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;long long x[50],y[50];
  cin >>n>>k;
  for (int i=0;i<n;i++){
    cin >>x[i]>>y[i];
  }
  long long ans = 9223372036854775807;
  for (int i1=0;i1<n;i1++){
    for (int i2=0;i2<n;i2++){
      for (int i3=0;i3<n;i3++){
        for (int i4=0;i4<n;i4++){
          int l = 0;
          for (int j=0;j<n;j++){
            if (x[i1]<=x[j] && x[j]<=x[i2] && y[i3]<=y[j] && y[j]<=y[i4]){
              l++;
            }
          if (l==k){
            ans = min (ans, abs((x[i1] - x[i2]) * (y[i3] -y[i4])));
  }
  }
  }
  }
  }}
  cout <<ans<<endl;}