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())
arr=list(map(int,input().split()))
ans=10**18
for i in range(2**n):
  flags=[0]*n
  pos=0
  while i!=0:
    if i%2==1:
      flags[pos]=1
      i-=1
    i=i//2
    pos+=1
  cost=0
  tmp=[0]*n
  tmp[0]=arr[0]
  maxs=arr[0]
  for j in range(1,n):
    if flags[j]==1:
      tmp[j]=max(maxs+1,arr[j])
    else:
      tmp[j]=arr[j]
    cost+=(tmp[j]-arr[j])
    maxs=max(maxs,tmp[j])
  if flags.count(1)>=k:
    ans=min(ans,cost)
print(ans)