Tifa's CP Library

:heavy_check_mark: src/test_cpverifier/aizu/ntl_2_c.test.cpp

Depends on

Code

#define PROBLEM "https://onlinejudge.u-aizu.ac.jp/courses/library/6/NTL/all/NTL_2_C"

#include "../../code/math/mpi.hpp"

int main() {
  std::ios::sync_with_stdio(false);
  std::cin.tie(nullptr);
  tifa_libs::math::mpi a, b;
  std::cin >> a >> b;
  std::cout << a * b << '\n';
  return 0;
}
#line 1 "src/test_cpverifier/aizu/ntl_2_c.test.cpp"
#define PROBLEM "https://onlinejudge.u-aizu.ac.jp/courses/library/6/NTL/all/NTL_2_C"

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



#line 1 "src/code/conv/conv_u128.hpp"



#line 1 "src/code/math/mint_s30.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 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/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_s30.hpp"

namespace tifa_libs::math {

template <u32 MOD>
class mint_s30 : public mint<mint_s30<MOD>, u32> {
  using base = mint<mint_s30<MOD>, u32>;
  friend base;

  static constexpr u32 MOD2 = MOD << 1;
  static constexpr u32 R = []() {
    u32 t = 2, iv = MOD * (t - MOD * MOD);
    iv *= t - MOD * iv, iv *= t - MOD * iv;
    return iv * (MOD * iv - t);
  }();
  static constexpr u32 R2 = -(u64)(MOD) % MOD;

  static_assert(MOD & 1);
  static_assert(-R * MOD == 1);
  static_assert((MOD >> 30) == 0);
  static_assert(MOD != 1);

  static constexpr u32 reduce(u64 x) { return u32((x + u64((u32)x * R) * MOD) >> 32); }
  static constexpr u32 norm(u32 x) { return x - (MOD & -((MOD - 1 - x) >> 31)); }

 public:
  static constexpr bool FIXED_MOD = true;
  constexpr mint_s30() {}
  template <int_c T>
  constexpr mint_s30(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) { return reduce(u64(v % (i32)mod_() + (i32)mod_()) * R2); }
  template <uint_c T>
  static constexpr raw_t mod_(T v) { return reduce(u64(v % mod_()) * R2); }
  static constexpr raw_t mod_() { return MOD; }
  constexpr raw_t val_() const { return norm(reduce(this->v_)); }
  constexpr raw_t &data_() { return this->v_; }

  constexpr mint_s30 neg_() const {
    mint_s30 res;
    res.v_ = (MOD2 & -(this->v_ != 0)) - this->v_;
    return res;
  }
  constexpr mint_s30 &adde_(mint_s30 const &r) {
    this->v_ += r.v_ - MOD2, this->v_ += MOD2 & -(this->v_ >> 31);
    return *this;
  }
  constexpr mint_s30 &sube_(mint_s30 const &r) {
    this->v_ -= r.v_, this->v_ += MOD2 & -(this->v_ >> 31);
    return *this;
  }
  constexpr mint_s30 &mule_(mint_s30 const &r) {
    this->v_ = reduce(u64(this->v_) * r.v_);
    return *this;
  }
};

}  // namespace tifa_libs::math


#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/ntt32.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/is_prime.hpp"



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



#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/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 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 8 "src/code/conv/ntt32.hpp"

namespace tifa_libs::math {

template <class mint>
struct NTT32 {
  using data_t = mint;

  static_assert(is_prime(mint::mod()) && sizeof(mint::mod()) <= 4 && (mint::mod() & 3) == 1, "MOD must be prime with 4k+1");
  static constexpr u32 max_size = bit::lowbit(mint::mod() - 1);

  static constexpr mint G = proot(mint::mod());

  explicit constexpr NTT32() : 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 8 "src/code/conv/conv_u128.hpp"

namespace tifa_libs::math {

// max = 167772161 * 469762049 * 754974721 \approx 5.95e25
template <class T>
vec<u128> conv_u128(vec<T> const &l, vec<T> const &r, u32 ans_size = 0) {
  static constexpr u32 m0 = 167772161, m1 = 469762049, m2 = 754974721;
  using mint0 = mint_s30<m0>;
  using mint1 = mint_s30<m1>;
  using mint2 = mint_s30<m2>;
  static constexpr u32 r01 = inverse(m0, mint1::mod()), r02 = inverse(m0, mint2::mod()), r12 = inverse(m1, mint2::mod()), r02r12 = (u64)r02 * r12 % m2;
  static constexpr u64 w1 = m0, w2 = (u64)m0 * m1;

