meetforever/GRPO_CL huggingface dataset:
user: Chef has just started Programming, he is in first year of Engineering. Chef is reading about Relational Operators. 

Relational Operators are operators which check relatioship between two values. Given two numerical values A and B you need to help chef in finding the relationship between them that is, 

- First one is greater than second or,
- First one is less than second or,
- First and second one are equal.

-----Input-----
First line contains an integer T, which denotes the number of testcases. Each of the T lines contain two integers A and B. 

-----Output-----
For each line of input produce one line of output. This line contains any one of the relational operators

'<' , '>' , '='.

-----Constraints-----

- 1 ≤ T ≤ 10000
- 1 ≤ A, B ≤ 1000000001

-----Example-----
Input:
3
10 20
20 10
10 10

Output:
<
>
=

-----Explanation-----
Example case 1. In this example 1 as 10 is lesser than 20.
user: Batman is about to face Superman so he decides to prepare for the battle by upgrading his Batmobile. He manufactures multiple duplicates of his standard Batmobile each tweaked in a different way such that the maximum speed of each is never less than that of the standard model.
After carrying out this process, he wishes to know how many of his prototypes are faster than his standard Batmobile?

-----Input-----
- The first line of the input contains an integer T denoting the number of test cases. The description of T test cases follow: 
- The first line of each test case contains a single integer N denoting the number of copies of the standard Batmobile.
- The second line contains a sequence of N+1 space-separated integers, S0 to SN, sorted in non-decreasing order separated by space. S0 is the maximum speed of the standard Batmobile. S1 to SN denote the maximum speeds of the prototypes.

-----Output-----
- For each test case, output a single line containing an integer denoting the answer.

-----Constraints-----
- 1 ≤ T ≤ 1000
- 1 ≤ N ≤ 1000
- 1 ≤ Si ≤ 109

-----Example-----
Input:
2
4
1 2 3 4 5
5
1 10 100 1000 10000 100000

Output:
4
5
user: Chef has $N$ dishes of different types arranged in a row: $A_1, A_2, \ldots, A_N$, where $A_i$ denotes the type of the $i^{th}$ dish. He wants to choose as many dishes as possible from the given list but while satisfying two conditions: 
- He can choose only one type of dish.   
- No two chosen dishes should be adjacent to each other. 
Chef wants to know which type of dish he should choose from, so that he can pick the maximum number of dishes.
Example:

Given $N$=$9$ and $A$=$[1, 2, 2, 1, 2, 1, 1, 1, 1]$.

For type 1, Chef can choose at most four dishes. One of the ways to choose four dishes of type 1 is $A_1$, $A_4$, $A_7$ and $A_9$.

For type 2, Chef can choose at most two dishes. One way is to choose $A_3$ and $A_5$.

So in this case, Chef should go for type 1, in which he can pick more dishes.

-----Input:-----
- The first line contains $T$, the number of test cases. Then the test cases follow.
- For each test case, the first line contains a single integer $N$.
- The second line contains $N$ integers $A_1, A_2, \ldots, A_N$. 

-----Output:-----
For each test case, print a single line containing one integer ― the type of the dish that Chef should choose from. If there are multiple answers, print the smallest one.

-----Constraints-----
- $1 \le T \le 10^3$
- $1 \le N \le 10^3$
- $1 \le A_i \le 10^3$
- Sum of $N$ over all test cases doesn't exceed $10^4$

-----Sample Input:-----
3
5
1 2 2 1 2
6
1 1 1 1 1 1
8
1 2 2 2 3 4 2 1

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

-----Explanation:-----
Test case 1:

For both type 1 and type 2, Chef can pick at most two dishes. In the case of multiple answers, we pick the smallest one. Hence the answer will be $1$.
Test case 2:

There are only dishes of type 1. So the answer is $1$.
Test case 3:

For type 1, Chef can choose at most two dishes. For type 2, he can choose three dishes. For type 3 and type 4, Chef can choose the only dish available. Hence the maximum is in type 2 and so the answer is $2$.
user: Sunita has lots of tasks pending and she has no time to complete.  She needs your help and wants you complete the task.
You are given a list of integers and two values $N$ and $K$ $-$ the size of array of integers and the numbers of partitions to be made respectively.
You have to partition the list of integers without changing the order of elements ,into exactly $K$ parts. 
Calculate Greatest Common Divisor of all $K$ partition and sum up the gcd values for each partition.
Maximize the sum obtained. 
Can you help Sunita ? 

