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: Runtime Error)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace CSharp_practice
{
    class Program
    {
        static void Main(string[] args)
        {
            var input = Console.ReadLine().Split(' ').Select(int.Parse).ToArray();
            var x = input[0];
            var y = input[1];
            var z = 1000000007;

            if ((x + y) % 3 != 0)
            {
                Console.WriteLine(0);
            }
            else
            {
                int n = (2 * y - x) / 3;
                int m = (2 * x - y) / 3;

                Console.WriteLine(GetCombinationValue(n + m, n) % z);
            }
        }

        static long GetCombinationValue(int n, int k)
        {
            long numerator = 1;
            
            for (int i = n; n - k + 1 <= i; i--)
            {
                numerator *= i;
            }

            long denominator = 1;
            for(int i = 1; i <= k; i++)
            {
                denominator *= i;
            }

            return numerator / denominator;
        }
    }
}