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 {

	/**
	 * @param args
	 */
	public static void main(String[] args) {
		// TODO Auto-generated method stub
		int flag = 0;
		Scanner scanner = new Scanner(System.in);
		String s = scanner.nextLine();
		String[] temp = s.split(" ");
		int N = Integer.parseInt(temp[0]);
		int M = Integer.parseInt(temp[1]);
		int K = Integer.parseInt(temp[2]);
		
		
		for(int i=0;i<N;i++){
			for(int j=0;j<M;j++){
				if(K==(i*M+j*N-2*i*j)){
					flag = 1;
				}
			}
		}
		if(flag==1){
			System.out.println("Yes");
		}
		else{
			System.out.println("No");
		}
	}

}