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: Wrong Answer)

#include <bits/stdc++.h>
using namespace std;

#define int long long
#define pb push_back 
#define mp make_pair
#define fr first
#define sc second
#define Rep(i, n) for( int i = 0; i < (n); i++ )
#define Rrep(i, a, n) for( int i = (a); i < (n); i++ )
#define All(v) v.begin(), v.end()

typedef pair<int, int> Pii; 
typedef pair<int, Pii> Pip;
const int INF = 1107110711071107;

signed main() {
  int N, M, K;
  cin >> N >> M >> K;

  int a = max(N, M);
  int b = min(N, M);
  Rep(i, M) {
    if ( (M - i - i) > 0 && N*i <= K ) {
      Rep(j, N) {
	if ( (K - N * i) - (M - i - i)*j == 0 ) {
	  cout << "Yes" << endl;
	  //cout << i << endl;
	  return 0;
	}
      }
    }
  }
  Rep(j, N) {
    if ((N - j - j) > 0 && M*j <= K ) {
      Rep(i, M) {
	if ( (K - M * j) - (N - j - j)*i == 0 ) {
	  cout << "Yes" << endl;
	  return 0;
	}
      }
    }
  }
  cout << "No" << endl;
  return 0;
}