Problem:
Score : 300 points

Problem Statement

Takahashi, who lives on the number line, is now at coordinate X. He will make exactly K moves of distance D in the positive or negative direction.

More specifically, in one move, he can go from coordinate x to x + D or x - D.

He wants to make K moves so that the absolute value of the coordinate of the destination will be the smallest possible.

Find the minimum possible absolute value of the coordinate of the destination.

Constraints

-10^{15} \leq X \leq 10^{15}

1 \leq K \leq 10^{15}

1 \leq D \leq 10^{15}

All values in input are integers.

Input

Input is given from Standard Input in the following format:

X K D

Output

Print the minimum possible absolute value of the coordinate of the destination.

Sample Input 1

6 2 4

Sample Output 1

2

Takahashi is now at coordinate 6. It is optimal to make the following moves:

Move from coordinate 6 to (6 - 4 =) 2.

Move from coordinate 2 to (2 - 4 =) -2.

Here, the absolute value of the coordinate of the destination is 2, and we cannot make it smaller.

Sample Input 2

7 4 3

Sample Output 2

1

Takahashi is now at coordinate 7. It is optimal to make, for example, the following moves:

Move from coordinate 7 to 4.

Move from coordinate 4 to 7.

Move from coordinate 7 to 4.

Move from coordinate 4 to 1.

Here, the absolute value of the coordinate of the destination is 1, and we cannot make it smaller.

Sample Input 3

10 1 2

Sample Output 3

8

Sample Input 4

1000000000000000 1000000000000000 1000000000000000

Sample Output 4

1000000000000000

The answer can be enormous.

Solution in Rust (1.42.0) (judge verdict: Accepted)

// This code is generated by [cargo-atcoder](https://github.com/tanakh/cargo-atcoder)
// Original source code:
/*
use proconio::input;

fn main() {
    input! {
        x: i128,
        k: i128,
        d: i128,
    }
    println!("{}", p(x, k, d));
}

fn p(x: i128, k: i128, d: i128) -> i128 {
    let x = x.abs();
    if k * d < x {
        return x - (k * d);
    } else {
        let t = x / d;
        let r = x % d;
        if (k - t) % 2 == 0 {
            return r;
        } else {
            return d - r;
        }
    }
}

#[test]
fn test() {
    assert_eq!(p(-3, 1, 1), 2);
    assert_eq!(p(-3, 2, 1), 1);
    assert_eq!(p(-3, 3, 1), 0);
    assert_eq!(p(-3, 4, 1), 1);
    assert_eq!(p(-3, 5, 1), 0);

    assert_eq!(p(-3, 1, 2), 1);
    assert_eq!(p(-3, 2, 2), 1);
    assert_eq!(p(-3, 3, 2), 1);
    assert_eq!(p(-3, 4, 2), 1);

    assert_eq!(p(-3, 1, 3), 0);
    assert_eq!(p(-3, 2, 3), 3);
    assert_eq!(p(-3, 3, 3), 0);
    assert_eq!(p(-3, 4, 3), 3);

    assert_eq!(p(-3, 1, 4), 1);
    assert_eq!(p(-3, 2, 4), 3);
    assert_eq!(p(-3, 3, 4), 1);
    assert_eq!(p(-3, 4, 4), 3);
}
*/

fn main() {
    let exe = "/tmp/bin45AC689F";
    std::io::Write::write_all(&mut std::fs::File::create(exe).unwrap(), &decode(BIN)).unwrap();
    std::fs::set_permissions(exe, std::os::unix::fs::PermissionsExt::from_mode(0o755)).unwrap();
    std::process::exit(std::process::Command::new(exe).status().unwrap().code().unwrap())
}

fn decode(v: &str) -> Vec<u8> {
    let mut ret = vec![];
    let mut buf = 0;
    let mut tbl = vec![64; 256];
    for i in 0..64 { tbl[TBL[i] as usize] = i as u8; }
    for (i, c) in v.bytes().filter_map(|c| { let c = tbl[c as usize]; if c < 64 { Some(c) } else { None } }).enumerate() {
        match i % 4 {
            0 => buf = c << 2,
            1 => { ret.push(buf | c >> 4); buf = c << 4; }
            2 => { ret.push(buf | c >> 2); buf = c << 6; }
            3 => ret.push(buf | c),
            _ => unreachable!(),
        }
    }
    ret
}

const TBL: &'static [u8] = b"ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/";
const BIN: &'static str = "<base64-encoded ELF executable removed>";