meetforever/GRPO_CL huggingface dataset:
user: Ram and Shyam are playing a game of Truth and Dare. In this game, Shyam will ask Ram to perform tasks of two types:
- Truth task: Ram has to truthfully answer a question.
- Dare task: Ram has to perform a given task.
Each task is described by an integer. (If a truth task and a dare task are described by the same integer, they are still different tasks.) You are given four lists of tasks:
- $T_{r, 1}, T_{r, 2}, \dots, T_{r, t_r}$: the truth tasks Ram can perform.
- $D_{r, 1}, D_{r, 2}, \dots, D_{r, d_r}$: the dare tasks Ram can perform.
- $T_{s, 1}, T_{s, 2}, \dots, T_{s, t_s}$: the truth tasks Shyam can ask Ram to perform.
- $D_{s, 1}, D_{s, 2}, \dots, D_{s, d_s}$: the dare tasks Shyam can ask Ram to perform.
Note that the elements of these lists are not necessarily distinct, each task may be repeated any number of times in each list.
Shyam wins the game if he can find a task Ram cannot perform. Ram wins if he performs all tasks Shyam asks him to. Find the winner of the game.
Let's take an example where Ram can perform truth tasks $3$, $2$ and $5$ and dare tasks $2$ and $100$, and Shyam can give him truth tasks $2$ and $3$ and a dare task $100$. We can see that whichever truth or dare tasks Shyam asks Ram to perform, Ram can easily perform them, so he wins. However, if Shyam can give him dare tasks $3$ and $100$, then Ram will not be able to perform dare task $3$, so Shyam wins.

-----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 $t_r$.
- The second line contains $t_r$ space-separated integers $T_{r, 1}, T_{r, 2}, \dots, T_{r, t_r}$.
- The third line contains a single integer $d_r$.
- The fourth line contains $d_r$ space-separated integers $D_{r, 1}, D_{r, 2}, \dots, D_{r, d_r}$.
- The fifth line contains a single integer $t_s$.
- The sixth line contains $t_s$ space-separated integers $T_{s, 1}, T_{s, 2}, \dots, T_{s, t_s}$.
- The seventh line contains a single integer $d_s$.
- The eighth line contains $d_s$ space-separated integers $D_{s, 1}, D_{s, 2}, \dots, D_{s, d_s}$.

-----Output-----
For each test case, print a single line containing the string "yes" if Ram wins the game or "no" otherwise.

-----Constraints-----
- $1 \le T \le 100$
- $1 \le t_r, d_r, t_s, d_s \le 100$
- $1 \le T_{r, i} \le 100$ for each valid $i$
- $1 \le D_{r, i} \le 100$ for each valid $i$
- $1 \le T_{s, i} \le 100$ for each valid $i$
- $1 \le D_{s, i} \le 100$ for each valid $i$

-----Example Input-----
4
2
1 2
3
1 3 2
1
2
2
3 2
2
1 2
3
1 3 2
1
2
3
3 2 4
3
3 2 5
2
2 100
1
2
1
100
2
1 2
3
1 3 2
1
2
3
3 2 2

-----Example Output-----
yes
no
yes
yes

-----Explanation-----
Example case 1: Ram's truth tasks are $[1, 2]$ and his dare tasks are $[1, 3, 2]$. Shyam's truth tasks are $[2]$ and his dare tasks are $[3, 2]$. Ram can perform all tasks Shyam gives him.
Example case 2: Ram's truth tasks are $[1, 2]$ and his dare tasks are $[1, 3, 2]$. Shyam's truth tasks are $[2]$ and his dare tasks are $[3, 2, 4]$. If Shyam asks Ram to perform dare task $4$, Ram will not be able to do it.
user: An encoder encodes the first $16$ lowercase English letters using $4$ bits each. The first bit (from the left) of the code is $0$ if the letter lies among the first $8$ letters, else it is $1$, signifying that it lies among the last $8$ letters. The second bit of the code is $0$ if the letter lies among the first $4$ letters of those $8$ letters found in the previous step, else it's $1$, signifying that it lies among the last $4$ letters of those $8$ letters. Similarly, the third and the fourth bit each signify the half in which the letter lies. 
For example, the letter $j$ would be encoded as :
- Among $(a,b,c,d,e,f,g,h$ $|$ $i,j,k,l,m,n,o,p)$, $j$ appears in the second half. So the first bit of its encoding is $1$.
- Now, among $(i,j,k,l$ $|$ $m,n,o,p)$, $j$ appears in the first half. So the second bit of its encoding is $0$.
- Now, among $(i,j$ $|$ $k,l)$, $j$ appears in the first half. So the third bit of its encoding is $0$.
- Now, among $(i$ $|$ $j)$, $j$ appears in the second half. So the fourth and last bit of its encoding is $1$.
So $j$'s encoding is $1001$,
Given a binary encoded string $S$, of length at most $10^5$, decode the string. That is, the first 4 bits are the encoding of the first letter of the secret message, the next 4 bits encode the second letter, and so on. It is guaranteed that the string's length is a multiple of 4.

