Tifa's CP Library

:heavy_check_mark: src/test_cpverifier/library-checker/pow_of_formal_power_series.pmtt-s63.test.cpp

Depends on

Code

#define AUTO_GENERATED
#define PROBLEM "https://judge.yosupo.jp/problem/pow_of_formal_power_series"

#include "../../code/io/fastio.hpp"
#include "../../code/poly/pow_fps.hpp"

constexpr u32 MOD = 998244353;

#include "../../code/math/mint_s63.hpp"
#include "../../code/poly/polymtt.hpp"

using mint = tifa_libs::math::mint_s63<MOD>;
using poly = tifa_libs::math::polymtt<mint>;

int main() {
  u32 n;
  u64 m;
  tifa_libs::fin >> n >> m;
  poly a(n);
  tifa_libs::fin >> a.data();
  tifa_libs::fout << tifa_libs::math::pow_fps(a, m).data() << '\n';
  return 0;
}
#line 1 "src/test_cpverifier/library-checker/pow_of_formal_power_series.pmtt-s63.test.cpp"
#define AUTO_GENERATED
#define PROBLEM "https://judge.yosupo.jp/problem/pow_of_formal_power_series"

#line 1 "src/code/io/fastio.hpp"



#line 1 "src/code/fast/u32tostr.hpp"



#line 1 "src/code/util/util.hpp"



#include <bits/stdc++.h>

template <class T>
constexpr T abs(T x) { return x < 0 ? -x : x; }

using i8 = int8_t;
using i16 = int16_t;
using i32 = int32_t;
using i64 = int64_t;
using i128 = __int128_t;
using isz = ptrdiff_t;

using u8 = uint8_t;
using u16 = uint16_t;
using u32 = uint32_t;
using u64 = uint64_t;
using u128 = __uint128_t;
using usz = size_t;

using f32 = float;
using f64 = double;
using f128 = long double;

template <class T>
using ptt = std::pair<T, T>;
template <class T>
using pt3 = std::tuple<T, T, T>;
template <class T>
using pt4 = std::tuple<T, T, T, T>;

template <class T, usz N>
using arr = std::array<T, N>;
template <class T>
using vec = std::vector<T>;
template <class T>
using vvec = vec<vec<T>>;
template <class T>
using v3ec = vec<vvec<T>>;
template <class U, class T>
using vecp = vec<std::pair<U, T>>;
template <class U, class T>
using vvecp = vvec<std::pair<U, T>>;
template <class T>
using vecpt = vec<ptt<T>>;
template <class T>
using vvecpt = vvec<ptt<T>>;

template <class T, class C = std::less<T>>
using pq = std::priority_queue<T, vec<T>, C>;
template <class T>
using pqg = std::priority_queue<T, vec<T>, std::greater<T>>;

using strn = std::string;
using strnv = std::string_view;

using vecu = vec<u32>;
using vvecu = vvec<u32>;
using v3ecu = v3ec<u32>;
using vecu64 = vec<u64>;
using vecb = vec<bool>;
using vvecb = vvec<bool>;

#ifdef ONLINE_JUDGE
#undef assert
#define assert(x) 42
#endif

using namespace std::literals;

constexpr i8 operator""_i8(unsigned long long x) { return (i8)x; }
constexpr i16 operator""_i16(unsigned long long x) { return (i16)x; }
constexpr i32 operator""_i32(unsigned long long x) { return (i32)x; }
constexpr i64 operator""_i64(unsigned long long x) { return (i64)x; }
constexpr isz operator""_iz(unsigned long long x) { return (isz)x; }

constexpr u8 operator""_u8(unsigned long long x) { return (u8)x; }
constexpr u16 operator""_u16(unsigned long long x) { return (u16)x; }
constexpr u32 operator""_u32(unsigned long long x) { return (u32)x; }
constexpr u64 operator""_u64(unsigned long long x) { return (u64)x; }
constexpr usz operator""_uz(unsigned long long x) { return (usz)x; }

inline const auto fn_0 = [](auto&&...) {};


#line 5 "src/code/fast/u32tostr.hpp"

namespace tifa_libs {

constexpr u32 u32tostr_si16(u64 x, char *s) {
  if (x <= 9) {
    *s = (char)(x | 0x30);
    return 1;
  } else if (x <= 99) {
    u64 low = x;
    u64 ll = ((low * 103) >> 9) & 0x1E;
    low += ll * 3;
    ll = ((low & 0xF0) >> 4) | ((low & 0x0F) << 8);
    *(u16 *)s = (u16)(ll | 0x3030);
    return 2;
  }
  return 0;
}
constexpr u32 u32tostr_si32(u64 x, char *s) {
  u64 low = 0, ll = 0;
  u32 digits = 0;
  if (x <= 99) return u32tostr_si16(x, s);
  low = x;
  digits = (low > 999) ? 4 : 3;
  ll = ((low * 5243) >> 19) & 0xFF;
  low -= ll * 100;
  low = (low << 16) | ll;
  ll = ((low * 103) >> 9) & 0x1E001E;
  low += ll * 3;
  ll = ((low & 0x00F000F0) << 28) | (low & 0x000F000F) << 40;
  ll |= 0x3030303000000000;
  u8 *p = (u8 *)&ll;
  if (digits == 4) *(u32 *)s = *(u32 *)(&p[4]);
  else {
    *(u16 *)s = *(u16 *)(&p[5]);
    *(((u8 *)s) + 2) = p[7];
  }

  return digits;
}

constexpr u32 u32tostr(u64 x, char *s) {
  u64 low = 0, ll = 0;
  u32 digits = 0;
  if (x <= 9999) return u32tostr_si32(x, s);
  if (x < 100000000) {
    if ((low = x) > 999999) digits = (low > 9999999) ? 8 : 7;
    else digits = (low > 99999) ? 6 : 5;
  } else {
    u64 high = (x * 0x55E63B89) >> 57;
    low = x - (high * 100000000);
    digits = u32tostr_si16(high, s);
    digits += 8;
  }

