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: Time Limit Exceeded)

using System;
using System.Linq;

namespace ConsoleApp1
{
    class Program
    {
        static void Main(string[] args)
        {
            var xkd = Console.ReadLine().Split()
                .Select(long.Parse).ToArray();
            var inputX = Math.Abs(xkd[0]);
            var k = xkd[1];
            var d = xkd[2];

            long x = inputX;
            long min = Math.Abs(x);
            long result = 0;

            if (inputX > 0)
            {
                for (int i = 0; i < k; i++)
                {
                    x = x - d;
                    if (x >= 0)
                    {
                        min = x;
                        if (i == k - 1)
                            result = min;
                    }
                    else
                    {
                        if(-x < min)
                        {
                            min = -x;
                            i++;
                        }

                        if ((k - i) % 2 == 0)
                            result = min;
                        else
                            result = Math.Min(Math.Abs(min + d), Math.Abs(min - d));
                        break;
                    }
                }
            }

            if(inputX == 0)
            {
                if (k % 2 == 0)
                {
                    result = 0;
                }
                else
                    result = d;
            }

            Console.WriteLine(result);
        }
    }
}