-----Input:-----
- First line will contain $T$, number of test cases. Then the test cases follow. 
- Each test case contains of a single line of input, two integers $N, K$. 
- Next line contains $N$ integers $-$ the list of integers.

-----Output:-----
For each test case, output in a single line integer $-$ the maximal result.

-----Constraints-----
- $1 \leq T \leq 100$
- $1 \leq N, K \leq 250$
- $1 \leq K \leq N$
- $1 \leq A[i] \leq 1e5$

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

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

-----EXPLANATION:-----
[5] [6 3 2] is the best partition [5 + GCD(6,3,2)] = 6
user: The chef has a number N, Cheffina challenges chef to form the largest number X from the digits of N.

-----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, $N$. 

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

-----Constraints-----
- $1 \leq T \leq 10^5$
- $1 \leq N \leq 10^6$

-----Sample Input:-----
2
2
212

-----Sample Output:-----
2
221
user: The  Chef  has bought $N$ boxes of Tiles. The number of tiles present in  $i^{th}$ box is  $i$  ($i   $ varies from $1$ to $N$) . The Chef  has two houses  with  $N$  rooms  each, whose  floors  is a square with area $(i*i)$ ,i varies from $(1....N)$. He want to distribute equal number of tiles from $i^{th}$ box to any two rooms (each room must belong to one house ) such that all tiles  of $i^ { th}$  box is used and floor of  both rooms of different houses are tiled completely.
Since chef is busy doing some other works so he wants your help to count the total number of rooms of both houses that will be tiled completely.
Note $:$ size of  each tile present in boxes has length and breadth equal to $1$. It is not mandatory to use all the boxes.
A room should be tilled completely from a single box.

-----Input:-----
- First line will contain $T$, number of testcases. Then the testcases follow. 
- Each testcase contains one integer $N$.

-----Output:-----
For each testcase print  the total number of rooms of both houses that will be tiled completely.

-----Constraints-----
- $1 \leq T \leq 5000$
- $1 \leq N \leq 10^{12}$

-----Sample Input:-----
1
16

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

-----EXPLANATION:-----
The room $1$ and $2$ of both the houses are completely tiled.
user: After the death of their mother, Alphonse and Edward now live with Pinako and Winry.

Pinako is worried about their obsession with Alchemy, and that they don't give attention to their studies.
So to improve their mathematical solving ability, every day she gives a mathematical problem to solve. They can go out to practice Alchemy only after they have solved the problem.
Help them by solving the given problem, so that they can go early today for their Alchemy practice.    
Given an array A$A$ of N$N$ non-negative integers and two integers K$K$ and M$M$. Find the number of subsequences of array A$A$ of length K$K$ which satisfies the following property:

Suppose the subsequence is S=S1S2…SK$S = S_1S_2 \ldots S_K$, then for all i$i$ such that 1≤i≤K$1 \leq i \leq K$,
Si%M=i%M S_i \% M = i \% M  
should hold true, where Si$S_i$ denotes the i$i$-th element of the subsequence, using 1-based indexing.
As the number of subsequences may be very large, output the answer modulo 1000000007$1000000007$.     
PS: We also proposed the idea of making a look-alike clone through alchemy and keeping it in front of the study table. But it seems impossible to convince Edward to make a clone of his exact same height, and not taller than him. So solving the problem for him was a better choice.   

