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 sys import stdin
from itertools import combinations
N,K = [int(x) for x in stdin.readline().rstrip().split()]
A = [int(x) for x in stdin.readline().rstrip().split()]
ans = 10**18
for i in combinations(range(1,N),K-1):
    tallest = A[0]
    tmp = 0
    for j in range(1,N):
        if j in i:
            if tallest >= A[j]:
                tmp += (tallest - A[j] + 1)
                tallest = (tallest + 1)
            else:
                tallest = max(tallest,A[j])
        else:
            tallest = max(tallest,A[j])
    ans = min(ans,tmp)
print(ans)