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<cstdio>
#include<cstdlib>
#include<cstring>
#include<cmath>
#include<ctime>
#include<cctype>
#include<climits>
#include<iostream>
#include<string>
#include<vector>
#include<map>
#include<list>
#include<queue>
#include<deque>
#include<algorithm>
#include<numeric>
#include<utility>
#include<complex>
#include<memory>
#include<functional>
#include<set>
 
using namespace std;
 
#define ALL(g) (g).begin(),(g).end()
#define REP(i, x, n) for(int i = x; i < n; i++)
#define rep(i,n) REP(i,0,n)
#define F(i,j,k) fill(i[0],i[0]+j*j,k)
#define P(p) cout<<(p)<<endl;
#define EXIST(s,e) ((s).find(e)!=(s).end())
#define INF 1<<25
#define pb push_back
 
typedef vector<int> vi;
typedef vector<long long> vl;
typedef vector<double> vd;
typedef pair<int,int> pii;
typedef pair<long,long> pll;
typedef long long ll;
int mem[1001][1001];

int main(){
	int n,m,k;
	cin>>n>>m>>k;
	for(int i=0;i<=n;i++){
		int tmp=0;
		tmp+=i*n;
		
		for(int j=0;j<=m;j++){
			if((tmp+j*(m-i*2))==k){
				cout<<"Yes"<<endl;
				return 0;

			}
		}
	}

	cout<<"Yes"<<endl;
	
/*	for(int i=0;i<n;i++){
		int tmp=i*n;
		for(int j=0;j<m;j++){

			if((tmp+j*(m-i*2))==k){
				cout<<"Yes"<<endl;
			}
			for(int k=0;k<n-m;k++){
				
			}
		}
	}
	*/
	return 0;
}