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.math.BigInteger;
import java.util.*;

public class Main {

	public static void main(String[] args) {
		Scanner reader = new Scanner(System.in);
		BigInteger start = new BigInteger("" + reader.nextLong()), moves = new BigInteger("" + reader.nextLong()), d = new BigInteger("" + reader.nextLong());
		if (start.compareTo(new BigInteger("0")) == 0) {
			if (moves.mod(new BigInteger("2")).compareTo(new BigInteger("0")) == 0) {
				System.out.println(0);
			}
			else {
				System.out.println(d);
			}
		}
		else {
			if (start.abs().compareTo(moves.multiply(d)) >= 0) {
				if (start.compareTo(new BigInteger("0")) < 0) {
					System.out.println(start.add(moves.multiply(d)).intValue());
				}
				else {
					System.out.println(start.subtract(moves.multiply(d)).intValue());
				}
			}
			else {
				if (start.compareTo(new BigInteger("0")) < 0) {
					long forward = Math.abs(start.divide(d).longValue()) + 1;
					moves = moves.subtract(new BigInteger("" + forward));
					start = start.add(d.multiply(new BigInteger("" + forward)));
				}
				else {
					long forward = start.divide(d).longValue();
					moves = moves.subtract(new BigInteger("" + forward));
					start = start.subtract(d.multiply(new BigInteger("" + forward)));
				}
				if (moves.mod(new BigInteger("2")).longValue() == 0) {
					System.out.println(start.longValue());
				}
				else {
					System.out.println(Math.abs(start.subtract(d).longValue()));
				}	
			}
			reader.close();
		}
	}
	
}