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>
using namespace std;
int n,k,cnt;
long long ans=5e18,x[60],y[60];
int main(){
    cin>>n>>k;
    for(int i=0;i<n;i++)cin>>x[i]>>y[i];
    for(int a=0;a<n;a++){
        for(int b=0;b<n;b++){
            if(x[b]<x[a])continue;
            for(int c=0;c<n;c++){
                for(int d=0;d<n;d++){
                    if(y[d]<y[c])continue;
                    cnt=0;
                    for(int i=0;i<n;i++)if(x[a]<=x[i]&&x[i]<=x[b]&&y[c]<=y[i]&&y[i]<=y[d])cnt++;
                    if(cnt>=k)ans=min(ans,(x[b]-x[a])*(y[d]-y[c]));
                }
            }
        }
    }
    cout<<ans<<endl;
}