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()))

res = 10 ** 15

for bit in range(2 ** N):
    cnt = 0
    for i in range(N):
        if (bit >> i) & 1:
            cnt += 1

    if cnt < K:
        continue

    cost = 0
    height = A[0]
    if (bit >> 0) & 1:
        for i in range(1, N):
            if (bit >> i) & 1 and height >= A[i]:
                cost += height - A[i] + 1
                height += 1
            elif height < A[i]:
                height = A[i]

        res = min(res, cost)

print(res)