結果
問題 | No.713 素数の和 |
ユーザー |
![]() |
提出日時 | 2024-09-27 12:17:37 |
言語 | C++23 (gcc 13.3.0 + boost 1.87.0) |
結果 |
AC
|
実行時間 | 2 ms / 2,000 ms |
コード長 | 47,063 bytes |
コンパイル時間 | 4,273 ms |
コンパイル使用メモリ | 281,044 KB |
実行使用メモリ | 6,944 KB |
最終ジャッジ日時 | 2024-09-27 12:17:43 |
合計ジャッジ時間 | 4,509 ms |
ジャッジサーバーID (参考情報) |
judge4 / judge3 |
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ファイルパターン | 結果 |
---|---|
sample | AC * 3 |
other | AC * 6 |
ソースコード
#include <bits/stdc++.h>using namespace std;//*#define INCLUDE_MODINT//*/#ifdef INCLUDE_MODINT#include <atcoder/modint>using namespace atcoder;using mint = modint998244353;// using mint = modint1000000007;// using mint = modint;#endifnamespace mytemplate{using ll = long long;using dbl = double;using ld = long double;using uint = unsigned int;using ull = unsigned long long;using pll = pair<ll, ll>;using tlll = tuple<ll, ll, ll>;using tllll = tuple<ll, ll, ll, ll>;template <class T> using vc = vector<T>;template <class T> using vvc = vector<vector<T>>;template <class T> using vvvc = vector<vector<vector<T>>>;using vb = vc<bool>;using vl = vc<ll>;using vpll = vc<pll>;using vtlll = vc<tlll>;using vtllll = vc<tllll>;using vstr = vc<string>;using vvb = vvc<bool>;using vvl = vvc<ll>;#ifdef __SIZEOF_INT128__using i128 = __int128_t;i128 stoi128(string s) { i128 res = 0; if (s.front() == '-') { for (int i = 1; i < (int)s.size(); i++) res = 10 * res + s[i] - '0'; res = -res;} else { for (auto c : s) res = 10 * res + c - '0'; } return res; }string i128tos(i128 x) { string sign = "", res = ""; if (x < 0) x = -x, sign = "-"; while (x > 0) { res += '0' + x % 10; x /= 10; } reverse(res.begin(), res.end()); if (res == "") return "0"; return sign + res; }istream &operator>>(istream &is, i128 &a) { string s; is >> s; a = stoi128(s); return is; }ostream &operator<<(ostream &os, const i128 &a) { os << i128tos(a); return os; }#endif#define cauto const auto#define overload4(_1, _2, _3, _4, name, ...) name#define rep1(i, n) for (ll i = 0, nnnnn = ll(n); i < nnnnn; i++)#define rep2(i, l, r) for (ll i = ll(l), rrrrr = ll(r); i < rrrrr; i++)#define rep3(i, l, r, d) for (ll i = ll(l), rrrrr = ll(r), ddddd = ll(d); ddddd > 0 ? i < rrrrr : i > rrrrr; i += d)#define rep(...) overload4(__VA_ARGS__, rep3, rep2, rep1)(__VA_ARGS__)#define repi1(i, n) for (int i = 0, nnnnn = int(n); i < nnnnn; i++)#define repi2(i, l, r) for (int i = int(l), rrrrr = int(r); i < rrrrr; i++)#define repi3(i, l, r, d) for (int i = int(l), rrrrr = int(r), ddddd = int(d); ddddd > 0 ? i < rrrrr : i > rrrrr; i += d)#define repi(...) overload4(__VA_ARGS__, repi3, repi2, repi1)(__VA_ARGS__)#define ALL(a) (a).begin(), (a).end()const ll INF = 4'000'000'000'000'000'037;bool chmin(auto &a, const auto &b) { return a > b ? a = b, true : false; }bool chmax(auto &a, const auto &b) { return a < b ? a = b, true : false; }template <class T1 = ll> T1 safemod(auto a, auto m) { T1 res = a % m; if (res < 0) res += m; return res; }template <class T1 = ll> T1 divfloor(auto a, auto b) { if (b < 0) a = -a, b = -b; return (a - safemod(a, b)) / b; }template <class T1 = ll> T1 divceil(auto a, auto b) { if (b < 0) a = -a, b = -b; return divfloor(a + b - 1, b); }template <class T1 = ll> T1 ipow(auto a, auto b) { if (a == 0) return b == 0 ? 