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.BigDecimal;
import java.util.*;

public class Main {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        long X = Math.abs(sc.nextLong());
        long K = sc.nextLong();
        long D = sc.nextLong();
        BigDecimal x = new BigDecimal(X);
        BigDecimal k = new BigDecimal(K);
        BigDecimal d = new BigDecimal(D);
        if (X == 0) {
            System.out.println(K%2 == 0 ? 0 : D);
            return;
        }
        if (k.multiply(d).compareTo(x) == -1) {
            System.out.println(X-D*K);
            return;
        } else {
            long near = X/D;
            K -= near;
            X -= D*near;
            System.out.println(K%2 == 0 ? X : Math.abs(X-D));
        }
    }
}