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 <algorithm>
#include <climits>
#include <iostream>
#include <string>
#include <utility>
#include<vector>
#include<iomanip>
#include<map>
#include <queue>
#include<cmath>
#include<cstdio>
#include<iomanip>

using namespace std;
using ll = long long int; 


ll keta(ll a){
  ll ans = 1;
  while(1){
    if(a/10 > 0){
      ans++;
      a = a/10;
    }
    if(a<10) break;
  }
  return ans;
}


int main(void){

   ll n, m, k;
   cin>>n>>m>>k;
   ll sum = 0;

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

  cout<<"No"<<endl;
    return 0;
}