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>
#define rep(i, n) for(int i = 0; i < (n); i++)
using namespace std;
using ll = long long;

const ll INF = 1LL << 60;

int main() {
	int n, k;
	cin >> n >> k;
	vector<ll> a(n);
	rep(i, n) cin >> a[i];
	ll ans = INF;
	rep(bit, (1 << n)) {
		vector<int> s;
		rep(i, n) {
			if (bit & (1 << i)) {
				s.push_back(i);
			}
		}
		vector<ll> t(n);
		rep(i, s.size()) {
			int u = s[i];
			rep(j, u) {
				if (a[j] + t[j] >= a[u] + t[u]) {
					t[u] = a[j] + t[j] - a[u] + 1;
				}
			}
		}
		int cnt = 1;
		rep(i, (int)s.size() - 1) {
			int u = s[i];
			int v = s[i + 1];
			if (a[u] + t[u] < a[v] + t[v]) cnt++;
		}
		if (cnt < k) continue;
		ll mn = 0;
		rep(i, n) mn += t[i];
		ans = min(ans, mn);
	}
	cout << ans << endl;
	return 0;
}