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

namespace atcoder
{
    public class Program
    {
        public static void Main(string[] args)
        {
            var buffer = Console.ReadLine().Split();
            long X = long.Parse(buffer[0]);
            long K = long.Parse(buffer[1]);
            long D = long.Parse(buffer[2]);

            if (X == D)
            {
                if (K % 2 == 0)
                    Console.WriteLine(Math.Abs(X));
                else
                    Console.WriteLine(0);

                return;
            }

            int arr = 1;
            if (Math.Abs(X - D) < Math.Abs(X + D))
                arr = -1;
            long cnt = X / D;
            if (cnt >= K)
            {
                Console.WriteLine(Math.Abs(X + (arr * K * D)));
                return;
            }

            var tmp = X + arr * cnt * D;
            if ((K - cnt) % 2 == 0)
            {
                Console.WriteLine(Math.Abs(tmp));
            }
            else
            {
                tmp += arr * D;
                Console.WriteLine(Math.Abs(tmp));
            }
        }
    }
}