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 (1.42.0) (judge verdict: Accepted)

use std::io::Read;
use std::cmp::{min, max};

fn main() {
    let mut buf = String::new();
    std::io::stdin().read_to_string(&mut buf).unwrap();

    let answer = solve(&buf);

    println!("{}", answer);
}

fn solve(input: &str) -> String {
    let mut iterator = input.split_whitespace();

    let h: usize = iterator.next().unwrap().parse().unwrap();
    let w: usize = iterator.next().unwrap().parse().unwrap();

    if h % 3 == 0 || w % 3 == 0 {
        return "0".to_string();
    }

    let result = min(calc(h, w), calc(w, h));
    result.to_string()
}

fn calc(h: usize, w: usize) -> usize {
    let mut result = std::usize::MAX;
    for h1 in 1..h {
        let s1 = h1 * w;

        let s2 = (h - h1) * (w / 2);
        let s3 = h * w - s1 - s2;
        let smax = max(s1, max(s2, s3));
        let smin = min(s1, min(s2, s3));
        result = min(result, smax - smin);

        let s2 = ((h - h1) / 2) * w;
        let s3 = h * w - s1 - s2;
        let smax = max(s1, max(s2, s3));
        let smin = min(s1, min(s2, s3));
        result = min(result, smax - smin);
    }
    result
}