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 ** 18
for build in product(range(2), repeat=N - 1):
    if sum(build) != K - 1:
        continue

    # 左のやつは絶対見る
    cost = 0
    h = A[0]
    for i, p in enumerate(build, start=1):
        if p == 0:
            h = max(h, A[i])
            continue
        if A[i] > h:
            h = A[i]
            continue
        else:
            h += 1
            cost += (h - A[i])
    ans = min(ans, cost)

print(ans)