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 i in range(2**N):
    count = 0
    maxh = 0
    money = 0
    for j in range(N):
        if i >> j & 1:
            count += 1
            if maxh < A[j]:
                maxh = A[j]
            else:
                money += maxh+1-A[j]
                maxh += 1
        else:
            maxh = max(maxh,A[j])
    if count >= K:
        ans = min(ans,money)

print(ans)