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.*;
public class Main{
  public static void main(String[] args){
    Scanner sc = new Scanner(System.in);

    int N = sc.nextInt();
    int M = sc.nextInt();
    int K = sc.nextInt();

    //行をi列打って列をj列打った時に黒になる数がKかどうか全探索する
    for(int i=0;i<=N;i++){
      for(int j=0;j<=M;j++){
        //i行j列打つと、黒になる数は、i*N+j*M-i*j*2
        if(K==i*M+j*N-i*j*2){
          System.out.println("Yes");
          return;
        }
      }
    }
    //見つからなかったら終わり
    System.out.println("No");




  }

    


}