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.io.*;
import java.math.*;
import java.util.*;
public class Main { //Simulate flip processes
	//UPD: Don't always need to take max rows

	public static void main(String[] args) {
		Scanner input = new Scanner(System.in);
		int N = input.nextInt();
		int M = input.nextInt();
		int K = input.nextInt();
		System.out.println(Valid(N,M,K)?"Yes":"No");
	}	
	public static boolean Valid(int N,int M,int K) {
		for (int r = 0; r <= N; r++) {
			int numB = r*M;
			for (int c = 0; c <= M; c++) {
				int leftrows = N-r;
				int net = leftrows-r;
				int total = numB+c*net;
				if (total==K) {
					return true;
				}
			}
		}
		return false;
	}
}