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

ans = 10**18
for P in product(range(2), repeat=N-1):
    if sum(P) < K-1:
        continue
    res = 0
    base = A[0]
    for i in range(N-1):
        if P[i]:
            if A[i+1] <= base:
                res += (base+1 - A[i+1])
                base += 1
            else:
                base = A[i+1]
        else:
            if base < A[i+1]:
                res += (A[i+1] - base)
                base = A[i+1]
    ans = min(ans, res)
print(ans)
