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 C# (.NET Core 3.1.201) (judge verdict: Accepted)

using System;
using System.Linq;

public class Program{
    public static void Main(){
        long[] numbers = Console.ReadLine().Split(' ').Select(s => long.Parse(s)).ToArray();
        numbers[0] = Math.Abs(numbers[0]);
        long minToZero = numbers[0] / numbers[2];
        long result = 0;
        
        if ((numbers[0] % numbers[2]) * 2 > numbers[2]) minToZero++;
        
        if (numbers[1] < minToZero){
            result = numbers[0] - numbers[1] * numbers[2];
        }else {
            long tmp = Math.Abs(numbers[0] - numbers[2] * minToZero);
            if ((numbers[1] - minToZero) % 2 == 0){
                result = tmp;
            }else {
                result = Math.Abs(tmp - numbers[2]);
            }
            
        }
        
        Console.WriteLine(result);
    }
}