Problem p03016 (C++)

Buggy submission (status: Runtime Error):
// >>> TEMPLATES
#include <bits/stdc++.h>
using namespace std;
#define rep(i, n) for (int i = 0; i < int(n); i++)
#define rep1(i, n) for (int i = 1; i <= int(n); i++)
#define repR(i, n) for (int i = int(n) - 1; i >= 0; i--)
#define rep1R(i, n) for (int i = int(n); i >= 1; i--)
#define loop(i, a, B) for (int i = a; i B; i++)
#define loopR(i, a, B) for (int i = a; i B; i--)
#define all(x) (x).begin(), (x).end()
#define allR(x) (x).rbegin(), (x).rend()
#define eb emplace_back
#define mp make_pair
#define fst first
#define snd second
#ifdef LOCAL
#define dump(...)                                                              \
  cerr << "[" << __LINE__ << ":" << __FUNCTION__ << "] ",                      \
      dump_impl(#__VA_ARGS__, __VA_ARGS__)
#define say(x)                                                                 \
  cerr << "[" << __LINE__ << ":" << __FUNCTION__ << "] " << x << endl;
#define debug if (1)
void dump_impl(const char *) { cerr << endl; }
template <class T, class... U>
void dump_impl(const char *s, T const &x, U const &...y) {
  const char *o = "({[", *e = "]})";
  for (int i = 0; *s != '\0'; cerr << *s++) {
    if (count(o, o + 3, *s))
      i++;
    if (count(e, e + 3, *s))
      i--;
    if (!i && *s == ',')
      break;
  }
  cerr << " = " << x;
  if (*s == ',')
    cerr << ", ", s++;
  dump_impl(s, y...);
}
#else
#define dump(...)
#define say(x)
#define debug if (0)
#endif
using ll = long long;
using ld = long double;
#define int ll
#define double ld
template <class T> using pque_max = priority_queue<T>;
template <class T> using pque_min = priority_queue<T, vector<T>, greater<T>>;
template <class T, class = typename T::iterator,
          class = typename enable_if<!is_same<T, string>::value>::type>
ostream &operator<<(ostream &os, T const &v) {
  os << "{";
  for (auto const &x : v)
    os << " " << x;
  return os << " }";
}
template <class T> istream &operator>>(istream &is, vector<T> &v) {
  for (auto &x : v)
    is >> x;
  return is;
}
template <class T, class S>
ostream &operator<<(ostream &os, pair<T, S> const &p) {
  return os << "(" << p.first << ", " << p.second << ")";
}
template <class T, class S> istream &operator>>(istream &is, pair<T, S> &p) {
  return is >> p.first >> p.second;
}
template <size_t i, class T>
typename enable_if<i >= tuple_size<T>::value>::type output_tuple(ostream &,
                                                                 T const &) {}
template <size_t i = 0, class T>
    typename enable_if <
    i<tuple_size<T>::value>::type output_tuple(ostream &os, T const &t) {
  os << (i ? " " : "") << get<i>(t);
  output_tuple<i + 1, T>(os, t);
}
template <class... T> ostream &operator<<(ostream &os, tuple<T...> const &t) {
  return output_tuple(os, t), os;
}
struct IOSetup {
  IOSetup() {
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
    cout << fixed << setprecision(15);
  }
} iosetup;
template <class T, size_t d> struct vec_impl {
  using type = vector<typename vec_impl<T, d - 1>::type>;
  template <class... U> static type make_v(size_t n, U &&...x) {
    return type(n, vec_impl<T, d - 1>::make_v(forward<U>(x)...));
  }
};
template <class T> struct vec_impl<T, 0> {
  using type = T;
  static type make_v(T const &x = {}) { return x; }
};
template <class T, size_t d = 1> using vec = typename vec_impl<T, d>::type;
template <class T, size_t d = 1, class... Args> auto make_v(Args &&...args) {
  return vec_impl<T, d>::make_v(forward<Args>(args)...);
}
template <class T> void quit(T const &x) {
  cout << x << endl;
  exit(0);
}
template <class T> constexpr bool chmin(T &x, T const &y) {
  if (x > y) {
    x = y;
    return true;
  }
  return false;
}
template <class T> constexpr bool chmax(T &x, T const &y) {
  if (x < y) {
    x = y;
    return true;
  }
  return false;
}
template <class It> constexpr auto sumof(It b, It e) {
  return accumulate(b, e, typename iterator_traits<It>::value_type{});
}
template <class T> int sz(T const &x) { return x.size(); }
const ll INF = (1LL << 62) - 1; // ~ 4.6e18
// <<<
// >>> runtime modint
using ll = long long;
class runtime_modint {
  using M = runtime_modint;
  ll x;

