meetforever/GRPO_CL huggingface dataset:
user: The new Formula 1 season is about to begin and Chef has got the chance to work with the Formula 1 technical team.  
Recently, the pre-season testing ended and the technical team found out that their timing system for qualifying was a little bit buggy. So, they asked Chef to fix it before the season begins.  
His task is to write a program to find the starting lineup of the race by taking the timings of the drivers in qualifying.
(If you don’t know the rules that make the starting grid in Formula 1, consider that the driver with the least time will start at the front). 
Note: 
- Two or more drivers can have the same name.  
- Every driver will have a distinct time.  

-----Input:-----
- The first line of the input consists of a single integer $T$ denoting the number of test cases.  
- First line of each test case consists of a single integer $N$ denoting the number of drivers to set a time.  
- The following $2*N$ lines consists of the driver’s name $S$ in one line and its timing details  $X$ (in milliseconds) in the next line.  

-----Output:-----
- For each test case output the starting lineup of the race i.e., name of each driver in the order they will start the race. Print each name in a new line.  

-----Constraints-----
- 1 <= $T$ <= 10  
- 1 <= $N$ <= 105 
- 1 <= $|S|$ <= 20  
- 1 <= $X$ <= 109 

-----Subtasks-----
Subtask #1 (20 points): 
- 1 <= $N$ <= 100  
Subtask #2 (80 points): 
- Original Constraints  

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

3

Hamilton

75000

Vettel

76000

Bottas

75500

2

Leclerc

666666

Verstappen

666777  

-----Sample Output:-----
Hamilton

Bottas

Vettel

Leclerc

Verstappen  

-----EXPLANATION:-----
The drivers with the least time are ahead in the lineup.
user: A beautiful sequence is defined as a sequence that do not have any repeating elements in it.
You will be given any random sequence of integers, and you have to tell whether it is a beautiful sequence or not. 

-----Input:-----
- The first line of the input contains a single integer $T$. $T$ denoting the number of test cases. The description of $T$ test cases is as follows.
- The next line of the input contains a single integer $N$. $N$ denotes the total number of elements in the sequence.
- The next line of the input contains $N$ space-separated integers $A1, A2, A3...An$ denoting the sequence.

-----Output:-----
- Print "prekrasnyy"(without quotes) if the given sequence is a beautiful sequence, else print "ne krasivo"(without quotes)
Note: each test case output must be printed on new line

-----Constraints:-----
- $1 \leq T \leq 10^2$
- $1 \leq N \leq 10^3$
- $1 \leq A1, A2, A3...An \leq 10^5$

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

-----Sample Output:-----
prekrasnyy
ne krasivo

-----Explanation:-----
- 
As 1st sequence do not have any elements repeating, hence it is a beautiful sequence
- 
As in 2nd sequence the element 1 is repeated twice, hence it is not a beautiful sequence
user: Accepts a string from the user and print the reverse string as the output without using any built-in function.

-----Input:-----
Each testcase contains of a single line of input, a string.

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

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

-----Sample Output:-----
ycarT
user: You are given a dataset consisting of $N$ items. Each item is a pair of a word and a boolean denoting whether the given word is a spam word or not.
We want to use this dataset for training our latest machine learning model. Thus we want to choose some subset of this dataset as training dataset. We want to make sure that there are no contradictions in our training set, i.e. there shouldn't be a word included in the training set that's marked both as spam and not-spam. For example item {"fck", 1}, and item {"fck, 0"} can't be present in the training set, because first item says the word "fck" is a spam, whereas the second item says it is not, which is a contradiction.
Your task is to select the maximum number of items in the training set.
Note that same pair of {word, bool} can appear multiple times in input. The training set can also contain the same pair multiple times.

-----Input-----
- First line will contain $T$, number of test cases. Then the test cases follow.
- The first line of each test case contains a single integer $N$.
- $N$ lines follow. For each valid $i$, the $i$-th of these lines contains a string $w_i$, followed by a space and an integer(boolean) $s_i$, denoting the $i$-th item.

