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 <utility>
#include <limits.h>
#include <algorithm>
using namespace std;
 
int N,K;
int main(){
	cin >> N >> K;
	vector<int> X(N,0),Y(N,0);
	vector<int> x,y;
	for(int i=0;i<N;i++){
		cin >> X[i] >> Y[i];
		x.push_back(X[i]);
		y.push_back(Y[i]);
	}
	sort(x.begin(),x.end());
	sort(y.begin(),y.end());
	long long ans = 1LL*(x[N-1]-x[0])*(y[N-1]-y[0]);
	for(int xi=0;xi<N;xi++){
		for(int xj=xi+1;xj<N;xj++){
			for(int yi=0;yi<N;yi++){
				for(int yj=yi+1;yj<N;yj++){
					int num = 0;
					long long lx = x[xi],rx = x[xj];
					long long by = y[yi],uy = y[yj];
					for(int i=0;i<N;i++){
						if(lx<=X[i] && X[i]<=rx && by<=Y[i] && Y[i]<=uy) num++;
					}
					if(num>=K) ans = min(ans,1LL*(rx-lx)*(uy-by));
				}
			}
		}
	}
	cout << ans << endl;
}