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.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Scanner;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author Silviase
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        Scanner in = new Scanner(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        DKnight solver = new DKnight();
        solver.solve(1, in, out);
        out.close();
    }

    static class DKnight {
        static int MOD = (int) 1e9 + 7;

        public void solve(int testNumber, Scanner in, PrintWriter out) {
            int x = in.nextInt();
            int y = in.nextInt();
            long res = 0;
            if ((x + y) % 3 != 0) {
                // res == 0
            } else {
                int el = (x + y) / 3;
                x -= el;
                y -= el;
                if (x >= 0 && y >= 0) {
                    res = ((
                            (modfact(x + y) * modinv(modfact(x))) % MOD)
                            * modinv(modfact(y))) % MOD;
                }
            }
            out.println(res);
        }

        public static long modfact(long n) {
            long res = 1;
            for (int i = 1; i <= n; i++) {
                res = (res * i) % MOD;
            }
            return res;
        }

        public static long modinv(long n) {
            return modpow(n, MOD - 2);
        }

        public static long modpow(long n, long a) {
            long res = 1;
            while (a != 0) {
                if (a % 2 == 1) {
                    res = n * res % MOD;
                }
                a /= 2;
                n = (n * n) % MOD;
            }
            return (int) res;
        }

    }
}