meetforever/GRPO_CL huggingface dataset:
user: "It does not matter how slowly you go as long as you do not stop." - Confucius
You are given an array $A_1, A_2, \ldots, A_N$ and an integer $K$. For each subarray $S = [A_l, A_{l+1}, \ldots, A_r]$ ($1 \le l \le r \le N$):
- Let's define an array $B$ as $S$ concatenated with itself $m$ times, where $m$ is the smallest integer such that $m(r-l+1) \ge K$.
- Next, let's sort $B$ and define $X = B_K$, i.e. as a $K$-th smallest element of $B$. Note that $|B| \ge K$.
- Then, let's define $F$ as the number of occurrences of $X$ in $S$.
- The subarray $S$ is beautiful if $F$ occurs in $S$ at least once.
Find the number of beautiful subarrays of $A$. Two subarrays $A_l, A_{l+1}, \ldots, A_r$ and $A_p, A_{p+1}, \ldots, A_q$ are different if $l \neq p$ or $r \neq q$.

-----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 $A_1, A_2, \ldots, A_N$.

-----Output-----
For each test case, print a single line containing one integer - the number of beautiful subarrays.

-----Constraints-----
- $1 \le T \le 5$
- $1 \le N \le 2,000$
- $1 \le K \le 10^9$
- $1 \le A_i \le 2000$ for each valid $i$

-----Subtasks-----
Subtask #1 (20 points): $1 \le N \le 200$
Subtask #2 (80 points): original constraints

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

-----Example Output-----
3

-----Explanation-----
Example case 1: There are six subarrays of $A$: $[1]$, $[2]$, $[3]$, $[1, 2]$, $[2, 3]$, $[1, 2, 3]$. The corresponding arrays $B$ are $[1, 1, 1]$, $[2, 2, 2]$, $[3, 3, 3]$, $[1, 2, 1, 2]$, $[2, 3, 2, 3]$, $[1, 2, 3]$.
Three of the subarrays are beautiful: $[1]$, $[1, 2]$ and $[1, 2, 3]$. For these subarrays, $X$ is $1$, $2$ and $3$ respectively (for example, for $S = [1, 2]$, $B = [1, 2, 1, 2]$ is sorted to $[1, 1, 2, 2]$ and $X = 2$ is the $3$-rd element). Then, $F = 1$ for each of these subarrays, and each of these subarrays contains $1$.
user: The entire network is under the inspection and direct control of the Decepticons. They have learned our language through the World Wide Web and can easily understand the messages which are being sent. Sam is trying to send the information to Autobots to locate “ALL SPARK” which is the only source of energy that can be used to create universe. He is bit cautious in sending the message. He is sending the messages in a form of special pattern of string that contains important message in form of substrings. But Decepticons have learnt to recognize the Data Mining and string comparison patterns. He is sending a big message in form of a string (say M) and let there are N smaller substrings. Decepticons have to find whether each of these N substrings is a sub-string of M. All strings consist of only alphanumeric characters.

-----Input-----
Input to the program consists of two line. The first line contains the string M (where size of M should be <=40). The next line contain a string S.

-----Output-----
Output should consist of a line with a character 'Y'/'N' indicating whether the string S is a sub-string of String M or not.

-----Example-----
Input:
techtrishna online event
onlin
Output:
Y
user: We say that a binary string (a string containing only characters '0' and '1') is pure if it does not contain either of the strings "0101" or "1010" as a subsequence.
Recall that string T is a subsequence of string S if we can delete some of the letters of S (possibly none) such that the resulting string will become T.
You are given a binary string $S$ with length $N$. We want to make this string pure by deleting some (possibly zero) characters from it. What is the minimum number of characters we have to delete?

-----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 and only line of each test case contains a single string $S$ with length $N$.

-----Output-----
For each test case, print a single line containing one integer — the minimum number of characters we have to delete from $S$.

