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.Numerics;
using System.Collections.Generic;

namespace ForAtcoder
{
    class Program
    {
        static void Main(string[] args)
        {
            long[] inputLongArray = Console.ReadLine().Split(' ').Select(i => long.Parse(i)).ToArray();
            var x = inputLongArray[0];
            var k = inputLongArray[1];
            var d = inputLongArray[2];
            for (var i = 1; i <= k; i++)
            {
                long ax = Math.Abs(x);
                long axpd = Math.Abs(x + d);
                long axnd = Math.Abs(x - d);
                if (i == 1 && ax - k * d >= 0)
                {
                    x = x - k * d;
                    break;
                }
                else if (i == 1 && ax - k * d >= 0)
                {
                    x = x + k * d;
                    break;
                }
                if ((ax > axnd || ax > axpd) && axnd >= axpd) x = x + d;
                else if (ax > axnd || ax > axpd) x = x - d;
                else if ((k - i + 1) % 2 == 0) break;
                else
                {
                    if (axnd >= axpd) x = x + d;
                    else x = x - d;
                    break;
                }
            }
            Console.WriteLine(Math.Abs(x));
        }
    }
}