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# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace atcoder
{
	class Program
	{
		static void Main(string[] args)
		{
			var input = Console.ReadLine().Split(' ').Select(int.Parse).ToArray();
			bool ans = false;
			for(int i = 0;i <= input[0];i++)
			{
				for(int j = 0;j <= input[1];j++)
				{
					if((long)j * input[0] + (long)i * input[1] - 2 * i * j == input[2])
					{
						ans = true;
					}
				}
			}
			if (ans) Console.WriteLine("Yes");
			else Console.WriteLine("No");
			//Console.ReadLine();
		}
	}
}