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.ComponentModel.DataAnnotations.Schema;
using System.Linq;
using System.Reflection.Metadata;
using System.Runtime.InteropServices;
using System.Threading;

namespace ForATCODER
{
    public class Program
    {
        ///template
        ///
        /// String[] s = Console.ReadLine().Split(' ');
        ///   long[] nk =  s2larray(Console.ReadLine().Split(' '));
        ///  

        public static void Main(string[] args)
        {
            int[] nk = s2iarray(Console.ReadLine().Split(' '));
          decimal[,] coeff = new decimal[,]  {
      {2*1, 2*1, 2*nk[0]},  //2x+2y=2a
	  {2, 4, nk[1]}, //2x+4y=b
	};
            //yについて解く
            coeff[1,1] -= coeff[0,1];
            coeff[1,2] -= coeff[0,2];
            coeff[1,2] /= coeff[1,1]*1.0m;
            decimal y = coeff[1,2]; //亀の数
                                 //xについて解く
            coeff[0,2] -= coeff[0,1] * y;
            coeff[0,2] /= coeff[0,0]*1.0m;
           decimal x = coeff[0,2]; //鶴の数
            if (x < 0 || y < 0)
            {
                RESULT("No");
            }
            else
                RESULT("Yes");
        }

        /// <summary>
        /// Original Tree Class
        /// </summary>
        /// <typeparam name="T"></typeparam>
        class TreeNode<T>
        {
            List<TreeNode<T>> Children;

            T Item { get; set; }

            public TreeNode(T item)
            {
                Item = item;
            }

            public TreeNode<T> AddChild(T item)
            {
                TreeNode<T> nodeItem = new TreeNode<T>(item);
                Children.Add(nodeItem);
                return nodeItem;
            }
            public void AddChildRelative(TreeNode<T> item)
            {
                Children.Add(item);
            }
            public List<TreeNode<T>> GetChildren(T val)
            {
                if (val.Equals(Item))
                {
                    var l = new List<TreeNode<T>>();
                    l.Add(this);
                    return l;
                }
                return Children.FindAll(x => x.Item.Equals(val));
            }
        }

        static void addarray(long[] arr, int start, int end)
        {
            for (int i = start; i <= end; i++)
            {
                arr[i]++;
            }
        }
        public static decimal Sqrt(decimal x)
        {
            decimal sqrt_x = (decimal)Math.Sqrt((long)x);
            for (int i = 0; i < 10; ++i)
                sqrt_x = 0.5m * (sqrt_x + x / sqrt_x);
            return sqrt_x;
        }
        static long summ(long s)
        {
            if (s == 1) return 1;
            return s + summ(s - 1);
        }
        public static bool checka(int[] a, int m)
        {
            int back = 1;
            for (int i = 0; i < a.Length; i++)
            {
                if (a[i] >= 1 && a[i] <= m)
                {
                    if (a[i] >= back)
                    {
                        back = a[i];
                    }
                    else
                    {
                        return false;
                    }
                }
                else
                {
                    return false;
                }
            }
            return true;
        }
        public static ulong pow(int a, int b)
        {
            ulong res = 1;
            for (int i = 0; i < b; i++)
            {
                res *= (ulong)a;
            }
            return res;
        }
        static int s2i(String s)
        {
            return Convert.ToInt32(s);
        }
        static long s2l(String s)
        {
            return Convert.ToInt64(s);
        }
        static void RESULT(double res)
        {
            Console.WriteLine(res);
        }
        static void RESULT(long res)
        {
            Console.WriteLine(res);
        }
        static void RESULT(ulong res)
        {
            Console.WriteLine(res);
        }
        static void RESULT(int res)
        {
            Console.WriteLine(res);
        }
        static void RESULT(String res)
        {
            Console.WriteLine(res);
        }
        static String[] ReadLineAll(int count)
        {
            String[] res = new String[count];
            for (int i = 0; i < count; i++)
            {
                res[i] = Console.ReadLine();
            }
            return res;
        }

        static int[] s2iarray(String[] src)
        {
            int len = src.Length;
            int[] res = new int[len];
            for (int i = 0; i < len; i++)
            {
                res[i] = Convert.ToInt32(src[i]);
            }
            return res;
        }
        static long[] s2larray(String[] src)
        {
            int len = src.Length;
            long[] res = new long[len];
            for (int i = 0; i < len; i++)
            {
                res[i] = Convert.ToInt64(src[i]);
            }
            return res;
        }
        static decimal[] s2darray(String[] src)
        {
            int len = src.Length;
            decimal[] res = new decimal[len];
            for (int i = 0; i < len; i++)
            {
                res[i] = Convert.ToDecimal(src[i]);
            }
            return res;
        }
        static ulong[] s2larray2(String[] src)
        {
            int len = src.Length;
            ulong[] res = new ulong[len];
            for (int i = 0; i < len; i++)
            {
                res[i] = Convert.ToUInt64(src[i]);
            }
            return res;
        }

        static long C(int n, int r)
        {
            if (n <= 1) return 0;
            if (r > n - r) r = n - r; // because C(n, r) == C(n, n - r)
            long ans = 1;
            int i;

            for (i = 1; i <= r; i++)
            {
                ans *= n - r + i;
                ans /= i;
            }

            return ans;
        }
        static long C(long n, long r)
        {
            if (n <= 1) return 0;
            if (r > n - r) r = n - r; // because C(n, r) == C(n, n - r)
            long ans = 1;
            int i;

            for (i = 1; i <= r; i++)
            {
                ans *= n - r + i;
                ans /= i;
            }

            return ans;
        }
        static ulong C(ulong n, ulong r)
        {
            if (n <= 1) return 0;
            if (r > n - r) r = n - r; // because C(n, r) == C(n, n - r)
            ulong ans = 1;
            ulong i;

            for (i = 1; i <= r; i++)
            {
                ans *= n - r + i;
                ans /= i;
            }

            return ans;
        }


    }

}