-----Output-----
For each test case, output an integer corresponding to the maximum number of items that can be included in the training set in a single line.

-----Constraints-----
- $1 \le T \le 10$
- $1 \le N \le 25,000$
- $1 \le |w_i| \le 5$ for each valid $i$
- $0 \le s_i \le 1$ for each valid $i$
- $w_1, w_2, \ldots, w_N$ contain only lowercase English letters

-----Example Input-----
3
3
abc 0
abc 1
efg 1
7
fck 1
fck 0
fck 1
body 0
body 0
body 0
ram 0
5
vv 1
vv 0
vv 0
vv 1
vv 1

-----Example Output-----
2
6
3

-----Explanation-----
Example case 1: You can include either of the first and the second item, but not both. The third item can also be taken. This way the training set can contain at the very max 2 items.
Example case 2: You can include all the items except the second item in the training set.
user: Problem description.
Dominic Toretto has taken his crew to compete in this years' Race Wars, a crew-on-crew tournament in which each member of one crew competes with a member of the other crew in a quarter mile drag race. Each win counts as one point for the winning crew. Draws and loses are awarded zero points. In the end the crew with more points is declared the winner of that round and can advance while the losing crew is knocked out. One member can compete in only one race per round and all crews have the same number of members.
Dom and his crew have a reputation of being the best and naturally everyone expects them to win this year as well.
However, during the tournament he spots a new crew of racers who are participating for the first time in this event. People expect them to be a dark horse so naturally Dom wants to keep an eye on their performance.
Being the experienced racer that he is, Dom has figured out the time in which each racer of the opposing crew completes his quarter mile race.

He also knows his own crew inside out and can estimate with absolute certainty, the time it would take each of his members to complete the race. Dominic is the reigning champion and thus has an advantage that he can select the order of the matches i.e.: he can select which member of his crew will go up against which member of the opposition. Given this data he wants to figure out the number of races he will win should his crew come face to face with their newest rivals.

Unfortunately he is a racer and not a problem solver so he comes to you for help.

Given the time each member of the two crews take to complete the race you have to figure out a way to arrange the matches so that Dominic can win maximum points possible for him.

-----Input-----

The first line of input is the T, the number of test cases.

Each test case starts with a single number N, the number of racers on each crew.

This is followed by two lines, each having N space separated integers containing the time taken by each member of Dominic's crew and the rival crew respectively.

-----Output-----
Output a single integer. The maximum number of points that Dominic can get.

-----Constraints-----
1<=T<=100
1<=N<=100
Time taken by each member will be between 1 and 500

-----Example-----
Input:

1
3
5 4 1
5 4 1

Output:
2

-----Explanation-----
If Dom selects Racer 1 of his team to go against Racer 2 of the other team, Racer 2 of his team against Racer 3 of the other team and Racer 3 of his team against Racer 1 of the other team then he ends up with two wins and a loss which gives him 2 points. ...
user: For Diwali, Chef arranges all $K$ laddus in a row in his sweet shop. Whenever a customer comes to buy laddus, chef follows a rule that each customer must buy all laddus on odd position. After the selection of the laddu, a new row is formed, and again out of these only laddus on odd position are selected. This continues until the chef left with the last laddu. Find out the position of that last laddu in the original row.

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

-----Output:-----
For each testcase, print the position of that laddu who is left, in the original row.

-----Constraints-----
- $1 \leq T \leq 10^5$
- $1 \leq K \leq 10^5$

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

-----Sample Output:-----
1
4
8

-----EXPLANATION:-----
For 1) Only one laddu which is last so print 1.
For 2) Customer 1: [1, 3, 5]
New row = [2, 4]

Customer 2: [2]

Last laddu = 4
user: Voritex a big data scientist collected huge amount of big data having structure of two rows and n columns.
Voritex is storing all the valid data for manipulations and pressing invalid command when data not satisfying the constraints.
Voritex likes brute force method and he calls it as BT, he decided to run newly created BT engine for getting good result.
At each instance when BT engine is outputting a newly created number Voritex calls it as BT number.
Voritex is daydreaming and thinking that his engine is extremely optimised and will get an interview call in which he will be explaining the structure of BT engine and which will be staring from 1 and simultaneously performing $i$-th xor operation with $i$ and previously(one step before) obtained BT number.
BT engine is outputting the $K$-th highest BT number in the first $N$ natural numbers.
Chef : (thinking) I also want to create BT engine……..

