Tifa's CP Library

:heavy_check_mark: src/test_cpverifier/library-checker/shift_of_sampling_points_of_polynomial.pntt-ss.test.cpp

Depends on

Code

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

#include "../../code/poly/ctsh_fps.hpp"

constexpr u32 MOD = 998244353;

#include "../../code/math/mint_ss.hpp"
#include "../../code/poly/polyntt.hpp"

using mint = tifa_libs::math::mint_ss<MOD>;
using poly = tifa_libs::math::polyntt<mint>;

int main() {
  std::ios::sync_with_stdio(false);
  std::cin.tie(nullptr);
  u32 n, m, c;
  std::cin >> n >> m >> c;
  poly a(n);
  std::cin >> a;
  std::cout << tifa_libs::math::ctsh_fps(a, mint(c), m) << '\n';
  return 0;
}
#line 1 "src/test_cpverifier/library-checker/shift_of_sampling_points_of_polynomial.pntt-ss.test.cpp"
#define AUTO_GENERATED
#define PROBLEM "https://judge.yosupo.jp/problem/shift_of_sampling_points_of_polynomial"

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



#line 1 "src/code/comb/gen_ifact.hpp"



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

namespace tifa_libs::math {

constexpr u64 mul_mod_u(u64 a, u64 b, u64 mod) {
  if (std::bit_width(a) + std::bit_width(b) <= 64) return a * b % mod;
  else return (u64)((u128)a * b % mod);
}

}  // namespace tifa_libs::math


#line 1 "src/code/comb/gen_inv.hpp"



#line 5 "src/code/comb/gen_inv.hpp"

namespace tifa_libs::math {

// i^{-1} from i=0..n-1
constexpr vecu64 gen_inv(u32 n, u64 mod) {
  if (n == 0) return {};
  if (n == 1) return {1};
  vecu64 ans(n);
  ans[0] = ans[1] = 1;
  for (u32 i = 2; i < n; ++i) ans[i] = mul_mod_u(mod - mod / i, ans[mod % i], mod);
  return ans;
}
// i^{-1} from i=0..n-1
template <class mint>
constexpr vec<mint> gen_inv(u32 n) {
  vec<mint> ans(n);
  auto _ = gen_inv(n, mint::mod());
  for (u32 i = 0; i < n; ++i) ans[i] = _[i];
  return ans;
}

}  // namespace tifa_libs::math


#line 6 "src/code/comb/gen_ifact.hpp"

namespace tifa_libs::math {

// (i!)^{-1} from i=0..n-1
constexpr vecu64 gen_ifact(u32 n, u64 mod, vecu64 inv) {
  for (u32 i = 2; i < n; ++i) inv[i] = mul_mod_u(inv[i], inv[i - 1], mod);
  return inv;
}
// (i!)^{-1} from i=0..n-1
constexpr vecu64 gen_ifact(u32 n, u64 mod) { return gen_ifact(n, mod, gen_inv(n, mod)); }
// (i!)^{-1} from i=0..n-1
template <class mint>
constexpr vec<mint> gen_ifact(u32 n, vec<mint> inv) {
  for (u32 i = 2; i < n; ++i) inv[i] *= inv[i - 1];
  return inv;
}
// (i!)^{-1} from i=0..n-1
template <class mint>
constexpr vec<mint> gen_ifact(u32 n) { return gen_ifact(n, gen_inv<mint>(n)); }

}  // namespace tifa_libs::math


#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 6 "src/code/poly/ctsh_fps.hpp"

