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 = Integer.parseInt(sc.next());
    int y = Integer.parseInt(sc.next());
    int ans = 0;
    int tmpx = x;
    int tmpy = y;
    if((x % 3 == 0 && y % 3 == 0) || (x % 3 == 1 && y % 3 == 2) || (x % 3 == 2 && y % 3 == 1)) {
      int count = 0;
      while(!(tmpx == 0 && tmpy == 0)) {
        if(tmpx >= tmpy) {
          count++;
          tmpx -= 2;
          tmpy -= 1;
        } else {
          tmpx -= 1;
          tmpy -= 2;
        }
      }
      ans = nCk((x + y) / 3, count);
    }
    System.out.println(ans);
  }

  public static int nCk(int n,int k) {
    int M = 1000000007;
    long ret = 1;
    int min = Math.min(k, n-k);
    for(int i=1;i<=min;i++) {
      ret = (long)(ret * (Math.pow(i,M-2) % M)) % M;
    }
    for(int i=n-min+1;i<=n;i++) {
      ret = (ret * i) % M;
    }
    return (int)ret;
  }
}