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: Time Limit Exceeded)

use std::io::stdin;

#[derive(Default)]
struct Scanner {
	buffer: Vec<String>
}

impl Scanner {
	fn next<T: std::str::FromStr> (&mut self) -> T {
		loop {
			if let Some(token) = self.buffer.pop() {
				return token.parse().ok().expect("Failed parse");
			}
			let mut input = String::new();
			stdin().read_line(&mut input).expect("Failed read");
			self.buffer = input.split_whitespace().rev().map(String::from).collect();
		}
	}
}

fn main() {
	let mut scan = Scanner::default();

	let mut x: i128 = scan.next();
	let mut k: i128 = scan.next();
	let d: i128 = scan.next();

	while k > 0 {
		if x == 0 {
			if k % 2 != 0 {x = d;}
			break;
		}
		let mut y = x.abs() / d;
		if y == 0 {y = 1;}
		let t = if y < k {y} else {k};
		x = (x.abs() - d * t).abs();
		k -= t;
	}
	println!("{}", x);
}