meetforever/GRPO_CL huggingface dataset:
user: Mr. Das is a teacher teaching for several years in a school. He is not computer savvy. Due to lockdown, now he has to take classes online. Recently he took an online exam for students of different classes. Now, he will call parents of all the students who scored lower than average marks for the class. He has requested you to give the name $X$, parent's phone number $P$, and marks obtained $M$ to him.

-----Input:-----
- First line contains $T$ no. of test cases
- for every test case, first line contains an integer $N$, no. of students of his class 
- Next $N$ lines contain $X$, $P$ , and $M$ separated by space

-----Output:-----
For every test case, find details of the students who scored below average, then print $X, P, M$  separated by space on a new line as per the increasing order of their marks. In case there are multiple students with the same marks, print them as per the order of their occurrence in the input

-----Constraints-----
- $1 \leq T \leq 20$
- X contains characters between a-z and A-Z  with a maximum length of 20
- $1 \leq N \leq 100$
- P is 10 digits
- $0 \leq M \leq 100$

-----Sample Input:-----
2  
3
Rahul 1345964789 47
Rupendra 1457856987 58
Priya 1478569820 45
2
Tanuja 4310779415 97
Akash 3689781245 43

-----Sample Output:-----
Priya 1478569820 45
Rahul 1345964789 47
Akash 3689781245 43

-----EXPLANATION:-----
In #1, Priya and Rahul's number was lower than average.
In #2, Akash's number was lower than average
user: Chef and his mother are going travelling. Chef's world consists of $N$ cities (numbered $1$ through $N$) connected by $N-1$ bidirectional roads such that each city can be reached from any other city using roads. For each city, we know its age — the number of years elapsed since the foundation of the city; let's denote the age of city $i$ by $a_i$.
First of all, Chef and his mother have to decide what city they should visit first. Suppose that Chef chooses a city $c_c$ and his mother chooses a (not necessarily different) city $c_m$. The difference of their choices is the number of different bits in the binary representations of $a_{c_c}$ and $a_{c_m}$.
Chef will not argue with his mother if the parity of this difference is not equal to the parity of the length of the shortest path between cities $c_c$ and $c_m$ (the number of roads on the shortest path between them). Find the number of ways to choose the cities $c_c$ and $c_m$ such that Chef avoids quarreling with his mother.

-----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 $N$. 
- Each of the following $N-1$ lines contains two space-separated integers $A$ and $B$ denoting a road between cities $A$ and $B$.
- The last line contains $N$ space-separated integers $a_1, a_2, \dots, a_N$.

-----Output-----
For each test case, print a single line containing one integer — the number of valid pairs $c_c, c_m$.

-----Constraints-----
- $1 \le T \le 10$
- $1 \le N \le 10^5$
- $1 \le A, B \le N$
- $0 \le a_i \le 10^9$ for each valid $i$

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

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

-----Explanation-----
Example case 1: The two possible choices are $c_c=2, c_m=3$ (their binary representations differ by one bit, the shortest path has length $2$) and $c_c=1, c_m=2$ (there are two different bits in their binary representations and the shortest path has length $1$).
user: Shivam owns a gambling house, which has a special wheel called The Wheel of Fortune. 
This wheel is meant for giving free coins to people coming in the house. 

The wheel of fortune is a game of chance. It uses a spinning wheel with exactly N numbered pockets and a coin is placed in between every consecutive pocket. The wheel is spun in either of the two ways.
Before the wheel is turned, all the coins are restored and players bet on a number K.
Then a needle is made to point to any one of the pocket which has number K written on it.
Wheel is then spun till the needle encounters number K again and the player gets all the coins the needle has encountered.

Shivam being the owner of the gambling house, has the authority to place the needle on any of the K numbered pockets and also he could rotate the wheel in either of the two ways.
Shivam has to figure out a way to minimize number of coins that he has to spend on every given bet.
You are given a wheel having N elements and Q players. Each player bets on a number K from the wheel. For each player you have to print minimum number of coins Shivam has to spend.


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

- The first line of each test case contains single integer N .

