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>
#include <boost/multiprecision/cpp_int.hpp>

using namespace std;
using namespace boost::multiprecision;

#define REP(i, n) for (int i = 0; i < (int)(n); i++)
#define REPI(i,a,b) for(int i=int(a);i<int(b);++i)
#define ALL(x) (x).begin(),(x).end()

inline cpp_int between(cpp_int n, cpp_int x) {
  if(n >= 0)
    return (n/x)+1;
  else
    return 0;
}

int main () {
  int w, h, k;
  cin >> w >> h >> k;

  REP(i, h+1) {
    REP(j, w+1) {
      if((i * (w-j)) + ((h-i) * j) == k) {
        cout << "Yes" << endl;
        return 0;
      }

    }
  }

  cout << "No" << endl;
  return 0;
}