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 PHP7 (7.0.15) (judge verdict: Accepted)

<?php
ini_set('error_reporting', E_ALL & ~E_NOTICE);

fscanf(STDIN, "%d %d %d", $N, $M, $K);

$array = array();

for ($i = 0; $i <= $N; $i++) {
    for ($j = 0; $j <= $M; $j++) {
        $x = $i * $j + ($N - $i) * ($M - $j);
        $array[$x] = 1;
    }
}

echo $array[$K] ? "Yes" . "\n" : "No" . "\n";