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 ((2 * X - Y) % 3 != 0 || (2 * Y - X) % 3 != 0) {
    cout << 0 << endl;
  }
  else {
    int a, b;
    a = (2 * X - Y) / 3;
    b = (2 * Y - X) / 3;
    int child, mother;
    child = 1;
    mother = 1;
    for (int i = a + 1; i <= a + b; i++) child *= i;
    for (int j = 2; j <= b; j++) mother *= j;
    cout << child / mother << endl;
  }
}