meetforever/GRPO_CL huggingface dataset:
user: Chef is playing a game which contains a binary string. 
He can perform one operation only:
- Toggle the i_th bit of the string (0 to 1 or 1 to 0)
By performing operations on the string (can be zero times), you have to convert the string with no adjacent bit being the same.
Can you help chef ?

-----Input:-----
- First line will contain $T$, number of test cases. Then the test cases follow. 
- First line of each test case, contains the size of the  string $N$
- Seond line contains a single line of input, the binary string. 

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

-----Constraints-----
- $1 \leq T \leq 100$
- $2 \leq |S| \leq 10^3$

-----Sample Input:-----
1
4
1011

-----Sample Output:-----
1
user: It's Diwali time and you are on a tour of Codepur, a city consisting of buildings of equal length and breadth because they were designed by a computer architect with a bit of OCD.
The ruling party of Codepur wants to have a blockbuster Diwali celebration but lack enough funds and decided to open a donation channel called Codepur Cares Fund (CCF). So they decided to run a survey.
Each building eihter has permanent donors, whose impact value is represented as a positive integer, or potential donors, whose impact value is represented by negative integers.
Overwhelmed by the response, and sticking to their resource optimized philosophy, they decided to hire you to determine the contiguous buildings which are allowed to donate to CCF with the following rule:
The contiguous buildings / areas with the maximum sum impact shall be allowed for donating to Codepur Cares Fund (CCF).
Help them out to get a stunning Diwali bonus and rest of your trip sponsered!

-----Input:-----
The first line consists of two tab spaced integers m and n, indicating number of rows and columns respectively in the Codepur's city plan (which is a 2-D Matrix).
The next $m$ lines consist of $n$ tab spaced integers $ti$ indicating rows in the matrix.

-----Output:-----
Print the bulidings (represented by their donors numbers) which are eligible to donate to CCF (i.e, have the largest sum contiguously) as a 2-D matrix with the elements being tab-spaced.

-----Constraints-----
- $0 \leq m,n \leq 10^{15}$
- $-10^{15} \leq ti \leq 10^5$

-----Sample Input:-----
6    5
0    -2    -7    0    -1
9    2    -6    2    0
-4    1    -4    1    0
-1    8    0    -2    1
-10    1    1    -5    6
-15    -1    1    5    -4

-----Sample Output:-----
9    2
-4    1
-1    8
user: Due to the COVID pandemic, maintaining social distancing is of utmost importance. In this problem, you'd calculate how many days would it take to reach an apocalypse from an initial case if nobody maintains social distancing.
The Earth is flat (for this question) and it's dimensions are $R$ x $C$
The whole Earth is already divided into blocks and the virus can spread in all directions except diagonally. The virus from each newly infected person will spread in all directions in the next day, thus growing exponentially.

-----Input:-----
- First line will contain $T$, number of testcases. Then the testcases follow. 
- Next line contains $R$ and $C$ respectively separated by a space.
- Next line contains $x$ and $y$ respectively separated by a space, denoting the indices of the initial case in the world.

-----Output:-----
For each testcase, output in a single line an integer denoting the number of days after which everyone will be infected.

-----Constraints-----
- $1 \leq T \leq 10^4$
- $2 \leq R,C \leq 10^7$
- $0 \leq x,y \leq 10^7$

-----Subtasks-----
- 10 points : $1 \leq T \leq 5$ and $2 \leq R,C \leq 10$
- 20 points : $2 \leq R,C \leq 10^5$
- 70 points : Original constraints

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

-----Sample Output:-----
5
3

-----EXPLANATION:-----
2nd test case:
Assuming, it's a small world of $3$ x $4$
0 is not infected. 1 is infected.
World indexing is like a 2D array:
(0,0) (0,1) (0,2) (0,3)
(1,0) (1,1) (1,2) (1,3)
(2,0) (2,1) (2,2) (2,3)
If this is the case on Day 0:
0 0 0 0
0 1 0 0
0 0 0 0
This will be the case on Day 1:
0 1 0 0
1 1 1 0
0 1 0 0
This will be the case on Day 2:
1 1 1 0
1 1 1 1
1 1 1 0
The End on Day 3:
1 1 1 1
1 1 1 1
1 1 1 1
Thus, answer will be 3
user: Chef is stuck on the minute hand of a giant clock. To escape from this clock he needs to get onto the hour hand which has an exit door. 
Since the minute hand and and hour hand are not connected at any point, chef will surely need to make a jump. Since he wants minimum risks, he chooses to jump on the hour hand so that the angle he has to cover is minimum possible.
You will be given a clock time in $UTC$ format denoting time of chef's jump and you have to compute the minimum angle that chef needs to cover while completing the jump.
For some reason chef times his jump only when the number of minutes is a multiple of 5.

