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: Time Limit Exceeded)

using System;
using System.Collections.Generic;
using System.IO;
using System.Linq;
using System.Net;
using static System.Console;
using static System.Math;
using static CS_Contest.Utils;
using System.Numerics;
using System.Linq.Expressions;

//using static CS_Contest.Library;

namespace CS_Contest {
	using Li = List<int>;
	using LLi = List<List<int>>;
	using Ll = List<long>;

	internal class Program {
		private static void Main(string[] args) {
			var sw = new StreamWriter(OpenStandardOutput()) { AutoFlush = false };
			SetOut(sw);
			new Calc().Solve();
			Out.Flush();
		}
		

		private class Calc {

			public void Solve() {
				int N, M, K;
				ReadMulti(out N,out M,out K);
				var list = new List<List<bool>>();
				REP(N, _ => {
					list.Add(new List<bool>());
					list[_] = Enumerable.Repeat(true, M).ToList();
				});

				if (K==0) {
					Yes();
					return;
				}
				int cnt = 0;
				for (var i = 0; i < M; i++) {
					REP(N,_=>list[_][i]=!list[_][i]);
					cnt = N * (i + 1);
					for (var j = 0; j < N; j++) {
						if (cnt == K) {
							Yes();
							return;
						}
						int now = list[j].Select(x => x = !x).Count(x => x);
						cnt = cnt - now + (M - now);
					}
				}
				No();

				return;
			}

			
		}
	}

	public static class Utils {
		public static int ModValue = (int)(1000000007);
		public static long INF = long.MaxValue;

		public static long Mod(long x) => x % ModValue;

		public static long ModPow(long x, long n) {
			long tmp = 1; while (n != 0) { if (n % 2 == 1) { tmp = Mod(tmp * x); } x = Mod(x * x); n /= 2; }
			return tmp;
		}

		public static long DivMod(long x, long y) => Mod(x * ModPow(y, (long)(1e9 + 5)));

		public static void WL(this object obj) => WriteLine(obj);

		public static void WL(this string obj) => WriteLine(obj);

		public static void WL<T>(this IEnumerable<T> list) => list.ToList().ForEach(x => x.WL());

		public static int ReadInt() => int.Parse(ReadLine());

		public static List<int> ReadInts(char s = ' ') => ReadLine().Split(s).Where(x => x != "").Select(int.Parse).ToList();

		public static long ReadLong() => long.Parse(ReadLine());

		public static List<long> ReadLongs(char s = ' ') => ReadLine().Split(s).Select(long.Parse).ToList();

		public static void ReadMulti(out int x, out int y) {
			var i = ReadInts(' ');
			x = i[0]; y = i[1];
		}

		public static void ReadMulti(out long x, out long y) {
			var i = ReadLongs(' ');
			x = i[0]; y = i[1];
		}

		public static void ReadMulti(out int x, out int y, out int z) {
			var i = ReadInts(' ');
			x = i[0]; y = i[1]; z = i[2];
		}

		public static void ReadMulti(out int x, out int y, out int z, out int v) {
			var i = ReadInts(' ');
			x = i[0]; y = i[1]; z = i[2]; v = i[3];
		}

		public static string StringJoin<T>(this IEnumerable<T> l, string separator = "") => string.Join(separator, l);

		public static long GCD(long m, long n) {
			long tmp;
			if (m < n) { tmp = n; n = m; m = tmp; }
			while (m % n != 0) {
				tmp = n;
				n = m % n;
				m = tmp;
			}
			return n;
		}

		public static long LCM(long m, long n) => m * (n / GCD(m, n));

		public static void REP(int n, Action<int> act) {
			for (var i = 0; i < n; i++) {
				act(i);
			}
		}

		public static void RREP(int n, Action<int> act) {
			for (var i = n - 1; i >= 0; i--) {
				act(i);
			}
		}

		public static void Yes() => "Yes".WL();

		public static void No() => "No".WL();

		public static void YES() => "YES".WL();

		public static void NO() => "NO".WL();

		public static void YesNo(bool cond) {
			if (cond) Yes();
			else No();
		}

		public static int ManhattanDistance(int x1, int y1, int x2, int y2) => Abs(x2 - x1) + Abs(y2 - y1);

		public struct IndexT<T> {
			public T Value { get; set; }
			public int Index { get; set; }

			public IndexT(T v, int i) {
				Value = v; Index = i;
			}
			public override string ToString() {
				return Value + " " + Index;
			}
		}

		public static IEnumerable<IndexT<T>> ToIndexEnumerable<T>(this IEnumerable<T> list) => list.Select((x, i) => new IndexT<T>(x, i));

		public static Queue<T> ToQueue<T>(this IEnumerable<T> iEnumerable) {
			var rt = new Queue<T>();
			foreach (var item in iEnumerable) {
				rt.Enqueue(item);
			}
			return rt;
		}

		public static IndexT<T> IndexOfMin<T>(this IEnumerable<T> ie) where T : IComparable<T>
			=> ie.ToIndexEnumerable().Aggregate((src, acu) => (src.Value.CompareTo(acu.Value) < 0) ? src : acu);

		public static Tuple<TKey, TSource> ToTuple<TKey, TSource>(this KeyValuePair<TKey, TSource> kvp) => new Tuple<TKey, TSource>(kvp.Key, kvp.Value);

		public static IEnumerable<Tuple<TKey, TSource>> ToTupleList<TKey, TSource>(this Dictionary<TKey, TSource> d) => d.Select(_ => _.ToTuple());

		public static IEnumerable<T> When<T>(this IEnumerable<T> iEnumerable, Func<T, bool> condition, Func<T,T> filterFunc) {
			var rt = iEnumerable.ToArray();
			var index = 0;
			foreach (var item in iEnumerable) {
				rt[index] = condition(item) ? filterFunc(item) : item;
				index++;
			}
			return rt;
		}

		public static T[] Range<T>(int range,Func<int,T> func) {
			var rt = new T[range];
			for (var i = 0; i < range; i++) rt[i] = func(i);
			return rt;
		}
		public static void Swap<T>(ref T x,ref T y) {
			var tmp = x;
			x = y;
			y = tmp;
		}
	}
}