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.

Examples

Input

6 2 4


Output

2


Input

7 4 3


Output

1


Input

10 1 2


Output

8


Input

1000000000000000 1000000000000000 1000000000000000


Output

1000000000000000
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.PrintWriter;

public class Main {

  static long x, k, d, ans;

  public static void main(String[] args) throws Exception {

    BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
    PrintWriter out = new PrintWriter(System.out);

    String[] in = br.readLine().split(" ");
    x = Long.parseLong(in[0]);
    k = Long.parseLong(in[1]);
    d = Long.parseLong(in[2]);

    br.close();

    if (in[1].length() + in[2].length() > 17) {
      long p = x % d;
      boolean is_even = ((x / d) % 2 == 0);
      if ((k - x / d) % 2 == 0) {
        ans = p;
      } else {
        if (p < 0) {
          ans = p + d;
        } else {
          ans = p - d;
        }
      }
    } else if (Math.abs(x) <= k * d) {
      long p = x % d;
      boolean is_even = ((x / d) % 2 == 0);
      if ((k - x / d) % 2 == 0) {
        ans = p;
      } else {
        if (p < 0) {
          ans = p + d;
        } else {
          ans = p - d;
        }
      }
    } else {
      ans = Math.abs(x) - k * d;
    }

    out.println(Math.abs(ans));

    out.flush();
  }
}
