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:
#pragma GCC optimize ("O3")
#pragma GCC optimize("unroll-loops")
#pragma GCC target("sse4")
#include"bits/stdc++.h"
using namespace std;
typedef long long ll;
#define int ll
#define sz(x) (int)(x).size();
#define all(x) x.begin(), x.end()
#define trav(i,a) for(auto &i:a) 
inline int in(){int x;scanf("%lld",&x);return x;}
int32_t main()
{
	int n=in();int K=in();
	int x[n],y[n];
	for(int i=0;i<n;i++){x[i]=in();y[i]=in();}
	int ans=4e18;int ct=0;
	for(int i=0;i<n;i++)
	for(int j=0;j<n;j++)
	{
		if(x[i]>=x[j])continue;
		
		for(int k=0;k<n;k++)
		for(int l=0;l<n;l++)
		{
			if(y[k]<=y[l])continue;
			ct=0;
			for(int g=0;g<n;g++)
			{
				if(x[i]<=x[g] and x[g]<=x[j] and y[l]<=y[g] and y[g]<=y[k])ct++;
			}
			if(ct>=K)ans=min(ans,(x[j]-x[i])*(y[k]-y[l]));
		}	
	}
	cout<<ans;
	
}