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.InputStream;
import java.io.PrintStream;
import java.math.BigInteger;
import java.util.Scanner;

public class Main {

  public static void main(String[] args) {
    resolve(System.in, System.out);
  }

  static void resolve(InputStream is, PrintStream pw) {
    Scanner sc = new Scanner(is);
    BigInteger x = BigInteger.valueOf(Long.parseLong(sc.next()));
    BigInteger k = BigInteger.valueOf(Long.parseLong(sc.next()));
    BigInteger d = BigInteger.valueOf(Long.parseLong(sc.next()));
    BigInteger maxMove = k.multiply(d);
    if (x.abs().compareTo(maxMove) >= 0) {
      pw.println(x.abs().add(maxMove.abs().negate()));
    } else {
      BigInteger[] goToNearest = x.divideAndRemainder(d);
      if (k.add(goToNearest[0].negate()).remainder(BigInteger.TWO).compareTo(BigInteger.ZERO)
        == 0) {
        pw.println(goToNearest[1].abs());
      } else {
        pw.println(goToNearest[1].add(d).abs().min(goToNearest[1].add(d.negate()).abs()));
      }
    }
  }
}
