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
n, k = map(int, input().split())
a = list(map(int, input().split()))

a_list = [i for i in range(n)]

ans = 10**12
for A in combinations(a_list[1:], k-1):
    a_max = a[0]
    tmp = 0
    for i in range(1, n):
        if i in A:
            if a[i] <= a_max:
                tmp += a_max-a[i]+1
                a_max += 1
        if a[i] > a_max:
            a_max = a[i]
    ans = min(ans, tmp)
print(ans)