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
from itertools import product as p
n,k=map(int,input().split())
a=list(map(int,input().split()))
an=float("INF")
for i in p([0,1],repeat=n):
    s=0
    c=a[::]
    p=0
    q=0
    for j in range(n):
        if i[j]:
            if s<c[j]:
                p+=1
                s=c[j]
            else:
                q+=s+1-c[j]
                c[j]=s+1
                p+=1
                s+=1
        else:
            if s<c[j]:
                p+=1
                s=c[j]
    if p>=k:
        an=min(q,an)
print(an)