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.Arrays;
import java.util.Scanner;
public class Main {
	public static void main(String[] args){
		Scanner sc = new Scanner(System.in);
		int N = Integer.parseInt(sc.next());
		int K = Integer.parseInt(sc.next());
		int[][] z = new int[N][2];
		int[] x = new int[N];
		int[] y = new int[N];
		for (int i = 0; i < N; i++) {
			z[i][0] = Integer.parseInt(sc.next());
			z[i][1] = Integer.parseInt(sc.next());
			x[i] = z[i][0];
			y[i] = z[i][1];
		}
		Arrays.sort(x);
		Arrays.sort(y);
		long ans = Long.MAX_VALUE;
		for (int i = 0; i < N; i++) {
			for (int j = i + 1; j < N; j++) {
				for (int k = 0; k < N; k++) {
					for (int l = k + 1; l < N; l++) {
						int count = 0;
						int left = x[i];
						int right = x[j];
						int down = y[k];
						int up = y[l];
						for (int c = 0; c < N; c++) {
							if (left <= z[c][0] && z[c][0] <= right && down <= z[c][1] && z[c][1] <= up)
								count++;
						}
						if (count >= K)
							ans = Math.min(ans, (long)(right - left) * (up - down));
					}
				}
			}
		}
		System.out.println(ans);
	}
}