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 <string>
#include <vector>
#include <cmath>
#include <limits.h>
typedef long long ll;
ll MOD = 1e9+7;

using namespace std;

int main()
{
	int n,k;
	int cnt=0;
	ll x[50];
	ll y[50];
	ll Mx;
	ll mx;
	ll My;
	ll my;
	ll ans=LLONG_MAX;
	
	cin>>n>>k;
	for(int i=0;i<n;i++)
	{
		cin>>x[i]>>y[i];
	}

	for(int xi=0;xi<n;xi++)
	{
		for(int xj=xi+1;xj<n;xj++)
		{
			for(int yi=0;yi<n;yi++)
			{
				for(int yj=yi+1;yj<n;yj++)
				{
					cnt=0;
					Mx = max(x[xi],x[xj]);
					mx = min(x[xi],x[xj]);
					My = max(y[yi],y[yj]);
					my = min(y[yi],y[yj]);
					for(int h=0;h<n;h++)
					{
						if(x[h]>=mx && x[h]<=Mx && y[h]>=my && y[h]<=My)
							cnt++;
					}
					if(cnt>=k)
						ans=min((Mx-mx)*(My-my),ans);
				}
			}
		}
	}
	cout<<ans<<endl;
	return 0;
}