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: Accepted)

(defun f ()
  (let ((N (read)) (M (read)) (K (read)))
    (defun fLIP? (N M K)
      (defun iter (i j)
	  (if (= i (+ N 1))
	      nil
	      (if (= (+ M 1) j)
		  (iter (+ i 1) 0)
		  (if (= (+ (* i j) (* (- N i) (- M j)))
			 K)
		      t
		      (iter i (+ j 1))))))
      (iter 0 0))
    (if (fLIP? N M K)
	(format t "~A~%" "Yes")
	(format t "~A~%" "No"))))

(f)