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.*;
import java.util.function.*;
import java.lang.*;
import java.io.*;

public class Main {
    static boolean solve(int heads, int legs){
        for(int crane=0; crane<=heads; crane++){
            int turtle = heads-crane;
            if(crane*2+turtle*4==legs) return true;
        }
        return false;
    }
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int heads = sc.nextInt();
        int legs = sc.nextInt();
        System.out.println(solve(heads, legs) ? "Yes" : "No");
        
    }
}