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 int64_t mod = 1000000007;

int64_t power(int64_t n, int64_t k) {
  if (k == 0) return 1;
  int64_t half = power(n, k / 2), half2 = half * half % mod;
  if (k % 2) {
    return n * half2 % mod;
  } else {
    return half2;
  }
}

int main() {
  int x0, y0, n, x, y;
  cin >> x0 >> y0;
  if ((x0 + y0) % 3) {
    cout << 0 << endl;
    return 0;
  }
  n = (x0 + y0) / 3;
  x = x0 - n;
  y = n - x;
  if (x < 0 || y < 0) {
    cout << 0 << endl;
    return 0;
  }
  vector<int64_t> fact(n + 1, 1), inv(n + 1, 1);
  for (int i = 1; i <= n; i++) {
    fact.at(i) = fact.at(i - 1) * i % mod;
    inv.at(i) = power(fact.at(i), mod - 2);
  }
  cout << fact.at(n) * inv.at(x) % mod * inv.at(y) % mod << endl;
}