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 <iostream>
#include <set>
#include <math.h>
#include <string.h>
#include <algorithm>
using namespace std;

long long N,M,K;

int main()
{
    cin>>N>>M>>K;
    if(N>M) { long long temp = M;M = N;N = temp; }
    if(N==1) { cout<<"Yes"<<endl;}
    else if(N==2)
    {
        if(K%2==0||K%M==0)cout<<"Yes"<<endl;
        else cout<<"No"<<endl;
    }
    else if(K==0) cout<<"Yes"<<endl;
    else
    {
        if(K%N==0||K%M==0)
            cout<<"Yes"<<endl;
        else if(K%N == N-2||K%N == M-2)
            cout<<"Yes"<<endl;
        else if(K%M==N-2||K%M==M-2)
            cout<<"Yes"<<endl;
        else
            cout<<"No"<<endl;
    }

    return 0;
}