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 static System.Console;
using static System.Math;
using System.Numerics;
using System.Collections.Generic;
using System.Linq;


namespace AtCoder
{
    public class Program
    {
        public static void Main(string[] args)
        {
            var s = myRead.readLongArray();
            long a = Abs(s[0]) / s[2];
            long b = Abs(s[0]) % s[2];
            long ans = 0;
            if (a < s[1])
            {
                long n = s[1] - a;
                int hugo = s[0] > 0 ? 1 : -1;
                ans = hugo * (n % 2 == 0 ? b : -(b - s[2]));
            }
            else
            {
                ans = s[0] > 0 ? s[0] - s[1] * s[2] : s[0] + s[1] * s[2];
            }
            WriteLine(ans);
        }
    }
    public static class myRead
    {
        public static int readInt() { return int.Parse(ReadLine()); }
        public static long readLong() { return long.Parse(ReadLine()); }
        public static string reatStr() { return ReadLine(); }
        public static int[] readIntArray() { return ReadLine().Split(' ').Select(int.Parse).ToArray(); }
        public static long[] readLongArray() { return ReadLine().Split(' ').Select(long.Parse).ToArray(); }
        public static string[] readStrArray() { return ReadLine().Split(' '); }
    }


    public static class MyMath
    {
        public static long Factorical(long n)
        { return n <= 1 ? 1L : n * Factorical(n - 1); }
        public static long Permutation(long n, long m)
        { return m == 0 ? 1L : (m == n) ? Permutation(n, m - 1) : n * Permutation(n - 1, m - 1); }
        public static long Combination(long n, long m)
        { return n - m > m ? Permutation(n, m) / Factorical(m) : Permutation(n, n - m) / Factorical(n - m); }
        public static long Gcd(long n, long m)
        { return n % m == 0 ? m : Gcd(m, n % m); }
        public static long Lcm(long n, long m)
        { return n * m / Gcd(n, m); }
        public static long Pow(long n, long m)
        { return m == 0 ? 1L : m == 1 ? n : n * Pow(n, m - 1); }
    }


}