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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.util.*;
public class Main {
	
    public static long gcd(long x,long y){
        if(x < y) return gcd(y, x);
        if(y == 0) return x;
        return gcd(y, x % y);
    }
    public static long lcm(long x,long y){                                                              
        return x*(y/gcd(x,y));                                                                                                                                                                                                                
    }
    public static long com(long x,long y){
        if(x<=1 || y==0 || y==x) return 1; 
        return com(x-1,y-1) + com(x-1,y);
    }
    public static void main(String[] args){
		Scanner sc = new Scanner(System.in);
		long x = sc.nextLong();
		long y = sc.nextLong();
        long ans = 0;
        if((x+y)%3==0 && y<=x/2 && y<=2*x){long n = (x+y)/3; 
                                           long k = x-n;
                                          ans = com(n,k);}
		System.out.println(ans);
	}
}