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 <bits/stdc++.h>
using namespace std;

int n,k;
long long X[50],Y[50],X2[50],Y2[50],ans;

int main(){
	cin>>n>>k;
	for(int i=0;i<n;i++){
		cin>>X[i]>>Y[i];
		X2[i]=X[i];
		Y2[i]=Y[i];
	}
	sort(X2,X2+n);
	sort(Y2,Y2+n);
	
	ans=(X2[n-1]-X2[0])*(Y2[n-1]-Y2[0]);
	
	for(int i=0;i<n-1;i++){
		for(int j=i+1;j<n;j++){
			for(int ii=0;ii<n-1;ii++){
				for(int jj=ii+1;jj<n;jj++){
					int cnt=0;
					for(int q=0;q<n;q++){
						if(X2[i]<=X[q] and X[q]<=X2[j] and Y2[ii]<=Y[q] and Y[q]<=Y2[jj]){
							cnt++;
						}
					}
					if(cnt>=k){
						ans=min(ans,(X2[j]-X2[i])*(Y2[jj]-Y2[ii]));
					}
				}
			}
		}
	}
	cout<<ans<<endl;
}