meetforever/GRPO_CL huggingface dataset:
user: Chef likes to play with big numbers. Today, he has a big positive integer N. He can select any two digits from this number (the digits can be same but their positions should be different) and orders them in any one of the two possible ways. For each of these ways, he creates a two digit number from it (might contain leading zeros). Then, he will pick a character corresponding to the ASCII value equal to this number, i.e. the number 65 corresponds to 'A', 66 to 'B' and so on till 90 for 'Z'. Chef is only interested in finding which of the characters in the range 'A' to 'Z' can possibly be picked this way. 

-----Input-----
The first line of the input contains an integer T denoting the number of test cases.
The first line of the input contains an integer N. 

-----Output-----
For each test case, output a string containing characters Chef can pick in sorted order If the resulting size of string is zero, you should output a new line.

-----Constraints-----
- 1 ≤ T ≤ 10
- 1 ≤ N ≤ 10100000

-----Subtasks-----
- Subtask #1 (40 points) N ≤ 1010
- Subtask #2 (60 points) Original Constraints

-----Example-----
Input:
4
65
566
11
1623455078

Output:
A
AB

ACDFGHIJKLNPQRSTUVW

-----Explanation-----
Example case 1. Chef can pick digits 6 and 5 and create integers 56 and 65. The integer 65 corresponds to 'A'.
Example case 2. Chef can pick digits 6 and 5 and create 'A' as it equals 65. He can pick 6 and 6 (they are picked from position 2 and position 3, respectively) to create 'B' too. Hence answer is "AB".
Example case 3. It's not possible to create any character from 'A' to 'Z'. Hence, we just print a new line.
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:-----
2
2
4

-----Sample Output:-----
2
21
210
21
2
4
43
432
4321
43210
4321
432
43
4

-----EXPLANATION:-----
No need, else pattern can be decode easily.
user: The chef is having one array of natural numbers. Cheffina challenges chef that find the sum of weights all the natural numbers present in the array, but the main problem is that all numbers have not original weights. After every 6 natural numbers weight is set to 1 as weight increases by 1 after that. (i.e. weight of 1 is 1, weight of 2 is 2 but the weight of 7 is 1 and weight of 8 is 2 and so on…). Help the chef to find the sum. 

-----Input:-----
- First line will contain $T$, number of testcases. Then the testcases follow. 
- Each testcase contains two lines of input, one integer $N$.
- Next line has N space separate natural numbers. 

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

-----Constraints-----
- $1 \leq T \leq 10$
- $1 \leq N \leq 10^5$
- $1 \leq arr[i] \leq 10^6$

-----Sample Input:-----
1
6
6 7 9 11 4 16

-----Sample Output:-----
23

-----EXPLANATION:-----
Array after conversion = [6, 1, 3, 5, 4, 4]
user: "Don't Drink and Drive, but when you do, Better Call Saul."
Once Jesse and Walter were fighting over extra cash, and Saul decided to settle it with a game of stone piles whose winner gets the extra money. The game is described as follows :
There are N$N$ piles of stones with A$A$1$1$,$,$ A$A$2$2$,$,$ ...$...$ A$A$N$N$ stones in each pile. 
Jesse and Walter move alternately, and in one move, they remove one pile entirely. 
After a total of X$X$ moves, if the Sum of all the remaining piles is odd, Walter wins the game and gets the extra cash, else Jesse is the winner.
Walter moves first. 
Determine the winner of the game if both of them play optimally. 

-----Input:-----
- The first line will contain T$T$, number of testcases. T$T$ testcases follow : 
- The first line of each testcase contains two space-separated integers N,X$N, X$. 
- The second line of each testcase contains N$N$ space-separated integers A$A$1$1$,$,$ A$A$2$2$,$,$ ...,$...,$A$A$N$N$.

-----Output:-----
For each test case, print a single line containing the string "Jesse" (without quotes), if Jesse wins the game or "Walter" (without quotes) if Walter wins.

