vgel/INTELLECT-2-RL-Dataset-Code-Only huggingface dataset:
Chef loves cooking. Also, he is very hygienic. Hence, Chef grows his own vegetables in his mini kitchen garden. He has $M$ lanes in which he grows vegetables. The $ith$  lane has $Ai$ vegetables growing in it.

Vegetables in $ith$ lane become edible on day $Di$ and day $Di+1$(that is, the vegetables are edible only on days $Di$ and $Di+1$,where $Di+1$ is the next day of $Di$).   For Example, if $Di$ is 2, then vegetable is edible on day 2 and day 3 only.   If not collected in these days, they cannot be cooked.

Also, Chef is a lone worker. Hence, with respect to his capacity, he can collect only $V$ vegetables per day.
But, Chef is a hard worker, and is willing to work every day, starting from day 1.

Chef is busy sowing the seeds. So, he assigns you the task to find out the maximum number of vegetables he can collect, provided that he collects optimally.

-----Input:-----
- First line contains of 2 space separated integers $M$ and $V$, number of lanes and capacity of Chef.
- Next $M$ lines follow
- Each $ith$ line contains 2 space separated integers, $Di$ and $Ai$, the day when the vegetable of the $ith$ lane become edible and the number of vegetables in that lane.

-----Output:-----
For each testcase, output in a single integer, that is the maximum number of vegetables that can be cooked

-----Constraints-----
- $1 \leq M,V \leq 3000$
- $1 \leq Di,Ai \leq 3000$

-----Subtasks-----
- 20 points : $1 \leq M \leq 100$
- 30 points : $1 \leq M \leq 1000$
- 50 points : $Original  Constraints$

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

-----Sample Output 1:-----
11

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

-----Sample Output 2:-----
9

-----EXPLANATION:-----
In the first sample, in order to obtain the optimal answer, you should do the following:-
- On day 1, collect 4 vegetables from lane 1
- On day 2, collect 2 vegetables from lane 1 and 2 vegetables from lane 2
- On day 3, collect 3 vegetables from lane 2
In the first sample, in order to obtain the optimal answer, you should do the following:-
- On day 1, collect 3 vegetables from lane 1
- On day 2, collect 1 vegetable from lane 1
- On day 5, collect 3 vegetables from lane 3
- On day 6, collect 2 vegetables from lane 2

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
In the kingdom of Winterfield, there are several cities and each pair of cities is connected by exactly one old dirt road. The king of Winterfield has decided that he will upgrade some of those roads. The set of roads that he upgrades must be such that it is possible to get from any city in the kingdom to any other city via some sequence of upgraded roads.

Because there is so much snow in Winterfield, the king has also decided to plow some of those upgraded roads. The local plow company, Mr. Plow, and the king have agreed on the following: the king labels each of the upgraded roads $1, 2, \dots , m$ (the label of each road is the number of gold pieces it costs to plow that road) and each road must receive a distinct label. Mr. Plow will plow a set of upgraded roads so that it is possible to get from any city to any other city via some sequence of plowed roads. Mr. Plow will select the cheapest possible set of roads that satisfies the above condition.

For example, if the kingdom has six cities and the king decides to upgrade and label the 8 bolded dirt roads as follows, then Mr. Plow will then plow the roads with labels 1, 2, 3, 4 and 6 (costing a total of 16 gold pieces).

The king has decided on the number of roads to upgrade, but he is not sure how to label them, so he has turned to Barney (the kingdom’s mathematician) to help decide. However, the king is unaware that Barney is actually invested in Mr. Plow, so Barney will choose the set of roads to upgrade and how to label them so that the total cost is as large as possible. What is the maximum cost of plowing the roads?

-----Input-----
The input consists of a single line containing two integers $n$ ($2 \leq n \leq 1000000$), which is the number of cities, and $m$ ($n-1 \leq m \leq \frac{n(n-1)}{2}$), which is the number of roads to be upgraded.

-----Output-----
Display the maximum possible cost of plowing the roads following the rules above.

-----Examples-----
Sample Input 1:
4 3
Sample Output 1:
6

Sample Input 2:
6 8
Sample Output 2:
22

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
The only difference between easy and hard versions is the number of elements in the array.

