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;

class Program
{
    static void Main()
    {
        string[] array = Console.ReadLine().Split(' ');
        int n = int.Parse(array[0]);
        int m = int.Parse(array[1]);
        int k = int.Parse(array[2]);

        bool[] db = new bool[n * m + 1];
        for (int i = 0; i <= n; i++)
            db[i * m] = true;
        for (int i = 0; i <= m; i++)
            db[i * n] = true;

        for (int i = 1; i <= m / 2; i++)
        {
            for (int j = 1; j < n; j++)
            {
                db[i * n + j * (m - i * 2)] = true;
            }
        }

        for (int i = 1; i <= n / 2; i++)
        {
            for (int j = 1; j < m; j++)
            {
                db[i * m + j * (n - i * 2)] = true;
            }
        }

        if (db[k]) Console.WriteLine("Yes");
        else Console.WriteLine("No");
    }
}