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 <algorithm>
#include <queue>
#include <vector>
using namespace std;
typedef long long ll;
typedef struct pair<int,int> P;
typedef struct pair<int,P> P2;

const ll INF=1000000000000000001;
int main() {

	int n,k;
	ll x[50]={};
	ll y[50]={};

	cin>>n>>k;
	ll total=4000000000000000001;
	for(int i=0;i<n;++i)cin>>x[i]>>y[i];
	for(int i=0;i<n;i++){
		for(int j=0;j<n;j++){
			for(int o=0;o<n;o++){
				for(int l=0;l<n;l++){
					int t=0;
					ll x1=max(x[i],x[j]);
					ll x2=min(x[i],x[j]);
					ll y1=max(y[o],y[l]);
					ll y2=min(y[o],y[l]);
					for(int m=0;m<n;m++){
						if(((x[m]<=x1)&&(x[m]>=x2))&&((y[m]<=y1)&&(y[m]>=y2)))t++;
					}
					if(t>=k)total=min(total,(x1-x2)*(y1-y2));
				}
			}
		}
	}
	cout<<total<<endl;
	return 0;
}