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
import sys

def solve(H: int, W: int):
    if H%3==0 or W%3==0:
        print(0)
        return 
    
    ## 小さい方をHにする
    H,W = min(H,W),max(H,W)
    answer = 10**10
    for w in range(1,W+1):
        first = H*w
        h,remain_w = H,W-w
        if h%2==0 or remain_w%2==0:
            third = int(h*remain_w/2)
            answer = min(answer,abs(first-third))
        else:
            tate_third = h*(remain_w//2)
            tate_second = h*remain_w-tate_third

            yoko_third = (h//2)*remain_w
            yoko_second = h*remain_w-yoko_third

            answer = min(answer,max(abs(yoko_third-yoko_second),abs(first-yoko_third)),max(abs(tate_third-tate_second),abs(first-tate_third)))

    for h in range(1,H+1):
        first = W*h
        remain_h,w = H-h,W
        if remain_h%2==0 or w%2==0:
            third = int(remain_h*w/2)
            answer = min(answer,abs(first-third))
        else:
            tate_third = remain_h*(w//2)
            tate_second = remain_h*w-tate_third

            yoko_third = (remain_h//2)*w
            yoko_second = remain_h*w-yoko_third

            answer = min(answer,max(abs(yoko_third-yoko_second),abs(first-yoko_third)),max(abs(tate_third-tate_second),abs(first-tate_third)))
    print(answer)

    return

def main():
    def iterate_tokens():
        for line in sys.stdin:
            for word in line.split():
                yield word
    tokens = iterate_tokens()
    H = int(next(tokens))  # type: int
    W = int(next(tokens))  # type: int
    solve(H, W)

if __name__ == '__main__':
    main()