vgel/INTELLECT-2-RL-Dataset-Code-Only huggingface dataset:
The game of Berland poker is played with a deck of $n$ cards, $m$ of which are jokers. $k$ players play this game ($n$ is divisible by $k$).

At the beginning of the game, each player takes $\frac{n}{k}$ cards from the deck (so each card is taken by exactly one player). The player who has the maximum number of jokers is the winner, and he gets the number of points equal to $x - y$, where $x$ is the number of jokers in the winner's hand, and $y$ is the maximum number of jokers among all other players. If there are two or more players with maximum number of jokers, all of them are winners and they get $0$ points.

Here are some examples:  $n = 8$, $m = 3$, $k = 2$. If one player gets $3$ jokers and $1$ plain card, and another player gets $0$ jokers and $4$ plain cards, then the first player is the winner and gets $3 - 0 = 3$ points;  $n = 4$, $m = 2$, $k = 4$. Two players get plain cards, and the other two players get jokers, so both of them are winners and get $0$ points;  $n = 9$, $m = 6$, $k = 3$. If the first player gets $3$ jokers, the second player gets $1$ joker and $2$ plain cards, and the third player gets $2$ jokers and $1$ plain card, then the first player is the winner, and he gets $3 - 2 = 1$ point;  $n = 42$, $m = 0$, $k = 7$. Since there are no jokers, everyone gets $0$ jokers, everyone is a winner, and everyone gets $0$ points. 

Given $n$, $m$ and $k$, calculate the maximum number of points a player can get for winning the game.


-----Input-----

The first line of the input contains one integer $t$ ($1 \le t \le 500$) — the number of test cases.

Then the test cases follow. Each test case contains three integers $n$, $m$ and $k$ ($2 \le n \le 50$, $0 \le m \le n$, $2 \le k \le n$, $k$ is a divisors of $n$).


-----Output-----

For each test case, print one integer — the maximum number of points a player can get for winning the game.


-----Example-----
Input
4
8 3 2
4 2 4
9 6 3
42 0 7

Output
3
0
1
0



-----Note-----

Test cases of the example are described in the statement.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
A company manager gave projects to the employees of his company. The employees have to form a team of two for doing the project. The manager left the employees to decide the teams. The number of employees in a company will be even.

Every employee has knowledge level.It tells how much knowledge each employee has.The knowledge level of team is the sum of the knowledge level of both the employees. The.The employees decide to form groups such that the difference between the team with highest knowledge and the one with lowest knowledge is minimum.

Input:

First line of the input will contain number of test cases t.

In the next t lines the first number is n the number of employees in the company followed by n integers denoting the knowledge levels of the n employees.

Output:

Your output should be a single line containing the lowest possible difference between the team with highest knowledge and the one with lowest knowledge.

SAMPLE INPUT
2
4 2 6 4 3        
6 1 1 1 1 1 1

SAMPLE OUTPUT
1
0

Explanation

Explanation:

Input Constraints are:

1 ≤ t ≤ 100   

1 ≤ n ≤ 100    

1 ≤ knowledge level ≤ 10000

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
You have a given picture with size $w \times h$. Determine if the given picture has a single "+" shape or not. A "+" shape is described below:

  A "+" shape has one center nonempty cell.  There should be some (at least one) consecutive non-empty cells in each direction (left, right, up, down) from the center. In other words, there should be a ray in each direction.  All other cells are empty. 

Find out if the given picture has single "+" shape.


-----Input-----

The first line contains two integers $h$ and $w$ ($1 \le h$, $w \le 500$) — the height and width of the picture.

The $i$-th of the next $h$ lines contains string $s_{i}$ of length $w$ consisting "." and "*" where "." denotes the empty space and "*" denotes the non-empty space.


-----Output-----

If the given picture satisfies all conditions, print "YES". Otherwise, print "NO".

You can output each letter in any case (upper or lower).


-----Examples-----
Input
5 6
......
..*...
.****.
..*...
..*...

Output
YES

Input
3 5
..*..
****.
.*...

Output
NO

Input
7 7
.......
...*...
..****.
...*...
...*...
.......
.*.....

Output
NO

Input
5 6
..**..
..**..
******
..**..
..**..

Output
NO

Input
3 7
.*...*.
***.***
.*...*.

Output
NO

Input
5 10
..........
..*.......
.*.******.
..*.......
..........

Output
NO



-----Note-----

In the first example, the given picture contains one "+".

In the second example, two vertical branches are located in a different column.