  ll = (low * 109951163) >> 40;
  (low -= ll * 10000) |= ll << 32;
  ll = ((low * 5243) >> 19) & 0x000000FF000000FF;
  low -= ll * 100;
  low = (low << 16) | ll;
  ll = ((low * 103) >> 9) & 0x001E001E001E001E;
  low += ll * 3;
  ll = ((low & 0x00F000F000F000F0) >> 4) | (low & 0x000F000F000F000F) << 8;
  ll = (ll >> 32) | (ll << 32) | 0x3030303030303030;

  if (digits >= 8) memcpy(s + digits - 8, &ll, 8);
  else {
    u32 d = digits;
    char *s1 = s, *pll = &(((char *)&ll)[8 - digits]);
    if (d >= 4) {
      memcpy(s1, pll, 4);
      s1 += 4, pll += 4, d -= 4;
    }
    if (d >= 2) {
      memcpy(s1, pll, 2);
      s1 += 2, pll += 2, d -= 2;
    }
    if (d > 0) *(u8 *)s1 = *(u8 *)pll;
  }
  return digits;
}

}  // namespace tifa_libs


#line 1 "src/code/util/traits.hpp"



#line 5 "src/code/util/traits.hpp"

namespace tifa_libs {

template <class T>
concept iterable_c = requires(T v) {
  { v.begin() } -> std::same_as<typename T::iterator>;
  { v.end() } -> std::same_as<typename T::iterator>;
};

template <class T>
concept container_c = iterable_c<T> && !std::derived_from<T, std::basic_string<typename T::value_type>>;

template <class T>
constexpr bool is_char_v = std::is_same_v<T, char> || std::is_same_v<T, signed char> || std::is_same_v<T, unsigned char>;
template <class T>
concept char_c = is_char_v<T>;

template <class T>
constexpr bool is_s128_v = std::is_same_v<T, __int128_t> || std::is_same_v<T, __int128>;
template <class T>
concept s128_c = is_s128_v<T>;

template <class T>
constexpr bool is_u128_v = std::is_same_v<T, __uint128_t> || std::is_same_v<T, unsigned __int128>;
template <class T>
concept u128_c = is_u128_v<T>;

template <class T>
constexpr bool is_i128_v = is_s128_v<T> || is_u128_v<T>;
template <class T>
concept i128_c = is_u128_v<T>;

template <class T>
constexpr bool is_int_v = std::is_integral_v<T> || is_i128_v<T>;
template <class T>
concept int_c = is_int_v<T>;

template <class T>
constexpr bool is_sint_v = is_s128_v<T> || (is_int_v<T> && std::is_signed_v<T>);
template <class T>
concept sint_c = is_sint_v<T>;

template <class T>
constexpr bool is_uint_v = is_u128_v<T> || (is_int_v<T> && std::is_unsigned_v<T>);
template <class T>
concept uint_c = is_uint_v<T>;

template <class T>
concept mint_c = requires(T x) {
  { x.mod() } -> uint_c;
  { x.val() } -> uint_c;
};

template <class T>
constexpr bool is_arithm_v = std::is_arithmetic_v<T> || is_int_v<T>;
template <class T>
concept arithm_c = is_arithm_v<T>;

template <class T>
struct to_sint : std::make_signed<T> {};
template <>
struct to_sint<u128> {
  using type = u128;
};
template <>
struct to_sint<i128> {
  using type = u128;
};
template <class T>
using to_sint_t = typename to_sint<T>::type;

template <class T>
struct to_uint : std::make_unsigned<T> {};
template <>
struct to_uint<u128> {
  using type = u128;
};
template <>
struct to_uint<i128> {
  using type = u128;
};
template <class T>
using to_uint_t = typename to_uint<T>::type;

}  // namespace tifa_libs


#line 6 "src/code/io/fastio.hpp"

namespace tifa_libs {
namespace fastio_impl_ {
//! UB if EOF occured during reading
template <u32 BUF>
class fastin {
  char bf_[BUF], *now_ = bf_, *end_ = bf_;
  FILE *f_;

 public:
  explicit fastin(FILE *f = stdin) : f_(f) {}

  char get() { return now_ == end_ && (end_ = (now_ = bf_) + fread(bf_, 1, BUF, f_), now_ == end_) ? EOF : *(now_)++; }
  char peek() { return now_ == end_ && (end_ = (now_ = bf_) + fread(bf_, 1, BUF, f_), now_ == end_) ? EOF : *(now_); }
  void rebind(FILE *f) {
    f_ = f;
    now_ = end_ = bf_;
  }

