109 + 7 in a single line.

-----Constraints-----
- 1≤T≤3$1 \leq T \leq 3$
- 1≤n≤105$1 \leq n \leq 10^5$
- 2≤Pi≤106$2 \leq P_{i} \leq 10^6$
- 1≤Ai≤109$1 \leq A_{i} \leq 10^9$
- 0≤Bi≤Ai$0 \leq B_{i} \leq Ai$

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

-----Sample Output:-----
540

-----EXPLANATION:-----
22 * 31 * 52= 300 which is N over here. 
The four numbers less than or equal to 300 are 30, 60, 150 and 300.

30 = 21 * 31 * 51 , 60 =  22 * 31 * 51, 150 =  21 * 31 * 52 and 300 =  22 * 31 * 52. 
In the 4 numbers, the minimum powers for 2, 3 and 5 are 1, 1 and 1 or more than them in every case.
user: There are $N$ friends in a group. Each of them have $A_{i}$ candies.
Can they share all of these candies among themselves such that each one of them have equal no. of candies.

-----Input:-----
- First line will contain $T$, number of testcases. Then the testcases follow. 
- First line of each testcase contains of a single line of input, an integer $N$ denoting no. of friends in the group. 
- Next line contains $N$ space separated integers $A_{i}$  denoting the no. candies  $i^{th}$ friend has.

-----Output:-----
For each testcase, output $"Yes"$ if it is possible to share equally else $"No"$ (without " ").

-----Constraints-----
- $1 \leq T \leq 10$
- $1 \leq N \leq 100$
- $0 \leq A_{i} \leq 1000$

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

3

1 2 3

-----Sample Output:-----
Yes

-----EXPLANATION:-----
Each of them have $2$ candies after sharing.
user: Chef has $K$ chocolates and he wants to distribute them to $N$ people (numbered $1$ through $N$). These people are standing in a line in such a way that for each $i$ ($1 \le i \le N-1$), person $i$ and person $i+1$ are adjacent.
First, consider some way to distribute chocolates such that for each valid $i$, the number of chocolates the $i$-th person would receive from Chef is $A_i$ and the sum $S_1 = \sum_{i=1}^{N-1} \left|A_i - A_{i+1}\right|$ is minimum possible. Of course, each person must receive a non-negative integer number of chocolates.
Then, Chef wants to create a new sequence $B_1, B_2, \ldots, B_N$ by rearranging (permuting) the elements of the sequence $A_1, A_2, \ldots, A_N$. For each valid $i$, the number of chocolates the $i$-th person actually receives from Chef is $B_i$. Chef wants to distribute the chocolates (choose $B_1, B_2, \ldots, B_N$ by permuting the sequence $A$ and give $B_i$ chocolates to the $i$-th person for each valid $i$) in such a way that $S_2 = \sum_{i=1}^{N-1} \left|B_i – B_{i+1}\right|$ is maximum possible. You need to find the maximum value of $S_2$.
It is guaranteed that $S_2$ does not depend on the exact choice of the sequence $A_1, A_2, \ldots, A_N$, as long as it is a sequence that minimises $S_1$.

-----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 a single integer $K$.

-----Output-----
For each test case, print a single line containing one integer — the maximum value of the sum $S_2$.

-----Constraints-----
- $1 \le T \le 10$
- $2 \le N \le 10^5$
- $2 \le K \le 10^{100,000}$

-----Subtasks-----
Subtask #1 (30 points): $2 \le N, K \le 1,000$
Subtask #2 (70 points): original constraints

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

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

-----Explanation-----
Example case 1: To minimise $S_1$, Chef could give $1$ chocolate to person $1$ and $1$ chocolate to person $2$, so $S_1 = |1-1| + |1-0| = 1$.
To maximise $S_2$, Chef can give $1$ chocolate to person $1$ and $1$ chocolate to person $3$, since the sequence $B = (1, 0, 1)$ is a permutation of $A = (1, 1, 0)$. Then, $S_2 = |1-0| + |0-1| = 2$.
user: Given a string $s$.
You can perform the following operation on given string any number of time.
Delete two successive elements of the string if they are same.
After performing the above operation you have to return the least possible length of the string.

