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 {

    public static void main(String[] args) {

        Scanner in = new Scanner(System.in);
        String[] params = in.nextLine().split(" ");
        int x = Integer.parseInt( params[0] );
        int y = Integer.parseInt( params[1] );

        if( y > 2 * x ){
            System.out.println( 0 );
            return;
        }
        if( y == 2 * x ){
            System.out.println( 1 );
            return;
        }
        if( (float)y < (float)x / 2 ){
            System.out.println( 0 );
            return;
        }
        if( (float)y == (float)x / 2 ){
            System.out.println( 1 );
            return;
        }

        int b = y + x;
        if( b % 3 != 0 ){
            System.out.println( 0 );
            return;
        }







        System.out.println( 0 );
        return;

    }

}