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;

namespace AtCoderBeginnerContest175
{
	class Program
	{
		static void Main(string[] args)
		{
			var inputs = Console.ReadLine().Split().Select(x => long.Parse(x)).ToList();

			var current = inputs[0];
			var n = inputs[1];
			var d = inputs[2];

			// 0をまたぐ移動になるまでの数
			var number = Math.Abs(current) / d;
			if (number >= n)
			{
				// 0に到達しない場合
				if (current >= 0)
				{
					// 正なら単純に引く
					Console.WriteLine(current - n * d);
				}
				else
				{
					Console.WriteLine(Math.Abs(current + n * d));
				}
			}
			else
			{
				if (current >= 0)
				{
					// 0までの移動した場合の位置と残り回数を計算
					current -= number * d;
					n -= number;
					if (n % 2 == 0)
					{
						Console.WriteLine(current);
					}
					else
					{
						Console.WriteLine(Math.Abs(current - d));
					}
				}
				else
				{
					current += number * d;
					n -= number;
					if (n % 2 == 0)
					{
						Console.WriteLine(Math.Abs(current));
					}
					else
					{
						Console.WriteLine(Math.Abs(current + d));
					}
				}
			}
		}
	}
}