Problem:
Score : 300 points

Problem Statement

There is a rectangle in a coordinate plane. The coordinates of the four vertices are (0,0), (W,0), (W,H), and (0,H).
You are given a point (x,y) which is within the rectangle or on its border. We will draw a straight line passing through (x,y) to cut the rectangle into two parts. Find the maximum possible area of the part whose area is not larger than that of the other. Additionally, determine if there are multiple ways to cut the rectangle and achieve that maximum.

Constraints

1 \leq W,H \leq 10^9

0\leq x\leq W

0\leq y\leq H

All values in input are integers.

Input

Input is given from Standard Input in the following format:

W H x y

Output

Print the maximum possible area of the part whose area is not larger than that of the other, followed by 1 if there are multiple ways to cut the rectangle and achieve that maximum, and 0 otherwise.

The area printed will be judged correct when its absolute or relative error is at most 10^{-9}.

Sample Input 1

2 3 1 2

Sample Output 1

3.000000 0

The line x=1 gives the optimal cut, and no other line does.

Sample Input 2

2 2 1 1

Sample Output 2

2.000000 1

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.util.Scanner;

public class Main {
    public static void main(String[] args) {
        Scanner scan = new Scanner(new BufferedReader(new InputStreamReader(System.in)));
        long W = scan.nextLong();
        long H = scan.nextLong();
        long x = scan.nextLong();
        long y = scan.nextLong();
        if (is_corner(W, H, x, y)) {
            double area = ((double) W * H) / 2;
            System.out.println(String.format("%.10f",area) + " " + 0);
            return;
        }
        if (x == 0 || x == W) {
            double area1 = y * W;
            double area2 = (H - y) * W;
            double area = Math.min(area1,area2);
            System.out.println(String.format("%.10f",area) + " " + 0);
            return;
        }
        if (y == 0 || y == H) {
            double area1 = x * H;
            double area2 = (W - x) * H;
            double area = Math.min(area1,area2);
            System.out.println(String.format("%.10f",area) + " " + 0);
            return;
        }
        double area11 = x * H;
        double area12 = (W - x) * H;
        double area1 = Math.min(area11, area12);
        double area21 = y * W;
        double area22 = (H - y) * W;
        double area2 = Math.min(area21, area22);
        double area = Math.max(area1, area2);
        String multiple = area1 == area2 ? "1" : "0";
        if (on(W, H, x, y)) {
            double area3 = ((double) W * H) / 2;
            if (area < area3) {
                area = area3;
                multiple = "0";
            } else if (area == area3) {
                multiple = "1";
            }
        }
        System.out.println(String.format("%.10f",area) + " " + multiple);

    }
    public static boolean on(long W, long H, long x, long y) {
        if (H * x - W * y == 0) {
            return true;
        }
        if (H * x + W * y - H * W == 0) {
            return true;
        }
        return false;
    }
    public static boolean is_corner(long W, long H, long x, long y) {
        if (x == 0 && y == 0) {
            return true;
        }
        if (x == 0 && y == H) {
            return true;
        }
        if (x == W && y == 0) {
            return true;
        }
        if (x == W && y == H) {
            return true;
        }
        return false;
    }
}