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 Rust (1.15.1) (judge verdict: Wrong Answer)


use std::io::stdin;
// code...
fn main() {
    let mut buf = String::new();
    stdin().read_line(&mut buf).unwrap();
    let (n, m, k): (usize, usize, usize) = {
        let p: Vec<usize> = buf.trim().split_whitespace().map(|x| x.parse().unwrap()).collect();
        (p[0], p[1], p[2])
    };

    let mut ans = "No";
    for i in 0..n+1 {
        for j in 0..m+1 {
            if i * n + j * m - 2 * i * j == k || i * m + j * n - 2 * i * j == k {
                ans = "Yes";
                break;
            }
        }
    }

    println!("{}", ans);
}