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)

#region Using directives
using System;
using static System.Console;
using static System.Convert;
using System.Collections.Generic;
using System.Linq;
#endregion

namespace ConsoleApp2
{
    class Program
    {
        static void Main(string[] args)
        {
            string[] s = (ReadLine()).Split();
            long N = ToInt64(s[0]);
            long M = ToInt64(s[1]);
            long K = ToInt64(s[2]);
            for (long i = 0; i <= N; i++)
            {
                long answ = 0;
                for(long j = 0; j <= M; j++)
                {
                    answ = i*j + (N-i)*(M-j);
                    if (answ == K)
                    {
                        WriteLine("Yes");
                        ReadKey();
                        return;
                    }
                }
            }
            WriteLine("No");
            ReadKey();
        }
    }
}