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
from itertools import product
n, k = list(map(int, input().split()))
al = list(map(int, input().split()))
INF = float("inf")
ans = INF
for bit in product([0, 1], repeat=(n-1)):
    if sum(bit)+1 >= k:
        t = 0
        pre = al[0]
        for i, a in enumerate(al):
            if i != 0:
                if bit[i-1] == 1:
                    t += max(0, (pre+1)-al[i])
                    pre = max(al[i], pre+1)
                    continue
                pre = max(pre, al[i])
        ans = min(ans, t)
print(ans)