-----Constraints-----
- 1≤T≤104$1 \leq T \leq 10^4$
- 2≤N≤105$2 \leq N \leq 10^5$
- 1≤X≤N−1$1 \leq X \leq N-1$
- 1≤A$1 \leq A$i$i$ ≤100$ \leq 100$
- The sum of N$N$ over all test cases does not exceed 106$10^6$

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

-----Sample Output:-----
Jesse
Walter

-----EXPLANATION:-----
- 
For Test Case 1 : Playing optimally, Walter removes 4. Jesse removes 3 and then Walter removes 4. Jesse wins as 4+4=8$4 + 4 = 8$ is even.
- 
For Test Case 2 : Playing optimally, Walter removes 4, Jesse removes 3, Walter removes 2 and Jesse removes 1. Walter wins as  3+3+1=7$3 + 3 + 1 = 7$ is odd.
user: Chef loves to play with arrays by himself. Today, he has an array A consisting of N distinct integers. He wants to perform the following operation on his array A.

- Select a pair of adjacent integers and remove the larger one of these two. This decreases the array size by 1. Cost of this operation will be equal to the smaller of them.

Find out minimum sum of costs of operations needed to convert the array into a single element.

-----Input-----
First line of input contains a single integer T denoting the number of test cases. First line of each test case starts with an integer N denoting the size of the array A. Next line of input contains N space separated integers, where the ith integer denotes the value Ai.

-----Output-----
For each test case, print the minimum cost required for the transformation.

-----Constraints-----
- 1 ≤ T ≤ 10 
- 2 ≤ N ≤ 50000 
- 1 ≤ Ai ≤ 105 

-----Subtasks-----
- Subtask 1 : 2 ≤ N ≤ 15 : 35 pts 
- Subtask 2 : 2 ≤ N ≤ 100 : 25 pts 
- Subtask 3 : 2 ≤ N ≤ 50000 : 40 pts 

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

Output
3
4

-----Explanation-----Test 1 :  Chef will make only 1 move: pick up both the elements (that is, 3 and 4), remove the larger one (4), incurring a cost equal to the smaller one (3).
user: Chef has a number N, Cheffina challenges the chef to check the divisibility of all the permutation of N by 5. If any of the permutations is divisible by 5 then print 1 else print 0.

-----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 1 or 0.

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

-----Sample Input:-----
2
19
385

-----Sample Output:-----
0
1
user: A Train started its journey at x=-infinity is travelling on the x-Coordinate Axis. Given n passengers and the coordinates $b_i$ and $d_i$ for each of the $ith$ passenger at which they board and leave from the train respectively. Due to current COVID-19 crisis, the train is monitored at each mile/coordinate. The infection degree of the train at each mile is equal to the total passengers present in the train at that mile/coordinate. The train stops its journey if no more passengers are there to board the train. The term infection severity of the journey is defined as the sum of infection degrees noted at each mile. Find the Infection severity of the journey. Note: A passenger is considered for calculation of infection degree at both boarding and leaving stations.

Since the answer can be very large, print it modulo $(10^9)+7$.

-----Input:-----
- First line will contain $N$, number of passengers. Then the $N$ lines follow. 
- $i$th line contains two integers $b_i, d_i$ , the boarding and departure mile of $i$th passenger.

-----Output:-----
Print a single value, the Infection Severity of the journey modulo $(10^9)+7$.

-----Constraints-----
- $0 \leq N \leq 100000$
- $-500000 \leq b_i \leq 500000$
- $-500000 \leq d_i \leq 500000$

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

0 2

1 3

-1 4  

-----Sample Output:-----
12    

-----EXPLANATION:-----
Infection degree at :

-1 is 1

0 is 2

1 is 3

2 is 3

3 is 2

4 is 1

Calculation started at mile -1 and ended at mile 4. Infection Severity = 1+2+3+3+2+1 =12
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
13
57
135
7911
131517
1357
9111315
17192123
25272931

