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
def MII(): return map(int,input().split())
def LMI(): return list(map(int,input().split()))
import copy

n,k=MII()
hights=LMI()
money_list=[]
for i in range(2**(n-1)):
    bit = [i>>j&1 for j in range(n-1)]
    hights_copy=copy.deepcopy(hights)
    money=0
    if sum(bit)==k-1:
        for a in range(n-1):
            if bit[a]==1:
                tmp=max(hights_copy[:a+1])+1
                if tmp>hights_copy[a+1]:
                    money+=(tmp-hights_copy[a+1])
                    hights_copy[a+1]=tmp
        money_list.append(money)
print(min(money_list))