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;
#define MOD 1000000007

int pow(int a, int n) {
  int res = 1;
  for (; n; n >>= 1) {
    if (n & 1) res = 1LL * res * a % MOD;
    a = 1LL * a * a % MOD;
  }
  return res;
}

int fact(int n) {
  int res = 1;
  for (int i = 1; i <= n; i++)
    res = 1LL * res * i % MOD;
  return res;
}

int comb(int p, int q) {
  int inv_fact_p = pow(fact(p), MOD-2);
  int inv_fact_q = pow(fact(q), MOD-2);
  int tmp = 1LL * inv_fact_p * inv_fact_q % MOD;
  return 1LL * tmp * fact(p+q) % MOD;
}

int main() {
  int x, y;
  cin >> x >> y;
  if ((x + y) % 3) {
    cout << 0 << endl;
    return 0;
  }
  int p = (y * 2 - x) / 3;
  int q = y - p * 2;
  if (p < 0 || q < 0) {
    cout << 0 << endl;
    return 0;
  }
  cout << comb(p, q) << endl;
}