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>
using namespace std;

int main() {
	int n,k;
	scanf("%d%d", &n, &k);
	int arr[n];
	for (int i=0; i<n; i++) scanf("%d", &arr[i]);
	long long ans=LLONG_MAX;
	for (int i=0; i<(1<<(n+1)); i++) {
		int num=0;
		long long tot=0;
		int prev=0;
		for (int j=0; j<n; j++) {
			if (1<<j & i) {
				num++;
				tot+=max(prev+1-arr[j],0);
				prev=max(prev+1,arr[j]);
			}
			prev=max(prev,arr[j]);
		}
		if (num==k) ans=min(ans,tot);
	}
	printf("%lld\n", ans);
}
