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')
def search(x):
    if len(x)==n:
        if x.count(1)>=k:
            global ans
            m = a[0]
            c = 0
            for i in range(1,n):
                if x[i]==1:
                    c += max(0,m-a[i]+1)
                    m = max(m+1,a[i])
                m = max(m,a[i])
            ans = min(ans,c)
    else:
        search(x+[1])
        search(x+[0])
search([])
print(ans)