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

ans = 10 ** 11
for b in range(1 << n):
    if bin(b).count("1") != k:
        continue

    max_ai = 0
    cost = 0
    for i in range(n):
        if (b & 1 << i):
            if A[i] > max_ai:
                max_ai = A[i]
            else:
                cost += (max_ai + 1) - A[i]
                max_ai += 1
        else:
            max_ai = max(max_ai, A[i])

    ans = min(ans, cost)

print(ans)


