Tifa's CP Library

:heavy_check_mark: src/test_cpverifier/library-checker/sum_of_totient_function.du-ls2-d31.test.cpp

Depends on

Code

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

#include "../../code/math/isqrt.hpp"
#include "../../code/nt/du_sieve.hpp"
#include "../../code/nt/lsieve2.hpp"

constexpr u32 MOD = 998244353;

#include "../../code/math/mint_d31.hpp"

using mint = tifa_libs::math::mint_d31<-1>;

int main() {
  mint::set_mod(MOD);
  std::ios::sync_with_stdio(false);
  std::cin.tie(nullptr);
  u64 n;
  std::cin >> n;
  vec<mint> sphi;
  {
    mint lst = 1;
    sphi = tifa_libs::math::lsieve2(tifa_libs::math::isqrt(n)).template run<mint>([&lst](u32 p, u32 e) {
      if (e == 1) return lst = p - 1;
      else return lst = lst * p;
    });
    std::partial_sum(sphi.begin(), sphi.end(), sphi.begin());
  }
  auto sf = [sphi](u64 x) -> mint { return sphi[x]; };
  auto sg = [](u64 x) -> mint { return x; };
  auto sh = [](u64 x) -> mint { return mint{x} * (x + 1) * ((mint::mod() + 1) / 2); };
  std::cout << tifa_libs::math::du_sieve<mint, decltype(sf), decltype(sg), decltype(sh)>(sphi.size() - 1, sf, sg, sh)(n) << '\n';
  return 0;
}
#line 1 "src/test_cpverifier/library-checker/sum_of_totient_function.du-ls2-d31.test.cpp"
#define AUTO_GENERATED
#define PROBLEM "https://judge.yosupo.jp/problem/sum_of_totient_function"

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



#line 1 "src/code/edh/hash_splitmix64.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/edh/hash_splitmix64.hpp"

namespace tifa_libs {

class hash_splitmix64 {
  static inline u64 seed = 114514;
  static constexpr u64 splitmix64(u64 x) {
    x += 0x9e3779b97f4a7c15;
    x = (x ^ (x >> 30)) * 0xbf58476d1ce4e5b9;
    x = (x ^ (x >> 27)) * 0x94d049bb133111eb;
    return x ^ (x >> 31);
  }
  static constexpr u64 append(u64 x, u64 y) { return x ^ (y >> 1) ^ ((y & 1) << 63); }

 public:
  explicit hash_splitmix64() { set_seed(); }
  explicit constexpr hash_splitmix64(u64 s) { set_seed(s); }

  static void set_seed() { seed = (u64)std::chrono::steady_clock::now().time_since_epoch().count(); }
  static constexpr void set_seed(u64 s) { seed = s; }
  u64 operator()(u64 x) const { return splitmix64(x + seed); }

  template <class T, class U>
  u64 operator()(std::pair<T, U> const &p) const { return append((*this)(p.first), (*this)(p.second)); }
  template <class... Ts>
  u64 operator()(std::tuple<Ts...> const &tp) const {
    u64 ret = 0;
    std::apply([&](Ts const &...targs) { ((ret = append(ret, (*this)(targs))), ...); }, tp);
    return ret;
  }
  template <iterable_c T>
  u64 operator()(T const &tp) const {
    u64 ret = 0;
    for (auto &&i : tp) ret = append(ret, (*this)(i));
    return ret;
  }
};
template <class T>
using hset = std::unordered_set<T, hash_splitmix64>;
template <class K, class V>
using hmap = std::unordered_map<K, V, hash_splitmix64>;

}  // namespace tifa_libs


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



#line 1 "src/code/math/div64.hpp"



#line 5 "src/code/math/div64.hpp"

namespace tifa_libs::math {

constexpr i64 div_i64d(i64 a, i64 b) { return i64(f64(a) / f64(b)); }
constexpr u64 div_u64d(u64 a, u64 b) { return u64(f64(a) / f64(b)); }
constexpr i64 div_i64(i64 a, i64 b) { return a <= 1000000000000 ? div_i64d(a, b) : a / b; }
constexpr u64 div_u64(u64 a, u64 b) { return a <= 1000000000000 ? div_u64d(a, b) : a / b; }

}  // namespace tifa_libs::math


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

namespace tifa_libs::math {

template <class F>
requires requires(F f, u64 n) {
  f(n, n, n);
}
constexpr void do_quot(u64 n, F f, u64 l_begin = 1) {
  for (u64 l = l_begin, r = 0, ed_ = n; l <= ed_; l = r + 1) f(l, r = div_u64(n, div_u64(n, l)), div_u64(n, l));
}

