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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.util.*;
import java.io.*;
import java.math.BigDecimal;
import java.math.BigInteger;
import java.math.MathContext;
 
class Main
{
	static class Pair implements Comparable
	{
		int first;
		double second;
		
		public Pair(int f, double s)
		{
			first = f;
			second = s;
		}
		
		public String toString()
		{
			return first + " " + second;
		}
		
		public int compareTo(Object o)
		{
			Pair p2 = (Pair)o;
			if(this.first < p2.first)
				return -1;
			if(this.first > p2.first)
				return 1;
			if(this.second < p2.second)
				return -1;
			if(this.second > p2.second)
				return 1;
			return 0;
		}
	}
	
	static int log2(double a)
	{
		return (int)(Math.log(a) / Math.log(2));
	}
	
	static long gcd(long a, long b)
	{
		long r;
		while((r = a % b) > 0)
		{
			a = b;
			b = r;
		}
		return b;
	}
	
	public static void main(String[] args) throws IOException
	{
		int n = in.nextInt();
		int m = in.nextInt();
		int k = in.nextInt();
		boolean ans = false;
		for(int i = 0; i <= n && !ans; i ++)
		{
			for(int j = 0; j <= m && !ans; j ++)
			{
				if((m - j) * i + (n - i) * j == k)
				{
					ans = true;
				}
			}
		}
		sop(ans ? "Yes" : "No");
	}
    
	static class FastReader
    {
        BufferedReader br;
        StringTokenizer st;
 
        public FastReader()
        {
            br = new BufferedReader(new InputStreamReader(System.in));
        }
        
        String next()
        {
            while (st == null || !st.hasMoreElements())
            {
                try
                {
                    st = new StringTokenizer(br.readLine());
                }
                catch (IOException  e)
                {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }
 
        int nextInt()
        {
            return Integer.parseInt(next());
        }
 
        long nextLong()
        {
            return Long.parseLong(next());
        }
 
        double nextDouble()
        {
            return Double.parseDouble(next());
        }
 
        String nextLine()
        {
            String str = "";
            try
            {
                str = br.readLine();
            }
            catch (IOException e)
            {
                e.printStackTrace();
            }
            return str;
        }
    }
	
    static FastReader in = new FastReader();
  
    public static void sop(Object o)
    {
    	System.out.print(o);
    }
}