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) {
		Scanner sc = new Scanner(System.in);

		int turtle_num;
		int turu_num;
		int turtle_legs;
		int turu_legs;

		int X, Y;
		X = sc.nextInt();
		Y = sc.nextInt();
		boolean hasKai=false;
		for (turtle_num = 0; turtle_num <= X; turtle_num++) {
			turu_num = X - turtle_num;
			turtle_legs = 4 * turtle_num;
			turu_legs = 2 * turu_num;
			if (turtle_legs + turu_legs == Y) {
				hasKai=true;
				break;
			}
		}
		if(hasKai) {
			System.out.println("Yes");
		}else {
			System.out.println("No");
		}

	}
}