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: Time Limit Exceeded)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace CS
{
    using P = System.Drawing.Point;
    class Utls
    {
        public static int[][] int2(int x, int y)
        {

            var ret = new int[x][];
            for (var i = 0; i < x; i++)
            {
                ret[i] = new int[y];
            }
            return ret;
        }
    }


    public class Class1
    {
        public Func<string> ReadLine = Console.ReadLine;
        public struct InputData
        {
            public long X, K, D;
           

        }
        public InputData input;
        public int[] hc, wc, hml, wml;
        public int hm, wm;
        public HashSet<P> f;



        static void Main()
        {
            var c = new Class1();
           
            c.Func();

        }
        public long Func()
        {

            this.input = this.Input();

            var x = Math.Abs(input.X);
            long ret = 0;
       
            if ( input.K > x)
            {
                if (input.D  % 2 == 0)
                {
                    ret = x;
                }
                else
                {
                    ret = input.K - (x);
                }
            }

        else  if (x / input.D >= input.K )
            {
             for ( var i = 0; i < input.D; i++)
                {
                    x -= input.K;
                }
                ret = x;
            }
          
            else
            {
                var a = x / input.K;
                if ((input.D - a )%2 == 0)
                {
                    ret = x % input.K;
                }else
                {
                    ret = input.K - (x % input.K);
                }
            }


            Console.WriteLine(ret);
            return ret;
        }

        public dynamic Input()
        {
            var ret = new InputData();

            var l = this.ReadLine().Split(' ').Select(long.Parse).ToArray();

            ret.X = l[0];
            ret.K = l[2];
            ret.D = l[1];

            return ret;
        }


    }
}