- The second line of each test case contains N space seperated integers denoting the numbers on the wheel.

- The third line of each test case contains a single integer Q denoting the number of players.
- Then, Q lines follow a single integer K from the N numbers of the wheel 

-----Output-----
For each player, output the minimum number of coins Shivam has to spend.


-----Constraints-----

- 1 ≤ T ≤ 10
- 1 ≤ N ≤ 100000
- 1 ≤ Number written on the Wheel ≤ 1000
- 1 ≤ Q ≤ 10000
- 1 ≤ K ≤ 1000
-  It is guaranteed that K belongs to the N numbers written on the wheel.

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

2

3

1 2 3

3

1

2

3

6

2 1 5 3 2 1

4

1

2

3

5
Output:

3

3

3

2

2

6

6
user: Chef is playing a game with two of his friends. In this game, each player chooses an integer between $1$ and $P$ inclusive. Let's denote the integers chosen by Chef, friend 1 and friend 2 by $i$, $j$ and $k$ respectively; then,  Chef's score is
(((Nmodi)modj)modk)modN.(((Nmodi)modj)modk)modN.(((N\,\mathrm{mod}\,i)\,\mathrm{mod}\,j)\,\mathrm{mod}\,k)\,\mathrm{mod}\,N\,.

Chef wants to obtain the maximum possible score. Let's denote this maximum score by $M$. Find the number of ways to choose the triple $(i,j,k)$ so that Chef's score is equal to $M$.

-----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 $P$.

-----Output-----
For each test case, print a single line containing one integer — the number of ways to obtain the maximum score.

-----Constraints-----
- $1 \le T \le 10^6$
- $1 \le N \le P \le 10^6$

-----Subtasks-----
Subtask #1 (10 points):
- $1 \le T \le 100$
- $1 \le N \le P \le 100$
Subtask #2 (90 points): original constraints

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

-----Example Output-----
9
13

-----Explanation-----
Example case 1: Chef's maximum possible score is $M = 1$. All possible values of $(i, j, k)$ such that the score is $1$ are
$(3, 2, 2)$,
$(3, 2, 3)$,
$(3, 2, 4)$,
$(3, 3, 2)$,
$(3, 3, 3)$,
$(3, 3, 4)$,
$(3, 4, 2)$,
$(3, 4, 3)$,
$(3, 4, 4)$.
user: There is a girl named ''Akansha''. She is very fond of eating chocolates but she has a weak immune system due to which she gets cold after eating chocolate during morning, evening and night and can only eat at most $x$ number of chocolate each afternoon. A friend of hers gifted her some $n$ number of chocolates that she doesn't want to share with anyone. Those chocolate have to be finished before they expire. (no. of days in which they are going to expire from the day she has been gifted the chocolate is given for each chocolate)   $Note:$ Chocolate cannot be consumed on the day it expires.

Help Akansha to know if it is possible for her to finish all the chocolates before they expire or not.

-----Input:-----
- First line will contain $T$, number of test cases. Then the test cases follow. 
- First line contains $n$,the number of chocolates gifted to her
- Second line contains $x$,the number of chocolates she can eat each afternoon
- Third line contains $n$ space separated integers $A1,A2...An$,denoting the expiry of each of the $n$ chocolates

-----Output:-----
For each testcase, print $Possible$, if she can complete all the chocolates gifted to her. Otherwise, print $Impossible$, if she can not finish all the chocolates.

-----Constraints-----
- $1 \leq T \leq 100$
- $1 \leq n \leq 1500$
- $1 \leq x \leq 1500$
- $1 \leq Ai \leq 1500$

-----Subtasks-----
- 100 points : $Original Constraints$

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

3

5

4 1 2

5

2

4 4 3 2 2

5

1

4 2 3 1 1   

-----Sample Output:-----
Impossible

Possible

Impossible   

-----EXPLANATION:-----
- 
Example case 1

1st and 3rd chocolate on the 1st afternoon as she can consume at most 5. one chocolate will be wasted.
$Note:$ she cannot eat the 2nd chocolate because chocolates cannot be consumed on the day of expiry.
- 
Example case 2

