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::cmp::*;
use std::io::*;

fn main() {
    let mut s: String = String::new();
    std::io::stdin().read_to_string(&mut s).ok();
    let mut itr = s.trim().split_whitespace();
    let h: usize = itr.next().unwrap().parse().unwrap();
    let w: usize = itr.next().unwrap().parse().unwrap();

    let mut ans = 1usize << 60;
    for i in 1..=h - 1 {
        let j = h - i;
        let s1 = w * i;
        if j > 1 {
            let s2 = j / 2 * w;
            let s3 = (j + 1) / 2 * w;
            ans = min(ans, max(s1, max(s2, s3)) - min(s1, min(s2, s3)));
        }
        let s2 = w / 2 * j;
        let s3 = (w + 1) / 2 * j;
        ans = min(ans, max(s1, max(s2, s3)) - min(s1, min(s2, s3)));
    }
    for i in 1..=w - 1 {
        let j = w - i;
        let s1 = h * i;
        if j > 1 {
            let s2 = j / 2 * h;
            let s3 = (j + 1) / 2 * h;
            ans = min(ans, max(s1, max(s2, s3)) - min(s1, min(s2, s3)));
        }
        let s2 = h / 2 * j;
        let s3 = (h + 1) / 2 * j;
        ans = min(ans, max(s1, max(s2, s3)) - min(s1, min(s2, s3)));
    }
    println!("{}", ans);
}