Problem:
Score : 200 points

Problem Statement

There are some animals in a garden. Each of them is a crane with two legs or a turtle with four legs.

Takahashi says: "there are X animals in total in the garden, and they have Y legs in total." Determine whether there is a combination of numbers of cranes and turtles in which this statement is correct.

Constraints

1 \leq X \leq 100

1 \leq Y \leq 100

All values in input are integers.

Input

Input is given from Standard Input in the following format:

X Y

Output

If there is a combination of numbers of cranes and turtles in which the statement is correct, print Yes; otherwise, print No.

Sample Input 1

3 8

Sample Output 1

Yes

The statement "there are 3 animals in total in the garden, and they have 8 legs in total" is correct if there are two cranes and one turtle. Thus, there is a combination of numbers of cranes and turtles in which the statement is correct.

Sample Input 2

2 100

Sample Output 2

No

There is no combination of numbers of cranes and turtles in which this statement is correct.

Sample Input 3

1 2

Sample Output 3

Yes

We also consider the case in which there are only cranes or only turtles.

Solution in Rust (1.42.0) (judge verdict: Accepted)

use std::error::Error;
use std::io;

pub fn main() {
    if let Err(_e) = run() {
        panic!("failed.");
    }
}

fn run() -> Result<(), Box<dyn Error>> {
    let mut input = String::new();
    io::stdin().read_line(&mut input)?;
    let nums: Vec<i64> = input
        .trim()
        .split_whitespace()
        .map(|s| s.parse::<i64>().unwrap())
        .collect();
    input.clear();

    if nums[1] % 2 == 1 {
        println!("No");
        return Ok(());
    }

    let max = nums[1] / 2;
    let mut min = nums[1] / 4;
    if nums[1] % 4 != 0 {
        min += 1;
    }
    if nums[0] <= max && nums[0] >= min {
        println!("Yes");
    } else {
        println!("No");
    }

    Ok(())
}