namespace tifa_libs::math {

template <class mint, class ccore>
constexpr poly<mint, ccore> ctsh_fps(poly<mint, ccore> const &f, mint c, vecu64 const &ifact, u32 m = 0) {
  using poly_t = poly<mint, ccore>;
  u32 n = f.size(), k = f.size() - 1;
  if (!m) m = n;
  u64 t = c.val();
  if (t <= k) {
    poly_t ret(m);
    u32 ptr = 0;
    for (u32 i = (u32)t; i <= k && ptr < m; ++i) ret[ptr++] = f[i];
    if (k + 1 < t + m) {
      auto suf = ctsh_fps<mint, ccore>(f, k + 1, ifact, m - ptr);
      for (u32 i = k + 1; i < t + m; ++i) ret[ptr++] = suf[i - (k + 1)];
    }
    return ret;
  }
  if (t + m > mint::mod()) {
    auto pref = ctsh_fps<mint, ccore>(f, t, ifact, u32(mint::mod() - t)), suf = ctsh_fps<mint, ccore>(f, 0, ifact, m - pref.size());
    std::ranges::copy(suf.data(), std::back_inserter(pref.data()));
    return pref;
  }
  poly_t d(k + 1);
  for (u32 i = 0; i <= k; ++i) {
    d[i] = ifact[i], (d[i] *= ifact[k - i]) *= f[i];
    if ((k - i) & 1) d[i] = -d[i];
  }
  poly_t h(m + k);
  for (u32 i = 0; i < m + k; ++i) h[i] = mint(t - k + i).inv();
  auto dh = d * h;
  poly_t ret(m);
  mint cur = t;
  for (u32 i = 1; i <= k; ++i) cur *= t - i;
  for (u32 i = 0; i < m; ++i) {
    ret[i] = cur * dh[k + i];
    (cur *= t + i + 1) *= h[i];
  }
  return ret;
}
template <class mint, class ccore>
constexpr poly<mint, ccore> ctsh_fps(poly<mint, ccore> const &f, mint c, u32 m = 0) { return ctsh_fps<mint, ccore>(f, c, gen_ifact(f.size(), mint::mod()), m); }

}  // namespace tifa_libs::math


#line 5 "src/test_cpverifier/library-checker/shift_of_sampling_points_of_polynomial.pntt-ss.test.cpp"

constexpr u32 MOD = 998244353;

#line 1 "src/code/math/mint_ss.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 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 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_ss.hpp"

namespace tifa_libs::math {

template <u32 MOD>
class mint_ss : public mint<mint_ss<MOD>, u32> {
  using base = mint<mint_ss<MOD>, u32>;
  friend base;
  static_assert(MOD >= 1);

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

 private:
  using raw_t = typename base::raw_type;
  using sraw_t = typename base::sraw_type;
  template <sint_c T>
  static constexpr raw_t mod_(T v) {
    i64 x = i64(v % (i64)mod_());
    return raw_t(x + (x < 0 ? mod_() : 0));
  }
  template <uint_c T>
  static constexpr raw_t mod_(T v) { return raw_t(v % mod_()); }
  static constexpr raw_t mod_() { return MOD; }
  constexpr raw_t val_() const { return this->v_; }
  constexpr raw_t &data_() { return this->v_; }

  constexpr mint_ss neg_() const { return -(sraw_t)val_(); }
  constexpr mint_ss &adde_(mint_ss const &r) {
    data_() += r.val_();
    if (val_() >= mod_()) data_() -= mod_();
    return *this;
  }
  constexpr mint_ss &sube_(mint_ss const &r) {
    data_() -= r.val_();
    if (val_() >= mod_()) data_() += mod_();
    return *this;
  }
  constexpr mint_ss &mule_(mint_ss const &r) {
    data_() = u32((u64)val_() * r.val_() % mod_());
    return *this;
  }
};

}  // namespace tifa_libs::math


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



#line 1 "src/code/conv/conv_dft.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/dft_traits.hpp"



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

namespace tifa_libs {

template <class T>
concept dft_c = requires(T x, vec<typename T::data_t> v, u32 n) {
  { x.size() } -> std::same_as<u32>;
  x.bzr(n);
  x.dif(v, n);
  x.dit(v, n);
};

template <class T>
concept ntt_c = dft_c<T> && requires(T x) {
  T::max_size;
  T::G;
};

