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 (1.42.0) (judge verdict: Accepted)

#![allow(unused, non_snake_case, dead_code, non_upper_case_globals)]
use {
    proconio::{marker::*, *},
    std::{cmp::*, collections::*, mem::*},
};

fn main() {
    input! {
        n:usize,m:usize,k:usize
    }

    let mut dp = vec![vec![0; m + 1]; n + 1];
    dp[0][0] = 0;
    dp[0][1] = n;
    dp[1][0] = m;
    for i in 0..n {
        for j in 0..m {
            dp[i + 1][j] = dp[i][j] + m - j * 2;
            dp[i][j + 1] = dp[i][j] + n - i * 2;
        }
    }
    let mut ans = false;

    ans = dp
        .iter()
        .filter(|&x| x.iter().filter(|&y| y == &k).count() > 0)
        .count()
        > 0;
    yn(ans);
}
pub fn yn(ans: bool) {
    if ans {
        println!("Yes");
    } else {
        println!("No");
    }
}