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;
using System.Collections.Generic;
using System.Linq;

namespace atcoder
{
    public class Program
    {
        public static void Main(string[] args)
        {
            var buffer = Console.ReadLine().Split();
            var X = int.Parse(buffer[0]);
            var Y = int.Parse(buffer[1]);

            if (Y % 2 != 0)
            {
                Console.WriteLine("No");
                return;
            }


            for (int i = 0; i <= X; i++)
            {
                for (int j = 0; j <= X; j++)
                {
                    if (2 + i + j * 4 == Y)
                    {
                        Console.WriteLine("Yes");
                        return;
                    }
                }
            }
            Console.WriteLine("No");
        }
    }
}