Problem:
Score : 300 points

Problem Statement

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.

Sample Input 1

6 2 4

Sample Output 1

2

Takahashi is now at coordinate 6. It is optimal to make the following moves:

Move from coordinate 6 to (6 - 4 =) 2.

Move from coordinate 2 to (2 - 4 =) -2.

Here, the absolute value of the coordinate of the destination is 2, and we cannot make it smaller.

Sample Input 2

7 4 3

Sample Output 2

1

Takahashi is now at coordinate 7. It is optimal to make, for example, the following moves:

Move from coordinate 7 to 4.

Move from coordinate 4 to 7.

Move from coordinate 7 to 4.

Move from coordinate 4 to 1.

Here, the absolute value of the coordinate of the destination is 1, and we cannot make it smaller.

Sample Input 3

10 1 2

Sample Output 3

8

Sample Input 4

1000000000000000 1000000000000000 1000000000000000

Sample Output 4

1000000000000000

The answer can be enormous.

Solution in Java (OpenJDK 11.0.6) (judge verdict: Wrong Answer)

import java.util.*;
import java.io.*;

public class Main {
    public static void main(String[] args) throws IOException {
        FastScanner in = new FastScanner(System.in);
        PrintWriter out = new PrintWriter(System.out);
        long x = in.nextLong();
        long k = in.nextLong();
        long d = in.nextLong();

        for (int i = 0; i < k; i++) {
            if (Math.abs(x) <= d) {
                if (k % 2 == 1) {
                    x = d - Math.abs(x);
                }
                break;
            }

            if (x > 0) x -= d;
            else x += d;
        }

        out.println(Math.abs(x));
        out.close();

    }


    static class FastScanner {
        BufferedReader br;
        StringTokenizer st;
        public FastScanner(InputStream i) {
            br = new BufferedReader(new InputStreamReader(i));
            st = new StringTokenizer("");
        }
        public String next() throws IOException {
            if (st.hasMoreTokens()) {
                return st.nextToken();
            }
            else
                st = new StringTokenizer(br.readLine());
            return next();
        }
        public int nextInt() throws IOException {
            return Integer.parseInt(next());
        }
        public double nextDouble() throws IOException {
            return Double.parseDouble(next());
        }
        public long nextLong() throws IOException {
            return Long.parseLong(next());
        }
        public String nextLine() throws IOException {
            if (!st.hasMoreTokens()) {
                st = new StringTokenizer(br.readLine());
                return nextLine();
            }

            String ret = "";
            while (st.hasMoreTokens()) {
                ret += st.nextToken();
            }
            return ret;
        }
        public int[] nextIntArr(int size) throws IOException {
            int[] arr = new int[size];
            for (int i = 0; i < arr.length; i++) {
                arr[i] = nextInt();
            }
            return arr;
        }
        public long[] nextLongArr(int size) throws IOException {
            long[] arr = new long[size];
            for (int i = 0; i < arr.length; i++) {
                arr[i] = nextLong();
            }
            return arr;
        }
        public double[] nextDoubleArr(int size) throws IOException {
            double[] arr = new double[size];
            for (int i = 0; i < arr.length; i++) {
                arr[i] = nextDouble();
            }
            return arr;
        }
    }
}