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.*;
import java.awt.Point;

public class Main {
	static int mod = 1000000007;
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		long x = sc.nextLong();
		long y = sc.nextLong();
		if((x+y)%3 != 0) {
			System.out.println(0);
			return;
		}
		long n = (x+y)/3;
		x = x-n;
		y = y-n;
		if(x<0 || y<0) {
			System.out.println(0);
			return;
		}
		System.out.println(modCombination(x+y, x, mod));
	}
	public static long modCombination(long n, long r, long mod) {
		long top = 1;
		long bottom = 1;
		for (int i = 1; i <= r; i++) {
			top *= n;
			top %= mod;
			n--;
			bottom *= i;
			bottom %= mod;
		}
		bottom = modPow(bottom, mod-2, mod);
		return (top * bottom) % mod;
	}
	public static long modPow(long base, long exp, long mod) {
		if (exp == 0)
			return 1;
		if (exp == 1)
			return base % mod;
		if (exp % 2 == 1)
			return (base * modPow(base, exp - 1, mod) % mod);
		long tmp = modPow(base, exp / 2, mod);
		return (tmp * tmp) % mod;
	}
}