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>
#include<climits>
using namespace std;

const int N=55;
int x[N],y[N];
int n,k;
int val[N],c;

signed main()
{
	cin>>n>>k;
	for(register int i=1;i<=n;i++)
		cin>>x[i]>>y[i];
	
	long long ans=LLONG_MAX;
	for(register int a=1;a<=n;a++)
		for(register int b=1;b<=n;b++)
			for(register int c=1;c<=n;c++)
				for(register int d=1;d<=n;d++)
				{
					int x1=x[a],y1=y[b],x2=x[c],y2=y[d];
					if(x1>x2||y1>y2) continue;
					int cnt=0;
					for(register int i=1;i<=n&&cnt<k;i++)
						if(x1<=x[i]&&x[i]<=x2&&y1<=y[i]&&y[i]<=y2)
							cnt++;
					if(cnt==k) ans=min(ans,(x2-x1)*1ll*(y2-y1));
				}
	cout<<ans<<endl;
	return 0;
}