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: Wrong Answer)

#include <stdio.h>
int main(void){
    // Here your code !
    int i, j;
    int N, M, K;
    int flag = 0;
    
    scanf("%d %d %d", &N, &M, &K);
    
    int box[1000][1000] = {0};
    
    if (K == 0) flag = 1;
    
    int sum = 0;
    
    for (i = 0; i < N; i++) {
        for (j = 0; j < M; j++) {
            if (flag) {
                break;
            }
            
            int x;
            for (x = 0; x < N; x++) {
                if (box[x][j]) {
                    sum--;
                    box[x][j] = 0;
                } else {
                    sum++;
                    box[x][j] = 1;
                }
            }
            for (x = 0; x < M; x++) {
                if (box[i][x]) {
                    sum--;
                    box[i][x] = 0;
                } else {
                    sum++;
                    box[i][x] = 1;
                }
            }
            
            if (sum == K) {
                flag = 1;
                break;
            }
        }
    }
    
    if (flag) {
        puts("Yes");
    } else {
        puts("No");
    }
    
    return 0;
}