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;

public class Main {
    public long getDestination(long x, long k, long d) {
        long prevValue = 0;
        long prevPrevValue = 0;
        while (k > 0) {
            if (x == 0) {
                if (k % 2 == 0) {
                    return 0;
                } else {
                    return d;
                }
            } else {
                long jumpK = Math.abs(x) / d;
                jumpK = Math.max(jumpK, 1);
                jumpK = Math.min(jumpK, k);

                k -= jumpK;
                if (x > 0) {
                    x -= jumpK * d;
                } else {
                    x += jumpK * d;
                }
                
                if (prevPrevValue == x) {
                    if (k % 2 == 0) return x;
                    if (x > 0) return x - d;
                    if (x < 0) return x + d;
                }
                prevPrevValue = prevValue;
                prevValue = x;
            }
        }

        return Math.abs(x);
    }

    public static void main(String[] args) throws Exception {
        Main solution = new Main();

        Scanner scanner = new Scanner(System.in);
        long x = scanner.nextLong();
        long k = scanner.nextLong();
        long d = scanner.nextLong();

        long answer = solution.getDestination(x, k, d);
        System.out.println(answer);
    }
}