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())
src = list(map(int,input().split()))

if N == 1:
    print(0)
    exit()

ans = float('inf')
for bs in range(1<<(N-1)):
    colors = 1
    cost = 0
    tmp = src[0]
    for k in range(N-1):
        if tmp < src[k+1]:
            colors += 1
            tmp = src[k+1]
            continue
        if bs&(1<<k):
            cost += tmp - src[k+1] + 1
            colors += 1
            tmp += 1
    if colors >= K:
        ans = min(ans, cost)

print(ans)