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_mut)]
#![allow(dead_code)]
#![allow(unused_macros)]

use proconio::{input};

// The debug version
#[cfg(feature = "debug")]
macro_rules! debug {
    ($( $args:expr ),*) => { eprintln!( $( $args ),* ); }
}
// Non-debug version
#[cfg(not(feature = "debug"))]
macro_rules! debug {
       ($( $args:expr ),*) => {}
}


use num_traits::int::PrimInt;
// #[overflow_checks(off)]
// i32 -> i32, i64 -> i64
fn accum<T: PrimInt>(a: &Vec<T>) -> Vec<T> {
    let n: usize = a.len();
    let mut ac: Vec<T> = Vec::with_capacity(n + 1);
    ac.push(a[0] - a[0]);  // ac.push(0) がしたいんですけど
    for i in 0..n {
        ac.push(ac[i] + a[i]);
    }
    ac
}
/// i32 -> i64
fn accum64(a: &Vec<i32>) -> Vec<i64> {
    let n: usize = a.len();
    let mut ac: Vec<i64> = Vec::with_capacity(n + 1);
    ac.push(0);
    for i in 0..n {
        ac.push(ac[i] + i64::from(a[i]));
    }
    ac
}

fn rle<T: PrimInt>(a: &Vec<T>) -> Vec<(T,u32)> {
    let mut res: Vec<(T,u32)> = Vec::with_capacity(0);

    let mut last : T = T::zero();
    let mut cnt : u32 = 0;

    for c in a.iter() {
        if *c == last {
            cnt += 1;
        } else {
            if cnt > 0 {
                res.push((last, cnt));
            }
            last = *c;
            cnt = 1;
        }
    };
    if cnt > 0 {
        res.push((last, cnt));
    }
    res
}
fn rle_str(a: &str) -> Vec<(char,u32)> {
    let mut res: Vec<(char,u32)> = Vec::with_capacity(0);

    let mut last : char = '\0';
    let mut cnt : u32 = 0;

    for c in a.chars() {
        if c == last {
            cnt += 1;
        } else {
            if cnt > 0 {
                res.push((last, cnt));
            }
            last = c;
            cnt = 1;
        }
    };
    if cnt > 0 {
        res.push((last, cnt));
    }
    res
}

fn yesno(b: bool) -> &'static str {
    if b {
        return "Yes";
    } else {
        return "No";
    }
}

fn solve(mut x:i64, k:i64, d:i64) -> i64 {
    debug!("Input: x={}, k={}, d={}", x,k,d);
    if x < 0 {
        x = -x;
    }
    let q = x / d;
    let r = x % d;
    debug!(" q={}, r={}", q, r);

    if k <= q {
        return x - d*k;
    }
    // k > q
    // let r_comp = d - r;
    if (k - q) % 2 == 1 {
        return d - r;
    } else {
        return r;
    }
}

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