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# (Mono-mcs 6.8.0.105) (judge verdict: Wrong Answer)

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

namespace AtCoder
{
    class Program
    {
        static void Main()
        {
            string[] inputs = Console.ReadLine().Split(" ");
            int legsSum = int.Parse(inputs[1]);
            int animals = int.Parse(inputs[0]);
            bool possible = false;
            if (legsSum % 2 == 1) possible = false;
            else
            {
                if (4 * animals < legsSum) possible = false;
                else
                {
                    for (int i = 0; i <= animals; i++)
                    {
                        for (int j = i; i + j <= animals ; j++)
                        {
                            if (i * 4 + j * 2 == legsSum)
                            {
                                if (possible == false) possible = true;
                            }
                        }
                    }
                }
            }

            Console.WriteLine(possible ? "Yes" : "No");
        }
    }
}