}  // namespace tifa_libs


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

namespace tifa_libs::math {

template <dft_c DFT_t, std::same_as<typename DFT_t::data_t> DFT_data_t>
constexpr vec<DFT_data_t> conv_dft(DFT_t &dft, vec<DFT_data_t> l, vec<DFT_data_t> 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);
  dft.bzr(std::max({(u32)l.size(), (u32)r.size(), std::min(u32(l.size() + r.size() - 1), ans_size)}));
  dft.dif(l);
  dft.dif(r);
  for (u32 i = 0; i < dft.size(); ++i) l[i] *= r[i];
  dft.dit(l);
  l.resize(ans_size);
  return l;
}
template <class DFT_t, class mint, class T = u64>
constexpr vec<mint> conv_dft_u64(DFT_t &dft, vec<T> const &l, vec<T> const &r, u32 ans_size = 0) {
  if (!ans_size) ans_size = u32(l.size() + r.size() - 1);
  vec<mint> l_, r_;
  l_.reserve(l.size());
  r_.reserve(r.size());
  for (auto i : l) l_.push_back(i);
  for (auto i : r) r_.push_back(i);
  return conv_dft(dft, l_, r_, ans_size);
}

}  // namespace tifa_libs::math


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



#line 1 "src/code/bit/lowbit.hpp"



#line 5 "src/code/bit/lowbit.hpp"

namespace tifa_libs::bit {

template <class T>
constexpr T lowbit(T x) { return T(1) << std::countr_zero(x); }

}  // namespace tifa_libs::bit


#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/nt/proot_u64.hpp"



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



#line 1 "src/code/rand/gen.hpp"



#line 5 "src/code/rand/gen.hpp"

namespace tifa_libs::rand {

template <class Distri>
class Gen {
  std::conditional_t<sizeof(typename Distri::result_type) <= 4, std::mt19937, std::mt19937_64> re;
  Distri dist;

 public:
  using random_engine = decltype(re);
  using distribution = Distri;
  using result_type = typename Distri::result_type;

  constexpr Gen() : re(std::random_device{}()), dist() {}
  constexpr Gen(result_type a, result_type b) : re(std::random_device{}()), dist(a, b) {}

  constexpr void set_range(result_type a, result_type b) { dist = Distri(a, b); }
  constexpr random_engine& rand_eng() { return re; }
  constexpr Distri& distrib() { return dist; }

  void reset_seed() { re.seed((result_type)std::chrono::duration_cast<std::conditional_t<sizeof(typename Distri::result_type) <= 4, std::chrono::seconds, std::chrono::nanoseconds>>(std::chrono::high_resolution_clock::now().time_since_epoch()).count()); }
  constexpr result_type operator()() { return dist(re); }
  result_type next() { return dist(re); }
};

}  // namespace tifa_libs::rand


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



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



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

namespace tifa_libs::math {

constexpr u64 qpow_mod(u64 a, u64 b, u64 mod) {
  u64 res(1);
  for (a %= mod; b; b >>= 1, a = mul_mod_u(a, a, mod))
    if (b & 1) res = mul_mod_u(res, a, mod);
  return res;
}

}  // namespace tifa_libs::math


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

namespace tifa_libs::math {

constexpr bool is_prime(u64 n) {
  if (n <= 2) return n == 2;
  if (~n & 1) return false;
  if (n < 8 || n == 61) return true;

  auto f = [n, d = (n - 1) >> std::countr_zero(n - 1)](auto const& bases) -> bool {
    for (u64 i : bases) {
      if (!(i % n)) continue;
      u64 t = d, y = qpow_mod(i, t, n);
      while (t != n - 1 && y != 1 && y != n - 1) {
        y = mul_mod_u(y, y, n);
        t *= 2;
      }
      if (y != n - 1 && (~t & 1)) return false;
    }
    return true;
  };

  if (n < (1 << 30)) {
    constexpr u64 bases[3] = {2, 7, 61};
    return f(bases);
  }
  constexpr u64 bases[7] = {2, 325, 9375, 28178, 450775, 9780504, 1795265022};
  return f(bases);
}

