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: Runtime Error)

import java.io.*;
import java.math.*;
import java.util.*;
public class Main { //Simulate flip processes

	public static void main(String[] args) {
		Scanner input = new Scanner(System.in);
		int N = input.nextInt();
		int M = input.nextInt();
		int K = input.nextInt();
		int tempK = K;
		int tempM = M;
		int tempN = N;
		String ans = "";
		//Row first basis
		int numRows = K/M;
		tempK%=M;
		int rowsleft = N-numRows;
		int factor = rowsleft-numRows;
		if (factor!=0&&tempK%factor!=0) ans="No";
		else ans="Yes";
		if (ans.equals("No")) {
			M=tempN; //Flipping dimensions
			N=tempM;
			numRows = K/M;
			tempK%=M;
			rowsleft = N-numRows;
			factor = rowsleft-numRows;
			if (tempK%factor!=0) ans="No";
			else ans="Yes";
		}
		System.out.println(ans);
	}	
}