  if (!ans_size) ans_size = u32(l.size() + r.size() - 1);
  if (l.empty() && r.empty()) return {};
  if (std::min(l.size(), r.size()) < 128) return conv_naive<T, u128>(l, r, ans_size);

  static NTT32<mint0> ntt0;
  static NTT32<mint1> ntt1;
  static NTT32<mint2> ntt2;

  vec<mint0> d0 = conv_dft_u64<NTT32<mint0>, mint0>(ntt0, l, r, ans_size);
  vec<mint1> d1 = conv_dft_u64<NTT32<mint1>, mint1>(ntt1, l, r, ans_size);
  vec<mint2> d2 = conv_dft_u64<NTT32<mint2>, mint2>(ntt2, l, r, ans_size);

  vec<u128> ret(ans_size);
  for (u32 i = 0; i < ans_size; ++i) {
    u64 n1 = d1[i].val(), n2 = d2[i].val(), a = d0[i].val(), b = (n1 + m1 - a) * r01 % m1;
    u128 c = ((n2 + m2 - a) * r02r12 + (m2 - b) * r12) % m2;
    ret[i] = a + b * w1 + c * w2;
  }
  return ret;
}

}  // namespace tifa_libs::math


#line 1 "src/code/fast/str2uint_si64.hpp"



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



namespace tifa_libs::bit {

// From GCC lib
template <class T>
constexpr T bswap(T x) {
  if constexpr (sizeof(T) == 2) return __builtin_bswap16(x);
  if constexpr (sizeof(T) == 4) return __builtin_bswap32(x);
  if constexpr (sizeof(T) == 8) return __builtin_bswap64(x);
  if constexpr (sizeof(T) == 16) return __builtin_bswap128(x);
  // if constexpr (sizeof(T) == 16) return (__builtin_bswap64(x >> 64) | (static_cast<T>(__builtin_bswap64(x)) << 64));
}

}  // namespace tifa_libs::bit


#line 6 "src/code/fast/str2uint_si64.hpp"

namespace tifa_libs {

constexpr u32 str2uint_si64(const char* const s) {
  u64 _ = *((u64*)(s));
  if constexpr (std::endian::native == std::endian::big) _ = bit::bswap(_);
  _ = (_ & 0x0F0F0F0F0F0F0F0F) * 2561 >> 8;
  _ = (_ & 0x00FF00FF00FF00FF) * 6553601 >> 16;
  _ = (_ & 0x0000FFFF0000FFFF) * 42949672960001 >> 32;
  return (u32)_;
}

}  // namespace tifa_libs


#line 7 "src/code/math/mpi.hpp"

namespace tifa_libs::math {

class mpi {
  static constexpr u32 D = 100000000, lgD = 8;
  bool neg;
  vecu dt;

 public:
  explicit constexpr mpi() : neg(false), dt() {}
  constexpr mpi(bool n, vecu const& d) : neg(n), dt(d) {}
  template <int_c T>
  constexpr mpi(T x) : neg(false) {
    if constexpr (is_sint_v<T>)
      if (x < 0) neg = true, x = -x;
    while (x) dt.push_back(u32(to_uint_t<T>(x) % D)), x /= D;
  }
  constexpr mpi(strn s) : neg(false) {
    assert(!s.empty());
    if (s.size() == 1u) {
      if (s[0] == '0') return;
      assert(isdigit(s[0]));
      dt.push_back(s[0] & 15);
      return;
    }
    u32 l = 0;
    if (s[0] == '-') ++l, neg = true;
    u32 _ = 0;
    if ((s.size() - l) & 7) {
      for (u32 i = l; i < l + ((s.size() - l) & 7); ++i) _ = _ * 10 + (s[i] & 15);
      l += (s.size() - l) & 7;
    }
    if (l) s = s.substr(l);
    for (u32 ie = (u32)s.size(); ie >= lgD; ie -= lgD)
      dt.push_back(str2uint_si64(s.data() + ie - lgD));
    if (_) dt.push_back(_);
  }

  static constexpr u32 digit() { return D; }
  static constexpr u32 log_digit() { return lgD; }
  constexpr void set_neg(bool s) { neg = s; }
  constexpr bool is_neg() const { return neg; }
  constexpr vecu& data() { return dt; }
  constexpr vecu const& data() const { return dt; }

