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.chomp.split(" ").map(&:to_i)
ans = h*w
if h%3 == 0 || w%3 == 0
  ans = 0
else
  for i in h/3..h/3+1
    s = [i*w,(h-i)*(w/2),(h-i)*(w-w/2)]
    ans = [ans,[(s[0]-s[1]).abs,(s[1]-s[2]).abs,(s[2]-s[0]).abs].max].min
  end
  for i in w/3..w/3+1
    s = [i*h,(w-i)*(h/2),(w-i)*(h-h/2)]
    ans = [ans,[(s[0]-s[1]).abs,(s[1]-s[2]).abs,(s[2]-s[0]).abs].max].min
  end
  ans = [ans,h,w].min
end
puts ans