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 JAVA):

Solution:
import java.util.*;
public class Main{
  public static void main(String[] args){
    Scanner sc = new Scanner(System.in);
    int n = sc.nextInt();
    int k = sc.nextInt();
    long[] x = new long[n];
    long[] y = new long[n];
    for(int i=0;i<n;i++){
      x[i]=sc.nextLong();
      y[i]=sc.nextLong();
    }
    long num = (long)Math.pow(10,18)*4;
    for(int i=0;i<n;i++){
      for(int j=0;j<n;j++){
        for(int m=0;m<n;m++){
          for(int u=0;u<n;u++){
            long minX = Math.min(Math.min(x[i],x[u]),Math.min(x[j],x[m]));
            long minY = Math.min(Math.min(y[i],y[u]),Math.min(y[j],y[m]));
            long maxX = Math.max(Math.max(x[i],x[u]),Math.max(x[j],x[m]));
            long maxY = Math.max(Math.max(y[i],y[u]),Math.max(y[j],y[m]));
            if(minX==maxX||minY==maxY)continue;
            int cnt=0;
            for(int l=0;l<n;l++){
              if(minX<=x[l]&&x[l]<=maxX&&minY<=y[l]&&y[l]<=maxY)cnt++;
            }
            if(cnt>=k)num = Math.min(num,(maxX-minX)*(maxY-minY));
          }
        }
      }
    }
    System.out.println(num);
  }
}