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.Numerics;
using static System.Math;
using System;

public class Hello
{
    public static void Main()
    {
        string[] line = Console.ReadLine().Trim().Split(' ');
        BigInteger x = Abs(long.Parse(line[0]));
        BigInteger k = long.Parse(line[1]);
        BigInteger d = long.Parse(line[2]);
        getAns(x, k, d);
    }
    static void getAns(BigInteger x, BigInteger k, BigInteger d)
    {
        if (x - k * d >= 0) { Console.WriteLine(BigInteger.Abs(x - k * d)); return; }
        var t = x / d;
        if ((k - t) % 2 == 0) Console.WriteLine(BigInteger.Abs(x - t * d));
        else Console.WriteLine(BigInteger.Abs(x - d * (t + 1)));
    }
}