In the third example, there is a dot outside of the shape.

In the fourth example, the width of the two vertical branches is $2$.

In the fifth example, there are two shapes.

In the sixth example, there is an empty space inside of the shape.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
You are given an array of N integers arr, find the count of reverse pairs. 
A pair of indices (i, j) is said to be a reverse pair if both the following conditions are met:
	0 <= i < j < N 
	arr[i] > 2 * arr[j]
Example 1:
Input:
N = 6
arr = [3, 2, 4, 5, 1, 20]
Output:
3
Explanation:
The Reverse pairs are 
(i)  (0, 4), arr[0] = 3, arr[4] = 1, 3 > 2(1) 
(ii) (2, 4), arr[2] = 4, arr[4] = 1, 4 > 2(1) 
(iii)(3, 4), arr[3] = 5, arr[4] = 1, 5 > 2(1) 
 
Example 2:
Input: 
N = 5
arr= [2, 4, 3, 5, 1]
Output: 
3
Explanation: 
(i)   (1, 4), arr[1] = 4, arr[4] = 1, 4 > 2 * 1
(ii)  (2, 4), arr[2] = 3, arr[4] = 1, 3 > 2 * 1
(iii) (3, 4), arr[3] = 5, arr[4] = 1, 5 > 2 * 1
 
Your Task:
Complete the function countRevPairs(), which takes integer a list of N integers as input and returns the count of Reverse Pairs.
Expected Time Complexity: O(N logN)
Expected Auxiliary Space: O(N)
Constraints:
1 <= N <= 50000
1 <= arr[i] <= 10^{9}

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Title: Wizards and Demonstration

Time Limit: None seconds

Memory Limit: None megabytes

Problem Description:
Some country is populated by wizards. They want to organize a demonstration.

There are *n* people living in the city, *x* of them are the wizards who will surely go to the demonstration. Other city people (*n*<=-<=*x* people) do not support the wizards and aren't going to go to the demonstration. We know that the city administration will react only to the demonstration involving at least *y* percent of the city people. Having considered the matter, the wizards decided to create clone puppets which can substitute the city people on the demonstration. 

So all in all, the demonstration will involve only the wizards and their puppets. The city administration cannot tell the difference between a puppet and a person, so, as they calculate the percentage, the administration will consider the city to be consisting of only *n* people and not containing any clone puppets. 

Help the wizards and find the minimum number of clones to create to that the demonstration had no less than *y* percent of the city people.

Input Specification:
The first line contains three space-separated integers, *n*, *x*, *y* (1<=≤<=*n*,<=*x*,<=*y*<=≤<=104,<=*x*<=≤<=*n*) — the number of citizens in the city, the number of wizards and the percentage the administration needs, correspondingly.

Please note that *y* can exceed 100 percent, that is, the administration wants to see on a demonstration more people that actually live in the city (<=&gt;<=*n*).

Output Specification:
Print a single integer — the answer to the problem, the minimum number of clones to create, so that the demonstration involved no less than *y* percent of *n* (the real total city population).

Demo Input:
['10 1 14\n', '20 10 50\n', '1000 352 146\n']

Demo Output:
['1\n', '0\n', '1108\n']

Note:
In the first sample it is necessary that at least 14% of 10 people came to the demonstration. As the number of people should be integer, then at least two people should come. There is only one wizard living in the city and he is going to come. That isn't enough, so he needs to create one clone. 

In the second sample 10 people should come to the demonstration. The city has 10 wizards. They will all come to the demonstration, so nobody has to create any clones.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
You have most definitely heard the legend of King Arthur and the Knights of the Round Table. Almost all versions of this story proudly point out that the roundness of the Round Table is closely related to Arthur’s belief of equality among the Knights. That is a lie! In fact, Arthur’s choice of table is conditioned by his childhood traumas.

In fact, Arthur was forced to clean up quadratic tables from a young age after a tournament in pick-up sticks1 had been played on them. After the tournament, typically there would be a bunch of sticks on the table that do not touch each other. In the spirit of the game, the organizers issued strict regulations for the table cleaners. More precisely, the sticks on the table need to be removed one by one in a way that the cleaners pull them in the shortest way towards the edge of the table closest to where they are currently sitting. They also mustn’t rotate or touch the other sticks while doing this (not even in the edge points).

