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 = list(map(int, input().split()))
A = list(map(int, input().split()))
height = [max(A[:i+1]) for i in range(N)]

ans = 10**11
for i in range(2**N):
    task = []
    for j in range(N):
        if (i >> j) & 1:
            task.append(j)
    if len(task) != K:
        continue
    c = 0
    h = -1
    for t in task:
        h = max(height[t], A[t], h+1)
        c += h-A[t]
    ans = min(ans, c)
print(ans)