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: Accepted)

import java.util.Scanner;

public class Main {

	public static void main(String[] args) {
		Scanner scan = new Scanner(System.in);

		int x = scan.nextInt();
		int y = scan.nextInt();

		long a = 0;	//答え．何通りか

		if(x > 2*y || y > 2*x) {
			a = 0;
		}else if ((x + y)%3 != 0) {
			a = 0;
		}else {
			int n = (x+y)/3;
			int dif = Math.abs(x-y);
			int r = (n - dif)/2;

			int m = (int) (Math.pow(10, 9) + 7);

			a = 1;
			for(int i = 0; i < r; i++) {
				a = a * (n - i)%m * powMod(i+1, m-2, m) % m;
			}
		}

		System.out.println(a);

	}


	/**
	 *
	 * @param a 底
	 * @param b 指数
	 * @param m 法
	 * @return
	 */
	public static long powMod(long a, long b, long m) {
		long pow = 1;

		while (b > 0) {
			if((b & 1) == 1) {
				pow *= a%m;
				pow %= m;
			}
			a *= a%m;
			a %= m;
			b >>= 1;
		}

		return pow;
	}

}