-----Constraints-----
- $1 \le T \le 40$
- $1 \le N \le 1,000$
- $S$ contains only characters '0' and '1'

-----Example Input-----
4
010111101
1011100001011101
0110
111111

-----Example Output-----
2
3
0
0

-----Explanation-----
Example case 1: We can delete the first and third character of our string. There is no way to make the string pure by deleting only one character.
Example case 3: The given string is already pure, so the answer is zero.
user: You are given a grid with $R$ rows (numbered $1$ through $R$) and $C$ columns (numbered $1$ through $C$). Initially, each cell of this grid is either empty, contains an ant or an anteater. Each ant is moving in a fixed direction: up, down, left or right. The anteaters do not move.
The movement of ants happens in discrete steps. For example, when an ant is in the cell in the $i$-th row and $j$-th column at some point in time (in some step) and it is moving down, then in the next step, it enters the cell in the $(i+1)$-th row and $j$-th column. Two ants meet each other when they enter the same cell at the same point in time (in the same step). When ants meet, they do not interact in any way and keep moving in their fixed directions.
If an ant reaches an anteater, that anteater eats the ant, so the ant completely disappears. If an ant attempts to leave the grid, it also disappears. When two ants enter a cell containing an anteater at the same time, they are eaten before they could meet.
Calculate the total number of pairs of ants that meet each other.

-----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 $R$ and $C$.
- Each of the following $R$ lines contains a single string with length $C$. For each valid $i, j$, the $j$-th character in the $i$-th string is:
- '#' if the cell in the $i$-th row and $j$-th column of the grid contains an anteater
- 'U', 'D', 'L' or 'R' if this cell contains an ant moving up, down, left or right respectively
- '-' if this cell is empty

-----Output-----
For each test case, print a single line containing one integer — the number of pairs of ants that meet.

-----Constraints-----
- $1 \le T \le 10$
- $1 \le R, C \le 50$
- each string contains only characters 'U', 'D', 'L', 'R', '#' and '-'

-----Example Input-----
10
3 3
R--
---
--U
1 4
R--R
2 2
--
--
1 4
R--L
1 4
-R-L
1 4
-R#L
3 3
R-D
-#-
R-U
3 3
R-D
---
R#U
3 3
-D-
R-L
-U-
1 7
RLLLLLL

-----Example Output-----
1
0
0
0
1
0
3
2
6
3
user: Appy and Chef are participating in a contest. There are $N$ problems in this contest; each problem has a unique problem code between $1$ and $N$ inclusive. Appy and Chef decided to split the problems to solve between them ― Appy should solve the problems whose problem codes are divisible by $A$ but not divisible by $B$, and Chef should solve the problems whose problem codes are divisible by $B$ but not divisible by $A$ (they decided to not solve the problems whose codes are divisible by both $A$ and $B$).
To win, it is necessary to solve at least $K$ problems. You have to tell Appy whether they are going to win or lose.

-----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 and only line of each test case contains four space-separated integers $N$, $A$, $B$ and $K$.

-----Output-----
For each test case, print a single line containing the string "Win" if they can solve at least $K$ problems or "Lose" otherwise (without quotes).

-----Constraints-----
- $1 \le T \le 15$
- $1 \le K \le N \le 10^{18}$
- $1 \le A, B \le 10^9$

-----Subtasks-----
Subtask #1 (15 points):
- $1 \le T \le 15$
- $1 \le K \le N \le 10^6$
- $1 \le A, B \le 10^3$
Subtask #2 (85 points): original constraints

-----Example Input-----
1
6 2 3 3

-----Example Output-----
Win

-----Explanation-----
Example case 1: Appy is solving the problems with codes $2$ and $4$, Chef is solving the problem with code $3$. Nobody is solving problem $6$, since $6$ is divisible by both $2$ and $3$. Therefore, they can solve $3$ problems and win.
user: The following graph G is called a Petersen graph and its vertices have been numbered from 0 to 9. Some letters have also been assigned to vertices of G, as can be seen from the following picture:

	Let's consider a walk W in graph G, which consists of L vertices W1, W2, ..., WL, such that Wi is connected with Wi + 1 for 1 ≤ i < L. A string S of L letters 'A'-'E' is realized by walk W if the sequence of letters written along W is equal to S. Vertices can be visited multiple times while walking along W.

For example, S = 'ABBECCD' is realized by W = (0, 1, 6, 9, 7, 2, 3).
Your task is to determine whether there is a walk W which realizes a given string S in graph G, and if so, find the lexicographically least such walk.

-----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 S. It is guaranteed that S only consists of symbols 'A'-'E'.

