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 (GCC 5.4.1) (judge verdict: Accepted)

#include <stdio.h>



int main (void){
    int i,j;
    int a=0; 
    int b;
    int n,m,k;
   

    scanf("%d %d %d",&n,&m,&k);
    
    for(i=0;i<=n;i++){
        for(j=0;j<=m;j++){
            if(i*m+j*n-2*i*j == k){
            printf("Yes\n");
            a++;
            break;
            }
        }
        if(a != 0){
            break;
        }
    }
    
    if(a == 0){
        printf("No\n");
    }
    
    
    
    return 0;
}