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

namespace AtCorder
{
	public class Program
	{
		static long P = 1000000007;
		static void Main(string[] args)
		{
			var xy = Console.ReadLine().Split(' ').Select(int.Parse).ToArray();
			int x = xy[0];
			int y = xy[1];

			int max = Math.Max(x, y);
			int min = Math.Min(x, y);
			int dif = max - min;
			if ((min - dif) % 3 != 0) {
				Console.WriteLine(0);
				return;
			}

			int n = dif + (min - dif) / 3 * 2;
			int k = (min - dif) / 3;

			long[] fact = new long[n + 1];
			long[] invfact = new long[n + 1];
			long[] inv = new long[n + 1];
			fact[0] = fact[1] = 1;
			invfact[0] = invfact[1] = 1;
			inv[1] = 1;
			for (int i = 2; i < n + 1; i++) {
				fact[i] = fact[i - 1] * i % P;
				inv[i] = P - inv[P % i] * (P / i) % P;
				invfact[i] = invfact[i - 1] * inv[i] % P;
			}

			long ans = (((fact[n] * invfact[n - k]) % P) * invfact[k]) % P;
			Console.WriteLine(ans);
		}
	}
}