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 proconio::input;
 
fn main() {
    input! {
        (x, y): (u64, u64)
    }

    let a = x * 4;
    if y > a {
        println!("No");
        return ;
    }

    let b = y % 2;
    if b == 1 {
        println!("No");
        return ;
    }
    
    let c = x * 2;
    if c == y {
        println!("Yes");
        return ;
    }
   
    let d = x * 4;
    if d == y {
        println!("Yes");
        return ;
    }
   
    for i in 1..=x {
        let ans = (i * 2) + (x - i) * 4;
        if ans == y {
            println!("Yes");
            return;
        };
    }

    println!("No")
}