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 = list(map(int, input().split()))
res = min(H,W)
hr,vr = H%3*W,W%3*H
def min_s_diff(x, y):
    if x % 3 == 0:
        return 0
    if x % 3 == 1:
        a = x // 3
        b = y // 2
        s1 = a * y
        s2 = (x - a) * b
        s3 = x * y - s1 - s2
        return max(s1, s2, s3) - min(s1, s2, s3)
    if x % 3 == 2:
        a = x // 3 + 1
        b = y // 2
        s1 = a * y
        s2 = (x - a) * b
        s3 = x * y - s1 -s2
        return max(s1, s2, s3) - min(s1, s2, s3)

print(min(min_s_diff(H, W), min_s_diff(W, H), res, hr, vr))