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.split.map(&:to_i)
if H % 3 == 0 || W % 3 == 0
  p 0
  exit
end

ans = Float::INFINITY
ah = H / 2
bh = H - ah
(1..(W-1)).each do |cw|
  a = [ah * (W-cw), bh * (W-cw), H * cw]
  ans = [ans, a.max - a.min].min
end

aw = W / 2
bw = W - aw
(1..(H-1)).each do |ch|
  a = [aw * (H-ch), bw * (H-ch), W * ch]
  ans = [ans, a.max - a.min].min
end

aw = W / 3
bw = (W - aw) / 2
cw = W - aw - bw
a = [H*aw, H*bw, H*cw]
ans = [ans, a.max - a.min].min

ah = H / 3
bh = (H - ah) / 2
ch = H - ah - bh
a = [W*ah, W*bh, W*ch]
ans = [ans, a.max - a.min].min

p ans