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
#include<iostream>
#include<algorithm>
using namespace std;
int main()
{
	int n,k;cin>>n>>k;
	long a[15];for(int i=0;i<n;i++)cin>>a[i];
	long ans=1LL<<60;
	for(long i=1;i<1<<n;i++)
	{
		int pcount=0;
		for(int j=0;j<n;j++)if(i&(1<<j))pcount++;
		if(pcount!=k)continue;
		long maxa=-(1e10);
		long b[15],nans=0;
		for(int j=0;j<n;j++)b[j]=a[j];
		for(int j=0;j<n;j++)
		{
			if(i&(1<<j))
			{
				if(b[j]<=maxa)
				{
					nans+=maxa-b[j]+1;
					b[j]=maxa+1;
				}
			}
			maxa=max(maxa,b[j]);
		}
		ans=min(ans,nans);
	}
	cout<<ans<<endl;
}