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: Time Limit Exceeded)

import java.util.Scanner;

public class Main {
    public boolean isCorrect(int animalCount, int legCount) {
        // base case
        if (animalCount == 0) {
            return legCount == 0;
        }

        return isCorrect(animalCount - 1, legCount - 2) || isCorrect(animalCount - 1, legCount - 4);
    }

    public static void main(String[] args) throws Exception {
        Main solution = new Main();

        Scanner scanner = new Scanner(System.in);
        int x = scanner.nextInt();
        int y = scanner.nextInt();

        boolean answer = solution.isCorrect(x, y);
        if (answer) {
            System.out.println("Yes");
        } else {
            System.out.println("No");
        }
    }
}