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 = tuple(map(int, input().split(' ')))

min_cost = 10 ** 12
for indexes in combinations(range(N), r=K):
    indexes = set(indexes)
    highest = 0
    cost = 0
    for i in range(N):
        height = A[i]
        if i in indexes and height <= highest:
            dh = highest - height + 1
            cost += dh
            height += dh
        highest = max(highest, height)
    min_cost = min(min_cost, cost)

print(min_cost)
