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.Collections.Generic;
using System.Linq;
using System.Security.Cryptography;

namespace C
{
    class Program
    {
        static void Main(string[] args)
        {
            string[] s = Console.ReadLine().Split(' ');
            long x = long.Parse(s[0]);
            long k = long.Parse(s[1]);
            long d = long.Parse(s[2]);

            #region 自作
            long ans = 0;

            x = Math.Abs(x);
            long temp_x = x;
            if( x - k * d >= 0 )
            {
                ans = x - k * d;
                Console.WriteLine(ans);
                return;
            }
            else
            {
                for (int i = 0; i < k; i++)
                {
                    temp_x -= d;
                    if (temp_x <= 0)
                    {
                        if (k == i+1)
                        {
                            if (temp_x > temp_x + d)
                            {
                                Console.WriteLine(temp_x + d);
                            }
                            else
                            {
                                Console.WriteLine(temp_x);
                            }
                            return;
                        }
                        else if (k - i % 2 == 0)
                        {
                            ans = temp_x;
                            Console.WriteLine(ans);
                            return;
                        }
                        else 
                        { 
                            ans = temp_x + d;
                            Console.WriteLine(ans);
                            return;
                        }
                    }
                }
            }

            Console.WriteLine(ans);
            return;
            #endregion

            #region 模範解答
            /*x = Math.Abs(x);

            long a = Math.Min(x/d, k);
            k -= a;
            x -= a * d;

            if(k % 2 == 0)
            {
                Console.WriteLine(x);
            }
            else
            {
                Console.WriteLine(d-x);
            }*/
            #endregion
        }
    }
}