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 Java7 (OpenJDK 1.7.0) (judge verdict: Time Limit Exceeded)

import java.util.*;
public class Main{
	
	//int[][] ar=new int[]
	public static int ways(int x,int y,int i,int j) {
		if(x==i && y==j)
			return 1;
		if(x<i || y<j)
			return 0;
		return (ways(x,y,i+1,j+2)%1000000007+ways(x,y,i+2,j+1)%1000000007)%100000007;
	}
	public static void main(String[] args) {
		Scanner sc=new Scanner(System.in);
		int x=sc.nextInt();
		int y=sc.nextInt();
		System.out.println(ways(x,y,0,0)%1000000007);
	}
}