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 <cstdio>
using namespace std;
long long n, m, mx0, mx1, my0, my1, c, mn=9e20, x[55], y[55];
int main() {
	long long i, j, i2, j2, x0, x1, y0, y1, k;
	cin>>n>>m;
	for(i=0; i<n; i++) cin>>x[i]>>y[i];
	for(i=0; i<n; i++) for(j=i+1; j<n; j++) {
		x0 = min(x[i], x[j]);
		y0 = min(y[i], y[j]);
		for(i2=0; i2<n; i2++) for(j2=i2+1; j2<n; j2++) {
			x1 = max(x[i2], x[j2]);
			y1 = max(y[i2], y[j2]);
			mx0 = min(x0, x1);
			mx1 = max(x0, x1);
			my0 = min(y0, y1);
			my1 = max(y0, y1);
			c = 0;
			for(k=0; k<n; k++) {
				if(mx0<=x[k] && x[k]<=mx1 && my0<=y[k] && y[k]<=my1) c++;
			}
			if(c>=m) mn = min(mn, (mx1-mx0)*(my1-my0));
		}
	}
	cout<<mn;
	return 0;
}