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: Time Limit Exceeded)

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

namespace procon
{
    class Program
    {
        static void Main()
        {
            long[] input = Console.ReadLine().Split().Select(Int64.Parse).ToArray();
            long stock1 = int.MaxValue;
            long stock2 = int.MaxValue;
            long stock3 = int.MaxValue;

            for(int i=0; i< input[1]; i++)
            {
                if (i == 0)
                {
                    stock1 = Math.Abs(input[0] + input[2]);
                    stock2 = Math.Abs(input[0] - input[2]);
                    stock3 = stock1 < stock2 ? stock1 : stock2;

                    stock1 = int.MaxValue;
                    stock2 = int.MaxValue;
                }
                else
                {
                    stock1 = Math.Abs(stock3 + input[2]);
                    stock2 = Math.Abs(stock3 - input[2]);

                    if (stock3 > stock1 || stock3 > stock2)
                    {
                        stock3 = stock1 < stock2 ? stock1 : stock2;
                    }
                }

                stock1 = int.MaxValue;
                stock2 = int.MaxValue;
            }

            Console.WriteLine(stock3);
        }
    }
}