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 <iostream>
#include <algorithm>
using namespace std;
struct cc
{
	long long x,y;
}c[10005];
bool cmp(cc x,cc y)
{
	if (x.x==y.x) return x.y<y.y;
		else return x.x<y.x;
}
long long n,m,i,j,k,l,p,cnt,ans=1ll<<62;
int main()
{
	cin>>n>>m;
	for (i=1;i<=n;i++) cin>>c[i].x>>c[i].y;
	sort(c+1,c+n+1,cmp);
	for (i=1;i<=n;i++)
	{
		for (j=i+1;j<=n;j++)
		{
			for (k=1;k<=n;k++)
			{
				for (l=1;l<=n;l++)
				{
					if (c[k].y<c[l].y)
					{
						cnt=0;
						for (p=1;p<=n;p++)
						{
							if (c[i].x<=c[p].x&&c[j].x>=c[p].x&&c[k].y<=c[p].y&&c[l].y>=c[p].y) cnt++;
						}
						if (cnt>=m) ans=min(ans,(c[j].x-c[i].x)*(c[l].y-c[k].y));
					}
				}
			}
		}
	}
	cout<<ans;
	return 0;
}