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.Scanner;

public class Main{

     public static void main(String []args){
        long X,K,D;
        Scanner sc = new Scanner(System.in);
        
        X = sc.nextLong();
        K = sc.nextLong();
        D = sc.nextLong();
        
        
        long Xa = Math.abs(X);
        long ans = 0;
        
        long n = Xa / D;
        
        if(n >= K) {
            ans = Xa - K*D;
            
        }
        
        else {
            /*if((Xa - n*D) > -(Xa-(n+1)*D)) {
                if((K-(n+1))%2==0)
                    ans = -(Xa-(n+1)*D);
                else
                    ans = (Xa - n*D);
            }
            else {
                if((K-(n))%2==0)
                    ans = (Xa - n*D); 
                else
                    ans = -(Xa-(n+1)*D);
                
            }*/
            if ((K-n)%2==0) {
                ans = Xa - n*D;
            }
            else {
                ans = -(Xa - (n+1)*D);
                
            }
        }    
        //ans *=  (X<0?-1:1);
        System.out.println(ans);
         
     }
}