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>

int main(){
   long d,x,y,a,b,t,i;
 
   scanf("%ld %ld",&x,&y);
   if ((2*x-y)%3==0 && (2*y-x)%3==0) {
      a=(2*x-y)/3;b=(2*y-x)/3;
      if (a<b) {
         t=a;a=b;b=t;
      }
      d=1;a++;
      for (i=0;i<b;i++)
         d=(d*a)%1000000007;
      printf("%ld\n",d);
   } else
      puts("0");
   return 0;
}