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.Collections;
using System.Collections.Generic;
//using System.Collections.Immutable;
using System.Diagnostics;
using System.IO;
using System.Linq;
using System.Numerics;
using System.Runtime.InteropServices;
using System.Text;
using System.Text.RegularExpressions;
using System.Threading.Tasks;
using static System.Math;
using static Math2;
using static Output;
using static Utils;

public class CP
{
    Input sc;
    public void Solve()
    {
        sc = new Input();
        bool multicases = false;
        var t = multicases ? sc.Int : 1;
        // var sw = new Stopwatch();
        // sw.Start();
        while (t-- > 0)
        {
            c2();
        }
        // sw.Stop();
        //Put(sw.ElapsedMilliseconds + "ms");
    }
    public void c1()
    {
        int n = sc.Int;
        var l = sc.Longarr;
        int ans = 0;
        for (int i = 0; i < n; ++i)
        {
            for (int j = i + 1; j < n; ++j)
            {
                for (int k = j + 1; k < n; ++k)
                {
                    if (l[i] != l[j] && l[j] != l[k] && l[k] != l[i])
                    {
                        if ((l[i] + l[j] > l[k]) && (l[i] + l[k] > l[j]) && (l[j] + l[j] > l[i])) ++ans;
                    }
                }
            }
        }
        Put(ans);
    }
    public void c2()
    {
        long x = sc.Long;
        long k = sc.Long;
        long d = sc.Long;
        var y = Abs(x) / d;
        if (y >= k)
        {
            if (x > 0)
            {
                Put(x - d * k);
            }
            else
            {
                Put(x + d * k);
            }
        }
        else
        {
            if (x > 0)
            {
                var nx = x - d * y;
                var nk = k - y;
                if (nk % 2 == 0)
                {
                    Put(nx);
                }
                else Put(Abs(nx - d));
            }
            else
            {
                var nx = x + d * y;
                var nk = k - y;
                if (nk % 2 == 0)
                {
                    Put(Abs(nx));
                }
                else
                {
                    Put(x + d);
                }
            }
        }
    }



}

public class PriorityQueue<T>
{
    List<T> _item;
    public int Count { get { return _item.Count; } }
    bool _isascend { get; set; }
    public T Peek { get { return _item[0]; } }
    Comparison<T> Comp;
    public PriorityQueue(bool IsAscend = true, IEnumerable<T> list = null) : this(Comparer<T>.Default.Compare, IsAscend, list) { }
    public PriorityQueue(Comparison<T> cmp, bool IsAscend = true, IEnumerable<T> list = null)
    {
        _item = new List<T>();
        _isascend = IsAscend;
        this.Comp = cmp;
        if (list != null)
        {
            _item.AddRange(list);
            Build();
        }
    }

    private int Compare(int i, int j) => (_isascend ? -1 : 1) * Comp(_item[i], _item[j]);
    private void Swap(int i, int j) { var t = _item[i]; _item[i] = _item[j]; _item[j] = t; }
    private int Parent(int i) => (i - 1) >> 1;
    private int Left(int i) => (i << 1) + 1;
    public T Enqueue(T val)
    {
        int i = _item.Count;
        _item.Add(val);
        while (i > 0)
        {
            int p = Parent(i);
            if (Compare(i, p) > 0)
                Swap(i, p);
            i = p;
        }
        return val;
    }
    private void Heapify(int index)
    {
        for (int i = index, j;
            (j = Left(i)) < _item.Count; i = j)
        {
            if (j != _item.Count - 1 && Compare(j, j + 1) < 0) j++;
            if (Compare(i, j) < 0)
                Swap(i, j);
        }
    }
    public T Dequeue()
    {
        T val = _item[0];
        _item[0] = _item[_item.Count - 1];
        _item.RemoveAt(_item.Count - 1);
        Heapify(0);
        return val;
    }
    private void Build()
    {
        for (var i = (_item.Count >> 1) - 1; i >= 0; i--)
            Heapify(i);
    }
    public bool Any() => Count > 0;
}
public class BinarySearch
{
    public static int Lower_Bound<T>(IList<T> Array, T Target)
    {
        return Lower_Bound<T>(Array, Target, Comparer<T>.Default.Compare);
    }
    public static int Lower_Bound<T>(IList<T> Array, T Target, Comparison<T> Comp)
    {
        var cmp = Comparer<T>.Create(Comp);
        var l = -1; //always ng
        var r = Array.Count(); //always ok
        while (r - l > 1)
        {
            var mid = l + (r - l) / 2;
            var res = cmp.Compare(Array[mid], Target);
            if (res >= 0) r = mid;
            else l = mid;
        }
        return r;
    }
    public static int Upper_Bound<T>(IList<T> Array, T Target)
    {
        return Upper_Bound<T>(Array, Target, Comparer<T>.Default.Compare);
    }
    public static int Upper_Bound<T>(IList<T> Array, T Target, Comparison<T> Comp)
    {
        var cmp = Comparer<T>.Create(Comp);
        var l = -1;
        var r = Array.Count;
        while (r - l > 1)
        {
            var mid = l + (r - l) / 2;
            var res = cmp.Compare(Array[mid], Target);
            if (res > 0) r = mid;
            else l = mid;
        }
        return r;
    }
    public static bool Contains<T>(IList<T> Arr, T Target)
    {
        return Contains<T>(Arr, Target, Comparer<T>.Default.Compare);
    }
    public static bool Contains<T>(IList<T> Arr, T Target, Comparison<T> Comp)
    {
        return (Upper_Bound(Arr, Target, Comp) - Lower_Bound(Arr, Target, Comp) > 0);
    }
}
public static class Math2
{
    public const int INF = 1 << 29;
    public const long INFL = 1L << 62;
    public const long MOD = 1000000007;
    public const long MOD2 = 998244353;

