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 = list(map(int,input().split()))
ans = float("inf")
 
for i in range(2**n):
    highest = a[0]
    color = 1
    money = 0
    for j in range(1,n):
        if a[j] > highest:
            color += 1
            highest = a[j]
        elif (i>>j)&1:
            color += 1
            highest = highest + 1
            money += highest - a[j]
        
    if color >= k:
        ans = min(ans,money)
print(ans)