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 static System.Math;using static System.Console;using System.Collections.Generic;using System.Linq;using System;using System.Collections;
using System.Transactions;

class Program
{
    #region Reader
    static string ReadStr => Console.ReadLine();
    static string[] ReadStrs => Console.ReadLine().Split(' ');
    static int ReadInt => Convert.ToInt32(Console.ReadLine().Trim());
    static int[] ReadInts => Console.ReadLine().Trim().Split(' ').Select(s => Convert.ToInt32(s)).ToArray();
    static long ReadLong => Convert.ToInt64(Console.ReadLine().Trim());
    static long[] ReadLongs => Console.ReadLine().Trim().Split(' ').Select(s => Convert.ToInt64(s)).ToArray();
    #endregion
    #region Method
    const int mod = 1000000007;
    public static int Mod(int a,int mod) { return a % mod >= 0 ? a % mod : a % mod + mod; }
    public static long Mod(long a, long mod = mod) { return a % mod >= 0 ? a % mod : a % mod + mod; }
    #endregion

    static void Main()
    {

        long[] AS = ReadLongs;

        long X = Abs(AS[0]);
        long K = AS[1];
        long D = AS[2];

        if (X - K * D >= 0) WriteLine(X - K * D);
        else
        {
            long r = X % D;
            long d = X / D;

            long current = r;
            long nokori = K - d;

            WriteLine(nokori%2==0?Abs(current):D-current);

        }

    }
}