  bool iseof() { return peek() == EOF; }

  template <class T>
  requires(sint_c<T> && !char_c<T>)
  fastin &read(T &n) {
    bool is_neg = false;
    char ch = get();
    while (!isdigit(ch)) {
      is_neg |= ch == '-';
      ch = get();
    }
    n = 0;
    while (isdigit(ch)) {
      (n *= 10) += ch & 15;
      ch = get();
    }
    if (is_neg) n = -n;
    return *this;
  }
  template <class T>
  requires(uint_c<T> && !char_c<T>)
  fastin &read(T &n) {
    char ch = get();
    while (!isdigit(ch)) ch = get();
    n = 0;
    while (isdigit(ch)) {
      (n *= 10) += ch & 15;
      ch = get();
    }
    return *this;
  }
  template <mint_c T>
  fastin &read(T &n) {
    decltype(std::declval<T>().sval()) x;
    read(x);
    n = T(x);
    return *this;
  }
  //! ignore cntrl and space
  template <char_c T>
  fastin &read(T &n) {
    while (!isgraph(n = get()));
    return *this;
  }
  fastin &read(char *n) {
    char *n_ = n;
    while (!isgraph(*n_ = get()));
    while (isgraph(*(++n_) = get()));
    *n_ = '\0';
    return *this;
  }
  fastin &read(strn &n) {
    n.clear();
    char n_;
    while (!isgraph(n_ = get()));
    n.push_back(n_);
    while (isgraph(n_ = get())) n.push_back(n_);
    return *this;
  }
  template <class T, class U>
  fastin &read(std::pair<T, U> &p) { return read(p.first).read(p.second); }
  template <class... Ts>
  fastin &read(std::tuple<Ts...> &p) {
    std::apply([&](Ts &...targs) { ((read(targs)), ...); }, p);
    return *this;
  }
  template <container_c T>
  fastin &read(T &p) {
    if (p.begin() == p.end()) return *this;
    for (auto &i : p) read(i);
    return *this;
  }

  fastin &getline(char *n) {
    char *n_ = n;
    while (!isprint(*n_ = get()));
    while (isprint(*(++n_) = get()));
    *n_ = '\0';
    return *this;
  }
  fastin &getline(strn &n) {
    char n_;
    while (!isprint(n_ = get()));
    n.push_back(n_);
    while (isprint(n_ = get())) n.push_back(n_);
    return *this;
  }

  //! NOT ignore cntrl and space
  template <char_c T>
  fastin &strict_read(T &n) {
    n = get();
    return *this;
  }

  template <class T>
  fastin &operator>>(T &val) { return read(val); }
};
template <u32 BUF, u32 INTBUF>
class fastout {
  char int_bf_[INTBUF], *now_ib_ = int_bf_;

  FILE *f_;
  char *now_, bf_[BUF];
  const char *const end_ = bf_ + BUF;

 public:
  explicit fastout(FILE *file = stdout) : f_(file), now_(bf_) {}

  fastout &operator=(fastout const &r) {
    f_ = r.f_;
    now_ = bf_ + (r.now_ - r.bf_);
    memcpy(bf_, r.bf_, sizeof(*bf_) * (r.now_ - r.bf_));
    return *this;
  }
  fastout(fastout const &r) { *this = r; }

  ~fastout() { flush(); }

  void flush() {
    fwrite(bf_, 1, usz(now_ - bf_), f_);
    now_ = bf_;
  }
  void rebind(FILE *file) { f_ = file; }

  template <char_c T>
  fastout &write(T const &n) {
    if (now_ == end_) flush();
    *(now_++) = n;
    return *this;
  }
  fastout &write(const char *n) {
    usz len = strlen(n), l_;
    const char *n_ = n;
    while (now_ + len >= end_) {
      memcpy(now_, n_, l_ = usz(end_ - now_));
      now_ += l_;
      n_ += l_;
      len -= l_;
      flush();
    }
    memcpy(now_, n_, len);
    now_ += len;
    return *this;
  }
  template <class T>
  requires(sint_c<T> && !char_c<T>)
  fastout &write(T n) {
    if (n < 0) {
      write('-');
      n = -n;
    }
    return write(to_uint_t<T>(n));
  }
  template <class T>
  requires(uint_c<T> && !char_c<T>)
  fastout &write(T n) {
    if constexpr (sizeof(T) <= 4) {
      memset(now_ib_ = int_bf_, 0, 11);
      u32tostr(n, now_ib_);
      return write(now_ib_);
    }
    now_ib_ = int_bf_ + INTBUF - 1;
    do {
      *(--(now_ib_)) = char(n % 10) | '0';
    } while (n /= 10);
    return write(now_ib_);
  }
  template <mint_c T>
  fastout &write(T n) { return write(n.val()); }
  fastout &write(strn const &str) { return write(str.c_str()); }
  template <class T, class U>
  fastout &write(std::pair<T, U> const &p) { return write(p.first).space().write(p.second); }
  template <class... Ts>
  fastout &write(std::tuple<Ts...> const &p) {
    std::apply(
        [&](Ts const &...targs) {
          usz n{0};
          ((write(targs).space_if(++n != sizeof...(Ts))), ...);
        },
        p);
    return *this;
  }
  template <container_c T>
  fastout &write(T const &p) {
    if (p.begin() == p.end()) return *this;
    auto it = p.begin();
    write(*it++);
    for (; it != p.end(); ++it) space().write(*it);
    return *this;
  }

  fastout &linebreak() { return write('\n'); }
  fastout &linebreak_if(bool flag) { return flag ? linebreak() : *this; }
  fastout &space() { return write(' '); }
  fastout &space_if(bool flag) { return flag ? space() : *this; }

  template <class T>
  fastout &operator<<(T const &val) { return write(val); }
};
}  // namespace fastio_impl_

inline fastio_impl_::fastin<0x200005> fin;
inline fastio_impl_::fastout<0x200005, 41> fout;

}  // namespace tifa_libs


#line 1 "src/code/poly/pow_fps.hpp"



#line 1 "src/code/math/qpow.hpp"



#line 5 "src/code/math/qpow.hpp"

namespace tifa_libs::math {

template <class T>
constexpr T qpow(T a, u64 b, T const& init_v = T{1}) {
  T res = init_v;
  for (; b; b >>= 1, a = a * a)
    if (b & 1) res = res * a;
  return res;
}

}  // namespace tifa_libs::math


#line 1 "src/code/poly/exp_fps.hpp"



#line 1 "src/code/poly/ln_fps.hpp"



#line 1 "src/code/poly/deriv_fps.hpp"



#line 1 "src/code/poly/poly.hpp"