-----EXPLANATION:-----
No need, else pattern can be decode easily.
user: Walter White and Jesse Pinkman (a drug addict) both love to play with chemicals. One day they were playing with some chemicals to make an energy drink. Unknowingly they made a highly powerful drink. To test the drink on others also they called some of their friends and gave a drop of it to everyone. Now they all were feeling highly energetic and thought of an unique game to play with each other.
After pondering for a while, Jesse came up with an extraordinary idea of competing in a race around a circular globe with N checkpoints each of one unit. Walter and all their other friends agreed with it.They divided themselves in $2$ teams with $N$ teammates in each team.This race has two commencing points $A$ and $B$ strictly facing each other. Walter and his team commences from $A$ point and other team starts from $B$. Both the teams start running at the same time clockwise around the globe. Speed of every player is constant throughout the race. If a player has a speed $X$ then it means that he covers a distance of $X$ units in one second.The race ends when some member of one team overtakes all members of opposite team at any point of time. Now you have to tell if any team will win the race or not.They all are stubborn and can run forever just to win the race. Help them to know if it is possible in anyway that the race will come to an end. 
For Clarity, you can visualize the path as a circular paths where $A$ and $B$ are opposite ends of diameter. It can be proven that the actual circumference of circle do not affect the answer.
It is also possible that someone don't run at all.Keep in mind that the fastest one wins the race so does the code.

-----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 $N$ number of teammates in both team.
- The second line contains $N$ space-separated integers $A_1, A_2 \ldots A_N$ denoting speed of A's Team
- The third line contains $N$ space-separated integers  $B_1, B_2 \ldots B_N$ denoting speed of B's Team

-----Output:------
For each test case, print a single line denoting YES if the race ends at any point of time else NO

-----Constraints-----
- $1 \leq T \leq 10$
- $1 \leq N \leq 10^5$
- $0 \leq A_i \leq 2^{15}$
- $0 \leq B_i \leq 2^{15}$

-----Subtasks-----
Subtask #1 (30 points): 
- $1 \le N \le 20$
- $0 \le  A_i  \le 11$
- $0 \le  B_i  \le 11$
Subtask #2 (70 points): 
- Original constraints

-----Sample input:-----
1
5
1 2 3 4 5
2 7 8 9 9

-----Sample output-----
YES

-----Sample Explanation:------
Team B can overtake all members of Team A.
user: Chef received a permutation $P_1, P_2, \ldots, P_N$ and also an integer $D$ from his good friend Grux, because Grux was afraid he would forget them somewhere. However, since Grux was just playing with the permutation, it was all shuffled, and Chef only likes sorted permutations, so he decided to sort it by performing some swaps.
Chef wants to use the integer $D$ he just received, so he is only willing to swap two elements of the permutation whenever their absolute difference is exactly $D$. He has limited time, so you should determine the minimum number of swaps he needs to perform to sort the permutation, or tell him that it is impossible to sort it his way.

-----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 $D$.
- The second line contains $N$ space-separated integers $P_1, P_2, \ldots, P_N$.

-----Output-----
For each test case, print a single line containing one integer ― the minimum number of swaps, or $-1$ if it is impossible to sort the permutation.

-----Constraints-----
- $1 \le T \le 20$
- $1 \le N \le 200,000$
- $1 \le D \le N$
- $1 \le P_i \le N$ for each valid $i$
- $P_1, P_2, \ldots, P_N$ are pairwise distinct
- the sum of $N$ over all test cases does not exceed $10^6$

-----Subtasks-----
Subtask #1 (20 points): $D = 1$
Subtask #2 (30 points):
- $N \le 1,000$
- the sum of $N$ over all test cases does not exceed $10,000$
Subtask #3 (50 points): original constraints

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

-----Example Output-----
3
-1

-----Explanation-----
Example case 1: Chef can perform the following swaps in this order:
- swap the first and fifth element
- swap the third and fifth element
- swap the second and fourth element
user: Chef has recently learned about number bases and is becoming fascinated.
Chef learned that for bases greater than ten, new digit symbols need to be introduced, and that the convention is to use the first few letters of the English alphabet. For example, in base 16, the digits are 0123456789ABCDEF. Chef thought that this is unsustainable; the English alphabet only has 26 letters, so this scheme can only work up to base 36. But this is no problem for Chef, because Chef is very creative and can just invent new digit symbols when she needs them. (Chef is very creative.)
Chef also noticed that in base two, all positive integers start with the digit 1! However, this is the only base where this is true. So naturally, Chef wonders: Given some integer N, how many bases b are there such that the base-b representation of N starts with a 1?

-----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 case consists of one line containing a single integer N (in base ten).

-----Output-----
For each test case, output a single line containing the number of bases b, or INFINITY if there are an infinite number of them.