-----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 line of each test case contains a two integers $N$ and $K$.

-----Output:-----
For each test case, print a single line containing integer $K$-th highest number else print -$1$ when invalid command pressed.

-----Constraints-----
- $1 \leq T \leq 100000$
- $1 \leq N \leq 100000$
- $1 \leq K \leq N$

-----Sample Input:-----
2
4 2
5 5

-----Sample Output:-----
2
0

-----EXPLANATION:-----
For first valid constraints generating output as 0 2 1 5 
1^1 first BT number is 0
2^0 second BT number is 2
3^2 third BT number is 1
4^1 fourth BT number is 5
Hence the answer is 2.
user: Minion Chef likes to eat bananas a lot. There are N piles of bananas in front of Chef; for each i (1 ≤ i ≤ N), the i-th pile contains Ai bananas.
Chef's mother wants her to eat the bananas and be healthy. She has gone to the office right now and will come back in H hours. Chef would like to make sure that she can finish eating all bananas by that time.
Suppose Chef has an eating speed of K bananas per hour. Each hour, she will choose some pile of bananas. If this pile contains at least K bananas, then she will eat K bananas from it. Otherwise, she will simply eat the whole pile (and won't eat any more bananas during this hour).
Chef likes to eat slowly, but still wants to finish eating all the bananas on time. Therefore, she would like to choose the minimum K such that she is able to eat all the bananas in H hours. Help Chef find that value of K.

-----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 H denoting the number of piles and the number of hours after which Chef's mom will come home.
- The second line contains N space-separated integers A1, A2, ..., AN.

-----Output-----
For each test case, print a single line containing one integer — the minimum possible value of K.

-----Constraints-----
- 1 ≤ T ≤ 10
- 1 ≤ N ≤ 105
- N ≤ H ≤ 109
- 1 ≤ Ai ≤ 109 for each valid i

-----Subtasks-----
Subtask #1 (30 points):
- 1 ≤ N ≤ 100
- Ai ≤ 103 for each valid i

Subtask #2 (70 points): original constraints

-----Example-----
Input:

3
3 3
1 2 3
3 4
1 2 3
4 5
4 3 2 7

Output:

3
2
4

-----Explanation-----
Example case 1: With a speed of K = 3 bananas per hour, Chef can finish eating all the bananas in 3 hours. It's the minimum possible speed with which she can eat all the bananas in 3 hours. With a speed of 2 bananas per hour, she would take at least 4 hours and with a speed of 1 banana per hour, she would take at least 6 hours.
user: Recall the definition of the Fibonacci numbers:


f1 := 1

f2 := 2

fn := fn-1 + fn-2 (n>=3)

Given two numbers a and b, calculate how many Fibonacci numbers are in the range [a,b].


-----Input-----

The input contains several test cases. Each test case consists of two non-negative integer numbers a and b. Input is terminated by a=b=0. Otherwise, a<=b<=10^100. The numbers a and b are given with no superfluous leading zeros.

-----Output-----

For each test case output on a single line the number of Fibonacci numbers fi with a<=fi<=b.

-----Example-----
Input:

10 100
1234567890 9876543210
0 0

Output:

5
4
user: As we all know, Dhoni loves drinking milk. Once he and Sir Jadeja were invited in the inauguration of a Dairy company in Ranchi.

The company had arranged  n   jars of milk from various breeds of cows , jar number  i  containing  a[i]  litres of milk. Since Dhoni loves driking milk more than Sir Jadeja, so Kohli suggested a plan for them. His plan was that each time Dhoni will choose a jar containing the maximum amount of milk. If this jar has less than  k   litres of milk or if Dhoni has already drunk more than  m  number of times from this jar, then the milk contained in the jar will be drunk by Sir Jadeja. Sir Jadeja will drink all the milk left in that jar. Otherwise Dhoni will drink exactly k  litres of milk from the jar and put it back at its position. Dhoni will do so until he has given all jars to Sir Jadeja.

