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.util.*;

// AGC 28-A
// https://beta.atcoder.jp/contests/agc028/tasks/agc028_a

public class Main {

	public static void main(String[] args) {
		Scanner in = new Scanner(System.in);

		long W = in.nextLong();
		long H = in.nextLong();
		long x = in.nextLong();
		long y = in.nextLong();
		
		if ((x == W && y == H) || (x == W && y == 0) || (x == 0 && y == H) || (x == 0 && y == 0)) {
			out(String.format("%f 0", W * H / 2.0));
		} else {
			long tate = Math.min(x * H, H * (W - x));
			long yoko = Math.min(W * y, W * (H - y));
			
			out(String.format("%d %d", Math.max(tate, yoko), tate == yoko ? 1 : 0));
		}
		
	}
	
	public static double calculate(double base, double n) {
        return Math.pow(Math.E, Math.log(base)/n);
    }
	
	public static int partition(int[] nums, int low, int high) { // [1,2], 0, 1
		// Pick the first element as pivot
		// int pivot = nums[low]; // 1
		//
		// int left = low + 1; // 2
		// int right = high; // 1
		//
		//
		// while (left <= right) { // This equal to is important to move right
		// cursor left cursor correct position
		// if (nums[left] <= pivot) {
		// left++;
		// continue;
		// }
		// if (pivot <= nums[right]) {
		// right--;
		// continue;
		// }
		// int tmp = nums[left];
		// nums[left] = nums[right];
		// nums[right] = tmp;
		// }
		// int tmp = nums[low];
		// nums[low] = nums[right];
		// nums[right] = tmp;
		//
		// return right;

		// Pick the last element as pivot
		int pivot = nums[high];

		int left = low;
		int right = high - 1;

		while (left <= right) {
			if (nums[left] <= pivot) {
				
				left++;
				continue;
			}
			if (pivot <= nums[right]) {
				right--;
				continue;
			}
			int tmp = nums[left];
			nums[left] = nums[right];
			nums[right] = tmp;
		}
		int tmp = nums[high];
		nums[high] = nums[left];
		nums[left] = tmp;

		return left;
	}

	// Pivot is the first element
	public static int partitionFront(int[] nums, int low, int high) {
		int pivot = nums[low];

		int left = low + 1;

		while (left <= high) {
			// Increment left until it reaches the element greater than pivot
			while (left <= high && nums[left] <= pivot)
				left++;
			while (left <= high && nums[high] >= pivot)
				high--;

			if (left < high) {
				int tmp = nums[left];
				nums[left] = nums[high];
				nums[high] = tmp;
			}
		}
		int tmp = nums[low];
		nums[low] = nums[high];
		nums[high] = tmp;

		return high;
	}

	// Pivot is the last element
	public static int partitionBack(int[] nums, int low, int high) {
		int pivot = nums[high];

		int right = high - 1;

		while (low <= right) {
			// Increment low until it is greater than pivot
			while (low <= right && nums[low] <= pivot)
				low++;
			// Decrement right until it is less than pivot
			while (low <= right && nums[right] >= pivot)
				right--;

			if (low < right) {
				int tmp = nums[low];
				nums[low] = nums[right];
				nums[right] = tmp;
			}
		}

		int tmp = nums[low];
		nums[low] = nums[high];
		nums[high] = tmp;

		return low;
	}

	public static void out(Object o) {
		System.out.println(o);
	}

	public static void print(Object o) {
		System.out.print(o);
	}

	public static void printNumArray(int[] nums) {
		System.out.printf("[");
		for (int i = 0; i < nums.length; i++) {
			System.out.printf("%d%s", nums[i], i != nums.length - 1 ? ", " : "");
		}
		System.out.println("]");
	}

	public static void printNumArray(long[] nums) {
		System.out.printf("[");
		for (int i = 0; i < nums.length; i++) {
			System.out.printf("%d%s", nums[i], i != nums.length - 1 ? ", " : "");
		}
		System.out.println("]");
	}

	public static void printDoubleArray(double[] nums) {
		System.out.printf("[");
		for (int i = 0; i < nums.length; i++) {
			System.out.printf("%f%s", nums[i], i != nums.length - 1 ? ", " : "");
		}
		System.out.println("]");
	}

	public static void printDoubleList(List<List<Integer>> nums) {
		for (int i = 0; i < nums.size(); i++) {
			printNumList(nums.get(i));
		}
	}

	public static void printNumList(List<Integer> nums) {
		System.out.printf("[");
		for (int i = 0; i < nums.size(); i++) {
			System.out.printf("%d%s", nums.get(i), i != nums.size() - 1 ? ", " : "");
		}
		System.out.println("]");
	}

	public static void printStringList(List<String> list) {
		System.out.printf("[");
		for (int i = 0; i < list.size(); i++) {
			System.out.printf("%s%s", list.get(i), i != list.size() - 1 ? ", " : "");
		}
		System.out.println("]");
	}

	public static void printStringArray(String[] arr) {
		print("[");
		for (int i = 0; i < arr.length; i++) {
			print(String.format("%s%s", arr[i], i != arr.length - 1 ? ", " : ""));
		}
		out("]");
	}

	public static void printStringListOfStringList(List<List<String>> list) {
		for (int i = 0; i < list.size(); i++) {
			printStringList(list.get(i));
		}
	}

	public static void printNumListOfNumList(List<List<Integer>> num) {
		for (int i = 0; i < num.size(); i++) {
			printNumList(num.get(i));
		}
	}
	
