Tifa's CP Library

:heavy_check_mark: src/test_cpverifier/library-checker/sum_of_totient_function.min25-d63.test.cpp

Depends on

Code

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

#include "../../code/nt/min25_sieve.hpp"

constexpr u32 MOD = 998244353;

#include "../../code/math/mint_d63.hpp"

using mint = tifa_libs::math::mint_d63<-1>;

mint f(u64 p, u64 c) {
  u64 res = 1;
  while (--c) res = res * p;
  return res * (p - 1);
}

int main() {
  mint::set_mod(MOD);
  std::ios::sync_with_stdio(false);
  std::cin.tie(nullptr);
  u64 n;
  std::cin >> n;

  tifa_libs::math::min25_sieve<mint, f> min25(n);
  auto h0 = min25.sum_pk(0), h1 = min25.sum_pk(1);
  for (u32 i = 0; i < h1.size(); ++i) h1[i] -= h0[i];
  std::cout << min25.run(h1) << '\n';
  return 0;
}
#line 1 "src/test_cpverifier/library-checker/sum_of_totient_function.min25-d63.test.cpp"
#define AUTO_GENERATED
#define PROBLEM "https://judge.yosupo.jp/problem/sum_of_totient_function"

#line 1 "src/code/nt/min25_sieve.hpp"



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



namespace tifa_libs::math {

template <class T>
constexpr T sum_i0(T n) { return n; }
template <class T>
constexpr T sum_i1(T n) { return n * (n + 1) / 2; }
template <class T>
constexpr T sum_i2(T n) { return sum_i1(n) * (n * 2 + 1) / 3; }
template <class T>
constexpr T sum_i3(T n) {
  auto _ = sum_i1(n);
  return _ * _;
}
template <class T>
constexpr T sum_i4(T n) { return sum_i2(n) * (sum_i1(n) * 6 - 1) / 5; }
template <class T>
constexpr T sum_i5(T n) { return sum_i3(n) * (sum_i1(n) * 4 - 1) / 3; }
template <class T>
constexpr T sum_i6(T n) {
  auto _ = sum_i1(n);
  return sum_i2(n) * (_ * (_ * 2 - 1) * 6 + 1) / 7;
}
template <class T>
constexpr T sum_i7(T n) {
  auto _ = sum_i3(n);
  return _ * _ * 2 - sum_i5(n);
}

template <class T>
constexpr T (*sum_ik[])(T) = {sum_i0<T>, sum_i1<T>, sum_i2<T>, sum_i3<T>, sum_i4<T>, sum_i5<T>, sum_i6<T>, sum_i7<T>};

}  // namespace tifa_libs::math


#line 1 "src/code/nt/prime_seq.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 5 "src/code/nt/prime_seq.hpp"

namespace tifa_libs::math {

constexpr vecu prime_seq(u32 n) {
  vecb sieve(n / 3 + 1, 1);
  for (u32 p = 5, d = 4, i = 1, sqn = isqrt(n); p <= sqn; p += d = 6 - d, ++i) {
    if (!sieve[i]) continue;
    for (u64 q = p * p / 3, r = d * p / 3 + (d * p % 3 == 2), s = 2 * p, qe = sieve.size(); q < qe; q += r = s - r) sieve[q] = 0;
  }
  vecu ret{2, 3};
  for (u32 p = 5, d = 4, i = 1; p <= n; p += d = 6 - d, ++i)
    if (sieve[i]) ret.push_back(p);
  while (!ret.empty() && ret.back() > n) ret.pop_back();
  return ret;
}

}  // namespace tifa_libs::math


#line 8 "src/code/nt/min25_sieve.hpp"

namespace tifa_libs::math {

// f(p, c) = value of f(p^c)
template <class T, T (*f)(u64, u64)>
class min25_sieve {
  u64 m, sqm, s;
  vecu p;

  constexpr u64 idx(u64 n) const { return n <= sqm ? s - n : div_u64d(m, n); }

 public:
  // m^{3/2} in u64
  explicit constexpr min25_sieve(u64 m) : m(m), sqm(isqrt(m)) {
    assert(m < (1ll << 42));
    if (m) {
      u64 hls = div_u64d(m, sqm);
      if (hls != 1 && div_u64d(m, hls - 1) == sqm) --hls;
      s = hls + sqm;
      p = prime_seq((u32)sqm);
    }
  }

