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>
#include <utility>
using namespace std;
typedef long long int lli;
int main(){
	int n,k;
	cin >> n >> k;
	
	vector<lli> x(n), y(n);
	for(int i=0; i<n; i++){
		cin >> x[i] >> y[i];
	}
	
	lli ans = 6*1e18;
	for(int i=0; i<n; i++){
		for(int j=i+1; j<n; j++){
			for(int s=0; s<n; s++){
				for(int t=s+1; t<n; t++){
					lli xmax = max(x[i], x[j]);
					lli xmin = min(x[i], x[j]);
					lli ymax = max(y[s], y[t]);
					lli ymin = min(y[s], y[t]);
					int count = 0;
					for(int c=0; c<n; c++){
						if(xmin <= x[c] && x[c] <= xmax &&
						ymin <= y[c] && y[c] <= ymax){
							count++;
						}
					}
					if(count >= k){
						ans = min(ans, (xmax-xmin)*(ymax-ymin));
					}
				}
			}
		}
	}
	
	cout << ans << endl;
	return 0;
}