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 std::cout;
using std::endl;
using std::cin;

int main(){
	int n, k; cin >> n >> k; std::vector<long> a(n);
	for(int i = 0; i < n; i++) cin >> a[i];
	
	long ans = 1e18;
	for(int i = 0; i < (1 << n); i++){
		if(__builtin_popcount(i) < k) continue;
		
		long cost = 0, ma = 0, c = 0;
		for(int j = 0; j < n; j++){
			if((i >> j) & 1){
				if(a[j] <= ma){
					cost += ma - a[j] + 1;
					ma = ma + 1;
				}
			}
			
			ma = std::max<long>(ma, a[j]);
		}
		
		ans = std::min(ans, cost);
	}
	
	cout << ans << endl;
	return 0;
}
