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())
buildings = list(map(int, input().split()))

ans = float('inf')
for i in range(2 ** n):
    res = 0
    cnt = 0
    prev_build = buildings[0]
    for j in range(n):
        if (i >> j) & 1 == 1:
            cnt += 1
            if prev_build >= buildings[j] and not j == 0:
                res += ((prev_build + 1) - buildings[j])
                prev_build = prev_build + 1
            else:
                prev_build = buildings[j]
        else:
            if prev_build < buildings[j]:
                prev_build = buildings[j]

    if cnt == k:
        ans = min(ans, res)

print(ans)