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 ConsoleApp3
{
    class Program
    {
        static void Main(string[] args)
        {
            long[] N = Console.ReadLine().Split().Select(long.Parse).ToArray();
            long x = N[0];
            long k = N[1];
            long d = N[2];
            
            for (int i = 0; i < k; i++)
            {
                long xd = 0;
                long dx = 0;
                long x1 = 0;
                if (x - d < 0) { xd = d - x; }
                if (x - d > 0) { xd = x - d; }
                if (x - d == 0) { xd = 0; }
                if (xd < 0){xd = -xd;}
                if (x + d < 0) { dx = x + d; }
                if (x + d > 0) { dx = x + d; }
                if (x + d == 0) { dx = 0; }
                if (dx < 0){dx = -dx;}
                if (xd < dx) { x = xd; }
                if (xd > dx) { x = dx; }
                if (xd == dx) { x = xd; }
                x1 = x;
                if (i >= 1)
                {
                    if(x == x1) { break; }
                }
            }
            if(x < 0) { x = -x; }
            Console.WriteLine(x);
            Console.ReadLine();
        }
    }
}