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

ans = 10**18
for bit in product(range(2), repeat=n):#k+1個以上の建物の高さを増やす必要はない
    ma = 0
    cost = 0
    see = 0
    for i in range(n):
        ai = a[i]
        if ai>ma:
            see += 1
            ma = ai
        elif bit[i]:
            ma = ma + 1
            see += 1
            co = ma - ai
            cost += co
    if see>=k:
        ans = min(ans, cost)
            
print(ans)