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)

all = H*W

if H % 3 == 0 || W % 3 == 0
    puts 0
    exit
end

min = [H, W].min

[H/3-1, H/3, H/3+1].each do |h1|
    next if h1 <= 0
    a1 = h1 * W
    h2 = H - h1
    [W/2, W/2+1].each do |w2|
        a2 = w2 * h2
        a3 = all - a1 - a2
        dmin = [a1 - a2, a2 - a3, a3 - a1].map(&:abs).max
        min = dmin if min > dmin
    end
end

tmp = H
H = W
W = tmp

[H/3-1, H/3, H/3+1].each do |h1|
    next if h1 <= 0
    a1 = h1 * W
    h2 = H - h1
    [W/2, W/2+1].each do |w2|
        a2 = w2 * h2
        a3 = all - a1 - a2
        dmin = [a1 - a2, a2 - a3, a3 - a1].map(&:abs).max
        min = dmin if min > dmin
    end
end

puts min