}  // namespace tifa_libs::math


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

namespace tifa_libs::math {

template <class T, class SF, class SG, class SH>
class du_sieve {
  const u64 sf_max;
  SF sf;
  SG sg;
  SH sh;
  hmap<u64, T> mem;

  constexpr T calc(u64 x) {
    if (x <= sf_max) return sf(x);
    if (auto d = mem.find(x); d != mem.end()) return d->second;
    T ans = 0;
    do_quot(
        x,
        [&](u64 l, u64 r, u64 q) { ans += (sg(r) - sg(l - 1)) * calc(q); },
        2);
    return mem[x] = (ans = sh(x) - ans) /= sg(1);
  }

 public:
  constexpr du_sieve(u64 sf_max, SF sf, SG sg, SH sh) : sf_max(sf_max), sf(sf), sg(sg), sh(sh) {}

  constexpr T operator()(u64 n) { return !n ? 0 : calc(n); }
};

}  // namespace tifa_libs::math


#line 1 "src/code/nt/lsieve2.hpp"



#line 5 "src/code/nt/lsieve2.hpp"

namespace tifa_libs::math {

class lsieve2 {
  vecpt<u32> pr;
  vecu fr;

 public:
  explicit constexpr lsieve2(u32 n) : fr(n + 1) {
    for (u32 i = 2, x = n / 2, p1, p2, e; i <= n; x = n / (++i)) {
      if (!fr[i]) {
        for (p1 = 1, p2 = i, e = 0; p1 <= x; p1 = p2, p2 *= i, ++e) fr[p2] = 1;
        pr.emplace_back(i, e);
      }
      for (u32 t = 0; t < pr.size(); ++t)
        if (u32 p = pr[t].first; p > x) break;
        else if (i % p) fr[p * i] = i;
        else {
          fr[p * i] = fr[i];
          break;
        }
    }
  }

  // @param F: T(u32, u32)
  // @param %fpi(p, i) = $f(p^i)$
  // @return v[i] = f(i), for i in [0, n]
  template <class T, class F>
  requires requires(F f, u32 p, u32 i) {
    { f(p, i) } -> std::same_as<T>;
  }
  constexpr vec<T> run(F fpi, T init = T{1}) {
    vec<T> v(fr.size());
    v[1] = init;
    for (u32 i = 0; i < pr.size(); ++i)
      for (u32 p = pr[i].first, e = pr[i].second, pe = p, ex = 1; ex <= e; ++ex, pe *= p) v[pe] = fpi(p, ex);
    for (u32 i = 2; i < fr.size(); ++i) v[i] = v[i / fr[i]] * v[fr[i]];
    return v;
  }
};

}  // namespace tifa_libs::math


#line 7 "src/test_cpverifier/library-checker/sum_of_totient_function.du-ls2-d31.test.cpp"

constexpr u32 MOD = 998244353;

#line 1 "src/code/math/mint_d31.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 {

// Binary exgcd
template <uint_c U, bool only_x = false>
constexpr auto exgcd_b(U a, U b) {
  using T = to_sint_t<U>;
  if constexpr (only_x) {
    if (!a) return std::make_tuple(b, (T)0);
    if (!b) return std::make_tuple(a, (T)1);
  } else {
    if (!a) return std::make_tuple(b, (T)0, (T) !!b);
    if (!b) return std::make_tuple(a, (T)1, (T)0);
  }
  auto r = std::__countr_zero(a | b);
  a >>= r, b >>= r;
  T x = (T)a, y = (T)b;
  T s = 1, t = 0, u = 0, v = 1;
  while (x) {
    while (!(x & 1)) {
      x /= 2;
      if (!((s | t) & 1)) s /= 2, t /= 2;
      else s = (s + (T)b) / 2, t = (t - (T)a) / 2;
    }
    while (!(y & 1)) {
      y /= 2;
      if (!((u | v) & 1)) u /= 2, v /= 2;
      else u = (u + (T)b) / 2, v = (v - (T)a) / 2;
    }
    if (x >= y) x -= y, s -= u, t -= v;
    else y -= x, u -= s, v -= t;
  }
  if (y > 1) a /= (U)y, b /= (U)y;
  if (a && (U)abs(v) >= a) {
    T _ = v / (T)a;
    v -= _ * (T)a, u += _ * (T)b;
  }
  if (b && (U)abs(u) >= b) {
    T _ = u / (T)b;
    u -= _ * (T)b, v += _ * (T)a;
  }
  if (T u_ = u + (T)b, v_ = v - (T)a; abs(u_) + abs(v_) <= abs(u) + abs(v)) u = u_, v = v_;
  if (T u_ = u - (T)b, v_ = v + (T)a; abs(u_) + abs(v_) <= abs(u) + abs(v)) u = u_, v = v_;
  if constexpr (only_x) return std::make_tuple(U(y << r), u);
  else return std::make_tuple(U(y << r), u, v);
}
// @return then 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, bool only_x = false>
constexpr auto exgcd(T a, T b) {
  using U = to_uint_t<T>;
  if (auto [x, y] = std::minmax(a, b); x >= 0 && y <= T(U(-1) >> sizeof(U))) return exgcd_b<U, only_x>((U)a, (U)b);
  if constexpr (only_x) {
    T s = 1, u = 0;
    while (b) {
      T c = a / b;
      std::tie(s, u, a, b) = std::make_tuple(u, s - u * c, b, a - b * c);
    }
    return std::make_tuple((U)a, s);
  } else {
    T s = 1, t = 0, u = 0, v = 1;
    while (b) {
      T c = a / b;
      std::tie(s, t, u, v, a, b) = std::make_tuple(u, v, s - u * c, t - v * c, b, a - b * c);
    }
    return std::make_tuple((U)a, s, t);
  }
}

