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)

def div2 h,w
 
  return [h*w/2, h*w/2] if h % 2 == 0 or w % 2 == 0
  h,w = [h, w].sort
  return [w/2*h, (w+1)/2*h]
end
  
def f h,w
  
  return 0 if h % 3 == 0 or w % 3 == 0
  
  res0 = res1 = h*w
  
  0.upto h%3 do |i|
    
    s = w*(h/3 + i)
    ss =div2(h-h/3-i, w).push(s)
    res0 = [res0, ss.max - ss.min].min
  end
  
  0.upto w%3 do |i|
    
    s = h*(w/3 + i)
    ss =div2(w-w/3-i, h).push(s)
    res1 = [res1, ss.max - ss.min].min 
  end
  
  [res0, res1].min
end  

H, W = gets.split.map(&:to_i).sort
puts [f(H,W), f(W,H)].min