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 Algorithm
{
    class Program
    {
        static int Mod = 1000000007;
        static void Main(string[] args)
        {
            var l = Console.ReadLine().Split().Select(int.Parse).ToArray();
            int X = l[0], Y = l[1];

            if ((X + Y) % 3 != 0 || 2 * Y < X || 2 * X < Y)
            {
                Console.WriteLine(0);
                return;
            }

            var n = (X + Y) / 3;
            var m = X - n;

            Console.WriteLine(ModNcr(n, m));
        }

        static long ModPow(long b, int i)
        {
            for (var r = 1L; ; b = b * b % Mod)
            {
                if (i % 2 > 0) r = r * b % Mod;
                if ((i /= 2) < 1) return r;
            }
        }

        static long ModInv(int x)
        {
            return ModPow(x, Mod - 2);
        }

        static long ModFactorial(int n)
        {
            for (long x = 1, i = 1; ; x = x * ++i % Mod)
                if (i >= n) return x;
        }

        static long ModNpr(int n, int r)
        {
            if (n < r) return 0;
            for (long x = 1, i = n - r; ; x = x * ++i % Mod) if (i >= n) return x;
        }

        static long ModNcr(int n, int r)
        {
            if (n < r)
                return 0;
            else if (n - r < r)
                return ModNcr(n, n - r);
            else
                return ModNpr(n, r) * ModInv((int)ModFactorial(r)) % Mod;
        }
    }
}