-----Output-----

	The output should contain exactly T lines, one line per each testcase in the order of their appearance. For each testcase, if there is no walk W which realizes S, then output -1. Otherwise, you should output the least lexicographical walk W which realizes S. Since all of the vertices are numbered from 0 to 9, then it can be encoded as a string consisting of symbols '0'-'9' (see the "Examples" section for more details).

-----Constraints-----
1 ≤ T ≤ 8;
1 ≤ |S| ≤ 100000(105).

-----Examples-----
Input:
2
AAB
AABE

Output:
501
-1
user: ZCO is approaching, and you want to be well prepared!  
There are $N$ topics to cover and the $i^{th}$ topic takes $H_i$ hours to prepare (where $1 \le i \le N$). You have only $M$ days left to prepare, and you want to utilise this time wisely. You know that you can't spend more than $S$ hours in a day preparing, as you get tired after that. You don't want to study more than one topic in a day, and also, don't want to spend more than two days on any topic, as you feel that this is inefficient.  
Given these constraints, can you find the maximum number of topics you can prepare, if you choose the topics wisely?

-----Input:-----
- First line will contain $T$, number of testcases. Then the testcases follow. 
- The first line of each test case contains three space-separated integers: $N$, $M$ and $S$, denoting the number of topics, the number of days remaining and the number of hours you can study in a day.  
- The second line of each test case contains $N$ space-separated integers $H_i$, denoting the number of hours needed to prepare for the $i^{th}$ topic.

-----Output:-----
For each testcase, output in a single line: the maximum number of topics you can prepare.

-----Constraints-----
- $1 \leq T \leq 10$
- $1 \leq N \leq 10^5$
- $1 \leq M \leq 10^5$
- $1 \leq S \leq 16$
- $1 \leq H_i \leq 50$

-----Subtasks-----
- 30 points : Every topic takes the same number of hours to prepare (i.e. all $H_i$ are equal).
- 70 points : Original constraints.

-----Sample Input:-----
2
5 4 10
10 24 30 19 40
5 4 16
7 16 35 10 15

-----Sample Output:-----
2
4

-----Explanation:-----
Testcase 1:

You can choose topics $1$ and $4$. Topic $1$ will consume a single day , while topic $4$ will consume two days.  Thus, you'll be able to prepare these two topics within the 4 remaining days. But you can check that you cannot do any better.
Testcase 2:

You can choose topics $1$, $2$, $4$, and $5$. Each of them will consume one day each. Thus you'll be able to cover $4$ topics.
user: Vanja and Miksi really like games. After playing one game for a long time, they decided to invent another game!
In this game, they have a sequence $A_1, A_2, \dots, A_N$ and two numbers $Z_1$ and $Z_2$. The rules of the game are as follows:
- The players take turns alternately, starting with Vanja.
- There is an integer $S$; at the beginning, $S = 0$.
- In each turn, the current player must choose an arbitrary element of $A$ and either add that number to $S$ or subtract it from $S$. Each element can be selected multiple times.
- Afterwards, if $S = Z_1$ or $S = Z_2$, the current player (the player who made $S$ equal to $Z_1$ or $Z_2$) is the winner of the game.
- If the game lasts for $10^{10}$ turns, Vanja and Miksi decide to declare it a tie.
Can you help the boys determine the winner of the game? Please note that the game can end in a tie (if nobody can make $S = Z_1$ or $S = Z_2$ in the first $10^{10}$ moves).
Both players play optimally, i.e. if there is a move which guarantees the current player's victory regardless of the other player's moves, the current player will make such a move. If the current player cannot win and there is a move which guarantees that the game will end in a tie, the current player will make such a move.

-----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 $N$, $Z_1$ and $Z_2$.
- The second line contains $N$ space-separated integers $A_1, A_2, \dots, A_N$.

