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,k=list(map(int,input().split()))
A=list(map(int,input().split()))
ans=[]

for li in itertools.product([0,1], repeat=n-1):
  if li.count(1) < k-1:
    continue
  cost,height=0,A[0]
  for i in range(1,n):
    if height < A[i]:
      height=A[i]
      continue
    if li[i-1]:
      cost += (height-A[i]+1)
      height += 1 
  ans.append(cost)
  
print(min(ans))