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>

int n,k;
long long x[55],y[55];
long long cx[55],cy[55];
int main(){
  std::cin>>n>>k;
  for(int i=0;i<n;++i)
    std::cin>>x[i]>>y[i];
  
  std::copy(x,x+n,cx);
  std::copy(y,y+n,cy);
  std::sort(x,x+n);
  std::sort(y,y+n);
  
  long long ans=9223372036854775807;
  
  for(int xl=0;xl<n;++xl)
    for(int xr=xl+1;xr<n;++xr)
      for(int yl=0;yl<n;++yl)
        for(int yr=yl+1;yr<n;++yr){
          auto x1=x[xl],x2=x[xr];
          auto y1=y[yl],y2=y[yr];
          int num=0;
          for(int i=0;i<n;++i)
            if(x1<=cx[i]&&cx[i]<=x2&&y1<=cy[i]&&cy[i]<=y2)
              ++num;
          if(num>=k)
            ans=std::min(ans,(x2-x1)*(y2-y1));
        }
  std::cout<<ans<<std::endl;
  return 0;
}