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

import itertools

N, K = map(int, input().split())
A = list(map(int, input().split()))

mn = 1e12

for v in itertools.product([0,1], repeat=N-1):
    h = A[0]
    p = 0
    if sum(v) < K - 1:
        continue
    for i, vv in enumerate(v):
        if vv == 1:
            p += max(h - A[i+1] + 1, 0)
            h = max(A[i+1], h + 1)
        else:
            h = max(A[i+1], h)
    mn = min(mn, p)

print(mn)