Language: C++

#include <bits/stdc++.h>
using namespace std;
using lint = long long int;
using pint = pair<int, int>;
using plint = pair<lint, lint>;
struct fast_ios { fast_ios(){ cin.tie(0); ios::sync_with_stdio(false); cout << fixed << setprecision(20); }; } fast_ios_;
#define ALL(x) (x).begin(), (x).end()
#define SZ(x) ((lint)(x).size())
#define POW2(n) (1LL << (n))
#define FOR(i, begin, end) for(int i=(begin),i##_end_=(end);i<i##_end_;i++)
#define IFOR(i, begin, end) for(int i=(end)-1,i##_begin_=(begin);i>=i##_begin_;i--)
#define REP(i, n) FOR(i,0,n)
#define IREP(i, n) IFOR(i,0,n)
template<typename T> istream &operator>>(istream &is, vector<T> &vec){ for (auto &v : vec) is >> v; return is; }
template<typename T> ostream &operator<<(ostream &os, const vector<T> &vec){ os << "["; for (auto v : vec) os << v << ","; os << "]"; return os; }
template<typename T> ostream &operator<<(ostream &os, const deque<T> &vec){ os << "deq["; for (auto v : vec) os << v << ","; os << "]"; return os; }
template<typename T> ostream &operator<<(ostream &os, const set<T> &vec){ os << "{"; for (auto v : vec) os << v << ","; os << "}"; return os; }
template<typename T> ostream &operator<<(ostream &os, const unordered_set<T> &vec){ os << "{"; for (auto v : vec) os << v << ","; os << "}"; return os; }
template<typename T> ostream &operator<<(ostream &os, const multiset<T> &vec){ os << "{"; for (auto v : vec) os << v << ","; os << "}"; return os; }
template<typename T> ostream &operator<<(ostream &os, const unordered_multiset<T> &vec){ os << "{"; for (auto v : vec) os << v << ","; os << "}"; return os; }
template<typename T1, typename T2> ostream &operator<<(ostream &os, const pair<T1, T2> &pa){ os << "(" << pa.first << "," << pa.second << ")"; return os; }
template<typename TK, typename TV> ostream &operator<<(ostream &os, const map<TK, TV> &mp){ os << "{"; for (auto v : mp) os << v.first << "=>" << v.second << ","; os << "}"; return os; }
template<typename TK, typename TV> ostream &operator<<(ostream &os, const unordered_map<TK, TV> &mp){ os << "{"; for (auto v : mp) os << v.first << "=>" << v.second << ","; os << "}"; return os; }
template<typename T> void ndarray(vector<T> &vec, int len) { vec.resize(len); }
template<typename T, typename... Args> void ndarray(vector<T> &vec, int len, Args... args) { vec.resize(len); for (auto &v : vec) ndarray(v, args...); }
template<typename T> bool mmax(T &m, const T q) { if (m < q) {m = q; return true;} else return false; }
template<typename T> bool mmin(T &m, const T q) { if (m > q) {m = q; return true;} else return false; }
template<typename T1, typename T2> pair<T1, T2> operator+(const pair<T1, T2> &l, const pair<T1, T2> &r) { return make_pair(l.first + r.first, l.second + r.second); }
template<typename T1, typename T2> pair<T1, T2> operator-(const pair<T1, T2> &l, const pair<T1, T2> &r) { return make_pair(l.first - r.first, l.second - r.second); }
#define dbg(x) cerr << #x << " = " << (x) << " (L" << __LINE__ << ") " << __FILE__ << endl;

#include <boost/multiprecision/cpp_int.hpp>
using mpint = boost::multiprecision::cpp_int;

mpint tos(mpint n, mpint X, mpint D)
{
    return X * n + D * n * (n - 1) / 2;
}

int main()
{
    int N;
    mpint X, D;
    cin >> N >> X >> D;
    if (D == 0) {
        if (X == 0) puts("1");
        else cout << N + 1 << endl;
        return 0;
    }

    int g;
    if (X != 0) g = __gcd(abs(int(X)), abs(int(D)));
    else g = abs(int(D));
    X /= g, D /= g;

    int AD = abs(int(D));

    using P = pair<mpint, mpint>;
    vector<vector<P>> Q(min(N + 1, AD));
    REP(i, N + 1) {
        mpint lo("100000000000000000000000"), hi("-100000000000000000000000");
        vector<mpint> c;
        c.emplace_back(tos(i, X, D));
        c.emplace_back(tos(i, X + D * (N - 1), -D));
        for (auto x : c) mmin(lo, x), mmax(hi, x);
        Q[i % AD].emplace_back(lo, hi);
    }
    mpint ret = 0;
    for (auto &vec : Q) if (vec.size()) {
        sort(ALL(vec));
        mpint h = vec[0].first - AD;
        for (P x : vec) {
            mmax(h, mpint(x.first - AD));
            ret += max((x.second - h) / AD, mpint(0));
            mmax(h, x.second);
        }
    }
    cout << ret << endl;
}


Compiler output:
a.cc:32:10: fatal error: boost/multiprecision/cpp_int.hpp: No such file or directory
   32 | #include <boost/multiprecision/cpp_int.hpp>
      |          ^~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
compilation terminated.