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)

h, w = gets.split.map(&:to_i)
if (h % 3 == 0) || (w % 3 == 0)
  puts 0
  exit(0)
end
if h == 2 || w == 2
  puts 1
  exit(0)
end
results = []
ax = h
(w / 2 + 1).times do |i|
  ay = i + 1
  as = ax * ay
  bx = ax / 2
  cx = ax - bx
  by = w - ay
  cy = w - ay
  bs = bx * by
  cs = cx * cy
  results << [(as - bs).abs, (bs - cs).abs, (cs - as).abs].max
end
if h == w
  puts results.min
  exit(0)
end
ax = w
(h / 2 + 1).times do |i|
  ay = i + 1
  as = ax * ay
  bx = ax / 2
  cx = ax - bx
  by = h - ay
  cy = h - ay
  bs = bx * by
  cs = cx * cy
  results << [(as - bs).abs, (bs - cs).abs, (cs - as).abs].max
end
puts results.min