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<cstdio>
#include<cctype>
#define For(i,j,k) for(int i=j;i<=k;++i)
using namespace std;
int read(){
	int l=1,x=0; char ch=getchar();
	while(!isdigit(ch)) {if (ch=='-') l=-1; ch=getchar();}
	while(isdigit(ch)) x=x*10+(ch^48),ch=getchar();
	return x*l;
}
int main(){
	int x,n=read(),m=read(),k=read();
	For(i,0,n)
		For(j,0,m){
			x=i*m+j*n-2*i*j;
			if (x==k) {printf("Yes"); return 0;}
		}
	printf("No");
	return 0;
}