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){
    //long n=0 , m=0, k=0;
    int n=0 , m=0, k=0;

    int ans = 0;
    //scanf("%ld %ld %ld", &n, &m, &k);
    scanf("%d %d %d", &n, &m, &k);

    for(int a = 0; a <= n && ans == 0; a++){
        for(int b = 0; b <= m && ans == 0; b++){
            if( (a*m - 2*a*b + b*n) == k ){
                ans = 1;
                break;
            }
        }
    }
    if(ans) printf("Yes\n");
    else printf("No\n");
}