	public static void printNumListOfNumArray(List<int[]> list) {
		for (int i = 0; i < list.size(); i++) {
			printNumArray(list.get(i));
		}
	}

	public static void printNum2DArray(int[][] map) {
		for (int i = 0; i < map.length; i++) {
			for (int j = 0; j < map[i].length; j++) {
				System.out.printf("%2d ", map[i][j]);
			}
			System.out.println();
		}
	}

	public static void printNum2DArray(long[][] map) {
		for (int i = 0; i < map.length; i++) {
			for (int j = 0; j < map[i].length; j++) {
				System.out.printf("%2d ", map[i][j]);
			}
			System.out.println();
		}
	}
	
	public static void printCharArray(char[] arr) {
		print("[");
		for (int i = 0; i < arr.length; i++) {
			System.out.printf("%c%s", arr[i], i == arr.length - 1 ? "" : ", ");
		}
		out("]");
	}

	public static void printChar2DArray(char[][] map) {
		for (char[] arr : map) {
			for (char c : arr) {
				print(String.format("%c ", c));
			}
			out("");
		}
	}

	public static void printBoolean2DArray(boolean[][] map) {
		for (int i = 0; i < map.length; i++) {
			for (int j = 0; j < map[0].length; j++) {
				print(map[i][j] ? "T " : "F ");
			}
			out("");
		}
	}

	public static void printListNode(ListNode node) {
		boolean first = true;
		while (node != null) {
			if (!first) {
				print("->");
			}
			print(node.val);
			node = node.next;
			first = false;
		}
	}

	public static void printStringSet(Set<String> set) {
		for (String s : set) {
			out(s);
		}
	}

	/**
	 * Receives an integer and print in numBits from the right
	 * 
	 * @param n
	 * @param numBits
	 */
	public static void printBinary(int n, int numBitsFromRight) {
		String s = "";
		for (int i = numBitsFromRight - 1; i >= 0; i--) {
			s += (n & (1 << i)) > 0 ? "1" : "0";
		}
		out(s);
	}

	// Taken from
	// https://www.geeksforgeeks.org/c-program-find-gcd-hcf-two-numbers/
	public static long gcd(long a, long b) {
		if (b == 0) {
			return a;
		}
		return gcd(b, a % b);
	}
	
	public static int gcd(int a, int b) {
		if (b == 0) {
			return a;
		}
		return gcd(b, a % b);
	}

	public static long lcm(long a, long b) {
		return a * b / gcd(a, b);
	}
	
	public static int lcm(int a, int b) {
		return a * b / gcd(a, b);
	}
}

class TreeNode {
	int val;
	TreeNode left;
	TreeNode right;

	TreeNode(int x) {
		val = x;
	}
}

class CustomClass {
	String to;
	double dist;

	public CustomClass(String to, double dist) {
		this.to = to;
		this.dist = dist;
	}
}

class TreeDrawer {
	public static String treeNodeToString(TreeNode root) {
		if (root == null) {
			return "[]";
		}

		String output = "";
		Queue<TreeNode> nodeQueue = new LinkedList<>();
		nodeQueue.add(root);
		while (!nodeQueue.isEmpty()) {
			TreeNode node = nodeQueue.remove();

			if (node == null) {
				output += "null, ";
				continue;
			}

			output += String.valueOf(node.val) + ", ";
			nodeQueue.add(node.left);
			nodeQueue.add(node.right);
		}
		return "[" + output.substring(0, output.length() - 2) + "]";
	}

	public static TreeNode stringToTreeNode(String input) {
		input = input.trim();
		input = input.substring(1, input.length() - 1);
		if (input.length() == 0) {
			return null;
		}

		String[] parts = input.split(",");
		String item = parts[0];
		TreeNode root = new TreeNode(Integer.parseInt(item));
		Queue<TreeNode> nodeQueue = new LinkedList<>();
		nodeQueue.add(root);

		int index = 1;
		while (!nodeQueue.isEmpty()) {
			TreeNode node = nodeQueue.remove();

			if (index == parts.length) {
				break;
			}

			item = parts[index++];
			item = item.trim();
			if (!item.equals("null")) {
				int leftNumber = Integer.parseInt(item);
				node.left = new TreeNode(leftNumber);
				nodeQueue.add(node.left);
			}

			if (index == parts.length) {
				break;
			}

			item = parts[index++];
			item = item.trim();
			if (!item.equals("null")) {
				int rightNumber = Integer.parseInt(item);
				node.right = new TreeNode(rightNumber);
				nodeQueue.add(node.right);
			}
		}
		return root;
	}

	public static void prettyPrintTree(TreeNode node, String prefix, boolean isLeft) {
		if (node == null) {
			System.out.println("Empty tree");
			return;
		}

		if (node.right != null) {
			prettyPrintTree(node.right, prefix + (isLeft ? "│   " : "    "), false);
		}

		System.out.println(prefix + (isLeft ? "└── " : "┌── ") + node.val);

		if (node.left != null) {
			prettyPrintTree(node.left, prefix + (isLeft ? "    " : "│   "), true);
		}
	}

	public static void draw(TreeNode node) {
		prettyPrintTree(node, "", true);
	}
}

class Interval {
	int start;
	int end;

	Interval() {
		start = 0;
		end = 0;
	}

	Interval(int s, int e) {
		start = s;
		end = e;
	}
}

class ListNode {
	int val;
	ListNode next;

	ListNode(int x) {
		val = x;
	}
}