  friend constexpr mpi operator+(mpi const& l, mpi const& r) {
    if (l.neg == r.neg) return {l.neg, add_(l.dt, r.dt)};
    if (leq_(l.dt, r.dt)) {
      auto c = sub_(r.dt, l.dt);
      return {is0_(c) ? false : r.neg, c};
    }
    auto c = sub_(l.dt, r.dt);
    return {is0_(c) ? false : l.neg, c};
  }
  friend constexpr mpi operator-(mpi const& l, mpi const& r) { return l + (-r); }
  friend constexpr mpi operator*(mpi const& l, mpi const& r) {
    auto c = mul_(l.dt, r.dt);
    bool n = is0_(c) ? false : (l.neg ^ r.neg);
    return {n, c};
  }
  friend constexpr ptt<mpi> divmod(mpi const& l, mpi const& r) {
    auto dm = divmod_newton_(l.dt, r.dt);
    return {mpi{is0_(dm.first) ? false : l.neg != r.neg, dm.first}, mpi{is0_(dm.second) ? false : l.neg, dm.second}};
  }
  friend constexpr mpi operator/(mpi const& l, mpi const& r) { return divmod(l, r).first; }
  friend constexpr mpi operator%(mpi const& l, mpi const& r) { return divmod(l, r).second; }

  constexpr mpi& operator+=(mpi const& r) { return (*this) = (*this) + r; }
  constexpr mpi& operator-=(mpi const& r) { return (*this) = (*this) - r; }
  constexpr mpi& operator*=(mpi const& r) { return (*this) = (*this) * r; }
  constexpr mpi& operator/=(mpi const& r) { return (*this) = (*this) / r; }
  constexpr mpi& operator%=(mpi const& r) { return (*this) = (*this) % r; }

  constexpr mpi operator-() const {
    if (is_zero()) return *this;
    return {!neg, dt};
  }
  constexpr mpi operator+() const { return *this; }
  friend constexpr mpi abs(mpi const& m) { return {false, m.dt}; }
  constexpr bool is_zero() const { return is0_(dt); }

  friend constexpr bool operator==(mpi const& l, mpi const& r) { return l.neg == r.neg && l.dt == r.dt; }
  // clang-format off
  friend constexpr auto operator<=>(mpi const& l, mpi const& r) { return l == r ? 0 : neq_lt_(l, r) ? -1 : 1; }
  // clang-format on

  constexpr u32 size() const { return (u32)dt.size(); }
  constexpr void shrink() { shrink_(dt); }

  constexpr strn to_str() const {
    if (is_zero()) return "0";
    strn res;
    if (neg) res.push_back('-');
    for (u32 i = size() - 1; ~i; --i) res += itos_((u32)dt[i], i != size() - 1);
    return res;
  }
  constexpr i64 to_i64() const {
    i64 res = to_i64_(dt);
    return neg ? -res : res;
  }
  constexpr i128 to_i128() const {
    i128 res = 0;
    for (u32 i = (u32)dt.size() - 1; ~i; --i) res = res * D + dt[i];
    return neg ? -res : res;
  }

  friend std::istream& operator>>(std::istream& is, mpi& m) {
    strn s;
    is >> s;
    m = mpi{s};
    return is;
  }
  friend std::ostream& operator<<(std::ostream& os, mpi const& m) { return os << m.to_str(); }

 private:
  static constexpr bool lt_(vecu const& a, vecu const& b) {
    if (a.size() != b.size()) return a.size() < b.size();
    for (u32 i = (u32)a.size() - 1; ~i; --i)
      if (a[i] != b[i]) return a[i] < b[i];
    return false;
  }
  static constexpr bool leq_(vecu const& a, vecu const& b) { return a == b || lt_(a, b); }
  // a < b (s.t. a != b)
  static constexpr bool neq_lt_(mpi const& l, mpi const& r) {
    assert(l != r);
    if (l.neg != r.neg) return l.neg;
    return lt_(l.dt, r.dt) ^ l.neg;
  }
  static constexpr bool is0_(vecu const& a) { return a.empty(); }
  static constexpr bool is1_(vecu const& a) { return a.size() == 1 && a[0] == 1; }
  static constexpr void shrink_(vecu& a) {
    while (a.size() && !a.back()) a.pop_back();
  }

