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: Accepted)

use std::io;
use std::cmp::*;

fn main() {
    let mut string = String::new();
    io::stdin().read_line(&mut string).expect("read error");
    let int_vec: Vec<u32> = string.trim().split(" ")
        .map(|x| {
            x.parse::<u32>()
                .expect("Not an integer!")
        })
        .collect();
    
    let m = min(int_vec[0], int_vec[1]);
    let n = max(int_vec[0], int_vec[1]);
    let k = int_vec[2];

    for i in 0..(m + 1) {
        for j in 0..(n + 1) {
            if m * n - (m - i) * (n - j) - i * j == k {
                println!("Yes");
                return;
            }
        }
    }
    println!("No");
}