-----Output-----
- For each test case, print a single line containing one integer — the final result of the game:
- $1$ if Vanja (the first player) has a winning strategy
- $2$ if Miksi (the second player) has a winning strategy
- $0$ if the game ends in a tie

-----Constraints-----
- $1 \le T \le 50$
- $1 \le N \le 50$
- $|Z_1|, |Z_2| \le 10^9$
- $|A_i| \le 10^9$ for each valid $i$

-----Subtasks-----
Subtask #1 (25 points): $N = 2$
Subtask #2 (75 points): original constraints

-----Example Input-----
3
2 6 4
-4 10
1 1 -1
2
2 0 7
3 4

-----Example Output-----
1
0
2

-----Explanation-----
Example case 1: The first player can choose the value $A_1 = -4$, subtract it from $S = 0$ and obtain $S = - (-4) = 4 = Z_2$. The winner is the first player.  
Example case 2: It can be proven that neither player is able to reach $S = Z_1$ or $S = Z_2$. The result is a tie.
user: Rachel has some candies and she decided to distribute them among $N$ kids. The ith kid receives $A_i$ candies. The kids are happy iff the difference between the highest and lowest number of candies received is less than $X$.
Find out if the children are happy or not.

-----Input:-----
- First line will contain $T$, number of testcases. Then the testcases follow. 
- The first line contains $N$ and $X$. 
- The second line contains $N$ integers $A_1,A_2,...,A_N$. 

-----Output:-----
For each test case print either "YES"(without quotes) if the kids are happy else "NO"(without quotes)

-----Constraints-----
- $1 \leq T \leq 100$
- $1 \leq N, X \leq 10^5$
- $1 \leq A_i \leq 10^5$

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

5 6

3 5 6 8 1

3 10

5 2 9

-----Sample Output:-----
NO

YES

-----EXPLANATION:-----
- Example 1: Difference between maximum and minimum candies received is 8-1=7. 7 is greater than 6, therefore, the kids are not happy.
user: A policeman wants to catch a thief. Both the policeman and the thief can only move on a line on integer coordinates between $0$ and $N$ (inclusive).
Initially, the policeman is at a coordinate $x$ and the thief is at a coordinate $y$. During each second, each of them must move to the left or right (not necessarily both in the same direction) by distance $\textbf{exactly}$ equal to $K$. No one may go to the left of the coordinate $0$ or to the right of $N$. Both the policeman and the thief move simultaneously and they cannot meet while moving, only at the end of each second.
Will the policeman be able to catch the thief if they both move optimally? The thief is caught as soon as the policeman and thief meet at the same position at the same time.

-----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 and only line of each test case contains four space-separated integers $x$, $y$, $K$ and $N$.

-----Output-----
For each test case, print a single line containing the string "Yes" if the thief can be caught or "No" if the thief cannot be caught (without quotes).

-----Constraints-----
- $1 \le T \le 1,000$
- $1 \le N \le 10^9$
- $1 \le K \le N$
- $0 \le x, y \le N$
- $x \neq y$

-----Example Input-----
5
0 1 1 1
1 4 1 5
4 2 1 7
3 7 2 10
8 2 3 15

-----Example Output-----
No
No
Yes
Yes
Yes

-----Explanation-----
Example case 1: The policeman is at $0$ and the thief is at $1$. After the $1$-st second, the policeman is at $1$ and the thief is at $0$. After the next second, the policeman is again at $0$ and the thief at $1$. They cannot end up at the same coordinate.
user: There is a big staircase with $N$ steps (numbered $1$ through $N$) in ChefLand. Let's denote the height of the top of step $i$ by $h_i$. Chef Ada is currently under the staircase at height $0$ and she wants to reach the top of the staircase (the top of the last step). However, she can only jump from height $h_i$ to the top of a step at height $h_f$ if $h_f-h_i \le K$. To help Ada, we are going to construct some intermediate steps; each of them may be constructed between any two steps, or before the first step, and have any height. What is the minimum number of steps that need to be added to the staircase so that Ada could reach the top?

-----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-seperated integers $h_1, h_2, \dots, h_N$.

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

-----Constraints-----
- $1 \le T \le 64$
- $1 \le N \le 128$
- $1 \le K \le 1,024$
- $1 \le h_i \le 1,024$ for each valid $i$
- $h_i < h_{i+1}$ for each valid $i$

-----Example Input-----
1
4 3
2 4 8 16

-----Example Output-----
3
user: There are $X$ people participating in a quiz competition and their IDs have been numbered from $1$ to $X$ (both inclusive). Beth needs to form a team among these $X$ participants. She has been given an integer $Y$. She can choose participants whose ID numbers are divisible by $Y$. 
Now that the team is formed, Beth wants to know the strength of her team. The strength of a team is the sum of all the last digits of the team members’ ID numbers.
Can you help Beth in finding the strength of her team?

