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 <algorithm>
using namespace std;
#define rep(i,n) for(int i=0;i<n;i++)
int n, k;
long long a[16];
long long ans = 1e18 * 2;
int main() {
	cin >> n >> k;
	rep(i, n)cin >> a[i];
	rep(i, 1 << n) {
		int c = 0;
		rep(j, n)if (i&(1 << j))c++;
		if (c != k)continue;
		long long cnt = 0;
		long long mem = 0;
		rep(j, n) {
			if (i&(1 << j)) {
				cnt += max((long long)0, mem - a[j] + 1);
				mem++;
			}
			mem = max(mem, a[j]);
		}
		ans = min(ans, cnt);
	}
	cout << ans << endl;
	getchar();getchar();
}