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.math.BigInteger;
import java.util.Scanner;

public class Main {

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int X = sc.nextInt();
		int Y = sc.nextInt();
		sc.close();

		BigInteger MOD = BigInteger.valueOf(1000000007L);
		if ( (X + Y) % 3 != 0 ) {
			System.out.println(0);
		} else {
			int N = (X + Y) / 3;
			int x = X - N;
			int y = Y - N;
			
			BigInteger ans = BigInteger.ONE;
			for ( int i = N ; i > x ; i-- ) {
				ans = ans.multiply(BigInteger.valueOf(i)).mod(MOD);
			}
			for ( int i = 1 ; i <= x ; i++ ) {
				ans = ans.multiply(BigInteger.valueOf(i).modInverse(MOD)).mod(MOD);
			}
			System.out.println(ans.toString());
		}
	}
}