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>

using namespace std;

int main(void)
{
	int n,k;
	cin >> n >> k;
	long long x[n],y[n];
	for(int i=1;i<=n;i++)
		cin >> x[i-1] >> y[i-1];
	
	long long ans = 9000000000000000000;

	for(int i=1;i<=n;i++)
	{
	for(int i2=1;i2<=n;i2++)
	{
		for(int j=1;j<=n;j++)
		{
		for(int j2=1;j2<=n;j2++)
		{
			if(i==j)break;
			int count=0;
			for(int l=1;l<=n;l++)
			{
				if(((x[i-1]<=x[l-1] && x[l-1]<=x[j-1]) || (x[j-1]<=x[l-1] && x[l-1]<=x[i-1])) && ((y[i2-1]<=y[l-1] && y[l-1]<=y[j2-1]) || (y[j2-1]<=y[l-1] && y[l-1]<=y[i2-1])))count++;
			}
			if(count>=k)
				ans=min(ans,abs(x[i-1]-x[j-1])*abs(y[i2-1]-y[j2-1]));
		}
		}
	}
	}

	cout << ans << endl;
}