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>
using namespace std;
typedef long long ll;
ll a[16];
int n,k;
int main(){
	ios::sync_with_stdio(false);
	cin >> n >> k;
	for(int i=0; i<n ;i++) cin >> a[i];
	ll ans=8e18;
	for(int i=0; i<(1<<n) ;i++){
		ll cost=0;
		int cnt=0;
		ll prv=0;
		for(int j=0; j<n ;j++){
			if(i&(1<<j)){
				cnt++;
				cost+=max(0LL,prv+1-a[j]);
				prv++;
			}
			prv=max(prv,a[j]);
		}
		if(cnt==k) ans=min(ans,cost);
	}
	cout << ans << endl;
}