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=list(map(int,input().split()))
ans=float('inf')
for i in range(2**n):
    x=format(i,'015b')
    Max=0
    yen=0
    for j in range(1,n+1):
        if x[-j]=='1':
            if Max<a[j-1]:
                Max=a[j-1]
            else:
                Max+=1
                yen+=Max-a[j-1]
        else:
            Max=max(Max,a[j-1])
    #print(x)
    temp=0
    for j in range(15):
        temp+=int(x[j])
    #print(temp,k)
    if temp>=k:
        ans=min(ans,yen)
print(ans)