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 INF 5e+19
#define ll long long
int main(){
  ll ans = INF;
  int n,k;
  cin >> n >> k;
  ll x[n], y[n];
  for(int i=0;i<n;i++){
    cin >> x[i] >> y[i];
  }
  for(int rx=0;rx<n;rx++){
    for(int lx=0;lx<n;lx++){
      for(int uy=0;uy<n;uy++){
        for(int dy=0;dy<n;dy++){
          ll xmax = max(x[lx], x[rx]);
          ll xmin = min(x[lx], x[rx]);
          ll ymax = max(y[uy], y[dy]);
          ll ymin = min(y[uy], y[dy]);
          int cnt = 0;
          for(int s=0;s<n;s++){
            if(xmax>=x[s] && xmin<=x[s] && ymax >= y[s] && ymin <= y[s]){
              cnt++;
            }
          }
          if(cnt >= k)
            ans = min(ans, (xmax-xmin)*(ymax-ymin));
        }
      }
    }
  }
  cout << ans << endl;
}