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 main(){
  long long int a,b,x[55]={0},y[55]={0};
  cin >> a >> b;
  
  for(int i=0;i<a;i++){
    cin >> x[i] >> y[i];
  }
  
  long long int  ans=9e18;
  
  for(int xi=0;xi<a;xi++){
    for(int xj=0;xj<a;xj++){
      for(int yi=0;yi<a;yi++){
        for(int yj=0;yj<a;yj++){
          long long int xa=x[xi],xb=x[xj],ya=y[yi],yb=y[yj];
          
          int res=0;
          for(int i=0;i<a;i++){
            if(min(xa,xb)<=x[i] && x[i]<=max(xa,xb)&& min(ya,yb)<=y[i] && y[i]<=max(ya,yb)){
              res++;
            }
          }
          
          if(res>=b){
            ans= min(ans,abs(xa-xb)*abs(ya-yb));
          }
        }
      }
    }
  }
  cout << ans << endl;
}