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.

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.

Input Format


N K
a_1 a_2 a_3 ... a_N

Example

Input

5 5
3949 3774 3598 3469 3424


Output

1541
import sys
read = sys.stdin.read
readline = sys.stdin.readline
readlines = sys.stdin.readlines

def main():
    N,K,*A = map(int, read().split())

    ans = float('inf')
    for i in range(2**(N-1)):
        if bin(i).count("1") != K-1:
            continue
        height = A[0]
        tmp = 0
        for j in range(N-1):
            if (i >> j) & 1:
                height += 1
                if A[j+1] >= height:
                    height = A[j+1]
                    continue
                tmp += height - A[j+1]
            height = max(height, A[j+1])
        ans = min(ans, tmp)
    
    print(ans)


if __name__ == "__main__":
    main()
