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 $10^9 + 7$.