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 combinations

inf = 2 * 10 ** 10

n, k = map(int, input().split())
*a, = map(int, input().split())

ret = inf

for combi in combinations(range(n), r=k):
    set_ = set(combi)

    t = 0
    p = a[0] - 1
    for i, x in enumerate(a):
        if i in set_:
            if p >= x:
                t += p + 1 - x
                p += 1
            else:
                p = x
        else:
            if p < x:
                p = x
    ret = min(ret, t)

print(ret)
