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;

#define rep(i,n) for(int i=0;i<n;i++)

int main(){
 long n,k;
  cin >> n >> k;
  vector<long> x(n),y(n);
  vector<long> xary,yary;
  rep(i,n) {
    cin >> x[i] >> y[i];
     xary.push_back(x[i]);
     yary.push_back(y[i]);
  }
  sort(xary.begin(),xary.end());
  sort(yary.begin(),yary.end());
  
  long res=(xary[n-1]-xary[0])*(yary[n-1]-yary[0]);
  
  rep(xi,n){
   for(int xj=xi+1;xj<n;xj++){
    rep(yi,n){
       for(int yj=yi+1;yj<n;yj++){
          long num=0; 
         
         rep(i,n){
         if(xary[xi]<=x[i]&&x[i]<=xary[xj]&&yary[yi]<=y[i]&&y[i]<=yary[yj]) num++;
         }
         
         if(num>=k) res=min(res,(xary[xj]-xary[xi])*(yary[yj]-yary[yi]));
       }   
       }    
    }
   }   
  
  cout << res << endl;
  
}