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)

fn main() {
	proconio::input!{
		mut h: usize,
		mut w: usize,
	}

	if h % 3 == 0 || w % 3 == 0 {
		println!("0");
		return;
	}

	let mut total: usize = 9999999999;

	let h1 = h / 3;
	let b1 = h1 * w;
	let w2 = w / 2;
	let b2 = (h-h1) * w2;
	let b3 = h*w - b1 - b2;
	let ans = std::cmp::max(std::cmp::max(b1, b2), b3) - std::cmp::min(std::cmp::min(b1, b2), b3);
	//println!("ans={}", ans);
	total = std::cmp::min(total, ans);

	let h2 = (h-h1) / 2;
	let b2 = h2 * w;
	let b3 = h*w - b1 - b2;
	let ans = std::cmp::max(std::cmp::max(b1, b2), b3) - std::cmp::min(std::cmp::min(b1, b2), b3);
	//println!("ans={}", ans);
	total = std::cmp::min(total, ans);

	let h1 = h / 3 + 1;
	let b1 = h1 * w;
	let w2 = w / 2;
	let b2 = (h-h1) * w2;
	let b3 = h*w - b1 - b2;
	let ans = std::cmp::max(std::cmp::max(b1, b2), b3) - std::cmp::min(std::cmp::min(b1, b2), b3);
	//println!("ans={}", ans);
	total = std::cmp::min(total, ans);

	let h2 = (h-h1) / 2;
	let b2 = h2 * w;
	let b3 = h*w - b1 - b2;
	let ans = std::cmp::max(std::cmp::max(b1, b2), b3) - std::cmp::min(std::cmp::min(b1, b2), b3);
	//println!("ans={}", ans);
	total = std::cmp::min(total, ans);

	let tmp = h;
	h = w;
	w = tmp;

	let h1 = h / 3;
	let b1 = h1 * w;
	let w2 = w / 2;
	let b2 = (h-h1) * w2;
	let b3 = h*w - b1 - b2;
	let ans = std::cmp::max(std::cmp::max(b1, b2), b3) - std::cmp::min(std::cmp::min(b1, b2), b3);
	//println!("ans={}", ans);
	total = std::cmp::min(total, ans);

	let h2 = (h-h1) / 2;
	let b2 = h2 * w;
	let b3 = h*w - b1 - b2;
	let ans = std::cmp::max(std::cmp::max(b1, b2), b3) - std::cmp::min(std::cmp::min(b1, b2), b3);
	//println!("ans={}", ans);
	total = std::cmp::min(total, ans);

	let h1 = h / 3 + 1;
	let b1 = h1 * w;
	let w2 = w / 2;
	let b2 = (h-h1) * w2;
	let b3 = h*w - b1 - b2;
	let ans = std::cmp::max(std::cmp::max(b1, b2), b3) - std::cmp::min(std::cmp::min(b1, b2), b3);
	//println!("ans={}", ans);
	total = std::cmp::min(total, ans);

	let h2 = (h-h1) / 2;
	let b2 = h2 * w;
	let b3 = h*w - b1 - b2;
	let ans = std::cmp::max(std::cmp::max(b1, b2), b3) - std::cmp::min(std::cmp::min(b1, b2), b3);
	//println!("ans={}", ans);
	total = std::cmp::min(total, ans);

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