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;
using ll = long long;
using ld = long double;
#define rep(i,n) for(int i=0;i<(int)(n);i++)
#define reps(i,s,n) for(int i=(int)(s);i<(int)(n);i++)
const ll mod = 1e9 + 7;
const int INF = 1e9;

int main() {
	cin.sync_with_stdio(false);
	int N, M, K;
	cin >> N >> M >> K;
	rep(i, N) {
		rep(j, M) {
			if (i == 0 || j == 0) {
				if (i*N + j*M == K) {
					cout << "Yes" << endl;
					return 0;
				}
			}
			if (i != 0 && j != 0) {
				if (N*i + M*j - 2*(i+j) == K) {
					cout << "Yes" << endl;
					return 0;
				}
			}
		}
	}
			cout << "No" << endl;

	return 0;
}