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 % 3 == 0 or W % 3 == 0:
    print(0)
else:
    if H > W :
        l = H
        s = W
    else :
        l = W
        s = H
    l2 = (l // 3) + 1
    smax = l2 * s
    if (l - l2) % 2 == 0 or s % 2 == 0:
        smin = (l - l2) * s // 2
    elif (l - l2) > s:
        smin = ((l - l2) // 2) * s
    else : 
        smin = (l - l2)  *  (s // 2)
    temp1 = smax - smin
    l2 = (l // 3) 
    smin = l2 * s
    if (l - l2) % 2 == 0 or s % 2 == 0:
        smax = (l - l2) * s // 2
    elif (l - l2) > s:
        smax = ((l - l2) // 2 + 1) * s
    else : 
        smax = (l - l2)  *  (s // 2 + 1)
    temp2 = smax - smin
    print(min(temp1,temp2))