Score : 200 points
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.
Input is given from Standard Input in the following format:
N M K
If Takahashi can have exactly K black squares in the grid, print Yes
; otherwise, print No
.
2 2 2
Yes
Press the buttons in the order of the first row, the first column.
2 2 1
No
3 5 8
Yes
Press the buttons in the order of the first column, third column, second row, fifth column.
7 9 20
No