-----Constraints-----

-----Subtasks-----Subtask #1 (16 points):
- 1 ≤ T ≤ 103
- 0 ≤ N < 103
Subtask #2 (24 points):
- 1 ≤ T ≤ 103
- 0 ≤ N < 106
Subtask #3 (28 points):
- 1 ≤ T ≤ 103
- 0 ≤ N < 1012
Subtask #4 (32 points):
- 1 ≤ T ≤ 105
- 0 ≤ N < 1012

-----Example-----
Input:4
6
9
11
24

Output:4
7
8
14

-----Explanation-----
In the first test case, 6 has a leading digit 1 in bases 2, 4, 5 and 6: 610 = 1102 = 124 = 115 = 106.
user: For a permutation P = (p1, p2, ..., pN) of numbers [1, 2, ..., N], we define the function f(P) = max(p1, p2) + max(p2, p3) + ... + max(pN-1, pN).
You are given N and an integer K. Find and report a permutation P of [1, 2, ..., N] such that f(P) = K, if such a permutation exists.
Note f([1]) = 0.

-----Input-----
- The first line of the input contains an integer T denoting the number of test cases. The description of T test cases follows.
- The only line of each test case consists of two space-separated integers N, K respectively.

-----Output-----
For each test case, if a permutation satisfying the condition exists, output a single line containing N space-separated integers which denotes any such permutation. If no such permutation exists, output a single integer -1 instead.
Use fast I/O methods since the size of the output is large.

-----Constraints-----
- 1 ≤ T ≤ 40
- 1 ≤ N ≤ 105
- Sum of N over all test cases in each file ≤ 106
- 0 ≤ K ≤ 2 * 1010

-----Example-----
Input:
3
4 12
2 2
5 14

Output:
-1
1 2
5 4 3 2 1

-----Explanation-----
Example 1. There doesn't exist any permutation of numbers [1, 2, 3, 4] that can have its f value equal to 4. Hence answer is -1.
Example 2. The permutations [1, 2] and [2, 1] both have their f values equal to 2. You can print any of these two permutations. 
Example 3. The permutation [5, 4, 3, 2, 1]
has f value = max(5, 4) + max(4, 3) + max(3, 2) + max(2, 1) = 5 + 4 + 3 + 2 = 14.
user: Our chef has been assigned a task to make a necklace of length N, from gold, diamond and platinum.There is single kind of gold, two types of diamond and three types of platinum available.
A necklace can be represented as strings of the form (G)∗(D1|D2)∗(P1|P2|P3)∗$ (G)*(D1|D2)*(P1|P2|P3)* $ where (x|y) means we can use x or y and ∗$ * $ means we can repeat the previous parenthesized expression 0 or more times.
Instead of making necklace he choose to count all such distinct necklaces possible for a given length N.

-----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.
-Only line of every test case contains an integer N$N$ denoting the length of the necklace required.

-----Output:-----
For each test case, print the number of all such distinct necklaces, with given length. As the number can be really large, print it modulo  109+7$10^{9}+7$.

-----Constraints-----
- 1≤T≤10000$1 \leq T \leq 10000$
- 2≤N≤1000000000$2 \leq N \leq 1000000000$
- String S$S$ consists of only upper case english alphabets.

-----Subtasks-----
- 20 points : 1≤N≤5$1 \leq N \leq 5$
- 70 points : Original$Original$ Constraints$Constraints$

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

-----Sample Output:-----
6
25
user: Given a number $n$, give the last digit of sum of all the prime numbers from 1 to $n$ inclusive.

-----Input:-----
- First line contains number of testcase $t$.
- Each testcase contains of a single line of input, number $n$. 

-----Output:-----
Last digit of sum of every prime number till n.

-----Constraints-----
- $1 \leq T \leq 10$
- $2 \leq N \leq 10^6$

-----Sample Input:-----
1
10

-----Sample Output:-----
7
user: People in Karunanagar are infected with Coronavirus. To understand the spread of disease and help contain it as early as possible, Chef wants to analyze the situation in the town. Therefore, he does the following:
- Chef represents the population of Karunanagar as a binary string of length $N$ standing in a line numbered from $1$ to $N$ from left to right, where an infected person is represented as $1$ and an uninfected person as $0$.
- Every day, an infected person in this binary string can infect an adjacent (the immediate left and right) uninfected person.
- Therefore, if before Day 1, the population is $00100$, then at the end of Day 1, it becomes $01110$ and at the end of Day 2, it becomes $11111$.
But people of Karunanagar are smart and they know that if they 'socially isolate' themselves as early as possible, they reduce the chances of the virus spreading. Therefore on $i$-th day, person numbered $P_i$ isolates himself from person numbered $P_i - 1$, thus cannot affect each other. This continues in the town for $D$ days.
Given the population binary string before Day 1, Chef wants to calculate the total number of infected people in Karunanagar at the end of the day $D$. Since Chef has gone to wash his hands now, can you help do the calculation for him?