-----Input:-----
- First line will contain $T$, number of testcases. Then the testcases follow. 
- Each testcase contains of a single line of input, a string $s$. 

-----Output:-----
For each testcase, output in a single line answer- minimum length of string possible after performing given operations.

-----Constraints-----
- $1 \leq T \leq 1000$
- $2 \leq length of string \leq 10^5$
$s$ contains only lowercase letters.

-----Sample Input:-----
3
abccd
abbac
aaaa

-----Sample Output:-----
3
1
0

-----EXPLANATION:-----
- In first case, $"abd"$ will be final string.
- in second case, $"c"$ will be final string
user: Ashley wrote a random number generator code.
Due to some reasons, the code only generates random positive integers which are not evenly divisible by 10. She gives $N$ and $S$ as input to the random number generator. The code generates a random number with number of digits equal to $N$ and sum of digits equal to $S$. The code returns -1 if no number can be generated. Print "-1" in such cases (without quotes). Else print the minimum possible product of digits of the random number generated.

-----Input:-----
- First line will contain a single integer $T$, the number of testcases. 
- Each testcase consists of two space separated integers, $N$ and $S$. 

-----Output:-----
For each testcase, output the answer on a new line.

-----Constraints-----
- $1 \leq T \leq 10^5$
- $1 \leq N \leq 18$
- $1 \leq S \leq 5 * N$

-----Sample Input:-----
2
1 5

2 2

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

1

-----EXPLANATION:-----
In first testcase, the only possible number of length 1 having digit sum 5 is 5. And it's product of digits is 5. 
In second testcase,  only possible two digit number as a generator output is 11(as 20 is divisible by 10, it is never generated) and product of it's digits is 1.
user: Chef is going to organize a hill jumping competition and he is going to be one of the judges in it. In this competition there are N hills in a row, and the initial height of i-th hill is Ai. Participants are required to demonstrate their jumping skills by doing what the judges tell them.
Judges will give each participant a card which has two numbers, i and k, which means that the participant should start at the i-th hill and jump k times, where one jump should be from the current hill to the nearest hill to the right which is strictly higher (in height) than the current one. If there is no such hill or its distance (i.e. difference between their indices)  is more than 100 then the participant should remain in his current hill.
Please help Chef by creating a program to use it during the competitions. It should read the initial heights of the hill and should support two kinds of operations:
Type 1: Given a two numbers: i and k, your program should output the index of the hill the participant is expected to finish if he starts from the i-th hill (as explained above).
Type 2: Given three numbers: L, R, X, the heights of all the hills between L and R, both end points inclusive, should be increased by X (if X is negative then their height is decreased).

-----Input-----
- First line contains two integers N and Q, denoting the number of hills and number of operations respectively.
- Second line contains N space-separated integers A1, A2, ..., AN denoting the initial heights of the hills.
- Each of the next Q lines describes an operation. If the first integer is equal to 1, it means that the operation is of Type 1, and it will be followed by two integers i and k. Otherwise the first number will be equal to 2, and it means that the operation is of Type 2, and so it will be followed by three integers L, R and X.

-----Output-----
For each operation of Type 1, output the index of the hill in which the participant will finish.

-----Constraints-----
- 1 ≤ N, Q ≤ 100,000
- 1 ≤ Ai ≤ 1,000,000
- 1 ≤ L ≤ R ≤ N
- -1,000,000 ≤ X ≤ 1,000,000
- 1 ≤ i, k ≤ N

