Problem:
Score : 400 points

Problem Statement

There is a knight - the chess piece - at the origin (0, 0) of a two-dimensional grid.

When the knight is at the square (i, j), it can be moved to either (i+1,j+2) or (i+2, j+1).

In how many ways can the knight reach the square (X, Y)?

Find the number of ways modulo 10^9 + 7.

Constraints

1 \leq X \leq 10^6

1 \leq Y \leq 10^6

All values in input are integers.

Input

Input is given from Standard Input in the following format:

X Y

Output

Print the number of ways for the knight to reach (X, Y) from (0, 0), modulo 10^9 + 7.

Sample Input 1

3 3

Sample Output 1

2

There are two ways: (0,0) \to (1,2) \to (3,3) and (0,0) \to (2,1) \to (3,3).

Sample Input 2

2 2

Sample Output 2

0

The knight cannot reach (2,2).

Sample Input 3

999999 999999

Sample Output 3

151840682

Print the number of ways modulo 10^9 + 7.

Solution in C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
using System.IO;
using System.Text;
using static System.Math;
using static System.Array;
using static AtCoder.Tool;

namespace AtCoder
{
    class AC
    {
        const int MOD = 1000000007;
        const int INF = int.MaxValue / 2;
        const long SINF = long.MaxValue / 2;
        const double EPS = 1e-8;
        static readonly int[] dx = { 0, 1, 0, -1 };
        static readonly int[] dy = { 1, 0, -1, 0 };
        //static List<List<int>> G = new List<List<int>>();
        //static List<List<Edge>>G = new List<List<Edge>>();
        //static List<Edge> E = new List<Edge>();
        
        
        static void Main(string[] args)
        {
            //var sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
            //Console.SetOut(sw);
            var cin = new Scanner();

            var p = cin.SplitRead();
            int X = p[0];
            int Y = p[1];

            long ans = 0;
            
            for(var i = 0; i <= X / 2; i++)
            {
                if (2 * X - 3 * i == Y)
                {
                    var md = new Modulo(X - i);
                    ans += md.Ncr(X - i, i);
                }
            }

            Console.WriteLine(ans);

            //Console.Out.Flush();
        }

        struct Edge
        {
            public int from;

            public int to;
            public long dist;
            public Edge(int t, long c)
            {
                from = -1;
                to = t;
                dist = c;
            }
            public Edge(int f, int t, long c)
            {
                from = f;
                to = t;
                dist = c;
            }

        }
        struct Pair<T, U> : IComparable<Pair<T, U>>
        where T : IComparable<T>
        where U : IComparable<U>
        {
            public T first;
            public U second;
            private readonly bool CompWithFirst;

            public Pair(T f, U s, int comp)
            {
                first = f;
                second = s;
                CompWithFirst = comp == 1;
            }
            public Pair(T f,U s)
            {
                first = f;
                second = s;
                CompWithFirst = true;
            }

            public int CompareTo(Pair<T, U> other)
            {
                return CompWithFirst ? first.CompareTo(other.first) : second.CompareTo(other.second);
            }
        }
    }
    class Modulo
    {
        private const int M = 1000000007;
        private readonly int[] m_facs;
        public int Mul(int a, int b) //掛け算
        {
            return (int)(Math.BigMul(a, b) % M);
        }
        public Modulo(int n)
        {
            m_facs = new int[n + 1];
            m_facs[0] = 1;
            for (int i = 1; i <= n; ++i)
            {
                m_facs[i] = Mul(m_facs[i - 1], i);
            }
        }
        public int Fac(int n)
        {
            return m_facs[n];
        }
        public int Pow(int a, int m) //累乗
        {
            switch (m)
            {
                case 0:
                    return 1;
                case 1:
                    return a;
                default:
                    int p1 = Pow(a, m / 2);
                    int p2 = Mul(p1, p1);
                    return ((m % 2) == 0) ? p2 : Mul(p2, a);
            }
        }
        public int Div(int a, int b) //除算
        {
            return Mul(a, Pow(b, M - 2));
        }
        public int Ncr(int n, int r) //二項係数
        {
            if (n < r) { return 0; }
            if (n == r) { return 1; }
            int res = Fac(n);
            res = Div(res, Fac(r));
            res = Div(res, Fac(n - r));
            return res;
        }
        public Modulo() { }
    }
    public class PriorityQueue<T> where T : IComparable<T>
    {

        private List<T> Q;
        private readonly int r;

        public PriorityQueue(bool ascending)
        {
            if (ascending)
            {
                r = 1;
            }
            else
            {
                r = -1;
            }
            Q = new List<T>();
        }


        private void PushHeap(List<T> list, T item)
        {
            int n = list.Count();
            list.Add(item);

            while (n != 0)
            {
                int pIndex = (n - 1) / 2;

                if (list[n].CompareTo(list[pIndex]) * r > 0)
                {
                    Swap(Q, n, pIndex);
                }
                else { break; }

                n = pIndex;
            }
        }

        private void PopHeap(List<T> list)
        {
            int n = list.Count() - 1;
            list[0] = list[n];
            list.RemoveAt(n);

            int cur = 0;
            int comp;

            while (2 * cur + 1 <= n - 1)
            {
                int c1 = 2 * cur + 1;
                int c2 = 2 * (cur + 1);
                if (c1 == n - 1)
                {
                    comp = c1;
                }
                else
                {

                    comp = list[c1].CompareTo(list[c2]) * r > 0 ? c1 : c2;
                }

                if (list[cur].CompareTo(list[comp]) * r < 0)
                {
                    Swap(Q, cur, comp);
                }
                else { break; }

                cur = comp;
            }
        }

        private void Swap(List<T> list, int a, int b)
        {
            T keep = list[a];
            list[a] = list[b];
            list[b] = keep;
        }



        public void Enqueue(T value)
        {
            PushHeap(Q, value);
        }

        public T Dequeue()
        {
            T ret = Q[0];
            PopHeap(Q);
            return ret;
        }

        public T Peek()
        {
            return Q[0];
        }

        public int Count()
        {
            return Q.Count();
        }

        public bool Contains(T search)
        {
            return Q.Contains(search);
        }
    }
    public class Scanner
    {
        public int[] SplitRead()
        {
            int[] array = Console.ReadLine().Split().Select(int.Parse).ToArray();
            return array;
        }
        public long[] SplitReadL()
        {
            long[] array = Console.ReadLine().Split().Select(long.Parse).ToArray();
            return array;
        }
    }
    public static class Tool
    {
        static public void Initialize<T>(ref T[] array, T initialvalue)
        {
            for (var i = 0; i < array.Length; i++)
            {
                array[i] = initialvalue;
            }
        }

        static public T MaxLot<T>(params T[] val) where T : IComparable<T>
        {
            T ret = val[0];
            for (var i = 1; i < val.Count(); i++)
            {
                if (ret.CompareTo(val[i]) < 0) { ret = val[i]; }
            }
            return ret;
        }
        static public T MinLot<T>(params T[] val) where T : IComparable<T>
        {
            T ret = val[0];
            for (var i = 1; i < val.Count(); i++)
            {
                if (ret.CompareTo(val[i]) > 0) { ret = val[i]; }
            }
            return ret;
        }

        static public void Swap<T>(T[] a, int i, int j)
        {
            T k = a[i];
            a[i] = a[j];
            a[j] = k;
        }
        
    }

}