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: Wrong Answer)

import java.util.Scanner;

public class Main {
	void run() {
		Scanner scan = new Scanner(System.in);
		int n = scan.nextInt();
		int m = scan.nextInt();
		int k = scan.nextInt();
		for (int i = 0; i <= n; i++) {
			for (int j = 0; j <= m; j++) {
//				System.out.println((i * n) + (j * m) - (2 * i * j));
				int num = 0;
				if (i == 1 || j == i) {
					num = (i * n) + (j * m) - (i * j);
				} else {
					num = (i * n) + (j * m) - (2 * i * j);
				}
				if (k == num) {
					System.out.println("Yes");
					return;
				}

			}
		}
		System.out.println("No");
	}
	public static void main(String[] args) {
		new Main().run();
	}
}