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.FileInputStream;
import java.io.InputStream;
import java.util.Scanner;

public class Main{
	static Scanner sc;

	static int N, M ,K;

	public static void main(String[] args) throws Exception {
		//InputStream in = new FileInputStream("src/input.txt");
		InputStream in = System.in;
		//PrintStream out = new PrintStream("src/output.txt");

		//System.setOut(out);

		sc = new Scanner(in);

		N = sc.nextInt();
		M = sc.nextInt();
		K = sc.nextInt();

		boolean answer = false;
		for(int i = 0; i <= M; i++){
			for(int j = 0; j <= N; j++){
				if(K == (M-i)*j + (N-j)*i){
					answer = true;
					break;
				}
			}
			if(answer == true){
				break;
			}
		}
		if(answer == true){
			System.out.println("Yes");
		}else{
			System.out.println("No");
		}
	}
}