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 codefes2017
{
    class Program
    {
        static void Main()
        {
            var s = Console.ReadLine().Split(' ').Select(st => int.Parse(st)).ToArray();

            int n = s[0];
            int m = s[1];
            int k = s[2];
            bool can = false;

            int all_panel = n * m;

            for(int r = 0; r <= n; r++){
                for(int c = 0; c <= m; c++){
                    int black = r * (m - c) + c * (n - r);
                    if(k == black || k == all_panel - black) {
                        can = true;
                        break;
                    }
                }
            }

            if (can){
                Console.WriteLine("Yes");
            } else {
                Console.WriteLine("No");
            }
        }
    }
}