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 = [int(i) for i in input().split()]
ans = float("INF")
for i in range(1<<N):
    cnt = 0
    tmp = a[:]
    m = tmp[0]
    for j in range(1,N):
        if i >> j & 1 and m >= tmp[j]:
            cnt += m - tmp[j] + 1
            tmp[j] = m + 1
        m = max(m,tmp[j])
    color = 1
    m = tmp[0]
    for j in range(1,N):
        if tmp[j] > m:
            color += 1
            m = tmp[j]
    if color >= K: ans = min(ans,cnt)
print(ans)