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)

fn main() {
    ioset! { inp, buf }
    macro_rules! scan {
        ($($r:tt)*) => {
            input! { inp, $($r)* }
        }
    }
    macro_rules! print {
        ($($t:expr),*) => {
            write!(buf, $($t),*).unwrap();
        } 
    }
    scan! {
        mut x: i64,
        mut k: i64,
        d: i64,
    }
    if x > 0 {
        let t = x / d;
        let t = std::cmp::min(t, k);
        x -= t * d;
        k -= t;
    }
    else {
        let t = - x / d;
        let t = std::cmp::min(t, k);
        x += t * d;
        k -= t;
    }
    if k % 2 == 1 {
        if x > 0 {
            x -= d;
        }
        else {
            x += d;
        }
    }
    print!("{}\n", std::cmp::max(x, -x));
}

use std::io::{ stdout, BufWriter, Write };

#[macro_export]
macro_rules! ioset {
    ($inp:ident, $buf:ident) => {
        inset!($inp);
        outset!($buf);
    }
}

#[macro_export]
macro_rules! inset {
    (source = $s:expr, $iter:ident) => {
        let mut $iter = $s.split_whitespace();
    };
    ($iter:ident) => {
        let s = {
            use std::io::Read;
            let mut s = String::new();
            std::io::stdin().read_to_string(&mut s).unwrap();
            s
        };
        let mut $iter = s.split_whitespace();
    }
}

#[macro_export]
macro_rules! input {
    ($iter:expr) => {};
    ($iter:expr, ) => {};
    ($iter:expr, $var:ident : $t:tt, $($r:tt)*) => {
        let $var = read_value!($iter, $t);
        input! { $iter, $($r)* }
    };
    ($iter:expr, mut $var:ident : $t:tt, $($r:tt)*) => {
        let mut $var = read_value!($iter, $t);
        input! { $iter, $($r)* }
    };
    ($iter:expr, ($var:expr) : $t:tt, $($r:tt)*) => {
        $var = read_value!($iter, $t);
        input! { $iter, $($r)* }
    };
}

#[macro_export]
macro_rules! read_value {

    // tuple
    ($iter:expr, ( $($t:tt), * )) => {
        ( $(read_value!($iter, $t)), * )
    };
    
    // array
    ($iter:expr, [ $t:tt; $len:expr ]) => {
        (0..$len).map(|_| read_value!($iter, $t)).collect::<Vec<_>>()
    };
    
    // string
    ($iter:expr, chars) => {
        read_value!($iter, String).chars().collect::<Vec<char>>()
    };

    ($iter:expr, usize1) => {
        $iter.next().unwrap().parse::<usize>().expect("Parse error") - 1
    };
    
    // any other
    ($iter:expr, $t:ty) => {
        $iter.next().unwrap().parse::<$t>().expect("Parse error")
    };
}

#[macro_export]
macro_rules! outset {
    ($buf:ident) => {
        let sout = stdout();
        let mut $buf = BufWriter::new(sout.lock());
    }
}

#[macro_export]
macro_rules! output {
    ($buf:expr, $($t:expr),*) => {
        write!($buf, $($t),*).unwrap();
    }
}

struct Chars<'a>(&'a Vec<char>);

impl<'a> std::fmt::Display for Chars<'a> {
    fn fmt(&self, f: &mut std::fmt::Formatter) -> Result<(), std::fmt::Error> {
        write!(f, "{}", self.0.iter().collect::<String>())
    }
}