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.Scanner;

public class Main {

    public static void main(String[] args) {
        
        var sc = new Scanner(System.in);
    
        long x = Long.parseLong(sc.next());
        long k = Long.parseLong(sc.next());
        long d = Long.parseLong(sc.next());
    
        BigInteger bx = BigInteger.valueOf(x);
        BigInteger bk = BigInteger.valueOf(k);
        BigInteger bd = BigInteger.valueOf(d);
        
        if(bx.abs().compareTo(bd.multiply(bk)) >= 0){
            if(x < 0) x = -x;
            System.out.println(x - d*k);
        }else if(x == 0){
            if(k%2 == 0){
                System.out.println(0);
            }else{
                System.out.println(d);
            }
        }else{
            if(x < 0) x = -x;
            long a = k - x/d;
            if(a%2 == 0){
                System.out.println(x%d);
            }else{
                System.out.println(d - x%d);
            }
        }
    }
}