You have to calculate how much milk Sir Jadega will get after Dhoni satisfies his hunger modulo 1,000,000,007.

-----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 first line of each test case contains integer N , M, K denoting the number of milk jars, maximum number of time Dhoni will drink from any jar and maximum amount of milk Dhoni will drink at any time respectively. The second line contains N space-separated integers A1, A2, ..., AN denoting the amount of milk in each jar. 

-----Output-----
- For each test case, output a single line containing the amount of milk Sir Jadega will get modulo 1,000,000,007.

-----Constraints-----
- 1 ≤ T ≤  10 
- 1 ≤ N ≤  10^5 
- 0 ≤ M ≤  10^6 
- 1 ≤ K ≤  10^6 
- 0 ≤ Ai ≤  10^9 

-----Example-----
Input:
1
3 3 3
15 8 10

Output:
9
user: The government has invited bids from contractors to run canteens at all railway stations. Contractors will be allowed to bid for the catering contract at more than one station. However, to avoid monopolistic price-fixing, the government has declared that no contractor may bid for a pair of neighbouring stations.
The railway network has exactly one route between any pair of stations. Each station is directly connected by a railway line to at most $50$ neighbouring stations.
To help contractors plan their bids, the government has provided data on the number of passengers who pass through each station each year. Contractors would like to bid for stations with a higher volume of passenger traffic to increase their turnover.
For instance, suppose the railway network is as follows, where the volume of passenger traffic is indicated by the side of each station.

In this network, the best option for the contractor is to bid for stations $1, 2, 5$ and $6$, for a total passenger volume of $90$.
Your task is to choose a set of stations that the contractor should bid for so that the total volume of traffic across all the stations in the bid is maximized.

-----Input:-----
The first line of the input contains one integer $N$ indicating the number of railways stations in the network. The stations are numbered $1,2,...,N$. This is followed by $N$ lines of input, lines $2, 3,..., N+1$, indicating the volume of traffic at each station. The volume of traffic at station $i, 1 \leq i \leq N$, is given by a single integer in line $i+1$. The next $N-1$ lines of input, lines $N+2, N+3, ..., 2N$, describe the railway network. Each of these lines contains two integers, denoting a pair of stations that are neighbours.

-----Output:-----
The output should be a single integer, corresponding to the total volume of traffic across the set of stations in the optimal bid made by the contractor.

-----Constraints:-----
- $1 \leq N \leq 100000$. 
- Each railway station has at most $50$ neighbours.

-----Sample Input-----
6
10
20
25
40
30
30
4 5
1 3
3 4
2 3
6 4

-----Sample Output-----
90
user: These days, chef is very much interested in Mathematics. He has started attending Recitations too! His hunger for problems is increasing day by day!
Today, chef was a given a crumpled maths problem, which he is stuck with . He needs your help to do it
Here's what his teacher said: "Find sum of all numbers till N, do not include numbers which are powers of K from K, K2, K3... which are less than or equal to N"
Easy, right? Can you solve it?

-----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 first line of each test contains two integers N and K, as per the above given problem specification.

-----OUTPUT-----
For each test case, output a single line printing the sum of the each test case, in format Case #T: S, where T is the Tth test case running and S is sum of corresponding test case.

-----CONSTRAINTS-----

10 < T < 50

10 < N < 104

0 < K < 100

-----EXAMPLE-----
Input:

2

10 3

20 2

Output:

Case #1: 43

Case #2: 180
user: Given N, count how many permutations of [1, 2, 3, ..., N] satisfy the following property.

Let P1, P2, ..., PN denote the permutation. The property we want to satisfy is that there exists an i between 2 and n-1 (inclusive) such that

- Pj > Pj + 1  ∀    i ≤ j ≤ N - 1.
- Pj > Pj - 1  ∀    2 ≤ j ≤ i.

