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()]

#ビット全探索
ans=1000000000*N
for i in range(1<<N):
    bitlist=[]
    for j in range(N):
        bitlist.append((i >> j) & 1)
    if sum(bitlist) < K:
        continue

    tmp_max=0
    nedan=0
    for j in range(N):
        if bitlist[j]==1:
            if tmp_max >= A[j]:
                nedan+=(tmp_max-A[j]+1)
                tmp_max=tmp_max+1
            elif tmp_max < A[j]:
                tmp_max=A[j]
        elif bitlist[j]==0:
            if tmp_max < A[j]:
                tmp_max=A[j]
    ans=min(ans,nedan)
print(ans)
