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 = 10**9 * 15
for bit in range(1<<N):
    cnt = 0
    for i in range(N):
        # print(bin(bit), i, bit>>i, (bit>>i) & 1)
        if (bit>>i) & 1 == 1:
            cnt += 1
    # print(bin(bit), cnt)
    if cnt == K:
        max_height = a[0]
        price = 0
        for i in range(1, N):
            if ((bit>>i) & 1 == 1
                    and a[i] <= max_height):
                price += max_height + 1 - a[i]
                max_height += 1
            max_height = max(max_height, a[i])
        ans = min(ans, price)
print(ans)
