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())

ans = 10 ** 10
for i in range(h):
    x = (i + 1) * w
    mid = (h - i - 1) // 2
    y = mid * w
    z = (h - i - 1 - mid) * w
    ans = min(ans, max(x, y, z) - min(x, y, z))

    mid = w // 2
    y = (h - i - 1) * mid
    z = (h - i - 1) * (w - mid)
    ans = min(ans, max(x, y, z) - min(x, y, z))

for j in range(w):
    x = (j + 1) * h
    mid = (w - j - 1) // 2
    y = mid * h
    z = (w - j - 1 - mid) * h
    ans = min(ans, max(x, y, z) - min(x, y, z))

    mid = h // 2
    y = (w - j - 1) * mid
    z = (w - j - 1) * (h - mid)
    ans = min(ans, max(x, y, z) - min(x, y, z))

print(ans)