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())
if k==1:
    print(0)
    exit()
a=list(map(int,input().split()))
k-=1
n-=1
c=(1<<k)-1
b=10**18
while c<1<<n:
    w=a[0]
    t=0
    f=1
    for i in range(n):
        if c>>i&1:
            t+=max(0,w-a[i+1]+1)
            w=max(a[i+1],w+1)
        else:
            if a[i+1]>w:
            	f=0
            	break
    if f:
        b=min(b,t)
    x=c&-c
    y=c+x 
    c=((c&~y)//x>>1)|y 
print(b)