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
def inpl():
    return list(map(int, input().split()))


def count(i):
    cost, k = 0, 1
    h = A[0]
    for j in range(1, N):
        if A[j] > h:
            k += 1
            h = A[j]
        elif (i >> j) & 1:
            k += 1
            cost += max(h - A[j] + 1, 0)
            h += 1
    return cost, k


N, K = inpl()
A = inpl()

ans = float('inf')
for i in range(1 << N):
    cost, k = count(i)
    if k >= K:
        ans = min(ans, cost)

print(ans)
