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.Linq;
using System.Collections.Generic;

namespace Algorithm
{
    class Program
    {
        static void Main(string[] args)
        {
            var l = Console.ReadLine().Split().Select(int.Parse).ToArray();
            int N = l[0], M = l[1], K = l[2];
            var set = new HashSet<int>();
            
            set.Add(0);
            set.Add(N*M);
            for (var i = N; i < N*M; i+=N)
                set.Add(i);
            for (var i = M; i < N*M; i+=M)
                set.Add(i);
            for (var i = 1; i < N; i++)
                set.Add((N-1)*i+M-i);
            for (var i = 1; i < M; i++)
                set.Add((M-1)*i+N-i);
                
            Console.WriteLine(set.Contains(K)?"Yes":"No");
        }
    }
}