}  // namespace tifa_libs::math


#line 7 "src/code/nt/pfactors.hpp"

namespace tifa_libs::math {
namespace pfactors_impl_ {
class PollardRho {
  rand::Gen<std::uniform_int_distribution<u64>> e;

  constexpr u64 rho(u64 n) {
    e.set_range(2, n - 1);
    auto f = [n, r = e()](u64 x) { return (mul_mod_u(x, x, n) + r) % n; };
    u64 g = 1, x = 0, y = e(), yy = 0;
    const u32 LIM = 128;
    for (u64 r = 1, q = 1; g == 1; r *= 2) {
      x = y;
      for (u64 i = 0; i < r; ++i) y = f(y);
      for (u64 k = 0; g == 1 && k < r; k += LIM) {
        yy = y;
        for (u64 i = 0; i < LIM && i < r - k; ++i) q = mul_mod_u(q, (x + (n - (y = f(y)))) % n, n);
        g = std::gcd(q, n);
      }
    }
    if (g == n) do {
        g = std::gcd((x + (n - (yy = f(yy)))) % n, n);
      } while (g == 1);
    return g == n ? rho(n) : g;
  }

 public:
  explicit constexpr PollardRho() : e() {}

  constexpr void operator()(u64 n, std::map<u64, u32> &ans) {
    if (n < 2) return;
    if (is_prime(n)) {
      ++ans[n];
      return;
    }
    auto g = rho(n);
    (*this)(n / g, ans);
    (*this)(g, ans);
  }
};
}  // namespace pfactors_impl_

inline std::map<u64, u32> pfactors(u64 n) {
  std::map<u64, u32> ans;
  if (n < 2) return ans;
  if (~n & 1) n >>= (ans[2] = (u32)std::countr_zero(n));
  pfactors_impl_::PollardRho()(n, ans);
  return ans;
}

}  // namespace tifa_libs::math


#line 1 "src/code/nt/proot_u32.hpp"



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



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

namespace tifa_libs::math {

constexpr u32 isqrt(u64 x) {
  if (!x) return 0;
  int c = i32(std::bit_width(x) - 1) / 2, sh = 31 - c;
  u32 u = [](u64 x) {
    constexpr u8 TAB[192] = {128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 144, 145, 146, 147, 148, 149, 150, 151, 151, 152, 153, 154, 155, 156, 156, 157, 158, 159, 160, 160, 161, 162, 163, 164, 164, 165, 166, 167, 167, 168, 169, 170, 170, 171, 172, 173, 173, 174, 175, 176, 176, 177, 178, 179, 179, 180, 181, 181, 182, 183, 183, 184, 185, 186, 186, 187, 188, 188, 189, 190, 190, 191, 192, 192, 193, 194, 194, 195, 196, 196, 197, 198, 198, 199, 200, 200, 201, 201, 202, 203, 203, 204, 205, 205, 206, 206, 207, 208, 208, 209, 210, 210, 211, 211, 212, 213, 213, 214, 214, 215, 216, 216, 217, 217, 218, 219, 219, 220, 220, 221, 221, 222, 223, 223, 224, 224, 225, 225, 226, 227, 227, 228, 228, 229, 229, 230, 230, 231, 232, 232, 233, 233, 234, 234, 235, 235, 236, 237, 237, 238, 238, 239, 239, 240, 240, 241, 241, 242, 242, 243, 243, 244, 244, 245, 246, 246, 247, 247, 248, 248, 249, 249, 250, 250, 251, 251, 252, 252, 253, 253, 254, 254, 255, 255, 255};
    u32 u = TAB[(x >> 56) - 64];
    u = (u << 7) + (u32)(x >> 41) / u;
    return (u << 15) + (u32)((x >> 17) / u);
  }(x << 2 * sh);
  u >>= sh;
  u -= (u64)u * u > x;
  return u;
}

}  // namespace tifa_libs::math


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



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

namespace tifa_libs::math {

template <std::unsigned_integral T, class It>
constexpr bool is_proot(T g, T m, It pf_begin, It pf_end) {
  if (!g) return false;
  for (; pf_begin != pf_end; ++pf_begin)
    if (qpow_mod(g, (m - 1) / *pf_begin, m) == 1) return false;
  return true;
}

