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.Text;
using System.Collections.Generic;
using System.Collections;
using static System.Math;
using System.Linq;
using static System.Array;

namespace ConsoleApp2
{
    class Program
    {
        
        //static long mod = 1000000007;
        //static char[] az = Enumerable.Range('a', 'z' - 'a' + 1).Select(i => (Char)i).ToArray();
        static void Main(string[] args)
        {
            //var A = Console.ReadLine().Split(' ').Select(x => long.Parse(x)).ToArray();
            //var N = long.Parse(Console.ReadLine());
            //var NK = Console.ReadLine().Split(' ').Select(x => int.Parse(x)).ToArray();
            //var N = NK[0];
            //var K = NK[1];
            var XKD = Console.ReadLine().Split(' ').Select(x => long.Parse(x)).ToList();
            var X = XKD[0];
            var K = XKD[1];
            var D = XKD[2];

            if(K%2 == 0)
            {
                //最大移動回数
                var move = K / 2;
                //1回の移動で動く距離
                var from = 2 * D;
                //
                var tmp = X / from;
                if (Abs(X - from * tmp) > Abs(X - from * (tmp + 1))) tmp++;
                var tmp2 = (long)Min(tmp, move);
                Console.WriteLine(Abs(X - tmp2*from));
            }
            else
            {
                K--;
                X = X - D;
                var X1 = X;
                //最大移動回数
                var move = K / 2;
                //1回の移動で動く距離
                var from = 2 * D;
                //
                var tmp = X / from;
                if (Abs(X - from * tmp) > Abs(X - from * (tmp + 1))) tmp++;
                var tmp2 = (long)Min(tmp, move);

                X = X + 2*D;
                //最大移動回数
                var move2 = K / 2;
                //1回の移動で動く距離
                var from2 = 2 * D;
                //
                var tmp3 = X / from2;
                if (Abs(X - from2 * tmp3) > Abs(X - from2 * (tmp3 + 1))) tmp3++;
                var tmp4 = (long)Min(tmp3, move2);
                if(Abs(X1 - tmp2 * from) < Abs(X - tmp4 * from2))
                {
                    Console.WriteLine(Abs(X1 - tmp2 * from));
                }
                else
                {
                    Console.WriteLine(Abs(X - tmp4 * from2));
                }
                
            }

           
        }


    }
}