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.Linq;

namespace abc175.c
{
    class Program
    {
        static void Main(string[] args)
        {
            long[] paramArray = getLongParams();

            long X = Math.Abs(paramArray[0]);
            long K = paramArray[1];
            long D = paramArray[2];

            long q = X / D;
            long mod = X % D;

            long ret = 0;

            if (q > K)
            {
                ret = X - (K * D);
            }
            else
            {
                K -= q;

                if (K % 2 == 0)
                {
                    ret = mod;
                }
                else
                {
                    ret = Math.Abs(mod - D) < mod + D ? Math.Abs(mod - D) : mod + D;
                }
            }
            Console.WriteLine(ret);
        }
        //↓↓↓ shared function ↓↓↓
        static int getIntParam()
        {
            return int.Parse(Console.ReadLine());
        }
        static int[] getIntParams()
        {
            return Console.ReadLine().Split(' ').Select(i => int.Parse(i)).ToArray();
        }
        static long getLongParam()
        {
            return long.Parse(Console.ReadLine());
        }
        static long[] getLongParams()
        {
            return Console.ReadLine().Split(' ').Select(i => long.Parse(i)).ToArray();
        }
        static string getStringParam()
        {
            return Console.ReadLine();
        }
        static string[] getStringParams()
        {
            return Console.ReadLine().Split(' ');
        }
    }
}