-----Input:-----
- The first line contains T$T$, the number of test cases. Then the test cases follow. 
- For every test case, the first line contains N$N$, K$K$ and M$M$.
- For every test case, the second line contains N$N$ integers Ai$A_{i}$ ( 1≤i≤N$1 \leq i \leq N$).

-----Output:-----
For every test case, output in a single line an integer denoting the number of valid subsequences modulo 109+7$10^9+7$

-----Constraints-----
- 1≤T≤100$1 \leq T \leq 100$ 
- 1≤N≤104$1 \leq N \leq 10^{4}$ 
- 1≤K≤N$1 \leq K \leq N$ 
- ⌈K100⌉≤M≤100×K$\lceil \frac{K}{100}\rceil \leq M \leq  100\times K$ 
- 0≤Ai≤109$0 \leq A_{i} \leq 10^{9}$ 

-----Sample Input:-----
1
12 4 3
4 5 6 7 1 4 6 9 0 0 10 2

-----Sample Output:-----
8

-----Explanation:-----
The subsequences of length 4$4$, satisfying the given criteria are [4,5,6,7]$[4, 5, 6, 7]$, [4,5,6,10]$[4, 5, 6, 10]$, [4,5,6,10]$[4, 5, 6, 10]$, [4,5,6,1]$[4, 5, 6, 1]$, [4,5,9,10]$[4, 5, 9, 10]$ ,[4,5,6,4]$[4, 5, 6, 4]$ , [4,5,0,10]$[4, 5, 0, 10]$ and [4,5,0,10]$[4, 5, 0, 10]$. This accounts for a total of 8$8$ valid subsequences.
Let us take one subsequence and see why it satisfies the given property. Consider [4,5,9,10]$[4, 5, 9, 10]$. 
- S1%M=4%3=1=1%3=1%M$ S_1 \% M = 4 \% 3 = 1 = 1 \% 3 = 1 \% M $
- S2%M=5%3=2=2%3=2%M$ S_2 \% M = 5 \% 3 = 2 = 2 \% 3 = 2 \% M $
- S3%M=9%3=0=3%3=3%M$ S_3 \% M = 9 \% 3 = 0 = 3 \% 3 = 3 \% M $
- S4%M=10%3=1=4%3=4%M$ S_4 \% M = 10 \% 3 = 1 = 4 \% 3 = 4 \% M $
All the valid i$i$ satisfy the condition, and hence this is a valid subsequence.
user: It is an interesting exercise to write a program to print out all permutations of $1, 2, …, n$. However, since there are $6227020800$ permutations of $1, 2, …, 13$, it is unlikely that we would ever run this program on an input of size more than $10$.
However, here is another interesting problem whose solution can also be used to generate permutations. We can order the permutations of $1, 2, …, n$ under the lexicographic (or dictionary) order. Here are the permutations of $1,2,3$ in lexicographic order:
123132213231312321123132213231312321 1 \, 2 \, 3 \quad    1 \, 3 \, 2 \quad     2 \, 1 \, 3 \quad     2 \, 3 \, 1 \quad     3 \, 1 \, 2 \quad     3 \, 2 \, 1 
The problem we have is the following: given a permutation of $1,2, …, n$, generate the next permutation in lexicographic order. For example, for $2 3 1 4$ the answer is $2 3 4 1$.

-----Input:-----
The first line of the input contains two integers, $N$ and $K$. This is followed by $K$ lines, each of which contains one permutation of $1, 2,…,N$.

-----Output:-----
The output should consist of $K$ lines. Line $i$ should contain the lexicographically next permutation correponding to the permutation on line $i+1$ in the input.

-----Constraints:-----
- $1 \leq N \leq 1000$.
- $1 \leq K \leq 10$.