-----Input:-----
- The first line of the input contains an integer $T$, denoting the number of test cases.
- The first line of each test case contains an integer $N$, the length of the encoded string.
- The second line of each test case contains the encoded string $S$.

-----Output:-----
For each test case, print the decoded string, in a separate line.

-----Constraints-----
- $1 \leq T \leq 10$
- $4 \leq N \leq 10^5$
- The length of the encoded string is a multiple of $4$.
- $0 \le S_i \le 1$

-----Subtasks-----
- $100$ points : Original constraints. 

-----Sample Input:-----
3
4
0000
8
00001111
4
1001

-----Sample Output:-----
a
ap
j

-----Explanation:-----
- Sample Case $1$ : 
The first bit is $0$, so the letter lies among the first $8$ letters, i.e., among $a,b,c,d,e,f,g,h$. The second bit is $0$, so it lies among the first four of these, i.e., among $a,b,c,d$. 
The third bit is $0$, so it again lies in the first half, i.e., it's either $a$ or $b$. Finally, the fourth bit is also $0$, so we know that the letter is $a$.
- Sample Case $2$ : 
Each four bits correspond to a character. Just like in sample case $1$, $0000$ is equivalent to $a$. Similarly, $1111$ is equivalent to $p$. So, the decoded string is $ap$.
- Sample Case $3$ : 
The first bit is $1$, so the letter lies among the last $8$ letters, i.e., among $i,j,k,l,m,n,o,p$. The second bit is $0$, so it lies among the first four of these, i.e., among $i,j,k,l$. 
The third bit is $0$, so it again lies in the first half, i.e., it's either $i$ or $j$. Finally, the fourth bit is $1$, so we know that the letter is $j$.
user: Chef wants to serve mankind by making people immortal by preparing a dish, a dish of life - a dish with the best taste in the universe, one with the smell and splash of fresh water flowing down the springs of the mountain, one with the smell of the best lily flowers of the garden, one that has contained the very essence of life in a real sense. 
This dish will contain K ingredients that are found only in remote islands amid mountains. For sake of convenience, we enumerate the ingredients by the integers from 1 to K, both inclusive. There are N islands and each of them offers some ingredients. Chef being a little child did not know how to collect the ingredients for the recipe. He went to all the islands and bought all the ingredients offered in each island. Could he possibly have saved some time by skipping some island? If it was not possible for Chef to collect the required ingredients (i.e. all the K ingredients), output "sad". If it was possible for him to skip some islands, output "some", otherwise output "all".

-----Input-----
First line of the input contains an integer T denoting number of test cases. The description of T test cases follow.
The first line of each test case contains two space separated integers N, K.
The i-th of the next lines will contain first an integer Pi, denoting the number of ingredients grown in the i-th island, followed by Pi distinct integers in the range [1, K]. All the integers are space separated. 

-----Output-----
For each test case, output a single line containing one of the strings "sad", "all" or "some" (without quotes) according to the situation. 

-----Constraints-----
- 1 ≤ T  ≤ 10
- 1 ≤ N, K ≤ 105
- 1 ≤ Pi ≤ K
- Sum of Pi over all test cases ≤ 106

-----Subtasks-----
Subtask #1 (30 points)
- 1 ≤ N, K ≤ 50

Subtask #2 (30 points)
- 1 ≤ K ≤ 50

Subtask #3 (40 points)
- original constraints

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

Output
sad
some
all

-----Explanation-----
Example 1. The ingredient 4 is not available in any island, so Chef can't make the dish of life. Hence, the answer is "sad".
Example 2. Chef can just go to the first island and collect all the three ingredients required. He does not need to visit the second island. So, the answer is "some".
Example 3. Chef has to visit both the islands in order to obtain all the three ingredients. So, the answer is "all".
user: Motu and Patlu are playing with a Magical Ball. Patlu find some interesting pattern in the motion of the ball that ball always bounce back from the ground after travelling a linear distance whose value is some power of $2$. Patlu gave Motu total distance $D$ travelled by the ball and ask him to calculate the minimum number of bounces that the ball makes before coming to rest.

