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++ (GCC 9.2.1) (judge verdict: Wrong Answer)

#include <bits/stdc++.h>
using namespace std;

static const auto fast_io = [] {
 ios_base::sync_with_stdio(false); 
 cin.tie(nullptr); cout.tie(nullptr); 
 return nullptr;
}();

mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());

int rnd() {
 return uniform_int_distribution<int> (1, (int) 1e9) (rng);
}

template<class A> 
A rnd(A x, A y) {
 return uniform_int_distribution<A> (x, y) (rng);
}

string to_string(string s) {
 return '"' + s + '"';
}

string to_string(const char* ch) {
 return to_string((string)ch);
}

string to_string(char ch) {
 return (string)"'" + ch + (string)"'";
}

string to_string(bool b) {
 return (b ? "true" : "false");
}

string to_string(vector<bool> v) {
 bool first = true;
 string res = "{";
 for (int i = 0; i < static_cast<int>(v.size()); i++) {
  if (!first) {
   res += ", ";
  }
  first = false;
  res += to_string(v[i]);
 }
 res += "}";
 return res;
}
 
template <size_t N>
string to_string(bitset<N> v) {
 string res = "";
 for (size_t i = 0; i < N; i++) {
  res += static_cast<char>('0' + v[i]);
 }
 return res;
}

template<class A, class B>
string to_string(pair<A, B> p) {
 return "(" + to_string(p.first) + ", " + to_string(p.second) + ")";
}

template<class A>
string to_string(A a) {
 string res = "{";
 bool first = true;
 for(const auto& x: a) {
  if(first == false) res += ", ";
  first = false;
  res += to_string(x);
 }
 res += "}";
 return res;
}

template<class A, class B, class C>
string to_string(priority_queue<A, B, C> a) {
 vector<A> res;
 while(a.empty() == false) {
  res.push_back(a.top());
  a.pop();
 }
 reverse(res.begin(), res.end());
 return to_string(res);
}

template<class A>
string to_string(priority_queue<A> a) {
 vector<A> res;
 while(a.empty() == false) {
  res.push_back(a.top());
  a.pop();
 }
 reverse(res.begin(), res.end());
 return to_string(res);
}

template<class A>
string to_string(stack<A> a) {
 vector<A> res;
 while(a.empty() == false) {
  res.push_back(a.top());
  a.pop();
 }
 return to_string(res);
}

template<class A>
string to_string(queue<A> a) {
 vector<A> res;
 while(a.empty() == false) {
  res.push_back(a.front());
  a.pop();
 }
 return to_string(res);
}

vector<string> __vector_tuple;
template<int index, class... A>
struct print_tuple {
 auto operator() (tuple<A...> a) {
  __vector_tuple.push_back(to_string(get<index>(a)));
  print_tuple<index-1, A...>{}(a);
 }
};

template<class... A>
struct print_tuple<0, A...> {
 auto operator() (tuple<A...> a) {
  __vector_tuple.push_back(to_string(get<0>(a)));
 }
};

template<class... T>
string to_string(tuple<T...> a) {
 const int ttsz = tuple_size<decltype(a)>::value;
 print_tuple<ttsz-1, T...>{}(a);
 string __ss = to_string(__vector_tuple);
 __vector_tuple.clear();
 return __ss;
}

void debug() {cerr << "]\n";}

template<class H, class... T>
void debug(H head, T... tail) {
 cerr << to_string(head) << " ";
 debug(tail...);
}

#ifdef LOCAL
 #define debug(...) cerr << "[" << #__VA_ARGS__ << " ] = ["; debug(__VA_ARGS__);
#else 
 #define debug(...) 
#endif

typedef long long int ll;

int main()
{
 ll x, k, d;
 cin >> x >> k >> d;
 ll cnt = x / d;
 if(cnt >= k) {
  x -= k * d;
  cout << x << '\n';
  return 0;
 }
 k -= cnt;
 x %= d;
 if(d - x < x) x = d - x, cnt--;
 if(cnt % 2) x = d-x;
 cout << x << '\n';
 return 0;
}