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 <vector>
#include <string>
#include <algorithm>
#include <cmath>
#include <iomanip>
#include <map>
#include <unordered_map>

using namespace std;
using ll = long long;
using pint = pair<int, int>;

ll INF = 1LL << 60;

int main() {
	int N, K;
	cin >> N >> K;
	vector<int> a(N), b(N);
	for (int i = 0; i < N; i++) cin >> a[i];

	ll ans = INF;
	for (int bit = 0; bit < (1 << N); bit++) {
		b = a;
		ll cost = 0;
		int M = b[0];
		int color = 1;
		for (int i = 0; i < N; i++) {
			if (i == 0) continue;
			if (bit & (1 << i)) {
				color++;
				if (M >= b[i]) {
					cost += (M + 1) - b[i];
					b[i] = M + 1;
				}
			}
			M = max(M, b[i]);
		}
		if (color >= K) ans = min(ans, cost);
	}
	cout << ans << endl;
	return 0;
}