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)

#![allow(unused_imports)]
use itertools::Itertools;
use proconio::{input, marker::*};
use std::cmp::*;
use std::collections::*;
use superslice::*;

fn main() {
    input! {
        h: u64,
        w: u64
    }

    // 縦三等分
    let w1 = w / 3;
    let w2 = (w - w1) + 1 / 2;
    let ans1 = (w2 - w1) * h;

    let w1 = (w + 2) / 3;
    let w2 = (w - w1) / 2;
    let ans2 = (w1 - w2) * h;

    // 横三等分
    let h1 = h / 3;
    let h2 = (h - h1) + 1 / 2;
    let ans3 = (h2 - h1) * w;

    let h1 = (h + 2) / 3;
    let h2 = (h - h1) / 2;
    let ans4 = (h1 - h2) * w;

    // 縦三分の一、残り横に二分割
    let w1 = w / 3;
    let h1 = (h + 1) / 2;
    let ans5 = (w - w1) * h1 - w1 * h;

    let w1 = (w + 2) / 3;
    let h1 = h / 2;
    let ans6 = w1 * h - (w - w1) * h1;

    // 横三分の一、残り縦に二分割
    let h1 = h / 3;
    let w1 = (w + 1) / 2;
    let ans7 = (h - h1) * w1 - h1 * w;

    let h1 = (h + 2) / 3;
    let w1 = w / 2;
    let ans8 = h1 * w - (h - h1) * w1;

    let &ans = vec![ans1, ans2, ans3, ans4, ans5, ans6, ans7, ans8]
        .iter()
        .min()
        .unwrap();

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