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: Accepted)

import java.util.Scanner;

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 k = (x+y)/3;
      	int ans = 0;
      	if((x+y)%3==0 && x-k>=0 && y-k>=0){
          ans = modCombination(x+y-2*k,x-k,1000000007);
        }
      	System.out.print(ans);
        System.out.flush();
    }
    public static int modCombination(int n , int k , int div){
        long fact = 1;
        long inverse = 1;
        for(int i=n;i>=n-k+1;i--){
            fact = (fact*i)%div;
            inverse = (inverse*(i-n+k))%div;
        }

        return (int)((fact*pow(inverse,div-2,div))%div);
    }
    //xのn乗をmodで割ったあまりを返す
    public static long pow(long x,int n,int div){
        long ans = 1;
        while(n>0){
            if((n & 1)==1){
                ans = (ans*x)%div;
            }
            x = (x*x)%div;
            n>>=1;
        }
        return ans;
    }
}