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

int main(){
  long long x, y; cin >> x >> y;
  if((2 * x - y) % 3 != 0 | (2 * y - x) % 3 != 0){
    cout << 0;
    return 0;
  }
  long long a, b;
  a = (2 * x - y) / 3;
  b = (2 * y - x) / 3;
  long long abx = 1, ax = 1, bx = 1;
  for(int i = 1; i < a + 1; i++){
    ax *= i;
    ax = ax % 1000000007;
  }
  for(int i = 1; i < b + 1; i++){
    bx *= i;
    bx = bx % 1000000007;
  }
  for(int i = 1; i < a + b + 1; i++){
    abx *= i;
    abx = abx % 1000000007;
  }
  cout << abx / (ax * bx);
}