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 copy
N,K=map(int,input().split())
A=list(map(int,input().split()))
B=copy.copy(A)
ans=[]

for i in range(2**(N-1)):
    L=[0]*(N-1)
    total=0
    count=0
    for j in range(N-1):
        if ((i>>j)&1):
            L[j]=1
            count+=1
    if count>=K-1:
        A=copy.copy(B)
        for m in range(N-1):
            
            if L[m]==1:
                height=max(max(A[:m+1])+1,A[m+1])
                total+=height-A[m+1]
                A[m+1]=height
                
        ans.append(total)
        

print(min(ans))