    public static long Power(long a, long b, long MOD = 1000000007) //i^N
    {
        long res = 1;
        while (b > 0)
        {
            if ((b & 1) != 0) res = res * a % MOD;
            a = a * a % MOD;
            b >>= 1;
        }
        return (res + 2 * MOD) % MOD;
    }
    public static long Power2(long a, long b) //i^N
    {
        long res = 1;
        while (b > 0)
        {
            if ((b & 1) != 0) res = res * a;
            a = a * a;
            b >>= 1;
        }
        return res;
    }
    public static BigInteger Power2BI(BigInteger a, BigInteger b) //i^N
    {
        BigInteger res = 1;
        while (b > 0)
        {
            if ((b & 1) != 0) res = res * a;
            a = a * a;
            b >>= 1;
        }
        return res;
    }
    public static long GCD(long a, long b)
    {
        if (a == 0) return b;
        while (b > 0)
        {
            var r = a % b;
            a = b;
            b = r;
        }
        return a;
    }
    public static long LCM(long a, long b) => (b / GCD(a, b)) * a;
    public static long Comb(long n, long r, int MOD = 1000000007)
    {
        if (r > n - r) r = n - r;
        long Nume = 1;
        long Deno = 1;

        if (r > n - r) r = n - r;
        for (long i = 1; i <= r; ++i)
        {
            Deno = (Deno * i) % MOD;
            Nume = Nume * (n - i + 1) % MOD;
        }
        return (Nume * inv(Deno)) % MOD;
    }
    public static long Comb2(long n, long r)
    {
        long Nume = 1;
        long Deno = 1;

        if (r > n - r) r = n - r;
        for (long i = 1; i <= r; ++i)
        {
            Deno *= i;
            Nume *= n - i + 1;
        }
        return Nume / Deno;
    }
    public static long inv(long x, int MOD = 1000000007)
    {
        return Power(x, MOD - 2, MOD);
    }
}
public static class Utils
{
    public static T[] sort<T>(this T[] a)
    {
        Array.Sort(a);
        return a;
    }
    public static long popcnt(long n)
    {
        n = (n & 0x55555555) + (n >> 1 & 0x55555555);
        n = (n & 0x33333333) + (n >> 2 & 0x33333333);
        n = (n & 0x0f0f0f0f) + (n >> 4 & 0x0f0f0f0f);
        n = (n & 0x00ff00ff) + (n >> 8 & 0x00ff00ff);
        n = (n & 0x0000ffff) + (n >> 16 & 0x0000ffff);
        return n;
    }
    public static int popcnt(BigInteger a)
    {
        int cnt = 0;
        while (a > 0)
        {
            if ((a & 1) == 1) ++cnt;
            a >>= 1;
        }
        return cnt;
    }
    public static void Swap<T>(ref T A, ref T B)
    {
        T x = A;
        A = B;
        B = x;
    }
    public static int DigitSum(string N)
    {

        int ret = 0;
        for (int i = 0; i < N.Length; ++i) ret += N[i] - '0';
        return ret;
    }
    public static string ConvertBase(char[] Num, int from, int to)
    {
        if (new string(Num) == "0") return "0";
        char[] sample = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ".ToCharArray();
        BigInteger ten = 0;
        int power = 0;
        for (int i = Num.Length - 1; i >= 0; --i)
        {
            ten += (BigInteger)(Array.IndexOf(sample, Num[i])) * Power2BI(from, power);
            ++power;
        }
        if (to == 10)
        {
            return ten.ToString();
        }
        var ret = new List<char>();
        while (ten > 0)
        {
            ret.Add(sample[(int)ten % to]);
            ten /= to;
        }
        ret.Reverse();
        return new string(ret.ToArray());
    }
    public static bool NextPermutation<T>(IList<T> lis, Comparison<T> cmp)
    {
        int n = lis.Count;
        int i = n - 1;
        while (i - 1 >= 0)
        {
            if (cmp(lis[i - 1], lis[i]) < 0) break;
            --i;
        }
        if (i == 0) return false;
        int j = i;
        while (j + 1 < n)
        {
            if (cmp(lis[i - 1], lis[j + 1]) > 0) break;
            ++j;
        }
        var _q = lis[j];
        lis[j] = lis[i - 1];
        lis[i - 1] = _q;
        int k = i;
        int l = n - 1;
        while (k < l)
        {
            var _p = lis[k];
            lis[k] = lis[l];
            lis[l] = _p;

