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: Accepted)


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, min};

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

  let mut ans = 10000000;

  for i in 1..w {
    let a = h * i;

    // 縦方向に2分割
    let b1 = h * (((w - i) + (w - i) % 2) / 2);
    let c1 = h * (((w - i) - (w - i) % 2) / 2);
    let max1_v = max(a, max(b1, c1));
    let min1_v = min(a, min(b1, c1));
    ans = min(max1_v - min1_v, ans);

    // 縦方向 -> 横方向
    let b2 = (w - i) * ((h + (h % 2)) / 2);
    let c2 = (w - i) * ((h - (h % 2)) / 2);
    let max2_v = max(a, max(b2, c2));
    let min2_v = min(a, min(b2, c2));
    ans = min(max2_v - min2_v, ans);
  }

  for i in 1..h {
    let a = w * i;

    // 横方向に2分割
    let b1 = w * (((h - i) + (h - i) % 2) / 2);
    let c1 = w * (((h - i) - (h - i) % 2) / 2);
    let max1_v = max(a, max(b1, c1));
    let min1_v = min(a, min(b1, c1));
    ans = min(max1_v - min1_v, ans);

    // 横方向 -> 縦方向
    let b2 = (h - i) * ((w + (w % 2)) / 2);
    let c2 = (h - i) * ((w - (w % 2)) / 2);
    let max2_v = max(a, max(b2, c2));
    let min2_v = min(a, min(b2, c2));
    ans = min(max2_v - min2_v, ans);
  }

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