-----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 string denoting time in UTC format (e.g. 10:20 i.e. 10 hours and 20 minutes)

-----Output-----
For each test case, print a single line denoting the smallest angle of jump.

-----Constraints-----
- $1 \leq T \leq 10^3$
- $0 \leq hours \leq 23$
- $0 \leq minutes \leq 59$

-----Example Input-----
3
14:20
02:10
09:30

-----Example Output-----
50 degree 
5 degree  
105 degree

-----Explanation-----
- In the second case, once the hour hand reaches 2 it starts moving towards 3 with the passing of every minute, hence when the minute hand points 10 minutes, the hour hand has already covered some angle towards 3. 
In this scenario the two angles made by hour and minute hand are 355 and 5 degrees. Since chef will jump on the side with minimum angle, he chooses the one with 5-degree angle.
user: Ravi is very good student in mathematics and he also like Even numbers very much .

On the other hand his friend Jhon like Odd numbers . Both of them are preparing for IIT JEE Advance .One day they are solving a  question together the question was Find the sum of first $n$ terms of the given series  $1^2+2.2^2+3^2+2.4^2+5^2+2.6^2+...........$
If the sum is odd then Jhon will be happy and will solve 2 more questions,and Ravi will not attempt more questions. If sum is even Ravi will  be happy and will solve 2 more questions and Jhon will not attempt more questions. 
So Your task is to decide who will solve more questions.

-----Input:-----
- First line will contain $n$, number of terms  in the given series.

-----Output:-----
Output single line "Ravi" if he solve more questions or "Jhon" if he solve more questions.

-----Constraints-----
- $1 \leq n \leq 100$

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

3   

-----Sample Output:-----
Jhon       
Ravi       

-----EXPLANATION:-----
In the first test cases  sum of 2 terms is 9 (according to the given series) which is an odd number   so Jhon will solve 2 more questions and Ravi will not attempt more questions.
In second test case sum of 3 terms is 18 (according to the given series) which is an  even number according to the given series  so Ravi will solve 3 more questions and Jhon will not attempt more questions.
user: Chef has decided to start home delivery from his restaurant. He hopes that he will get a lot of orders for delivery, however there is a concern. He doesn't have enough work forces for all the deliveries.  For this he has came up with an idea - he will group together all those orders which have to be delivered in nearby areas. 

In particular, he has identified certain bidirectional roads which he calls as fast roads. They are short and usually traffic free, so the fast travel is possible along these roads. His plan is that he will send orders to locations A and B together if and only if it is possible to travel between A and B using only fast roads. Your task is, given the configuration of fast roads, identify which orders are to be sent together.

-----Input-----
First line of input contains an integer T, the number of test cases. Then T test cases follow. First line of each test case contains two space separated integers N and M, denoting number of locations and the number of fast roads. Then M lines follow each containing two space separated integers A and B, denoting that there is a fast road between locations A and B. Assume that locations are indexed by numbers from 0 to N-1. 

Next line contains an integer Q denoting the number of queries. Each of the next Q lines contain two integers X and Y. For each query you have to find out if orders meant for locations X and Y are to be sent together or not.

Note that there might be multiple fast roads between same pair of locations, also there might be a fast road that links a location to itself.

-----Output-----
For each test case print Q lines - one for each query. Output "YO" if the orders are to be 
delivered together and "NO" otherwise (quotes for clarity).

