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 System;
using System.Collections.Generic;
using System.Linq;
using System.Numerics;
using System.Runtime.InteropServices;
using System.Text;

namespace AtCoder.ABC
{
    class QuestionA
    {
        public static void Main(string[] args)
        {
            var xkd = Console.ReadLine().Split(" ").Select(x => long.Parse(x)).ToArray();
            var x = xkd[0];
            var k = xkd[1];
            var d = xkd[2];

            var max = Math.Abs(x);

            var a = new BigInteger(k);
            var b = new BigInteger(max);
            a *= d;

            if(a <= b) {
                Console.WriteLine(b - a);
                return;
			}

            if( k % 2 == 0) {
                if (max % d == 0) {
                    var s = max / d;

                    if (s % 2 == 0) {
                        max = 0;
                    } else {
                        max = d;
                    }
                } if (max < d) {
                    //現在地が最小
                } else {
                    var s = max / d;

                    if(s % 2 != 0) {
                        s--;
					}

                    max = Math.Min(max - (d * s), Math.Abs(max - (d * (s + 2))));
                }
			} else {
                if (max % d == 0) {
                    var s = max / d;

                    if (s % 2 == 0) {
                        max = d;
                    } else {
                        max = 0;
                    }
                }
                if (max < d) {
                    max = Math.Abs(max - d);
                } else {
                    var s = max / d;
                    if (s % 2 == 0) {
                        s--;
                    }

                    max = Math.Min(max - (d * s), Math.Abs(max - (d * (s + 2))));
                }
            }

            Console.WriteLine(max);
        }
    }
}