You are given an array $a$ consisting of $n$ integers. In one move you can choose any $a_i$ and divide it by $2$ rounding down (in other words, in one move you can set $a_i := \lfloor\frac{a_i}{2}\rfloor$).

You can perform such an operation any (possibly, zero) number of times with any $a_i$.

Your task is to calculate the minimum possible number of operations required to obtain at least $k$ equal numbers in the array.

Don't forget that it is possible to have $a_i = 0$ after some operations, thus the answer always exists.


-----Input-----

The first line of the input contains two integers $n$ and $k$ ($1 \le k \le n \le 2 \cdot 10^5$) — the number of elements in the array and the number of equal numbers required.

The second line of the input contains $n$ integers $a_1, a_2, \dots, a_n$ ($1 \le a_i \le 2 \cdot 10^5$), where $a_i$ is the $i$-th element of $a$.


-----Output-----

Print one integer — the minimum possible number of operations required to obtain at least $k$ equal numbers in the array.


-----Examples-----
Input
5 3
1 2 2 4 5

Output
1

Input
5 3
1 2 3 4 5

Output
2

Input
5 3
1 2 3 3 3

Output
0

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
You are playing the following game with Joisino.
 - Initially, you have a blank sheet of paper.
 - Joisino announces a number. If that number is written on the sheet, erase the number from the sheet; if not, write the number on the sheet. This process is repeated N times.
 - Then, you are asked a question: How many numbers are written on the sheet now?
The numbers announced by Joisino are given as A_1, ... ,A_N in the order she announces them. How many numbers will be written on the sheet at the end of the game?

-----Constraints-----
 - 1≤N≤100000
 - 1≤A_i≤1000000000(=10^9)
 - All input values are integers.

-----Input-----
Input is given from Standard Input in the following format:
N
A_1
:
A_N

-----Output-----
Print how many numbers will be written on the sheet at the end of the game.

-----Sample Input-----
3
6
2
6

-----Sample Output-----
1

The game proceeds as follows:
 - 6 is not written on the sheet, so write 6.
 - 2 is not written on the sheet, so write 2.
 - 6 is written on the sheet, so erase 6.
Thus, the sheet contains only 2 in the end. The answer is 1.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Soroush's room is a square with side length n. Before this contest he bought k fine Persian carpets to carpet his room for celebrating the 100th contest on his favorite site. Each Persian carpet is a square of side length n1.

Soroush wants to cover all the area of his room. Carpets can be put over each other but it is not allowed to rotate the carpets. Can Soroush carpet his room completely?

Input

The input consists of three integer numbers n, k and n1 (10 ≤ n ≤ 12, 1 ≤ k ≤ 10, <image>).

Output

Write a single YES or NO. Write YES if and only if Sorush can carpet his room completely.

Examples

Input

10 4 6


Output

YES


Input

10 2 5


Output

NO

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Given an array a[] of size N which contains elements from 0 to N-1, you need to find all the elements occurring more than once in the given array. Return the answer in ascending order.
Note: The extra space is only for the array to be returned.
Try and perform all operations within the provided array. 
Example 1:
Input:
N = 4
a[] = {0,3,1,2}
Output: -1
Explanation: N=4 and all elements from 0
to (N-1 = 3) are present in the given
array. Therefore output is -1.
Example 2:
Input:
N = 5
a[] = {2,3,1,2,3}
Output: 2 3 
Explanation: 2 and 3 occur more than once
in the given array.
Your Task:
Complete the function duplicates() which takes array a[] and n as input as parameters and returns a list of elements that occur more than once in the given array in a sorted manner. If no such element is found, return list containing [-1]. 
Expected Time Complexity: O(n).
Expected Auxiliary Space: O(n).
Constraints:
1 <= N <= 10^{5}
0 <= A[i] <= N-1, for each valid i

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Yelisey has an array $a$ of $n$ integers.

If $a$ has length strictly greater than $1$, then Yelisei can apply an operation called minimum extraction to it:

First, Yelisei finds the minimal number $m$ in the array. If there are several identical minima, Yelisey can choose any of them.

Then the selected minimal element is removed from the array. After that, $m$ is subtracted from each remaining element.

Thus, after each operation, the length of the array is reduced by $1$.

