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: Wrong Answer)

use std::io::*;
use std::str::FromStr;

pub fn read<T: FromStr>() -> T {
    let stdin = stdin();
    let stdin = stdin.lock();
    let token: String = stdin
        .bytes()
        .map(|c| c.expect("failed to read char") as char)
        .skip_while(|c| c.is_whitespace())
        .take_while(|c| !c.is_whitespace())
        .collect();
    token.parse().ok().expect("failed to parse token")
}

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

fn main() {
    let h: i64 = read();
    let w: i64 = read();

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

    let mut minv = std::i64::MAX;
    for i in 1..h {
        let a = (i * w);
        let b = ((h - i) * (w / 2));
        let c = ((h - i) * (w / 2) + (w % 2));
        let s = max(a, max(b, c)) - min(a, min(b, c));
        minv = min(minv, s);
        let d = ((h - i) / 2 + (h - i) % 2) * w;
        let e = ((h - i) / 2) * w;
        let s = max(a, max(d, e)) - min(a, min(d, e));
        minv = min(minv, s);
    }
    for i in 1..w {
        let a = (i * h);
        let b = (w - i) * (h / 2);
        let c = (w - i) * ((h / 2) + (h % 2));
        let s = max(a, max(b, c)) - min(a, min(b, c));
        minv = min(minv, s);
        let d = ((w - i) / 2 + (w - i) % 2) * h;
        let e = ((w - i) / 2) * h;
        let s = max(a, max(d, e)) - min(a, min(d, e));
        minv = min(minv, s);
    }
    println!("{}", minv);
}