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.*;

public class Main {

    public static void main(String[] args) {

        Scanner sc = new Scanner(System.in);
        long X = sc.nextLong();
        long K = sc.nextLong();
        long D = sc.nextLong();
        if (X < 0) X *= -1;
        long mod = X%D;
        long cnt;
        long min1;
        long min2;
        if (mod <= D-mod) {
            cnt = (X-mod)/D;
            min1 = mod;
            min2 = D-mod;
        } else {
            cnt = (X+(D-mod))/D;
            min1 = D-mod;
            min2 = mod;
        }
        if (K <= cnt) {
            System.out.println(Math.abs(X-K*D));
        } else if ((K-cnt)%2 == 0) {
            System.out.println(min1);
        } else {
            System.out.println(min2);
        }
    }
}
