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 = [int(i) for i in input().split()]
a = [int(i) for i in input().split()]
if k == 1:
  print(0)
  exit()
  
b = [int(i)+1 for i in range(n-1)]
ans = float('inf')
import itertools
for j in itertools.combinations(b, k-1):
  s = list(j)
  now_high = a[0]
  cost = 0
  for l in range(1,n):
    if l in s:
      if a[l] > now_high:
        now_high = a[l]
        continue
      else:
        cost += (now_high-a[l]+1)
        now_high += 1
    now_high = max(now_high, a[l])
  ans =  min(ans,cost)
print(ans)