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 = [int(i) for i in input().split()]
ans = 10**11

for i in range(2 ** N):
    B = ""
    lenB = 0
    for j in range(N):
        if (i >> j) & 1:
            B += "1"
            lenB += 1
        else:
            B += "0"
    if lenB == K:
        s = 0
        cur = A[0]
        for k in range(1, N):
            if B[k] == "1" and A[k] <= cur:
                s += cur - A[k] + 1
                cur += 1
            else:
                cur = max(cur, A[k])
        #print(B, s)
        ans = min(ans, s)
print(ans)
