Problem:
Max Score: 350 Points

Problem Statement

There are N buildings along the line. The i-th building from the left is colored in color i, and its height is currently a_i meters.

Chokudai is a mayor of the city, and he loves colorful thigs. And now he wants to see at least K buildings from the left.

You can increase height of buildings, but it costs 1 yens to increase 1 meters. It means you cannot make building that height is not integer.

You cannot decrease height of buildings.

Calculate the minimum cost of satisfying Chokudai's objective.

Note: "Building i can see from the left" means there are no j exists that (height of building j) ≥ (height of building i) and j < i.

Input Format

N K
a_1 a_2 a_3 ... a_N

Output Format

Print the minimum cost in one line. In the end put a line break.

Constraints

1 ≤ K ≤ N ≤ 15

1 ≤ a_i ≤ 10^9

Scoring

Subtask 1 [120 points]

N = K

Subtask 2 [90 points]

N ≤ 5

a_i ≤ 7

Subtask 3 [140 points]

There are no additional constraints.

Sample Input 1

5 5
3949 3774 3598 3469 3424

Sample Output 1

1541

The optimal solution is (height of buildings from the left) = [3949, 3950, 3951, 3952, 3953].

Sample Input 2

5 3
7 4 2 6 4

Sample Output 2

7

The optimal solution is (height of buildings from the left) = [7, 8, 2, 9, 4].

Solution in PyPy3 (2.4.0) (judge verdict: Wrong Answer)

# import math
# import bisect
#import numpy as np
import itertools
# import copy
import sys

input = sys.stdin.readline
MOD = 10 ** 9 + 7
INF = float('INF')
sys.setrecursionlimit(10 ** 5)


def main():
    n, k = list(map(int,input().split()))
    a = list(map(int,input().split()))

    cmb = list(itertools.combinations([i for i in range(1, n)], k-1))
    ans = INF

    if k > 1:
            for ele in cmb:
                prc = 0
                prev = a[0]

                for idx in ele:
                    cur = a[idx]
                    if cur - prev <= 0:
                        prc += prev - cur + 1
                        cur = prev + 1
                    prev = cur
                if prev >= max(a):
                    ans = min(ans, prc)
    else:
        ans = 0

    print(ans)


if __name__ == '__main__':
    main()