Problem:
Score : 200 points

Problem Statement

We have a grid with N rows and M columns of squares. Initially, all the squares are white.

There is a button attached to each row and each column.
When a button attached to a row is pressed, the colors of all the squares in that row are inverted; that is, white squares become black and vice versa.
When a button attached to a column is pressed, the colors of all the squares in that column are inverted.

Takahashi can freely press the buttons any number of times. Determine whether he can have exactly K black squares in the grid.

Constraints

1 \leq N,M \leq 1000

0 \leq K \leq NM

Input

Input is given from Standard Input in the following format:

N M K

Output

If Takahashi can have exactly K black squares in the grid, print Yes; otherwise, print No.

Sample Input 1

2 2 2

Sample Output 1

Yes

Press the buttons in the order of the first row, the first column.

Sample Input 2

2 2 1

Sample Output 2

No

Sample Input 3

3 5 8

Sample Output 3

Yes

Press the buttons in the order of the first column, third column, second row, fifth column.

Sample Input 4

7 9 20

Sample Output 4

No

Solution in Common Lisp (SBCL 1.1.14) (judge verdict: Wrong Answer)

;;cyclone-loop
(defun cyclone-reader (stream char)
  (declare (ignore char))
  `(loop ,@(read stream t nil t) do ,(read stream t nil t)))
(set-macro-character #\CYCLONE #'cyclone-reader)
;;

;;unnamed-block
(defun block-reader (stream char)
  (declare (ignore char))
  `(progn ,@(read-delimited-list #\} stream t)))
(set-macro-character #\{ #'block-reader)
(set-macro-character #\} (get-macro-character #\)))
;;

(let ((n (read))
      (m (read))
      (k (read))
      (ans "No"))
  🌀 (for r to n
            :for black = 0)
  🌀 (for l to m)
  {(incf black (* l n))
   (incf black (* r m))
   (decf black (* 2 l r))
   (when (= black k) (setf ans "Yes")) }
  (format t "~A~%" ans))