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=10010010010010010

for i in range(1<<n-1):
  if bin(i).count("1")!=k-1:
    continue
  cnt=0
  cost=0
  #print("cnt i",i)
  prevh=a[0]
  for j in range(n-1):
    if 1<<j & i:
      if prevh>=a[j+1]:
        cost+=prevh+1-a[j+1]
        prevh+=1
        #print("cost",j,cost)
      else:
        prevh=a[j+1]
    else:
      prevh=max(prevh,a[j+1])
  ans=min(ans,cost)
  #print("ans",ans)
print(ans)