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.Scanner;
public class Main {
static long ans=0;
@SuppressWarnings("resource")
public static void main(String[] args) {
	Scanner sc =new Scanner(System.in);
	int X=sc.nextInt();
	int Y=sc.nextInt();
	int m=0;
	int n=0;
	if(!((X+Y)%3==0)) {
		System.out.println(0);
		System.exit(0);
	}else {
		m=(2*X-Y)/3;
		n=X-2*m;
		if(n<0||m<0) {
			System.out.println(0);
			System.exit(0);
		}else {
			ans=1;
			for(int i=0;i<n;i++) {
				ans*=n+m-i;
				ans/=n-i;

			}
		}
		ans%=(Math.pow(10, 9)+7);
		System.out.println(ans);

	}
}
}