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, *A = map(int, open(0).read().split())

ans = 10 ** 9 * 20
for bit in range(2 ** N):
    if bin(bit).count("1") < K or not (bit >> 0 & 1):
        continue

    res = 0
    tmp = A[0]
    for i in range(1, N):
        if bit >> i & 1:
            res += max(0, tmp - A[i] + 1)
            tmp = max(A[i], tmp + 1)
        else:
            tmp = max(A[i], tmp)
    ans = min(ans, res)

print(ans)
