Problem:
Score : 400 points

Problem Statement

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.

Sample Input 1

4 4
1 4
3 3
6 2
8 1

Sample Output 1

21

One rectangle that satisfies the condition with the minimum possible area has the following vertices: (1,1), (8,1), (1,4) and (8,4).

Its area is (8-1) × (4-1) = 21.

Sample Input 2

4 2
0 0
1 1
2 2
3 3

Sample Output 2

1

Sample Input 3

4 3
-1000000000 -1000000000
1000000000 1000000000
-999999999 999999999
999999999 -999999999

Sample Output 3

3999999996000000001

Watch out for integer overflows.

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.util.Scanner;

public class Main {
	public static void main(String[] args) {
		solve();
	}

	public static void solve() {
		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.nextInt();
			y[i] = sc.nextInt();
		}
		sc.close();

		long area = Long.MAX_VALUE;
		for (int x1 = 0; x1 < n; x1++) {
			for (int x2 = 0; x2 < n; x2++) {
				for (int y1 = 0; y1 < n; y1++) {
					for (int y2 = 0; y2 < n; y2++) {
						int count = 0;
						for (int idx = 0; idx < n; idx++) {
							if (x[idx] < x[x1] || x[idx] > x[x2] || y[idx] < y[y1] || y[idx] > y[y2]) {
								continue;
							} else {
								count++;
							}
						}
						if (count >= k) {
							area = Math.min(area, (x[x2] - x[x1]) * (y[y2] - y[y1]));
						}
					}
				}
			}
		}
		System.out.println(area);
	}
}