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 C (GCC 5.4.1) (judge verdict: Accepted)

#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <math.h>

int main() {
  int i, j;
  int n, m, k;

  scanf("%d %d %d", &n, &m, &k);
  // printf("%d %d %d", n, m, k);

  int flag = 0;
  int temp;

  for (i = 0; i <= n;i++){
    if (flag != 0){
      break;
    }
    for (j = 0; j <= m; j++){
      temp = i * m + j * n - 2* i * j;
      // printf("%d %d %d\n", i, j, temp);
      if (temp == k){
        flag = 1;
        break;
      }
    } }

  if (flag == 1){
    printf("Yes");
  }
  else {
    printf("No");
  }
  
  return 0;
}