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<bits/stdc++.h>
#include<boost/multiprecision/cpp_int.hpp>
using namespace std;
using namespace boost::multiprecision;
#define BEGIN ios_base::sync_with_stdio(false);cin.tie(NULL);cout.tie(NULL)
#define END return EXIT_SUCCESS
#define rep(I,N) for(auto I=0;I<(N);++I)
#define up(I,A,B) for(auto I=(A);I<=(B);++I)
#define dw(I,A,B) for(auto I=(A);I>=(B);--I)
#define all(C) (C).begin(),(C).end()
#define rall(C) (C).rbegin(),(C).rend()
#define ft first
#define sd second
#define mp make_pair
#define mt make_tuple
#define pf push_front
#define pb push_back
#define pt pop_front
#define pk pop_back
#define eb emplace_back
#define lb lower_bound
#define ub upper_bound
#define rs resize
template<class T> T count_bit(T p){
  if(typeid(p)==typeid(int))return __builtin_popcount(p);
  else if(typeid(p)==typeid(long))return __builtin_popcountl(p);
  else return __builtin_popcountll(p);
}
template<class T>inline bool chmax(T& a,T b){if(a<b){a=b;return true;}return false;}
template<class T>inline bool chmin(T& a,T b){if(a>b){a=b;return true;}return false;}
template<class T>inline void                                      in(T &p){cin>>p;}
template<class T1,class T2>inline void                            in(T1 &p1,T2 &p2){cin>>p1>>p2;}
template<class T1,class T2,class T3>inline void                   in(T1 &p1,T2 &p2,T3 &p3){cin>>p1>>p2>>p3;}
template<class T1,class T2,class T3,class T4>inline void          in(T1 &p1,T2 &p2,T3 &p3,T4 &p4){cin>>p1>>p2>>p3>>p4;}
template<class T1,class T2,class T3,class T4,class T5>inline void in(T1 &p1,T2 &p2,T3 &p3,T4 &p4,T5 &p5){cin>>p1>>p2>>p3>>p4>>p5;}
template<class T>inline void                                      ins(T &p){for_each(all(p),in<decltype(p[0])>);}
template<class T>inline void                             out(T p){cout<<p<<endl;}
template<class T1,class T2>inline void                   out(T1 p1,T2 p2){cout<<p1<<" "<<p2<<endl;}
template<class T1,class T2,class T3>inline void          out(T1 p1,T2 p2,T3 p3){cout<<p1<<" "<<p2<<" "<<p3<<endl;}
template<class T1,class T2,class T3,class T4>inline void out(T1 p1,T2 p2,T3 p3,T4 p4){cout<<p1<<" "<<p2<<" "<<p3<<" "<<p4<<endl;}
inline                                              void out(double p){printf("%.10f\n",p);}
template<class T>inline                             void outs(T p){for_each(all(p),out<decltype(p[0])>);}

inline void solve(void){
  double W,H,x,y,EPS=1e-10;
  in(W,H,x,y);
  printf("%.11f ",max(min(W*y,W*(H-y)),min(x*H,(W-x)*H)));
  if(abs(x-W/2)<EPS&&abs(y-H/2)<EPS)cout<<1<<endl;
  else cout<<0<<endl;
}
int main(int argc,char**argv){
  BEGIN;
  solve();
  END;
}