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<0||y<0||(y+x)%3!=0) System.out.println(0);
else if(x>=y){
 int k = x - y;
  int t = (y - k)/3;
    
  System.out.println(nCk(2*t+k, t,1000000007));
}
   else{
 int k = y - x;
  int t = (x - k)/3;
    
  System.out.println(nCk(2*t+k, t,1000000007));

}

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

    public static long pow(long a,long b,int M) {
        long ret = 1;
        long tmp = a;
        while(b>0) {
            if((b&1)==1) ret = (ret * tmp) % M;
            tmp = (tmp * tmp) % M;
            b = b>>1;
        }
        return ret;
    }
}