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()))

ans = 1 << 60
for i in range(1 << N):
    if i % 2 == 0:
        continue
    
    selected = [j for j in range(N) if i & (1 << j)]
    if len(selected) != K:
        continue
    
    h_max = a[0]
    cost = 0
    for j in range(1, N):
        if j in selected:
            if a[j] <= h_max:
                cost += h_max + 1 - a[j]
                h_max += 1
            else:
                h_max = a[j]
        else:
            h_max = max(h_max, a[j])
    
    ans = min(ans, cost)

print(ans)