-----Sample input-----
3 2
3 1 2
2 3 1

-----Sample output-----
3 2 1
3 1 2
user: Due to the COVID pandemic, there has been an increase in the number of cases if a hospital. The management has decided to clear a large square area for the patients and arrange for beds. But the beds can't be too near to each other.
The area is of dimension $N$ x $N$
The whole area is already divided into blocks. $1$ means there's a bed in the block, $0$ denotes there isn't. Note, beds placed on consecutive diagonal blocks are safe.
This is a SAFE example:
1 0
0 1
This is an UNSAFE example:
0 1 1
0 0 0
1 0 0
To avoid spreading the virus even further, you have to make sure no two adjacent blocks have beds in them. This is done to maintain distance between beds.
Return an output of "SAFE" if you find the workers have arranged the beds with due consideration to the distance needed. Return "UNSAFE" otherwise.

-----Input:-----
- First line will contain $T$, number of testcases. Then the testcases follow. 
- Next line contains $N$.
- Next $N$ lines will contain $N$ number of space-separated integers $Ai$ which make denote the beds in the area.

-----Output:-----
For each test case, output in a single line whether the total arrangement is "SAFE" or "UNSAFE". Even if there's a single unsafe bed in the whole area, report the whole area as "UNSAFE".

-----Constraints-----
- $1 \leq T \leq 100$
- $0 \leq Ai \leq 1$
- $2 \leq N \leq 100$

-----Subtasks-----
- 30 points : $1 \leq N \leq 7$
- 70 points : Original constraints

-----Sample Input:-----
2
4
1 0 1 0
0 0 0 1
0 1 0 0
1 0 0 1
4
1 0 1 0
0 0 0 0
1 0 1 1
0 1 0 0

-----Sample Output:-----
SAFE
UNSAFE

-----EXPLANATION:-----
Beds placed on blocks diagonally are not a problem.
user: You are given a string S constisting of uppercase Latin letters. Is it possible to reorder the characters in this string to get a string with prefix "LTIME" and suffix "EMITL"?
We remind you that a prefix of a string is any substring which contains its first character, while a suffix of a string is substring containing its last character.

-----Input-----
The first line contains a single integer T, denoting the number of testcases. The descriptions of T test cases follow.
The first and only line of the test case description has one non-empty string S consisting of uppercase Latin letters only.

-----Output-----
For each testcase output a single line containing the string "YES" (without quotes) if it's possible to reorder the characters to get the required prefix and suffix, or "NO" (without quotes) otherwise.

-----Constraints-----
- Subtask 1 (23 points) : 1 ≤ T ≤ 100, 1 ≤ |S| ≤ 9
- Subtask 2 (77 points) : 1 ≤ T ≤ 1000, 1 ≤ |S| ≤ 100

-----Example-----
Input:3
LTIMEAZAZAITLME
LLLTTTIIIMMMEEEAHA
LTIMEM

Output:YES
YES
NO

-----Explanation-----
Test case 1: we can permute the last 5 letters and get LTIMEAZAZAEMITL
Test case 2: we have 3 copies of each of the letters 'L', 'T', 'I', 'M', 'E' so we can leave 5 of them in the beginning and move 5 of them to the end.
Test case 3: we have only one letter 'L' so we can't make necessary prefix and suffix at the same time.
user: As we all know, F.C. Barcelona is the best soccer team of our era! Their entangling and mesmerizing game style usually translates into very high ball possession, consecutive counter-attack plays and goals. Lots of goals, thanks to the natural talent of their attacker and best player in history, Lionel Andres Messi.
However, at the most prestigious tournament of individual teams, the UEFA Champions League, there are no guarantees and believe it or not, Barcelona is in trouble.... They are tied versus Chelsea, which is a very defending team that usually relies on counter-strike to catch opposing teams off guard and we are in the last minute of the match. So Messi decided to settle things down for good and now he is conducting the ball on his teams' midfield and he will start a lethal counter-attack :D
After dribbling the 2 strikers from Chelsea, he now finds himself near the center of the field and he won't be able to dribble the entire team on his own, so he will need to pass the ball to one of his teammates, run forward and receive the ball once again to score the final goal.
Exactly K players are with him on his counter-attack and the coach, Tito Villanova knows that this counter-attack will end in a goal only if after exactly N passes are performed between the players, Messi ends up with the ball.
(Note that the ball only needs to end with Messi after exactly N passes are performed between all the K+1 players, i.e. Messi can receive the ball several times during the N passes. See the 2nd test case explanation for further clarification. ) 
However, he realized that there are many scenarios possible for this, so he asked you, his assistant coach, to tell him in how many ways can Messi score the important victory goal. So help him!!

