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;
class Program
{
    static void Main(string[] args)
    {
        string[] sp = Console.ReadLine().Split(' ');
        long x = long.Parse(sp[0]), k = long.Parse(sp[1]), d = long.Parse(sp[2]);

        if (x > 0)
        {

            long min = (x - (x % d)) / d;
            if (x % d != 0) min++;

            long a = (k - min) % 2;

            x -= Math.Min(min, k) * d;
            a = Math.Min(a, k - min);


            for (long i = 0; i < a; i++)
            {
                if (x > 0)
                    x -= d;
                else
                    x += d;
            }
        }
        else
        {
            long min = (x - (x % d)) / d;
            min = Math.Abs(min);
            if (x % d != 0) min++;

            long a = (k + min) % 2;

            x += Math.Min(min, k) * d;
            a = Math.Min(a, k - min);


            for (long i = 0; i < a; i++)
            {
                if (x > 0)
                    x -= d;
                else
                    x += d;
            }
        }

        Console.WriteLine(Math.Abs(x));
    }
}