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;

namespace Application
{
    class MainClass
    {
        const long MOD = 1000000007;

        public static void Main(string[] args)
        {
            var xy = Console.ReadLine().Split();
            var x = long.Parse(xy[0]);
            var y = long.Parse(xy[1]);

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

            var n = (2 * y - x) / 3;
            var m = (2 * x - y) / 3;

            if (n < 0 || m < 0)
            {
                Console.WriteLine(0);
                return;
            }

            var ans = divM(
                factM(n + m),
                factM(n) * factM(m) % MOD);

            Console.WriteLine(ans);
        }

        static long factM(long n)
        {
            var ans = 1L;
            for (long i = 2; i <= n; i++)
            {
                ans *= i;
                ans %= MOD;
            }
            return ans;
        }

        static long powM(long n, long m)
        {
            if (m == 0) return 1;
            if (m % 2 == 1) return n * powM(n, m - 1) % MOD;
            var x = powM(n, m / 2);
            return x * x % MOD;
        }

        static long divM(long n, long m)
        {
            return n * powM(m, MOD - 2) % MOD;
        }
    }
}