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.Text;
using System.Threading.Tasks;

namespace AtCoder.Abc
{
    class QuestionC
    {
        public static void Main(string[] args)
        {
            var sw = new System.IO.StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
            Console.SetOut(sw);

            string[] str = Console.ReadLine().Split(' ');
            var x = Math.Abs(long.Parse(str[0]));  //開始場所、負の場合は
            var k = long.Parse(str[1]);  //移動可能回数
            var d = long.Parse(str[2]);  //1回の移動量
            var result = 0L;

            /*---------
             * 方針
             * →X＞=K＊D　の場合、答えはX-K*D
             * →X＜K×Dの場合、答えは、XをDで割ったあまり。　XをDで割った答えが、移動回数。
             * →割り終わったタイミングで、残り移動回数を見る。（k-x/d)が残り移動回数。
             * 上記、残り移動回数が偶数の場合、答えは、XをDで割ったあまり（の絶対値）、奇数の場合、D-X％D　の絶対値が、答えとなる。
             * 
             ----------*/

            if (x/d >= k)
            {
                //移動回数が小さい場合
                result = x - k * d;
            }
            else
            {
                if ((k - x / d) % 2 == 0)
                {
                    result = x % d;
                }
                else
                {
                    result = d - x % d;
                }
            }

            Console.WriteLine(result);

            Console.Out.Flush();
        }
    }
}