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;
typedef struct{
    long x;
    long y;
} ax;
int main(){
    int n,K; cin>>n>>K;
    vector<ax> v(n);
    for(int i=0;i<n;i++){
        long x,y; cin>>x>>y;
        v[i].x=x,v[i].y=y;
    }
    unsigned long min=-1;
    for(int i=0;i<n;i++){
        for(int j=0;j<n;j++){
            for(int k=0;k<n;k++){
                for(int l=0;l<n;l++){
                    int count=0;
                    for(int m=0;m<n;m++){
                        if(v[m].y>=v[i].y&&v[m].y<=v[j].y&&v[m].x<=v[k].x&&v[m].x>=v[l].x)
                            count++;
                    }
                    unsigned long area=abs(v[i].y-v[j].y)*abs(v[k].x-v[l].x);
                    if(count>=K&&area<min)
                        min=area;
                }
            }
        }
    }
    cout<<min;
}