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)

#include <bits/stdc++.h>
using namespace std;

const int MOD = 1000000000 + 7;
const int MAX = 2000000;

long long combination(long long N_, long long R_) {
    const int NUM_ = MAX;
    static long long fact[NUM_+1], invfact[NUM_+1], mod_inv[NUM_+1];
    fact[0] = fact[1] = invfact[0] = invfact[1] = mod_inv[1] = 1;
    for (int i = 2; i < NUM_; i++) {
        if (i > N_ && i > R_) break;
        fact[i] = fact[i - 1] * i % MOD;
        mod_inv[i] = mod_inv[MOD % i] * (MOD - MOD / i) % MOD;
        invfact[i] = invfact[i - 1] * mod_inv[i] % MOD;
    }
    return fact[N_] * invfact[R_] % MOD * invfact[N_-R_] % MOD;
}

int main() {
    int x,y;
    cin >> x >> y;

    if ((x + y) % 3 != 0) {
        cout << 0 << endl;
        return 0;
    }

    int count = (x + y) / 3;
    int n = y - count;
    int m = x - count;

    if (n < 0 || m < 0) {
        cout << 0 << endl;
        return 0;
    }

    cout << combination(n + m, n) << endl;
    
    return 0;
}