-----Input-----
First line contains T, the number of test cases. Each test case consists of N in one line.

-----Output-----
For each test case, output the answer modulo 109+7.

-----Constraints-----
- 1 ≤ T ≤ 100
- 1 ≤ N ≤ 109

-----Subtasks-----
- Subtask #1(40 points): 1 ≤ N ≤ 1000
- Subtask #2(60 points): original constraints

-----Example-----
Input:
2
2
3

Output:
0
2

-----Explanation-----

Test case 1:

No permutation satisfies.

Test case 2:

Permutations [1, 3, 2] and [2, 3, 1] satisfy the property.
user: There are n chef's in Chefland. There is a festival in Chefland in which each chef is asked to vote a person as his best friend. Obviously, a person can't vote himself as his best friend.  Note that the best friend relationship is not necessarily bi-directional, i.e. it might be possible that x is best friend of y, but y is not a best friend of x.

Devu was the election commissioner who conducted this voting. Unfortunately, he was sleeping during the voting time. So, he could not see the actual vote of each person, instead after the voting, he counted the number of votes of each person and found that number of votes of i-th person was equal to ci. 

Now he is wondering whether this distribution of votes corresponds to some actual voting or some fraudulent voting has happened. If the current distribution of votes does not correspond to any real voting, print -1. Otherwise, print any one of the possible voting which might have lead to the current distribution. If there are more than one possible ways of voting leading to the current distribution, you can print any one of them.

-----Input-----
- First line of the input contains a single integer T denoting number of test cases.
- First line of each test case, contains a single integer n.
- Second line of each test case, contains n space separated integers denoting array c.

-----Output-----
For each test case,

- If there is no real voting corresponding to given distribution of votes, print -1 in a single line.
- Otherwise, print n space separated integers denoting a possible voting leading to current distribution of votes. i-th integer should denote the index of the person (1 based indexing) whom i-th person has voted as his best friend.

-----Constraints and Subtasks-----
- 1 ≤ T ≤ 500
- 1 ≤ n ≤ 50
- 0 ≤ ci ≤ n

-----Example-----
Input:
3
3
1 1 1
3
3 0 0
3
2 2 0

Output:
2 3 1
-1
-1

-----Explanation-----
Example 1: In this example, each person has received one vote. One possible example of real voting leading to this distribution is {2, 3, 1}. In this distribution, number of votes of all three persons are equal to 1. Also it is real voting because no person votes himself as his best friend. 

You can also output another possible distribution {3, 1, 2} too.

Example 2: There is no real voting  corresponding to this voting distribution.

Example 3: There is no real voting  corresponding to this voting distribution.
user: For her next karate demonstration, Ada will break some bricks.
Ada stacked three bricks on top of each other. Initially, their widths (from top to bottom) are W1,W2,W3.
Ada's strength is S. Whenever she hits a stack of bricks, consider the largest k≥0 such that the sum of widths of the topmost k bricks does not exceed S; the topmost k bricks break and are removed from the stack. Before each hit, Ada may also decide to reverse the current stack of bricks, with no cost.
Find the minimum number of hits Ada needs in order to break all bricks if she performs the reversals optimally. You are not required to minimise the number of reversals.
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 S, W1, W2 and W3.Output
For each test case, print a single line containing one integer ― the minimum required number of hits.Constraints
- 1≤T≤64
- 1≤S≤8
- 1≤Wi≤2 for each valid i
it is guaranteed that Ada can break all bricksExample Input

3

3 1 2 2

2 1 1 1

3 2 2 1
Example Output

2

2

2
Explanation

Example case 1:

Ada can reverse the stack and then hit it two times. Before the first hit, the widths of bricks in the stack (from top to bottom) are (2,2,1). After the first hit, the topmost brick breaks and the stack becomes (2,1). The second hit breaks both remaining bricks.

In this particular case, it is also possible to hit the stack two times without reversing. Before the first hit, it is (1,2,2). The first hit breaks the two bricks at the top (so the stack becomes (2)) and the second hit breaks the last brick.