}  // namespace tifa_libs::math


#line 6 "src/code/nt/proot_u32.hpp"

namespace tifa_libs::math {

constexpr u32 proot(u32 m) {
  if (m == 2) return 1;
  if (m == 3 || m == 5) return 2;
  if (m == 104857601 || m == 167772161 || m == 469762049) return 3;
  if (m == 754974721) return 11;
  if (m == 998244353 || m == 1004535809) return 3;
  u32 divs[20] = {2};
  u32 cnt = 1, x = (m - 1) / 2;
  x >>= std::countr_zero(x);
  for (u32 i = 3, ed_ = isqrt(x); i <= ed_; i += 2)
    if (x % i == 0) {
      divs[cnt++] = i;
      while (x % i == 0) x /= i;
    }
  if (x > 1) divs[cnt++] = x;
  for (u32 g = 2;; ++g)
    if (is_proot(g, m, divs, divs + cnt)) return g;
}

}  // namespace tifa_libs::math


#line 6 "src/code/nt/proot_u64.hpp"

namespace tifa_libs::math {

inline u64 proot(u64 m) {
  if (m <= (u64)-1_u32) return proot((u32)m);
  vecu64 pf;
  {
    auto _ = pfactors(m - 1);
    pf.reserve(_.size());
    for (auto [k, v] : _) pf.push_back(k);
  }
  u64 g = 2;
  for (;; ++g)
    if (is_proot(g, m, pf.begin(), pf.end())) break;
  return g;
}

}  // namespace tifa_libs::math


#line 7 "src/code/conv/ntt.hpp"

namespace tifa_libs::math {

template <class mint>
struct NTT {
  using data_t = mint;

  static_assert(is_prime(mint::mod()) && (mint::mod() & 3) == 1, "MOD must be prime with 4k+1");
  static constexpr u64 max_size = bit::lowbit(mint::mod() - 1);

  const mint G = proot(mint::mod());

  explicit constexpr NTT() : root() {}

  constexpr u32 size() const { return (u32)root.size(); }
  constexpr void bzr(u32 len = max_size) {
    u32 n = std::bit_ceil(len);
    assert(n <= max_size);
    if (n == size()) return;
    root.resize(n);
    root[0] = 1;
    mint w = qpow(G, (mint::mod() - 1) / n);
    for (u32 i = 1; i < n; ++i) root[i] = root[i - 1] * w;
  }

#pragma GCC diagnostic ignored "-Wsign-conversion"
  constexpr void dif(vec<mint> &f, u32 n = 0) const {
    assert(size());
    if (!n) n = size();
    if (f.size() < n) f.resize(n);
    assert(std::has_single_bit(n) && n <= size());
    for (u32 i = n / 2, d = 1; i; i /= 2, d *= 2)
      for (u32 j = 0; j < n; j += i * 2) {
        auto w = root.begin();
        mint u, t;
        for (u32 k = 0; k < i; ++k, w += d) {
          f[j | k] = (u = f[j | k]) + (t = f[i | j | k]);
          f[i | j | k] = (u - t) * (*w);
        }
      }
  }
  constexpr void dit(vec<mint> &f, u32 n = 0) const {
    assert(size());
    if (!n) n = size();
    if (f.size() < n) f.resize(n);
    assert(std::has_single_bit(n) && n <= size());
    for (u32 i = 1, d = n / 2; d; i *= 2, d /= 2)
      for (u32 j = 0; j < n; j += i * 2) {
        auto w = root.begin();
        mint t;
        for (u32 k = 0; k < i; ++k, w += d) {
          f[i | j | k] = f[j | k] - (t = f[i | j | k] * (*w));
          f[j | k] += t;
        }
      }
    std::reverse(f.begin() + 1, f.end());
    mint t = mint(n).inv();
    for (u32 i = 0; i < n; ++i) f[i] *= t;
  }
#pragma GCC diagnostic warning "-Wsign-conversion"

 private:
  vec<mint> root;
};

