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 (7.4.4) (judge verdict: Accepted)

<?php
list($n, $m, $k) = ints();
for ($i = 0; $i <= $n; ++$i) {
    for ($j = 0; $j <= $m; ++$j) {
        $cnt = $i * $m + $j * $n - 2 * $i * $j;
        if ($cnt === $k) exit('Yes');
    }
}
echo 'No';
function ints()
{
    return array_map('intval', explode(' ', trim(fgets(STDIN))));
}