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: Accepted)


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

public class Main {

    public static void main(String[] args) throws IOException {

        //BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        BufferedWriter bw = new BufferedWriter(new OutputStreamWriter(System.out));
        FastScanner fs = new FastScanner();
        long x = Math.abs(fs.nextLong());
        long k = fs.nextLong();
        long d = fs.nextLong();
        if (x / d >= k) {
            System.out.println(x - (k * d));
        } else {
            long remain = k - (x / d);
            long start = x % d;
            if (remain % 2 == 0) {
                System.out.println(start);
            } else {
                System.out.println(Math.min(Math.abs(start + d), Math.abs(start - d)));
            }
        }
        bw.flush();
    }
//==============================================//
//==============================================//

    static void sort(int[] a) {
        ArrayList<Integer> l = new ArrayList<>();
        for (int i : a) {
            l.add(i);
        }
        Collections.sort(l);
        for (int i = 0; i < a.length; i++) {
            a[i] = l.get(i);
        }
    }

    static class FastScanner {

        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st = new StringTokenizer("");

        String next() {
            while (!st.hasMoreTokens()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

        int[] readArray(int n) {
            int[] a = new int[n];
            for (int i = 0; i < n; i++) {
                a[i] = nextInt();
            }
            return a;
        }

        long nextLong() {
            return Long.parseLong(next());
        }
    }

    static class Pair implements Comparable<Pair> {

        int a, b;

        public Pair(int x, int y) {
            a = x;
            b = y;
        }

        @Override
        public int compareTo(Pair p) {
            return a - p.a;
        }
    }

    static void forl_0(int n, int[] array, Scanner sc) {
        for (int i = 0; i < n; i++) {
            array[i] = sc.nextInt();
        }
    }

    static void forl_1(int n, int[] array, Scanner sc) {
        for (int i = 1; i <= n; i++) {
            array[i] = sc.nextInt();
        }
    }

    static boolean isPrime(long n) {
        if (n < 2) {
            return false;
        } else if (n == 2 || n == 3) {
            return true;
        } else if (n % 2 == 0 || n % 3 == 0) {
            return false;
        }
        long sqrtN = (long) Math.sqrt(n) + 1;
        for (long i = 6L; i <= sqrtN; i += 6) {
            if (n % (i - 1) == 0 || n % (i + 1) == 0) {
                return false;
            }
        }
        return true;
    }

    public static long gcd(long a, long b) {
        return (b == 0) ? a : gcd(b, a % b);
    }

    public static long lcm(long a, long b) {
        return a / gcd(a, b) * b;
    }
}