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
import copy
N, K = map(int, input().split())
A = list(map(int, input().split()))

money = 10 ** 12

for i in range(2 ** N):
  B = copy.copy(A)
  #print(B)
  count = 0
  money2 = 0
  for j in range(N):
    if ((i >> j) & 1):
      count += 1
      if j != 0:
        x = max(0, max(B[:j]) - B[j] + 1)
        if x != 0:
          B[j] = max(B[:j]) + 1
        money2 += x
        #print(i, j, x, money2, count)
  if count >= K:
    money = min(money, money2)
      
print(money)
      
