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: Wrong Answer)

import java.util.*;

public class Main {
  public static void main(String[] args) {
    Scanner sc = new Scanner(System.in);
    int X = sc.nextInt();
    int Y = sc.nextInt();
    sc.close();
    if ((X+Y)%3 != 0) {
      System.out.println(0);
      return;
    }
    int a = X - (X+Y)/3, b = Y - (X+Y)/3;
    long out = 1;
    long modv = (long)Math.pow(10, 9) + 7;
    for (int i = a+1; i <= a+b; i++) {
      out *= i;
      out = out % modv;
    }

    long div = 1;
    for (int i = 1; i <= b; i++) {
      div *= i;
      div %= modv;
    }

    long invDiv = inv(div, modv);
    System.out.println(out*invDiv % modv);
  }

  private static long inv(long a, long p) {
    if (a == 1) return 1;
    return (p - p/a) * inv(p % a, p) % p;
  }
}