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.Collections.Generic;

namespace abc175_c
{
  class Program
  {
    static void Main(string[] args)
    {
      var X = Math.Abs(CIn.ReadLong());
      var K = CIn.ReadLong();
      var D = CIn.ReadLong();

      var c = X / D;

      if (K < c)
      {
        Console.WriteLine(X - K * D);
        return;
      }

      var m = X % D;

      if ((K - c) % 2 == 0)
      {
        Console.WriteLine(m);
      }
      else
      {
        Console.WriteLine(Math.Abs(m - D));
      }
    }
  }

  static class CIn
  {
    private static readonly Queue<string> fieldBuffer = new Queue<string>();

    public static string Read()
    {
      if (fieldBuffer.Count == 0)
      {
        foreach (var field in Console.ReadLine().Split())
        {
          fieldBuffer.Enqueue(field);
        }
      }
      return fieldBuffer.Dequeue();
    }

    public static int ReadInt() => int.Parse(Read());
    public static long ReadLong() => long.Parse(Read());
    public static double ReadDouble() => double.Parse(Read());

    public static string[] ReadStringArray(int n)
    {
      var array = new string[n];
      for (var i = 0; i < n; i++)
      {
        array[i] = Read();
      }
      return array;
    }

    public static int[] ReadIntArray(int n)
    {
      var array = new int[n];
      for (var i = 0; i < n; i++)
      {
        array[i] = ReadInt();
      }
      return array;
    }

    public static long[] ReadLongArray(int n)
    {
      var array = new long[n];
      for (var i = 0; i < n; i++)
      {
        array[i] = ReadLong();
      }
      return array;
    }

    public static double[] ReadDoubleArray(int n)
    {
      var array = new double[n];
      for (var i = 0; i < n; i++)
      {
        array[i] = ReadDouble();
      }
      return array;
    }

    public static char[,] ReadCharMatrix(int h, int w)
    {
      var array = new char[h, w];
      for (var i = 0; i < h; i++)
      {
        var l = Console.ReadLine().ToCharArray();
        for (var j = 0; j < w; j++)
        {
          array[i, j] = l[j];
        }
      }
      return array;
    }
  }
}