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 as comb
N,K = map(int,input().split())
a = [int(i) for i in input().split()]
ans = float("INF")

for c in comb(range(1,N),K-1):
    cnt = 0
    color = 0
    mh = a[0]
    for i in range(1,N):
        if i == c[color]:
            cnt += max(mh-a[i]+1,0)
            color += 1
            if color == K-1: break
            mh = max(mh+1,a[i])
        else:
            mh = max(mh,a[i])
    ans = min(cnt ,ans)
print(ans)