In this task, we will represent the table in the coordinate system with a square that has opposite points in the coordinates $(0,0)$ and $(10000, 10000)$, whereas the sticks will be represented with straight line segments that lie within that square. We will assume that Arthur is sitting at the edge of the table lying on the $x$-axis. Then the movement of the stick comes down to translating the line segment along the shortest path towards the $x$-axis until the stick falls off the table (as shown in the image). It is your task to help Arthur determine the order of stick movements that meets the requirements from the previous paragraph.

-----Input-----
The first line of input contains the integer $N$ ($1 \leq N \leq 5000$), the number of sticks on the table. Each of the following $N$ lines contains four integers $x_1$, $y_1$, $x_2$, $y_2$ ($0 \leq x_1, y_1, x_2, y_2 \leq 10000$) that denote the edge points of a stick.

-----Output-----
The first and only line of output must contain space-separated stick labels in the order which they need to be taken off the table. A stick’s label corresponds to its position in the input sequence.

If there are multiple possible solutions, output any of them.

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

Sample Input 2:
4
0 0 1 1
1 2 0 3
2 2 3 3
4 0 3 1
Sample Output 2:
4 3 1 2

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Given are an integer N and four characters c_{\mathrm{AA}}, c_{\mathrm{AB}}, c_{\mathrm{BA}}, and c_{\mathrm{BB}}.
Here, it is guaranteed that each of those four characters is A or B.
Snuke has a string s, which is initially AB.
Let |s| denote the length of s.
Snuke can do the four kinds of operations below zero or more times in any order:
 - Choose i such that 1 \leq i < |s|, s_{i} = A, s_{i+1} = A and insert c_{\mathrm{AA}} between the i-th and (i+1)-th characters of s.
 - Choose i such that 1 \leq i < |s|, s_{i} = A, s_{i+1} = B and insert c_{\mathrm{AB}} between the i-th and (i+1)-th characters of s.
 - Choose i such that 1 \leq i < |s|, s_{i} = B, s_{i+1} = A and insert c_{\mathrm{BA}} between the i-th and (i+1)-th characters of s.
 - Choose i such that 1 \leq i < |s|, s_{i} = B, s_{i+1} = B and insert c_{\mathrm{BB}} between the i-th and (i+1)-th characters of s.
Find the number, modulo (10^9+7), of strings that can be s when Snuke has done the operations so that the length of s becomes N.

-----Constraints-----
 - 2 \leq N \leq 1000
 - Each of c_{\mathrm{AA}}, c_{\mathrm{AB}}, c_{\mathrm{BA}}, and c_{\mathrm{BB}} is A or B.

-----Input-----
Input is given from Standard Input in the following format:
N
c_{\mathrm{AA}}
c_{\mathrm{AB}}
c_{\mathrm{BA}}
c_{\mathrm{BB}}

-----Output-----
Print the number, modulo (10^9+7), of strings that can be s when Snuke has done the operations so that the length of s becomes N.

-----Sample Input-----
4
A
B
B
A

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

 - There are two strings that can be s when Snuke is done: ABAB and ABBB.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Given a set of non-overlapping intervals, insert a new interval into the intervals (merge if necessary).

You may assume that the intervals were initially sorted according to their start times.

Example 1:


Input: intervals = [[1,3],[6,9]], newInterval = [2,5]
Output: [[1,5],[6,9]]


Example 2:


Input: intervals = [[1,2],[3,5],[6,7],[8,10],[12,16]], newInterval = [4,8]
Output: [[1,2],[3,10],[12,16]]
Explanation: Because the new interval [4,8] overlaps with [3,5],[6,7],[8,10].

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Title: Sagheer and Crossroads

Time Limit: None seconds

Memory Limit: None megabytes

Problem Description:
Sagheer is walking in the street when he comes to an intersection of two roads. Each road can be represented as two parts where each part has 3 lanes getting into the intersection (one for each direction) and 3 lanes getting out of the intersection, so we have 4 parts in total. Each part has 4 lights, one for each lane getting into the intersection (*l* — left, *s* — straight, *r* — right) and a light *p* for a pedestrian crossing. 

An accident is possible if a car can hit a pedestrian. This can happen if the light of a pedestrian crossing of some part and the light of a lane that can get to or from that same part are green at the same time.

Now, Sagheer is monitoring the configuration of the traffic lights. Your task is to help him detect whether an accident is possible.

Input Specification:
The input consists of four lines with each line describing a road part given in a counter-clockwise order.

Each line contains four integers *l*, *s*, *r*, *p* — for the left, straight, right and pedestrian lights, respectively. The possible values are 0 for red light and 1 for green light.

