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<cstdio>
#include<algorithm>
using namespace std;
typedef long long ll;
int main(){
	int n,k;
	ll a[15];
	ll ans = 1000000000000;
	scanf("%d%d",&n,&k);
	for(int i=0;i<n;i++) scanf("%lld",a+i);
	for(int S=0;S<(1<<n);S++){
		int cnt = 0;
		for(int j=0;j<n;j++) if((S>>j)&1) cnt++;
		if(cnt!=k) continue;
		ll h = 0;
		ll res = 0;
		for(int j=0;j<n;j++){
			if((S>>j)&1){
				if(h<a[j]) h = a[j];
				else{
					res += h - a[j] + 1;
					h++;
				}
			}else{
				h = max(h,a[j]);
			}
		}
		ans = min(ans,res);
	}
	printf("%lld\n",ans);
}
