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
N, K = map(int, input().split())
A = list(map(int, input().split()))

from itertools import combinations as com

folds = com(range(N), K)
ans = float('inf')
for fold in folds:
    B = A[:]
    tmp = 0
    for i in range(1, K):
        if B[fold[i]] <= B[fold[i-1]]:
            diff = B[fold[i-1]] - B[fold[i]] + 1
            tmp += diff
            B[fold[i]] += diff

    k = 1
    border = B[0]
    for i in range(1, N):
        if border < B[i]:
            k += 1
            border = B[i]

    if k >= K:
        ans = min(ans, tmp)

print(ans)
