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 mut buf = String::new();
    stdin().read_line(&mut buf).unwrap();

    let nums: Vec<i32> = buf.split_whitespace().map(|n| n.parse().unwrap()).collect::<Vec<i32>>();
    
    let x = nums[0];
    let y = nums[1];

    let mut yes = false;

    for i in 0..x+1 {
        let kame = i;
        let tsuru = x-i;
        if 4 * kame + tsuru * 2 == y {
            yes = true;
            break;
        }
    }

    let out = stdout();
    let mut out = out.lock();
    if yes {
        writeln!(out, "{}\n", "Yes").unwrap();
    } else {

        writeln!(out, "{}\n", "No").unwrap();
    }
}