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.Collections.Generic;
using System.Linq;
using System.Security.Cryptography;
using System.Text;
using System.Threading.Tasks;

namespace ConsoleApp2
{
    class Program
    {
        static void Main(string[] args)
        {
            var input = GetLongNumArray();
            var X = input[0];
            var K = input[1];
            var D = input[2];
            long ans = 0;

            for (int i = 0; i < K; i++)
            {
                ans = Math.Abs(X - D);
                if (ans >= D)
                {
                    X = ans;
                    continue;
                }
                if ((K - (i + 1)) % 2 != 0)
                {
                    if (ans == 0)
                    {
                        ans = Math.Abs(ans - D);
                        break;
                    }
                    X = ans;
                    continue;
                }
                break;
            }

            Console.WriteLine(ans);
        }

        private static long[] GetLongNumArray()
        {
            var input = Console.ReadLine().Split(' ');
            return input.Select(x => long.Parse(x)).ToArray();
        }

        private static long GetLongNum()
        {
            return long.Parse(Console.ReadLine());
        }

        private static string[] GetStringArray()
        {
            return Console.ReadLine().Split(' ');
        }

        private static string GetString()
        {
            return Console.ReadLine();
        }
    }
}