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 proconio::input;

fn f(h: i64, w: i64) -> i64 {
    let mut res = 1_000_000_000_000;

    // a|b|c
    // a|b|c
    // a|b|c
    for i in 1..w - 1 {
        let j = (w - i) / 2;
        let s_a = i * h;
        let s_b = j * h;
        let s_c = h * w - s_a - s_b;
        let s_max = std::cmp::max(s_a, std::cmp::max(s_b, s_c));
        let s_min = std::cmp::min(s_a, std::cmp::min(s_b, s_c));
        res = std::cmp::min(res, s_max - s_min);
    }

    // a|bb
    // a+--
    // a|cc
    for i in 1..w {
        let j = h / 2;
        let s_a = i * h;
        let s_b = j * (w - i);
        let s_c = h * w - s_a - s_b;
        let s_max = std::cmp::max(s_a, std::cmp::max(s_b, s_c));
        let s_min = std::cmp::min(s_a, std::cmp::min(s_b, s_c));
        res = std::cmp::min(res, s_max - s_min);
    }

    res
}

fn main() {
    input! {
        h: i64,
        w: i64
    };
    let ans = std::cmp::min(f(h, w), f(w, h));
    println!("{}", ans);
}