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 input_line() -> Vec<String> {
  let mut buf = String::new();
  std::io::stdin().read_line(&mut buf).unwrap();
  return buf
    .split_whitespace()
    .map(|word| String::from(word))
    .collect();
}

fn main() {
  let inputs = input_line();
  let x: i64 = inputs[0].parse().unwrap();
  let k: i64 = inputs[1].parse().unwrap();
  let d: i64 = inputs[2].parse().unwrap();

  let plus_x = if x < 0 {
    -x
  } else {
    x
  };

  let x_per_d = plus_x / d;

  let ans = if k <= x_per_d {
    plus_x - d * k
  } else {
    let x_mod_d = plus_x % d;

    if (k - x_per_d) % 2 == 0 {
      x_mod_d
    } else {
      -(x_mod_d - d)
    }
  };

  println!("{}", ans);
}