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++14 (GCC 5.4.1) (judge verdict: Runtime Error)

#include <iostream>

int main()
{
  int N, M, K;
  std::cin >> N >> M >> K;
  int* mat = new int[(N+1)*(M+1)];
  int i = 0;
  for (int c = 0; c <= M; ++c) {
    mat[i++] = c * N;
  }
  for (int r = 0; r <= N; ++r) {
    for (int c = 0; c <= M; ++c, ++i) {
      int count = mat[i] = mat[i - M - 1] + M - c * 2;
      if (count == K) {
        std::cout << "Yes" << std::endl;
        goto FIN;
      }
    }
  }
  std::cout << "No" << std::endl;
FIN:
  return 0;
}