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
#square869120Contest#4_B
n,k=map(int,input().split())
a=list(map(int,input().split()))

ans=10**15
for i in range(2**n):
    if bin(i).count('1')<k:
        continue
    max_tmp=0
    res=0
    for j in range(n):
        if (i>>j)&1:
            if a[j]>max_tmp:
                max_tmp=a[j]
            else:
                res+=max_tmp-a[j]+1
                max_tmp+=1
        else:
            max_tmp=max(max_tmp,a[j])
    ans=min(res,ans)
print(ans)