-----Input:-----
- First line will contain $T$, number of testcases. Then the testcases follow. 
- Each testcase contains of a single line of input, single integers $D$.
- Note : Power of $2$ must be a non-negative integer. 

-----Output:-----
For each testcase, output in a single line answer, the minimum number of bounces the ball makes before coming to rest.

-----Constraints-----
- $1 \leq T \leq 10^5$
- $1$ $\leq$ $M$< $10$^18

-----Sample Input:-----
1
13 

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

-----EXPLANATION:-----
user: Two players are playing a game. The game is played on a sequence of positive integer pairs. The players make their moves alternatively. During his move the player chooses a pair and decreases the larger integer in the pair by a positive multiple of the smaller integer in the pair in such a way that both integers in the pair remain positive. If two numbers in some pair become equal then the pair is removed from the sequence. The player who can not make any move loses (or in another words the player who encounters an empty sequence loses). Given the sequence of positive integer pairs determine whether the first player can win or not (assuming that both players are playing optimally).

-----Input-----
The first line of the input contains an integer T denoting the number of test cases. The description of T test cases follows.
Each test starts with an integer N denoting the number of pairs. Each of the next N lines contains a pair of positive integers. 

-----Output-----
For each test case, output a single line containing "YES" if the first player can win and "NO" otherwise. 

-----Constraints-----
- 1 ≤ T ≤ 100
- 1 ≤ N ≤ 100
- All other integers are between 1 to 108
- The integers in each pair will be different

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

Output:
NO
NO
YES


-----Explanation-----
Example case 1. The first player don't have any choice other subtracting 2 from 3. So during the turn of the second player integer pair will be (2,1). The second player will win by subtracting 1 from 2. 
Example case 2. If the first player choose to move (4,5) to (4,1) the second player will make it to (1,1). If the first player choose to move (5,6) to (5,1) the second player will make it to (1,1). So regardless of the move of the first player, the second will always win.
Example case 3. The first player will select pair (3,5) and make it to (3,2). Now both pairs are equal. So whatever the move of second player he will just mirror that move in another pair. This will ensure his win.
user: The chef is trying to solve some pattern problems, Chef wants your help to code it. Chef has one number K 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
2
3
4

-----Sample Output:-----
*
*
*
*
***
***
*
*
***
***
*****
*****
*
*
***
***
*****
*****
*******
*******

-----EXPLANATION:-----
No need, else pattern can be decode easily.
user: In a fictitious city of CODASLAM there were many skyscrapers. The mayor of the city decided to make the city beautiful and for this he decided to arrange the skyscrapers in descending order of their height, and the order must be strictly decreasing but he also didn’t want to waste much money so he decided to get the minimum cuts possible. Your job is to output the minimum value of cut that is possible to arrange the skyscrapers in descending order.

-----Input-----

*First line of input is the number of sky-scrappers in the city
*Second line of input is the height of the respective sky-scrappers


-----Output-----

* Your output should be the minimum value of cut required to arrange these sky-scrappers in descending order.

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

Output:
8

By:
Chintan,Asad,Ashayam,Akanksha
user: There is Chef and Chef’s Crush who are playing a game of numbers.

Chef’s crush has a number $A$ and Chef has a number $B$.

Now, Chef wants Chef’s crush to win the game always, since she is his crush. The game ends when the greatest value of A^B is reached after performing some number of operations (possibly zero), Where ^ is Bitwise XOR.

Before performing any operation you have to ensure that both $A$ and $B$ have the same number of bits without any change in the values. It is not guaranteed that $A$ and $B$ should have same number of bits in the input.
For example, if $A$ is $2$ and $B$ is $15$, then the binary representation of both the numbers will have to be $0010$ and $1111$ respectively, before performing any operation.  
The operation is defined as  : 
- Right circular shift of the bits of only $B$ from MSB$_B$ to LSB$_B$ i.e. if we consider $B_1 B_2 B_3 B_4$ as binary number, then after one circular right shift, it would be $B_4 B_1 B_2 B_3$
They both are busy with themselves, can you find the number of operations to end the game?

