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 = float('inf')

for i in range(1<<N):
    seen = 1
    pay = 0
    now = a[0]
    for j in range(1, N):
        if (i >> j) & 1:
            if a[j] <= now:
                pay += now - a[j] + 1
                now += 1
                seen += 1
            else:
                break
        else:
            if a[j] > now:
                seen += 1
                now = a[j]
        if seen >= K:
            ans = min(ans, pay)
            break


print(ans)