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=[]
for i in range(1<<n):
    
    if bin(i).count("1")==k:
        cst=0
        use=a.copy()
        for u in range(1,n):
            if(i>>u&1):
                left_max=max(use[:u])
                cst+=left_max-use[u]+1 if left_max>=use[u] else 0
                use[u]= max(left_max+1, use[u])
        ans.append(cst)
print(min(ans))
