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.*;
import java.util.*;

public class Main {
    public static void main(String[] args) {
        BigInteger TWO = new BigInteger("2");
        Scanner sc = new Scanner(System.in);
        BigInteger x = new BigInteger(sc.next());
        BigInteger k = new BigInteger(sc.next());
        BigInteger d = new BigInteger(sc.next());
        if (x.abs().compareTo(k.multiply(d)) >= 0) {
            System.out.println(x.abs().subtract(k.multiply(d)).abs());
        } else if (x.abs().compareTo(d) < 0) {
            if (k.remainder(TWO).equals(BigInteger.ZERO)) System.out.println(x.abs());
            else System.out.println(x.abs().subtract(d).abs());
        } else {
            BigInteger[] dr = x.abs().divideAndRemainder(d);
            if (k.remainder(TWO).equals(BigInteger.ZERO)) {
                if (dr[0].remainder(TWO).equals(BigInteger.ZERO)) System.out.println(dr[1].abs());
                else System.out.println(d.subtract(dr[1]).abs());
            } else {
                if (dr[0].remainder(TWO).equals(BigInteger.ONE)) System.out.println(dr[1].abs());
                else System.out.println(d.subtract(dr[1]).abs());
            }
        }
    }
}