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 rec power ( * ) e m n =
  if n <= 0 then e
  else power ( * ) (if n land 1 = 0 then e else m * e) (m * m) (n lsr 1)

let m = 1000000007
let ( *^ ) x y = (x * y) mod m

let perm n k = Array.fold_left ( *^ ) 1 @@ Array.init k @@ ( + ) @@ n - k + 1
let comb n k = power ( *^ ) (perm n k) (perm k k) (m - 2)

let () = Scanf.scanf "%d %d\n" @@ fun x y ->
  Printf.printf "%d\n" @@ if
    2 * x - y < 0 ||
    0 < (2 * x - y) mod 3 ||
    2 * y - x < 0 ||
    0 < (2 * y - x) mod 3
  then 0
  else comb ((x + y) / 3) ((2 * x - y) / 3)