}  // 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] = exgcd<U, true>(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_d31.hpp"

namespace tifa_libs::math {

template <int ID>
class mint_d31 : public mint<mint_d31<ID>, u32> {
  using base = mint<mint_d31<ID>, u32>;
  friend base;

  static inline u32 R, R2, MOD, MOD_ODD, OFFSET, MASK;

  static constexpr u32 norm(i32 x) { return u32(x + (-(x < 0) & (i32)MOD)); }
  static constexpr u32 redc(u64 x) {
    u32 t = u32((x + u64((u32)x * R) * MOD_ODD) >> 32);
    return t - (MOD_ODD & -((MOD_ODD - 1 - t) >> 31));
  }
  static constexpr u32 tsf(u32 x) { return redc(u64(x % MOD_ODD) * R2) << OFFSET | (x & MASK); }

 public:
  static constexpr bool FIXED_MOD = false;
  static constexpr void set_mod(u32 m) {
    assert(!(m == 1 || m >> 31));
    for (MOD = MOD_ODD = m, OFFSET = 0; (MOD_ODD & 1) == 0; ++OFFSET, MOD_ODD /= 2);
    MASK = (1 << OFFSET) - 1;
    u32 t = 2, iv = MOD_ODD * (t - MOD_ODD * MOD_ODD);
    iv *= t - MOD_ODD * iv, iv *= t - MOD_ODD * iv;
    R = iv * (MOD_ODD * iv - t);
    R2 = u32(-u64(MOD_ODD) % MOD_ODD);
  }

  constexpr mint_d31() {}
  template <int_c T>
  constexpr mint_d31(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 tsf(norm(i32(v % (std::conditional_t<sint_c<T>, i32, u32>)mod_()))); }
  static constexpr raw_t mod_() { return MOD; }
  constexpr raw_t val_() const {
    raw_t h = redc(this->v_ >> OFFSET);
    return ((h - this->v_) * R & MASK) * MOD_ODD + h;
  }
  constexpr raw_t &data_() { return this->v_; }

  constexpr mint_d31 neg_() const {
    mint_d31 res;
    raw_t h = this->v_ >> OFFSET;
    res.v_ = (((MOD_ODD & -(h != 0)) - h) << OFFSET) | (-this->v_ & MASK);
    return res;
  }
  constexpr mint_d31 &adde_(mint_d31 const &r) {
    raw_t h = (this->v_ >> OFFSET) + (r.v_ >> OFFSET) - MOD_ODD;
    this->v_ = ((h + (MOD_ODD & -(h >> 31))) << OFFSET) | ((this->v_ + r.v_) & MASK);
    return *this;
  }
  constexpr mint_d31 &sube_(mint_d31 const &r) {
    raw_t h = (this->v_ >> OFFSET) - (r.v_ >> OFFSET);
    this->v_ = ((h + (MOD_ODD & -(h >> 31))) << OFFSET) | ((this->v_ - r.v_) & MASK);
    return *this;
  }
  constexpr mint_d31 &mule_(mint_d31 const &r) {
    this->v_ = (redc((u64)(this->v_ >> OFFSET) * (r.v_ >> OFFSET)) << OFFSET) | ((this->v_ * r.v_) & MASK);
    return *this;
  }
};

}  // namespace tifa_libs::math


#line 11 "src/test_cpverifier/library-checker/sum_of_totient_function.du-ls2-d31.test.cpp"

using mint = tifa_libs::math::mint_d31<-1>;

int main() {
  mint::set_mod(MOD);
  std::ios::sync_with_stdio(false);
  std::cin.tie(nullptr);
  u64 n;
  std::cin >> n;
  vec<mint> sphi;
  {
    mint lst = 1;
    sphi = tifa_libs::math::lsieve2(tifa_libs::math::isqrt(n)).template run<mint>([&lst](u32 p, u32 e) {
      if (e == 1) return lst = p - 1;
      else return lst = lst * p;
    });
    std::partial_sum(sphi.begin(), sphi.end(), sphi.begin());
  }
  auto sf = [sphi](u64 x) -> mint { return sphi[x]; };
  auto sg = [](u64 x) -> mint { return x; };
  auto sh = [](u64 x) -> mint { return mint{x} * (x + 1) * ((mint::mod() + 1) / 2); };
  std::cout << tifa_libs::math::du_sieve<mint, decltype(sf), decltype(sg), decltype(sh)>(sphi.size() - 1, sf, sg, sh)(n) << '\n';
  return 0;
}

