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 ll long long

#define all(x) x.begin(), x.end()

const int mod = 998244353;


bool solve2(int n, int m, int k){

	for(int i = 0; i <= n; ++i){
		for(int j = 0; j <= m; ++j){
			int res = i * (m - j) + j * (n - i);
			if(res == k){
				return true;
			}
		}
	}
	return false;
}

int main(){

	cin.tie(0);
	cin.sync_with_stdio(0);

	#ifdef Cyborg101
		freopen("input.txt", "r", stdin);
		freopen("output.txt", "w", stdout);
	#endif

	int n, m, k;
	cin >> n >> m >> k;
	puts(solve2(n, m, k) ? "Yes" : "No");
}