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 Ruby (2.3.3) (judge verdict: Runtime Error)

# util functions

# debug
$debugFlag = ( ARGV[0] != nil )
p "==== DEBUG MODE ====" if $debugFlag

def pd(str)
  p str if $debugFlag
end

def printd(str)
  print str if $debugFlag
end

# input
inputs = []
lc = 0
while l = $stdin.gets do
  if false
    inputs << l.chomp.split(" ").map(&:to_s)
  else
    inputs << l.chomp.split(" ").map(&:to_i)
  end
  lc += 1
end

aa = inputs[0][0]
bb = inputs[0][1]
uu = inputs[0][2]
vv = inputs[0][3]

if aa < bb
  ww = bb
  hh = aa
  uu, vv = vv, uu
else
  ww = aa
  hh = bb
end
xx = [uu, ww-uu].max
yy = [vv, hh-vv].max

# input check
if $debugFlag
  p "--- INPUT (begin) ---"
  inputs.each do |l_i|
    p l_i
  end
  p "--- INPUT (end) ---"
  print "\n"
end

# body
if $debugFlag
  p "aa=#{aa}"
  p "bb=#{bb}"
  p "uu=#{uu}"
  p "vv=#{vv}"
  p "ww=#{ww}"
  p "hh=#{hh}"    
  p "xx=#{xx}"
  p "yy=#{yy}"  
end

area = 0
flag = 0

if ((ww % 2 == 0) and (ww/2 == xx)) and ((hh % 2 == 0) and (hh/2 == yy))
  area = (ww*hh).to_f/2
  flag = 1
elsif !((ww % 2 == 0) and (ww/2 == xx)) and ((hh % 2 == 0) and (hh/2 == yy))
  area = (ww*hh).to_f/2
  if ww == hh
    flag = 1
  else
    flag = 0
  end
elsif ((ww % 2 == 0) and (ww/2 == xx)) and !((hh % 2 == 0) and (hh/2 == yy))
  area = (ww*hh).to_f/2
  if ww == hh
    flag = 1
  else
    flag = 0
  end
else
  aa = y.to_f/x.to_f
  aa_bound = hh.to_f/ww.to_f

  if aa > aa_bound
    area = (ww + ww - hh.to_f/aa)*hh/2
  elsif aa == aa_bound
    area = (ww*hh).to_f/2
  else
    area = ww*aa*ww/2
  end

  flag = 0
end

puts area
puts flag