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)

def solve(h, w):
  ans = 10**10
  if h >= 3:
    if h % 3 == 0:
      return 0
    else:
      ans = w
  if h == 2:
    ans = min(ans, w-w//2)
  else:
    t = h//3
    for d in range(h%3+1):
      a = 2*t+d
      b = W//2
      M = max(a*b, a*(w-b), (h-a)*w)
      m = min(a*b, a*(w-b), (h-a)*w)
      if M-m < ans:
        ans = M-m
  return ans
H, W = map(int, input().split())
print(min(solve(H, W), solve(W, H)))