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

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

Output:
3
4

-----Explanation-----
The initial heights are (1, 2, 3, 4, 5). The first operation is of Type 1 and starts from Hill 1 and wants to jump twice. The first jump will be to Hill 2, and the second jump will be to Hill 3. Hence the output for this is 3.
The second operation changes the heights to (1, 2, 2, 3, 5).
The last operation starts from Hill 1. The first jump is to Hill 2. But the next jump will skip Hill 3 (because it's height is not strictly greater than the current hill's height), and will go to Hill 4. Hence the output is 4.
user: Mandarin chinese
, Russian and Vietnamese as well.
You are given a grid with $n$ rows and $m$ columns. Each cell of this grid can either be empty or it contains one particle. It can never contain more than one particle. Let's denote the cell in the $i$-th row and $j$-th column by $(i, j)$, with the top left corner being $(0, 0)$. From a cell $(i, j)$, a particle could move in one of the following four directions:
- to the left, i.e. to the cell $(i, j - 1)$
- to the right, i.e. to the cell $(i, j + 1)$
- up, i.e. to the cell $(i - 1, j)$
- down, i.e. to the cell $(i + 1, j)$
It is not possible for a particle to move to a cell that already contains a particle or to a cell that does not exist (leave the grid).
It is possible to apply a force in each of these directions. When a force is applied in a given direction, all particles will simultaneously start moving in this direction as long as it is still possible for them to move.
You are given a sequence of forces. Each subsequent force is applied only after all particles have stopped moving. Determine which cells of the grid contain particles after all forces from this sequence are applied in the given order.

-----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 $m$.
- $n$ lines describing the initial grid follow. For each $i$ ($1 \le i \le n$), the $i$-th of these lines contains a binary string with length $m$ describing the $i$-th row of the grid. For each $j$ ($1 \le j \le m$), if the $j$-th character of this string is '1', then the cell $(i, j)$ contains a particle, and if it is '0', then the cell $(i, j)$ is empty.
- The last line contains a single string $S$ describing the sequence of applied forces. Each character of this string corresponds to applying a force in some direction; forces applied in the directions left, right, up, down correspond to characters 'L', 'R', 'U', 'D' respectively.

-----Output-----
For each test case, print $n$ lines each containing a binary string of length $m$, describing the resulting grid (after all the forces are applied) in the same format as the input grid.

-----Constraints-----
- $1 \le T \le 200$
- $1 \le n, m \le 100$
- $1 \le |S| \le 2 \cdot 10^4$

-----Subtasks-----
Subtaks #1 (30 points):
- $1 \le T \le 10$
- $1 \le n, m \le 10$
- $1 \le |S| \le 100$
Subtask #2 (70 points): Original constraints

-----Example Input-----
3
4 4
1010
0010
1001
0100
LRDU
4 3
000
010
001
101
LRL
3 2
01
10
00
D

-----Example Output-----
0011
0011
0001
0001
000
100
100
110
00
00
11

-----Explanation-----
Example case 1: The initial grid is:
1010
0010
1001
0100

After applying the first force (in the direction "L", i.e. to the left), the grid is:
1100
1000
1100
1000

After applying the second force (in the direction "R"), the grid is:
0011
0001
0011
0001

After applying the third force (in the direction "D"), the grid is:
0001
0001
0011
0011

After applying the fourth force (in the direction "U"), the final grid is:
0011
0011
0001
0001
user: Chef is the event manager of his college. He has been assigned the task to manage the upcoming tech fest. There are $K$ rooms where the event can take place, and at a particular time only one event can be organized in a room for a particular time interval.
Each event coordinator has their strictly preferred room $P_i$, and if the room is already occupied he simply cancels that event.Chef wants to maximize the total number of events,and so he allows or disallows certain events in order to achieve the task . Chef is busy handling his events so the chef needs your help .
Given a list of $N$ events with their start time $S_i$,end time $E_i$ and preferred room $P_i$,you need to calculate the maximum number of events that can take place.
Note that the $i$th event wants to occupy the $p_i$ room from [$s_i$, $f_i$) .

-----Input:-----
The first line contains an integer $T$ denoting the number of test cases . Each of the next $T$ lines contains two integers $N$ and $K$ , the number of events and the number of rooms respectively . Each of the next $N$ lines contains three integers $s_i$ ,$e_i$ and $p_i$,the start time ,end time and the preferred room of ith event.

-----Output:-----
Print the maximum number of events that can take place.