#line 5 "src/code/poly/poly.hpp"

namespace tifa_libs::math {

// clang-format off
enum ccore_t { ct_FFT, ct_3NTT, ct_NTT, ct_CNTT };
// clang-format on

template <class mint, class ccore>
requires requires(ccore cc, vec<mint> l, vec<mint> const &r, u32 sz) {
  { ccore::ct_cat } -> std::same_as<ccore_t const &>;
  cc.conv(l, r);
  cc.conv(l, r, sz);
}
class poly {
  vec<mint> d;

 public:
  using value_type = mint;
  using data_type = vec<value_type>;
  using ccore_type = ccore;
  static inline ccore_type conv_core;

  explicit constexpr poly(u32 sz = 1, value_type const &val = value_type{}) : d(sz, val) {}
  constexpr poly(typename data_type::const_iterator begin, typename data_type::const_iterator end) : d(begin, end) {}
  constexpr poly(std::initializer_list<value_type> v) : d(v) {}
  template <class T>
  explicit constexpr poly(vec<T> const &v) : d(v) {}

  friend constexpr std::istream &operator>>(std::istream &is, poly &poly) {
    for (auto &val : poly.d) is >> val;
    return is;
  }
  friend constexpr std::ostream &operator<<(std::ostream &os, poly const &poly) {
    if (!poly.size()) return os;
    for (u32 i = 1; i < poly.size(); ++i) os << poly[i - 1] << ' ';
    return os << poly.d.back();
  }

  constexpr u32 size() const { return (u32)d.size(); }
  constexpr bool empty() const {
    for (auto &&i : d)
      if (i != 0) return 0;
    return 1;
  }
  constexpr data_type &data() { return d; }
  constexpr data_type const &data() const { return d; }

  constexpr value_type &operator[](u32 x) { return d[x]; }
  constexpr value_type const &operator[](u32 x) const { return d[x]; }
  constexpr value_type operator()(value_type x) const {
    value_type ans = 0;
    for (u32 i = size() - 1; ~i; --i) ans = ans * x + d[i];
    return ans;
  }

  template <class F>
  requires requires(F f, u32 idx, mint &val) {
    f(idx, val);
  }
  constexpr void apply_range(u32 l, u32 r, F &&f) {
    assert(l < r && r <= size());
    for (u32 i = l; i < r; ++i) f(i, d[i]);
  }
  template <class F>
  constexpr void apply(F &&f) { apply_range(0, size(), std::forward<F>(f)); }
  constexpr void resize(u32 size) { d.resize(size); }
  constexpr poly pre(u32 size) const {
    poly _ = *this;
    _.resize(size);
    return _;
  }
  constexpr void strip() {
    auto it = std::find_if(d.rbegin(), d.rend(), [](auto const &x) { return x != 0; });
    d.resize(usz(d.rend() - it));
    if (d.empty()) d.push_back(value_type(0));
  }
  friend poly stripped(poly p) {
    p.strip();
    return p;
  }
  constexpr void reverse(u32 n = 0) { std::reverse(d.begin(), d.begin() + (n ? n : size())); }
  constexpr void conv(poly const &r, u32 ans_size = 0) { conv_core.conv(d, r.d, ans_size); }

  constexpr poly operator-() const {
    poly ret = *this;
    ret.apply([](u32, auto &v) { v = -v; });
    return ret;
  }

  friend constexpr poly operator+(poly p, value_type c) {
    p[0] += c;
    return p;
  }
  friend constexpr poly operator+(value_type c, poly const &p) { return p + c; }
  friend constexpr poly operator-(poly p, value_type c) {
    p[0] -= c;
    return p;
  }
  friend constexpr poly operator-(value_type c, poly const &p) { return p - c; }

  constexpr poly &operator*=(value_type c) {
    apply([&c](u32, auto &v) { v *= c; });
    return *this;
  }
  friend constexpr poly operator*(poly p, value_type c) { return p *= c; }
  friend constexpr poly operator*(value_type c, poly p) { return p *= c; }

  constexpr poly &operator+=(poly const &r) {
    if (!r.size()) return *this;
    resize(std::max(size(), r.size()));
    apply_range(0, r.size(), [&r](u32 i, auto &v) { v += r[i]; });
    return *this;
  }
  friend constexpr poly operator+(poly l, poly const &r) { return l += r; }

  constexpr poly &operator-=(poly const &r) {
    if (!r.size()) return *this;
    resize(std::max(size(), r.size()));
    apply_range(0, r.size(), [&r](u32 i, auto &v) { v -= r[i]; });
    return *this;
  }
  friend constexpr poly operator-(poly l, poly const &r) { return l -= r; }

  constexpr poly &operator*=(poly const &r) {
    if (!r.size()) {
      resize(1);
      d[0] = 0;
      return *this;
    }
    conv(r);
    return *this;
  }
  friend constexpr poly operator*(poly l, poly const &r) { return l *= r; }

  constexpr auto operator<=>(poly const &r) const { return stripped(*this).d <=> stripped(r).d; }
  constexpr bool operator==(poly const &r) const { return stripped(*this).d == stripped(r).d; }
};

}  // namespace tifa_libs::math


#line 5 "src/code/poly/deriv_fps.hpp"

namespace tifa_libs::math {

template <class mint, class ccore>
constexpr poly<mint, ccore> deriv_fps(poly<mint, ccore> const &p) {
  auto _ = p;
  for (u32 i = 1; i < _.size(); ++i) _[i - 1] = _[i] * i;
  _.data().back() = 0;
  return _;
}

}  // namespace tifa_libs::math


#line 1 "src/code/poly/int_fps.hpp"



