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)

#[allow(unused_imports)]
use std::{cmp::Reverse, collections::*};

#[allow(unused_imports)]
use proconio::{
    fastout, input,
    marker::{Chars, Usize1},
};

#[allow(unused_imports)]
use itertools::Itertools;

#[allow(unused_imports)]
use num::Integer;

#[fastout]
pub fn main() {
    input! {
        x: i128, k: i128, d: i128,
    }

    if x == 0 {
        println!("{}", if k % 2 == 0 { 0 } else { d.abs() });
    } else if x > 0 {
        let n = (x as f64 / d as f64).ceil() as i128;
        if n > k {
            println!("{}", (x - k * d).abs());
        } else if (x - n * d).abs() > (x - (n - 1) * d).abs() {
            println!(
                "{}",
                if (k - (n - 1)) % 2 == 0 {
                    (x - (n - 1) * d).abs()
                } else {
                    (x - n * d).abs()
                }
            );
        } else {
            println!(
                "{}",
                if (k - n) % 2 == 0 {
                    (x - n * d).abs()
                } else {
                    (x - (n - 1) * d).abs()
                }
            );
        }
    } else {
        let n = (-x as f64 / d as f64).ceil() as i128;
        if n > k {
            println!("{}", (x + k * d).abs());
        } else if (x + n * d).abs() > (x + (n - 1) * d).abs() {
            println!(
                "{}",
                if (k - (n - 1)) % 2 == 0 {
                    (x + (n - 1) * d).abs()
                } else {
                    (x + n * d).abs()
                }
            );
        } else {
            println!(
                "{}",
                if (k - n) % 2 == 0 {
                    (x + n * d).abs()
                } else {
                    (x + (n - 1) * d).abs()
                }
            );
        }
    }
}