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;
long long a[20],ans = 10000000000000000;
int main(){
	int i,j,n,k;
	cin >> n >> k;
	for(i=0;i<n;i++){
		cin >> a[i];
	}
	for(i=0;i<(1<<n);i++){
		if(__builtin_popcount(i)<k) continue;
		long long h = 0,res = 0;
		for(j=0;j<n;j++){
			if((1<<j)&i){
				if(h>=a[j]){
					res += h + 1 - a[j];
					h++;
				}
			}
			h = max(h,a[j]);
		}
		ans = min(ans,res);
	}
	cout << ans << endl;
}
			