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 = 1145141919810364364334
for i in range(1,2**n):
    ls = [0] * n
    qq = []
    
    for j in range(n):
        if (i >> j) & 1:
            ls[j] = 1
            qq.append(j)
            
    if sum(ls) < k:
        continue
        
    else:
        mt = a[0]
        cost = 0
        for j in range(1,n) :
            if mt < a[j]:
                mt = a[j]
            else:
                if ls[j] == 1:
                    cost += mt + 1 - a[j]
                    mt += 1
    ans = min(ans,cost)
    
print(ans)