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: Wrong Answer)

using System;
using static System.Console;
using static System.Int32;
using static System.Math;
using System.Linq;
using System.Collections.Generic;

class Solution
{
    static void Main()
    {
    lb:
        WriteLine(hoge());
    }

    static long hoge()
    {
        const int con = 1000000007;
        var sp = ReadLine().Split();
        int x = Parse(sp[0]);
        int y = Parse(sp[1]);
        int diff = Abs(x - y);
        if (x < y) x -= diff;
        else x -= diff * 2;
        if ((x % 3) != 0) return 0;
        x /= 3;
        y = x + diff;
        long result = 1;
        for (int i = x + y; y < i; --i)
        {
            result *= i;
            result %= con;
        }
        long waru = 1;
        for(int i = 2; i <= x; ++i)
        {
            waru *= i;
            waru %= con;
        }
        while (result < waru) result += con;
        while (0 < result % waru) result += con;
        return (result / waru) % con;
    }
}