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)

fn main() {
    let input: Vec<i32> = read_vec();
    let x = input[0];
    let y = input[1];

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

fn read<T: std::str::FromStr>() -> T {
    let mut buf = String::new();
    std::io::stdin().read_line(&mut buf).ok();
    buf.trim().parse().ok().unwrap()
}

fn read_vec<T: std::str::FromStr>() -> Vec<T> {
    read::<String>()
        .split_whitespace()
        .map(|s| s.parse().ok().unwrap())
        .collect()
}

fn solve(x: i32, y: i32) -> bool {
    // つまりは鶴亀算。
    //
    // 鶴と亀の数をそれぞれa,bとすると、以下の連立方程式が成り立つ。
    //   a + b = x
    //   2a + 4b = y
    // これをa,bについて解くと
    //   a = (4x - y)/2
    //   b = (y - 2x)/2
    // a,bがともに0以上の整数になれば、(x,y)は存在する。
    let a = 4 * x - y;
    let b = y - 2 * x;

    a >= 0 && a % 2 == 0 && b >= 0 && b % 2 == 0
}

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

    #[test]
    fn test_solve_1() {
        assert_eq!(true, solve(3, 8));
    }

    #[test]
    fn test_solve_2() {
        assert_eq!(false, solve(2, 100));
    }

    #[test]
    fn test_solve_3() {
        assert_eq!(true, solve(1, 2));
    }
}