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: Time Limit Exceeded)

using System;
using System.Linq;

namespace C
{
    class Program
    {
        static void Main(string[] args)
        {
            long[] In = Console.ReadLine().Split(' ').Select(x => long.Parse(x)).ToArray();
            long x = In[0];
            long k = In[1];
            long d = In[2];
            long min = 1001001001001001;
            if ((int)Math.Sqrt(x / d) >= 1000000)
            {
                if (x >= 0)
                {
                    x -= d * k;
                    if (x >= 0) min = x;
                    else
                    {
                        if (k % 2 == 1) { x -= d; k++; }
                        for (int i = 0; i <= k / 2; i+=1000)
                        {
                            long v = x + 2 * d * i;
                            if ((long)Math.Abs(min) > (long)Math.Abs(v)) min = v;
                            if (v > 0) break;
                        }
                    }
                }
                else
                {
                    x += d * k;
                    if (x < 0) min = x;
                    else
                    {
                        if (k % 2 == 1) { x += d; k++; }
                        for (int i = 0; i <= k / 2; i+=1000)
                        {
                            long v = x - 2 * d * i;
                            if ((long)Math.Abs(min) > (long)Math.Abs(v)) min = v;
                            if (v < 0) break;
                        }
                    }
                }


            }
            else
            {
                if (x >= 0)
                {
                    if (k % 2 == 1) { x += d; k++; }
                    for (int i = 0; i <= k / 2; i++)
                    {
                        long v = x - 2 * d * i;
                        if ((long)Math.Abs(min) > (long)Math.Abs(v)) min = v;
                        if (v < 0) break;
                    }
                }
                else
                {
                    if (k % 2 == 1) { x -= d; k++; }
                    for (int i = 0; i <= k / 2; i++)
                    {
                        long v = x + 2 * d * i;
                        if ((long)Math.Abs(min) > (long)Math.Abs(v)) min = v;
                        if (v > 0) break;
                    }
                }
            }
            Console.WriteLine((long)Math.Abs(min));
        }
    }
}

//namespace C
//{
//    class Program
//    {
//        static void Main(string[] args)
//        {
//            long[] In = Console.ReadLine().Split(' ').Select(x => long.Parse(x)).ToArray();
//            long x = In[0];
//            long k = In[1];
//            long d = In[2];
//            long min = 1001001001001001;
//            long back = x;
//            if ((int)Math.Sqrt(x / d) >= 100000)
//            {
//                if (x >= 0)
//                {
//                    x -= d * k;
//                    if (x >= 0) min = x;
//                    else
//                    {
//                        if((long)Math.Abs(back) >= (long)Math.Abs(x))
//                        {
//                            if (k % 2 == 1) { x += d; k++; }
//                            for (int i = 0; i <= k / 2; i++)
//                            {
//                                long v = x - 2 * d * i;
//                                if ((long)Math.Abs(min) > (long)Math.Abs(v)) min = v;
//                                if (v < 0) break;
//                            }
//                        }
//                        else
//                        {
//                            if (k % 2 == 1) { x -= d; k++; }
//                            for (int i = 0; i <= k / 2; i++)
//                            {
//                                long v = x + 2 * d * i;
//                                if ((long)Math.Abs(min) > (long)Math.Abs(v)) min = v;
//                                if (v > 0) break;
//                            }
//                        }
//                    }
//                }
//                else
//                {
//                    x += d * k;
//                    if (x < 0) min = x;
//                    else
//                    {
//                        if ((long)Math.Abs(back) >= (long)Math.Abs(x))
//                        {
//                            if (k % 2 == 1) { x -= d; k++; }
//                            for (int i = 0; i <= k / 2; i++)
//                            {
//                                long v = x + 2 * d * i;
//                                if ((long)Math.Abs(min) > (long)Math.Abs(v)) min = v;
//                                if (v > 0) break;
//                            }
//                        }
//                        else
//                        {
//                            if (k % 2 == 1) { x += d; k++; }
//                            for (int i = 0; i <= k / 2; i++)
//                            {
//                                long v = x - 2 * d * i;
//                                if ((long)Math.Abs(min) > (long)Math.Abs(v)) min = v;
//                                if (v < 0) break;
//                            }
//                        }
//                    }
//                }


//            }
//            else
//            {
//                if (x >= 0)
//                {
//                    if (k % 2 == 1) { x += d; k++; }
//                    for (int i = 0; i <= k / 2; i++)
//                    {
//                        long v = x - 2 * d * i;
//                        if ((long)Math.Abs(min) > (long)Math.Abs(v)) min = v;
//                        if (v < 0) break;
//                    }
//                }
//                else
//                {
//                    if (k % 2 == 1) { x -= d; k++; }
//                    for (int i = 0; i <= k / 2; i++)
//                    {
//                        long v = x + 2 * d * i;
//                        if ((long)Math.Abs(min) > (long)Math.Abs(v)) min = v;
//                        if (v > 0) break;
//                    }
//                }
//            }
//            Console.WriteLine((long)Math.Abs(min));
//        }
//    }
//}

//TLE
//namespace C
//{
//    class Program
//    {
//        static void Main(string[] args)
//        {
//            long[] In = Console.ReadLine().Split(' ').Select(x => long.Parse(x)).ToArray();
//            long x = In[0];
//            long k = In[1];
//            long d = In[2];
//            long min = 1001001001;
//            for(int i=0; i <= k; i++)
//            {
//                long v = 2 * d *i+ (x - d * k);
//                if ((long)Math.Abs(min) > (long)Math.Abs(v)) min = v;
//            }
//            Console.WriteLine((long)Math.Abs(min));
//        }
//    }
//}


//stack over
//namespace C
//{
//    class Program
//    {
//        static void Main(string[] args)
//        {
//            long[] In = Console.ReadLine().Split(' ').Select(x => long.Parse(x)).ToArray();
//            long x = In[0];
//            k = In[1];
//            d = In[2];
//            DFS(x, 0);
//            Console.WriteLine((long)Math.Abs(min));
//        }
//        static public long min = 1001001001;
//        static public long k,d;
//        static public void DFS(long v, int cnt)
//        {
//            if (cnt == k)
//            {
//                if ((long)Math.Abs(min) > (long)Math.Abs(v)) min = v;
//                return;
//            }
//            DFS(v + d,cnt+1);
//            DFS(v - d,cnt+1);
//        }
//    }
//}