-----Input-----
Input will contain a number T denoting the number of test cases.
Then T test cases follow, each one consisting of two space-sparated integers N and K.

-----Output-----
For each test case, output a single integer, the number of ways the winning play might happen modulo 1000000007 (109+7).

-----Constraints-----

- 1 ≤ T ≤ 100
- 2 ≤ N ≤ 1000
- 1 ≤ K ≤ 10

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

Output:
4
6

-----Explanation-----
In the first test case, say four players with Messi are Xavi, Busquets, Iniesta and Jordi Alba. Then the ways of the winning play to happen when exactly  2 passes are to be performed are:
1) Messi - Xavi - Messi
2) Messi - Busquets - Messi
3) Messi - Iniesta - Messi
4) Messi - Alba - Messi

In the second test case, also say that two players with Messi are Xavi and Iniesta. There are 6 ways for the winning play to happen when exactly 4 passes are performed. All the examples of such winning play are:
1) Messi - Xavi - Messi - Iniesta - Messi
2) Messi - Xavi - Iniesta - Xavi - Messi
3) Messi - Xavi - Messi - Xavi - Messi
4) Messi - Iniesta - Messi - Iniesta - Messi
5) Messi - Iniesta - Messi - Xavi - Messi
6) Messi - Iniesta - Xavi - Iniesta - Messi
user: Raj is suffering from shot term memory loss so  he is unable to remember his laptop password  but he has a list of some string and the only thing that he remember about his password is alphanumeric and also that all the characters are unique.
Given a list of strings, your task is to find a valid password.

-----Input-----
Each String contains lower case alphabets and 0-9.

-----Output-----
print "Invalid"(without quotes) if password is not valid else print "Valid"(without quotes) and stop processing input after it.

-----Constraints-----
1<=length of string <=100

-----Example-----
Input:
absdbads
asdjenfef
tyerbet
abc564

Output:
Invalid
Invalid
Invalid
Valid
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:-----
1
21
*1
321
*21
**1
4321
*321
**21
***1

-----EXPLANATION:-----
No need, else pattern can be decode easily.
user: Bohan loves milk tea so much and he drinks one cup of milk tea every day. The local shop sells milk tea in two sizes: a Medium cup for $3 and a Large cup for $4. For every cup of milk tea purchased Bohan receives a promotional stamp. Bohan may redeem 6 stamps for a free drink of milk tea regardless of the size. No stamp will be given for a free drink.


Determine the amount of money Bohan have spent on milk tea, given a sequence of milk tea sizes he got in the past a few days. Assume Bohan had no stamps in the beginning and he always redeemed the stamps for the next drink once he had collected 6 stamps.

-----Input-----
The input begins with the number of test cases T.
Each test case has a single line of letters. The i-th letter is either 'M' or 'L' denoting a Medium cup or a Large cup of milk tea Bohan got on the i-th day.

-----Output-----
For each case, output the amount of money in dollars Bohan have spent on milk tea.

-----Constraints-----
- T ≤ 100 
- 1 ≤  length of each sequence ≤ 100 

-----Example-----
Input:
3
MLM
MMLLMMLL
MMMMMMML

Output:
10
24
22

-----Explanation-----
Example 1: Bohan didn't redeem any stamps.
Example 2: Bohan redeemed 6 stamps for the Large cup of milk tea on the 7th day.
Example 3: Bohan redeemed 6 stamps for the Medium cup of milk tea on the 7th day.
user: You are given two positive integers $N$ and $K$, where $K \le N$. Find a sequence $A_1, A_2, \ldots, A_N$ such that:
- for each valid $i$, $A_i$ is either $i$ or $-i$
- there are exactly $K$ values of $i$ such that $1 \le i \le N$ and $A_1 + A_2 + \ldots + A_i > 0$
If there are multiple solutions, you may print any one of them. It can be proved that at least one solution always exists.

