#853757 (C++17) No.2580 Hyperinflation

• 問題: No.2580 Hyperinflation
• ユーザー: noshi91
• 提出日時: 2023-03-29 02:18:35
• 言語: C++17 (gcc 13.3.0 + boost 1.87.0)
• 結果: AC
• 実行時間: 1,328 ms / 4,000 ms
• コード長: 9,166 bytes
• コンパイル時間: 4,166 ms
• コンパイル使用メモリ: 243,972 KB
• 最終ジャッジ日時: 2025-02-11 18:56:38
• ジャッジサーバーID （参考情報）: judge1 / judge3

ファイルパターン	結果
sample	AC * 3
other	AC * 31

ソースコード

//#define NDEBUG
#pragma warning(disable : 4146)

#include <bits/stdc++.h>

namespace n91 {

using i32 = std::int32_t;
using i64 = std::int64_t;
using u32 = std::uint32_t;
using u64 = std::uint64_t;
using isize = std::ptrdiff_t;
using usize = std::size_t;
using f64 = double;

struct rep {
  struct itr {
    usize i;
    constexpr itr(const usize i) noexcept : i(i) {}
    void operator++() noexcept { ++i; }
    constexpr usize operator*() const noexcept { return i; }
    constexpr bool operator!=(const itr x) const noexcept { return i != x.i; }
  };
  const itr f, l;
  constexpr rep(const usize f, const usize l) noexcept
      : f(std::min(f, l)), l(l) {}
  constexpr auto begin() const noexcept { return f; }
  constexpr auto end() const noexcept { return l; }
};
struct revrep {
  struct itr {
    usize i;
    constexpr itr(const usize i) noexcept : i(i) {}
    void operator++() noexcept { --i; }
    constexpr usize operator*() const noexcept { return i; }
    constexpr bool operator!=(const itr x) const noexcept { return i != x.i; }
  };
  const itr f, l;
  constexpr revrep(const usize f, const usize l) noexcept
      : f(l - 1), l(std::min(f, l) - 1) {}
  constexpr auto begin() const noexcept { return f; }
  constexpr auto end() const noexcept { return l; }
};
template <class T> auto md_vec(const usize n, const T &value) {
  return std::vector<T>(n, value);
}
template <class... Args> auto md_vec(const usize n, Args... args) {
  return std::vector<decltype(md_vec(args...))>(n, md_vec(args...));
}
template <class T> constexpr T difference(const T &a, const T &b) noexcept {
  return a < b ? b - a : a - b;
}
template <class T> void chmin(T &a, const T &b) noexcept {
  if (b < a)
    a = b;
}
template <class T> void chmax(T &a, const T &b) noexcept {
  if (a < b)
    a = b;
}
template <class F> class rec_lambda {
  F f;

public:
  rec_lambda(F &&f_) : f(std::forward<F>(f_)) {}
  template <class... Args> auto operator()(Args &&... args) const {
    return f(*this, std::forward<Args>(args)...);
  }
};
template <class T> T scan() {
  T ret;
  std::cin >> ret;
  return ret;
}
constexpr char eoln = '\n';

i64 floor_div(const i64 n, const i64 d) {
  assert(d != 0);
  return n / d - static_cast<i64>((n ^ d) < 0 && n % d != 0);
}

i64 ceil_div(const i64 n, const i64 d) {
  assert(d != 0);
  return n / d + static_cast<i64>((n ^ d) >= 0 && n % d != 0);
}

#ifdef N91_LOCAL
#define OJ_LOCAL(a, b) b
#else
#define OJ_LOCAL(a, b) a
#endif

} // namespace n91

#ifndef NOSHI91_POLYNOMIAL_INTERNAL
#define NOSHI91_POLYNOMIAL_INTERNAL

#include <vector>

#include <atcoder/convolution>

namespace noshi91 {

namespace polynomial {

template <class T> const atcoder::internal::fft_info<T> info;

template <class T> void dft(std::vector<T> &a) {
  atcoder::internal::butterfly(a);
}

template <class T> void inv_dft(std::vector<T> &a) {
  atcoder::internal::butterfly_inv(a);
  T c = T::mod() - (T::mod() - 1) / a.size();
  for (auto &e : a)
    e *= c;
}

