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>
#include <string>
#include <vector>
#include <algorithm>

using namespace std;

int main() {
	int n, K;
	cin >> n >> K;
	vector<int> a(n);
	for (int i = 0; i < n; i++) {
		cin >> a[i];
	}
	long long ans = 1e18;
	for (int i = 0; i < 1 << n; i++) {
		int cnt = 0;
		int mx = 0;
		long long cost = 0;
		for (int j = 0; j < n; j++) {
			if (mx >= a[j]) {
				if (i >> j & 1) {
					cnt++;
					cost += mx - a[j] + 1;
					mx++;
				}
			} else {
				cnt++;
				mx = a[j];
			}
		}
		if (cnt >= K) {
			ans = min(ans, cost);
		}
	}
	cout << ans << endl;
}
