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 = [int(x) for x in input().split()]
a = [int(x) for x in input().split()]

ans = 10 ** 12
for i in range(1, 2 ** N):
    if bin(i)[2:].count('1') != K: continue
    tmp = 0
    hmax = a[0]
    for j in range(1, N):
        if (i >> j) & 1:
            h = max(hmax + 1, a[j])
            tmp += h - a[j]
            hmax = h
        else:
            hmax = max(hmax, a[j])
    ans = min(ans, tmp)

print(ans)