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)

use std::io;
use io_ext::Reader;
use parse::ParseAll;

fn main() {
    let stdin = io::stdin();
    let mut r = Reader::new(stdin.lock());
    let (x, moves, distance): (i64, i64, i64) = r.read_line().split_whitespace().parse_all();
    println!("{}", answer(x, moves, distance));
}

fn answer(x: i64, moves: i64, distance: i64) -> i64 {
    let x = x.abs();
    if x / distance >= moves {
        return x - distance * moves;
    }

    let moves_to_near = x / distance;
    let x = x - distance * moves_to_near;
    let moves = moves - moves_to_near;
    if moves % 2 == 0 {
        x
    } else {
        distance - x
    }
}

#[cfg(test)]
mod tests {
    use super::answer;

    #[test]
    fn test() {
        assert_eq!(answer(6, 2, 4), 2);
        assert_eq!(answer(7, 4, 3), 1);
        assert_eq!(answer(10, 1, 2), 8);
        assert_eq!(answer(1000000000000000,1000000000000000,1000000000000000), 1000000000000000);
    }
}

pub mod int_ext {
    pub fn digits10(n: i64) -> i64 {
        assert!(n >= 0);

        let mut d = 1;
        let mut p = 10;
        while p <= n {
            p *= 10;
            d += 1;
        }
        d
    }

    pub fn permutation(n: i64, k: i64) -> i64 {
        assert!(k >= 0);
        assert!(n >= k);

        let mut p = 1;
        for i in 0..k {
            p = p * (n - i);
        }
        p
    }

    pub fn combination(n: i64, k: i64) -> i64 {
        use std::cmp;

        assert!(k >= 0);
        assert!(n >= k);

        let k = cmp::min(k, n - k);
        let num = permutation(n, k);
        let mut den = 1;
        for i in 0..k {
            den = den * (i + 1);
        }
        num / den
    }
}

/// A module for easy use of io.
pub mod io_ext {
    use std::io::BufRead;

    pub struct Reader<R> {
        buf: String,
        inner: R,
    }

    impl<R> Reader<R> {
        #[inline]
        pub fn new(inner: R) -> Self {
            Reader { buf: String::new(), inner: inner }
        }

        #[inline]
        pub fn into_inner(self) -> R {
            self.inner
        }
    }

    impl<R: BufRead> Reader<R> {
        #[allow(deprecated)]
        #[inline]
        pub fn read_line(&mut self) -> &str {
            self.buf.clear();
            self.inner.read_line(&mut self.buf).unwrap_or_else(|e| panic!("{}", e));
            self.buf.trim_right()
        }
    }
}

/// Parsing Iterator.
pub mod parse {
    use std::borrow::Borrow;
    use std::str::FromStr;

    pub trait FromStrIterator {
        fn from_str_iter<S: Borrow<str>, I: Iterator<Item=S>>(i: I) -> Self;
    }

    pub trait ParseAll {
        fn parse_all<F: FromStrIterator>(self) -> F;
    }

    impl<S: Borrow<str>, I: Iterator<Item=S>> ParseAll for I {
        #[inline]
        fn parse_all<F: FromStrIterator>(self) -> F {
            F::from_str_iter(self)
        }
    }

    fn parse<S: Borrow<str>, I: Iterator<Item=S>, F: FromStr>(i: &mut I) -> F {
        i.next().unwrap_or_else(|| panic!("too few strings error")).borrow().parse().unwrap_or_else(|_| panic!("parse error"))
    }

    // To avoid conflict, this is not implemented for `A` but `(A,)`.
    impl<A: FromStr> FromStrIterator for (A, ) {
        fn from_str_iter<S: Borrow<str>, I: Iterator<Item=S>>(mut i: I) -> Self {
            let a = parse(&mut i);
            if i.next().is_some() {
                panic!("too many strings error");
            }
            (a, )
        }
    }

    impl<A: FromStr, B: FromStr> FromStrIterator for (A, B) {
        fn from_str_iter<S: Borrow<str>, I: Iterator<Item=S>>(mut i: I) -> Self {
            let a = parse(&mut i);
            let b = parse(&mut i);
            if i.next().is_some() {
                panic!("too many strings error");
            }
            (a, b)
        }
    }

