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: Accepted)

/**
 * code generated by JHelper
 * More info: https://github.com/AlexeyDmitriev/JHelper
 * @author indy256
 */

#include <bits/stdc++.h>

using namespace std;

template<int mod>
struct modint {
    int value;

    modint(long long x = 0) {
        value = normalize(x);
    }

    int normalize(long long x) {
        if (x < -mod || x >= mod)
            x %= mod;
        if (x < 0) x += mod;
        return static_cast<int>(x);
    }

    explicit operator int() const { return value; }

    modint operator-() const { return modint(-value); }

    modint &operator+=(modint rhs) {
        if ((value += rhs.value) >= mod) value -= mod;
        return *this;
    }

    modint &operator-=(modint rhs) {
        if ((value -= rhs.value) < 0) value += mod;
        return *this;
    }

    modint &operator*=(modint rhs) {
        value = normalize(static_cast<long long>(value) * rhs.value % mod);
        return *this;
    }

    modint &operator/=(modint rhs) { return *this *= modint(inverse(rhs.value, mod)); }

    int inverse(int a, int m) {
        int u = 0, v = 1;
        while (a != 0) {
            int t = m / a;
            m -= t * a;
            swap(a, m);
            u -= t * v;
            swap(u, v);
        }
        assert(m == 1);
        return u;
    }

    friend modint operator+(modint lhs, modint rhs) { return lhs += rhs; }

    friend modint operator-(modint lhs, modint rhs) { return lhs -= rhs; }

    friend modint operator*(modint lhs, modint rhs) { return lhs *= rhs; }

    friend modint operator/(modint lhs, modint rhs) { return lhs /= rhs; }

    friend bool operator==(modint lhs, modint rhs) { return lhs.value == rhs.value; }

    friend bool operator!=(modint lhs, modint rhs) { return lhs.value != rhs.value; }
};

constexpr int mod = (int) 1e9 + 7;
using mint = modint<mod>;

void solve(istream &in, ostream &out) {
    int x, y;
    in >> x >> y;
    if (x > y)swap(x, y);
    mint res;
    if ((x + y) % 3 != 0) {
        res = 0;
    } else {
        int n = (x + y) / 3;
        int k = n / 2;
        while (x+1 <= y-1) {
            ++x;
            --y;
            --k;
        }
        if (k < 0 || k > n) {
            res = 0;
        } else {
            res = 1;
            for (int i = 0; i < k; i++) {
                res = res * (n - i) / (i + 1);
            }
        }
    }
    out << (int) res << '\n';
}


int main() {
    ios::sync_with_stdio(false);
    cin.tie(nullptr);
    std::istream& in(std::cin);
    std::ostream& out(std::cout);
    solve(in, out);
}