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

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

b = list(range(1, n))
c = combinations(b, k-1)

min_sum = 10**30
for i in c:
    sum = 0
    target = a[0] + 1
    for j in range(1, n):
        if j in i:
            if target >= a[j]:
                sum += (target - a[j])
                target += 1
            else:
                target = a[j] + 1
        elif j not in i and a[j] > target:
            target = a[j] + 1
    if sum < min_sum:
        min_sum = sum

print(min_sum)