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<algorithm>
#include<iostream>
using namespace std;
typedef long long ll;
int main(){
	int n, k, x[50], y[50], _x[50], _y[50];
	cin>>n>>k;
	for(int i=0;i<n;i++){
		cin>>x[i]>>y[i];
		_x[i] = x[i];
		_y[i] = y[i];
	} 
	sort(_x, _x+n); sort(_y, _y+n);
	ll area = 1ll*(_x[n-1]-_x[0])*(_y[n-1]-_y[0]);
	//cout<<area<<endl;
	for(int xi=0;xi<n;xi++){
		for(int xj=0;xj<n;xj++){
			for(int yi=0;yi<n;yi++){
				for(int yj=0;yj<n;yj++){
 
					int cnt=0;
 
					ll lx = _x[xi], rx = _x[xj],
					   by = _y[yi], uy = _y[yj]; 
					for(int i=0;i<n;i++){
						if(lx<=x[i]&&x[i]<=rx&&by<=y[i]&&uy>=y[i])
							cnt++;
					}
					if(cnt>=k)
						area = min(area, 1ll*(rx-lx)*(uy-by));
				}
			}
		}
 
	}
	cout<<area<<endl;
}