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.io.*;
import java.util.function.*;

class Main {
    static Scanner scanner = new Scanner();
    static int mod = 1000000007;
    static int inf = 0x7ffffff;

    void solve() {
        int x = scanner.nextInt();
        int y = scanner.nextInt();
        if ((x + y) % 3 != 0) {
            System.out.println(0);
        } else {
            int n = (x + y) / 3;
            int r = x - n;
            if (r < 0 || n < r) {
                System.out.println(0);
            } else {
                System.out.println(combinationAndMod(n, r));
            }
        }
    }

    static long combinationAndMod(long n, long r) {
        long x = 1, y = 1;
        for (long i = 1; i <= r; i++) {
            x = x * (n - r + i) % mod;
            y = y * i % mod;
        }
        return x * powAndMod(y, mod - 2) % mod;
    }

    static long powAndMod(long a, long b) {
        return b == 0 ? 1 : b % 2 == 1 ? a * powAndMod(a, b - 1) % mod : powAndMod(a * a % mod, b / 2);
    }

    public static void main(String[]$) throws Exception {
        new Main().solve();
        System.out.flush();
    }
}

class System {
    static PrintWriter out = new PrintWriter(java.lang.System.out);

    static void exit() {
        java.lang.System.exit(0);
    }
}

class Scanner {
    private BufferedReader reader = new BufferedReader(new InputStreamReader(java.lang.System.in), 0x10000);
    private StringTokenizer tokenizer;

    String next() {
        try {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                tokenizer = new StringTokenizer(reader.readLine());
            }
        } catch (IOException ignored) {
        }
        return tokenizer.nextToken();
    }

    int nextInt() {
        return Integer.parseInt(next());
    }

    long nextLong() {
        return Long.parseLong(next());
    }

    char[][] nextCharArray(int n, int m) {
        char[][] a = new char[n][m];
        for (int i = 0; i < n; i++) {
            a[i] = next().toCharArray();
        }
        return a;
    }

    int[] nextIntArray(int n) {
        int[] a = new int[n];
        for (int i = 0; i < n; i++) {
            a[i] = nextInt();
        }
        return a;
    }

    int[] nextIntArray(int n, IntUnaryOperator op) {
        int[] a = new int[n];
        for (int i = 0; i < n; i++) {
            a[i] = op.applyAsInt(nextInt());
        }
        return a;
    }

    long[] nextLongArray(int n) {
        long[] a = new long[n];
        for (int i = 0; i < n; i++) {
            a[i] = nextLong();
        }
        return a;
    }

    long[] nextLongArray(int n, LongUnaryOperator op) {
        long[] a = new long[n];
        for (int i = 0; i < n; i++) {
            a[i] = op.applyAsLong(nextLong());
        }
        return a;
    }
}