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;

namespace ConsoleApp8
{
    class Program
    {
        static void Main(string[] args)
        {
            long[]  xkd = Array.ConvertAll(System.Console.ReadLine().Split(' '),long.Parse);
            if(xkd[0]<0)
            {
                xkd[0]= -xkd[0];
            }
            long kai = xkd[0] / xkd[2];
            long kotae = 0;
            kotae = xkd[0] - kai * xkd[2];
            if (kai<=xkd[1])
            {
                long zansu = xkd[1] - kai;
                if( zansu%2 ==1)
                {
                    long kai1 =Math.Abs( kotae + xkd[2]);
                    long kai2 =Math.Abs( kotae - xkd[2]);
                    if (kai1 > kai2)
                    {
                        kotae = kai2;
                    }
                    else
                    {
                        kotae = kai1;
                    }
                }
                else
                {
                    long kai1 = Math.Abs(kotae);
                    long kai2 = Math.Abs(kotae - 2*xkd[2]);
                    if (kai1 > kai2)
                    {
                        kotae = kai2;
                    }
                    else
                    {
                        kotae = kai1;
                    }

                }

            }
            else
            {
                kotae = xkd[0] - xkd[1] * xkd[2];
            }
            Console.WriteLine(kotae);
        }
    }
}