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;
using ll = long long;
using P = pair<int, int>;
using vint = vector<int>;
using vvint = vector<vint>;
using vll = vector<ll>;
using vvll = vector<vll>;
using vchar = vector<char>;
using vvchar = vector<vchar>;
using vp = vector<P>;
using vpp = vector<pair<P, P>>;
using vvp = vector<vp>;

#define rep(i, n) for (int i = 0; i < n; ++i)
#pragma region Debug
istream &operator>>(istream &is, P &a)
{
    return is >> a.first >> a.second;
}
ostream &operator<<(ostream &os, const P &a) { return os << "(" << a.first << "," << a.second << ")"; }

template <typename T>

void view(const std::vector<T> &v)
{
#ifndef ONLINE_JUDGE
    for (const auto &e : v)
    {
        std::cout << e << " ";
    }
    std::cout << std::endl;
#endif
}
template <typename T>
void view(const std::vector<std::vector<T>> &vv)
{
    for (const auto &v : vv)
    {
        view(v);
    }
}
#pragma endregion

int main()
{
    ll x, k, d;
    cin >> x >> k >> d;

    ll step = min(k, x / d);
    k -= step;
    ll now = x - step * d;
    ll ans = INT64_MAX;
    if (k % 2)
    {
        ans = min(abs(now + d), abs(now - d));
    }
    else
    {
        ans = now;
    }

    cout << ans << endl;

    return 0;
}