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;
using System.Threading.Tasks;
using System.Text.RegularExpressions;

namespace AtCoder {
	class Program {
		#region Reserve
		static int cin() { return cin(-1); }
		static int cin(int D) {
			string s = Console.ReadLine();
			if (string.IsNullOrEmpty(s))
				return D;
			return int.Parse(s);
		}
		static long cln(long D = -1) {
			string s = Console.ReadLine();
			if (string.IsNullOrEmpty(s))
				return D;
			return long.Parse(s);
		}
		static int[] cins(char spliter) {
			string s = Console.ReadLine();
			if (string.IsNullOrEmpty(s))
				return new int[] { };
			string[] ss = s.Split(spliter);
			var Res = new int[ss.Length];
			for (int i = 0; i < ss.Length; i++)
				Res[i] = int.Parse(ss[i]);
			return Res;
		}
		static int[] cins() { return cins(' '); }
		static void print(object j) { Console.WriteLine(j.ToString()); }
		static void print(string j) { Console.WriteLine(j); }
		static string read() { return Console.ReadLine(); }
		#endregion

		static void Main(string[] args) {
			var L = cins();
			int N = L[0], M = L[1], K = L[2];
			var aim = N * M - K;
			var res = false;
			for (int b = 0; b <= N; b++) {
				for (int a = 0; a <= M; a++) {
					if (aim == a * N + b * M - 2 * a * b) res = true;
				}
			}
			print(res?"Yes":"No");
			read();
		}
	}
}