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 final long mod = 1000000007;

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int x = sc.nextInt();
		int y = sc.nextInt();
		if((2*y-x)%3 == 0 && (2*x-y)%3 == 0) {
			long X = (2*x-y)/3;
			long Y = (2*y-x)/3;
			long ans = 1;
			if(X >= Y) {
				long XY = X+Y;
				while(XY > Y) {
					ans = ans*XY%mod;
					XY -= 1;
				}
				ans = ans*pow(kaijo(X), mod-2)%mod;
			}else{
				long XY = X+Y;
				while(XY > X) {
					ans = ans*XY%mod;
					XY -= 1;
				}
				ans = ans*pow(kaijo(Y), mod-2)%mod;
			}
			System.out.println(ans);
		}else {
			System.out.println(0);
		}
		sc.close();
	}

	private static long kaijo(long n) {
	    long a = 1;
		while(n != 0) {
			a = a*n%mod;
			n = n-1;
		}
		return a;
	}

	public static final long pow(long x, long n) {
	    long sum = 1;
	    while (n > 0) {
	        if ((n & 1) == 1) {
	            sum = sum * x % mod;
	        }
	        x = x*x%mod;
	        n >>= 1;
	    }
	    return sum;
	}
}