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: Wrong Answer)

fn main(){
    let (x, y) = {
        let mut s = String::new();
        std::io::stdin().read_line(&mut s).unwrap();
        let mut ws = s.trim_end().to_owned().split_whitespace();
        let mut ws = s.split_whitespace();
        let x: i32 = ws.next().unwrap().parse().unwrap();
        let y: i32 = ws.next().unwrap().parse().unwrap();
        (x, y)
    };

    for i in 1..=x {
        {
            let mut cranes = 0;
            let mut turtles = 0;
            cranes += 1;
            turtles = x - cranes;

            if cranes * 2 + turtles * 4 == y {
                println!("Yes");
                return;
            }
        }
        {
            let mut cranes = 0;
            let mut turtles = 0;
            turtles += 1;
            cranes = x - turtles;

            if cranes * 2 + turtles * 4 == y {
                println!("Yes");
                return;
            }
        }
    }
    println!("No");
}