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.Threading;

class Program
{
    static void Main(string[] args)
    {
        var s = Console.ReadLine().Split(" ");
        var x = long.Parse(s[0]);
        var k = long.Parse(s[1]);
        var d = long.Parse(s[2]);

        if (x > 0)
        {
            long プラスからマイナスになるまでの回数 = (long)(x / d);
            x = x - (Math.Min(k, プラスからマイナスになるまでの回数) * d);
            k = k - Math.Min(k, プラスからマイナスになるまでの回数);
        }
        if (x < 0)
        {
            long マイナスからプラスになるまでの回数 = Math.Abs((long)(x / d));
            x = x + (Math.Min(k, マイナスからプラスになるまでの回数) * d);
            k = k + Math.Min(k, マイナスからプラスになるまでの回数);
        }
        //long min = 0;
        if (k % 2 == 0)
        {
            // 偶数回の移動
            // x
            Console.WriteLine(Math.Abs(x));
            return;
        }
        else
        {
            // 奇数回の移動
            if (x <= 0)
            {
                x += d;
            }
            else
            {
                x -= d;
            }
            Console.WriteLine(Math.Abs(x));
        }
        //for (long i = 0; i < k; i++)
        //{
        //    if (x < 0)
        //    {
        //        x += d;
        //    }
        //    else
        //    {
        //        x -= d;
        //    }
        //    //min = Math.Min(min, Math.Abs(x));
        //    //if (i > 10)
        //    //{
        //    //    break;
        //    //}
        //}
        //Console.WriteLine(Math.Abs(x));
    }
}