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(2**n):
    height = a[0]
    count = 1
    cost = 0
    for j in range(1,n):
        if (i>>j)&1:
            cost += max(0,(height-a[j]+1))
            height = max(height+1, a[j])
            count +=1
        else:
            if a[j] > height:
                count +=1
                height = a[j]
    if count >= k:
        ans = min(ans, cost)
print(ans)