CODE FESTIVAL 2017 qual A

B - fLIP

Time limit時間制限 : 2sec / Memory limitメモリ制限 : 256MB

問題文

NM 列のマス目があり、最初は全てのマスが白いです。

制約

• 1 \leq N,M \leq 1000
• 0 \leq K \leq NM

入力

N M K


入力例 1

2 2 2


出力例 1

Yes


1 行目、 1 列目の順にボタンを押せばよいです。

入力例 2

2 2 1


出力例 2

No


入力例 3

3 5 8


出力例 3

Yes


1 列目、3 列目、2 行目、5 列目の順にボタンを押せばよいです。

入力例 4

7 9 20


出力例 4

No


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