            ++k;
            --l;
        }
        return true;
    }
    public static bool NextPermutation<T>(IList<T> lis) => NextPermutation(lis, Comparer<T>.Default.Compare);
}
class Program
{
    static void Main(string[] args)
    {
        var CP = new CP();
        CP.Solve();
    }
}
public static class Output
{

    public static void Put(string a) => Console.WriteLine(a);
    public static void Put(params object[] i) => Put(string.Join(" ", i));
    public static void Put<T>(IEnumerable<T> a) => Put(string.Join(" ", a));
    public static void PutV<T>(IEnumerable<T> a) { foreach (var z in a) Put(z); }
    public static void YN(bool i)
    {
        if (i) Put("Yes");
        else Put("No");
    }
}
public class Input
{
    public static string Str => Console.ReadLine();
    public static bool IsTypeEqual<T, U>() => typeof(T).Equals(typeof(U));
    public static T ConvertType<T, U>(U a) => (T)Convert.ChangeType(a, typeof(T));
    public static T Cast<T>(string s)
    {
        if (IsTypeEqual<T, int>()) return ConvertType<T, int>(int.Parse(s));
        else if (IsTypeEqual<T, long>()) return ConvertType<T, long>(long.Parse(s));
        else if (IsTypeEqual<T, double>()) return ConvertType<T, double>(double.Parse(s));
        else if (IsTypeEqual<T, char>()) return ConvertType<T, char>(char.Parse(s));
        else if (IsTypeEqual<T, BigInteger>()) return ConvertType<T, BigInteger>(BigInteger.Parse(s));
        else if (IsTypeEqual<T, decimal>()) return ConvertType<T, decimal>(decimal.Parse(s));
        else return ConvertType<T, string>(s);
    }
    public static T[] Castarr<T>(string[] s)
    {

        var ret = new T[s.Length];
        int i = 0;
        if (IsTypeEqual<T, char>())
        {
            var list = new List<T>();
            foreach (var t in s)
            {
                foreach (var u in t)
                {
                    list.Add(ConvertType<T, char>(char.Parse(u.ToString())));
                }
            }
            return list.ToArray();
        }
        foreach (var t in s)
        {
            if (IsTypeEqual<T, int>()) ret[i++] = ConvertType<T, int>(int.Parse(t));
            else if (IsTypeEqual<T, long>()) ret[i++] = ConvertType<T, long>(long.Parse(t));
            else if (IsTypeEqual<T, double>()) ret[i++] = ConvertType<T, double>(double.Parse(t));
            else if (IsTypeEqual<T, BigInteger>()) ret[i++] = ConvertType<T, BigInteger>(BigInteger.Parse(t));
            else ret[i++] = ConvertType<T, string>(t);
        }
        return ret;
    }
    Queue<string> q = new Queue<string>();
    void next() { var ss = Str.Split(' '); foreach (var item in ss) q.Enqueue(item); }
    public T cin<T>() { if (!q.Any()) next(); return Cast<T>(q.Dequeue()); }
    public T[] cinarr<T>() { return Castarr<T>(Str.Split(' ')); }
    public T[] cinarr<T>(int n) { var ret = new T[n]; for (int i = 0; i < n; ++i) ret[i] = cin<T>(); return ret; }
    public int Int => cin<int>();
    public long Long => cin<long>();
    public double Double => cin<double>();
    public char Char => cin<char>();
    public string String => cin<string>();
    public BigInteger BI => cin<BigInteger>();
    public int[] Intarr => cinarr<int>();
    public long[] Longarr => cinarr<long>();
    public double[] Doublearr => cinarr<double>();
    public char[] Chararr => cinarr<char>();
    public string[] Stringarr => cinarr<string>();
    public BigInteger[] BIarr => cinarr<BigInteger>();
    public void cin<T>(out T t) { t = cin<T>(); }
    public void mul<T, U>(out T t, out U u) { t = cin<T>(); u = cin<U>(); }
    public void mul<T, U, V>(out T t, out U u, out V v) { t = cin<T>(); u = cin<U>(); v = cin<V>(); }
    public void mul<T, U, V, W>(out T t, out U u, out V v, out W w) { t = cin<T>(); u = cin<U>(); v = cin<V>(); w = cin<W>(); }
    public void mul<T, U, V, W, X>(out T t, out U u, out V v, out W w, out X x) { t = cin<T>(); u = cin<U>(); v = cin<V>(); w = cin<W>(); x = cin<X>(); }
    public void mul<T, U, V, W, X, Y>(out T t, out U u, out V v, out W w, out X x, out Y y) { t = cin<T>(); u = cin<U>(); v = cin<V>(); w = cin<W>(); x = cin<X>(); y = cin<Y>(); }
    public void mul<T, U, V, W, X, Y, Z>(out T t, out U u, out V v, out W w, out X x, out Y y, out Z z) { t = cin<T>(); u = cin<U>(); v = cin<V>(); w = cin<W>(); x = cin<X>(); y = cin<Y>(); z = cin<Z>(); }
}