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 (Clang 3.8.0) (judge verdict: Runtime Error)

#include <stdio.h>
int factorial(int num) {
  int sol = 1;
  for (int n = 0; n < num; n++) {
    sol = sol * (n + 1);
  }
  return sol;
}

int main(void) {
  int x, y;
  int r = scanf("%d %d", &x, &y);
  int move = (int)(x + y) / 3;
  int abs = y - x;
  printf("%d",
         (factorial(move) /
          (factorial((move - abs) / 2) * factorial((move - abs) / 2 + abs)) %
          1000000007));
}