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;

class Program
{
    private const int CRANE_LEGS = 2;
    private const int TURTLE_LEGS = 4;
    public static void Main(string[] args)
    {
        int[] input = Array.ConvertAll(Console.ReadLine().Split(' '), int.Parse);
        Program pg = new Program();
        Console.WriteLine(pg.Exe(input));
    }

    public string Exe(int[] input)
    {
        string answer = "No";
        int animals = input[0];
        int legs = input[1];

        if(legs % 2 == 1) return answer;

        int crane_cnt = animals;
        int turtle_cnt = 0;
        int num_legs = crane_cnt * CRANE_LEGS;

        if((legs - num_legs) / 2 > animals) return answer;
        else answer = "Yes";
        return answer;
    }
}