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>
using namespace std;

int main(){
	int i,j,k,l,n,m,c,z;
	cin >> n >> z;
	long long x[n],y[n],a[n],b[n],ans=5000000000000000000;
	for(i=0;i<n;i++){
		cin >> x[i] >> y[i];
		a[i] = x[i];
		b[i] = y[i];
	}
	sort(x,x+n);
	sort(y,y+n);
	for(i=0;i<n;i++){
		for(j=i;j<n;j++){
			for(k=0;k<n;k++){
				for(l=k;l<n;l++){
					c = 0;
					for(m=0;m<n;m++){
						if(x[i]<=a[m] && a[m]<=x[j] && y[k]<=b[m] && b[m]<=y[l]){
							c++;
						}
					}
					if(c>=z){
					ans = min(ans,(x[j]-x[i])*(y[l]-y[k]));
					}
				}
			}
		}
	}
	cout << ans << endl;
}