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 std::cmp::*;
use std::collections::*;
use itertools::Itertools;
use num::clamp;
use proconio::{input, marker::*, fastout};
use superslice::*;

#[fastout()]
fn main() {
    input! {
        mut h: i64, mut w: i64
    }
    let s = h * w;

    let mut ans = 1i64<<60;

    for _ in 0..2 {
        for x in 1..w {
            let s1 = x * h;
            let x2 = w - x;

            let s21 = (x2/2) * h;
            let s22 = s - s1 - s21;
            let smin = min(s1, min(s21, s22));
            let smax = max(s1, max(s21, s22));
            ans = min(ans, smax - smin);
    
            let s21 = x2 * (h/2);
            let s22 = s - s1 - s21;
            let smin = min(s1, min(s21, s22));
            let smax = max(s1, max(s21, s22));
            ans = min(ans, smax - smin);
        }
        std::mem::swap(&mut h, &mut w);
    }
    println!("{}", ans);
}