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 = [int(i)for i in input().split()]
A = [int(i) for i in input().split()]

#%%
ans = float("inf")
for b in range(2 ** (N - 1)):
    cnt = 0
    cost = 0
    height = A[0]
    for i in range(N - 1):
        if height - A[i + 1] < 0:
            cnt += 1
            height = A[i + 1]
        elif (b >> i) & 1:
            cnt += 1
            cost += height - A[i + 1] + 1
            height += 1
    if cnt + 1 >= K:
        ans = min(ans, cost)

print(ans)