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.

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.

Constraints

• $1 \leq X \leq 10^6$
• $1 \leq Y \leq 10^6$
• All values in input are integers.

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.

见题面 Input 部分

见题面 Output 部分