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: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Numerics;

namespace ConsoleApp1
{
    class Program
    {
        static void Main(string[] args)
        {
            //ll X, K, D;
            long[] XKD = Console.ReadLine().Split(" ").Select(x => long.Parse(x)).ToArray();

            //cin >> X >> K >> D;

            long X = XKD[0];
            long K = XKD[1];
            long D = XKD[2];
            X = Math.Abs(X);

            //X = abs(X);

            long straight = Math.Min(K, X / D);
            K -= straight;
            X -= straight * D;

            if (K % 2 == 0)
            {
                Console.WriteLine(X);
            }
            else
            {
                Console.WriteLine(D - X);
                
            }
        }
    }
}
//int[] N = Console.ReadLine().Split(" ").Select(x => int.Parse(x)).ToArray();