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)
    exit()
else:
    cand = []
    for i in range(1, H):
        # 横に分割
        S1 = i * W
        S2 = (H - i) * (W // 2)
        S3 = (H - i) * (W - W // 2)
        cand.append(max(S1, S2, S3) - min(S1, S2, S3))
        # 縦に分割
        S2 = (H - i) // 2 * W
        S3 = ((H - i) - (H - i) // 2) * W
        cand.append(max(S1, S2, S3) - min(S1, S2, S3))
    for i in range(1, W):
        # 横に分割
        S1 = i * H
        S2 = (W - i) * (H // 2)
        S3 = (W - i) * (H - H // 2)
        cand.append(max(S1, S2, S3) - min(S1, S2, S3))
        # 縦に分割
        S2 = (W - i) // 2 * H
        S3 = ((W - i) - (W - i) // 2) * H
        cand.append(max(S1, S2, S3) - min(S1, S2, S3))
    print(min(cand))