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)

min = 1e+10

# +----------+
# |          |
# +----------+ 
# |          |
# +----------+
# |          |
# +----------+
h.times do |y1|
  y2 = (h - y1) / 2
  
  s = []
  s[0] = y1 * w
  s[1] = y2 * w
  s[2] = (h - (y1 + y2)) * w
  
  s.sort!
  min = [s[2] - s[0], min].min
end

# +----------+
# |          |
# +----+-----+ 
# |    |     |
# |    |     |
# +----+-----+
h.times do |y|
  x = w / 2
  
  s = []
  s[0] = y * w
  s[1] = (h - y) * x
  s[2] = (h - y) * (w - x)
  
  s.sort!
  min = [s[2] - s[0], min].min
end

# +---+------+
# |   |      |
# |   +------+
# |   |      |
# |   |      |
# +---+------+
w.times do |x|
  y = h / 2
  
  s = []
  s[0] = h * x
  s[1] = y * (w - x)
  s[2] = (h - y) * (w - x)
  
  s.sort!
  min = [s[2] - s[0], min].min
end

# +---+---+--+
# |   |   |  |
# |   |   |  |
# |   |   |  |
# |   |   |  |
# |   |   |  |
# +---+---+--+
w.times do |x1|
  x2 = (w - x1) / 2
  
  s = []
  s[0] = h * x1
  s[1] = h * x2
  s[2] = h * (w - (x1 + x2))
  
  s.sort!
  min = [s[2] - s[0], min].min
end

puts min.to_s