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: Wrong Answer)

#!/usr/bin/env python3


def main():
    H, W = map(int, input().split())
    if H % 3 == 0 or W % 3 == 0:
        print(0)
    else:
        ans = 10**18

        # Hを1:2で分割
        for i in range(3):
            d = (H // 3)- 1 + i
            choco = [d * W, (H-d) * (W//2), (H-d) * (W - W//2)]
            ans = min(ans, max(choco) - min(choco))
            # print(choco)
        
        # Wを1:2で分割
        for i in range(3):
            d = (W // 3)- 1 + i
            choco = [d * H, (W-d) * (H//2), (W-d) * (H - H//2)]
            ans = min(ans, max(choco) - min(choco))
            # print(choco)
        
        print(ans)


if __name__ == "__main__":
    main()