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)

import sys

inf = 1<<60
ans = inf

def solve():
    H, W = map(int, input().split())
    
    calc(H, W)
    calc(W, H)

    print(ans)

def calc(H, W):
    global ans
    x = W // 3

    s0 = x * H
    s1 = H * ((W - x + 1) // 2)
    s2 = H * ((W - x) // 2)

    ans = min(ans, max(s0, s1, s2) - min(s0, s1, s2))

    s1 = (W - x) * ((H + 1) // 2)
    s2 = (W - x) * (H // 2)

    ans = min(ans, max(s0, s1, s2) - min(s0, s1, s2))

    x = (W + 2) // 3

    s0 = x * H
    s1 = H * ((W - x + 1) // 2)
    s2 = H * ((W - x) // 2)

    ans = min(ans, max(s0, s1, s2) - min(s0, s1, s2))

    s1 = (W - x) * ((H + 1) // 2)
    s2 = (W - x) * (H // 2)

    ans = min(ans, max(s0, s1, s2) - min(s0, s1, s2))

if __name__ == '__main__':
    solve()