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.Linq;
using System.Collections.Generic;

namespace ConsoleApp2
{
    public class Program
    {

        static long D = (long)Math.Pow(10, 9) + 7;

        public static void Main(string[] args)
        {
            int[] XY = Read(Console.ReadLine());
            int X = XY[0];
            int Y = XY[1];

            if ((X + Y) % 3 != 0)
            {
                Console.WriteLine(0);
                Console.ReadLine();
                return;
            }

            int section = (X + Y) / 3;

            int diffFromEnd = X - section;
            if (diffFromEnd < 0 || diffFromEnd > section)
            {
                Console.WriteLine(0);
                Console.ReadLine();
                return;
            }

            Console.WriteLine(Combination(section,diffFromEnd,D));
            Console.ReadLine();
        }


        public static long GetInv(long a, long mod)
        {
            return PowerMod(a, mod - 2, mod);
        }

        public static long Combination(long a, long b, long mod)
        {
            long numerator = Factorial(a, mod);
            long denominator = (Factorial(b, mod) * Factorial(a - b, mod)) % mod;

            return (numerator * GetInv(denominator, mod)) % mod;
        }

        public static long Factorial(long n, long mod)
        {
            if (n == 0) return 1;
            if (n == 1) return 1;
            long ans = n;
            for (int i = 2; i < n; i++)
            {
                ans = (ans * i) % mod;
            }

            return ans;
        }

        private static long PowerMod(long a, long n, long mod)
        {
            if (n == 1) return a;

            long p = PowerMod(a, n / 2, mod);
            if (n % 2 == 1) return ((p * p) % mod * a) % mod;
            else return (p * p) % mod;
        }

        public class BFSClass
        {
            /// <summary>
            /// 1...道、2...障害物(0は未知)
            /// </summary>
            /// <param name="map"></param>
            public BFSClass(int[][] map)
            {
                Map = map;
            }

            private class TileFrom
            {
                public TileFrom(int[] thisTile, int[] from)
                {
                    ThisTile = thisTile;
                    From = from;
                }
                public int[] ThisTile { get; }
                public int[] From { get; }
            }

            public int[][] Map { get; }

            //調べる予定の位置を入れる
            Queue<int[]> search = new Queue<int[]>();

            //調べ終わった位置
            List<TileFrom> done = new List<TileFrom>();

            /// <summary>
            /// 
            /// </summary>
            /// <param name="map"></param>
            public int BFS(int[] startPos, int[] goalPos)
            {
                done.Add(new TileFrom(startPos, null));

                //現在の位置
                int[] currentPos = startPos;

                return StartBFS(0,currentPos, goalPos);
            }

            /// <summary>
            /// 終わったらtrue
            /// </summary>
            /// <param name="currentPos"></param>
            /// <param name="goalPos"></param>
            private int StartBFS(int currentCount,int[] currentPos, int[] goalPos)
            {
                if (currentPos.SequenceEqual(goalPos)) return currentCount;

                List<int[]> around = GetAroundTile(currentPos);
                foreach (var item in around)
                {
                    if (!done.Exists(i => i.ThisTile.SequenceEqual(item)))
                    {
                        done.Add(new TileFrom(item, currentPos));
                        search.Enqueue(item);
                        Console.WriteLine(item[0] + "," + item[1] + "を調べます");
                    }
                    else
                    {
                        Console.WriteLine(item[0] + "," + item[1] + "は済んでいます");
                    }
                }

                while (search.Count > 0)
                {
                    var nextStartPos = search.Dequeue();
                    if (Map[nextStartPos[0]][nextStartPos[1]] == 1)
                    {
                        return StartBFS(currentCount+1,nextStartPos, goalPos);
                    }
                }

                return 0;
            }

            private List<int[]> GetAroundTile(int[] pos)
            {
                List<int[]> ans = new List<int[]>();
                int[][] deltas = {  new int[2] { 0, 1 },
                                new int[2] { 1, 0 },
                                new int[2] { 0, -1 },
                                new int[2] { -1, 0 } };

                foreach (var delta in deltas)
                {
                    int[] newPos = { pos[0] + delta[0], pos[1] + delta[1] };
                    if (OnMap(newPos)) ans.Add(newPos);
                }
                return ans;
            }

            private bool OnMap(int[] pos)
            {
                if (pos[0] >= 0 && pos[0] < Map.Length)
                {
                    if (pos[1] >= 0 && pos[1] < Map[0].Length)
                    {
                        return true;
                    }
                }
                return false;
            }

            private int FindRoot(int[] goalPos)
            {
                Stack<int[]> root = new Stack<int[]>();
                root.Push(goalPos);

                TileFrom f = done.Find(i => i.ThisTile[0] == goalPos[0] && i.ThisTile[1] == goalPos[1]);
                while (true)
                {
                    root.Push(f.From);
                   // Console.WriteLine("[" + f.ThisTile[0] + "," + f.ThisTile[1] + "]" + "から[" + f.From[0] + "," + f.From[1] + "]");

                    TileFrom test = done.Find(i => i.ThisTile[0] == f.From[0] && i.ThisTile[1] == f.From[1]);

                    if (test.From == null) break;
                    f = test;
                }
                //while (root.Count > 0)
                //{
                //    int[] r = root.Pop();
                //    Console.WriteLine("[" + r[0] + "," + r[1] + "]");
                //}
                return root.Count - 1;
            }
        }
      
        private static int[] Read(string input)
        {
            string[] strings = input.Split(' ');
            int num = strings.Length;
            int[] ints = new int[num];
            for (int i = 0; i < num; i++)
            {
                ints[i] = int.Parse(strings[i]);
            }
            
            return ints;
        }


    }


}