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.Linq;
using System.Security.Cryptography.X509Certificates;

namespace _0815
{
    class Program
    {
        static long x, k, d;
        static void Main(string[] args)
        {
            var xkd = Console.ReadLine().Split(' ').Select(i => long.Parse(i)).ToArray();
            x = xkd[0];
            k = xkd[1];
            d = xkd[2];

            long result = Solution();
            Console.WriteLine(result);
        }

        static long Solution()
        {
            int mi = 1;
            if (x < 0)
            {
                x = -x;
                mi = -1;
            }
            long res = 0;
            if (x - k * d >= 0)
            {
                res = mi * (x - k * d);
            }
            else
            {
                while (x >= d)
                {
                    x -= d;
                    k--;
                }
                k = k % 2;
                res = mi * (x - d * k);
            }
            return res;
        }
    }
}