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')
for i in range(1<<(N-1)):
  cost,cnt,h=0,1,a[0]+1
  for j in range(N-1):
    x=a[j+1]
    if i>>j&1:
      cnt+=1
      if x>h:
        h=x+1
      else:
        cost+=h-x
        h+=1
    h=max(h,x+1)
  if cnt>=K:
    ans=min(ans,cost)
print(ans)