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 mut a = String::new();
    // std::io::stdin().read_line(&mut a).ok();
    // let _a: i32 = a.trim().parse().unwrap();

    let mut buf = String::new();
    std::io::stdin().read_line(&mut buf).ok();
    let mut iter = buf.trim().split_whitespace();

    let x = iter.next().unwrap().parse::<i32>().unwrap();
    let y = iter.next().unwrap().parse::<i32>().unwrap();

    let b = solve(x, y);

    println!("{}", if b {"Yes"} else {"No"});
}

fn solve(x: i32, y: i32) -> bool {
    let mut b = false;

    for i in 0..=x {
        if (x - i) * 4 + i * 2 == y {
            b = true;
            break
        }
    }

    b
}