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=list(map(int,input().split()))
a=list(map(int,input().split()))

ans=10**12

for i in range(2**N):
    cnt=0
    cost=0
    h=0
    for j in range(N):
        if (i>>j)&1==1:
            cnt+=1
            if h>=a[j]:
                cost+=h+1-a[j]
                h+=1
            else:
                h=max(h,a[j])
        else:
            h=max(h,a[j])

    if cnt>=K:
        ans=min(ans,cost)

print(ans)
