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)

import math

H, W = map(int, input().split())

if H % 3 == 0 or W % 3 == 0:
    print(0)
    exit()

min_num = 100000000000
for i in range(1, H):
    a = i*W
    b = W//2 * (H-i)
    c = math.ceil(W/2) * (H-i)
    _max_num = max(a, max(b, c))
    _min_num = min(a, min(b, c))
    n = _max_num - _min_num
    if n < min_num:
        min_num = n

for i in range(1, W):
    a = i*H
    b = H//2 * (W-i)
    c = math.ceil(H/2) * (W-i)
    _max_num = max(a, max(b, c))
    _min_num = min(a, min(b, c))
    n = _max_num - _min_num
    if n < min_num:
        min_num = n

print(min_num)