public:
  static ll &mod() {
    static int mod = 0;
    return mod;
  }
  runtime_modint(ll x = 0) {
    assert(mod() > 0);
    this->x = ((x %= mod()) < 0 ? x + mod() : x);
  }
  ll val() const { return x; }
  bool operator==(M r) const { return x == r.x; }
  bool operator!=(M r) const { return x != r.x; }
  M operator+() const { return *this; }
  M operator-() const { return {mod() - x}; }
  M &operator+=(M r) {
    if ((x += r.x) >= mod())
      x -= mod();
    return *this;
  }
  M &operator-=(M r) {
    if ((x += mod() - r.x) >= mod())
      x -= mod();
    return *this;
  }
  M &operator*=(M r) {
    (x *= r.x) %= mod();
    return *this;
  }
  M operator+(M r) const { return M(*this) += r; }
  M operator-(M r) const { return M(*this) -= r; }
  M operator*(M r) const { return M(*this) *= r; }
  M &operator/=(M r) { return *this *= r.inv(); }
  M operator/(M r) const { return *this * r.inv(); }
  M pow(ll n) const {
    if (n < 0)
      return inv().pow(-n);
    M v = *this, r = 1;
    for (; n > 0; n >>= 1, v *= v)
      if (n & 1)
        r *= v;
    return r;
  }
  M inv() const {
    assert(x != 0);
    ll t = 1, v = x, q, r;
    while (v != 1) {
      q = mod() / v;
      r = mod() % v;
      if (r * 2 < v) {
        t *= -q;
        t %= mod();
        v = r;
      } else {
        t *= q + 1;
        t %= mod();
        v -= r;
      }
    }
    return t;
  }
  static int gen() { // assume mod():prime
    if (mod() == 2)
      return 1;
    vector<int> ps;
    int n = mod() - 1;
    for (int i = 2; i * i <= n; ++i) {
      if (n % i)
        continue;
      ps.push_back(i);
      do
        n /= i;
      while (n % i == 0);
    }
    if (n > 1)
      ps.push_back(n);
    n = mod() - 1;
    auto check = [&](M g) {
      for (int p : ps)
        if (g.pow(n / p) == 1)
          return false;
      return true;
    };
    for (int g = 2; g <= n; ++g)
      if (check(g))
        return g;
    return -1;
  }
};
ostream &operator<<(ostream &os, runtime_modint r) { return os << r.val(); }
istream &operator>>(istream &is, runtime_modint &r) {
  ll x;
  is >> x;
  r = x;
  return is;
}

