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>
#define rep(i,n) for(int i=0;i<n;i++)
#define eps LDBL_EPSILON
#define moder 1000000007
#define int long long
#define double long double
#define ll long long
#define INF LLONG_MAX/3
#define P pair<int,int>
#define prique priority_queue<int,vector<int>,greater<int>>
#define ggr getchar();getchar();return 0
using namespace std;
int n,k,a[20];
signed main(){
	cin>>n>>k;
	rep(i,n)cin>>a[i];
	int ans=INF;
	rep(i,((ll)1<<n)){
		int count=0;
		rep(j,n){
			if((i>>j)&1)count++;
		}
		if(count!=k)continue;
		int cnt=0,now=-1,ma=0;
		rep(j,n){
			if((i>>j)&1){
				if(now!=-1){
					cnt+=max((ll)0,now+1-a[j]);
					now=max(now+1,a[j]);
				}
				else now=a[j];
			}
			now=max(now,a[j]);
		}
		ans=min(ans,cnt);
	}
	cout<<ans<<endl;
	ggr;
}