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)

use std::cmp;

fn main() {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).unwrap();
    let mut v: Vec<usize> = s.trim().split_whitespace().map(|x| x.parse().unwrap()).collect();
    let mut d: usize = std::usize::MAX;

    for _ in 0..2 {
        for i in 1..v[0]/2+1 {
            let x = i * v[1];

            let mut y = ((v[0] - i) / 2) * v[1];
            let mut z = ((v[0] - i) / 2 + (v[0] - i) % 2) * v[1];
            d = cmp::min(d, cmp::max(x, cmp::max(y, z))-cmp::min(x, cmp::min(x, y)));

            y = v[1] / 2 * (v[0] - i);
            z = (v[1] / 2 + v[1] % 2) * (v[0] - i);
            d = cmp::min(d, cmp::max(x, cmp::max(y, z))-cmp::min(x, cmp::min(x, y)));
        }
        v.reverse();
    }
    println!("{}", d);
}