For example, if $a = [1, 6, -4, -2, -4]$, then the minimum element in it is $a_3 = -4$, which means that after this operation the array will be equal to $a=[1 {- (-4)}, 6 {- (-4)}, -2 {- (-4)}, -4 {- (-4)}] = [5, 10, 2, 0]$.

Since Yelisey likes big numbers, he wants the numbers in the array $a$ to be as big as possible.

Formally speaking, he wants to make the minimum of the numbers in array $a$ to be maximal possible (i.e. he want to maximize a minimum). To do this, Yelisey can apply the minimum extraction operation to the array as many times as he wants (possibly, zero). Note that the operation cannot be applied to an array of length $1$.

Help him find what maximal value can the minimal element of the array have after applying several (possibly, zero) minimum extraction operations to the array.


-----Input-----

The first line contains an integer $t$ ($1 \leq t \leq 10^4$) — the number of test cases.

The next $2t$ lines contain descriptions of the test cases.

In the description of each test case, the first line contains an integer $n$ ($1 \leq n \leq 2 \cdot 10^5$) — the original length of the array $a$. The second line of the description lists $n$ space-separated integers $a_i$ ($-10^9 \leq a_i \leq 10^9$) — elements of the array $a$.

It is guaranteed that the sum of $n$ over all test cases does not exceed $2 \cdot 10^5$.


-----Output-----

Print $t$ lines, each of them containing the answer to the corresponding test case. The answer to the test case is a single integer — the maximal possible minimum in $a$, which can be obtained by several applications of the described operation to it.


-----Examples-----

Input
8
1
10
2
0 0
3
-1 2 0
4
2 10 1 7
2
2 3
5
3 2 -4 -2 0
2
-1 1
1
-2
Output
10
0
2
5
2
2
2
-2


-----Note-----

In the first example test case, the original length of the array $n = 1$. Therefore minimum extraction cannot be applied to it. Thus, the array remains unchanged and the answer is $a_1 = 10$.

In the second set of input data, the array will always consist only of zeros.

In the third set, the array will be changing as follows: $[\color{blue}{-1}, 2, 0] \to [3, \color{blue}{1}] \to [\color{blue}{2}]$. The minimum elements are highlighted with $\color{blue}{\text{blue}}$. The maximal one is $2$.

In the fourth set, the array will be modified as $[2, 10, \color{blue}{1}, 7] \to [\color{blue}{1}, 9, 6] \to [8, \color{blue}{5}] \to [\color{blue}{3}]$. Similarly, the maximum of the minimum elements is $5$.

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

Time Limit: None seconds

Memory Limit: None megabytes

Problem Description:
Amr is a young coder who likes music a lot. He always wanted to learn how to play music but he was busy coding so he got an idea.

Amr has *n* instruments, it takes *a**i* days to learn *i*-th instrument. Being busy, Amr dedicated *k* days to learn how to play the maximum possible number of instruments.

Amr asked for your help to distribute his free days between instruments so that he can achieve his goal.

Input Specification:
The first line contains two numbers *n*, *k* (1<=≤<=*n*<=≤<=100, 0<=≤<=*k*<=≤<=10<=000), the number of instruments and number of days respectively.

The second line contains *n* integers *a**i* (1<=≤<=*a**i*<=≤<=100), representing number of days required to learn the *i*-th instrument.

Output Specification:
In the first line output one integer *m* representing the maximum number of instruments Amr can learn.

In the second line output *m* space-separated integers: the indices of instruments to be learnt. You may output indices in any order.

if there are multiple optimal solutions output any. It is not necessary to use all days for studying.

Demo Input:
['4 10\n4 3 1 2\n', '5 6\n4 3 1 1 2\n', '1 3\n4\n']

Demo Output:
['4\n1 2 3 4', '3\n1 3 4', '0\n']

Note:
In the first test Amr can learn all 4 instruments.

In the second test other possible solutions are: {2, 3, 5} or {3, 4, 5}.

In the third test Amr doesn't have enough time to learn the only presented instrument.

