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.util.*;
import java.io.*;
import java.lang.*;
class Main{
    public static void main(String args[]) throws IOException{
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st = new StringTokenizer(br.readLine());
        long x = Long.parseLong(st.nextToken());
        long k = Long.parseLong(st.nextToken());
        long d = Long.parseLong(st.nextToken());

        long mov = Math.abs(x/d);

        if(mov >= k){
            if(x<0){
               System.out.println(Math.abs(x+k*d)); 
            }
            else{
                System.out.println(Math.abs(x-k*d));
            }
        }
        else if(mov < k){
            long num = k-mov;
            if(x<0){
                
                x = x+mov*d;
                if(num%2==1){
                    long dist  = Math.min(Math.abs(x-d),Math.abs(x+d));
                    System.out.println(dist);
                }
                else{
                    System.out.println(Math.abs(x));
                }

            }
            else{
                x = x-mov*d;
                //x = x+mov*d;
                if(num%2==1){
                    long dist  = Math.min(Math.abs(x-d),Math.abs(x+d));
                    System.out.println(dist);
                }
                else{
                    System.out.println(Math.abs(x));
                }
            }
        }
    }
}