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: Wrong Answer)

using System;
using System.Runtime.Serialization.Formatters;

namespace ConsoleApp8
{
    class Program
    {
        static void Main(string[] args)
        {
            string b = Console.ReadLine();
            string[] vs = b.Split(' ');
            long[] c = new long[3];
            for (int i = 0; i < 3; i++)
            {
                c[i]= long.Parse(vs[i]);
            }
            long z = c[0];
            bool pulasu = false;
            if (c[0] >= 0)
            {
                pulasu = true;
            }
            long zz = 0;
            long zzz = -1;

            for (int i = 0; i < c[1]; i++)
            {
                if (z >= 0)
                {
                    z = z - c[2];
                    if (z < 0)
                    {
                        zz = z; 
                    }
                }
                else
                {
                    z = z + c[2];
                    if (z >= 0)
                    {
                        zzz = z;
                    }
                }
                if (zz != 0 && zzz != -1)
                {
                    if (i % 2 == 1)
                    {
                        z = zzz;
                        break;
                    }
                    else 
                    {
                        z = zz;
                        break;
                    }
                }
            }
            Console.WriteLine(Math.Abs( z));
        }
    }
}