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())

def defs(h, w):
    ans = 10 ** 12
    for i in range(1, h):
        sa = i * w
        h2 = h - i

        for j in range(2):
            if j == 0:
                sb = h2 * (w // 2)
                sc = h2 * (w - (w // 2))
            else:
                sb = (h2 // 2) * w
                sc = (h - i - (h2 // 2)) * w

            s_max = max(sa, sb, sc)
            s_min = min(sa, sb, sc)

            ans = min(ans, s_max - s_min)
    return ans

print(min(defs(h, w), defs(w, h)))