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(){
  int n, k;
  cin >> n >> k;
  ll x[n], y[n], sx[n], sy[n];
  for(int i=0; i<n; i++){
    cin >> x[i] >> y[i];
    sx[i] = x[i];
    sy[i] = y[i];
  }
  sort(sx, sx+n);
  sort(sy, sy+n);
  ll ans = (sx[n-1] - sx[0]) * (sy[n-1] - sy[0]);
  for(int xi=0; xi<n; xi++){
    for(int xis=xi+1; xis<n; xis++){
      for(int yi=0; yi<n; yi++){
        for(int yis=yi+1; yis<n; yis++){
          ll minx = sx[xi], maxx = sx[xis];
          ll miny = sy[yi], maxy = sy[yis];
          int cnt = 0;
          for(int j=0; j<n; j++){
            if(minx<=x[j]&&x[j]<=maxx&&miny<=y[j]&&y[j]<=maxy) cnt++;
          }
          if(cnt >= k) ans = min(ans, (maxx-minx)*(maxy-miny));
        }
      }
    }
  }
  cout << ans << endl;
  return 0;
}