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,N) for(int i=0;i<(N);i++)
#define FOR(i,a,b) for(int i=(a);i<(b);i++)
using namespace std;
const long long MOD = 1e9 + 7;
const long long INF = 1e12;
const int inf = 1e9;
const int mod = 1e9+7;
typedef long long ll;
typedef pair<ll,int> P;
typedef set<int> S;
int main(){
    cout << fixed << setprecision(10);
    int n,m,k;
    cin >> n >> m >>k;
    rep(i,n+1){
        rep(j,m+1){
            if(i*(m-j)+j*(n-i)==k){
                cout << "Yes" << endl;
                return 0;
            }
        }
    }
    cout << "No" << endl;
    return 0;
}