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=float("inf")
for i in range(2**n):
    bit=[(i>>j)&1 for j in range(n)]
    if sum(bit)==k and bit[0]==1:
        cost=0
        kijun=a[0]
        for j in range(1,n):
            if bit[j]==0:
                kijun=max(kijun,a[j])
            elif a[j]>=kijun+1:
                kijun=a[j]
            else:
                cost+=kijun+1-a[j]
                kijun+=1
        ans=min(ans,cost)
print(ans)