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 (2.7.6) (judge verdict: Wrong Answer)

# wrong answer
h, w = map(int, raw_input().split())
if h % 3 == 0 or w % 3 == 0:
    print(0)
else:
    edge = [[0,0], [0,0], [0,0]]
    third = h * w / 3.0
    if h > w:
        eh, el = h, w
    else:
        eh, el = w, h
    edge[0][0] = el
    edge[0][1] = int(third) / el
    if third - edge[0][0]*edge[0][1] > el / 2.0:
        edge[0][1] += 1
    eh -= edge[0][1]
    if eh < el:
        tmp = eh
        eh = el
        el = tmp
    if el % 2 == 0:
        edge[1][0] = eh
        edge[2][0] = eh
        edge[1][1] = el / 2
        edge[2][1] = el / 2
    elif eh % 2 == 0:
        edge[1][0] = el
        edge[2][0] = el
        edge[1][1] = eh / 2
        edge[2][1] = eh / 2
    else:
        edge[1][0] = el
        edge[2][0] = el
        edge[1][1] = eh / 2 + 1
        edge[2][1] = eh / 2

    print(max(map(abs, [edge[0][0]*edge[0][1] - edge[1][0]*edge[1][1],
                        edge[1][0]*edge[1][1] - edge[2][0]*edge[2][1],
                        edge[2][0]*edge[2][1] - edge[0][0]*edge[0][1]])))