  static constexpr vecu add_(vecu const& a, vecu const& b) {
    vecu c(std::max(a.size(), b.size()) + 1);
    for (u32 i = 0; i < a.size(); ++i) c[i] += a[i];
    for (u32 i = 0; i < b.size(); ++i) c[i] += b[i];
    for (u32 i = 0; i < c.size() - 1; ++i)
      if (c[i] >= D) c[i] -= D, c[i + 1]++;
    shrink_(c);
    return c;
  }
  static constexpr vecu sub_(vecu const& a, vecu const& b) {
    assert(leq_(b, a));
    vecu c = a;
    u32 borrow = 0;
    for (u32 i = 0; i < a.size(); ++i) {
      if (i < b.size()) borrow += b[i];
      c[i] -= borrow;
      borrow = 0;
      if ((i32)c[i] < 0) c[i] += D, borrow = 1;
    }
    assert(!borrow);
    shrink_(c);
    return c;
  }
  static constexpr vecu mul_3ntt_(vecu const& a, vecu const& b) {
    if (a.empty() || b.empty()) return {};
    auto m = conv_u128(a, b);
    vecu c;
    c.reserve(m.size() + 3);
    u128 x = 0;
    for (u32 i = 0;; ++i) {
      if (i >= m.size() && !x) break;
      if (i < m.size()) x += m[i];
      c.push_back(u32(x % D));
      x /= D;
    }
    shrink_(c);
    return c;
  }
  static constexpr vecu mul_bf_(vecu const& a, vecu const& b) {
    if (a.empty() || b.empty()) return {};
    vecu64 prod(a.size() + b.size() - 1 + 1);
    for (u32 i = 0; i < a.size(); ++i)
      for (u32 j = 0; j < b.size(); ++j)
        if ((prod[i + j] += (u64)a[i] * b[j]) >= 4_u64 * D * D) prod[i + j] -= 4_u64 * D * D, prod[i + j + 1] += 4_u64 * D;
    vecu c(prod.size() + 1);
    u64 x = 0;
    u32 i = 0;
    for (; i < prod.size(); ++i) x += prod[i], c[i] = u32(x % D), x /= D;
    while (x) c[i] = u32(x % D), x /= D, ++i;
    shrink_(c);
    return c;
  }
  static constexpr vecu mul_(vecu const& a, vecu const& b) {
    if (is0_(a) || is0_(b)) return {};
    if (is1_(a)) return b;
    if (is1_(b)) return a;
    if (std::min(a.size(), b.size()) <= 128) return a.size() < b.size() ? mul_bf_(b, a) : mul_bf_(a, b);
    return mul_3ntt_(a, b);
  }
  // 0 <= A < 1e16, 1 <= B < 1e8
  static constexpr ptt<vecu> divmod_li_(vecu const& a, vecu const& b) {
    assert(a.size() <= 2 && b.size() == 1);
    i64 va = to_i64_(a);
    u32 vb = b[0];
    return {itov_(va / vb), itov_(va % vb)};
  }
  // 0 <= A < 1e16, 1 <= B < 1e16
  static constexpr ptt<vecu> divmod_ll_(vecu const& a, vecu const& b) {
    assert(a.size() <= 2 && b.size() && b.size() <= 2);
    i64 va = to_i64_(a), vb = to_i64_(b);
    return {itov_(va / vb), itov_(va % vb)};
  }
  // 1 <= B < 1e8
  static constexpr ptt<vecu> divmod_1e8_(vecu const& a, vecu const& b) {
    assert(b.size() == 1);
    if (b[0] == 1) return {a, {}};
    if (a.size() <= 2) return divmod_li_(a, b);
    vecu quo(a.size());
    u64 d = 0;
    u32 b0 = b[0];
    for (u32 i = (u32)a.size() - 1; ~i; --i) {
      d = d * D + a[i];
      assert(d < (u64)D * b0);
      quo[i] = u32(d / b0);
      d = d % b0;
    }
    shrink_(quo);
    return {quo, d ? vecu{u32(d)} : vecu{}};
  }
  // 0 <= A, 1 <= B
  static constexpr ptt<vecu> divmod_bf_(vecu const& a, vecu const& b) {
    assert(!is0_(b) && b.size());
    if (b.size() == 1) return divmod_1e8_(a, b);
    if (std::max(a.size(), b.size()) <= 2) return divmod_ll_(a, b);
    if (lt_(a, b)) return {{}, a};
    // B >= 1e8, A >= B
    u32 norm = D / (b.back() + 1);
    vecu x = mul_(a, {norm}), y = mul_(b, {norm});
    u32 yb = y.back();
    vecu quo(x.size() - y.size() + 1), rem(x.end() - (int)y.size(), x.end());
    for (u32 i = (u32)quo.size() - 1; ~i; --i) {
      if (rem.size() == y.size()) {
        if (leq_(y, rem)) quo[i] = 1, rem = sub_(rem, y);
      } else if (rem.size() > y.size()) {
        assert(y.size() + 1 == rem.size());
        u32 q = (u32)(((u64)rem[rem.size() - 1] * D + rem[rem.size() - 2]) / yb);
        vecu yq = mul_(y, {q});
        while (lt_(rem, yq)) --q, yq = sub_(yq, y);
        rem = sub_(rem, yq);
        while (leq_(y, rem)) ++q, rem = sub_(rem, y);
        quo[i] = q;
      }
      if (i) rem.insert(rem.begin(), x[i - 1]);
    }
    shrink_(quo), shrink_(rem);
    auto [q2, r2] = divmod_1e8_(rem, {norm});
    assert(is0_(r2));
    return {quo, q2};
  }

