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).sort # 常に W >= H であるものとする
answer = nil

if H % 3 == 0 || W % 3 == 0
  # 縦横どちらかが3で割れるならば3等分が可能ということなので答えは0になる
  answer = 0
else
  # 縦横どちらも3では割り切れない場合

  # まず長辺で分割するパターン
  w_cdds = []
  (-1..1).each do |num|
    temp = num + W/3
    w_cdds << temp if temp.between?(1, W-1)
  end
  # 1.step(W-1) do |x|
  w_cdds.each do |x|
    pieces = [x*H, (W-x)*(H/2), (W-x)*(H-(H/2))]
    answer = [answer, pieces.max - pieces.min].compact.min
  end

  # 次に短辺で分割するパターン
  h_cdds = []
  (-1..1).each do |num|
    temp = num + H/3
    h_cdds << temp if temp.between?(1, H-1)
  end
  # 1.step(H-1) do |y|
  h_cdds.each do |y|
    pieces = [y*W, (H-y)*(W/2), (H-y)*(W-(W/2))]
    answer = [answer, pieces.max - pieces.min].compact.min
  end
end

puts answer