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::io;

fn main() {
    let stdin = io::stdin();
    let (x,y) = {
	let mut buf = String::new();
	stdin.read_line(&mut buf).unwrap();
	let mut tmp = buf.split_ascii_whitespace().map(|n| n.parse::<i32>().unwrap());
	(tmp.next().unwrap(), tmp.next().unwrap())
    };

    if solve(x,y) {
	println!("Yes");
    }else{
	println!("No");
    }
}

fn solve(x: i32, y : i32) -> bool{
    let b = y - 2 * x;
    b >= 0 && b % 2 == 0 && x >= (b/2)
}

#[cfg(test)]
mod test{
    use super::*;

    #[test]
    fn on_web(){
	assert!(solve(3,8));
	assert!(!solve(2,100));
	assert!(solve(1,2));
    }
}