#line 5 "src/code/poly/int_fps.hpp"

namespace tifa_libs::math {

template <class mint, class ccore>
constexpr poly<mint, ccore> int_fps(poly<mint, ccore> const &p) {
  auto _ = p;
  for (u32 i = _.size() - 1; i; --i) _[i] = _[i - 1] * mint(i).inv();
  _[0] = 0;
  return _;
}

}  // namespace tifa_libs::math


#line 1 "src/code/poly/inv_fps.hpp"



#line 5 "src/code/poly/inv_fps.hpp"

namespace tifa_libs::math {

template <class mint, class ccore>
constexpr poly<mint, ccore> inv_fps(poly<mint, ccore> const &p, u32 n = 0) {
  assert(p[0] != 0);
  if (!n) n = p.size();
  poly<mint, ccore> a{p[0].inv()};
  for (u32 i = 1; i < n; i *= 2) a = (a * 2 - (a * a * p).pre(i * 2)).pre(i * 2);
  return a.pre(n);
}

}  // namespace tifa_libs::math


#line 7 "src/code/poly/ln_fps.hpp"

namespace tifa_libs::math {

template <class mint, class ccore>
constexpr poly<mint, ccore> ln_fps(poly<mint, ccore> const &p, u32 n = 0) {
  assert(p[0] == 1);
  if (!n) n = p.size();
  auto _ = deriv_fps(p).pre(n);
  _.conv(inv_fps(p, n));
  return int_fps(_).pre(n);
}

}  // namespace tifa_libs::math


#line 5 "src/code/poly/exp_fps.hpp"

namespace tifa_libs::math {

template <class mint, class ccore>
constexpr poly<mint, ccore> exp_fps(poly<mint, ccore> p, u32 n = 0) {
  assert(p[0] == 0);
  if (!n) n = p.size();
  p[0] += 1;
  poly<mint, ccore> a{1};
  for (u32 i = 1; i < n; i *= 2) a = (a * (p.pre(i * 2) - ln_fps(a, i * 2))).pre(i * 2);
  return a.pre(n);
}

}  // namespace tifa_libs::math


#line 1 "src/code/poly/shl_fps.hpp"



#line 5 "src/code/poly/shl_fps.hpp"

namespace tifa_libs::math {

template <class mint, class ccore>
constexpr poly<mint, ccore> shl_fps(poly<mint, ccore> const &p, usz x) {
  if (!x) return p;
  auto _ = p;
  if (x >= _.size()) {
    std::ranges::fill(_.data(), 0);
    return _;
  }
  std::fill(_.data().begin(), std::move_backward(_.data().begin(), std::prev(_.data().end(), (isz)x), _.data().end()), 0);
  return _;
}

}  // namespace tifa_libs::math


#line 1 "src/code/poly/shr_fps.hpp"



#line 5 "src/code/poly/shr_fps.hpp"

namespace tifa_libs::math {

template <class mint, class ccore>
constexpr poly<mint, ccore> shr_fps(poly<mint, ccore> const &p, usz x) {
  if (!x) return p;
  auto _ = p;
  if (x >= p.size()) {
    std::ranges::fill(_.data(), 0);
    return _;
  }
  std::fill(std::move(_.data().begin() + (isz)x, _.data().end(), _.data().begin()), _.data().end(), 0);
  return _;
}
template <class mint, class ccore>
constexpr poly<mint, ccore> shr_strip_fps(poly<mint, ccore> const &p, usz x) {
  auto _ = shr_fps(p, x);
  _.strip();
  return _;
}

}  // namespace tifa_libs::math


#line 9 "src/code/poly/pow_fps.hpp"

namespace tifa_libs::math {

template <class mint, class ccore>
constexpr poly<mint, ccore> pow_fps(poly<mint, ccore> const &p, u64 y, u32 n = 0) {
  if (!n) n = p.size();
  if (y == 0) {
    poly<mint, ccore> _(n);
    if (n) _[0] = 1;
    return _;
  }
  if (y == 1) return p;
  u32 l0 = u32(std::ranges::find_if(p.data(), [](auto const &x) { return x != 0; }) - p.data().begin());
  if ((u128)l0 * y >= n) return poly<mint, ccore>(n);
  if (l0) {
    auto _ = shr_fps(p, l0), g = pow_fps(_, y, u32(n - l0 * y));
    g.resize(n);
    return shl_fps(g, l0 * y);
  }
  auto _ = p;
  mint _0 = p[0];
  if (_0 != 1) _ *= _0.inv();
  _ = exp_fps(ln_fps(_) * y);
  if (_0 != 1) _ *= qpow(_0, y);
  _.resize(n);
  return _;
}

}  // namespace tifa_libs::math


#line 6 "src/test_cpverifier/library-checker/pow_of_formal_power_series.pmtt-s63.test.cpp"

constexpr u32 MOD = 998244353;

#line 1 "src/code/math/mint_s63.hpp"



#line 1 "src/code/math/mint.hpp"



#line 1 "src/code/nt/inverse.hpp"



#line 1 "src/code/nt/inv_gcd.hpp"



#line 1 "src/code/math/safe_mod.hpp"



#line 5 "src/code/math/safe_mod.hpp"

namespace tifa_libs::math {

template <sint_c T>
constexpr T safe_mod(T x, to_uint_t<T> mod) { return ((x %= (T)mod) < 0 ? x + (T)mod : x); }

}  // namespace tifa_libs::math


#line 1 "src/code/nt/exgcd.hpp"



#line 5 "src/code/nt/exgcd.hpp"

namespace tifa_libs::math {

// @return tuple(g, x, y) s.t. g = gcd(a, b), xa + yb = g, |x| + |y| is the minimal (primary) and x <= y (secondarily)
template <sint_c T>
constexpr auto exgcd(T a, T b) {
  T x1 = 1, x2 = 0, x3 = 0, x4 = 1;
  while (b) {
    T c = a / b;
    std::tie(x1, x2, x3, x4, a, b) = std::make_tuple(x3, x4, x1 - x3 * c, x2 - x4 * c, b, a - b * c);
  }
  return std::make_tuple(to_uint_t<T>(a), x1, x2);
}

