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.io.BufferedReader;
import java.io.IOException;
import java.io.PrintWriter;
import java.util.StringTokenizer;

public class Main {
    
    public static void main(String[] args) throws IOException {
        BufferedReader br = new BufferedReader(new java.io.InputStreamReader(System.in));
        PrintWriter pw = new PrintWriter(System.out);
        StringTokenizer st = new StringTokenizer(br.readLine());

        long X = Long.parseLong(st.nextToken());
        long K = Long.parseLong(st.nextToken());
        long D = Long.parseLong(st.nextToken());

        if(X < 0) X = X*-1;

        long quotient = X / D;
        long mod = X % D;

        long result = 0;

        if(quotient > K) {
            result = mod + D * (quotient - K);
        } else {
            if((K - quotient) % 2 == 0) {
                result = mod;
            } else {
                result = mod - D;
            }
        }

        pw.println(Math.abs(result));
        br.close();
        pw.close();
    }
}