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::str::FromStr;
use std::fmt::Debug;
use std::cmp;
#[allow(dead_code)]
fn read_as_vec<T>() -> Vec<T>
where T: FromStr, <T as FromStr>::Err : Debug{
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).unwrap();
    s.trim().split_whitespace().map(|c| T::from_str(c).unwrap()).collect()

}

#[allow(dead_code)]
fn read_as_string() -> String{
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).unwrap();
    s.trim().to_string()
}

fn main(){
    let line = read_as_vec::<i64>();
    let (h, w) = (line[0], line[1]);

    if h%3 == 0 || w%3 == 0{
        println!("0");
        return;
    }

    //chocolate is wide
    let (h, w) = (cmp::min(h, w), cmp::max(h, w));

    let (mut a, mut b) = (0, 0);
    let mut c = h*w;
    let mut ans1 = h*w;
    for _ in 0..w-1{
        a += h/2;
        b += (h+1)/2;
        c -= h;
        let smax = cmp::max(cmp::max(a, b), c);
        let smin = cmp::min(cmp::min(a, b), c);
        ans1 = cmp::min(cmp::max(smax-smin, 0), ans1);
    }

    let (mut a, mut b) = (0, 0);
    let mut c = h*w;
    let mut ans2 = h*w;
    for _ in 0..h-1{
        a += w/2;
        b += (w+1)/2;
        c -= w;
        let smax = cmp::max(cmp::max(a, b), c);
        let smin = cmp::min(cmp::min(a, b), c);
        ans2 = cmp::min(cmp::max(smax-smin, 0), ans2);
    }

    println!("{}", cmp::min(ans1, cmp::min(ans2, cmp::min(h, w))));
}