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
import itertools
N,K=map(int,input().split())
a=list(map(int,input().split()))
ans=float('inf')
for bit in itertools.product([0,1],repeat=N):
    if bit[0]==1 and bit.count(1)>=K:
        cost=0
        cr=a[0]
        for i in range(1,N):
            if bit[i]==1:
                if cr+1>=a[i]:
                    cost+=(cr+1-a[i])
                    cr=cr+1
                else:
                    cr=a[i]
            else:
                cr=max(cr,a[i])
        ans=min(ans,cost)
print(ans)