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++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#define PN 1000000007

#include <algorithm>
#include <iostream>

long long Modpow(long long a, long long n, long long mod)
{
    long long ans = 1;
    while(n > 0)
    {
        if(n & 1)
        {
            ans = ans * a % mod;
        }
        a = a * a % mod;
        n >>= 1;
    }
    return ans;
}

long long Modinv(long long a, long long mod)
{
    return Modpow(a, mod - 2, mod);
}

int main()
{
    long long goalX = 0;
    long long goalY = 0;
    std::cin >> goalX >> goalY;
    if((goalX + goalY) % 3 != 0)
    {
        std::cout << 0 << std::endl;
        return 0;
    }
    const long long n = (goalX + goalY) / 3;
    const long long r = std::min(goalX, goalY) - n;
    // nCr
    long long numer = 1;
    long long denom = 1;
    
    for(long long i = 0; i < r; ++i)
    {
        numer = numer * (n - i) % PN;
        denom = denom * (i + 1) % PN;
    }
    std::cout << numer * Modinv(denom, PN) % PN << std::endl;
}