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 product

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

ans = 10 ** 20
for bit in product([0, 1], repeat=n):
    if sum(bit) != k or bit[0] == 0:
        continue
    cnt = 0
    tmp = a[0]
    for i, v in enumerate(bit):
        if v == 1:
            if i != 0:
                cnt += max(tmp + 1 - a[i], 0)
                tmp = max(tmp + 1, a[i])
        else:
            tmp = max(tmp, a[i])
    ans = min(ans, cnt)
print(ans)
