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.Collections.Generic;
using System.Linq;
using System.Text;
class Program
{
    public static bool f = false, t = true;
    static void Main(string[] args)
    {
        int[] a = Console.ReadLine().Split().Select(int.Parse).ToArray();
        if (a[0] * a[1] < a[2]) { Console.WriteLine("No");return; }
            if (a[2] == 0) { Console.WriteLine("Yes");return; }
         for (int i = 0; i <= a[0]; i++)
        {
            for(int j = 0; j <= a[1]; j++)
            {
                if (i * a[1] + j * a[0] - i * j *2== a[2])
                {
                    Console.WriteLine("Yes");return;
                }
            }
        }Console.WriteLine("No");Console.ReadLine();
    }
    public static long gcd(long a, long b)
    {
        while (true)
        {
            if (a == 0) { return b; }
            if (b == 0) { return a; }
            if (a > b) { a -= b; }
            else { b -= a; }
        }
    }
    public static long lcm(long a, long b)
    {
        return a / gcd(a, b) * b;
    }
    public static bool IsPrime(long n)
    {
        if (n < 2) return false;
        if (n == 2) return true;

        for (long i = 2; i < n; i++)
        {
            if (n % i == 0) return false;
        }
        return true;
    }

}
public static class Read
{
    public static void outl(string n = "") { Console.WriteLine(n); return; }
    public static long Long()
    {
        return long.Parse(Console.ReadLine());
    }
    public static long[] longs()
    {
        return Console.ReadLine().Split().Select(long.Parse).ToArray();
    }
    public static int Int()
    {
        return int.Parse(Console.ReadLine());
    }
    public static int[] ints()
    {
        return Console.ReadLine().Split().Select(int.Parse).ToArray();
    }
    public static string Str() { return Console.ReadLine(); }
    public static string[] Strs() { return Console.ReadLine().Split(); }
}