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

min_cost = 1 << 50
for mask in range(1<<N):
    if bin(mask).count('1') < K:
        continue

    cost = 0
    prev_height = 0
    for i in range(N):
        # not chose this building
        if mask & (1<<i) == 0:
            prev_height = max(prev_height, A[i])
            continue

        # chose this building viewable
        if A[i] <= prev_height:
            cost += prev_height - A[i] + 1
            prev_height += 1
        else:
            prev_height = A[i]
    min_cost = min(min_cost, cost)

print(min_cost)