Problem:
Score : 400 points

Problem Statement

There is a bar of chocolate with a height of H blocks and a width of W blocks.
Snuke is dividing this bar into exactly three pieces.
He can only cut the bar along borders of blocks, and the shape of each piece must be a rectangle.

Snuke is trying to divide the bar as evenly as possible.
More specifically, he is trying to minimize S_{max} - S_{min}, where S_{max} is the area (the number of blocks contained) of the largest piece, and S_{min} is the area of the smallest piece.
Find the minimum possible value of S_{max} - S_{min}.

Constraints

2 ≤ H, W ≤ 10^5

Input

Input is given from Standard Input in the following format:

H W

Output

Print the minimum possible value of S_{max} - S_{min}.

Sample Input 1

3 5

Sample Output 1

0

In the division below, S_{max} - S_{min} = 5 - 5 = 0.

Sample Input 2

4 5

Sample Output 2

2

In the division below, S_{max} - S_{min} = 8 - 6 = 2.

Sample Input 3

5 5

Sample Output 3

4

In the division below, S_{max} - S_{min} = 10 - 6 = 4.

Sample Input 4

100000 2

Sample Output 4

1

Sample Input 5

100000 100000

Sample Output 5

50000

Solution in Ruby (2.3.3) (judge verdict: Wrong Answer)

h,w = gets.split.map(&:to_i)
total = h*w
ans = Float::INFINITY

if h % 3 == 0
  puts 0
  exit
elsif w % 3 == 0
  puts 0
  exit
end

h.times do |i|
  rem = h - (i+1)
  a = (i+1) * w
  if w % 2 == 0
    b = (w / 2) * rem
    c = (w / 2) * rem
  else
    b = (w / 2) * rem
    c = (w / 2 + 1) * rem
  end

  tmp = [a,b,c].sort
  ans = [ans, tmp[-1] - tmp[0]].min
end

w.times do |i|
  rem = w - (i+1)
  a = (i+1) * h
  if h % 2 == 0
    b = (h / 2) * rem
    c = (h / 2) * rem
  else
    b = (h / 2) * rem
    c = (h / 2 + 1) * rem
  end

  tmp = [a,b,c].sort
  ans = [ans, tmp[-1] - tmp[0]].min
end

puts ans