using mint = runtime_modint;
// <<<
// >>> matrix
template <class T> struct Matrix {
  int n, m;
  vector<vector<T>> a;
  Matrix() {}
  Matrix(int n, int m) : n(n), m(m), a(n) {
    assert(n > 0 && m > 0);
    rep(i, n) a[i].resize(m);
  }
  vector<T> const &operator[](int i) const {
    assert(0 <= i && i < n);
    return a[i];
  }
  vector<T> &operator[](int i) {
    assert(0 <= i && i < n);
    return a[i];
  }
  Matrix &operator+=(Matrix const &x) {
    assert(n == x.n && m == x.m);
    rep(i, n) rep(j, m) a[i][j] += x[i][j];
    return *this;
  }
  Matrix &operator-=(Matrix const &x) {
    assert(n == x.n && m == x.m);
    rep(i, n) rep(j, m) a[i][j] -= x[i][j];
    return *this;
  }
  Matrix operator+(Matrix const &x) const { return Matrix(*this) += x; }
  Matrix operator-(Matrix const &x) const { return Matrix(*this) -= x; }
  Matrix operator*(Matrix const &x) const {
    assert(m == x.n);
    Matrix ret(n, x.m);
    rep(i, n) rep(j, m) rep(k, x.m) ret[i][k] += a[i][j] * x[j][k];
    return ret;
  }
  Matrix &operator*=(Matrix const &x) {
    auto res = (*this) * x;
    swap(a, res.a);
    return *this;
  }
  Matrix operator+() const { return *this; }
  Matrix operator-() const {
    Matrix x = *this;
    rep(i, n) rep(j, m) x[i][j] = -x[i][j];
    return x;
  }
  Matrix &operator*=(T const &c) {
    rep(i, n) rep(j, m) a[i][j] *= c;
    return *this;
  }
  Matrix operator*(T const &c) const { return Matrix(*this) *= c; }
  friend Matrix operator*(T const &c, Matrix const &x) {
    Matrix ret = x;
    rep(i, x.n) rep(j, x.m) ret[i][j] = c * x[i][j];
    return ret;
  }
  // Matrix& operator/=(Matrix const& x, T const& c) {
  //     rep (i,n) rep (j,m) a[i][j] /= c;
  //     return *this;
  // }
  // Matrix operator/(T const& c) const {
  //     return Matrix(*this) /= c;
  // }
  static Matrix identity(int n) {
    Matrix ret(n, n);
    rep(i, n) ret[i][i] = 1;
    return ret;
  }
  Matrix pow(ll k) const {
    assert(n == m);
    assert(k >= 0);
    Matrix v = *this, r = Matrix::identity(n);
    for (; k > 0; k >>= 1, v *= v)
      if (k & 1)
        r *= v;
    return r;
  }
};
template <class T> ostream &operator<<(ostream &os, Matrix<T> const &x) {
  rep(i, x.n) {
    os << "\n";
    rep(j, x.m) os << x[i][j] << " ";
  }
  return os << "\n";
}
// <<<

mint f(mint x, int n) {
  if (n == 0)
    return 0;
  Matrix<mint> m(2, 2);
  mint init[2][2] = {{x, 1}, {0, 1}};
  rep(i, 2) rep(j, 2) m[i][j] = init[i][j];
  m = m.pow(n);
  return m[0][1];
}

mint g(mint x, int n) {
  if (n == 0)
    return 0;
  Matrix<mint> m(3, 3);
  mint init[3][3] = {{x, 1, 0}, {0, 1, -1}, {0, 0, 1}};
  rep(i, 3) rep(j, 3) m[i][j] = init[i][j];
  m = m.pow(n - 1);
  return m[0][0] * (n - 1) + m[0][1] * (n - 2) + m[0][2];
}

int32_t main() {
  int n, a, b, m;
  cin >> n >> a >> b >> m;
  mint::mod() = m;

  const int N = 18;
  vector<int> l(N + 1), r(N + 1);
  l[1] = 0;
  r[N] = n;
  rep1(i, N - 1) {
    int lw = -1, up = n;
    while (lw + 1 < up) {
      int mid = (lw + up) / 2;
      (sz(to_string(a + b * mid)) >= i + 1 ? up : lw) = mid;
    }
    r[i] = l[i + 1] = up;
  }
  // rep1 (i,N) dump(i,l[i],r[i]);

  vector<mint> v(N + 1);
  rep1(d, N) {
    v[d] = f(mint(10).pow(d), r[d] - l[d]) * (a + b * (r[d] - 1)) +
           g(mint(10).pow(d), r[d] - l[d]) * (-b);
  }
  vector<mint> s(N + 2);
  s[N + 1] = 1;
  rep1R(i, N) s[i] = s[i + 1] * mint(10).pow(i * (r[i] - l[i]));

  mint sum = 0;
  rep1(i, N) sum += v[i] * s[i + 1];
  cout << sum << endl;

  //
  dump(l);
  dump(r);
  dump(v);
  dump(s);
  // dump(f(100,6));
  // dump(g(100,6));
}