-----Constraints-----
- $1 \leq T \leq 100$
- $1 \leq N \leq 10^3$
- $1 \leq  K \leq 10^5$
- $1 \leq  Si <  Ei \leq 10^9$
- $1 \leq Pi \leq K$

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

4 2
1 10 1
10 20 2
15 50 2
20 30 2

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

-----EXPLANATION:-----
Chef can allow events 1st ,2nd and 4th,to get the maximum 3.
user: In these quarantine days, Chef and Chefina are getting bored. So, Chef came up with a game for her. He gets a pack of cards with numbers written on them. Chef then asks her to remove cards from the pack in the following manner: Chefina can choose any 3 cards at a time, having unique values, and remove the smallest and largest of them, and put back the middle one. For example, say Chefina chooses 3 cards that have numbers $x$, $y$, $z$ on them, such that $x <= y <= z$. Then she can throw away cards with number $x$ and $z$, but has to put the card with number $y$ on it back into the pack. Chefina can repeat this process any number of times. As soon as the pack contains cards with unique numbers, the game ends. If Chefina can determine the count of cards that will remain in the end, and tell it to Chef beforehand, she wins the game. Chefina asks for your help to win this game. Given the number written on the cards, help her find the count of cards in the pack when she wins.
$Note:$ You need to maximize the array length or the number of unique elements

-----Input:-----
- The first line of the input consists of a single integer $T$, denoting the number of test cases. Description of $T$ test cases follow.
- The first line of each test case consists of a single integer $N$, denoting the number of cards in the pack
- The next line consists of $N$ space separated numbers $A1$, $A2$ … $An$. For each valid $i (1 <= i <= N)$, the $i$-th card has the number $Ai$ written on it.

-----Output:-----
- For each test case, print the count of the cards that remain in the end.

-----Constraints-----
- $1 \leq T \leq 500$
- $1 \leq N \leq 10^6$
- $1 \leq Ai \leq N$

-----Subtasks-----
- 30 points : $1 \leq T \leq 20$; $ 1 \leq N \leq 5*10^5$
- 70 points : Original constraints

-----Sample Input:-----
2
5
1 2 2 3 5
9
1 2 2 3 3 5 8 8 9

-----Sample Output:-----
3
5

-----EXPLANATION:-----
Test case 1:
Chefina chooses the cards with number: 2, 3, 5, throws away 2 & 5, and puts back 3. So, the pack now contains cards with numbers: 1, 2, 3. Since the pack contains cards with unique numbers only, these are the 3 final cards. 
Test case 2:
Chefina chooses the cards with number: 2, 3, 8, throws away 2 & 8,  and puts back 3. Now the pack contains cards with numbers: 1, 2, 3, 3, 5, 8, 9. Next, she chooses cards with number: 3, 5, 8 throws away 3 & 8, and puts back 5. Now the pack contains cards with number: 1, 2, 3, 5, 9. Since the pack contains cards with unique numbers only, these are the 5 final cards.
Note: There might be multiple options to choose the 3 cards from the pack in any turn
user: Shubham recently learned the lexicographical order in strings.

Now, he has two strings s1  and  s2  of the equal size and Shubham wants to compare those two strings lexicographically.

Help Shubham with the strings comparison.

Note:

Letters are case insensitive. 


-----Input-----

First line contains a integer T denoting the number of test cases. Each test case contains two strings of equal size in two separate lines.

-----Output-----

For each test case,

If s1 < s2, print "first".

If s1 > s2, print "second".

If s1=s2, print "equal".


in separate lines.

-----Constraints-----

- 1 ≤ T ≤ 10^2
- 1 ≤ Length of the string ≤ 500

-----Example-----
Input:
2
abc
acb
AB
ba

Output:
first
first
user: You have a laser with P amount of energy in it. You are playing a game where you have to use the laser to destroy some crystals, each with some health of their own. Initially, you have 0 points.
Each crystal has an associated health. The health of the ith crystal is given by health[i]. You can perform one of the two actions:
- 
At the cost of health[i] energy, you can destroy the ith crystal and gain 1 point. You can only perform this action if your laser has atleast health[i] energy in it.
- 
At the cost of 1 point, you can destroy the ith crystal and refuel the laser's energy by an amount equal to health[i]. This action can only be performed if you have atleast one point.
Note: Each crystal can only be destroyed once.
Determine the maximum number of points you can obtain by destroying any number of crystals and performing either action as you wish.

