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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.math.BigInteger;
import java.util.*;
 
public class Main {
 
    void solve() throws IOException {
        long X = nl();
        long K = nl();
        long D = nl();

        X = Math.abs(X);
        long time = (X - (X%D))/D;
        long ans = X;
        if(time <= K){
            if(X%D==0){
                if((K-time)%2==0) ans = 0;
                if((K-time)%2==1) ans = D; 
            }else{
                if((K-time)%2==0) ans = X%D;
                if((K-time)%2==1) ans = Math.abs(X%D-D);
            }
        }else{
            BigInteger x = BigInteger.valueOf(X);
            BigInteger k = BigInteger.valueOf(K);
            BigInteger d = BigInteger.valueOf(D);
            x = x.subtract(k.multiply(d));
            ans = x.longValue();
        }
 
        out.println(ans);
    }

    final int mod = 1000000007;
    final BigInteger MOD = BigInteger.valueOf(mod);
    int upperBound(ArrayList<Long> list, Long target){
        int i = Collections.binarySearch(list, target, new UpperBoundComparator<Long>());
        return ~i;
    }
    class UpperBoundComparator<T extends Comparable<? super T>> implements Comparator<T>{
        public int compare(T x, T y){
            return (x.compareTo(y) > 0) ? 1 : -1;
        }
    }
    int lowerBound(ArrayList<Long> list, Long target){
        int i = Collections.binarySearch(list, target, new LowerBoundComparator<Long>());
        return ~i;
    }
    class LowerBoundComparator<T extends Comparable<? super T>> implements Comparator<T>{
        public int compare(T x, T y){
            return (x.compareTo(y) >= 0) ? 1 : -1;
        }
    }
    int mul(int x, int y){
        int val = (int)((x * 1L * y) % mod);
        return val>=0 ? val : val+mod;
    }
    int add(int x, int y) {
        x += y;
        if(x < 0) x += mod;
        if(x>=mod) x -= mod;
        return x;
    }
    int sub(int x, int y){
        x = add(x,mod-y);
        if(x < 0) x += mod;
        if(x>=mod) x -= mod;
        return x;
    }
    String ns() throws IOException {
        while (!tok.hasMoreTokens()) {
            tok = new StringTokenizer(in.readLine(), " ");
        }
        return tok.nextToken();
    }
 
    int ni() throws IOException {
        return Integer.parseInt(ns());
    }
 
    long nl() throws IOException {
        return Long.parseLong(ns());
    }
 
    double nd() throws IOException {
        return Double.parseDouble(ns());
    }
 
    String[] nsa(int n) throws IOException {
        String[] res = new String[n];
        for (int i = 0; i < n; i++) {
            res[i] = ns();
        }
        return res;
    }
 
    int[] nia(int n) throws IOException {
        int[] res = new int[n];
        for (int i = 0; i < n; i++) {
            res[i] = ni();
        }
        return res;
    }
 
    long[] nla(int n) throws IOException {
        long[] res = new long[n];
        for (int i = 0; i < n; i++) {
            res[i] = nl();
        }
        return res;
    }
 
    static BufferedReader in;
    static PrintWriter out;
    static StringTokenizer tok;
 
    public static void main(String[] args) throws IOException {
        in = new BufferedReader(new InputStreamReader(System.in));
        out = new PrintWriter(System.out);
        tok = new StringTokenizer("");
        Main main = new Main();
        main.solve();
        out.close();
    }
}