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.math.BigInteger;
import java.util.*;
import java.util.stream.Collectors;

public class Main {
  public static void main(String[] args){
    Scanner sc = new Scanner(System.in);
    BigInteger x = new BigInteger(sc.next()).abs();
    BigInteger k = new BigInteger(sc.next());
    BigInteger d = new BigInteger(sc.next());

    BigInteger[] bigIntegers = x.divideAndRemainder(d);
    BigInteger q = bigIntegers[0];
    BigInteger r = bigIntegers[1];
    if (q.compareTo(k) >= 0) {
      System.out.println(x.subtract(d.multiply(k)));
      return;
    }

    BigInteger remain = q.subtract(k);
    System.out.println(remain.remainder(BigInteger.valueOf(2)).compareTo(BigInteger.ZERO) == 0 ? r : d.subtract(r));
  }
}
