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# (Mono-mcs 6.8.0.105) (judge verdict: Time Limit Exceeded)

using System;
using System.Linq;

namespace _175.C
{
    internal class Program
    {
        private static void Main(string[] args)
        {
            var input = Console.ReadLine().Split().Select(long.Parse).ToList();
            var x = input[0];
            var singOfX = x > 0;
            var k = input[1];
            var d = input[2];

            x = CalcMin(x, singOfX, k, d);

            Console.WriteLine(Math.Abs(x).ToString());
        }

        private static long CalcMin(long x, bool singOfX, long k, long d)
        {
            for (var i = 0; i < k; i++)
            {
                if (x == 0)
                {
                    return (k - i) % 2 == 1 ? d : 0;
                }
                if (x > 0 != singOfX)
                {
                    return (k - i) % 2 == 0 ? Math.Abs(x) : x > 0 ? Math.Abs(x - d) : Math.Abs(x + d);
                }
                x = x >= 0 ? x - d : x + d;
            }

            return x;
        }
    }
}