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()))
import itertools

min_cost = float('inf')
for Buildings in itertools.combinations(range(N),K):
    min_height = 0
    cost = 0
    for i in range(N):
        if i in Buildings:
            h = A[i]
            if h>min_height:
                min_height = h
                continue
            cost+=(min_height+1) - h
            min_height += 1
            continue
        min_height = max(min_height,A[i])

    min_cost=min(min_cost,cost)

print(min_cost)
