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 PHP (5.6.30) (judge verdict: Wrong Answer)

<?php
error_reporting(0);
list($N,$M,$K) = explode(" ",trim(fgets(STDIN)));
//$N = trim(fgets(STDIN));
if ((($N % $K == 0) || ($M % $K == 0))&& $K!=1) {
  printf("Yes\n");
  exit;
}
if (min($N,$M)>$K) {
  printf("No\n");
  exit;
}
$m = max($N,$M);
$n = min($N,$M);
for($i=0;$i<$m;$i++) {
    printf("%d\n",$m-($i+1)+(($n-1)*($i+1)));
    if ($m - ($i+1) + (($n-1)*($i+1))==$K) {
      printf("Yes\n");
      exit;
    }
}
printf("No\n");