} // namespace polynomial

} // namespace noshi91

#endif

#ifndef NOSHI91_MODINT_UTILITY
#define NOSHI91_MODINT_UTILITY

#include <cassert>
#include <vector>

namespace noshi91 {

template <class T> class modint_utility {
  static inline std::vector<T> fact_ = {T::raw(1)};
  static inline std::vector<T> inv_fact_ = {T::raw(1)};
  static inline std::vector<T> inv_num_ = {T::raw(1)};

  static void extend(const int n) {
    if (n < fact_.size())
      return;
    const int s = fact_.size();
    int t = 2 * s;
    while (n >= t)
      t *= 2;
    fact_.resize(t);
    inv_fact_.resize(t);
    inv_num_.resize(t);
    for (int i = s; i < t; i++)
      fact_[i] = fact_[i - 1] * T::raw(i);
    inv_fact_.back() = T::raw(1) / fact_.back();
    for (int i = t - 1; i > s; i--)
      inv_fact_[i - 1] = inv_fact_[i] * T::raw(i);
    for (int i = t; i-- > s;)
      inv_num_[i] = inv_fact_[i] * fact_[i - 1];
  }

public:
  modint_utility() = delete;

  static T fact(const int n) {
    assert(0 <= n);
    extend(n);
    return fact_[n];
  }

  static T inv_fact(const int n) {
    assert(0 <= n);
    extend(n);
    return inv_fact_[n];
  }

  static T inv_num(const int n) {
    assert(0 <= n);
    extend(n);
    return inv_num_[n];
  }

  static T binom(const int n, const int r) {
    assert(0 <= n);
    if (r < 0 || n < r) {
      return T::raw(0);
    } else {
      extend(n);
      return fact_[n] * inv_fact_[r] * inv_fact_[n - r];
    }
  }

  static T binom2(const int a, const int b) {
    assert(0 <= a && 0 <= b);
    extend(a + b);
    return fact_[a + b] * inv_fact_[a] * inv_fact_[b];
  }

  static T homo(const int n, const int r) {
    assert(1 <= n && 0 <= r);
    extend(n + r - 1);
    return fact_[n + r - 1] * inv_fact_[n - 1] * inv_fact_[r];
  }

  static T perm(const int n, const int r) {
    assert(0 <= r);
    if (n < r) {
      return T::raw(0);
    } else {
      extend(n);
      return fact_[n] * inv_fact_[n - r];
    }
  }
};

} // namespace noshi91

#endif

#include <algorithm>
#include <cassert>
#include <functional>
#include <vector>

namespace noshi91 {

namespace polynomial {

template <class T> std::vector<T> inverse(const std::vector<T> &f) {
  int n = f.size();
  if (n == 0)
    return {};
  assert(f[0] != T(0));
  std::vector<T> g(n);
  g[0] = T(1) / f[0];
  int p = 1;
  while (p < n) {
    std::vector<T> f_(2 * p, T(0)), g_(2 * p, T(0));
    std::copy(f.begin(), f.begin() + std::min(2 * p, n), f_.begin());
    dft(f_);
    std::copy(g.begin(), g.begin() + p, g_.begin());
    dft(g_);
    for (int i = 0; i < 2 * p; i++)
      f_[i] *= g_[i];
    inv_dft(f_);
    std::fill(f_.begin(), f_.begin() + p, T(0));
    dft(f_);
    for (int i = 0; i < 2 * p; i++)
      f_[i] *= g_[i];
    inv_dft(f_);
    std::transform(f_.begin() + p, f_.begin() + std::min(2 * p, n),
                   g.begin() + p, std::negate<>());
    p *= 2;
  }
  return g;
}

