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# (Mono-mcs 6.8.0.105) (judge verdict: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Diagnostics;
using System.Linq;

class Program
{
    static void Main(string[] args)
    {
        var line = Console.ReadLine().Split(' ');

        var x = long.Parse(line[0]);
        var k = long.Parse(line[1]);
        var d = long.Parse(line[2]);

        var firstMoveCount = Math.Abs(x) / d;

        var firstMovedPlace = Math.Abs(x) % d;
        if(x < 0)
        {
            firstMovedPlace *= -1;
        }

        var rem = k - firstMoveCount;


        if (rem > 0)
        {
            if (rem % 2 == 0)
            {
                Console.WriteLine(firstMovedPlace);
            }
            else
            {
                var ans = Math.Abs(firstMovedPlace - d) > Math.Abs(firstMovedPlace + d) ? firstMovedPlace + d : firstMovedPlace - d;
                Console.WriteLine(ans);
            }
        }
        else
        {
            var ans = Math.Abs(x) - (k * d);
            if (x < 0)
            {
                ans *= -1;
            }

            Console.WriteLine(ans);
        }

        Console.ReadLine();
    }


}