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 = float("INF")
for i in range(1 << n):
    h = 0
    cost = 0
    count = 0
    for j in range(n):
        if j != 0:
            h = max(h, a[j - 1])
        if i >> j & 1:
            if h < a[j]:
                h = a[j]
                count += 1
            else:
                h += 1
                cost += h - a[j]
                count += 1
    if count >= k:
        ans = min(ans, cost)

print(ans)
        
            

