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: Time Limit Exceeded)

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

namespace ConsoleApp1
{
    class Program
    {
        static void Main(string[] args)
        {
            var input = Console.ReadLine().Split(' ').Select(s => long.Parse(s)).ToArray();
            var x = input[0];
            var y = input[1];
            var mod = 1000000007;

            if ((x + y) % 3 != 0)
            {
                Console.WriteLine(0);
                return;
            }

            var n = (x + y) / 3;
            if (x < n || y < n)
            {
                Console.WriteLine(0);
                return;
            }

            Console.WriteLine(nCr(n, x - n, mod) % mod);
        }

        private static long Factorial(long n, int mod)
        {
            var ret = 1L;
            for (long i = 1; i <= n; i++)
            {
                ret = ret * i % mod;
            }
            return ret;
        }

        private static long nCr(long n, long r, int mod)
        {
            r = n - r > r ? r : n - r;
            var ret = 1L;
            for (var i = n - r + 1; i <= n; i++)
            {
                ret = ret * i % mod;
            }
            return ret * Inverse(Factorial(r, mod), mod) % mod;
        }

        private static long Inverse(long n, int mod)
        {
            var ret = 1L;
            for (long i = 0; i < mod - 2; i++)
            {
                ret = ret * n % mod;
            }
            return ret;
        }
    }
}