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 <iostream>

using namespace std;

const int Q = (int)1e9 + 7;
int fact[1010101];
int revf[1010101];

int comb(int n, int r)
{
    if(n < r) return 0;
    return (long long)fact[n] * revf[n - r] % Q * revf[r] % Q;
}

int main()
{
    ios_base::sync_with_stdio(false);
    cin.tie(nullptr);

    int a, b; cin >> a >> b;
    if((a + b) % 3) {cout << 0; return 0;}
    int t = (a + b) / 3;
    a -= t; b -= t; if(a < 0 || b < 0) {cout << 0; return 0;}

    fact[0] = fact[1] = 1;
    for(int i = 2; i < 1010101; ++i) fact[i] = (long long)i * fact[i - 1] % Q;
    revf[0] = revf[1] = 1;
    for(int i = 2; i < 1010101; ++i) revf[i] = Q - (long long)revf[Q % i] * (Q / i) % Q;
    for(int i = 2; i < 1010101; ++i) revf[i] = (long long)revf[i] * revf[i - 1] % Q;

    cout << comb(a + b, b);
    return 0;
}