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.Text;
using System.Threading.Tasks;

namespace CS
{

    
        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;




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

            c.Func();

        }
        public long Func()
        {

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

            long X = l[0];
            long K = l[2];
            long D = l[1];

            long x = Math.Abs(X);
            long ret = 0;

            long straight = D < X / K ? D : X / K;
            //真ん中を超えられない場合
            D -= straight;
            X -= straight * K;
           

           if (D % 2 == 0)
            {
                ret = X;
            }
            else
            {
                ret = K - X;
            }

            Console.WriteLine(ret);
            return ret;
        }




    }
}