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.Scanner;
public class Main{
 public static void main(String[] args){
   Scanner sc = new Scanner(System.in);
    int x = sc.nextInt(); 
    int y = sc.nextInt(); 
if(x>=y){
 int k = x - y;
  if((y-k)%3!=0) System.out.println(0);
  else{
  int t = (y - k)/3;
    
  System.out.println(calcNumOfCombination(2*t+3*k, t+k)%1000000007);
   
  }
}
   else{
 int k = y - x;
  if((x-k)%3!=0) System.out.println(0);
  else{
  int t = (x - k)/3;
    
  System.out.println(calcNumOfCombination(2*t+3*k, t+k)%1000000007);
   
  }
}

 }
   static  long calcNumOfCombination(int n, int r){
        long num = 1;
        for(int i = 1; i <= r; i++){
            num = num * (n - i + 1) / i;
        }
        return num;
    }
}