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::min;
use std::cmp::max;

fn read<T: std::str::FromStr>() -> T {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    s.trim().parse().ok().unwrap()
}

fn read_vec<T: std::str::FromStr>() -> Vec<T> {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    s.trim().split_whitespace()
        .map(|e| e.parse().ok().unwrap()).collect()
}

fn read_vec2<T: std::str::FromStr>(n: usize) -> Vec<Vec<T>> {
    let mut v2 = Vec::new();
    for _ in 0..n {
        let mut s = String::new();
        std::io::stdin().read_line(&mut s).ok();
        let v = s.trim().split_whitespace()
            .map(|e| e.parse().ok().unwrap()).collect();
        v2.push(v);
    }
    v2
}

fn main() {
    let v = read_vec();
    let h: usize = v[0];
    let w: usize = v[1];

    let mut mn: usize = 100000000000;

    for a in 1..h {
        if h - a > 1 {
            let yoko:usize = (h - a) / 2;
            mn = if max(a*w, (h-a-yoko)*w) - min(yoko*w, a*w) < mn {
                max(a*w, (h-a-yoko)*w) - min(yoko*w, a*w)
            } else {
                mn
            };
        }

        if w > 1 {
            let tate:usize = w / 2;
            mn = if max(a*w, (w-tate)*(h-a)) - min(tate*(h-a), a*w) < mn {
                max(a*w, (w-tate)*(h-a)) - min(tate*(h-a), a*w)
            } else {
                mn
            };
        }
    }

    for a in 1..w {
        if w - a > 1 {
            let yoko:usize = (w - a) / 2;
            mn = if max(a*h, (w-a-yoko)*h) - min(yoko*h, a*h) < mn {
                max(a*h, (w-a-yoko)*h) - min(yoko*h, a*h)
            } else {
                mn
            };
        }

        if h > 1 {
            let tate:usize = h / 2;
            mn = if max(a*h, (h-tate)*(w-a)) - min(tate*(w-a), a*h) < mn {
                max(a*h, (h-tate)*(w-a)) - min(tate*(w-a), a*h)
            } else {
                mn
            };
        }
    }

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