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);
        BigDecimal X = new BigDecimal(Math.abs(sc.nextLong()));
        BigDecimal K = new BigDecimal(sc.nextLong());
        BigDecimal D = new BigDecimal(sc.nextLong());

        BigDecimal ans = BigDecimal.ZERO;
        BigDecimal KD = K.multiply(D);
        if(X.compareTo(KD) >=0 ){
            ans = X.subtract(KD);
        }else{
            BigDecimal t = new BigDecimal(Math.min(X.longValue()/D.longValue(),K.longValue()));
            K = K.subtract(t) ;
            X = X.subtract(t.multiply(D));
            if(K.longValue()%2==0){
                ans= X;
            }else{
                ans =X.subtract(D);
            }
        }

        System.out.println(Math.abs(ans.longValue()));}}