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);
        long X = sc.nextLong();
        long Y = sc.nextLong();
        long y = (2*Y-X);
        if(y%3!=0) System.out.println(0);
        else{
            y/=3;
            long x = Y-2*y;
            long x2=1;
            ArrayList<Long> X2 = new ArrayList<>();
            for(long i=1;i<=x;) {
                if(x2*i>1000000007) {
                    X2.add(x2);
                    x2 =1;
                }
                else i++;
            }
            long y2 =1;
            ArrayList<Long> Y2 = new ArrayList<>();
            for(long i=1;i<=y;) {
                if(y2*i>1000000007) {
                    Y2.add(y2);
                    y2 =1;
                }
                else i++;
            }
            long n = 1;
            for(long i=1;i<=x+y;i++) n = n*i%1000000007;
            long sum = n;
            for(int i=0;i<X2.size();i++) sum/=X2.get(i)%1000000007;
            for(int i=0;i<Y2.size();i++) sum/=Y2.get(i)%1000000007;
            System.out.println(sum);
        }
    }
}