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: Runtime Error)

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

int main() {
  int X, Y;
  cin >> X >> Y;
  if ((X + Y) % 3 == 0) {
    int a, b;
    a = (2 * Y - X) / 3;
    b = (2 * X - Y) / 3;
    if (a > 0 && b > 0) {
      long long int c, m;
      c = 1;
      m = 1;
      for (int i = a + 1; i <= a + b; i++) {
        c *= i;
      }
      for (int j = 1; j <= b; j++) {
        m *= j;
      }
      long long int ans;
      ans = (c / m) % 1000000007;
      cout << ans << endl;
    }
    else if (a < 0 || b < 0) {
      cout << 0 << endl;
    }
    else {
      cout << 1 << endl;
    }
  }
  else {
    cout << 0 << endl;
  }
}