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.IO;
using System.Linq;
using System.Collections.Generic;
using System.Text;

public class Program
{

	public void Proc()
	{
        int[] inpt = Reader.ReadLine().Split(' ').Select(a => int.Parse(a)).ToArray();

        this.RowCount = inpt[0];
        this.ColCount = inpt[1];
        this.Target = inpt[2];

        string ans = "No";
        for (int i = 0; i <= this.RowCount; i++) {
            if(this.ColCount * i == Target) {
                ans = "Yes";
                break;
            }
            for (int j = 0; j <= this.ColCount; j++) {
                long calc = this.ColCount * i;
                calc -= (i * j * 2);
                calc += this.RowCount * j;
                if(calc == Target) {
                    ans = "Yes";
                    break;
                }
            }
            if(ans.Equals("Yes")) {
                break;
            }
        }
        Console.WriteLine(ans);



    }

    private int RowCount;
    private int ColCount;
    private int Target;


    public class Reader
	{
		private static StringReader sr;
		public static bool IsDebug = false;
		public static string ReadLine()
		{
			if (IsDebug)
			{
				if (sr == null)
				{
					sr = new StringReader(InputText.Trim());
				}
				return sr.ReadLine();
			}
			else
			{
				return Console.ReadLine();
			}
		}
		private static string InputText = @"


7 9 20



";
	}

	public static void Main(string[] args)
	{
#if DEBUG
		Reader.IsDebug = true;
#endif
		Program prg = new Program();
		prg.Proc();
	}
}