-----Input:-----
- First line will contain $T$, number of testcases. Then the test cases follow. 
- The first line of each test case contains a single integer $N$ denoting the length of the binary string.
- The next line contains a binary string of length $N$ denoting the population before the first day, with $1$ for an infected person and $0$ for uninfected.
- The next line contains a single integer $D$ - the number of days people isolate themselves.
- The next line contains $P$ - a list of $D$ distinct space-separated integers where each $P_{i}$ denotes that at the start of $i^{th}$ day, person $P_{i}$ isolated him/herself from the person numbered $P_i-1$.

-----Output:-----
For each test case, print a single integer denoting the total number of people who are infected after the end of $D^{th}$ day.

-----Constraints-----
- $1 \leq T \leq 200$
- $2 \leq N \leq 10^{4}$
- $1 \leq D < N$
- $2 \leq P_{i} \leq N$ for $1 \le i \le D$

-----Subtasks-----
Subtask #1(30 points): $1 \leq T \leq 100$, $2 \leq N \leq 2000$
Subtask #2(70 points): Original Constraints

-----Sample Input:-----
2
9
000010000
3
2 5 8
5
00001
1
5

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

-----EXPLANATION:-----
For the purpose of this explanation, a social distance can be denoted with a '$|$'.
For the first testcase:
- 
Before Day $1$, the population is: $0|00010000$
- 
Before Day $2$, the population is: $0|001|11000$
- 
Before Day $3$, the population is: $0|011|111|00$
- 
Therefore, after Day $3$, the population will be: $0|111|111|00$
So, there are $6$ infected persons.
For the second testcase:
Before Day $1$, the population is: $0000|1$
Therefore, there is one infected person.
user: Chef wants to organize a contest. Predicting difficulty levels of the problems can be a daunting task. Chef wants his contests to be balanced in terms of difficulty levels of the problems.
Assume a contest had total P participants. A problem that was solved by at least half of the participants (i.e. P / 2 (integer division)) is said to be cakewalk difficulty. A problem solved by at max P / 10 (integer division) participants is categorized to be a hard difficulty.
Chef wants the contest to be balanced. According to him, a balanced contest must have exactly 1 cakewalk and exactly 2 hard problems. You are given the description of N problems and the number of participants solving those problems. Can you tell whether the contest was balanced or not?

-----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 two space separated integers, N, P denoting the number of problems, number of participants respectively.
The second line contains N space separated integers, i-th of which denotes number of participants solving the i-th problem.

-----Output-----
For each test case, output "yes" or "no" (without quotes) denoting whether the contest is balanced or not.

-----Constraints-----
- 1 ≤ T, N ≤ 500 
- 1 ≤ P ≤ 108 
- 1 ≤ Number of participants solving a problem ≤ P

-----Subtasks-----
- Subtask #1 (40 points): P is a multiple of 10
- Subtask #2 (60 points): Original constraints

-----Example-----
Input
6
3 100
10 1 100
3 100
11 1 100
3 100
10 1 10
3 100
10 1 50
4 100
50 50 50 50
4 100
1 1 1 1

Output
yes
no
no
yes
no
no

-----Explanation-----
Example case 1.: The problems are of hard, hard and cakewalk difficulty. There is 1 cakewalk and 2 hard problems, so the contest is balanced.
Example case 2.: The second problem is hard and the third is cakewalk. There is 1 cakewalk and 1 hard problem, so the contest is not balanced.
Example case 3.: All the three problems are hard. So the contest is not balanced.
Example case 4.: The problems are of hard, hard, cakewalk difficulty. The contest is balanced.
Example case 5.: All the problems are cakewalk. The contest is not balanced.
Example case 6.: All the problems are hard. The contest is not balanced.