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