4th and 5th chocolate on 1st afternoon, 3rd and 1st chocolate on 2nd afternoon. And 2nd chocolate on the 3rd afternoon.
It will take a total of 3 days to finish the chocolate.
- 
Example case 3

She cannot eat 4th and 5th chocolate as they will expire on the very 1st day, she can eat 2nd chocolate on 1st afternoon, then 3rd chocolate on 2nd afternoon, then 1st chocolate on 3rd afternoon, and 2 chocolates 4th and 5th will expire.
user: There are some websites that are accessible through several different addresses. For example, for a long time Codeforces was accessible with two hostnames codeforces.com and codeforces.ru.

You are given a list of page addresses being queried. For simplicity we consider all addresses to have the form http://<hostname>[/<path>], where:

  <hostname> — server name (consists of words and maybe some dots separating them),  /<path> — optional part, where <path> consists of words separated by slashes. 

We consider two <hostname> to correspond to one website if for each query to the first <hostname> there will be exactly the same query to the second one and vice versa — for each query to the second <hostname> there will be the same query to the first one. Take a look at the samples for further clarifications.

Your goal is to determine the groups of server names that correspond to one website. Ignore groups consisting of the only server name.

Please note, that according to the above definition queries http://<hostname> and http://<hostname>/ are different.


-----Input-----

The first line of the input contains a single integer n (1 ≤ n ≤ 100 000) — the number of page queries. Then follow n lines each containing exactly one address. Each address is of the form http://<hostname>[/<path>], where:

  <hostname> consists of lowercase English letters and dots, there are no two consecutive dots, <hostname> doesn't start or finish with a dot. The length of <hostname> is positive and doesn't exceed 20.  <path> consists of lowercase English letters, dots and slashes. There are no two consecutive slashes, <path> doesn't start with a slash and its length doesn't exceed 20. 

Addresses are not guaranteed to be distinct.


-----Output-----

First print k — the number of groups of server names that correspond to one website. You should count only groups of size greater than one.

Next k lines should contain the description of groups, one group per line. For each group print all server names separated by a single space. You are allowed to print both groups and names inside any group in arbitrary order.


-----Examples-----
Input
10
http://abacaba.ru/test
http://abacaba.ru/
http://abacaba.com
http://abacaba.com/test
http://abacaba.de/
http://abacaba.ru/test
http://abacaba.de/test
http://abacaba.com/
http://abacaba.com/t
http://abacaba.com/test

Output
1
http://abacaba.de http://abacaba.ru 

Input
14
http://c
http://ccc.bbbb/aba..b
http://cba.com
http://a.c/aba..b/a
http://abc/
http://a.c/
http://ccc.bbbb
http://ab.ac.bc.aa/
http://a.a.a/
http://ccc.bbbb/
http://cba.com/
http://cba.com/aba..b
http://a.a.a/aba..b/a
http://abc/aba..b/a

Output
2
http://cba.com http://ccc.bbbb 
http://a.a.a http://a.c http://abc
user: You are at the top left cell $(1, 1)$ of an $n \times m$ labyrinth. Your goal is to get to the bottom right cell $(n, m)$. You can only move right or down, one cell per step. Moving right from a cell $(x, y)$ takes you to the cell $(x, y + 1)$, while moving down takes you to the cell $(x + 1, y)$.

Some cells of the labyrinth contain rocks. When you move to a cell with rock, the rock is pushed to the next cell in the direction you're moving. If the next cell contains a rock, it gets pushed further, and so on.

The labyrinth is surrounded by impenetrable walls, thus any move that would put you or any rock outside of the labyrinth is illegal.

Count the number of different legal paths you can take from the start to the goal modulo $10^9 + 7$. Two paths are considered different if there is at least one cell that is visited in one path, but not visited in the other.


-----Input-----

The first line contains two integers $n, m$ — dimensions of the labyrinth ($1 \leq n, m \leq 2000$).

