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 Python (3.4.3) (judge verdict: Wrong Answer)

H, W = map(int, input().split())
if H < W:
  H, W = W, H
if H % 3 == 0 or W % 3 == 0:
  print(0)
elif W % 2 == 0:
  h = -(-H // 3)
  d1 = abs(h * W - (H - h) * W // 2)
  d2 = abs((h - 1) * W - (H - h + 1) * W // 2)
  print(min(d1, d2))
elif H % 2 == 0:
  w = -(-W // 3)
  d1 = abs(H * w - H * (W - w) // 2)
  d2 = abs(H * (w - 1) - H * (W - w + 1) // 2)
  print(min(d1, d2))
else:
  h = -(-H // 3)
  w = W // 2
  s1 = [h * W, (H - h) * w, (H - h) * (w + 1)]
  d1 = max(s1) - min(s1)
  s2 = [(h - 1) * W, (H - h + 1) * w, (H - h + 1) * (w + 1)]
  d2 = max(s2) - min(s2)
  print(min(d1, d2))