Output Specification:
On a single line, print "YES" if an accident is possible, and "NO" otherwise.

Demo Input:
['1 0 0 1\n0 1 0 0\n0 0 1 0\n0 0 0 1\n', '0 1 1 0\n1 0 1 0\n1 1 0 0\n0 0 0 1\n', '1 0 0 0\n0 0 0 1\n0 0 0 0\n1 0 1 0\n']

Demo Output:
['YES\n', 'NO\n', 'NO\n']

Note:
In the first example, some accidents are possible because cars of part 1 can hit pedestrians of parts 1 and 4. Also, cars of parts 2 and 3 can hit pedestrians of part 4.

In the second example, no car can pass the pedestrian crossing of part 4 which is the only green pedestrian light. So, no accident can occur.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Pasha has recently bought a new phone jPager and started adding his friends' phone numbers there. Each phone number consists of exactly n digits.

Also Pasha has a number k and two sequences of length n / k (n is divisible by k) a_1, a_2, ..., a_{n} / k and b_1, b_2, ..., b_{n} / k. Let's split the phone number into blocks of length k. The first block will be formed by digits from the phone number that are on positions 1, 2,..., k, the second block will be formed by digits from the phone number that are on positions k + 1, k + 2, ..., 2·k and so on. Pasha considers a phone number good, if the i-th block doesn't start from the digit b_{i} and is divisible by a_{i} if represented as an integer. 

To represent the block of length k as an integer, let's write it out as a sequence c_1, c_2,...,c_{k}. Then the integer is calculated as the result of the expression c_1·10^{k} - 1 + c_2·10^{k} - 2 + ... + c_{k}.

Pasha asks you to calculate the number of good phone numbers of length n, for the given k, a_{i} and b_{i}. As this number can be too big, print it modulo 10^9 + 7. 


-----Input-----

The first line of the input contains two integers n and k (1 ≤ n ≤ 100 000, 1 ≤ k ≤ min(n, 9)) — the length of all phone numbers and the length of each block, respectively. It is guaranteed that n is divisible by k.

The second line of the input contains n / k space-separated positive integers — sequence a_1, a_2, ..., a_{n} / k (1 ≤ a_{i} < 10^{k}).

The third line of the input contains n / k space-separated positive integers — sequence b_1, b_2, ..., b_{n} / k (0 ≤ b_{i} ≤ 9). 


-----Output-----

Print a single integer — the number of good phone numbers of length n modulo 10^9 + 7.


-----Examples-----
Input
6 2
38 56 49
7 3 4

Output
8

Input
8 2
1 22 3 44
5 4 3 2

Output
32400



-----Note-----

In the first test sample good phone numbers are: 000000, 000098, 005600, 005698, 380000, 380098, 385600, 385698.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
An english word is given as input and it is modified using some format. Identify the format using the examples given below (examples given are sufficient to identify the format) and print the modified word as output.
STEWART is modified as EWARTSTAY, AMAR is modified as AMAR, MAN is modified as ANMAY etc.
Note: Input contains uppercase english words.
 
Example 1:
Input:
S = "GEEK"
Output:
EEKGAY
Explanation:
The string when modified gives "EEKGAY".
Example 2:
Input:
S = "ALL"
Output:
ALL
Explanation:
The string when modified remains the same.
 
Your Task:
You don't need to read input or print anything. Your task is to complete the function englishWords() which takes a String S as input and returns the modified String.
 
Expected Time Complexity: O(|S|)
Expected Auxiliary Space: O(|S|)
 
Constraints:
1 <= |S| <= 10^{5}

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Mr. Funt now lives in a country with a very specific tax laws. The total income of mr. Funt during this year is equal to n (n ≥ 2) burles and the amount of tax he has to pay is calculated as the maximum divisor of n (not equal to n, of course). For example, if n = 6 then Funt has to pay 3 burles, while for n = 25 he needs to pay 5 and if n = 2 he pays only 1 burle.

As mr. Funt is a very opportunistic person he wants to cheat a bit. In particular, he wants to split the initial n in several parts n_1 + n_2 + ... + n_{k} = n (here k is arbitrary, even k = 1 is allowed) and pay the taxes for each part separately. He can't make some part equal to 1 because it will reveal him. So, the condition n_{i} ≥ 2 should hold for all i from 1 to k.

Ostap Bender wonders, how many money Funt has to pay (i.e. minimal) if he chooses and optimal way to split n in parts.


