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)

l, r = gets.split.map(&:to_i)
if l > r
  w = l
  h = r
else
  w = r
  h = l
end

ss = []

if w % 3 == 0 || h % 3 == 0
  puts 0
  exit 0
end
if h == 1
  puts 1
  exit 0
elsif h == 2
  puts 1
  exit 0
end

min_diff = w*h

1.upto(w) do |left_w|
  ss = []
  right_w = w - left_w
  top_h = h / 2
  bottom_h = h - top_h

  ss << left_w * h
  ss << right_w * top_h
  ss << right_w * bottom_h
  
  diff = ss.max - ss.min
  min_diff = diff if min_diff > diff
end


# p [[left_w, h], [right_w, top_h], [right_w, bottom_h] ]

puts min_diff