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++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <iostream>
#include <vector>
#include <algorithm>
#include <queue>
#include <stack>
#include <math.h>
#include <map>
#include <time.h>
#include <iomanip>
#include <bitset>

using namespace std;

typedef long long ll;
typedef unsigned long long ull;
typedef pair<ll, ll> P;

#define pb push_back
#define rep(i, a, n) for(int i = (a); i < (n); i++)
#define dep(i, a, n) for(int i = (a); i >= (n); i--)
#define mod (ll)(1e9+7)
#define int ll

__attribute__((constructor))
void initial() {
  cin.tie(0);
  ios::sync_with_stdio(false);
}

signed main() {
  int w, h, x, y;
  cin >> w >> h >> x >> y;

  int k1 = min(x, w - x) * h;
  int k2 = min(y, h - y) * w;

  bool kx = false;
  bool ky = false;
  if(x == 0 || x == w) kx = true;
  if(y == 0 || y == h) ky = true;

  if(kx && ky) {
    cout << double(w * h) / 2 << " 1" << endl;
  }else {
    if(k1 == 0) cout << k2 << " ";
    else if(k2 == 0) cout << k1 << " ";
    else cout << max(k1, k2) << " ";
    if(k1 == k2) cout << '1' << endl;
    else cout << '0' << endl;
  }
}