1 : 0; if (a == 1) return a; if (a == -1) return b & 1 ? -1 : 1; llres = 1; rep(_, b) res *= a; return res; }template <class T1 = ll> T1 mul_limited(auto a, auto b, T1 m = INF) { return b == 0 ? 0 : a > m / b ? m : a * b; }template <class T1 = ll> T1 pow_limited(auto a, auto b, T1 m = INF) { if (a == 0) return b == 0 ? 1 : 0; if (a == 1) return a; ll res = 1; rep(_,b) { if (res > m / a) return m; res *= a; } return res; }template <class T = ll>constexpr T iroot(cauto &a, cauto &k){assert(a >= 0 && k >= 1);if (a <= 1 || k == 1)return a;if (k == 2)return sqrtl(a);auto isok = [&](T x) -> bool{if (x == 0)return true;T res = 1;for (T k2 = k;;){if (k2 & 1){if (res > T(a) / x)return false;res *= x;}k2 >>= 1;if (k2 == 0)break;if (x > T(a) / x)return false;x *= x;}return res <= T(a);};T ok = pow(a, 1.0 / k);while (!isok(ok))ok--;while (ok < numeric_limits<T>::max() && isok(ok + 1))ok++;return ok;}template <class T1 = ll> vector<T1> b_ary(T1 x, int b) { vector<T1> a; while (x > 0) { a.emplace_back(x % b); x /= b; } reverse(a.begin(), a.end()); return a; }template <class T1 = ll> vector<T1> b_ary(T1 x, int b, int n) { vector<T1> a(n); rep(i, n) { a[i] = x % b; x /= b; } reverse(a.begin(), a.end());return a; }template <class T1 = ll> string b_ary_str(T1 x, int b) { auto a = b_ary(x, b); string s = ""; for (auto &&ai : a) s += (ai < 10 ? '0' + ai : 'A' +(ai - 10)); return s; }template <class T1 = ll> string b_ary_str(T1 x, int b, int n) { auto a = b_ary(x, b, n); string s = ""; for (auto &&ai : a) s += (ai < 10 ? '0' +ai : 'A' + (ai - 10)); return s; }template <class T>vector<vector<T>> iprod(const vector<T> &a){vector<vector<T>> res;vector<T> tmp(a.size());auto dfs = [&](auto self, int i){if (i == (int)a.size()){res.emplace_back(tmp);return;}rep(j, a[i]){tmp[i] = j;self(self, i + 1);}};dfs(dfs, 0);return res;}template <class T = ll> struct max_op { T operator()(const T &a, const T &b) const { return max(a, b); } };template <class T = ll> struct min_op { T operator()(const T &a, const T &b) const { return min(a, b); } };template <class T, const T val> struct const_fn { T operator()() const { return val; } };using max_e = const_fn<ll, -INF>;using min_e = const_fn<ll, INF>;using zero_fn = const_fn<ll, 0LL>;template <class T = ll> vector<T> digitvec(const string &s) { int n = s.size(); vector<T> a(n); rep(i, n) a[i] = s[i] - '0'; return a; }template <class T, size_t d, size_t i = 0> auto make_vec(const auto (&sz)[d], const T &init) { if constexpr (i < d) return vector(sz[i], make_vec<T, d, i + 1>(sz, init)); else return init; }template <class T = ll> vector<T> permid(int n, int base_index = 0) { vector<T> p(n); rep(i, n) p[i] = i + base_index; return p; }template <class T = ll> vector<T> perminv(const vector<T> &p) { vector<T> q(p.size()); rep(i, p.size()) q[p[i]] = i; return q; }template <class T = ll> vector<T> combid(int n, int k) { vector<T> p(n, 