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.ComponentModel;
using System.Collections.Generic;

namespace AtCoder {
    public class TestCode {
        static void Main(string[] args) {
            var (X,K,D) = ReadValue<long,long,long>();
            long ans = 0;
            var tmp = Math.Abs(X) / D;
            if (tmp < K) ans = Math.Abs(X) - (K * D);
            else {
                var t = Math.Abs(X) - (tmp * D);
                if((K - tmp) % 2 == 0) {
                    ans = t;
                } else {
                    ans = t - D;
                }
            }
            Console.Write(ans);
        }

        static T1 ReadValue<T1>() {
            var t1 = TypeDescriptor.GetConverter(typeof(T1));
            return (T1)t1.ConvertFromString(Console.ReadLine());
        }

        static (T1, T2) ReadValue<T1, T2>() {
            var rl = Console.ReadLine().Trim().Split().ToArray();
            var t1 = TypeDescriptor.GetConverter(typeof(T1));
            var t2 = TypeDescriptor.GetConverter(typeof(T2));
            return ((T1)t1.ConvertFromString(rl[0]),
                    (T2)t2.ConvertFromString(rl[1]));
        }

        static (T1, T2, T3) ReadValue<T1, T2, T3>() {
            var rl = Console.ReadLine().Trim().Split().ToArray();
            var t1 = TypeDescriptor.GetConverter(typeof(T1));
            var t2 = TypeDescriptor.GetConverter(typeof(T2));
            var t3 = TypeDescriptor.GetConverter(typeof(T3));
            return ((T1)t1.ConvertFromString(rl[0]),
                    (T2)t2.ConvertFromString(rl[1]),
                    (T3)t3.ConvertFromString(rl[2]));
        }

        static (T1, T2, T3, T4) ReadValue<T1, T2, T3, T4>() {
            var rl = Console.ReadLine().Trim().Split().ToArray();
            var t1 = TypeDescriptor.GetConverter(typeof(T1));
            var t2 = TypeDescriptor.GetConverter(typeof(T2));
            var t3 = TypeDescriptor.GetConverter(typeof(T3));
            var t4 = TypeDescriptor.GetConverter(typeof(T4));
            return ((T1)t1.ConvertFromString(rl[0]),
                    (T2)t2.ConvertFromString(rl[1]),
                    (T3)t3.ConvertFromString(rl[2]),
                    (T4)t4.ConvertFromString(rl[3]));
        }

        static (T1, T2, T3, T4, T5) ReadValue<T1, T2, T3, T4, T5>() {
            var rl = Console.ReadLine().Trim().Split().ToArray();
            var t1 = TypeDescriptor.GetConverter(typeof(T1));
            var t2 = TypeDescriptor.GetConverter(typeof(T2));
            var t3 = TypeDescriptor.GetConverter(typeof(T3));
            var t4 = TypeDescriptor.GetConverter(typeof(T4));
            var t5 = TypeDescriptor.GetConverter(typeof(T5));
            return ((T1)t1.ConvertFromString(rl[0]),
                    (T2)t2.ConvertFromString(rl[1]),
                    (T3)t3.ConvertFromString(rl[2]),
                    (T4)t4.ConvertFromString(rl[3]),
                    (T5)t5.ConvertFromString(rl[4]));
        }

        static string[] stringArray => Console.ReadLine().Split().ToArray();
        static int[] intArray => Console.ReadLine().Trim().Split().Select(int.Parse).ToArray();
        static long[] longArray => Console.ReadLine().Trim().Split().Select(long.Parse).ToArray();
        static double[] doubleArray => Console.ReadLine().Trim().Split().Select(double.Parse).ToArray();
        static decimal[] decimalArray => Console.ReadLine().Trim().Split().Select(decimal.Parse).ToArray();
    }
}