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 = float('inf')
for bit in range(1<<(n-1)):
  cand = [0]*(n-1)
  for i in range(n-1):
    if bit & 1<<i: cand[i] = 1
  if cand.count(1) != k-1: continue
  cost = 0
  mx = a[0]
  for i in range(1, n):
    if cand[i-1]:
      if a[i] <= mx:
        cost += mx-a[i]+1
        mx += 1
    mx = max(mx, a[i])
  ans = min(ans, cost)
print(ans)