}  // namespace tifa_libs::math


#line 6 "src/code/nt/inv_gcd.hpp"

namespace tifa_libs::math {

template <uint_c T>
constexpr ptt<T> inv_gcd(T n, T mod) {
  using U = to_sint_t<T>;
  auto [g, x, y] = exgcd(U(n % mod), (U)mod);
  return {g, safe_mod(x, mod)};
}

}  // namespace tifa_libs::math


#line 5 "src/code/nt/inverse.hpp"

namespace tifa_libs::math {

template <uint_c T, uint_c U>
constexpr U inverse(T n, U mod) {
  auto [g, x] = inv_gcd(U(n % mod), mod);
  assert(g == 1);
  return x;
}

}  // namespace tifa_libs::math


#line 6 "src/code/math/mint.hpp"

namespace tifa_libs::math {

template <class D, uint_c Rt>
class mint {
  constexpr D const &d() const { return static_cast<D const &>(*this); }
  constexpr D &d() { return static_cast<D &>(*this); }

 protected:
  Rt v_{};

 public:
  constexpr mint() {}
  template <int_c T>
  constexpr mint(T v) : v_(D::mod_(v)) {}
  constexpr operator D() { return d(); }

  using raw_type = Rt;
  using sraw_type = to_sint_t<Rt>;
  static constexpr raw_type mod() { return D::mod_(); }
  static constexpr sraw_type smod() { return (sraw_type)D::mod_(); }
  constexpr raw_type val() const { return d().val_(); }
  constexpr sraw_type sval() const { return (sraw_type)d().val_(); }
  constexpr raw_type &data() { return d().data_(); }

  template <int_c T>
  explicit constexpr operator T() const { return (T)val(); }
  constexpr mint &operator+=(mint const &r) { return d().adde_(r.d()); }
  constexpr mint &operator-=(mint const &r) { return d().sube_(r.d()); }
  constexpr mint &operator*=(mint const &r) { return d().mule_(r.d()); }
  constexpr mint &operator/=(mint const &r) { return *this = *this * r.inv(); }
  constexpr mint const &operator+() const { return *this; }
  constexpr mint operator-() const { return d().neg_(); }
  constexpr mint inv() const { return inverse(val(), mod()); }
  friend constexpr mint operator+(mint l, mint const &r) { return l += r; }
  friend constexpr mint operator-(mint l, mint const &r) { return l -= r; }
  friend constexpr mint operator*(mint l, mint const &r) { return l *= r; }
  friend constexpr mint operator/(mint l, mint const &r) { return l /= r; }
  friend constexpr bool operator==(mint const &l, mint const &r) { return l.val() == r.val(); }
  friend constexpr auto operator<=>(mint const &l, mint const &r) { return l.sval() - r.sval(); }
  friend std::istream &operator>>(std::istream &is, mint &x) {
    i64 _;
    is >> _;
    x = mint(_);
    return is;
  }
  friend std::ostream &operator<<(std::ostream &os, mint const &x) { return os << x.val(); }
  friend constexpr mint abs(mint const &x) { return x.val(); }
};

}  // namespace tifa_libs::math


#line 5 "src/code/math/mint_s63.hpp"

namespace tifa_libs::math {

template <u64 MOD>
class mint_s63 : public mint<mint_s63<MOD>, u64> {
  using base = mint<mint_s63<MOD>, u64>;
  friend base;

  static constexpr u64 R = []() {
    u64 t = 2, iv = MOD * (t - MOD * MOD);
    iv *= t - MOD * iv, iv *= t - MOD * iv, iv *= t - MOD * iv;
    return iv * (t - MOD * iv);
  }();
  static constexpr u64 R2 = []() {
    u64 iv = -MOD % MOD;
    for (u32 i = 0; i != 64; ++i)
      if ((iv *= 2) >= MOD) iv -= MOD;
    return iv;
  }();

  static_assert(MOD & 1);
  static_assert(R * MOD == 1);
  static_assert((MOD >> 63) == 0);
  static_assert(MOD != 1);

  static constexpr u64 mulh(u64 x, u64 y) {
    u64 a = x >> 32, b = (u32)(x), c = y >> 32, d = (u32)(y), ad = a * d, bc = b * c;
    return a * c + (ad >> 32) + (bc >> 32) + (((ad & 0xFFFFFFFF) + (bc & 0xFFFFFFFF) + (b * d >> 32)) >> 32);
  }
  static constexpr u64 redc_mul(u64 x, u64 y) {
    u64 res = mulh(x, y) - mulh(x * y * R, MOD);
    return res + (MOD & -(res >> 63));
  }
  static constexpr u64 norm(i64 x) { return (u64)x + (MOD & -(x < 0)); }

 public:
  static constexpr bool FIXED_MOD = true;
  constexpr mint_s63() {}
  template <int_c T>
  constexpr mint_s63(T v) { this->v_ = mod_(v); }

 private:
  using raw_t = typename base::raw_type;
  using sraw_t = typename base::sraw_type;
  template <int_c T>
  static constexpr raw_t mod_(T v) { return redc_mul(norm(v % (std::conditional_t<sint_c<T>, i64, u64>)mod_()), R2); }
  static constexpr raw_t mod_() { return MOD; }
  constexpr raw_t val_() const {
    raw_t res = -mulh(this->v_ * R, mod_());
    return res + (MOD & -(res >> 63));
  }
  constexpr raw_t &data_() { return this->v_; }

  constexpr mint_s63 neg_() const {
    mint_s63 res;
    res.v_ = (MOD & -(this->v_ != 0)) - this->v_;
    return res;
  }
  constexpr mint_s63 &adde_(mint_s63 const &r) {
    this->v_ += r.v_ - MOD, this->v_ += MOD & -(this->v_ >> 63);
    return *this;
  }
  constexpr mint_s63 &sube_(mint_s63 const &r) {
    this->v_ -= r.v_, this->v_ += MOD & -(this->v_ >> 63);
    return *this;
  }
  constexpr mint_s63 &mule_(mint_s63 const &r) {
    this->v_ = redc_mul(this->v_, r.v_);
    return *this;
  }
};

