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 comb
n, k = map(int, input().split())
ns = list(map(int, input().split()))
res = float('inf')
perms = list(range(1,n))
for p in comb(perms, k-1):
    res_tmp = 0
    tmp_max = 0
    p = [0] + list(p)
    for i in range(n):
        if i in p and ns[i] <= tmp_max:
            res_tmp += tmp_max - ns[i] + 1
            tmp_max = tmp_max + 1
        else:
            tmp_max = max(tmp_max, ns[i])
    res = min(res, res_tmp)
print(res)