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 itertools

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

amin=10**9*20
for i in itertools.product([0,1], repeat=n):
    if sum(i)==k:
        hs=a[0]
        acnt=0
        h=[]
        for j in range(n):
            if i[j]==1 and j>0:
                if hs>=a[j]:
                    acnt+=hs-a[j]+1
                    hs=hs+1
            if hs<a[j]:
                hs=a[j]
            h.append(hs)
#        print(i,acnt,h)
        amin=min(amin,acnt)
        
print(amin)