Fixed submission:
// >>> TEMPLATES
#include <bits/stdc++.h>
using namespace std;
#define rep(i, n) for (int i = 0; i < int(n); i++)
#define rep1(i, n) for (int i = 1; i <= int(n); i++)
#define repR(i, n) for (int i = int(n) - 1; i >= 0; i--)
#define rep1R(i, n) for (int i = int(n); i >= 1; i--)
#define loop(i, a, B) for (int i = a; i B; i++)
#define loopR(i, a, B) for (int i = a; i B; i--)
#define all(x) (x).begin(), (x).end()
#define allR(x) (x).rbegin(), (x).rend()
#define eb emplace_back
#define mp make_pair
#define fst first
#define snd second
#ifdef LOCAL
#define dump(...)                                                              \
  cerr << "[" << __LINE__ << ":" << __FUNCTION__ << "] ",                      \
      dump_impl(#__VA_ARGS__, __VA_ARGS__)
#define say(x)                                                                 \
  cerr << "[" << __LINE__ << ":" << __FUNCTION__ << "] " << x << endl;
#define debug if (1)
void dump_impl(const char *) { cerr << endl; }
template <class T, class... U>
void dump_impl(const char *s, T const &x, U const &...y) {
  const char *o = "({[", *e = "]})";
  for (int i = 0; *s != '\0'; cerr << *s++) {
    if (count(o, o + 3, *s))
      i++;
    if (count(e, e + 3, *s))
      i--;
    if (!i && *s == ',')
      break;
  }
  cerr << " = " << x;
  if (*s == ',')
    cerr << ", ", s++;
  dump_impl(s, y...);
}
#else
#define dump(...)
#define say(x)
#define debug if (0)
#endif
using ll = long long;
using ld = long double;
#define int ll
#define double ld
template <class T> using pque_max = priority_queue<T>;
template <class T> using pque_min = priority_queue<T, vector<T>, greater<T>>;
template <class T, class = typename T::iterator,
          class = typename enable_if<!is_same<T, string>::value>::type>
ostream &operator<<(ostream &os, T const &v) {
  os << "{";
  for (auto const &x : v)
    os << " " << x;
  return os << " }";
}
template <class T> istream &operator>>(istream &is, vector<T> &v) {
  for (auto &x : v)
    is >> x;
  return is;
}
template <class T, class S>
ostream &operator<<(ostream &os, pair<T, S> const &p) {
  return os << "(" << p.first << ", " << p.second << ")";
}
template <class T, class S> istream &operator>>(istream &is, pair<T, S> &p) {
  return is >> p.first >> p.second;
}
template <size_t i, class T>
typename enable_if<i >= tuple_size<T>::value>::type output_tuple(ostream &,
                                                                 T const &) {}
template <size_t i = 0, class T>
    typename enable_if <
    i<tuple_size<T>::value>::type output_tuple(ostream &os, T const &t) {
  os << (i ? " " : "") << get<i>(t);
  output_tuple<i + 1, T>(os, t);
}
template <class... T> ostream &operator<<(ostream &os, tuple<T...> const &t) {
  return output_tuple(os, t), os;
}
struct IOSetup {
  IOSetup() {
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
    cout << fixed << setprecision(15);
  }
} iosetup;
template <class T, size_t d> struct vec_impl {
  using type = vector<typename vec_impl<T, d - 1>::type>;
  template <class... U> static type make_v(size_t n, U &&...x) {
    return type(n, vec_impl<T, d - 1>::make_v(forward<U>(x)...));
  }
};
template <class T> struct vec_impl<T, 0> {
  using type = T;
  static type make_v(T const &x = {}) { return x; }
};
template <class T, size_t d = 1> using vec = typename vec_impl<T, d>::type;
template <class T, size_t d = 1, class... Args> auto make_v(Args &&...args) {
  return vec_impl<T, d>::make_v(forward<Args>(args)...);
}
template <class T> void quit(T const &x) {
  cout << x << endl;
  exit(0);
}
template <class T> constexpr bool chmin(T &x, T const &y) {
  if (x > y) {
    x = y;
    return true;
  }
  return false;
}
template <class T> constexpr bool chmax(T &x, T const &y) {
  if (x < y) {
    x = y;
    return true;
  }
  return false;
}
template <class It> constexpr auto sumof(It b, It e) {
  return accumulate(b, e, typename iterator_traits<It>::value_type{});
}
template <class T> int sz(T const &x) { return x.size(); }
const ll INF = (1LL << 62) - 1; // ~ 4.6e18
// <<<
// >>> runtime modint
using ll = long long;
class runtime_modint {
  using M = runtime_modint;
  ll x;