Next $n$ lines describe the labyrinth. Each of these lines contains $m$ characters. The $j$-th character of the $i$-th of these lines is equal to "R" if the cell $(i, j)$ contains a rock, or "." if the cell $(i, j)$ is empty.

It is guaranteed that the starting cell $(1, 1)$ is empty.


-----Output-----

Print a single integer — the number of different legal paths from $(1, 1)$ to $(n, m)$ modulo $10^9 + 7$.


-----Examples-----
Input
1 1
.

Output
1

Input
2 3
...
..R

Output
0

Input
4 4
...R
.RR.
.RR.
R...

Output
4



-----Note-----

In the first sample case we can't (and don't have to) move, hence the only path consists of a single cell $(1, 1)$.

In the second sample case the goal is blocked and is unreachable.

Illustrations for the third sample case can be found here: https://assets.codeforces.com/rounds/1225/index.html
user: Dreamoon loves summing up something for no reason. One day he obtains two integers a and b occasionally. He wants to calculate the sum of all nice integers. Positive integer x is called nice if $\operatorname{mod}(x, b) \neq 0$ and $\frac{\operatorname{div}(x, b)}{\operatorname{mod}(x, b)} = k$, where k is some integer number in range [1, a].

By $\operatorname{div}(x, y)$ we denote the quotient of integer division of x and y. By $\operatorname{mod}(x, y)$ we denote the remainder of integer division of x and y. You can read more about these operations here: http://goo.gl/AcsXhT.

The answer may be large, so please print its remainder modulo 1 000 000 007 (10^9 + 7). Can you compute it faster than Dreamoon?


-----Input-----

The single line of the input contains two integers a, b (1 ≤ a, b ≤ 10^7).


-----Output-----

Print a single integer representing the answer modulo 1 000 000 007 (10^9 + 7).


-----Examples-----
Input
1 1

Output
0

Input
2 2

Output
8



-----Note-----

For the first sample, there are no nice integers because $\operatorname{mod}(x, 1)$ is always zero.

For the second sample, the set of nice integers is {3, 5}.
user: Tavak and Seyyed are good friends. Seyyed is very funny and he told Tavak to solve the following problem instead of longest-path.

You are given l and r. For all integers from l to r, inclusive, we wrote down all of their integer divisors except 1. Find the integer that we wrote down the maximum number of times.

Solve the problem to show that it's not a NP problem.


-----Input-----

The first line contains two integers l and r (2 ≤ l ≤ r ≤ 10^9).


-----Output-----

Print single integer, the integer that appears maximum number of times in the divisors. 

If there are multiple answers, print any of them.


-----Examples-----
Input
19 29

Output
2

Input
3 6

Output
3



-----Note-----

Definition of a divisor: https://www.mathsisfun.com/definitions/divisor-of-an-integer-.html

The first example: from 19 to 29 these numbers are divisible by 2: {20, 22, 24, 26, 28}.

The second example: from 3 to 6 these numbers are divisible by 3: {3, 6}.
user: "QAQ" is a word to denote an expression of crying. Imagine "Q" as eyes with tears and "A" as a mouth.

Now Diamond has given Bort a string consisting of only uppercase English letters of length n. There is a great number of "QAQ" in the string (Diamond is so cute!). $8$ illustration by 猫屋 https://twitter.com/nekoyaliu 

Bort wants to know how many subsequences "QAQ" are in the string Diamond has given. Note that the letters "QAQ" don't have to be consecutive, but the order of letters should be exact.


-----Input-----

The only line contains a string of length n (1 ≤ n ≤ 100). It's guaranteed that the string only contains uppercase English letters.


-----Output-----

Print a single integer — the number of subsequences "QAQ" in the string.


-----Examples-----
Input
QAQAQYSYIOIWIN

Output
4

Input
QAQQQZZYNOIWIN

Output
3



-----Note-----

In the first example there are 4 subsequences "QAQ": "QAQAQYSYIOIWIN", "QAQAQYSYIOIWIN", "QAQAQYSYIOIWIN", "QAQAQYSYIOIWIN".
user: Write a function that accepts a square matrix (`N x N` 2D array) and returns the determinant of the matrix.

