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: Runtime Error)


import java.util.Scanner;

public class Main {
	public static void main(String[] args) {
		Main main = new Main();
		main.run();
	}

	int X;
	int Y;
	int MOD = (int)Math.pow(10, 9) + 7;
	int SIZE = (int)Math.pow(10, 6)+2;
	long fact[];
	long inv[];
	public void run() {
		Scanner sc = new Scanner(System.in);
		X = sc.nextInt();
		Y = sc.nextInt();
		init(SIZE);
		long ans = calc(X,Y);
		System.out.println(ans);
		sc.close();
	}

	private void init(int size) {
		fact = new long[size+1];
		inv = new long[size+1];

		fact[0]=1;
		inv[0]=1;

		for(int i=1; i<=size; i++) {
			fact[i] = (fact[i-1] * i) % MOD;
			inv[i] = pow(fact[i], MOD-2) % MOD;
		}
	}

	private long calc(int x, int y) {
		if((x+y) % 3 == 0) {
			int a = (2 * x - y) / 3;
			int b = (2 * y - x) / 3;
			long ans = comb(a+b, a);
			return ans;
		} else {
			return 0;
		}
	}
	private long comb(int n, int k) {
		return fact[n] * inv[k] % MOD * inv[n-k] % MOD;
	}

	//反復２乗法
	//x^y
	private long pow(long x, int n) {
		long ans = 1;
		while(n>0) {
			if((n & 1) == 1) {
				ans = ans * x % MOD;
			}
			x = x * x % MOD;
			n >>= 1;
		}
		return ans;
	}
}