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 2.0.3) (judge verdict: Wrong Answer)

;;;; mod
(let ((p 1000000007))
  (defun mod+ (a b)
    (mod (+ a b) p))
  
  (defun mod* (a b)
    (mod (* a b) p))
  
  (defun mod_expt (a z)
    (loop :with ans := 1
          :with pow := a
          :while (> z 0)
          :do (multiple-value-bind (x y) (floor z 2)
                (setf z x)
                (if (= y 1) (setf ans (mod* ans pow)))
                (setf pow (mod* pow pow)))
          :finally (return ans)))
  
  (defun mod_inv (a)
    ; TODO use Euclidean
    (mod_expt a (- p 2))))

;;;; main
(let* ((x (read))
       (y (read))
       (n (/ (- (* 2 x) y) 3))
       (m (/ (- (* 2 y) x) 3)))
  (if (and (<= n 0) (<= m 0) (integerp n) (integerp m))
      (let ((f (make-array (list (+ n m 1))))
            (f-1 (make-array (list (+ n m 1)))))
        (setf (aref f 0) 1)
        (setf (aref f-1 0) 1)
        (setf (aref f 1) 1)
        (setf (aref f-1 1) 1)
        (loop :for i :from 2 :to (+ m n)
              :do (setf (aref f i) (mod* (aref f (1- i)) i))
              :do (setf (aref f-1 i) (mod* (aref f-1 (1- i)) (mod_inv i))))
        (format t "~A~%" (mod* (aref f (+ m n)) (mod* (aref f-1 n) (aref f-1 m)))))
      (format t "0~%")))