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.*;

public 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();
	if (Math.abs(x) - k*d >= 0) {
	    System.out.print(Math.abs(Math.abs(x) - k*d));
	} else {
	    long near = (long)Math.abs(x)/d;
	    if ((k-near)%2==0) {
		if (Math.abs(x)-near*d >= Math.abs(Math.abs(x)-(near+2)*d) && near+2<=k)
		    System.out.print(Math.abs(Math.abs(x)-(near+2)*d));
		else { System.out.print(Math.abs(Math.abs(x)-near*d)); }
	    } else {
		if (near+1<=k && near+3>k) {
		    if (Math.abs(x)-(near-1)*d >= Math.abs(Math.abs(x)-(near+1)*d))
			System.out.print(Math.abs(Math.abs(x)-(near+1)*d));
		    else { System.out.print(Math.abs(Math.abs(x)-(near-1)*d)); }
		} else if (near+3<=k) {
		    if (Math.abs(x)-(near-1)*d >= Math.abs(Math.abs(x)-(near+1)*d) &&
			Math.abs(x)-(near+1)*d >= Math.abs(Math.abs(x)-(near+3)*d))
			System.out.print(Math.abs(Math.abs(x)-(near+3)*d));
		    else if (Math.abs(x)-(near-1)*d <= Math.abs(Math.abs(x)-(near+1)*d) &&
			Math.abs(x)-(near+1)*d <= Math.abs(Math.abs(x)-(near+3)*d))
			System.out.print(Math.abs(Math.abs(x)-(near-1)*d));
		    else { System.out.print(Math.abs(Math.abs(x)-(near+1)*d)); }
		}
	    }
	}
    }
}