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 OCaml (4.02.3) (judge verdict: Accepted)

let m = 1000000007
let ( * ) a b = a * b mod m
let rec f n a = if n <= 1 then a else f (n - 1) (a * n)
let rec g b n = if n <= 0 then 1 else let p = g b (n / 2) in p * p * if n mod 2 = 0 then 1 else b
let c n r = if n < r || n < 0 || r < 0 then 0 else f n 1 * g (f r 1) (m - 2) * g (f (n - r) 1) (m - 2)
let _ = Scanf.scanf "%d %d" @@ fun x y -> Printf.printf "%d\n" @@ if (x + y) mod 3 > 0 then 0 else c ((x + y) / 3) (y - (x + y) / 3)