Test cases

Env Name Status Elapsed Memory
g++-12 boundaryA_00 :heavy_check_mark: AC 531 ms 6 MB
g++-12 boundaryA_01 :heavy_check_mark: AC 1413 ms 8 MB
g++-12 boundaryA_02 :heavy_check_mark: AC 1953 ms 9 MB
g++-12 boundaryA_03 :heavy_check_mark: AC 2178 ms 11 MB
g++-12 boundaryA_04 :heavy_check_mark: AC 1268 ms 8 MB
g++-12 boundaryA_05 :heavy_check_mark: AC 1126 ms 8 MB
g++-12 boundaryA_06 :heavy_check_mark: AC 1987 ms 11 MB
g++-12 boundaryA_07 :heavy_check_mark: AC 2500 ms 11 MB
g++-12 boundaryA_08 :heavy_check_mark: AC 833 ms 7 MB
g++-12 boundaryA_09 :heavy_check_mark: AC 1304 ms 8 MB
g++-12 boundaryB_00 :heavy_check_mark: AC 533 ms 6 MB
g++-12 boundaryB_01 :heavy_check_mark: AC 1401 ms 8 MB
g++-12 boundaryB_02 :heavy_check_mark: AC 1957 ms 9 MB
g++-12 boundaryB_03 :heavy_check_mark: AC 2148 ms 11 MB
g++-12 boundaryB_04 :heavy_check_mark: AC 1259 ms 8 MB
g++-12 boundaryB_05 :heavy_check_mark: AC 1126 ms 8 MB
g++-12 boundaryB_06 :heavy_check_mark: AC 1998 ms 11 MB
g++-12 boundaryB_07 :heavy_check_mark: AC 2516 ms 11 MB
g++-12 boundaryB_08 :heavy_check_mark: AC 834 ms 7 MB
g++-12 boundaryB_09 :heavy_check_mark: AC 1301 ms 8 MB
g++-12 example_00 :heavy_check_mark: AC 7 ms 4 MB
g++-12 example_01 :heavy_check_mark: AC 7 ms 4 MB
g++-12 example_02 :heavy_check_mark: AC 7 ms 4 MB
g++-12 handmade_00 :heavy_check_mark: AC 7 ms 4 MB
g++-12 handmade_01 :heavy_check_mark: AC 7 ms 4 MB
g++-12 handmade_02 :heavy_check_mark: AC 7 ms 4 MB
g++-12 handmade_03 :heavy_check_mark: AC 7 ms 4 MB
g++-12 max_00 :heavy_check_mark: AC 2530 ms 11 MB
g++-12 max_01 :heavy_check_mark: AC 2517 ms 11 MB
g++-12 max_02 :heavy_check_mark: AC 2516 ms 11 MB
g++-12 max_03 :heavy_check_mark: AC 2549 ms 11 MB
g++-12 max_04 :heavy_check_mark: AC 2512 ms 11 MB
g++-12 max_05 :heavy_check_mark: AC 2539 ms 11 MB
g++-12 max_06 :heavy_check_mark: AC 2519 ms 11 MB
g++-12 max_07 :heavy_check_mark: AC 2515 ms 11 MB
g++-12 max_08 :heavy_check_mark: AC 2523 ms 11 MB
g++-12 max_09 :heavy_check_mark: AC 2514 ms 11 MB
g++-12 random_00 :heavy_check_mark: AC 532 ms 6 MB
g++-12 random_01 :heavy_check_mark: AC 1401 ms 8 MB
g++-12 random_02 :heavy_check_mark: AC 1968 ms 9 MB
g++-12 random_03 :heavy_check_mark: AC 2148 ms 11 MB
g++-12 random_04 :heavy_check_mark: AC 1267 ms 8 MB
g++-12 random_05 :heavy_check_mark: AC 1126 ms 8 MB
g++-12 random_06 :heavy_check_mark: AC 1986 ms 11 MB
g++-12 random_07 :heavy_check_mark: AC 2507 ms 11 MB
g++-12 random_08 :heavy_check_mark: AC 833 ms 7 MB
g++-12 random_09 :heavy_check_mark: AC 1301 ms 8 MB
g++-12 small_00 :heavy_check_mark: AC 8 ms 4 MB
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