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.split.map(&:to_i)

def mini(h,w)
  vv = w % 3 == 0 ? 0 : h
  vh = (1...w).map{ |i|
    ss = [
      h*i,
      (w-i)*(h/2),
      (w-i)*(h - (h/2)),
    ]
    #$stderr.puts "#{i}, #{h/2}, #{h-h/2}, #{w-i}, #{ss}"
    ss.max - ss.min
  }.min
  $stderr.puts "(#{H}, #{W}) -> [#{vv}, #{vh}]"
  [vv,vh].min
end

puts [mini(H,W), mini(W,H)].min