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.strip.split.map(&:to_i)

h = [_h, _w].min
w = [_h, _w].max

if h % 3 == 0 || w % 3 == 0
    puts 0
else
    min = h * w
    w.times do |i|
        a = h * i
        b = (h / 2) * (w - i)
        c = (h - (h/2)) * (w - i)
        s_max = [a, b, c].max
        s_min = [a, b, c].min
        min = [min, s_max - s_min].min
    end
    h.times do |i|
        a = w * i
        b = (w / 2) * (h - i)
        c = (w - (w/2)) * (h - i)
        s_max = [a, b, c].max
        s_min = [a, b, c].min
        min = [min, s_max - s_min].min
    end
    puts min
end