public:
  static ll &mod() {
    static int mod = 0;
    return mod;
  }
  runtime_modint(ll x = 0) {
    assert(mod() > 0);
    this->x = ((x %= mod()) < 0 ? x + mod() : x);
  }
  ll val() const { return x; }
  bool operator==(M r) const { return x == r.x; }
  bool operator!=(M r) const { return x != r.x; }
  M operator+() const { return *this; }
  M operator-() const { return {mod() - x}; }
  M &operator+=(M r) {
    if ((x += r.x) >= mod())
      x -= mod();
    return *this;
  }
  M &operator-=(M r) {
    if ((x += mod() - r.x) >= mod())
      x -= mod();
    return *this;
  }
  M &operator*=(M r) {
    (x *= r.x) %= mod();
    return *this;
  }
  M operator+(M r) const { return M(*this) += r; }
  M operator-(M r) const { return M(*this) -= r; }
  M operator*(M r) const { return M(*this) *= r; }
  M &operator/=(M r) { return *this *= r.inv(); }
  M operator/(M r) const { return *this * r.inv(); }
  M pow(ll n) const {
    if (n < 0)
      return inv().pow(-n);
    M v = *this, r = 1;
    for (; n > 0; n >>= 1, v *= v)
      if (n & 1)
        r *= v;
    return r;
  }
  M inv() const {
    assert(x != 0);
    ll t = 1, v = x, q, r;
    while (v != 1) {
      q = mod() / v;
      r = mod() % v;
      if (r * 2 < v) {
        t *= -q;
        t %= mod();
        v = r;
      } else {
        t *= q + 1;
        t %= mod();
        v -= r;
      }
    }
    return t;
  }
  static int gen() { // assume mod():prime
    if (mod() == 2)
      return 1;
    vector<int> ps;
    int n = mod() - 1;
    for (int i = 2; i * i <= n; ++i) {
      if (n % i)
        continue;
      ps.push_back(i);
      do
        n /= i;
      while (n % i == 0);
    }
    if (n > 1)
      ps.push_back(n);
    n = mod() - 1;
    auto check = [&](M g) {
      for (int p : ps)
        if (g.pow(n / p) == 1)
          return false;
      return true;
    };
    for (int g = 2; g <= n; ++g)
      if (check(g))
        return g;
    return -1;
  }
};
ostream &operator<<(ostream &os, runtime_modint r) { return os << r.val(); }
istream &operator>>(istream &is, runtime_modint &r) {
  ll x;
  is >> x;
  r = x;
  return is;
}

