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)

#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
#define rep(i, n) for (int i = 0; i < (int)(n); i++)

long long modinv(long long a, long long m)
{
    long long b = m, u = 1, v = 0;
    while (b)
    {
        long long t = a / b;
        a -= t * b;
        swap(a, b);
        u -= t * v;
        swap(u, v);
    }
    u %= m;
    if (u < 0)
        u += m;
    return u;
}

ll big = 1e9 + 7;
int main()
{
    ll X, Y;
    cin >> X >> Y;
    ll ans = 0;
    if (((-X + 2 * Y) % 3 != 0) || ((2 * X - Y) % 3 != 0))
    {
        ans = 0;
    }
    else
    {
        ll a = (-X + 2 * Y) / 3;
        ll b = (2 * X - Y) / 3;
        ll s = 1, ae = 1, be = 1, u;
        rep(i, a + b) s = ((i + 1) * s) % big;
        rep(i, a) ae = ((i + 1) * ae) % big;
        rep(i, b) be = ((i + 1) * be) % big;
        u = (ae * be) % big;
        u = modinv(u, big);
        ans = (s * u) % big;
    }
    cout << ans << endl;
    return 0;
}