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 <iostream>
#include <vector>
#define MOD 1000000007
#define MAX_N 2000000

using namespace std;

long long fact[MAX_N];
long long modpow(long long a, long long n)
{
  if (n == 0) return 1;
  long long b = modpow(a, n/2);
  b = b*b % MOD;
  if (n % 2 == 0) return b;
  else return a*b % MOD;
}
long long moddiv(long long a, long long b) {
  return (a * modpow(b, MOD - 2)) % MOD;
}
void factInit() {
  fact[0] = 1;
  for (int i = 1; i < MAX_N; i++) {
    fact[i] = (i * fact[i - 1]) % MOD;
  }
}
// Combination(binomial coefficients)
long long comb(int n, int r) {
  if (n < r || n < 0 || r < 0) return 0;
  return moddiv(fact[n], (fact[r] * fact[n - r]) % MOD);
}

int main() {
  factInit();
  int X, Y;
  cin >> X >> Y;

  long long ans = 0;
  for (int x = 0; x <= X; x++) {
    int k = X - x;
    if (x < k && Y == 2*k - x) {
      (ans += comb(k, x)) %= MOD;
    }
  }
  cout << ans << endl;
  return 0;
}