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=10**15
for i in range(1<<(N-1)):
  cnt,s,t=0,0,a[0]+1
  for j in range(N-1):
    if i>>j&1:
      x=a[j+1]
      cnt+=1
      if x>=t:
        t=x+1
      else:
        s+=(t-x)
        t+=1
    else:
      t=max(t,a[j+1]+1)
  if cnt>=K-1:
    ans=min(s,ans)
print(ans)