}  // namespace tifa_libs::math


#line 1 "src/code/poly/polymtt.hpp"



#line 1 "src/code/conv/conv_mtt.hpp"



#line 1 "src/code/conv/conv_naive.hpp"



#line 5 "src/code/conv/conv_naive.hpp"

namespace tifa_libs::math {

template <class U, class T = U>
requires(sizeof(U) <= sizeof(T))
constexpr vec<T> conv_naive(vec<U> const &l, vec<U> const &r, u32 ans_size = 0) {
  if (l.empty() || r.empty()) return {};
  if (!ans_size) ans_size = u32(l.size() + r.size() - 1);
  u32 n = (u32)l.size(), m = (u32)r.size();
  vec<T> ans(ans_size);
  if (n < m)
    for (u32 j = 0; j < m; ++j)
      for (u32 i = 0; i < n; ++i) {
        if (i + j >= ans_size) break;
        ans[i + j] += (T)l[i] * (T)r[j];
      }
  else
    for (u32 i = 0; i < n; ++i)
      for (u32 j = 0; j < m; ++j) {
        if (i + j >= ans_size) break;
        ans[i + j] += (T)l[i] * (T)r[j];
      }
  return ans;
}

}  // namespace tifa_libs::math


#line 1 "src/code/conv/fft.hpp"



#line 5 "src/code/conv/fft.hpp"

namespace tifa_libs::math {

template <std::floating_point FP>
struct FFT {
  using C = std::complex<FP>;
  using data_t = C;

  explicit constexpr FFT() : rev(), w() {}

  constexpr u32 size() const { return (u32)rev.size(); }
  constexpr void bzr(u32 len) {
    u32 n = std::max<u32>(std::bit_ceil(len), 2);
    if (n == size()) return;
    rev.resize(n, 0);
    u32 k = (u32)(std::bit_width(n) - 1);
    for (u32 i = 0; i < n; ++i) rev[i] = (rev[i / 2] / 2) | ((i & 1) << (k - 1));
    w.resize(n);
    w[0].real(1);
    for (u32 i = 1; i < n; ++i) w[i] = {std::cos(TAU * (FP)i / (FP)n), std::sin(TAU * (FP)i / (FP)n)};
  }

  constexpr void dif(vec<C> &f, u32 n = 0) const {
    if (!n) n = size();
    if (f.size() < n) f.resize(n);
    assert(n <= size());
    for (u32 i = 0; i < n; ++i)
      if (i < rev[i]) std::swap(f[rev[i]], f[i]);
#pragma GCC diagnostic ignored "-Wsign-conversion"
    for (u32 i = 2, d = n / 2; i <= n; i *= 2, d /= 2)
      for (u32 j = 0; j < n; j += i) {
        auto l = f.begin() + j, r = f.begin() + j + i / 2;
        auto p = w.begin();
        for (u32 k = 0; k < i / 2; ++k, ++l, ++r, p += d) {
          C tmp = *r * *p;
          *r = *l - tmp;
          *l = *l + tmp;
        }
      }
#pragma GCC diagnostic warning "-Wsign-conversion"
  }
  constexpr void dit(vec<C> &f, u32 n = 0) const {
    if (!n) n = size();
    dif(f, n);
    for (u32 i = 0; i < n; ++i) f[i] /= (FP)n;
  }

 private:
  const FP TAU = std::acos((FP)-1.) * 2;

  vecu rev;
  vec<C> w;
};

}  // namespace tifa_libs::math


#line 6 "src/code/conv/conv_mtt.hpp"

namespace tifa_libs::math {

template <class mint, class FP>
constexpr vec<mint> conv_mtt(FFT<FP> &fft, vec<mint> const &l, vec<mint> const &r, u32 ans_size = 0) {
  if (!ans_size) ans_size = u32(l.size() + r.size() - 1);
  if (ans_size < 32) return conv_naive(l, r, ans_size);
  using C = typename FFT<FP>::C;
  if (l.size() == 1) {
    vec<mint> ans = r;
    ans.resize(ans_size);
    for (auto &i : ans) i *= l[0];
    return ans;
  }
  if (r.size() == 1) {
    vec<mint> ans = l;
    ans.resize(ans_size);
    for (auto &i : ans) i *= r[0];
    return ans;
  }
  fft.bzr(std::max({(u32)l.size(), (u32)r.size(), std::min(u32(l.size() + r.size() - 1), ans_size)}));
  u32 n = fft.size();
  const int OFS = ((int)sizeof(decltype(mint::mod())) * 8 - std::countl_zero(mint::mod() - 1) + 1) / 2;
  const u32 MSK = ((1u << OFS) - 1);
  vec<mint> ans(ans_size);
  vec<C> a(n), b(n);
  for (u32 i = 0; i < l.size(); ++i) a[i] = {(FP)(l[i].val() & MSK), (FP)(l[i].val() >> OFS)};
  for (u32 i = 0; i < r.size(); ++i) b[i] = {(FP)(r[i].val() & MSK), (FP)(r[i].val() >> OFS)};
  fft.dif(a);
  fft.dif(b);
  {
    vec<C> p(n), q(n);
    for (u32 i = 0, j; i < n; ++i) {
      j = (n - i) & (n - 1);
      C da = (a[i] + std::conj(a[j])) * C(.5, 0), db = (a[i] - std::conj(a[j])) * C(0, -.5), dc = (b[i] + std::conj(b[j])) * C(.5, 0), dd = (b[i] - std::conj(b[j])) * C(.5, 0);
      p[j] = da * dc + da * dd;
      q[j] = db * dc + db * dd;
    }
    a = p;
    b = q;
  }
  fft.dif(a);
  fft.dif(b);
  for (u32 i = 0; i < ans_size; ++i) {
    i64 da = (i64)(a[i].real() / (FP)n + .5) % mint::smod(), db = (i64)(a[i].imag() / (FP)n + .5) % mint::smod(), dc = (i64)(b[i].real() / (FP)n + .5) % mint::smod(), dd = (i64)(b[i].imag() / (FP)n + .5) % mint::smod();
    ans[i] = da + ((db + dc) << OFS) % mint::smod() + (dd << (OFS * 2)) % mint::smod();
  }
  return ans;
}