}  // namespace tifa_libs::math


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

namespace tifa_libs::math {
namespace polyntt_impl_ {
template <class mint>
struct cconv_ntt : public NTT<mint> {
  static constexpr auto ct_cat = ct_NTT;
  constexpr void conv(vec<mint> &l, vec<mint> const &r, u32 sz = 0) { l = conv_dft(*this, l, r, sz); }
};
}  // namespace polyntt_impl_

template <class mint>
using polyntt = poly<mint, polyntt_impl_::cconv_ntt<mint>>;

}  // namespace tifa_libs::math


#line 10 "src/test_cpverifier/library-checker/shift_of_sampling_points_of_polynomial.pntt-ss.test.cpp"

using mint = tifa_libs::math::mint_ss<MOD>;
using poly = tifa_libs::math::polyntt<mint>;

int main() {
  std::ios::sync_with_stdio(false);
  std::cin.tie(nullptr);
  u32 n, m, c;
  std::cin >> n >> m >> c;
  poly a(n);
  std::cin >> a;
  std::cout << tifa_libs::math::ctsh_fps(a, mint(c), m) << '\n';
  return 0;
}

Test cases

Env Name Status Elapsed Memory
g++-12 N_1_00 :heavy_check_mark: AC 110 ms 12 MB
g++-12 c_0_00 :heavy_check_mark: AC 268 ms 28 MB
g++-12 example_00 :heavy_check_mark: AC 9 ms 4 MB
g++-12 example_01 :heavy_check_mark: AC 8 ms 4 MB
g++-12 max_random_00 :heavy_check_mark: AC 551 ms 46 MB
g++-12 max_random_01 :heavy_check_mark: AC 529 ms 46 MB
g++-12 max_random_02 :heavy_check_mark: AC 570 ms 46 MB
g++-12 max_random_03 :heavy_check_mark: AC 545 ms 46 MB
g++-12 medium_random_00 :heavy_check_mark: AC 15 ms 4 MB
g++-12 medium_random_01 :heavy_check_mark: AC 14 ms 4 MB
g++-12 medium_random_02 :heavy_check_mark: AC 14 ms 4 MB
g++-12 medium_random_03 :heavy_check_mark: AC 14 ms 4 MB
g++-12 small_random_00 :heavy_check_mark: AC 8 ms 4 MB
g++-12 small_random_01 :heavy_check_mark: AC 8 ms 4 MB
g++-12 small_random_02 :heavy_check_mark: AC 9 ms 4 MB
g++-12 small_random_03 :heavy_check_mark: AC 9 ms 4 MB
g++-12 type0_random_00 :heavy_check_mark: AC 41 ms 8 MB
g++-12 type0_random_01 :heavy_check_mark: AC 44 ms 9 MB
g++-12 type0_random_02 :heavy_check_mark: AC 13 ms 4 MB
g++-12 type0_random_03 :heavy_check_mark: AC 47 ms 9 MB
g++-12 type1_random_00 :heavy_check_mark: AC 467 ms 43 MB
g++-12 type1_random_01 :heavy_check_mark: AC 420 ms 43 MB
g++-12 type1_random_02 :heavy_check_mark: AC 30 ms 7 MB
g++-12 type1_random_03 :heavy_check_mark: AC 217 ms 30 MB
g++-12 type2_random_00 :heavy_check_mark: AC 484 ms 42 MB
g++-12 type2_random_01 :heavy_check_mark: AC 488 ms 44 MB
g++-12 type2_random_02 :heavy_check_mark: AC 116 ms 15 MB
g++-12 type2_random_03 :heavy_check_mark: AC 213 ms 28 MB
g++-12 type3_random_00 :heavy_check_mark: AC 250 ms 27 MB
g++-12 type3_random_01 :heavy_check_mark: AC 511 ms 43 MB
g++-12 type3_random_02 :heavy_check_mark: AC 133 ms 13 MB
g++-12 type3_random_03 :heavy_check_mark: AC 218 ms 27 MB
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