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.Linq;

class cs
{
    static void Main()
    {
        var l = Console.ReadLine().Split(' ').Select(x => long.Parse(x)).ToArray();

        long X = l[0]; 
        var K = l[1]; 
        var D = l[2]; 

        long ans = 0; 

        var moveTimesToRoundTrip = Math.Abs(X) / D;

        if (moveTimesToRoundTrip >= K)
        {
            // 往復移動をしない場合
            // 現在地から移動回数*移動距離を足し引きして求める
            if (X >= 0)
            {
                ans = X - K * D;
            }
            else
            {
                ans = X + K * D;
            }
        }
        else
        {
            // 往復移動をする場合

            // distanceBeforeRoundTrip: 往復移動する前の距離
            var distanceBeforeRoundTrip = X % D;

            // roundTripTimes: 往復回数
            // 原点近くにたどり着くまでにmoveTimesToRoundTripかかる
            // 残りの回数roundTripTimesは原点をまたいで-D, +Dを繰り返す
            var roundTripTimes = K - moveTimesToRoundTrip;

            if (roundTripTimes % 2 == 0)
            {
               
                ans = distanceBeforeRoundTrip;
            }
            else
            {
                
                if (distanceBeforeRoundTrip > 0)
                {
                    ans = distanceBeforeRoundTrip - D;
                }
                else
                {
                    ans = distanceBeforeRoundTrip + D;
                }
            }
        }

        Console.WriteLine(Math.Abs(ans));

    }
}