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)

if H%3==0 || H%3==0
  p 0
  exit
end

# first
short_height = (H.to_f/3.to_f).round
rest_height = (H-short_height)

# cut different directions
short_width = (W.to_f/2.to_f).round
rest_width = (W-short_width)
a = W * short_height
b = rest_height*short_width
c = rest_height*rest_width

# cut same directions
second_short_height = ((H-short_height).to_f/2.to_f).round
b2 = second_short_height*W
c2 = (rest_height-second_short_height)*W

pattern1 = [a,b,c].max - [a,b,c].min
pattern2 = [a,b2,c2].max - [a,b2,c2].min

result1 = [pattern1, pattern2].min

#second
short_width = (W.to_f/3.to_f).round
rest_width = (W-short_width)

# cut different directions
short_height = (H.to_f/2.to_f).round
rest_height = (H-short_height)
a = H * short_width
b = rest_width*short_height
c = rest_width*rest_height

# cut same directions
second_short_width = ((W-short_width).to_f/2.to_f).round
b2 = second_short_width*H
c2 = (rest_width-second_short_width)*H

pattern1 = [a,b,c].max - [a,b,c].min
pattern2 = [a,b2,c2].max - [a,b2,c2].min

result2 = [pattern1, pattern2].min



result = [result1, result2].min
p result