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: Wrong Answer)

a = []
a = gets.split.map(&:to_i)
sq = a[0] * a[1]
#p a
if a[0] % 3 == 0 || a[1] % 3 == 0
  puts 0
  exit
end
if a[0]  == 1 || a[1]  == 1
  puts 1
  exit
end
cnt = sq
for i in 1..a[0]-1
  to = a[1] * i
  le = (a[0] - i)*(a[1]/2)
  ri = sq - to - le
  #p a[0]-i
  #puts "#{to} #{le} #{ri}"
  if cnt >=  [(to - le).abs, (le - ri).abs, (ri - to).abs].max
    cnt = [(to - le).abs, (le - ri).abs, (ri - to).abs].max
  end
end
c = a[0]
a[0] = a[1]
a[1] = c
#p a
for i in 1..a[0]-1
  to = a[1] * i
  le = (a[0] - i)*(a[1]/2)
  ri = sq - to - le
  #p a[0]-i
  #puts "#{to} #{le} #{ri}"
  if cnt >=  [to, le, ri].max - [to, le, ri].min
    cnt = [to, le, ri].max - [to, le, ri].min
  end
end
puts cnt