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;

using ll = long long;

int bitcount(int a){
	int r = 0;
	while(a){
		a -= a & -a;
		r++;
	}
	return r;
}

int main(){
	int n, k;
	cin >> n >> k;
	ll a[n];
	for(int i = 0; i < n; i++) cin >> a[i];
	ll ans = 1e15;
	for(int i = 0; i < 1 << n; i++){
		if(bitcount(i) < k) continue;
		ll tmp = 0, maxi = -1;
		for(int j = 0; j < n; j++){
			if(i >> j & 1){
				if(maxi == -1){
					maxi = a[j] + 1;
					continue;
				}
				tmp += max(0ll, maxi - a[j]);
				maxi = max(maxi + 1, a[j] + 1);
			}
			maxi = max(maxi, a[j] + 1);
		}
		ans = min(ans, tmp);
	}
	cout << ans << endl;
}