Problem: We have N points in a two-dimensional plane.
The coordinates of the i-th point (1 \leq i \leq N) are (x_i,y_i).
Let us consider a rectangle whose sides are parallel to the coordinate axes that contains K or more of the N points in its interior.
Here, points on the sides of the rectangle are considered to be in the interior.
Find the minimum possible area of such a rectangle.

Constraints

* 2 \leq K \leq N \leq 50
* -10^9 \leq x_i,y_i \leq 10^9 (1 \leq i \leq N)
* x_i≠x_j (1 \leq i<j \leq N)
* y_i≠y_j (1 \leq i<j \leq N)
* All input values are integers. (Added at 21:50 JST)

Input

Input is given from Standard Input in the following format:


N K
x_1 y_1
:
x_{N} y_{N}


Output

Print the minimum possible area of a rectangle that satisfies the condition.

Examples

Input

4 4
1 4
3 3
6 2
8 1


Output

21


Input

4 2
0 0
1 1
2 2
3 3


Output

1


Input

4 3
-1000000000 -1000000000
1000000000 1000000000
-999999999 999999999
999999999 -999999999


Output

3999999996000000001

Solution (in CPP):

Solution:
#include <cstdio>
#include <cstring>
#include <algorithm>
#include <queue>
#include <cmath>
 
using namespace std;
typedef long long LL;
 
struct node{
	LL x , y;
}a[100];
 
int main()
{
	int n , m;
	scanf("%d %d",&n , &m);
	for(int i = 1 ; i <= n ; i++) scanf("%lld %lld",&a[i].x , &a[i].y);
	LL ans = 1LL << 62;
	for(int i = 1 ; i <= n ; i++){
		for(int j = i + 1 ; j <= n ; j++){
			for(int k = 1 ; k <= n ; k++){
				for(int l = k + 1 ; l <= n ; l++){
					int sum = 0;
					LL lx = min(a[i].x , a[j].x) , hy = max(a[i].y , a[j].y);
					LL ly = min(a[k].y , a[l].y) , hx = max(a[k].x , a[l].x);
					for(int h = 1 ; h <= n ; h++){
						if(a[h].x >= lx && a[h].x <= hx && a[h].y >= ly && a[h].y <= hy)
							sum++;
					}
					if(sum >= m) ans = min(ans , (hx - lx) * (hy - ly));
				}
			}
		}
	}
	printf("%lld\n",ans);
}