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: Accepted)


H, W = gets.chop.split.map(&:to_i)

@size = H * W

@gap_list = []

@h = H
@w = W

def calculate_gap
  i_list = [(@size.to_f / 3).ceil, (@size.to_f / 3).floor]
end


def calculate_gap
  i_list = [(@h.to_f / 3).ceil, (@h.to_f / 3).floor]
  i_list.each do |i|
    first_piece = i * @w
    if @h - i > 0
      (@h-i).times do |j|
        second_piece = j * @w
        third_piece = @size - first_piece - second_piece
        pieces = [first_piece, second_piece, third_piece]
        @gap_list << pieces.max - pieces.min
      end
      @w.times do |j|
        second_piece = (@h-i) * j
        third_piece = @size - first_piece - second_piece
        pieces = [first_piece, second_piece, third_piece]
        @gap_list << pieces.max - pieces.min
      end
    end
  end
end

@h = H
@w = W
calculate_gap

@h = W
@w = H
calculate_gap

puts @gap_list.min