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 <iostream>
#define rep(i,n)  for (int i=1;i<=n;i++)

using namespace std;
long int d=1000000000+7;
int main()
{
long int x,y;
cin>>x>>y;
if ((x+y)%3!=0)
cout <<0;
else
{long int a,b;
a=(2*y-x)/3;
b=(2*x-y)/3;
long int a0=1,a1=1;
rep(i,a)
a1*=i;
rep(i,a)
a0*=(a+b-i+1);
cout <<(a0/a1)%d;
}



}