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

public class Main {
    public static void main(String[] args) {
        Scanner s = new Scanner(System.in);
        BigInteger X = s.nextBigInteger().abs();
        BigInteger K = s.nextBigInteger();
        BigInteger D = s.nextBigInteger();

        if (X.subtract(K.multiply(D)).signum() >= 0) {
            System.out.println(X.subtract(K.multiply(D)).toString());
        } else {
            if(X.divide(D).remainder(BigInteger.valueOf(2)).equals(K.remainder(BigInteger.valueOf(2)))) {
                System.out.println(X.remainder(D).toString());
            } else System.out.println(X.remainder(D).subtract(D).abs().toString());
        }
    }
}