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.Linq;

namespace code_festival_2017_quala_b
{
    class Program
    {
        static void Main(string[] args)
        {
            int[] x = Console.ReadLine().Split().Select(int.Parse).ToArray();
            bool ret = false;
            for (int i = 0; i <= x[0]; i++)
            {
                for (int j = 0; j <= x[1]; j++)
                {
                    if ((x[0] - i) * j + (x[1] - j) * i == x[2]) ret = true;
                }
            }
            Console.WriteLine(ret ? "Yes" : "No");
        }
    }
}