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: Runtime Error)

import java.util.Scanner;

public class Main {
    public static void main(String[] args) {
        long c = (long) (10E9 + 1);
        Scanner sc = new Scanner(System.in);
        int x = sc.nextInt();
        int y = sc.nextInt();
        System.out.println(solve(x,y)%c);
    }
    private static long solve(int x, int y) {
        long[][] tab =  new long[x+1][y+1];
        tab[0][0] = 1;
        for(int i = 1; i <= x; i++) {
            for (int j = 1; j <= y; j++) {
                tab[i][j]  = ((j >= 2) ? tab[i-1][j-2]: 0) + ((i >=2) ? tab[i-2][j-1]: 0);
            }
        }
        return tab[x][y];
    }

}