  constexpr vec<T> sum_pk(u32 k) const {
    auto sik = sum_ik<T>[k];
    if (!m) return {};
    u64 hls = div_u64d(m, sqm);
    if (hls != 1 && div_u64d(m, hls - 1) == sqm) --hls;
    vec<T> h(s);
    for (u64 i = 1; i < hls; ++i) h[i] = sik(div_u64d(m, i)) - 1;
    for (u64 i = 1; i <= sqm; ++i) h[s - i] = sik(i) - 1;
    for (u32 x : p) {
      T _ = x, pi = h[s - x + 1];
      _ = qpow(_, k);
      u64 x2 = u64(x) * x, mx = std::min(hls, div_u64d(m, x2) + 1);
      for (u64 i = 1, ix = x; i < mx; ++i, ix += x) h[i] -= ((ix < hls ? h[ix] : h[s - div_u64d(m, ix)]) - pi) * _;
      for (u64 n = sqm; n >= x2; --n) h[s - n] -= (h[s - div_u64d(n, x)] - pi) * _;
    }
    assert(h.size() == s);
    return h;
  }

  constexpr T run(vec<T> fprime) const {
    if (!m) return {};
    assert(fprime.size() == s);
    T ans = fprime[idx(m)] + 1;
    auto dfs = [&, this](auto&& dfs, u32 i, u32 c, u64 prod, T cur) -> void {
      ans += cur * f(p[i], c + 1);
      u64 lim = div_u64d(m, prod);
      if (lim >= (u64)p[i] * p[i]) dfs(dfs, i, c + 1, p[i] * prod, cur);
      cur *= f(p[i], c);
      ans += cur * (fprime[idx(lim)] - fprime[idx(p[i])]);
      u32 j = i + 1;
      for (; j < p.size() && (u64)p[j] * p[j] * p[j] <= lim; ++j) dfs(dfs, j, 1, prod * p[j], cur);
      for (; j < p.size() && (u64)p[j] * p[j] <= lim; ++j) {
        T sm = f(p[j], 2);
        u64 id1 = idx(div_u64d(lim, p[j])), id2 = idx(p[j]);
        ans += cur * (sm += f(p[j], 1) * (fprime[id1] - fprime[id2]));
      }
    };
    for (u32 i = 0; i < p.size(); ++i) dfs(dfs, i, 1, p[i], 1);
    return ans;
  }
};

}  // namespace tifa_libs::math


#line 5 "src/test_cpverifier/library-checker/sum_of_totient_function.min25-d63.test.cpp"

constexpr u32 MOD = 998244353;

#line 1 "src/code/math/mint_d63.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 {

// 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_d63.hpp"

namespace tifa_libs::math {

template <int ID>
class mint_d63 : public mint<mint_d63<ID>, u64> {
  using base = mint<mint_d63<ID>, u64>;
  friend base;

  static inline u64 MOD, R, R2;

  static constexpr u64 mul_h(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 = mul_h(x, y) - mul_h(x * y * R, MOD);
    return res + (MOD & -(res >> 63));
  }
  static constexpr u64 norm(i64 x) { return u64(x + i64(MOD & u64(-(x < 0)))); }

 public:
  static constexpr bool FIXED_MOD = false;
  static constexpr void set_mod(u64 m) {
    assert(!((m & 1) == 0 || m == 1 || m >> 63));
    MOD = m;
    u64 t = 2, iv = MOD * (t - MOD * MOD);
    iv *= t - MOD * iv, iv *= t - MOD * iv, iv *= t - MOD * iv;
    R = iv * (t - MOD * iv);
    R2 = -MOD % MOD;
    for (u32 i = 0; i != 64; ++i)
      if ((R2 *= 2) >= MOD) R2 -= MOD;
  }

  constexpr mint_d63() {}
  template <int_c T>
  constexpr mint_d63(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(i64(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 = -mul_h(this->v_ * R, MOD);
    return res + (MOD & -(res >> 63));
  }
  constexpr raw_t &data_() { return this->v_; }

  constexpr mint_d63 neg_() const {
    mint_d63 res;
    res.v_ = (MOD & -(this->v_ != 0)) - this->v_;
    return res;
  }
  constexpr mint_d63 &adde_(mint_d63 const &r) {
    this->v_ += r.v_ - MOD, this->v_ += MOD & -(this->v_ >> 63);
    return *this;
  }
  constexpr mint_d63 &sube_(mint_d63 const &r) {
    this->v_ -= r.v_, this->v_ += MOD & -(this->v_ >> 63);
    return *this;
  }
  constexpr mint_d63 &mule_(mint_d63 const &r) {
    this->v_ = redc_mul(this->v_, r.v_);
    return *this;
  }
};

