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<iostream>
#include<algorithm>
#include<string>
#include<cstdlib>
#include<map>
#include<iomanip>
#include<sstream>
#include<vector>
#include<stack>
#include<math.h>
#include<queue>
#include<complex>
using namespace std;



int main() {
	complex<long double>cmpmp;
	const long long int mod = 1000000007;
	map<long long int, long long int>mp;
	//cout << fixed << setprecision(10);
	long long int n,m,k;
	cin >> n >> m>>k;
	for (int i = 0; i <= n; i++) {
		for (int j = 0; j <= m; j++) {
			if (n * m - i * j - (n - i) * (m - j)==k) {
				cout << "Yes" << endl;
				return 0;
			}
		}
	}
	cout << "No" << endl;
}