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()))

inf=float('inf')

ans=inf

for i in range(2**n):
  iro=0
  ch=0
  cost=0
  h_max=a[0]
  for j in range(n):
    if (i>>j)&1:
      iro+=1
      if j==0:
        ch+=1
  if iro==k and ch==1:
    for j in range(1,n):
      if (i>>j)&1:
        if h_max<a[j]:
          h_max=a[j]
        else:
          cost+=(h_max+1)-a[j]
          h_max+=1
      else:
        if h_max<a[j]:
          cost+=(a[j]+1)-h_max
          h_max=a[j]+1
    ans=min(ans,cost)
  
print(ans)
        
    
    