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;
int n,k,a[22];
int main(){
	scanf("%d%d",&n,&k);
	for(int i=0; i<n; i++)
		scanf("%d",&a[i]);
	long long int res = 1000000000000LL;
	for(int mask=1; mask<(1<<n); mask++){
		if(__builtin_popcount(mask)<k)continue;
		long long int now = 0;
		int mx = 0;
		for(int i=0; i<n; i++){
			int x = a[i];
			if(mask&(1<<i)){
				if(x <= mx){
					now += mx+1-x;
					x = mx+1;
				}
			}
			mx = max(mx,x);
		}
		if(now < res)res=now;
	}
	cout<<res<<endl;
	return 0;
}
