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 C++14 (Clang 3.8.0) (judge verdict: Wrong Answer)

#include<iostream>

int main()
{
	int h,w,t;
	bool found = false;
	std::cin >> h >> w >> t;
	for(int lx=0;lx<h;lx++)
	{
		for(int ly=0;ly<w;ly++)
		{
			if((lx*(w-ly)+(h-lx)*ly) == t)
			{
				found = true;
				goto end;
			}
		}
	}
end:
	std::cout << (found?"Yes":"No") << std::endl;
}