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: Time Limit Exceeded)

using System;

using System.Linq;
class Program
{
    static void Main(string[] args)
    {
        //整数の入力
        //int N = int.Parse(Console.ReadLine());
        //スペース区切りの整数の入力
        string[] input = Console.ReadLine().Split(' ');

        double X = double.Parse(input[0]);
        double K = double.Parse(input[1]);
        double D = double.Parse(input[2]);

        //var L2 = L.Distinct().OrderBy(o => o);
        //var L2 = L.OrderBy(o => o).ToArray();

        //string input = Console.ReadLine();
        //int b = int.Parse(input[0]);
        //int c = int.Parse(input[1]);
        //文字列の入力
        //string s = Console.ReadLine();
        //出力

        //onsole.WriteLine(N);
        //Console.WriteLine(string.Join(" ", L));

        double now = X;

        for(int i = 0; i < K; i++)
        {
            if(now > 0)
            {
                now -= D;
            }
            else
            {
                now += D;
            }

            //Console.WriteLine(now);
        }

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