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.Scanner;
class Main{
	public static void main(String[]args) {
		Scanner scan=new Scanner(System.in);
		int a=scan.nextInt();
		int b=scan.nextInt();
		int c=scan.nextInt();
		boolean bool=false;
		for(int i=0;i<=a;i++) {
			for(int j=0;j<=b;j++) {
				int bla=(a-i)*j+(b-j)*i;
				if(bla==c) {
					bool=true;
				}
			}
		}
		if(bool==true) {
			pl("Yes");
		}
		else {
			pl("No");
		}
	}
	public static void pl(String str) {
		System.out.println(str);
	}
}