}  // namespace tifa_libs::math


#line 6 "src/code/poly/polymtt.hpp"

namespace tifa_libs::math {
namespace polymtt_impl_ {
template <class FP = f64>
struct cconv_mtt : public FFT<FP> {
  static constexpr auto ct_cat = ct_FFT;
  template <class mint>
  constexpr void conv(vec<mint>& l, vec<mint> const& r, u32 sz = 0) { l = conv_mtt(*this, l, r, sz); }
};
}  // namespace polymtt_impl_

template <class mint, class FP = f64>
using polymtt = poly<mint, polymtt_impl_::cconv_mtt<FP>>;

}  // namespace tifa_libs::math


#line 11 "src/test_cpverifier/library-checker/pow_of_formal_power_series.pmtt-s63.test.cpp"

using mint = tifa_libs::math::mint_s63<MOD>;
using poly = tifa_libs::math::polymtt<mint>;

int main() {
  u32 n;
  u64 m;
  tifa_libs::fin >> n >> m;
  poly a(n);
  tifa_libs::fin >> a.data();
  tifa_libs::fout << tifa_libs::math::pow_fps(a, m).data() << '\n';
  return 0;
}

Test cases

Env Name Status Elapsed Memory
g++-12 M_zero_00 :heavy_check_mark: AC 23 ms 13 MB
g++-12 M_zero_01 :heavy_check_mark: AC 24 ms 14 MB
g++-12 all_zero_00 :heavy_check_mark: AC 20 ms 12 MB
g++-12 all_zero_01 :heavy_check_mark: AC 22 ms 14 MB
g++-12 binary_exp_max_00 :heavy_check_mark: AC 9589 ms 154 MB
g++-12 example_00 :heavy_check_mark: AC 9 ms 6 MB
g++-12 example_01 :heavy_check_mark: AC 8 ms 6 MB
g++-12 example_02 :heavy_check_mark: AC 9 ms 6 MB
g++-12 hack_00 :heavy_check_mark: AC 8 ms 6 MB
g++-12 lower_deg_zero2_00 :heavy_check_mark: AC 9585 ms 158 MB
g++-12 lower_deg_zero2_01 :heavy_check_mark: AC 9615 ms 157 MB
g++-12 lower_deg_zero2_02 :heavy_check_mark: AC 10378 ms 159 MB
g++-12 lower_deg_zero2_03 :heavy_check_mark: AC 9681 ms 158 MB
g++-12 lower_deg_zero_00 :heavy_check_mark: AC 25 ms 15 MB
g++-12 lower_deg_zero_01 :heavy_check_mark: AC 26 ms 15 MB
g++-12 lower_deg_zero_02 :heavy_check_mark: AC 23 ms 14 MB
g++-12 lower_deg_zero_03 :heavy_check_mark: AC 24 ms 15 MB
g++-12 lower_deg_zero_04 :heavy_check_mark: AC 25 ms 15 MB
g++-12 lower_deg_zero_05 :heavy_check_mark: AC 25 ms 15 MB
g++-12 lower_deg_zero_06 :heavy_check_mark: AC 26 ms 15 MB
g++-12 lower_deg_zero_07 :heavy_check_mark: AC 24 ms 15 MB
g++-12 max_random_00 :heavy_check_mark: AC 9509 ms 154 MB
g++-12 max_random_01 :heavy_check_mark: AC 9888 ms 155 MB
g++-12 max_random_02 :heavy_check_mark: AC 10015 ms 155 MB
g++-12 monomial_00 :heavy_check_mark: AC 23 ms 14 MB
g++-12 monomial_01 :heavy_check_mark: AC 23 ms 14 MB
g++-12 monomial_02 :heavy_check_mark: AC 22 ms 14 MB
g++-12 monomial_03 :heavy_check_mark: AC 23 ms 14 MB
g++-12 monomial_ans_low_deg_00 :heavy_check_mark: AC 8321 ms 150 MB
g++-12 monomial_ans_low_deg_01 :heavy_check_mark: AC 8936 ms 154 MB
g++-12 monomial_ans_low_deg_02 :heavy_check_mark: AC 622 ms 24 MB
g++-12 monomial_ans_low_deg_03 :heavy_check_mark: AC 10728 ms 155 MB
g++-12 overflow_killer_00 :heavy_check_mark: AC 9 ms 6 MB
g++-12 overflow_killer_01 :heavy_check_mark: AC 8 ms 6 MB
g++-12 random_00 :heavy_check_mark: AC 8385 ms 150 MB
g++-12 random_01 :heavy_check_mark: AC 10800 ms 150 MB
g++-12 random_02 :heavy_check_mark: AC 624 ms 24 MB
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