0); fill(p.rbegin(), p.rbegin() + k, 1); return p; }template <class F> auto gen_vec(int n, const F &f) { using T = decltype(f(0)); vector<T> res(n); rep(i, n) res[i] = f(i); return res; }// res[i] = op[0, i) for 0 <= i < n+1template <class T, class F = decltype(plus<>())> vector<T> cuml(vector<T> v, const F &op = plus<>(), const T &e = 0) { v.emplace_back(e);exclusive_scan(v.begin(), v.end(), v.begin(), e, op); return v; }// res[i] = op[i, n) for 0 <= i < n+1template <class T, class F = decltype(plus<>())> vector<T> cumr(vector<T> v, const F &op = plus<>(), const T &e = 0) { v.insert(v.begin(), e);exclusive_scan(v.rbegin(), v.rend(), v.rbegin(), e, op); return v; }// res[i] = v[i] - v[i-1] for 0 <= i < n+1template <class T> vector<T> adjd(vector<T> v) { v.emplace_back(0); adjacent_difference(v.begin(), v.end(), v.begin()); return v; }template <class T> vector<T> cumlmax(const vector<T> &v) { return cuml(v, max_op<T>(), max_e()()); }template <class T> vector<T> cumrmax(const vector<T> &v) { return cumr(v, max_op<T>(), max_e()()); }template <class T> vector<T> cumlmin(const vector<T> &v) { return cuml(v, min_op<T>(), min_e()()); }template <class T> vector<T> cumrmin(const vector<T> &v) { return cumr(v, min_op<T>(), min_e()()); }template <class T> vector<T> sorted(vector<T> v) { sort(v.begin(), v.end()); return v; }template <class T> vector<T> reversed(const vector<T> &v) { return {v.rbegin(), v.rend()}; }template <class T> void unique(vector<T> &v) { v.erase(unique(v.begin(), v.end()), v.end()); }template <class T> vector<T> uniqued(vector<T> v) { v.erase(unique(v.begin(), v.end()), v.end()); return v; }template <class T> void sortunique(vector<T> &v) { sort(v.begin(), v.end()); v.erase(unique(v.begin(), v.end()), v.end()); }template <class T> vector<T> sortuniqued(vector<T> v) { sort(v.begin(), v.end()); v.erase(unique(v.begin(), v.end()), v.end()); return v; }template <class T> void rotate(vector<T> &v, int k) { rotate(v.begin(), v.begin() + k, v.end()); }template <class T> vector<T> rotated(vector<T> v, int k) { rotate(v.begin(), v.begin() + k, v.end()); return v; }string sorted(string s) { sort(s.begin(), s.end()); return s; }string reversed(const string &s) { return {s.rbegin(), s.rend()}; }void unique(string &s) { s.erase(unique(s.begin(), s.end()), s.end()); }string uniqued(string s) { s.erase(unique(s.begin(), s.end()), s.end()); return s; }void sortunique(string &s) { sort(s.begin(), s.end()); s.erase(unique(s.begin(), s.end()), s.end()); }string sortuniqued(string s) { sort(s.begin(), s.end()); s.erase(unique(s.begin(), s.end()), s.end()); return s; }void rotate(string &s, int k) { rotate(s.begin(), s.begin() + k, s.end()); }string rotated(string s, int k) { rotate(s.begin(), s.begin() + k, s.end()); return s; }template <class T> vector<vector<T>> top(const vector<vector<T>> &a) { if (a.empty()) return {}; const size_t n = a.size(), m = a[0].size();vector<vector<T>> b(m, vector<T>(n)); for (size_t i = 0; i < n; i++) for (size_t j = 0; j < m; j++) b[j][i] = a[i].at(j); return b; }vstr top(const vstr &a) { if (a.empty()) return {}; const size_t n = a.size(), m = a[0].size(); vstr b(m, string(n, 0)); for (size_t i = 0; i < n;i++) for (size_t j = 0; j < m; j++) b[j][i] = a[i].at(j); return b; }template <class T> vector<vector<T>> rot90(const vector<vector<T>> &a) { if (a.empty()) return {}; const size_t n = a.size(), m = a[0].size();vector<vector<T>> b(m, vector<T>(n)); for (size_t i = 0; i < n; i++) for (size_t j = 0; j < m; j++) b[j][n - 1 - i] = a[i][j]; return b; }vstr rot90(const vstr &a) { if (a.empty()) return {}; const size_t n = a.size(), m = a[0].size(); vstr b(m, string(n, 0)); for (size_t i = 0; i <n; i++) for (size_t j = 0; j < m; j++) b[j][n - 1 - i] = a[i][j]; return b; }#if __cplusplus < 202002Lull bit_ceil(ull x) { ull y = 1; while (y < x) y <<= 1; return y; }ull bit_floor(ull x) { ull y = 1; while (y <= x) y <<= 1; return y >> 1; }ull bit_width(ull x) { ull y = 1, z = 0; while (y <= x) y <<= 1, z++; return z; }ull countr_zero(ull x) { return __builtin_ctzll(x); }ull popcount(ull x) { return __builtin_popcountll(x); }ull has_single_bit(ull x) { return popcount(x) == 1; }#endifull lsb_pos(ull x) { assert(x != 0); return countr_zero(x); }ull msb_pos(ull x) { assert(x != 0); return bit_width(x) - 1; }ull lsb_mask(ull x) { assert(x != 0); return x & -x; }ull msb_mask(ull x) { assert(x != 0); return bit_floor(x); }bool btest(ull x, uint k) { return (x >> k) & 1; }template <class T> void bset(T &x, uint k, bool b = 1) { b ? x |= (1ULL << k) : x &= ~(1ULL << k); }template <class T> void bflip(T &x, uint k) { x ^= (1ULL << k); }bool bsubset(ull x, ull y) { return (x & y) == x; }template <class T> vector<pair<T, T>> bsubsets(T x) { vector<pair<T, T>> res; for (T y = x; y > 0; y = (y - 1) & x) res.emplace_back(make_pair(y,x & ~y)); res.emplace_back(make_pair(0, x)); return res; }template <class Tuple, size_t... I> Tuple tuple_add(Tuple &a, const Tuple &b, const index_sequence<I...>) { ((get<I>(a) += get<I>(b)), ...);return a; }template <class Tuple> Tuple operator+=(Tuple &a, const Tuple &b) { return tuple_add(a, b, make_index_sequence<tuple_size_v<Tuple>>{}); }template <class Tuple> Tuple operator+(Tuple a, const Tuple &b) { return a += b; }template <class T, class U> void offset(vector<T> &v, U add) { for (auto &vi : v) vi += add; }template <class T, class U> void offset(vector<vector<T>> &v, U add) { for (auto &vi : v) for (auto &vij : vi) vij += add; }template <class T, const size_t m> array<vector<T>, m> top(const vector<array<T, m>> &a) { const size_t n = a.size(); array<vector<T>, m> b; b.fill(vector<T>(n)); for (size_t i = 0; i < n; i++) for (size_t j = 0; j < m; j++) b[j][i] = a[i][j]; return b; }template <class T, const size_t n> vector<array<T, n>> top(const array<vector<T>, n> &a) { if (a.empty()) return {}; const size_t m = a[0].size();vector<array<T, n>> b(m); for (size_t i = 0; i < n; i++) for (size_t j = 0; j < m; j++) b[j][i] = a[i].at(j); return b; }template <class T, class U> pair<vector<T>, vector<U>> top(const vector<pair<T, U>> &a) { const size_t n = a.size(); vector<T> b(n); vector<U> c(n); for (size_t i = 0; i < n; i++) tie(b[i], c[i]) = a[i]; return make_pair(b, c); }template <class T, class U> vector<pair<T, U>> top(const pair<vector<T>, vector<U>> &a) { const size_t n = a.first.size(); vector<pair<T, U>> b(n); for (size_t i = 0; i < n; i++) b[i] = make_pair(a.first[i], a.second.at(i)); return b; }template <class T1, class T2, class T3> tuple<vector<T1>, vector<T2>, vector<T3>> top(const vector<tuple<T1, T2, T3>> &a) { const size_t n = a.size(); vector<T1> b(n); vector<T2> c(n); vector<T3> d(n); for (size_t i = 0; i < n; i++) tie(b[i], c[i], d[i]) = a[i]; return make_tuple(b,c, d); }template <class T1, class T2, class T3> vector<tuple<T1, T2, T3>> top(const tuple<vector<T1>, vector<T2>, vector<T3>> &a) { const size_t n = get<0>(a).size(); vector<tuple<T1, T2, T3>> b(n); for (size_t i = 0; i < n; i++) b[i] = make_tuple(get<0>(a)[i], get<1>(a).at(i), get<2>(a).at(i));return b; }template <class T1, class T2, class T3, class T4> tuple<vector<T1>, vector<T2>, vector<T3>, vector<T4>> top(const vector<tuple<T1, T2, T3, T4>> &a) { const size_t n = a.size(); vector<T1> b(n); vector<T2> c(n); vector<T3> d(n); vector<T4> e(n); for (size_t i = 0; i < n; i++) tie(b[i],c[i], d[i], e[i]) = a[i]; return make_tuple(b, c, d, e); }template <class T1, class T2, class T3, class T4> vector<tuple<T1, T2, T3, T4>> top(const tuple<vector<T1>, vector<T2>, vector<T3>, vector<T4>> &a) { const size_t n = get<0>(a).size(); vector<tuple<T1, T2, T3, T4>> b(n); for (size_t i = 0; i < n; i++) b[i] = make_tuple(get<0>(a)[i], get<1>(a).at(i), get<2>(a).at(i), get<3>(a).at(i)); return b; }#ifdef INCLUDE_MODINTusing namespace atcoder;template <class T, internal::is_modint_t<T> * = nullptr> istream &operator>>(istream &is, T &a) { ll v; is >> v; a = v; return is; }template <class T, internal::is_modint_t<T> * = nullptr> ostream &operator<<(ostream &os, const T &a) { os << a.val(); return os; }#define MINT(...) mint __VA_ARGS__; INPUT(__VA_ARGS__)#endiftemplate <class Tuple, enable_if_t<__is_tuple_like<Tuple>::value == true> * = nullptr> istream &operator>>(istream &is, Tuple &t) { apply([&](auto&... a){ (is >> ... >> a); }, t); return is; }template <class... T> void INPUT(T&... a) { (cin >> ... >> a); }template <class T> void INPUTVEC(int n, vector<T> &v) { v.resize(n); rep(i, n) cin >> v[i]; }template <class T, class... Ts> void INPUTVEC(int n, vector<T>& v, vector<Ts>&... vs) { INPUTVEC(n, v); INPUTVEC(n, vs...); }template <class T> void INPUTVEC2(int n, int m, vector<vector<T>> &v) { v.assign(n, vector<T>(m)); rep(i, n) rep(j, m) cin >> v[i][j]; }template <class T, class... Ts> void INPUTVEC2(int n, int m, vector<T>& v, vector<Ts>&... vs) { INPUTVEC2(n, m, v); INPUTVEC2(n, m, vs...); }#define INT(...) int __VA_ARGS__; INPUT(__VA_ARGS__)#define LL(...) ll __VA_ARGS__; INPUT(__VA_ARGS__)#define STR(...) string __VA_ARGS__; INPUT(__VA_ARGS__)#define ARR(T, n, ...) array<T, n> __VA_ARGS__; INPUT(__VA_ARGS__)#define VEC(T, n, ...) vector<T> __VA_ARGS__; INPUTVEC(n, __VA_ARGS__)#define