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# (.NET Core 3.1.201) (judge verdict: Accepted)

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

namespace MSL001
{
    //public class A
    //{

    //    public static void Main(string[] args)
    //    {

    //        var c = new ConsoleInput(Console.In);
    //        var S = c.Read;
    //        var A = c.ReadLong;
    //        var B = c.ReadLong;
    //        var C = c.ReadLong;
    //        var D = c.ReadLong;
    //        var sb = new StringBuilder(S.Length + 10);

    //        for (int i = 0; i < S.Length; i++)
    //        {
    //            if(i == A || i == B || i == C || i == D)
    //            {
    //                sb.Append("\"");
    //            }
    //            sb.Append(S[i]);
    //        }
    //        if (D == S.Length) sb.Append("\"");
    //        Console.WriteLine(sb.ToString());
    //    }


    //}

    //public class B
    //{
    //    public static void Main(string[] args)
    //    {
    //        var c = new ConsoleInput(Console.In);
    //        Dictionary<string, long> dic = new Dictionary<string, long>();
    //        var N = c.ReadLong;
    //        for (int i = 0; i < N; i++)
    //        {
    //            string k = c.Read;
    //            if(dic.TryGetValue(k,out long value))
    //            {
    //                dic[k] = value + 1;
    //            }
    //            else{
    //                dic.Add(k, 1);
    //            }
    //        }
    //        var M = c.ReadLong;
    //        for (int i = 0; i < M; i++)
    //        {
    //            string k = c.Read;
    //            if(dic.TryGetValue(k,out long value))
    //            {
    //                dic[k] = value - 1;
    //            }
    //        }

    //        long max = dic.Values.Max();
    //        Console.WriteLine(max > 0 ? max : 0);

    //    }

    //}


    //public class C
    //{
    //    public static void Main(string[] args)
    //    {
    //        var c = new ConsoleInput(Console.In);
    //        var N = c.ReadInt;
    //        var A = new long[N];
    //        var B = new long[N];
    //        for (int i = 0; i < N; i++)
    //        {
    //            A[i] = c.ReadLong;
    //            B[i] = c.ReadLong;
    //        }

    //        long count = 0;
    //        for (int i = N - 1; i >= 0; i--)
    //        {
    //            long diff = B[i] - ((A[i] + count) % B[i]);
    //            if (diff == B[i]) diff = 0;
    //            count += diff;
    //        }
    //        Console.WriteLine(count);

    //    }
    //}

    public class D
    {
        public static void Main(string[] args)
        {
            var c = new ConsoleInput(Console.In);
            long N = c.ReadInt;
            long M = c.ReadInt;
            var K = c.ReadLong;

            for (int y = 0; y <= N; y++)
            {
                for (int x = 0; x <= M; x++)
                {
                    if(y*M + x*N - 2*x*y == K)
                    {
                        Console.WriteLine("Yes");
                        Environment.Exit(0);
                    }

                }

            }
            Console.WriteLine("No");

        }
    }


    public class ConsoleInput
    {
        private readonly System.IO.TextReader _stream;
        private char _separator = ' ';
        private Queue<string> inputStream;
        public ConsoleInput(System.IO.TextReader stream, char separator = ' ')
        {
            this._separator = separator;
            this._stream = stream;
            inputStream = new Queue<string>();
        }
        public string Read
        {
            get
            {
                if (inputStream.Count != 0) return inputStream.Dequeue();
                string[] tmp = _stream.ReadLine().Trim().Split(_separator);
                for (int i = 0; i < tmp.Length; ++i)
                    inputStream.Enqueue(tmp[i].Trim());
                return inputStream.Dequeue();
            }
        }
        public string ReadLine { get { return _stream.ReadLine(); } }
        public int ReadInt { get { return int.Parse(Read); } }
        public long ReadLong { get { return long.Parse(Read); } }
        public double ReadDouble { get { return double.Parse(Read); } }
        public string[] ReadStrArray(long N) { var ret = new string[N]; for (long i = 0; i < N; ++i) ret[i] = Read; return ret; }
        public int[] ReadIntArray(long N) { var ret = new int[N]; for (long i = 0; i < N; ++i) ret[i] = ReadInt; return ret; }
        public long[] ReadLongArray(long N) { var ret = new long[N]; for (long i = 0; i < N; ++i) ret[i] = ReadLong; return ret; }
    }
}