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);
		// 動物の総数
		int x = sc.nextInt();
		// 足の数
		int y = sc.nextInt();

		// yが奇数の場合はNo
		if (y % 2 != 0) {
			System.out.println("No");
			return;
		}
		// すべてカメと仮定する b:カメの数
		int b = x;
		if (4 * b == y) {
			// すべてカメの場合
			System.out.println("Yes");
			return;
		} else if (4 * b < y) {
			System.out.println("No");
			return;
		} else {
			// 差分の足の数鶴の数
			int a = (4 * b - y) / 2;
			if ((4 * b - y) % 2 != 0) {
				// 割り切れない場合
				System.out.println("No");
				return;
			}
			b -= a;
			if (a >= 0 && b >= 0 && (2 * a + 4 * b == y)) {
				System.out.println("Yes");
				return;
			}
		}
		System.out.println("No");
	}
}