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"
#define rep(i,a,n) for(int i = (a);i < (n);i++)
typedef unsigned long long ull;
typedef long long ll;
using namespace std;

int main(){
 	int h,w,n;
  	cin >> h >> w >> n;
   	bool is_exist[1000001];
  
  	rep(i,0,h+1){
      is_exist[i*w] = true;
    }
  
  	rep(i,0,w+1){
      is_exist[i*h] = true;
    }
  
  	rep(i,0,h+1){
      rep(j,0,w+1){
        is_exist[(i*(w-j))+(j*(h-i))] = true;
      }
    }
   
  	if(is_exist[n]) cout << "Yes"<< endl;
  	else cout << "No" << endl;
  	
 	return 0; 
}