-----Input:-----
- The first line of the input contains a single integer $T$ denoting the number of test cases. $T$ lines follow 
- The first line of each test case contains $X$ and $Y$. 

-----Output:-----
- For each test case print the strength of Beth's team

-----Constraints-----
- $1 \leq T \leq 1000$
- $1 \leq X,Y \leq 10^{20}$

-----Sample Input:-----
2
10 3

15 5

-----Sample Output:-----
18 

10

-----EXPLANATION:-----
- Example case 1: ID numbers divisible by 3 are 3,6,9 and the sum of the last digits are 3+6+9=18
user: Tracy loves Donuts. She purchased a lots of Donuts for her birthday party. She learnt to calculate the area of the circle a few days back and she is fascinated to know the area of the donuts as well !! Help her finding the area of the Donuts…..

-----Input:-----
- First line will contain, number of testcases. Then the testcases follow. 
- Each testcase contains of a single line of input, where in you have to provide the RADIUS of the Donuts. 

-----Output:-----
For each testcase, output in a single line answer is the AREA of the Donut.

-----Constraints-----
1 <= Radius <= 20.

-----Sample Input:-----
2
5 
12

-----Sample Output:-----
78.5

452.16
user: Given an array $A_1, A_2, ..., A_N$, count the number of subarrays of array $A$ which are non-decreasing.

A subarray $A[i, j]$, where $1 ≤ i ≤ j ≤ N$ is a sequence of integers $A_i, A_i+1, ..., A_j$.
A subarray $A[i, j]$ is non-decreasing if $A_i ≤ A_i+1 ≤ A_i+2 ≤ ... ≤ A_j$. You have to count the total number of such subarrays.

-----Input-----
- 
The first line of input contains an 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 $N$ denoting the size of array.
- 
The second line contains $N$ space-separated integers $A_1$, $A_2$, …, $A_N$ denoting the elements of the array.

-----Output-----
For each test case, output in a single line the required answer.

-----Constraints-----
- $1 ≤ T ≤ 5$
- $1 ≤ N ≤ 10^5$
- $1 ≤ A_i ≤ 10^9$

-----Subtasks-----
- Subtask 1 (20 points) : $1 ≤ N ≤ 100$
- Subtask 2 (30 points) : $1 ≤ N ≤ 1000$
- Subtask 3 (50 points) : Original constraints

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

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

-----Explanation-----
Example case 1.

All valid subarrays are $A[1, 1], A[1, 2], A[2, 2], A[3, 3], A[3, 4], A[4, 4]$.

Note that singleton subarrays are identically non-decreasing.
Example case 2.

Only single subarray $A[1, 1]$ is non-decreasing.
user: As we all know, Chef is cooking string for long days, his new discovery on string is the longest common pattern length. The longest common pattern length between two strings is the maximum number of characters that both strings have in common. Characters are case sensitive, that is, lower case and upper case characters are considered as different. Note that characters can repeat in a string and a character might have one or more occurrence in common between two strings. For example, if Chef has two strings A = "Codechef" and B = "elfedcc", then the longest common pattern length of A and B is 5 (common characters are c, d, e, e, f).
Chef wants to test you with the problem described above. He will give you two strings of Latin alphabets and digits, return him the longest common pattern length.

-----Input-----
The first line of the input contains an integer T, denoting the number of test cases. Then the description of T test cases follows.
The first line of each test case contains a string A. The next line contains another character string B.

-----Output-----
For each test case, output a single line containing a single integer, the longest common pattern length between A and B.

-----Constraints-----
- 1 ≤ T ≤ 100
- 1 ≤ |A|, |B| ≤ 10000 (104), where |S| denotes the length of the string S
- Both of A and B can contain only alphabet characters (both lower and upper case) and digits

-----Example-----
Input:
4
abcd
xyz
abcd
bcda
aabc
acaa
Codechef
elfedcc

Output:
0
4
3
5

-----Explanation-----
Example case 1. There is no common character.
Example case 2. All the characters are same.
Example case 3. Three characters (a, a and c) are same.
Example case 4. This sample is mentioned by the statement.