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 <iostream>
#include <algorithm>
#include <vector>
using namespace std;
int main(void){
  int n,k,i,i1,i2,i3,i4,l,x[55],y[55],p;
  long s,ans=5e18;
  vector<int> xl,yl;
  cin >> n >> k;
  for (i=0;i<n;i++){
    cin >> x[i] >> y[i];
    xl.push_back(x[i]);
    yl.push_back(y[i]);
  }
  sort(xl.begin(),xl.end());
  sort(yl.begin(),yl.end());
  for (i1=0;i1<n-1;i1++) for (i2=i1+1;i2<n;i2++) for (i3=0;i3<n-1;i3++) for (i4=i3+1;i4<n;i4++){
    p=0;
    for (l=0;l<n;l++) if (x[l]>=xl[i1] && x[l]<=xl[i2] && y[l]>=yl[i3] && y[l]<=yl[i4])
      p++;
    s=(long)(xl[i2]-xl[i1])*(yl[i4]-yl[i3]);
    if (p>=k && ans>s) ans=s;
  }
  cout << ans << endl;
  return 0;
}