How to take the determinant of a matrix -- it is simplest to start with the smallest cases:

A 1x1 matrix `|a|` has determinant `a`.

A 2x2 matrix `[ [a, b], [c, d] ]` or
```
|a  b|
|c  d|
```
has determinant: `a*d - b*c`.

The determinant of an `n x n` sized matrix is calculated by reducing the problem to the calculation of the determinants of `n` matrices of`n-1 x n-1` size.

For the 3x3 case, `[ [a, b, c], [d, e, f], [g, h, i] ]` or
```
|a b c|  
|d e f|  
|g h i|  
```
the determinant is: `a * det(a_minor) - b * det(b_minor) + c * det(c_minor)` where `det(a_minor)` refers to taking the determinant of the 2x2 matrix created by crossing out the row and column in which the element a occurs:
```
|- - -|
|- e f|
|- h i|  
```
Note the alternation of signs. 

The determinant of larger matrices are calculated analogously, e.g. if M is a 4x4 matrix with first row `[a, b, c, d]`, then:

`det(M) = a * det(a_minor) - b * det(b_minor) + c * det(c_minor) - d * det(d_minor)`

Answer: {"fn_name": "determinant", "inputs": [[[[5]]]], "outputs": [[5]]}
user: Write a function called `sumIntervals`/`sum_intervals()` that accepts an array of intervals, and returns the sum of all the interval lengths. Overlapping intervals should only be counted once.

### Intervals

Intervals are represented by a pair of integers in the form of an array. The first value of the interval will always be less than the second value. Interval example: `[1, 5]` is an interval from 1 to 5. The length of this interval is 4.

### Overlapping Intervals

List containing overlapping intervals:

```
[
   [1,4],
   [7, 10],
   [3, 5]
]
```

The sum of the lengths of these intervals is 7. Since [1, 4] and [3, 5] overlap, we can treat the interval as [1, 5], which has a length of 4.

### Examples:

```C#
// empty intervals
Intervals.SumIntervals(new (int, int)[]{ });  // => 0
Intervals.SumIntervals(new (int, int)[]{ (2, 2), (5, 5)});  // => 0

// disjoined intervals
Intervals.SumIntervals(new (int, int)[]{
  (1, 2), (3, 5)
});  // => (2-1) + (5-3) = 3

// overlapping intervals
Intervals.SumIntervals(new (int, int)[]{
  (1, 4), (3, 6), (2, 8)
});  // (1,8) => 7
```

Answer: {"fn_name": "sum_of_intervals", "inputs": [[[[1, 5]]]], "outputs": [[4]]}
user: # Task
 You are given integer `n` determining set S = {1, 2, ..., n}. Determine if the number of k-element subsets of S is `ODD` or `EVEN` for given integer k.

# Example

 For `n = 3, k = 2`, the result should be `"ODD"`
 
 In this case, we have 3 2-element subsets of {1, 2, 3}:
 
 `{1, 2}, {1, 3}, {2, 3}`

 For `n = 2, k = 1`, the result should be `"EVEN"`.
 
 In this case, we have 2 1-element subsets of {1, 2}:
 
 `{1}, {2}`

 `Don't bother with naive solution - numbers here are really big.`

# Input/Output


 - `[input]` integer `n`

    `1 <= n <= 10^9`


 - `[input]` integer `k`

    `1 <= k <= n`


 - `[output]` a string

    `"EVEN"` or `"ODD"` depending if the number of k-element subsets of S = {1, 2, ..., n} is ODD or EVEN.

