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 Common Lisp (SBCL 1.1.14) (judge verdict: Runtime Error)

(defun root (x y)
(declaim (optimize (speed 3) (debug 0) (safety 0)))
  (if (or (<= x 0) (<= y 0))
      (if (and (= x 0) (= y 0)) 1 0)
      (+ (root (- x 1) (- y 2)) (root (- x 2) (- y 1)))))

(defun knight ()
  (let* ((x (read))
        (y (read)))
    (format t "~d" (mod (root x y) (+ (expt 10 9) 7) ))))

(knight)