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 ll long long
using namespace std;
int n,k,a[10010];
ll ans = 1e18;

inline int max(int a, int b)
{
	if(a < b) return b;
	return a;
}

int main()
{
	scanf("%d%d", &n, &k);
	for(int i = 0; i < n; i ++) scanf("%d", a + i);
	for(int i = 0; i < (1 << n); i ++)
	{
		int cnt = 0;
		for(int j = 0; j < n; j ++)
			cnt += bool(i & (1 << j));
		if(cnt != k) continue;
		int ls = -1;
		ll cst = 0;
		for(int j = 0; j < n; j ++)
		{
			if(i & (1 << j));
			else
			{
				ls = max(ls, a[j]);
				continue;
			}
			int nx = max(a[j], ls + 1);
			cst += nx - a[j];
			ls = nx;
		}
		ans = min(ans, cst);
	}
	printf("%lld\n", ans);
	return 0;
}
