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 Java (OpenJDK 11.0.6) (judge verdict: Accepted)

import java.util.Scanner;

public class Main {

	public static void main(String[] args) {
		try(Scanner scanner = new Scanner(System.in)) {
			String data = scanner.nextLine();
			String[] dataArray = data.split(" ");

			int total = Integer.parseInt(dataArray[0]);
			int legs = Integer.parseInt(dataArray[1]);

			boolean hasPattern = false;
			if (legs % 2 == 0) {
				int min = 2 * total;
				int max = 4 * total;
				if (min <= legs && legs <= max) {
					hasPattern = true;
				}
			}

			System.out.println(hasPattern ? "Yes" : "No");
		}
	}
}