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.*;
import java.io.*;

class Main{
    public static void main(String[] args){
        Scanner sc=new Scanner(System.in);
        long x=sc.nextLong(), y=sc.nextLong();
        sc.close();
        if((x*2-y)%3!=0 || (y*2-x)%3!=0){
            System.out.println(0);
            return;
        }
        long mod=1_000_000_007;
        long a=(x*2-y)/3;
        long b=(y*2-x)/3;
        long ans=comb(a+b, a, mod);
        System.out.println(ans);
    }
    public static long modinv(long a, long MOD){
        long b=MOD, u=1, v=0;
        long tmp;
        while(b>=1){
            long t=a/b;
            a-=t*b;
            tmp=a; a=b; b=tmp;
            u-=t*v;
            tmp=u; u=v; v=tmp;
        }
        u%=MOD;
        return u>=0?u:u+MOD;
    }
    public static long comb(long n, long r, long MOD){
        if(n<r) return 0;
        r=Math.min(r, n-r);
        long res=1;
        for(int d=1;d<=r;d++){
            res*=n;
            res%=MOD;
            n--;
            res*=modinv(d, MOD);
            res%=MOD;
        }
        return res;
    }
}