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() {
  int n, K;
  cin>>n>>K;

  int x[n], y[n];
  for (int i=0; i<n; i++) {
    cin>>x[i]>>y[i];
  }
  long long ans = 1e18 * 4;
  for (int i=0; i<n; i++) {
    long long x1 = x[i];
    for (int j=0; j<n; j++) {
      long long x2 = x[j];
      if (x2 <= x1) continue;
      for (int k=0; k<n; k++) {
        long long y1 = y[k];
        for (int l=0; l<n; l++) {
          long long y2 = y[l];
          if (y2 <= y1) continue;
          int cnt = 0;
          for (int m=0; m<n; m++) {
            if (x[m] >= x1 && x[m] <= x2 && y[m] >= y1 && y[m] <= y2) ++cnt;
          }
          if (cnt >= K) {
            ans = min(ans, (x2 - x1) * (y2 - y1));
          }
        }
      }
    }
  }
  cout<<ans<<endl;
}