using mint = runtime_modint;
// <<<
// >>> matrix
template <class T> struct Matrix {
  int n, m;
  vector<vector<T>> a;
  Matrix() {}
  Matrix(int n, int m) : n(n), m(m), a(n) {
    assert(n > 0 && m > 0);
    rep(i, n) a[i].resize(m);
  }
  vector<T> const &operator[](int i) const {
    assert(0 <= i && i < n);
    return a[i];
  }
  vector<T> &operator[](int i) {
    assert(0 <= i && i < n);
    return a[i];
  }
  Matrix &operator+=(Matrix const &x) {
    assert(n == x.n && m == x.m);
    rep(i, n) rep(j, m) a[i][j] += x[i][j];
    return *this;
  }
  Matrix &operator-=(Matrix const &x) {
    assert(n == x.n && m == x.m);
    rep(i, n) rep(j, m) a[i][j] -= x[i][j];
    return *this;
  }
  Matrix operator+(Matrix const &x) const { return Matrix(*this) += x; }
  Matrix operator-(Matrix const &x) const { return Matrix(*this) -= x; }
  Matrix operator*(Matrix const &x) const {
    assert(m == x.n);
    Matrix ret(n, x.m);
    rep(i, n) rep(j, m) rep(k, x.m) ret[i][k] += a[i][j] * x[j][k];
    return ret;
  }
  Matrix &operator*=(Matrix const &x) {
    auto res = (*this) * x;
    swap(a, res.a);
    return *this;
  }
  Matrix operator+() const { return *this; }
  Matrix operator-() const {
    Matrix x = *this;
    rep(i, n) rep(j, m) x[i][j] = -x[i][j];
    return x;
  }
  Matrix &operator*=(T const &c) {
    rep(i, n) rep(j, m) a[i][j] *= c;
    return *this;
  }
  Matrix operator*(T const &c) const { return Matrix(*this) *= c; }
  friend Matrix operator*(T const &c, Matrix const &x) {
    Matrix ret = x;
    rep(i, x.n) rep(j, x.m) ret[i][j] = c * x[i][j];
    return ret;
  }
  // Matrix& operator/=(Matrix const& x, T const& c) {
  //     rep (i,n) rep (j,m) a[i][j] /= c;
  //     return *this;
  // }
  // Matrix operator/(T const& c) const {
  //     return Matrix(*this) /= c;
  // }
  static Matrix identity(int n) {
    Matrix ret(n, n);
    rep(i, n) ret[i][i] = 1;
    return ret;
  }
  Matrix pow(ll k) const {
    assert(n == m);
    assert(k >= 0);
    Matrix v = *this, r = Matrix::identity(n);
    for (; k > 0; k >>= 1, v *= v)
      if (k & 1)
        r *= v;
    return r;
  }
};
template <class T> ostream &operator<<(ostream &os, Matrix<T> const &x) {
  rep(i, x.n) {
    os << "\n";
    rep(j, x.m) os << x[i][j] << " ";
  }
  return os << "\n";
}
// <<<

mint f(mint x, int n) {
  if (n == 0)
    return 0;
  Matrix<mint> m(2, 2);
  mint init[2][2] = {{x, 1}, {0, 1}};
  rep(i, 2) rep(j, 2) m[i][j] = init[i][j];
  m = m.pow(n);
  return m[0][1];
}

mint g(mint x, int n) {
  if (n == 0)
    return 0;
  Matrix<mint> m(3, 3);
  mint init[3][3] = {{x, 1, 0}, {0, 1, -1}, {0, 0, 1}};
  rep(i, 3) rep(j, 3) m[i][j] = init[i][j];
  m = m.pow(n - 1);
  return m[0][0] * (n - 1) + m[0][1] * (n - 2) + m[0][2];
}

int32_t main() {
  int n, a, b, m;
  cin >> n >> a >> b >> m;
  mint::mod() = m;

  const int N = 18;
  vector<int> l(N + 1), r(N + 1);
  l[1] = 0;
  r[N] = n;
  rep1(i, N - 1) {
    int lw = -1, up = n;
    while (lw + 1 < up) {
      int mid = (lw + up) / 2;
      (sz(to_string(a + b * mid)) >= i + 1 ? up : lw) = mid;
    }
    r[i] = l[i + 1] = up;
  }
  // rep1 (i,N) dump(i,l[i],r[i]);

  vector<mint> v(N + 1);
  rep1(d, N) {
    v[d] = f(mint(10).pow(d), r[d] - l[d]) * (a + b * (r[d] - 1)) +
           g(mint(10).pow(d), r[d] - l[d]) * (-b);
  }
  vector<mint> s(N + 2);
  s[N + 1] = 1;
  rep1R(i, N) s[i] = s[i + 1] * mint(10).pow(i).pow(r[i] - l[i]);

  mint sum = 0;
  rep1(i, N) sum += v[i] * s[i + 1];
  cout << sum << endl;

  //
  dump(l);
  dump(r);
  dump(v);
  dump(s);
  // dump(f(100,6));
  // dump(g(100,6));
}