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

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

Time Limit: None seconds

Memory Limit: None megabytes

Problem Description:
Greg has a weighed directed graph, consisting of *n* vertices. In this graph any pair of distinct vertices has an edge between them in both directions. Greg loves playing with the graph and now he has invented a new game:
 -  The game consists of *n* steps. -  On the *i*-th step Greg removes vertex number *x**i* from the graph. As Greg removes a vertex, he also removes all the edges that go in and out of this vertex. -  Before executing each step, Greg wants to know the sum of lengths of the shortest paths between all pairs of the remaining vertices. The shortest path can go through any remaining vertex. In other words, if we assume that *d*(*i*,<=*v*,<=*u*) is the shortest path between vertices *v* and *u* in the graph that formed before deleting vertex *x**i*, then Greg wants to know the value of the following sum: . 
Help Greg, print the value of the required sum before each step.

Input Specification:
The first line contains integer *n* (1<=≤<=*n*<=≤<=500) — the number of vertices in the graph.

Next *n* lines contain *n* integers each — the graph adjacency matrix: the *j*-th number in the *i*-th line *a**ij* (1<=≤<=*a**ij*<=≤<=105,<=*a**ii*<==<=0) represents the weight of the edge that goes from vertex *i* to vertex *j*.

The next line contains *n* distinct integers: *x*1,<=*x*2,<=...,<=*x**n* (1<=≤<=*x**i*<=≤<=*n*) — the vertices that Greg deletes.

Output Specification:
Print *n* integers — the *i*-th number equals the required sum before the *i*-th step.

Please, do not use the %lld specifier to read or write 64-bit integers in C++. It is preferred to use the cin, cout streams of the %I64d specifier.

Demo Input:
['1\n0\n1\n', '2\n0 5\n4 0\n1 2\n', '4\n0 3 1 1\n6 0 400 1\n2 4 0 1\n1 1 1 0\n4 1 2 3\n']

Demo Output:
['0 ', '9 0 ', '17 23 404 0 ']

Note:
none

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

Time Limit: None seconds

Memory Limit: None megabytes

Problem Description:
Ayush is a cashier at the shopping center. Recently his department has started a ''click and collect" service which allows users to shop online. 

The store contains *k* items. *n* customers have already used the above service. Each user paid for *m* items. Let *a**ij* denote the *j*-th item in the *i*-th person's order.

Due to the space limitations all the items are arranged in one single row. When Ayush receives the *i*-th order he will find one by one all the items *a**ij* (1<=≤<=*j*<=≤<=*m*) in the row. Let *pos*(*x*) denote the position of the item *x* in the row at the moment of its collection. Then Ayush takes time equal to *pos*(*a**i*1)<=+<=*pos*(*a**i*2)<=+<=...<=+<=*pos*(*a**im*) for the *i*-th customer.

When Ayush accesses the *x*-th element he keeps a new stock in the front of the row and takes away the *x*-th element. Thus the values are updating.

Your task is to calculate the total time it takes for Ayush to process all the orders.

You can assume that the market has endless stock.

Input Specification:
The first line contains three integers *n*, *m* and *k* (1<=≤<=*n*,<=*k*<=≤<=100,<=1<=≤<=*m*<=≤<=*k*) — the number of users, the number of items each user wants to buy and the total number of items at the market.

The next line contains *k* distinct integers *p**l* (1<=≤<=*p**l*<=≤<=*k*) denoting the initial positions of the items in the store. The items are numbered with integers from 1 to *k*.

Each of the next *n* lines contains *m* distinct integers *a**ij* (1<=≤<=*a**ij*<=≤<=*k*) — the order of the *i*-th person.

Output Specification:
Print the only integer *t* — the total time needed for Ayush to process all the orders.

Demo Input:
['2 2 5\n3 4 1 2 5\n1 5\n3 1\n']

Demo Output:
['14\n']

Note:
Customer 1 wants the items 1 and 5.

*pos*(1) = 3, so the new positions are: [1, 3, 4, 2, 5].

*pos*(5) = 5, so the new positions are: [5, 1, 3, 4, 2].

Time taken for the first customer is 3 + 5 = 8.

Customer 2 wants the items 3 and 1.

*pos*(3) = 3, so the new positions are: [3, 5, 1, 4, 2].

*pos*(1) = 3, so the new positions are: [1, 3, 5, 4, 2].

Time taken for the second customer is 3 + 3 = 6.

Total time is 8 + 6 = 14.

