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 itertools
n,m=map(int,input().split())
a=list(map(int,input().split()))
ans=10**30
if m==0:
  print(0)
  exit()
for i in itertools.combinations(range(1,n),m-1):
  s=list(i)
  mx=a[0]
  cost=0
  for j in range(1,n):
    if j in s:
      if a[j]>mx:
        mx=a[j]
        continue
      else:
        cost+=mx+1-a[j]
        mx+=1
    mx=max(mx,a[j])
  ans=min(cost,ans)
print(ans)