  // 1 / a, abserr = B^{-deg}
  static constexpr vecu inv_(vecu const& a, u32 deg) {
    assert(!a.empty() && D / 2 <= a.back() && a.back() < D);
    u32 k = deg, c = (u32)a.size();
    while (k > 64) k = (k + 1) / 2;
    vecu z(c + k + 1);
    z.back() = 1;
    z = divmod_bf_(z, a).first;
    while (k < deg) {
      vecu s = mul_(z, z);
      s.insert(s.begin(), 0);
      u32 d = std::min(c, 2 * k + 1);
      vecu t{a.end() - d, a.end()}, u = mul_(s, t);
      u.erase(u.begin(), u.begin() + d);
      vecu w(k + 1), w2 = add_(z, z);
      std::ranges::copy(w2, std::back_inserter(w));
      (z = sub_(w, u)).erase(z.begin());
      k *= 2;
    }
    z.erase(z.begin(), z.begin() + k - deg);
    return z;
  }

  static constexpr ptt<vecu> divmod_newton_(vecu const& a, vecu const& b) {
    assert(!is0_(b));
    if (b.size() <= 64) return divmod_bf_(a, b);
    if ((int)(a.size() - b.size()) <= 64) return divmod_bf_(a, b);
    u32 norm = D / (b.back() + 1);
    vecu x = mul_(a, {norm}), y = mul_(b, {norm});
    u32 s = (u32)x.size(), t = (u32)y.size();
    u32 deg = s + 2 - t;
    vecu z = inv_(y, deg), q = mul_(x, z);
    q.erase(q.begin(), q.begin() + t + deg);
    vecu yq = mul_(y, {q});
    while (lt_(x, yq)) q = sub_(q, {1}), yq = sub_(yq, y);
    vecu r = sub_(x, yq);
    while (leq_(y, r)) q = add_(q, {1}), r = sub_(r, y);
    shrink_(q), shrink_(r);
    auto [q2, r2] = divmod_1e8_(r, {norm});
    assert(is0_(r2));
    return {q, q2};
  }

  static constexpr strn itos_(u32 x, bool zero_padding) {
    assert(x < D);
    strn res;
    for (u32 i = 0; i < lgD; ++i) res.push_back(char(48 + x % 10)), x /= 10;
    if (!zero_padding) {
      while (res.size() && res.back() == '0') res.pop_back();
      assert(!res.empty());
    }
    std::ranges::reverse(res);
    return res;
  }
  template <int_c T>
  static constexpr vecu itov_(T x) {
    if constexpr (is_sint_v<T>) assert(x >= 0);
    vecu res;
    while (x) res.push_back((u32)(x % D)), x /= D;
    return res;
  }
  static constexpr i64 to_i64_(vecu const& a) {
    i64 res = 0;
    for (u32 i = (u32)a.size() - 1; ~i; --i) res = res * D + a[i];
    return res;
  }
};

}  // namespace tifa_libs::math


#line 4 "src/test_cpverifier/aizu/ntl_2_c.test.cpp"

int main() {
  std::ios::sync_with_stdio(false);
  std::cin.tie(nullptr);
  tifa_libs::math::mpi a, b;
  std::cin >> a >> b;
  std::cout << a * b << '\n';
  return 0;
}

