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())
INF=10**18
a=list(map(int,input().split()))
ans=INF
for i in range(2**(n-1)):
  cst=0
  cnt=0
  b=a[0]
  for j in range(n-1):
    if (i>>j) & 1:
      cst+=max(b+1-a[j+1],0)
      b=max(a[j+1],b+1)
      cnt+=1
    elif a[j+1]>b:
      cst+=a[j+1]-b
      b=a[j+1]
  if cnt==k-1:
    ans=min(ans,cst)
print(ans)