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())
s = h * w
if s % 3 == 0:
    ans = 0
else:
    c = []
    for i in range(1, h):
        sa = i * w
        sb = (h - i) * (w // 2)
        sc = (h - i) * (w - (w // 2))
        min_s = min(sa, min(sb, sc))
        max_s = max(sa, max(sb, sc))
        c.append(max_s - min_s)
        sb = ((h - i) // 2) * w
        sc = s - sa - sb
        min_s = min(sa, min(sb, sc))
        max_s = max(sa, max(sb, sc))
        c.append(max_s - min_s)
    for i in range(1, w):
        sa = i * h
        sb = (w - i) * (h // 2)
        sc = (w - i) * (h - (h // 2))
        min_s = min(sa, min(sb, sc))
        max_s = max(sa, max(sb, sc))
        c.append(max_s - min_s)
        sb = ((w - i) // 2) * h
        sc = s - sa - sb
        min_s = min(sa, min(sb, sc))
        max_s = max(sa, max(sb, sc))
        c.append(max_s - min_s)
    ans = min(c)
print(ans)