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**18
for bit in range(1<<N):
    highest, cost, cnt = 0, 0, 0
    for i in range(N):
        if bit>>i & 1:
            if A[i] <= highest:
                cost += highest-A[i]+1
                highest += 1
            else:
                highest = max(highest,A[i])
            cnt += 1
        else:
            highest = max(highest,A[i])
    if cnt >= K:
        ans = min(ans, cost)

print(ans)
