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: Accepted)

h, w = map(int, input().split())
if h % 3 == 0 or w % 3 == 0:
    print(0)
else:
    if h > w:
        h, w = w, h
    ans = h
    for w1 in range(w//3-2, w//3+3):
        s1 = w1 * h
        w2 = w-w1
        for h1 in range(h//2 + 1):
            s2 = w2 * h1
            s3 = w2 * (h-h1)
            ans = min(ans, max(s1, s2, s3) - min(s1, s2, s3))
    h, w = w, h
    for w1 in range(w//3-2, w//3+3):
        s1 = w1 * h
        w2 = w-w1
        for h1 in range(h//2 + 1):
            s2 = w2 * h1
            s3 = w2 * (h-h1)
            ans = min(ans, max(s1, s2, s3) - min(s1, s2, s3))
    print(ans)