-----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 two space-separated integers $N$ and $K$.

-----Output-----
For each test case, print a single line containing $N$ space-separated integers $A_1, A_2, \ldots, A_N$.

-----Constraints-----
- $1 \le T \le 1,000$
- $1 \le K \le N \le 1,000$

-----Subtasks-----
Subtask #1 (10 points): $N \le 10$
Subtask #2 (90 points): original constraints

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

-----Example Output-----
1 2 3
user: Chef recently saw the movie Matrix. He loved the movie overall but he didn't agree with some things in it. Particularly he didn't agree with the bald boy when he declared - There is no spoon. Being a chef, he understands the importance of the spoon and realizes that the universe can't survive without it. Furthermore, he is sure there is a spoon; he saw it in his kitchen this morning. So he has set out to prove the bald boy is wrong and find a spoon in the matrix. He has even obtained a digital map already. Can you help him?

Formally you're given a matrix of lowercase and uppercase Latin letters. Your job is to find out if the word "Spoon" occurs somewhere in the matrix or not. A word is said to be occurred in the matrix if it is presented in some row from left to right or in some column from top to bottom. Note that match performed has to be case insensitive. 

-----Input-----
The first line of input contains a positive integer T, the number of test cases. After that T test cases follow. The first line of each test case contains two space separated integers R and C, the number of rows and the number of columns of the matrix M respectively. Thereafter R lines follow each containing C characters, the actual digital map itself.

-----Output-----
For each test case print one line. If a "Spoon" is found in Matrix, output "There is a spoon!" else output "There is indeed no spoon!" (Quotes only for clarity).

-----Constraints-----

1 ≤ T ≤ 100

1 ≤ R, C ≤ 100

-----Sample Input-----
3
3 6
abDefb
bSpoon
NIKHil
6 6
aaaaaa
ssssss
xuisdP
oooooo
ioowoo
bdylan
6 5
bdfhj
cacac
opqrs
ddddd
india
yucky

-----Sample Output-----
There is a spoon!
There is a spoon!
There is indeed no spoon!

-----Explanation-----
In the first test case, "Spoon" occurs in the second row. In the second test case, "spOon" occurs in the last column.
user: The Little Elephant from the Zoo of Lviv has an array A that consists of N positive integers. Let A[i] be the i-th number in this array (i = 1, 2, ..., N).

Find the minimal number x > 1 such that x is a divisor of all integers from array A. More formally, this x should satisfy the following relations:

A[1] mod x = 0, A[2] mod x = 0, ..., A[N] mod x = 0,

where mod stands for the modulo operation. For example,  8 mod 3 = 2,  2 mod 2 = 0, 100 mod 5 = 0 and so on. If such number does not exist, output -1.

-----Input-----

The first line of the input contains a single integer T, the number of test cases. T test cases follow. The first line of each test case contains a single integer N, the size of the array A for the corresponding test case. The second line contains N space separated integers A[1], A[2], ..., A[N].

-----Output-----

For each test case output a single line containing the answer for the corresponding test case.

-----Constraints-----
1 ≤ T ≤ 100000

1 ≤ N ≤ 100000

The sum of values of N in each test file does not exceed 100000

1 ≤ A[i] ≤ 100000

-----Example-----
Input:
2
3
2 4 8
3
4 7 5

Output:
2
-1

-----Explanation-----
Case 1. Clearly 2 is a divisor of each of the numbers 2, 4 and 8. Since 2 is the least number greater than 1 then it is the answer.

Case 2. Let's perform check for several first values of x.

x4 mod x7 mod x5 mod x20113112403154206415740584759475

As we see each number up to 9 does not divide all of the numbers in the array. Clearly all larger numbers also will fail to do this. So there is no such number x > 1 and the answer is -1.