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 C# (.NET Core 3.1.201) (judge verdict: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Linq;
public class Hello{
    public static void Main()
    {
        //入力を保持する
        var input = Console.ReadLine().Split().Select(v => int.Parse(v)).ToArray();
        var heads =input[0];
        var legs =input[1];
        
        var tempHeads = legs/4;
        var tempLegs = legs%4;
        
        if((tempHeads == 0 && tempLegs==2)&&(heads == 1))
        {
            Console.WriteLine("Yes");
            return;
        }
        if(tempLegs%2 == 1)
        {
            Console.WriteLine("No");
            return;
        }
        else
        {
            if(tempHeads == heads)
            {
                Console.WriteLine("Yes");
                return;
            }
        }
        
        
        while(true)
        {
            tempHeads = tempHeads-1;
            tempLegs = tempLegs + 4;
            if(tempHeads < 0)
            {
                Console.WriteLine("No");
                return;
            }
            if(tempHeads + (tempLegs/2) == heads)
            {
                Console.WriteLine("Yes");
                return;
            }
            if(tempHeads == 0)
            {
                break;
            }
        }
        Console.WriteLine("No");
        

    }
}