} // namespace polynomial

} // namespace noshi91

#include <atcoder/convolution>

namespace noshi91 {

namespace polynomial {

// p: polynomial
// s(k) = sum[i in [0, k)] p(i)
template <class T> std::vector<T> cumsum(std::vector<T> p) {
  using util = modint_utility<T>;
  const int n = p.size();
  std::vector<T> op(n);
  for (int i = 0; i < n; i++)
    op[i] = util::inv_fact(i + 1);
  op = inverse(op);
  for (int i = 0; i < n; i++)
    p[i] *= util::fact(i);
  std::reverse(p.begin(), p.end());
  p = atcoder::convolution(p, op);
  p.resize(n + 1);
  std::reverse(p.begin(), p.end());
  p[0] = T::raw(0);
  for (int i = 0; i < n + 1; i++)
    p[i] *= util::inv_fact(i);
  return p;
}

} // namespace polynomial

} // namespace noshi91

#include <atcoder/convolution>

namespace noshi91 {

namespace polynomial {

// p: polynomial
// return: p(x + c) = exp(cD)p
template <class T> std::vector<T> taylor_shift(std::vector<T> p, const T &c) {
  using util = modint_utility<T>;
  const int n = p.size();
  std::vector<T> op(n);
  T t = 1;
  for (int i = 0; i < n; i++)
    op[i] = t * util::inv_fact(i), t *= c;
  for (int i = 0; i < n; i++)
    p[i] *= util::fact(i);
  std::reverse(p.begin(), p.end());
  p = atcoder::convolution(p, op);
  p.resize(n);
  std::reverse(p.begin(), p.end());
  for (int i = 0; i < n; i++)
    p[i] *= util::inv_fact(i);
  return p;
}

} // namespace polynomial

} // namespace noshi91

#include <vector>

namespace noshi91 {

namespace polynomial {

template <class T> T evaluate(const std::vector<T> &p, const T &x) {
  T r = 0;
  for (int i = p.size(); i-- > 0;)
    r = r * x + p[i];
  return r;
}

} // namespace polynomial

} // namespace noshi91

#include <atcoder/modint>

namespace n91 {

using mint = atcoder::modint998244353;

void add(std::vector<u32> &m, u32 a) {
  isize p = m.size() - 1;
  while (a) {
    if (p < 0)
      m.insert(m.begin(), 0), p++;
    m[p] += a;
    a = m[p] / 10;
    m[p] %= 10;
    p--;
  }
}

u32 divrem(std::vector<u32> &m, const u32 d) {
  std::vector<u32> q;
  u32 r = 0;
  for (const auto &e : m) {
    if (!q.empty())
      q.push_back(0);
    r = r * 10 + e;
    add(q, r / d);
    r %= d;
  }
  m = std::move(q);
  return r;
}

mint takemod(const std::vector<u32> &m) {
  mint r = 0;
  for (const auto &e : m)
    r = r * 10 + e;
  return r;
}

void main_() {
  const usize n = scan<usize>();
  std::vector<usize> a(n);
  a[0] = 1;
  for (const usize i : rep(1, n)) {
    std::cin >> a[i];
  }
  std::vector<u32> m;
  {
    const std::string s = scan<std::string>();
    const usize x = s.size();
    m.resize(x);
    for (const usize i : rep(0, x)) {
      m[i] = s[i] - '0';
    }
  }

  std::vector<mint> p(1, 1);
  for (const usize i : rep(1, n)) {
    const u32 rem = divrem(m, a[i]);
    p = noshi91::polynomial::taylor_shift<mint>(p, rem);
    {
      mint t = 1;
      for (auto &e : p)
        e *= t, t *= mint::raw(a[i]);
    }
    p = noshi91::polynomial::cumsum(p);
    p = noshi91::polynomial::taylor_shift<mint>(p, 1);
  }

  std::cout << noshi91::polynomial::evaluate(p, takemod(m)).val() << "\n";
}

} // namespace n91

int main() {
  //*
  std::ios::sync_with_stdio(false);
  std::cin.tie(nullptr);
  //*/
  std::cout << std::fixed << std::setprecision(20);
  n91::main_();
  return 0;
}