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;

namespace atcoder
{
    class Atcoder170
    {
        static void Main(string[] args)
        {
            string[] input = Console.ReadLine().Split(" ");
            int a = Int32.Parse(input[0]);
            int b = Int32.Parse(input[1]);

            if (b % 2 == 1)
            {
                Console.WriteLine("NO");
                return;
            }

            if ((a * 4) < b)
            {
                Console.WriteLine("NO");
                return;
            }

            if ((a * 2) > b)
            {
                Console.WriteLine("NO");
                return;
            }

            if ((a / 2) == b || (a / 4) == b)
            {
                Console.WriteLine("YES");
                return;
            }

            int c = b / 2;
            for(int cc = c - 1, d = 1; cc > 0; cc--, d++) 
            {
                if ((cc * 2 + d * 4) == b && a == (cc + d))
                {
                    Console.WriteLine("YES");
                    return;
                }
            }
            Console.WriteLine("NO");
        }
    }
}