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)
if H % 3 == 0 || W % 3 == 0 then
  puts 0
  exit
end

ret = H * W
short, long = [H, W].minmax

long.times do |i|
  a = (i + 1) * short
  
  b = (short / 2) * (long - (i + 1))
  c = (short - short / 2) * (long - (i + 1))
  if a > 0 && b > 0 && c > 0 then
    ret = [([a, b, c].max - [a, b, c].min), ret].min 
  end

  b = ((long - i) / 2) * short
  c = (long - (i + 1) - ((long - i) / 2)) * short
  if b > 0 && c > 0 then
    ret = [([a, b, c].max - [a, b, c].min), ret].min 
  end

end

short, long = long, short
long.times do |i|
  a = (i + 1) * short

  b = (short / 2) * (long - (i + 1))
  c = (short - short / 2) * (long - (i + 1))
  if b > 0 && c > 0 then
    ret = [([a, b, c].max - [a, b, c].min), ret].min 
  end

  b = ((long - i) / 2) * short
  c = (long - (i + 1) - ((long - i) / 2)) * short
  if a > 0 && b > 0 && c > 0 then
    ret = [([a, b, c].max - [a, b, c].min), ret].min 
  end

end
puts ret