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=10**11
for i in range(2**(n-1)):
  s=format(i,"16b")
  a=0
  for j in range(16):
    if s[j]=="1":
      a=a+1
  if a>=k-1:
    cost=0
    B=[A[0]]
    for j in range(n-1):
      if s[-1-j]!="1":
        B.append(A[j+1])
      else:
        if A[j+1]>max(B):
          B.append(A[j+1])
          continue
        else:
          B.append(max(B)+1)
          cost=cost+max(B)-A[j+1]
    if cost<ans:
      ans=cost
print(ans)