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.util.function.*;
import java.lang.*;
import java.math.*;
import java.io.*;


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();

        long straight = X/D;
        if(straight >= K) System.out.println(X-K*D);
        else{
            X %= D;
            K -= straight;
            if(K%2==0) System.out.println(X);
            else System.out.println(D-X);
        }

    }
}
