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, non_snake_case, dead_code, non_upper_case_globals)]
use {
    proconio::{marker::*, *},
    std::{cmp::*, collections::*, mem::*},
};
macro_rules! chmin {
    ($ base : expr , $ cmp : expr ) => {
        if $base > $cmp {
            $base = $cmp;
        }
    };
}
macro_rules! chmax {
    ($ base : expr , $ cmp : expr ) => {
        if $base < $cmp {
            $base = $cmp;
        }
    };
}
fn main() {
    input! {//
        h:i64,w:i64,
    }
    let mut ans = INF;
    ans = min(ans, calc(h, w));
    ans = min(ans, calc(w, h));
    println!("{}", ans);
}
fn calc(h: i64, w: i64) -> i64 {
    let mut mn = INF;
    for i in 1..h {
        let ss = i * w;
        let s2 = (h - i) * (w / 2);
        let s3 = (h - i) * (w - w / 2);
        let mut ve = vec![ss, s2, s3];
        ve.sort();
        mn = min(mn, ve[2] - ve[0]);

        let lh = h - i;
        let mut vv = vec![i * w, lh / 2 * w, (lh - lh / 2) * w];
        vv.sort();
        mn = min(mn, vv[2] - vv[0]);
    }
    mn
}

const INF: i64 = 1 << 60;