-----Input :-----
- The first line of input contains $T$, (number of test cases)  
- Then each of the next $T$ lines contain : two integers $A$ and $B$ respectively.

-----Output :-----
For each test case print two space-separated integers, The number of operations to end the game and value of A^B when the game ends.

-----Constraints :-----
- $1 \leq T \leq100$ 
- $1\leq A,B \leq 10^{18}$

-----Subtasks  :-----
- 30 Points: $1\leq A,B \leq 10^5$
- 70 Points: Original Constraints

-----Sample Input :-----
1
4 5

-----Sample Output :-----
2 7

-----Explanation  :-----
Binary  representation of  $4$ is $100$ and binary  representation  $5$ is $101$.   
- After operation $1$ : $B$ $=$ $110$, so A^B $=$ $2$ 
- After operation $2$ : $B$ $=$ $011$, so A^B $=$ $7$ 
So, the value of A^B will be $7$. Which is the greatest possible value for A^B and the number of operations are $2$.
user: Chef Tobby is playing a rapid fire with Bhuvan. He gives Bhuvan a string S and each time, Bhuvan has to guess whether there exists 2 equal subsequences in the string or not.
Bhuvan got a perfect score in the game with Chef Tobby. However, Chef Tobby has now asked Bhuvan to write a program that will do this automatically given a string S. Bhuvan is an intelligent man but he does not know how to write a code. Can you help him?
Find two different subsequences such that they are equal in their value, more formally, find two sequences of indices (a1, a2, ..., ak-1, ak) and (b1, b2, ..., bk-1, bk) such that:

- 1≤ ai, bi ≤ |S|
- ai < ai+1 for all valid i
- bi < bi+1 for all valid i
- Sai = Sbi for all valid i
- there exist at least one i such that ai is not equal to bi

-----Input section-----
The first line contains T, the number of test cases.
Each of the next T lines contain one string S each.
Input will only consist of lowercase english characters

-----Output section-----
For each test case, output "yes" or "no" (without quotes) as the solution to the problem.

-----Input constraints-----
1 ≤ T ≤ 1000
1 ≤ length of S ≤ 100

-----Sample Input-----
4
likecs
venivedivici
bhuvan
codechef

-----Sample Output-----
no
yes
no
yes

-----Explanation-----
In test case 2, one of the possible equal subsequence is "vi" and "vi". (one at position {0, 3} and other at {4, 7}, assuming 0-based indexing).
In test case 4, one of the possible equal subsequence is "ce" and "ce". (one at position {0, 3} and other at {4, 6}, assuming 0-based indexing).
user: Chef has gone shopping with his 5-year old son. They have bought N items so far. The items are numbered from 1 to N, and the item i weighs Wi grams.

Chef's son insists on helping his father in carrying the items. He wants his dad to give him a few items. Chef does not want to burden his son. But he won't stop bothering him unless he is given a few items to carry. So Chef decides to give him some items. Obviously, Chef wants to give the kid less weight to carry.

However, his son is a smart kid. To avoid being given the bare minimum weight to carry, he suggests that the items are split into two groups, and one group contains exactly K items. Then Chef will carry the heavier group, and his son will carry the other group.

Help the Chef in deciding which items should the son take. Your task will be simple. Tell the Chef the maximum possible difference between the weight carried by him and the weight carried by the kid.

-----Input:-----
The first line of input contains an integer T, denoting the number of test cases. Then T test cases follow. The first line of each test contains two space-separated integers N and K. The next line contains N space-separated integers W1, W2, ..., WN.

-----Output:-----
For each test case, output the maximum possible difference between the weights carried by both in grams.

-----Constraints:-----
- 1 ≤ T ≤ 100
- 1 ≤ K < N ≤ 100
- 1 ≤ Wi ≤ 100000 (105)

-----Example:-----
Input:
2
5 2
8 4 5 2 10
8 3
1 1 1 1 1 1 1 1

Output:
17
2

-----Explanation:-----
Case #1: The optimal way is that Chef gives his son K=2 items with weights 2 and 4. Chef carries the rest of the items himself. Thus the difference is: (8+5+10) − (4+2) = 23 − 6 = 17.

