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: Accepted)

#include <bits/stdc++.h>

using namespace std;

#define llong long long
#define ii pair<int, int>
#define xx first
#define yy second
#define rep(i,n) for (int i = -1; ++ i < n; )
#define rep1(i,n) for (int i = 0; i ++ < n; )
#define len(x) ((int)x.size())

int main() {
  ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0);
  llong n, m, k; cin >> n >> m >> k;

  rep(i, n + 1) rep(f, m + 1) {
    if (i * m + f * n - 2 * i * f == k) {
      cout << "Yes";
      return 0;
    }
  }
  cout << "No";

  return 0;
}