-----Input:-----
- First line will contain n, number of crystals. 
- Second line will contain space separated integers, health of each crystal.
- Third line will contain an integer P, initial energy of the laser.

-----Output:-----
Print the largest number of points we can have after destroying any number of crystals.

-----Constraints-----
- health.length <= 1000
- 0 <= health[i] < 10000
- 0 <= P < 10000

-----Subtasks-----
- 40 points : 1 <= health.length <= 100
- 60 points : health.length > 100

-----Sample Input 1:-----
1
200
100

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

-----Explanation:-----
The laser initially has only 100 energy. Since the only crystal requires 200 energy to destroy, we cannot perform any action here, and the game ends. The number of points is zero.

-----Sample Input 2:-----
2
100 200
150

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

-----Explanation:-----
The laser has 150 energy. We can consume 100 energy and destroy the first crystal and gain 1 point. The remaining energy is 50, which is not enough to destroy the other crystal. We end the game here as we have the maximum possible points attainable.
user: Three numbers A, B and C are the inputs. Write a program to find second largest among them.

-----Input-----

The first line contains an integer T, the total number of testcases. Then T lines follow, each line contains three integers A, B and C. 

-----Output-----
For each test case, display the second largest among A, B and C, in a new line.

-----Constraints-----
- 1 ≤ T ≤ 1000
- 1 ≤ A,B,C ≤ 1000000

-----Example-----
Input
3 
120 11 400
10213 312 10
10 3 450

Output

120
312
10
user: Chef had a sequence of positive integers with length $N + K$. He managed to calculate the arithmetic average of all elements of this sequence (let's denote it by $V$), but then, his little brother deleted $K$ elements from it. All deleted elements had the same value.
Chef still knows the remaining $N$ elements — a sequence $A_1, A_2, \ldots, A_N$. Help him with restoring the original sequence by finding the value of the deleted elements or deciding that there is some mistake and the described scenario is impossible.
Note that the if it is possible for the deleted elements to have the same value, then it can be proven that it is unique. Also note that this value must be a positive integer.

-----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 three space-separated integers $N$, $K$ and $V$.
- 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 one integer — the value of the deleted elements, or $-1$ if there is a mistake.

-----Constraints-----
- $1 \le T \le 100$
- $1 \le N, K \le 100$
- $1 \le V \le 10^5$
- $1 \le A_i \le 10^5$ for each valid $i$

-----Subtasks-----
Subtask #1 (100 points): original constraints

-----Example Input-----
3
3 3 4
2 7 3
3 1 4
7 6 5
3 3 4
2 8 3

-----Example Output-----
4
-1
-1
user: Write a program to obtain a number $N$ and increment its value by 1 if the number is divisible by 4 $otherwise$ decrement its value by 1.

-----Input:-----
- First line will contain a number $N$.

-----Output:-----
Output a single line, the new value of the number.

-----Constraints-----
- $0 \leq N \leq 1000$

-----Sample Input:-----
5

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

-----EXPLANATION:-----
Since 5 is not divisible by 4 hence, its value is decreased by 1.
user: You will be given a two-dimensional array with row consisting values 0 or 1.  
A move consists of choosing any column or row, and toggling all the 0’s as 1’s and 1’s as 0’s.  
After making the required moves, every row represents a binary number and the score of the matrix will be sum of all the numbers represented as binary numbers in each row.  
Find the highest possible score.  
$Example:$ 
Input:

0 0 1 1

1 0 1 0

1 1 0 0  
Output:

39
Explanation:

Toggled to

1 1 1 1

1 0 0 1

1 1 1 1  
0b1111 + 0b1001 + 0b1111 = 15 + 9 + 15 = 39

-----Input:-----
- First line will contains $m$, $n$ for the size of the 2-D array. 
- Contains $m$ lines of $n$ space-separated values each. 

-----Output:-----
Single integer which is the maximum score obtained by the sum of binary numbers.

-----Constraints-----
- $1 \leq m, n \leq 20$
- $A[i][j] = 1$ or $0$ 

-----Sample Input:-----
3 4  
0 0 1 1  
1 0 1 0  
1 1 0 0  

-----Sample Output:-----
39