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):
  a = A[::]
  cur,add = 0,0
  see = 0
  for j in range(N):
    if (i>>j)&1:
      see += 1
      if cur >= a[j]:
        add += (cur-a[j])+1
        a[j] = cur+1
      cur = max(cur,a[j])
    else:
      cur = max(cur,a[j])

  if see == K:
    ans = min(ans, add)

print(ans)