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 (2.7.1) (judge verdict: Accepted)

H,W=$<.read.split.map(&:to_i)

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

min = [H,W].min

1.upto(H-1) do |i|
    a = i*W
    b = (H-i) * (W/2)
    c = (H-i) * (W/2 + (W.odd? ? 1 : 0))
    hmin,hmax = [a,b,c].minmax
    min = hmax-hmin if hmax-hmin < min
end

1.upto(W-1) do |i|
    a = i*H
    b = (W-i) * (H/2)
    c = (W-i) * (H/2 + (H.odd? ? 1 : 0))
    wmin,wmax = [a,b,c].minmax
    min = wmax-wmin if wmax-wmin < min
end

puts min