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);
    int x=sc.nextInt();
    int y=sc.nextInt();
    int m=0;
    int flag=0;
    if(y<=x*2||y<=x*4)
    {
      for(int i=1;i<=x;i++)
      {
        int j=i*2;
        m=i*4;
        int h=y-j;
        int h1=y-m;
        if((h1%2==0&&h1/2==x-i)||(h%4==0&&h/4==x-i))
        {
          flag=1;
          break;
        }
      }
    }
    if(flag==1)
      System.out.println("Yes");
    else
      System.out.println("No");
  }
}