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 Java7 (OpenJDK 1.7.0) (judge verdict: Wrong Answer)


public class Main {

    public static void main(String[] args) {
     try{
         java.util.Scanner s1 = new java.util.Scanner(System.in);
         int n=s1.nextInt();
         int m=s1.nextInt();
         int k=s1.nextInt();
         for(int i=0;i<=n;i++)
         {
             for(int j=0;j<=m;j++)
             {
                 if((i*m+j*n-i*j)==k)
                 {
                     System.out.println("Yes");
                     return;
                 }
             }
         }
         System.out.println("No");
     }
     catch(Exception e)
     {}
   }
}