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;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace abc175_c
{
    class Program
    {
        static void Main(string[] args)
        {
            var X = CIn.ReadLong();
            var K = CIn.ReadLong();
            var D = CIn.ReadLong();
            var x = Math.Abs(X);
            if(x / D >= K )
            {
                Console.WriteLine(x - K * D);
            }
            else
            {
                if(K % 2 == x / D % 2)
                {
                    Console.WriteLine(Math.Abs(x % D));
                }
                else
                {
                    Console.WriteLine(Math.Abs(x % D - D));
                }
            }
        }
    }
    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(long n)
        {
            var array = new string[n];

            for (var i = 0; i < n; i++)
            {
                array[i] = Read();
            }

            return array;
        }

        public static int[] ReadIntArray(long n)
        {
            var array = new int[n];

            for (var i = 0; i < n; i++)
            {
                array[i] = ReadInt();
            }

            return array;
        }

        public static long[] ReadLongArray(long n)
        {
            var array = new long[n];

            for (var i = 0; i < n; i++)
            {
                array[i] = ReadLong();
            }

            return array;
        }
        public static double[] ReadDoubleArray(long n)
        {
            var array = new double[n];

            for (var i = 0; i < n; i++)
            {
                array[i] = ReadDouble();
            }

            return array;
        }
    }

}