Answer: {"fn_name": "subsets_parity", "inputs": [[3, 2], [2, 1], [1, 1], [20, 10], [48, 12]], "outputs": [["ODD"], ["EVEN"], ["ODD"], ["EVEN"], ["EVEN"]]}
user: We are given a certain number ```n``` and we do the product partitions of it.
```[59, 3, 2, 2, 2]``` is a product partition of ```1416``` because:
```
59 * 3 * 2 * 2 * 2 = 1416
```
We form a score, ```sc``` for each partition in the following way:
- if ```d1, d2, ...., dk``` are the prime factors of ```n```, and ```f1, f2, ...., fk```, the corresponding frequencies for each factor, we calculate:



Suposse that we have that ```n = 1416``` 
The product partitions of this number with a corresponding special score are as follows:
```
Product Partition           Score(sc)
[59, 3, 2, 2, 2]             350    # equals to: (59^1 + 3^1 + 2^3) * 5
[177, 2, 2, 2]               740    # equals to: (177^1 + 2^3) * 4
[118, 3, 2, 2]               500
[59, 6, 2, 2]                276
[354, 2, 2]                 1074
[59, 4, 3, 2]                272
[236, 3, 2]                  723
[177, 4, 2]                  549
[118, 6, 2]                  378
[59, 12, 2]                  219
[708, 2]                    1420  <---- maximum value
[118, 4, 3]                  375
[59, 8, 3]                   210
[472, 3]                     950
[59, 6, 4]                   207
[354, 4]                     716
[236, 6]                     484
[177, 8]                     370
[118, 12]                    260
[59, 24]                     166  <---- minimum value
```
So we need a function that may give us the product partition with maximum or minimum score.

The function ```find_spec_prod_part()``` will receive two arguments:

- an integer ```n, n > 0```
- a command as a string, one of the following ones: ```'max' or 'min'```

The function should output a list with two elements: the found product partition (as a list sorted in descendin order) with its corresponding score.
```
find_spec_prod_part(n, com) ---> [prod_partition, score]
```
Let'see some cases:
```python
find_spec_prod_part(1416, 'max') == [[708, 2], 1420]

find_spec_prod_part(1416, 'min') == [[59, 24], 166]
```

The function should reject prime numbers:
```python
find_spec_prod_part(10007 , 'max') == "It is a prime number"
```
Enjoy it!

Hint: In this kata, optimization is one of the purposes or tags. The algorithm to produce the product partition is a key factor in terms of speed. Your code will be tested for an ```n``` value up to ```500000```.

Answer: {"fn_name": "find_spec_prod_part", "inputs": [[1416, "max"], [1416, "min"], [10007, "max"]], "outputs": [[[[708, 2], 1420]], [[[59, 24], 166]], ["It is a prime number"]]}
user: Complete the solution so that it strips all text that follows any of a set of comment markers passed in. Any whitespace at the end of the line should also be stripped out. 

**Example:**

Given an input string of:
```
apples, pears # and bananas
grapes
bananas !apples
```

The output expected would be:
```
apples, pears
grapes
bananas
```

The code would be called like so:

```python
result = solution("apples, pears # and bananas\ngrapes\nbananas !apples", ["#", "!"])
# result should == "apples, pears\ngrapes\nbananas"

```

Answer: {"fn_name": "solution", "inputs": [["apples, pears # and bananas\ngrapes\nbananas !apples", ["#", "!"]], ["a #b\nc\nd $e f g", ["#", "$"]], ["apples, pears # and bananas\ngrapes\nbananas !#apples", ["#", "!"]], ["apples, pears # and bananas\ngrapes\nbananas #!apples", ["#", "!"]], ["apples, pears # and bananas\ngrapes\navocado @apples", ["@", "!"]], ["apples, pears \u00a7 and bananas\ngrapes\navocado *apples", ["*", "\u00a7"]], ["", ["#", "!"]], ["#", ["#", "!"]], ["\n\u00a7", ["#", "\u00a7"]], ["apples, pears # and bananas\ngrapes\nbananas !apples", []]], "outputs": [["apples, pears\ngrapes\nbananas"], ["a\nc\nd"], ["apples, pears\ngrapes\nbananas"], ["apples, pears\ngrapes\nbananas"], ["apples, pears # and bananas\ngrapes\navocado"], ["apples, pears\ngrapes\navocado"], [""], [""], ["\n"], ["apples, pears # and bananas\ngrapes\nbananas !apples"]]}