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;
class Program
{
	static void Main(string[] args)
	{
		string[] str = Console.ReadLine().Split();
		long X = long.Parse(str[0]);
		long Y = long.Parse(str[1]);
		long ans = 0;
		long mod = 1000000007;
		if((X+Y)%3==0){
			if(X<=Y*2 && Y<=X*2){
				ans = Ncr((X+Y)/3,Y-(X+Y)/3,mod);
			}
		}
		Console.WriteLine(ans);
	}
	
	public static long Mpow(long x,long n,long m)
	{
		long ans = 1;
		while(n > 0){
			if(n % 2 == 1){
				ans = ans * x % m;
				n -= 1;
			}
			x = x * x % m;
			n /= 2;
		}
		return ans;
	}

	public static long Ncr(long n,long r,long m)
	{
		long ans = 1;
		for(var i=n-r+1;i<=n;i++){
			ans = ans * i % m;
		}
		for(var i=2;i<=r;i++){
			ans = ans * Mpow(i,m-2,m) % m;
		}
		return ans;
	}
}