}  // namespace tifa_libs::math


#line 9 "src/test_cpverifier/library-checker/sum_of_totient_function.min25-d63.test.cpp"

using mint = tifa_libs::math::mint_d63<-1>;

mint f(u64 p, u64 c) {
  u64 res = 1;
  while (--c) res = res * p;
  return res * (p - 1);
}

int main() {
  mint::set_mod(MOD);
  std::ios::sync_with_stdio(false);
  std::cin.tie(nullptr);
  u64 n;
  std::cin >> n;

  tifa_libs::math::min25_sieve<mint, f> min25(n);
  auto h0 = min25.sum_pk(0), h1 = min25.sum_pk(1);
  for (u32 i = 0; i < h1.size(); ++i) h1[i] -= h0[i];
  std::cout << min25.run(h1) << '\n';
  return 0;
}

Test cases

Env Name Status Elapsed Memory
g++-12 boundaryA_00 :heavy_check_mark: AC 131 ms 5 MB
g++-12 boundaryA_01 :heavy_check_mark: AC 315 ms 7 MB
g++-12 boundaryA_02 :heavy_check_mark: AC 429 ms 7 MB
g++-12 boundaryA_03 :heavy_check_mark: AC 469 ms 8 MB
g++-12 boundaryA_04 :heavy_check_mark: AC 286 ms 6 MB
g++-12 boundaryA_05 :heavy_check_mark: AC 257 ms 6 MB
g++-12 boundaryA_06 :heavy_check_mark: AC 435 ms 7 MB
g++-12 boundaryA_07 :heavy_check_mark: AC 545 ms 8 MB
g++-12 boundaryA_08 :heavy_check_mark: AC 196 ms 6 MB
g++-12 boundaryA_09 :heavy_check_mark: AC 295 ms 6 MB
g++-12 boundaryB_00 :heavy_check_mark: AC 130 ms 5 MB
g++-12 boundaryB_01 :heavy_check_mark: AC 316 ms 7 MB
g++-12 boundaryB_02 :heavy_check_mark: AC 429 ms 7 MB
g++-12 boundaryB_03 :heavy_check_mark: AC 469 ms 8 MB
g++-12 boundaryB_04 :heavy_check_mark: AC 286 ms 6 MB
g++-12 boundaryB_05 :heavy_check_mark: AC 257 ms 6 MB
g++-12 boundaryB_06 :heavy_check_mark: AC 436 ms 7 MB
g++-12 boundaryB_07 :heavy_check_mark: AC 539 ms 8 MB
g++-12 boundaryB_08 :heavy_check_mark: AC 196 ms 6 MB
g++-12 boundaryB_09 :heavy_check_mark: AC 294 ms 6 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 543 ms 8 MB
g++-12 max_01 :heavy_check_mark: AC 543 ms 8 MB
g++-12 max_02 :heavy_check_mark: AC 543 ms 8 MB
g++-12 max_03 :heavy_check_mark: AC 543 ms 8 MB
g++-12 max_04 :heavy_check_mark: AC 542 ms 8 MB
g++-12 max_05 :heavy_check_mark: AC 542 ms 8 MB
g++-12 max_06 :heavy_check_mark: AC 543 ms 8 MB
g++-12 max_07 :heavy_check_mark: AC 544 ms 8 MB
g++-12 max_08 :heavy_check_mark: AC 543 ms 8 MB
g++-12 max_09 :heavy_check_mark: AC 543 ms 8 MB
g++-12 random_00 :heavy_check_mark: AC 131 ms 5 MB
g++-12 random_01 :heavy_check_mark: AC 316 ms 7 MB
g++-12 random_02 :heavy_check_mark: AC 430 ms 7 MB
g++-12 random_03 :heavy_check_mark: AC 469 ms 8 MB
g++-12 random_04 :heavy_check_mark: AC 286 ms 7 MB
g++-12 random_05 :heavy_check_mark: AC 258 ms 6 MB
g++-12 random_06 :heavy_check_mark: AC 436 ms 7 MB
g++-12 random_07 :heavy_check_mark: AC 540 ms 8 MB
g++-12 random_08 :heavy_check_mark: AC 196 ms 6 MB
g++-12 random_09 :heavy_check_mark: AC 294 ms 6 MB
g++-12 small_00 :heavy_check_mark: AC 7 ms 4 MB
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