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
import sys 
input = sys.stdin.readline

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

min_cost = 10**11
for i in range(2**n):
    height = 0
    k_count = 0
    cost = 0
    for j in range(n):
        if (i>>j) & 1:
            if an[j] <= height:
                cost += height - an[j] + 1
                height += 1
            else:
                height = an[j]
            k_count += 1
        height = max(height, an[j])
    if k_count >= k:
        min_cost = min(min_cost, cost)

print(min_cost)

