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;

class Program
{
    static void Main(string[] args)
    {
        var input = Console.ReadLine().Split(' ');
        var x = int.Parse(input[0]);
        var y = int.Parse(input[1]);

        var MOD = 1000000007;

        var countMax = (x + y) / 3;

        if (x < countMax || y < countMax)
        {
            Console.WriteLine(0);
            return;
        }

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

        if (countMax == 1)
        {
            Console.WriteLine(1);
            return;
        }

        var ans = Mod.ModCombination(countMax, x - countMax, MOD);

        Console.WriteLine(ans);
        Console.ReadLine();
    }
}

class Mod
{
    public static long ModFactorial(long n, long mod)
    {
        var result = n;

        if (n > 0)
        {

            while (n > 1)
            {
                n--;
                result *= n;
                result %= mod;
            }

            return result;
        }
        else
        {
            return 1;
        }
    }

    public static long ModPow(long b, long pow, long mod)
    {
        if (pow == 1)
        {
            return b % mod;
        }

        long n = ModPow(b, pow / 2, mod) % mod;

        if (pow % 2 == 0)
        {
            return (n * n) % mod;
        }
        else
        {
            return (b * ((n * n) % mod)) % mod;
        }
    }

    public static long ModCombination(long sum, long num, long mod)
    {
        long x = 1;
        for (var i = 0; i < num; i++)
        {
            x *= (sum - i);
            x %= mod;
        }

        var result = (x * (ModPow(ModFactorial(num, mod), 1000000005, 1000000007))) % 1000000007;

        return result;
    }
}