Case #2: Chef gives his son 3 items and he carries 5 items himself.
user: Consider the following operations on a triple of integers. In one operation, you should:
- Choose an integer $d$ and an arithmetic operation ― either addition or multiplication.
- Choose a subset of elements of the triple.
- Apply the arithmetic operation to each of the chosen elements, i.e. either add $d$ to each of them or multiply each of them by $d$.
For example, if we have a triple $(3, 5, 7)$, we may choose to add $3$ to the first and third element, and we get $(6, 5, 10)$ using one operation.
You are given an initial triple $(p, q, r)$ and a target triple $(a, b, c)$. Find the minimum number of operations needed to transform $(p, q, r)$ into $(a, b, c)$.

-----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 $p$, $q$ and $r$.
- The second line contains three space-separated integers $a$, $b$ and $c$.

-----Output-----
For each test case, print a single line containing one integer ― the minimum required number of operations.

-----Constraints-----
- $1 \le T \le 1,000$
- $|p|, |q|, |r|, |a|, |b|, |c| \le 10^9$

-----Subtasks-----
Subtask #1 (10 points): $|p|, |q|, |r|, |a|, |b|, |c| \le 10$
Subtask #2 (90 points): original constraints

-----Example Input-----
2
3 5 7
6 5 10
8 6 3
9 7 8

-----Example Output-----
1
2

-----Explanation-----
Example case 1: We add $3$ to the first and third element of $(3, 5, 7)$ to form $(6, 5, 10)$.
Example case 2: We can add $1$ to each element to form $(9, 7, 4)$ and then multiply the third element by $2$.
user: Johnny was asked by his math teacher to compute nn (n to the power of n, where n is an integer), and has to read his answer out loud. This is a bit of a tiring task, since the result is probably an extremely large number, and would certainly keep Johnny occupied for a while if he were to do it honestly. But Johnny knows that the teacher will certainly get bored when listening to his answer, and will sleep through most of it! So, Johnny feels he will get away with reading only the first k digits of the result before the teacher falls asleep, and then the last k digits when the teacher wakes up.

Write a program to help Johnny to compute the digits he will need to read out.

-----Input-----
The first line contains t, the number of test cases (about 30000). Then t test cases follow.
Each test case consists of one line containing two numbers n and k (1 ≤ n ≤ 109, 1 ≤ k ≤ 9). It is guaranteed that k is not more than the number of digits of nn.

-----Output-----
For each test case, print out one line containing two numbers, separated by a space, which are the first and the last k digits of nn.

-----Example-----
Input
2
4 2
9 3

Output
25 56
387 489
user: Sherlock Holmes has decided to start a new academy to some of the young lads. He has conducted several tests and finally selected N equally brilliant

students.Now he don't know whether to train all the N students or not. Now since Holmes was in a confusion, Watson came up with an idea. He wanted to

test the obedience of the students. So during the camp, the students were given some Swiss Chocolates as gifts each time when they passed a level.Now some of them have

finished eating all the chocolates, some of them had some remaining. Now to test their team chemistry and IQ skills, Watson told the lads to arrange themselves in such 
a way that,  number of chocolates of the ith kid should be equal to the sum of   (i-1)th kid and (i-2)th kid. Now they have arranged themselves in an order.
Now Sherlock announced that he will select the students who have formed the line according to this order. But since there can be many such small groups among the

entire N kids, he will select a sequence of kids such that the length of the sequence is maximized, meanwhile satisfying the above condition 

-----Input-----
First line is an integer T which denotes the total number of test cases. Each of the next T lines contains an integer N which denotes, N students. The next 
line contains N spaced integers.where it denotes the order in which the kids arranged themselves. 

-----Output-----
Each line contains an integer which denotes the maximum number of students among the N students who have arranged themselves according the rule said by Watson.It is guaranteed that Holmes will select atleast 1 or 2 students

-----Constraints-----
- 1 ≤ T ≤ 10
- 1 ≤ N ≤ 10^5
- 1 ≤ Each of next N integers ≤ 10^9

-----Subtasks-----
Subtask #1 : (20 points)
- 1 ≤ T ≤ 10
- 1 ≤ N≤ 100
- 1 ≤ Each element≤ 10^3

Subtask 2 : (80 points) 

- 1 ≤ T ≤ 10
- 1 ≤ N≤ 100000
- 1 ≤ Each element≤ 10^9

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

Output:
3
3

-----Explanation-----
Example case 1. Here the first kid has 2 chocolates, second has 3 chocolates, third kid has 5 chocolates, which is the sum of first kid's total chocolates 
and second kid's chocolate. Forth student has only 1 chocolate where he did not follow the rule. So the maximum number of kids who arranged themselves in the order was 
3. That is students at index 1 to index 3.