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 ll long long
int main(){
  ll n,m;
  cin>>n>>m;
  ll x[51],y[51];
  ll xx[51],yy[51];
  for(int i=0;i<n;i++){
    cin>>x[i]>>y[i];
    xx[i]=x[i];
    yy[i]=y[i];
  }
  sort(xx,xx+n);
  sort(yy,yy+n);
  ll ans=4*1e18;
  for(int i=0;i<n;i++){
    for(int j=i+1;j<n;j++){
      for(int k=0;k<n;k++){
	for(int l=k+1;l<n;l++){
	  int cnt=0;
	  for(int a=0;a<n;a++){
	    if(x[a]<xx[i]||xx[j]<x[a])continue;
	    if(y[a]<yy[k]||yy[l]<y[a])continue;
	    cnt++;
	  }
	  if(cnt>=m)
	    ans=min(ans,(xx[j]-xx[i])*(yy[l]-yy[k]));
	}
      }
    }
  }
  cout<<ans<<endl;
  return 0;
}