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=15*10**10
for i in range(2**(n-1)):#1番目は確定だから
    cnt,s,mh=0,0,a[0]+1
    for j in range(n-1):
        if i>>j&1:
            cnt+=1
            x=a[j+1]
            if x>=mh:
                mh=x+1
            else:
                s+=mh-x
                mh+=1
        else:
            mh=max(mh,a[j+1]+1)
    if cnt>=k-1:
        ans=min(ans,s)
print(ans)