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: Runtime Error)

using System;

namespace AtBC175
{
    class Program
    {
        static void Main(string[] args)
        {
            int[] arr = new int[3];
            string[] str = Console.ReadLine().Split();
            for (int i = 0;i < 3; i++)
            {
                arr[i] = int.Parse(str[i]);
            }
            int X = arr[0];
            int K = arr[1];
            int D = arr[2];
            int[] output = new int[K + 1];
            int p = K * D;
            int s;
            for (int t = 0; t < K + 1; t++)
            {
                s = t * D * 2;
                output[t] = p - s;
                if (output[t] < 0)
                {
                    output[t] = output[t] * -1;
                }
            }
            Array.Reverse(output);
            Console.WriteLine(output[0]);
        }
    }
}