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
from itertools import combinations as cmb
import copy
n, k = map(int, input().split())
A = list(map(int, input().split()))
highest = [A[0]] * n
for i in range(1, n):
  highest[i] = max(A[i], highest[i-1])

def cost_calc(pattern):
  cost = 0
  max_height_re = 0
  A_copy = copy.copy(A)
  for num in pattern:
    cost += max(max_height_re, highest[num]) - A[num]
    max_height_re = max(max_height_re, highest[num]) + 1
  return cost

max_val = float("inf")
for pattern in cmb(range(n), k):
  max_val = min(max_val, cost_calc(pattern))
print(max_val)