    impl<A: FromStr, B: FromStr, C: FromStr> FromStrIterator for (A, B, C) {
        fn from_str_iter<S: Borrow<str>, I: Iterator<Item=S>>(mut i: I) -> Self {
            let a = parse(&mut i);
            let b = parse(&mut i);
            let c = parse(&mut i);
            if i.next().is_some() {
                panic!("too many strings error");
            }
            (a, b, c)
        }
    }

    impl<A: FromStr, B: FromStr, C: FromStr, D: FromStr> FromStrIterator for (A, B, C, D) {
        fn from_str_iter<S: Borrow<str>, I: Iterator<Item=S>>(mut i: I) -> Self {
            let a = parse(&mut i);
            let b = parse(&mut i);
            let c = parse(&mut i);
            let d = parse(&mut i);
            if i.next().is_some() {
                panic!("too many strings error");
            }
            (a, b, c, d)
        }
    }

    impl<T: FromStr> FromStrIterator for Vec<T> {
        fn from_str_iter<S: Borrow<str>, I: Iterator<Item=S>>(i: I) -> Self {
            i.map(|s| s.borrow().parse().unwrap_or_else(|_| panic!("parse error"))).collect()
        }
    }
}

pub mod modulo {
    /// Returns `x` + `y` mod `modulo`.
    ///
    /// `x < modulo` and `y < modulo` must hold.
    #[inline]
    pub fn add(x: u64, y: u64, modulo: u64) -> u64 {
        debug_assert!(modulo > 0);
        debug_assert!(x < modulo && y < modulo);
        let sum = x as u64 + y as u64;
        if sum <= modulo as u64 {
            sum
        } else {
            sum.wrapping_sub(modulo)
        }
    }

    /// Returns `x` - `y` mod `modulo`.
    ///
    /// `x < modulo` and `y < modulo` must hold.
    #[inline]
    pub fn sub(x: u64, y: u64, modulo: u64) -> u64 {
        debug_assert!(0 < modulo);
        debug_assert!(x < modulo && y < modulo);
        if x >= y {
            x - y
        } else {
            modulo + x - y
        }
    }

    /// Returns `x` * `y` mod `modulo`.
    #[inline]
    pub fn mul(x: u64, y: u64, modulo: u64) -> u64 {
        (x as u64 * y as u64) % modulo as u64
    }

    /// Returns `x`^ `y` mod `modulo`.
    pub fn pow(x: u64, mut y: u64, modulo: u64) -> u64 {
        debug_assert!(0 < modulo);
        let mut p = x;
        let mut ret = 1;

        while y != 0 {
            if y & 1 == 1 {
                ret = mul(ret, p, modulo);
            }
            p = mul(p, p, modulo);
            y >>= 1;
        }
        ret
    }

    fn is_prime(x: u64) -> bool {
        let sqrt = (x as f64).sqrt() as u64;
        for factor in 2..sqrt {
            if x % factor == 0 {
                return false;
            }
        }
        true
    }

    /// Returns 1 / `x`.
    ///
    /// `modulo` must be a prime number.
    #[inline]
    fn reciprocal(x: u64, modulo: u64) -> u64 {
        debug_assert!(0 < modulo && is_prime(modulo));
        pow(x, modulo - 2, modulo)
    }

    /// Returns `x` / `y` mod `modulo`.
    ///
    /// `modulo` must be a prime number.
    #[inline]
    pub fn div(x: u64, y: u64, modulo: u64) -> u64 {
        debug_assert!(0 < modulo && is_prime(modulo));
        mul(x, reciprocal(y, modulo), modulo)
    }

    /// Returns `n`P`k` mod `modulo`.
    pub fn perm(n: u64, k: u64, modulo: u64) -> u64 {
        let mut p = 1;
        for i in 0..k {
            p = mul(p, n - i, modulo);
        }
        p
    }

    /// Returns `n`C`k` mod `modulo`.
    pub fn comb(n: u64, k: u64, modulo: u64) -> u64 {
        let k = if k <= n / 2 { k } else { n - k };
        let num = perm(n, k, modulo);
        let mut den = 1;
        for i in 0..k {
            den = mul(den, i + 1, modulo);
        }
        div(num, den, modulo)
    }
}