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 N,K;
  cin >> N >> K;
  vector<long long> x(N),y(N),X(N),Y(N);
  for(int i=0;i<N;i++){cin >> x[i] >> y[i]; X[i]=x[i]; Y[i]=y[i];}
  sort(x.begin(),x.end());
  sort(y.begin(),y.end());
  long long ans=4000000000000000000;
  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++){
          long long cnt=0;
          for(int m=0;m<N;m++){
            if(x[i]<=X[m] && X[m]<=x[j] && y[k]<=Y[m] && Y[m]<=y[l]){cnt++;}
          }
          if(cnt>=K){ans=min(ans,(x[j]-x[i])*(y[l]-y[k]));}
        }
      }
    }
  }
  cout << ans << endl;
}