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=tuple(map(int,input().split()))
if k==1 or n==1:
    print(0)
    exit()
m=pow(10,12)
l=len(a)-1
for i in range(2**(n-1)):
    cnt=1
    h=a[0]
    num=0
    for j in range(l):
        if (i>>j)&1:
            num+=max(0,h-a[j+1]+1)
            if a[j+1]<=h:
                h+=1
            else:
                h=a[j+1]
            cnt+=1
        else:
            if a[j+1]>h:
                cnt+=1
                h=a[j+1]
    if cnt>=k:
        m=min(m,num)
print(m)
