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 Rust (1.15.1) (judge verdict: Accepted)

fn main() {
    let mut buf = String::new();
    std::io::stdin().read_line(&mut buf).unwrap();
    let mut itr = buf.split_whitespace().map(|i| i.parse::<i64>().unwrap());
    let h = itr.next().unwrap();
    let w = itr.next().unwrap();

    let mut ans = h*w;
    for &(x, y) in vec![(h, w), (w, h)].iter() {
        for t in 1..x {
            // 縦3分割
            let s_1 = t*y;
            let s_2 = (x-t)/2*y;
            let s_3 = (x-t)*y - s_2;
            let s_max = if s_1 > s_2 && s_1 > s_3 { s_1 } else if s_2 > s_3 { s_2 } else { s_3 };
            let s_min = if s_1 < s_2 && s_1 < s_3 { s_1 } else if s_2 < s_3 { s_2 } else { s_3 };
            let dif = s_max - s_min;
            if ans > dif { ans = dif; }

            // 縦横
            let s_1 = t*y;
            let s_2 = (x-t)*(y/2);
            let s_3 = (x-t)*y - s_2;
            let s_max = if s_1 > s_2 && s_1 > s_3 { s_1 } else if s_2 > s_3 { s_2 } else { s_3 };
            let s_min = if s_1 < s_2 && s_1 < s_3 { s_1 } else if s_2 < s_3 { s_2 } else { s_3 };
            let dif = s_max - s_min;
            if ans > dif { ans = dif; }
        }
    }
    println!("{}", ans);
}