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

namespace ABC175
{
    class Program
    {
        static void Main(string[] args)
        {
            var XKD = Console.ReadLine().Split().Select(long.Parse).ToArray();
            var X = XKD[0]; var K = XKD[1]; var D = XKD[2];
            // var A = Console.ReadLine().Split().Select(long.Parse).OrderBy(x => x).ToArray();
            // var CA = Enumerable.Repeat(0, (int)N).Select(_ => Console.ReadLine().Split().Select(long.Parse).ToArray()).ToArray();
            //var N = long.Parse(Console.ReadLine());
            //var L = Console.ReadLine().Split().Select(long.Parse).OrderBy(x => x).ToArray();

            var count = X / D; // 移動回数
            var dist = X % D; // 0までの距離
            var rest = K - count; // 残りの試行回数

            if (X == 0)
            {
                if (K % 2 == 0) Console.WriteLine(0);
                else Console.WriteLine(D);
                return;
            }

            if (rest <= 0 && 0 < X) { Console.WriteLine(Math.Abs(X - (K * D))); return; }
            if (rest <= 0 && X < 0) { Console.WriteLine(Math.Abs(X + (K * D))); return; }

            if (rest % 2 == 0) { Console.WriteLine(Math.Abs(dist)); return; }

            if (dist <= 0)
            {
                Console.WriteLine(Math.Abs(dist + D));
            }
            else
            {
                Console.WriteLine(Math.Abs(dist - D));
            }
        }
    }
}