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.Scanner;

public class Main {
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		int k = sc.nextInt();

		long[][] xy = new long[n][2];
		for (int i = 0; i < n; i++) {
			xy[i][0] = sc.nextInt();
			xy[i][1] = sc.nextInt();
		}

		long answer = Long.MAX_VALUE;

		for (int i = 0; i < n; i++) {
			for (int j = 0; j < n; j++) {
				for (int l = 0; l < n; l++) {
					for (int m = 0; m < n; m++) {
						long lx = xy[i][0];
						long hx = xy[j][0];
						long ly = xy[l][1];
						long hy = xy[m][1];
						if (lx > hx || ly > hy) continue;
						int count = 0;
						for (int o = 0; o < n; o++) {
							if (xy[o][0] >= lx && xy[o][0] <= hx
									&& xy[o][1] >= ly && xy[o][1] <= hy) {
								count++;
							}
						}
						if (count >= k) answer = Math.min(answer, (hx - lx) * (hy - ly));
					}
				}
			}
		}

		System.out.println(answer);
	}
}