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 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include<stdio.h>
long combi(int n, int r);
int main(void){
  int X,Y;
  scanf("%d,%d",&X,&Y);
  int a,b;
  a = (2*X-Y)/3;
  b = (2*Y-X)/3;
  if (((((2*Y-X)%3==0) && ((2*X-Y)%3==0)) && a>0) && b>0){
  printf("%d",combi(a+b,b)%1000000007);
  }else
  {
  printf("0");
  }
  
  }

long combi(int n, int r) {
    if (r == 0) {
        return 1;
    }
    return (n - r + 1) * combi(n, r - 1) / r;
}