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 <bits/stdc++.h>
const long long MOD = 1000000007;
const int INF = INT_MAX / 2;
const long double PI = 3.1415926;
using namespace std;
#define FOR(i, r, n) for(int i=(ll)(r); i<(ll)(n); i++) 
#define REP(i, n) FOR(i, (0), n)
#define ALL(r) r.begin(), r.end()
#define ll long long int
#define lld long double
typedef vector<ll> vi;
typedef vector<string> vs;
typedef vector<pair<ll, ll>> vp;
typedef vector<tuple<ll, ll, ll>> vt;
//vector<vector<ll>> vv(n, vector<ll>(n));

int main()
{
	ll n, m, k;
	cin >> n >> m >> k;
	set<ll> st;
	REP(i,n) REP(j,m)
	{
		ll tmp = i*m;
		tmp -= i*j;
		tmp += j*(n - i);
		st.insert(tmp);
	}
	if (st.count(k)) cout << "Yes" << endl;
	else cout << "No" << endl;
}