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 (Clang 3.8.0) (judge verdict: Accepted)

#include<stdio.h>
#include<string.h>

int main()
{
	int n,m,k;
	while(scanf("%d%d%d",&n,&m,&k)!=EOF)
	{
		int i,j,tp;
		int flag=0;
		for(i=0;i<=n;i++)
		{
			for(j=0;j<=m;j++)
			{
				tp=(m-j)*i+(n-i)*j;
				if(tp==k)
				{
					flag=1;
				}
			}
		}
		if(flag==0)printf("No\n");
		else printf("Yes\n");
	}
	return 0;
}