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 C# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Linq;
#if !DEBUG
    using System.IO;
#endif


public class Program {
    public static void Main() {
        #region SetAutoFlushIsFalse
#if !DEBUG
        var sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
        Console.SetOut(sw);
#endif
        #endregion

        var arr = ReadLib.ReadAsIntArray();
        var w = arr[0];
        var h = arr[1];
        var x = arr[2];
        var y = arr[3];

        var s = (double)(w * h) / 2d;

        decimal centerx = w / 2;
        decimal centery = h / 2;
        var multi = centerx == x && centery == y ? 1 : 0;

        Console.WriteLine($"{s} {multi}");

        #region Flush
#if !DEBUG
        Console.Out.Flush();
        sw.Close();
#endif
        #endregion
    }
}

static class ReadLib {
    public static long ReadAsLong() {
        return long.Parse(Console.ReadLine());
    }

    public static int ReadAsInt() {
        return int.Parse(Console.ReadLine());
    }

    public static int[] ReadAsIntArray(int step = 0) {
        return Console.ReadLine().Split(' ').Select(s => int.Parse(s) + step).ToArray();
    }

    public static long[] ReadAsLongArray(int step = 0) {
        return Console.ReadLine().Split(' ').Select(s => long.Parse(s) + step).ToArray();
    }

    public static ulong[] ReadAsULongArray() {
        return Console.ReadLine().Split(' ').Select(s => ulong.Parse(s)).ToArray();
    }

    public static string[] ReadAsStringArray() {
        return Console.ReadLine().Split(' ');
    }

    public static int[] ReadNTimesAsInt(int n, int step = 0) {
        return Enumerable.Range(1, n).Select(s => int.Parse(Console.ReadLine()) + step).ToArray();
    }

    public static int[][] ReadNTimesAsIntArray(int n, int step = 0) {
        return Enumerable.Range(1, n).Select(s => ReadAsIntArray(step)).ToArray();
    }

}

static class MyMath {
    /// <summary>階乗</summary>
    public static long Factorial(int n) {
        if (n == 0) {
            return 1;
        }

        return Permutation(n, 0);
    }

    public static long Permutation(int n, int k) {
        return Enumerable.Range(0, n - k).Select(i => n - i).Aggregate(1, (b, i) => b * i);
    }

    /// <summary>nCr, 組み合わせ</summary>
    public static long Combination(int n, int r) {
        if (r == 0) {
            return 1;
        }
        // 分子
        var moleculeArr = Enumerable
            .Range(0, Math.Min(n - r, r))
            .Select(i => n - i)
            .ToArray();
        var moleculeArrLength = moleculeArr.Length;
        // 分母
        var denominatorArr = Enumerable
            .Range(1, Math.Max(n - r, r))
            .ToArray();

        for (var m = 0; m < moleculeArrLength; m++) {
            while (true) {
                var mVal = moleculeArr[m];
                var gcds = denominatorArr.Select(b => Gcd(mVal, b));
                var maxGcd = gcds.Max();
                var maxI = gcds.ToList().IndexOf(maxGcd);

                if (maxGcd == 1) {
                    break;
                }

                denominatorArr[maxI] /= maxGcd;
                moleculeArr[m] /= maxGcd;
            }
        }

        return FullPower(moleculeArr);
    }

    #region FullPower
    /// <summary>総乗、π</summary>
    public static long FullPower(IEnumerable<long> vs) {
        return vs.Aggregate(1L, (a, b) => a * b);
    }

    public static long FullPower(IEnumerable<int> vs) {
        return vs.Aggregate(1L, (a, b) => a * b);
    }
    #endregion

    /// <summary>最大公約数</summary>
    public static int Gcd(long item1, long item2) {
        var a = Math.Max(item1, item2);
        var b = Math.Min(item1, item2);

        while (true) {
            var mod = a % b;
            if (mod == 0) {
                break;
            }

            a = b;
            b = mod;
        }
        return (int)b;
    }

    /// <summary>約分。最大公約数で割ったものを返す。</summary>
    public static Tuple<long, long> DeviedByGcd(long item1, long item2) {
        var gcd = Gcd(item1, item2);
        return new Tuple<long, long>(item1 / gcd, item2 / gcd);
    }
}