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: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace ConsoleApp3
{
    class Program
    {
        static void Main(string[] args)
        {
            var values = Console.ReadLine().Split(' ').Select(i => int.Parse(i)).ToArray();
            var N = values[0];
            var M = values[1];
            var K = values[2];

            var sum = 0;
            for (int i = 0; i < N; i++)
            {
                sum = i * M;
                if (sum == K)
                {
                    Console.WriteLine("Yes");
                    return;
                }
                for (int j = 0; j < M; j++)
                {
                    sum -= j * i;
                    sum += (N - j) * i * j; 
                    if (sum == K)
                    {
                        Console.WriteLine("Yes");
                        return;
                    }
                }
                sum = 0;
            }
            Console.WriteLine("No");
            Console.Read();
        }
    }
}