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.*;
public class Main {
	public static void main(String[] args){
		Scanner sc = new Scanner(System.in);
		// 整数の入力
		int numX = sc.nextInt();
		int numY = sc.nextInt();
		
        int numC = (2 * numX) - (numY / 2);
	    int numT = numX - numC;
		
		if ((numX == numC + numT) && (numY == 2 * numC + 4 * numT)) {
		    if ((numC < 0) || (numT < 0)) {
		        System.out.println("No");
		    }else if (((numC > 0) && (numC < 1)) || ((numT > 0) && (numT < 1))) {
		        System.out.println("No");
		    } else if ((numC >= 0) && (numT >= 0)) {
		        System.out.println("Yes");
		    } else {
		        System.out.println("No");
		    }
		} else {
		    System.out.println("No");
		}
		
	}
}