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 <bits/stdc++.h>
using namespace std;
typedef long long ll;
int main(){
	ll n,k,a[20];
	cin>>n>>k;
	for(int i=0;i<n;i++)cin>>a[i];
	ll ans=1e18;
	for(int i=0;i<(1ll<<n);i++){
		bool f[20]={};
		ll yojo=0;
		for(int j=0;j<n;j++){
			ll num=1ll<<j;
			if(i&num){
				f[j]=1;
				yojo++;
			}
		}
		if(yojo<k)continue;
		ll ma=a[0],cnt=0;
		for(int j=1;j<n;j++){
			if(f[j]&&a[j]<=ma){
				cnt+=ma-a[j]+1;
				ma++;
			}
			if(a[j]>ma)ma=a[j];
		}
		ans=min(ans,cnt);
	}
	cout<<ans<<endl;
	return 0;
}