-----Constraints-----
1 ≤ T ≤ 100
1 ≤ N ≤ 100
1 ≤ M ≤ 1000
0 ≤ A, B, X, Y ≤ N-1
1 ≤ Q ≤ 3000

-----Example-----
Input:
1
4 2
0 1
1 2
3
0 2
0 3
2 1

Output:
YO
NO
YO

-----Warning!-----
There are large input and output files in this problem. Make sure you use fast enough I/O methods.
user: Lumpy is a bus driver. Today, the conductor is absent so Lumpy has to do the conductor's job as well. There are N creatures in the bus. Sometimes the creatures don't carry change and can't pay the exact amount of the fare. Each creature in the bus today has paid an amount
greater than his/her fare. You are given information about the extra amount paid by each creature, by an array A of size N, where Ai denotes the extra amount paid by the i-th creature, in rupees.
After the end of the trip, Lumpy noticed that he had P one rupee coins and Q two rupee coins. He wants to pay back the creatures using this money. Being a kind hearted moose, Lumpy wants to pay back as many creatures as he can. Note that Lumpy will 
not pay back the i-th creature if he can't pay the exact amount that the i-th creature requires with the coins that he possesses. 
Lumpy is busy driving the bus and doesn't want to calculate the maximum number of creatures he can satisfy - He will surely cause an accident if he tries to do so. Can you help him out with this task? 

-----Input-----
- The first line of the input contains an integer T denoting the number of test cases. The description of T test cases follows.
- For each test case, first line consists of three space separated integers N, P and Q.
- Second line consists of N space separated integers A containing N space integers, where i-th integer denotes Ai.

-----Output-----
- For each test case, output a single line containing an integer corresponding to maximum number of creatures that Lumpy can pay back.

-----Constraints-----
- 1 ≤ T ≤ 106
- 1 ≤ N ≤ 105
- 1 ≤ Ai ≤ 109
- 0 ≤ P, Q ≤ 1014
- Sum of N over all the cases does not exceed 106

-----Subtasks-----
- Subtask #1 (15 points): P = 0
- Subtask #2 (15 points): Q = 0
- Subtask #3 (70 points): Original constraints

-----Example-----
Input:3
3 3 0
1 2 2
3 2 1
1 2 1
4 5 4
2 3 4 5

Output:2
3
3

-----Explanation-----
Example 1. Lumpy has just 3 one rupee coins. 

He can pay creatures numbered {1, 2} or creatures numbered {1, 3} with these coins. Thus, answer is 2. 
Example 2. Lumpy has 2 one rupee coins and 1 two rupee coin. 

In the optimal solution, Lumpy can give the two rupee coin to creature 2 and the one rupee coins to creatures 1 and 3. Thus, answer is 3.
user: You are the principal of the Cake school in chefland and today is your birthday. You want to treat each of the children with a small cupcake which is made by you. But there is a problem, You don't know how many students are present today.
The students have gathered of the morning assembly in $R$ rows and $C$ columns. Now you have to calculate how many cakes you have to make such that each child gets a cupcake. 

-----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, two integers $R$ and $C$. 

-----Output:-----
For each test case, output number of cupcakes you have to make.

-----Constraints-----
- $1 \leq T \leq 1000$
- $2 \leq R,C \leq 10^6$

-----Sample Input:-----
1
5 10

-----Sample Output:-----
50
user: "How did you get the deal,how did he agree?"
"Its's simple Tom I just made him an offer he couldn't refuse" 
Ayush is the owner of a big construction company and a close aide of Don Vito The Godfather, recently with the help of the Godfather his company has been assigned a big contract according to the contract he has to make n number of V shaped infinitely long roads(two V shaped roads may or  not intersect) on an infinitely large field.
Now the company assigning the contract needs to know the maximum number of regions they can get after making n such roads.
Help Ayush by answering the above question.

-----Input:-----
- The first line consists of the number of test cases $T$. 
- Next T lines consists of the number of V shaped roads $n$.

-----Output:-----
For each test case print a single line consisting of the maximum regions obtained.

-----Constraints-----
- $1 \leq T \leq 10$
- $1 \leq n \leq 10^9$

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

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

-----EXPLANATION:-----
Test case 1:       For one V shaped road there will be 2 regions

Test case 2:       For n=2 the following figure depicts the case of maximum regions:
user: Nitika was once reading a history book and wanted to analyze it. So she asked her brother to create a list of names of the various famous personalities in the book. Her brother gave Nitika the list. Nitika was furious when she saw the list. The names of the people were not properly formatted. She doesn't like this and would like to properly format it.
A name can have at most three parts: first name, middle name and last name. It will have at least one part. The last name is always present. The rules of formatting a name are very simple:

- Only the first letter of each part of the name should be capital.
- All the parts of the name except the last part should be represented by only two characters. The first character should be the first letter of the part and should be capitalized. The second character should be ".".

