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"
#define rep(i,b) for(ll i=0;i<b;i++)
#define ll long long
using namespace std;
/*--Input//////////////////////////////////////////////////*/
inline void IN(void){return;}
template <typename First, typename... Rest>
void IN(First& first, Rest&... rest){cin >> first;IN(rest...);return;}
#define SS(T, ...)      T __VA_ARGS__; IN(__VA_ARGS__);
#define SV(type,c,n) vector<type> c(n);for(auto& i:c)cin >> i;
/*--Output/////////////////////////////////////////////////*/
inline int p(void){cout << endl; return 0;}
template<class Head> int p(Head&& head){cout << head;p();return 0;} template<class Head,class... Tail> int p(Head&& head,Tail&&... tail){cout<<head<<" ";p(forward<Tail>(tail)...);return 0;}
struct ProconInit {
    static constexpr bool AUTOFLUSH = false;
    ProconInit() {
        cin.tie(nullptr);
        ios::sync_with_stdio(false);
        cout << fixed << setprecision(15);
        if(AUTOFLUSH)
            cout << unitbuf;
    }
} PROCON_INIT;

#define YES(n) cout << ((n) ? "YES" : "NO"  ) << endl
#define Yes(n) cout << ((n) ? "Yes" : "No"  ) << endl
#define vl vector<ll>
#define vvl vector<vector<ll>>
#define vvvl vector<vector<vector<ll>>>
#define debug(x) cerr<<#x<<" "<<x<<'\n';
#define all(x) (x).begin(),(x).end()
#define bit(n) (1LL<<(n))
template<class T>bool chmax(T &a, const T &b) { if (a<b) { a=b; return 1; } return 0; }
template<class T>bool chmin(T &a, const T &b) { if (b<a) { a=b; return 1; } return 0; }
bool cmp(pair<ll,ll> a, pair<ll,ll> b) { return a.second < b.second; }

const int MOD = 1000000007;

const int dx[4] = {1, 0, -1, 0};
const int dy[4] = {0, 1, 0, -1};

signed main() {
    SS(ll,h,w,k)
    bool flag=false;
    rep(i,h)rep(j,w)if(i*j+(h-i)*(w-j)==k)flag=true;
    Yes(flag);
}