-----Input-----

The first line of the input contains a single integer n (2 ≤ n ≤ 2·10^9) — the total year income of mr. Funt.


-----Output-----

Print one integer — minimum possible number of burles that mr. Funt has to pay as a tax.


-----Examples-----
Input
4

Output
2

Input
27

Output
3

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
You are given two positive integer lists with a random number of elements (1 <= n <= 100). Create a [GCD](https://en.wikipedia.org/wiki/Greatest_common_divisor) matrix and calculate the average of all values. 

Return a float value rounded to 3 decimal places. 


## Example

```
a = [1, 2, 3]
b = [4, 5, 6]

#       a =    1  2  3     b =
gcd(a, b) = [ [1, 2, 1],   # 4
              [1, 1, 1],   # 5
              [1, 2, 3] ]  # 6

average(gcd(a, b)) = 1.444
```

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Title: Mashmokh and Lights

Time Limit: None seconds

Memory Limit: None megabytes

Problem Description:
Mashmokh works in a factory. At the end of each day he must turn off all of the lights. 

The lights on the factory are indexed from 1 to *n*. There are *n* buttons in Mashmokh's room indexed from 1 to *n* as well. If Mashmokh pushes button with index *i*, then each light with index not less than *i* that is still turned on turns off.

Mashmokh is not very clever. So instead of pushing the first button he pushes some of the buttons randomly each night. He pushed *m* distinct buttons *b*1,<=*b*2,<=...,<=*b**m* (the buttons were pushed consecutively in the given order) this night. Now he wants to know for each light the index of the button that turned this light off. Please note that the index of button *b**i* is actually *b**i*, not *i*.

Please, help Mashmokh, print these indices.

Input Specification:
The first line of the input contains two space-separated integers *n* and *m* (1<=≤<=*n*,<=*m*<=≤<=100), the number of the factory lights and the pushed buttons respectively. The next line contains *m* distinct space-separated integers *b*1,<=*b*2,<=...,<=*b**m* (1<=≤<=*b**i*<=≤<=*n*).

It is guaranteed that all lights will be turned off after pushing all buttons.

Output Specification:
Output *n* space-separated integers where the *i*-th number is index of the button that turns the *i*-th light off.

Demo Input:
['5 4\n4 3 1 2\n', '5 5\n5 4 3 2 1\n']

Demo Output:
['1 1 3 4 4 \n', '1 2 3 4 5 \n']

Note:
In the first sample, after pressing button number 4, lights 4 and 5 are turned off and lights 1, 2 and 3 are still on. Then after pressing button number 3, light number 3 is turned off as well. Pressing button number 1 turns off lights number 1 and 2 as well so pressing button number 2 in the end has no effect. Thus button number 4 turned lights 4 and 5 off, button number 3 turned light 3 off and button number 1 turned light 1 and 2 off.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
You are planning the next FIFA World Cup and you are counting the number of highways that need to be built to connect the cities with the venue. 

Your country has $n$ cities and all cities lie on a single straight road called “Highway Road”. If you want to go from City ${x}$ to City $y$ ( where $x\leq y$ ), you need to go through city $x,x+1,x+2,\cdots,y-1,y$. 

The requirements for the highways are as follows:

All games will be held in the $n^{th}$ city.
New bidirectional roads, called "Super Highways", need to be built such that it is possible to visit the $n^{th}$ city from any other city directly.  

You also have the cost to fulfil the second condition. The engineering team knows that if the length of a Super Highway is ${l}$, then it will cost $l^{k}$, where ${k}}$ is an integer constant.The length of Super Highway between city $\boldsymbol{x}$ and $y$ is $|x-y|$.  

For this problem, you need to find only a rough estimation of the cost, hence, find Total Cost Modulo $1000000009$. 

Input Format

First line will contain a single positive integer ${q}$ denoting the number of queries. Then for each case there will be two positive integers, $n$ and ${k}}$.

Constraints

$1\leq q\leq200$  
$1\leq n\leq10^{18}$  
$1\leq k\leq1000$

Output Format

For each case find the cost to build Super Highways such that it is possible to visit $n^{th}$ city from any other city directly. You have to print this value Modulo $1000000009$.

Sample Input 0
1
4 2

Sample Output 0
13

Explanation 0

There are four cities. We need to build Super Highways that connect city ${1}$ to city ${4}$ and city $2$ to city ${4}$. No need to connect city 3 with city ${4}$ since they are adjacent on “Highway Road”. So cost is $(4-1)^2+(4-2)^2=3^2+2^2=13$.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.