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 combinations

n,k = map(int,input().split())
A = list(map(int,input().split()))

ans = 10**12
for cmb in combinations(range(1,n),k-1):    
  cost = 0
  h = A[0]
  
  for i in range(1,n):    
    if i in cmb: 
      if A[i] > h:        
        h = A[i]      
      else:
        cost += h - A[i] + 1
        h += 1    
    h = max(h,A[i])
        
  ans = min(ans,cost)
          
print(ans)  