Test cases

Env Name Status Elapsed Memory
g++-12 00_sample_00.in :heavy_check_mark: AC 9 ms 4 MB
g++-12 00_sample_01.in :heavy_check_mark: AC 8 ms 4 MB
g++-12 00_sample_02.in :heavy_check_mark: AC 8 ms 4 MB
g++-12 00_sample_03.in :heavy_check_mark: AC 8 ms 4 MB
g++-12 01_minimum_00.in :heavy_check_mark: AC 8 ms 4 MB
g++-12 01_minimum_01.in :heavy_check_mark: AC 8 ms 4 MB
g++-12 01_minimum_02.in :heavy_check_mark: AC 9 ms 4 MB
g++-12 01_minimum_03.in :heavy_check_mark: AC 8 ms 4 MB
g++-12 02_random_00.in :heavy_check_mark: AC 8 ms 4 MB
g++-12 02_random_01.in :heavy_check_mark: AC 8 ms 4 MB
g++-12 02_random_02.in :heavy_check_mark: AC 9 ms 4 MB
g++-12 02_random_03.in :heavy_check_mark: AC 8 ms 4 MB
g++-12 03_random_00.in :heavy_check_mark: AC 8 ms 4 MB
g++-12 03_random_01.in :heavy_check_mark: AC 8 ms 4 MB
g++-12 03_random_02.in :heavy_check_mark: AC 8 ms 4 MB
g++-12 03_random_03.in :heavy_check_mark: AC 9 ms 4 MB
g++-12 03_random_04.in :heavy_check_mark: AC 8 ms 4 MB
g++-12 03_random_05.in :heavy_check_mark: AC 8 ms 4 MB
g++-12 03_random_06.in :heavy_check_mark: AC 8 ms 4 MB
g++-12 03_random_07.in :heavy_check_mark: AC 8 ms 4 MB
g++-12 03_random_08.in :heavy_check_mark: AC 8 ms 4 MB
g++-12 03_random_09.in :heavy_check_mark: AC 8 ms 4 MB
g++-12 03_random_10.in :heavy_check_mark: AC 8 ms 4 MB
g++-12 04_large_00.in :heavy_check_mark: AC 9 ms 4 MB
g++-12 04_large_01.in :heavy_check_mark: AC 8 ms 4 MB
g++-12 04_large_02.in :heavy_check_mark: AC 9 ms 4 MB
g++-12 04_large_03.in :heavy_check_mark: AC 8 ms 4 MB
g++-12 04_large_04.in :heavy_check_mark: AC 9 ms 4 MB
g++-12 04_large_05.in :heavy_check_mark: AC 8 ms 4 MB
g++-12 04_large_06.in :heavy_check_mark: AC 8 ms 4 MB
g++-12 05_maximum_00.in :heavy_check_mark: AC 8 ms 4 MB
g++-12 05_maximum_01.in :heavy_check_mark: AC 9 ms 4 MB
g++-12 05_maximum_02.in :heavy_check_mark: AC 8 ms 4 MB
g++-12 05_maximum_03.in :heavy_check_mark: AC 9 ms 4 MB
g++-12 05_maximum_04.in :heavy_check_mark: AC 8 ms 4 MB
g++-12 05_maximum_05.in :heavy_check_mark: AC 9 ms 4 MB
g++-12 05_maximum_06.in :heavy_check_mark: AC 8 ms 4 MB
g++-12 05_maximum_07.in :heavy_check_mark: AC 9 ms 4 MB
g++-12 06_corner_00.in :heavy_check_mark: AC 8 ms 4 MB
g++-12 06_corner_01.in :heavy_check_mark: AC 9 ms 4 MB
g++-12 06_corner_02.in :heavy_check_mark: AC 9 ms 4 MB
g++-12 06_corner_03.in :heavy_check_mark: AC 8 ms 4 MB
g++-12 07_maximum_corner_00.in :heavy_check_mark: AC 9 ms 4 MB
g++-12 07_maximum_corner_01.in :heavy_check_mark: AC 8 ms 4 MB
g++-12 07_maximum_corner_02.in :heavy_check_mark: AC 8 ms 4 MB
g++-12 07_maximum_corner_03.in :heavy_check_mark: AC 8 ms 4 MB
g++-12 07_maximum_corner_04.in :heavy_check_mark: AC 8 ms 4 MB
g++-12 07_maximum_corner_05.in :heavy_check_mark: AC 8 ms 4 MB
g++-12 07_maximum_corner_06.in :heavy_check_mark: AC 9 ms 4 MB
g++-12 07_maximum_corner_07.in :heavy_check_mark: AC 8 ms 4 MB
Back to top page