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: Wrong Answer)

import java.util.ArrayList;
import java.util.List;
import java.util.Scanner;
import java.util.stream.IntStream;

public class Main {

	public static void main(String[] args) {
		try (Scanner scanner = new Scanner(System.in)) {
			int n = scanner.nextInt();
			int k = scanner.nextInt();
			List<Point> points = new ArrayList<>(n);
			IntStream.range(0, n).forEach(i -> points.add(new Point(scanner.nextInt(), scanner.nextInt())));
			long min = Long.MAX_VALUE;
			// x座標でソートする
			points.sort((p1, p2) -> p1.x - p2.x);
			for (int i = 0; i < n - k + 1; i++) {
				int minY = Integer.MAX_VALUE, maxY = Integer.MIN_VALUE;
				for (int j = i; j < i + k; j++) {
					minY = Math.min(minY, points.get(j).y);
					maxY = Math.max(maxY, points.get(j).y);
				}
				min = Math.min(min, ((long) (points.get(i + k - 1).x - points.get(i).x)) * (maxY - minY));
			}
			// y座標でソートする
			points.sort((p1, p2) -> p1.y - p2.y);
			for (int i = 0; i < n - k + 1; i++) {
				int minX = Integer.MAX_VALUE, maxX = Integer.MIN_VALUE;
				for (int j = i; j < i + k; j++) {
					minX = Math.min(minX, points.get(j).x);
					maxX = Math.max(maxX, points.get(j).x);
				}
				min = Math.min(min, ((long) (points.get(i + k - 1).y - points.get(i).y)) * (maxX - minX));
			}
			System.out.println(min);
		}
	}

	/**
	 * 座標を表すクラス
	 */
	private static class Point {
		int x;
		int y;

		Point(int x, int y) {
			super();
			this.x = x;
			this.y = y;
		}
	}
}