Formally *pos*(*x*) is the index of *x* in the current row.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
In Berland it is the holiday of equality. In honor of the holiday the king decided to equalize the welfare of all citizens in Berland by the expense of the state treasury. 

Totally in Berland there are n citizens, the welfare of each of them is estimated as the integer in a_{i} burles (burle is the currency in Berland).

You are the royal treasurer, which needs to count the minimum charges of the kingdom on the king's present. The king can only give money, he hasn't a power to take away them. 


-----Input-----

The first line contains the integer n (1 ≤ n ≤ 100) — the number of citizens in the kingdom.

The second line contains n integers a_1, a_2, ..., a_{n}, where a_{i} (0 ≤ a_{i} ≤ 10^6) — the welfare of the i-th citizen.


-----Output-----

In the only line print the integer S — the minimum number of burles which are had to spend.


-----Examples-----
Input
5
0 1 2 3 4

Output
10
Input
5
1 1 0 1 1

Output
1
Input
3
1 3 1

Output
4
Input
1
12

Output
0


-----Note-----

In the first example if we add to the first citizen 4 burles, to the second 3, to the third 2 and to the fourth 1, then the welfare of all citizens will equal 4.

In the second example it is enough to give one burle to the third citizen. 

In the third example it is necessary to give two burles to the first and the third citizens to make the welfare of citizens equal 3.

In the fourth example it is possible to give nothing to everyone because all citizens have 12 burles.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
The Ackermann function is a famous function that played a big role in computability theory as the first example of a total computable function that is not primitive recursive.

Since then the function has been a bit simplified but is still of good use. Due to its definition in terms of extremely deep recursion it can be used as a benchmark of a compiler's ability to optimize recursion. 

The goal of this kata is to code a function which will be given two inputs, m and n, and will return the Ackermann number A(m,n) defined by:

```
A(m,n) = n+1                          if m=0  
A(m,n) = A(m-1,1)                     if m>0 , n=0
A(m,n) = A(m-1,A(m,n-1))              if m,n > 0
```

m,n should be non-negative integers, the function should return null (Javascript), None (Python), or nil (Ruby) for other type, non-integer and negative numbers. In C, input is restricted to integer type.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
The other day Unnar was playing the video game Geezer Scripts, Geezer Scripts V to be precise. He opened a door (in the game) and before he knew he was in a large and complicated cave-system, full of enemies who will attack as soon as Unnar gets to close to them. What’s worse is that the game doesn’t remember which enemies the player has already defeated so if the player leaves and comes back again the enemy will have respawned. Since Unnar is quite prone to getting lost he needs your help to find a way through the cave which incurs minimal damage to him.

Unnar’s character has some $A$ attack points and $H$ health points. The same is true for his enemies. When Unnar fights an enemy Unnar goes first. He subtracts his attack points from the enemies health points and the enemy then does the same. This process is repeated until either Unnar or the enemy has fewer than $1$ health points. The loser is the one who ran out of health points. If Unnar loses it’s Game Over, but if Unnar wins he can continue traversing the cave-system but his lost health points do not regenerate.

The cave-system is not evenly elevated so its passages are one-way. The cave-system can be modelled using $n$ areas connected with $m$ one-way passages. Unnar starts in area $1$ and wants to get to area $n$. Every passage contains an enemy but the areas are safe.

-----Input-----
The first line of the input contains two integers $1 \leq A, H \leq 10^9$ where $A$ denotes Unnar’s attack points and $H$ his health points. The second line contains $1 \leq n, m \leq 10^5$ where $n$ is the number of ares in the cave and $m$ the number of passages. The next $m$ lines contain four integers $1 \leq e_ i, b_ i \leq n$ and $1 \leq a_ i, h_ i \leq 10^9$, indicating a passage from area $e_ i$ to $b_ i$ whose enemy has $a_ i$ attack points and $h_ i$ health points.

-----Output-----
If Unnar can’t get through the cave-system output ‘Oh no’, without the quotes. Otherwise output the maximum health Unnar can have after getting through the cave-system.

-----Examples-----
Sample Input 1:
1 2
3 2
1 2 1 2
2 3 1 2
Sample Output 1:
Oh no

Sample Input 2:
1 3
3 2
1 2 1 2
2 3 1 2
Sample Output 2:
1

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