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 n,k,ans=4000000000000000010;
  cin >> n >> k;
  vector<vector<long>> xy(n,vector<long>(2));
  for(long i=0;i<n;i++) cin >> xy[i][0] >> xy[i][1];
  sort(xy.begin(),xy.end());

  for(long i=0;i<n;i++) {
    for(long j=i+k-1;j<n;j++) {
      vector<long> y;
      for(long i2=i;i2<=j;i2++) y.push_back(xy[i2][1]);
      sort(y.begin(),y.end());
      for(long i2=0;i2<=j-i+1-k;i2++) ans=min(ans,(xy[j][0]-xy[i][0])*(y[i2+k-1]-y[i2]));
    }
  }
  cout << ans << endl;
}