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)
def find_area height, width, num
  wants = (height * width).to_f / num
  areas = []
  (1..height).each do |h|
    areas.push(h*width)
  end
  tmp = []
  areas.each{|area| tmp.push (area.to_f - wants).abs}
  s = areas[tmp.index(tmp.min)]
  h_new = height - areas.index(s) - 1
  w_new = width
  areas = []
  (1..width).each do |w|
    areas.push(height*w)
  end
  tmp = []
  areas.each{|area| tmp.push (area.to_f - wants).abs}
  temp = areas[tmp.index(tmp.min)]
  if (temp - wants).abs < (s - wants).abs
    s = temp
    w_new = width - areas.index(s) - 1
    h_new = height
  end
  return h_new, w_new, s
end
a = []
h_new, w_new, a[0] = find_area H, W, 3
h_new, w_new, a[1] = find_area h_new, w_new, 2
a[2] = h_new * w_new
puts a.max - a.min