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 Java (OpenJDK 11.0.6) (judge verdict: Wrong Answer)

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
 */
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);
        Knight solver = new Knight();
        solver.solve(1, in, out);
        out.close();
    }

    static class Knight {
        public static int MOD = 1000000007;
        static long[] fac;
        static long[] finv;
        static long[] inv;

        public void solve(int testNumber, Scanner in, PrintWriter out) {
            int x = in.nextInt();
            int y = in.nextInt();

            if ((x + y) % 3 != 0) {
                out.println(0);
                return;
            }

            comInit(2000000);
            int n = (2 * y - x) / 3;
            int m = (2 * x - y) / 3;

            out.println(combination((x + y) / 3, Math.min(n, m), MOD));

        }

        static void comInit(int max) {
            fac = new long[max + 1];
            finv = new long[max + 1];
            inv = new long[max + 1];

            // 階乗
            fac[0] = fac[1] = 1;
            // 逆元の階乗
            finv[0] = finv[1] = 1;
            // 逆元
            inv[1] = 1;

            for (int i = 2; i <= max; i++) {
                fac[i] = fac[i - 1] * i % MOD;
                inv[i] = MOD - inv[MOD % i] * (MOD / i) % MOD;
                finv[i] = finv[i - 1] * inv[i] % MOD;
            }
        }

        static long modPow(long x, long n, long mod) {
            if (n == 0) {
                return 1;
            }
            long result = modPow(x, n / 2, mod);

            if (n % 2 == 0) {
                return (result * result) % mod;
            }
            return (((result * result) % mod) * x) % mod;
        }

        static long modInv(long a, long mod) {
            return modPow(a, mod - 2, mod);
        }

        static long modDiv(long a, long b, long mod) {
            return a * modInv(b, mod) % mod;
        }

        static long combination(long n, long k, long mod) {

            long a = 1, b = 1;
            for (int i = 0; i < k; i++) {
                a = a * (n - i) % mod;
                b = b * (i + 1) % mod;
            }
            return modDiv(a, b, mod);
        }

    }
}