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)

macro_rules! get_tuple {
    ($($t:ty),*) => {
        {
            let mut line: String = String::new();
            std::io::stdin().read_line(&mut line).unwrap();
            let mut iter = line.split_whitespace();
            (
                $(iter.next().unwrap().parse::<$t>().unwrap(),)*
            )
        }
    };

    ($($t:ty),*; $n:expr) => {
        (0..$n).map(|_|
            get_tuple!($($t),*)
        ).collect::<Vec<_>>()
    };
}

fn main() {
    let (x, y) = get_tuple!(isize, isize);

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

fn has_solution(x: isize, y: isize) -> bool {
    if y % 2 != 0 {
        return false
    }

    if y / 2 - x < 0 {
        return false
    }

    if 2 * x - (y / 2) < 0 {
        return false
    }

    true
}