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.Scanner;

class Main{
    public static void main(String args[]){
        Scanner sc = new Scanner(System.in);
        long x = sc.nextLong();
        long k = sc.nextLong();
        long d = sc.nextLong();
        sc.close();
        long closest = x;
        long absX = Math.abs(x);

        if(x > 0 && x - k * d > 0){
            System.out.println(x - k * d);
        }
        if(x < 0 && x + k * d < 0){
            System.out.println( -x - k * d);
        }

        for(long i = 0; i < k; i++){
            if(x >= 0){
                x -= d;
            }
            else{
                x += d;
            }
            absX = Math.abs(x);
            if(closest < absX){
                if((k - i - 1) % 2 == 0){
                    System.out.println(absX);
                    return;
                }
                else{
                    System.out.println(closest);
                    return;
                }
            }
            if(closest > absX){
                closest = absX;
            }
        }
        System.out.println(absX);
    }
}