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 <vector>
#include <algorithm>
using namespace std;
typedef long long int ll;

int main(){
	cin.tie(nullptr);
	ios::sync_with_stdio(false);
	int n,k; cin >> n >> k;
	vector<int> x(n),y(n);
	vector<int> v,u;
	for(int i=0;i<n;i++){
		cin >> x[i] >> y[i];
		v.push_back(x[i]);
		u.push_back(y[i]);
	}
	sort(v.begin(),v.end());
	sort(u.begin(),u.end());
	ll ans=1LL*(v[n-1]-v[0])*(u[n-1]-u[0]);
	for(int i=0;i<n;i++){
		for(int j=i+1;j<n;j++){
			for(int p=0;p<n;p++){
				for(int q=p+1;q<n;q++){
					int num=0;
					for(int t=0;t<n;t++){
						if(v[i]<=x[t]&&x[t]<=v[j]&&u[p]<=y[t]&&y[t]<=u[q])num++;
					}
					if(num>=k){
						ans=min(ans,1LL*(v[j]-v[i])*(u[q]-u[p]));
					}
				}
			}
		}
	}
	cout << ans << endl;
}