Let us look at some examples of formatting according to these rules:
- gandhi -> Gandhi

- mahatma gandhI -> M. Gandhi 
- Mohndas KaramChand ganDhi -> M. K. Gandhi 

-----Input-----
The first line of the input contains an integer T denoting the number of test cases.
The only line of each test case contains the space separated parts of the name.

-----Output-----
For each case, output the properly formatted name.

-----Constraints-----
- 1 ≤ T ≤ 100
- 2 ≤ Length of each part of the name ≤ 10
- Each part of the name contains the letters from lower and upper case English alphabets (i.e. from 'a' to 'z', or 'A' to 'Z')

-----Subtasks-----
Subtask #1 (40 points)
- There is exactly one part in the name.

Subtask #2 (60 points)
- Original constraints.

-----Example-----
Input:
3
gandhi
mahatma gandhI
Mohndas KaramChand gandhi

Output:
Gandhi 
M. Gandhi 
M. K. Gandhi 

-----Explanation-----
The examples are already explained in the problem statement.
user: The Chef is given an array of numbers and asked to find the first balance point of an array. A balance point is an index in the array N where the sum of the integers to the left of N is equal to the sum of the integers to the right of N. If there is no such balance point, print -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.
The first line of each test case contains a single integer N denoting the number of weights on the array. The second line contains N space-separated integers A1, A2, ..., AN denoting the weights

-----Output-----
For each test case, output a single line containing the index of the first balance point. If no such index exists, output -1

-----Constraints-----
For Subtask 1:
- 1 ≤ T ≤ 10
- 1 ≤ N ≤ 10
- -1000 ≤ A1, A2, ..., AN ≤ 1000
For Subtask 1:
- 1 ≤ T ≤ 10
- 1 ≤ N ≤ 1000
- -10000 ≤ A1, A2, ..., AN ≤ 10000

-----Example-----
Input:
2
7
7 8 9 1 9 8 7
6
1 100 50 -51 1 1

Output:
3
1

-----Explanation-----
Example case 1. In the first case, at the midpoint of the array 1, the sum of the left side {7,8,9} is equal to the sum of the right side {9,8,7}
Example case 1. In the second case, at index 1, the sum of left side =1 is equal to the sum of the right side {50,-51,1,1}
user: Chef’s girlfriend is angry with him because he forgot her birthday. Chef decided to please her by gifting her a Love Graph. 
Chef has $N$ vertices: $V_1, V_2, \dots, V_N$. Love Graph is an undirected multigraph with no self-loops and can be constructed by performing the following operations:-
- Choose an integer $i$ ($1 \leq i \leq N$)
- Choose another integer $j \space \space \{ (i \neq j) \text{ and } (1 \leq j \leq N) \}$
- Make an edge between $V_i$ and $V_j$
- Set $i = j$
- Repeat steps $2, 3$ and $4$ in order $M-1$ more times.
Find the number of ways in which Chef can construct a Love Graph. Since the answer can be very large, compute it modulo $10^9+7$.

-----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 $M$.

-----Output-----
For each test case, print a single line containing one integer — the number of ways in which Chef can construct a Love Graph modulo $10^9+7$.

-----Constraints-----
- $1 \leq T \leq 10^5$
- $2 \leq N \leq 10^9$
- $1 \leq M \leq 10^{18}$

-----Subtasks-----
- 30 points:
- $1 \leq T \leq 100$
- $2 \leq N \leq 10$
- $1 \leq M \leq 10$ 
- 70 points: original constraints

-----Sample Input-----
1

2 1   

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

-----Explanation-----
There are two ways of constructing Love Graph.

In first way, we pick Vertex 1 and then join with Vertex 2.

In second way, we pick Vertex 2 and then join with Vertex 1.
user: Finally, a COVID vaccine is out on the market and the Chefland government has asked you to form a plan to distribute it to the public as soon as possible. There are a total of $N$ people with ages $a_1, a_2, \ldots, a_N$.
There is only one hospital where vaccination is done and it is only possible to vaccinate up to $D$ people per day. Anyone whose age is $\ge 80$ or $\le 9$ is considered to be at risk. On each day, you may not vaccinate both a person who is at risk and a person who is not at risk. Find the smallest number of days needed to vaccinate everyone.

