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 <cstdio>
#include <cstdlib>
#include <cstring>
#include <cmath>
#include <algorithm>
#include <queue>
#include <map>
#include <stack>
using namespace std;
typedef long long LL;
const int Maxn = 1e5 + 5;
const int inf = 1 << 30;
const LL Inf = 1LL << 60;
int n,m;
int vis[1000000];

int main ()
{
	scanf("%d%d",&n,&m);
	int k;
	scanf("%d",&k);
	memset(vis,0,sizeof(vis));
	for (int i = 0; i <= n; i++)
		for (int j = 0; j <= m; j++)
		{
			vis[i*n + j*m  - 2*i*j] = 1;
			}
			if (vis[k] == 1)
				printf("Yes");
				else printf("No");
	return 0;
}