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)

// https://twitter.com/chokudai/status/1294961358119739392
// https://atcoder.jp/contests/abc175/submissions/15987037

use proconio::input;

fn main() {
    input!(x: i64, k: i64, d: i64);
    println!("{}", solve(x, k, d))
}

fn solve(mut x: i64, mut k: i64, d: i64) -> i64 {
    x = x.abs();
    if x >= k.saturating_mul(d) {
        x - k * d
    } else {
        k -= x / d;
        x %= d;
        if k % 2 == 1 {
            d - x
        } else {
            x
        }
    }
}

fn solve_simply(mut x: i64, k: i64, d: i64) -> i64 {
    for _ in 0..k {
        if (x - d).abs() < (x + d).abs() {
            x -= d
        } else {
            x += d
        }
    }
    x.abs()
}

#[test]
fn test() {
    use rand::prelude::*;
    let mut rng = thread_rng();
    loop {
        let x = rng.gen_range(-1e15 as i64, 1e15 as i64 + 1);
        let k = rng.gen_range(1, 1e5 as i64 + 1);
        let d = rng.gen_range(1, 1e15 as i64 + 1);
        println!("checking input : {} {} {}", x, k, d);
        assert_eq!(solve(x, k, d), solve_simply(x, k, d));
    }
}