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 long long ll;
int main(){
  ll n,K;cin >> n >> K;
  vector<ll> x(n),y(n);
  for(int i=0;i<n;i++){
    cin >> x[i] >> y[i];
  }
  ll ans=5e18;
  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++){
          ll u=x[i],v=x[j],w=y[k],z=y[l];
          int cnt=0;
          for(int m=0;m<n;m++){
            if(min(u,v)<=x[m]&&x[m]<=max(u,v)&&min(w,z)<=y[m]&&y[m]<=max(w,z)){
              cnt++;
            }
          }
          if(cnt>=K){
            ans=min(ans,abs(v-u)*abs(z-w));
          }
        }
      }
    }
  }
  cout << ans << endl;
}