-----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 $a_1, a_2, \ldots, a_N$.

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

-----Constraints-----
- $1 \le T \le 10$
- $1 \le N \le 10^4$
- $1 \le D \le 10^5$
- $1 \le a_i \le 100$ for each valid $i$

-----Subtasks-----
Subtask #1 (100 points): original constraints

-----Example Input-----
2
10 1
10 20 30 40 50 60 90 80 100 1
5 2
9 80 27 72 79

-----Example Output-----
10
3

-----Explanation-----
Example case 1: We do not need to worry about how the people are grouped, since only one person can be vaccinated in a single day. We require as many days as there are people.
Example case 2: There are two people at risk and three people who are not at risk. One optimal strategy is to vaccinate the two people at risk on day $1$ and the remaining three on the next $2$ days.
user: Chef has an array of N natural numbers most of them are repeated. Cheffina challenges chef to find all numbers(in ascending order) whose frequency is strictly more than K.

-----Input:-----
- First-line will contain $T$, the number of test cases. Then the test cases follow. 
- Each test case contains two lines of input, two integers $N, K$.
- N space-separated natural numbers.

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

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

-----Sample Input:-----
1
5 1
5 2 1 2 5

-----Sample Output:-----
2 5
user: Shaun was given $N$ pairs of parenthesis ( )  by his teacher who gave him a difficult task.The task consists of two steps. First,Shaun should colour all $N$ pairs of parenthesis each with different color but opening and closing bracket of a particular pair should be of same colour. Then,Shaun should report to his teacher the number of ways he can arrange all $2*N$ brackets such that sequence form is valid. Teacher defined valid sequence by these rules:
- Any left parenthesis '(' must have a corresponding right parenthesis ')'.
- Any right parenthesis ')' must have a corresponding left parenthesis '('.
- Left parenthesis '(' must go before the corresponding right parenthesis ')'. 
Note: Shaun could match opening and closing brackets of different colours. 
Since number of ways can be large, Shaun would report the answer as modulo 1000000007 ($10^9 + 7$).

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

-----Output:-----
For each testcase, output in a single line answer given by Shaun to his teacher modulo 1000000007.

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

-----Sample Input:-----
3
1
2
3

-----Sample Output:-----
1
6
90

-----EXPLANATION:-----
Here numbers from $1$ to $N$ have been used to denote parenthesis.A unique number corresponds to a unique pair of parenthesis.
-In the first test case , you can use only one color to color the parenthesis  you could arrange it only in one way i.e, 1 1
-In the second test case  you can use two colors and the possible ways of arranging it are
1 1 2 2
1 2 2 1
1 2 1 2
2 2 1 1
2 1 1 2
2 1 2 1
user: Shivam is working on electric circuits. He requires some connecting wires. He needs to make a total of N connections and he has mentioned his wire length requirements for each connection in an integer sequence A. For buying wires, he need to decide the length of each wire piece, and he’ll get as many wire pieces of the chosen length each at unit cost (cost 1 per piece) but he can't get wires of different lengths. Also, he can't cut wire pieces to make new pieces of different (smaller) length(s).
But he can connect any number of wires together to form a new single wire piece whose length is the sum of lengths of the wires connected. So, Shivam needs to choose an integer length for buying wires. Shivam hates to waste anything, and he hates it even more if that thing is money.
Shivam is weak in mathematics and is asking you to help him in this situation. Help him decide the length of wires and total number of wires so as to minimize the total expenditure.
Note: You cannot make a connection which requires a wire piece of length X with a wire piece of length Y if X≠Y.
Input:
·        The first line of the input contains T = Number of Test cases
·        The first line of each test case contains an integer N
·        The second line contains N space separated integers A1, A2, …., AN.
Output:
For each test case print a single line containing two space separated integers, length of each wire and the corresponding minimum cost.
Constraints:
·       1 <= T <= 10
·       1 <= N <= 10^5
·        1 <= Ai <= 10^5, for each valid i
Sample Input:
1
3
2 4 8
Sample Output:
2 7