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;
 
class program
{
    static void Main()
    {
        var xkd = Console.ReadLine().Split().Select(x => long.Parse(x)).ToArray();
        long x = xkd[0], k = xkd[1], d = xkd[2];
        long move = x / d;
        if (Math.Abs(x - (move + 1) * d) < Math.Abs(x - move * d)) move++;
        if (Math.Abs(x - (move - 1) * d) < Math.Abs(x - move * d)) move--;
        long ans = 0;
        if (Math.Abs(move) > k)
        { 
          if(Math.Abs(x - k * d) < Math.Abs(x + k * d)) ans = Math.Abs(x - k * d);
          else ans = Math.Abs(x + k * d);
        }
        else
        {
            if ((k - move) % 2 == 1)
            {
                if (Math.Abs(x - (move + 1) * d) < Math.Abs(x - (move - 1) * d))
                    ans = Math.Abs(x - (move + 1) * d);
                else
                    ans = Math.Abs(x - (move - 1) * d);
            }
            else ans = Math.Abs(x - move * d);
        }
        Console.Write(ans);
 
    }
}