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,raw_input().split())
a=map(int,raw_input().split())
ans=float("inf")
for i in xrange(1<<n):
    cnt=0
    li=[]
    for j in xrange(1,n):
        if i>>j&1:
            cnt+=1
            li.append(j)
    if cnt<k-1:continue
    tmp=0
    h=a[0]
    for j in li:
        for l in xrange(j):
            h=max(h,a[l])
        tmp+=max(h+1-a[j],0)
        h=max(h+1,a[j])
    ans=min(ans,tmp)
print ans