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.*;
import java.util.*;

public class Main {
    public static void main(final String[] args) {
        final FastReader s=new FastReader();
        long x = Math.abs(s.nextLong());
        long k = s.nextLong();
        long d = s.nextLong();
        
        long min = x/d;
        
        if(min>k){
            System.out.println(x-(k*d));
            return;
        }
        k=k-(x/d);
        x=x-(d*(x/d));

        if(k%2!=0) x = d-x;

        System.out.println(x);

    }

    static class FastReader
    {
        BufferedReader br;
        StringTokenizer st;
        public FastReader() { br = new BufferedReader(new InputStreamReader(System.in)); }
        String next() {
            while (st == null || !st.hasMoreElements()) {
                try { st = new StringTokenizer(br.readLine()); }
                catch (final IOException  e) { e.printStackTrace(); }
            }
            return st.nextToken();
        }
        int nextInt() { return Integer.parseInt(next()); }
        long nextLong() { return Long.parseLong(next()); }
        double nextDouble() { return Double.parseDouble(next()); }
        String nextLine() {
            String str = "";
            try { str = br.readLine(); }
            catch (final IOException e) { e.printStackTrace(); }
            return str;
        }
    }
}