VEC2(T, n, m, ...) vector<vector<T>> __VA_ARGS__; INPUTVEC2(n, m, __VA_ARGS__)template <class T> void PRINT(const T &a) { cout << a << '\n'; }template <class T, class... Ts> void PRINT(const T& a, const Ts&... b) { cout << a; (cout << ... << (cout << ' ', b)); cout << '\n'; }template <class T> void PRINTVEC(const vector<T> &v) { int n = v.size(); rep(i, n) cout << v[i] << (i == n - 1 ? "" : " "); cout << '\n'; }template <class T> void PRINTVECT(const vector<T> &v) { for (auto &vi : v) cout << vi << '\n';}template <class T> void PRINTVEC2(const vector<vector<T>> &v) { for (auto &vi : v) PRINTVEC(vi); }#define PRINTEXIT(...) do { PRINT(__VA_ARGS__); exit(0); } while (false)#define PRINTRETURN(...) do { PRINT(__VA_ARGS__); return; } while (false)}using namespace mytemplate;#ifdef LOCAL#include <cpp-dump.hpp> // https://github.com/philip82148/cpp-dumpnamespace cpp_dump::_detail{inline string export_var(const i128 &x, const string &indent, size_t last_line_length,size_t current_depth, bool fail_on_newline, const export_command &command) {return export_var(i128tos(x), indent, last_line_length, current_depth, fail_on_newline, command);}#ifdef INCLUDE_MODINTtemplate <int m>inline std::string export_var(const atcoder::static_modint<m> &mint, const std::string &indent, std::size_t last_line_length,std::size_t current_depth, bool fail_on_newline, const export_command &command) {return export_var(mint.val(), indent, last_line_length, current_depth, fail_on_newline, command);}template <int m>inline std::string export_var(const atcoder::dynamic_modint<m> &mint, const std::string &indent, std::size_t last_line_length,std::size_t current_depth, bool fail_on_newline, const export_command &command) {return export_var(mint.val(), indent, last_line_length, current_depth, fail_on_newline, command);}#endif} // namespace cpp_dump::_detail#define dump(...) cpp_dump(__VA_ARGS__)namespace cp = cpp_dump;CPP_DUMP_SET_OPTION_GLOBAL(log_label_func, cp::log_label::line());CPP_DUMP_SET_OPTION_GLOBAL(max_iteration_count, 10000);#else#define dump(...)#endif#define SINGLE_TESTCASE// #define MULTI_TESTCASE// #define AOJ_TESTCASE#define FAST_IOtemplate <class P>struct PrimePower{P p;int e;P pe;PrimePower() : p(-1), e(-1), pe(-1) {}PrimePower(P p, int e = 1) : p(p), e(e), pe(ipow(p, e)) {}PrimePower(P p, int e, P pe) : p(p), e(e), pe(pe) {}void mulp() { e++, pe *= p; }void divp() { e--, pe /= p; }template <class P2>PrimePower(const PrimePower<P2> &pp) { p = pp.p, e = pp.e, pe = pp.pe; }};#ifdef LOCALCPP_DUMP_DEFINE_EXPORT_OBJECT(PrimePower<int>, p, e, pe);CPP_DUMP_DEFINE_EXPORT_OBJECT(PrimePower<ll>, p, e, pe);#endifstruct LinearSieve{private:static vector<int> prime_id;public:static int n;static vector<PrimePower<int>> _lpf;static vector<int> primes;static void extend(int _n){if (_n <= n)return;n = max(_n, 2 * n);prime_id.resize(n + 1, 0);_lpf.resize(n + 1);for (int d = 2; d <= n; d++){if (_lpf[d].p == -1)_lpf[d] = PrimePower<int>(d, 1, d), primes.emplace_back(d);for (int &i = prime_id[d]; i < (int)primes.size(); i++){int p = primes[i];if (p > n / d || p > _lpf[d].p)break;if (_lpf[d].p == p)_lpf[p * d] = PrimePower<int>(p, _lpf[d].e + 1, _lpf[d].pe * p);else_lpf[p * d] = PrimePower<int>(p, 1, p);}}}static PrimePower<int> lpf(int x){assert(x >= 1 && "LinearSieve::lpf");extend(x);return _lpf[x];}static bool is_prime(int x){if (x <= 1)return false;return lpf(x).p == x;}// 計算量: O(x の素因数の種類数) = O(log x / loglog x)static vector<PrimePower<int>> factorize(int x){assert(x >= 1 && "LinearSieve::factorize");extend(x);vector<PrimePower<int>> res;while (x > 1){res.emplace_back(_lpf[x]);x /= _lpf[x].pe;}return res;}};vector<int> LinearSieve::prime_id{};vector<PrimePower<int>> LinearSieve::_lpf{};int LinearSieve::n{};vector<int> LinearSieve::primes{};using sv = LinearSieve;struct SegmentedSieve{// pfs[x - l] は x の素因数 (x 以外)vector<vector<int>> pfs;ll l, r;SegmentedSieve() {}// 前計算の計算量: O( ( √r + (r-l) ) loglog r )SegmentedSieve(ll l, ll r) : l(l), r(r){LinearSieve::extend(sqrtl(r) + 1);pfs.resize(r - l + 1);for (const ll p : LinearSieve::primes)for (ll x = max(2 * p, divceil(l, p) * p); x <= r; x += p)pfs[x - l].emplace_back(p);}bool is_prime(ll x){if (l <= x && x <= r)return pfs[l - x].empty();assert(x <= INT32_MAX && "SegmentedSieve::is_prime");return LinearSieve::is_prime(x);}// 計算量: O(log x)vector<PrimePower<ll>> factorize(ll x){if (l <= x && x <= r){vector<PrimePower<ll>> res;for (const ll p : pfs[x - l]){int e = 0;ll pe = 1;while (x % p == 0)x /= p, e++, pe *= p;res.emplace_back(PrimePower<ll>(p, e, pe));}if (x != 1)res.emplace_back(PrimePower<ll>(x, 1, x));return res;}assert(x <= INT32_MAX && "SegmentedSieve::factorize");vector<PrimePower<int>> res = LinearSieve::factorize(x);return vector<PrimePower<ll>>(res.begin(), res.end());}};namespace zeta_mobius_small{// ζa(n) = Σ[d | n] a(d)// a[0] は用いないtemplate <class T>vector<T> zeta_divisor(const vector<T> &a){const int n = (int)a.size() - 1;LinearSieve::extend(n);vector<T> b(a);for (const int &p : LinearSieve::primes){if (p > n)break;for (int i = 1; i * p <= n; i++)b[i * p] += b[i];}return b;}// μ は ζ の逆変換// μa(n) = Σ{d | n} μ(n/d)a(d) cf. メビウスの反転公式// a[0] は用いないtemplate <class T>vector<T> mobius_divisor(const vector<T> &a){const int n = (int)a.size() - 1;LinearSieve::extend(n);vector<T> b(a);for (const int &p : LinearSieve::primes){if (p > n)break;for (int i = n / p; i >= 1; i--)b[i * p] -= b[i];}return b;}// ζ'a(n) = Σ{n | m} a(m)// a[0] は用いないtemplate <class T>vector<T> zeta_multiple(const vector<T> &a){const int n = (int)a.size() - 1;LinearSieve::extend(n);vector<T> b(a);for (const int &p : LinearSieve::primes){if (p > n)break;for (int i = n / p; i >= 1; i--)b[i] += b[i * p];}return b;}// μ' は ζ' の逆変換// μ'a(n) = Σ{n | m} μ(m/n)g(m)// a[0] は用いないtemplate <class T>vector<T> mobius_multiple(const vector<T> &a){const int n = (int)a.size() - 1;LinearSieve::extend(n);vector<T> b(a);for (const int &p : LinearSieve::primes){if (p > n)break;for (int i = 1; i * p <= n; i++)b[i] -= b[i * p];}return b;}// |a| = |b| を仮定// a[0], b[0] は用いないtemplate <class T>vector<T> lcm_convolution(const vector<T> &a, const vector<T> &b){assert(a.size() == b.size() && "lcm_convolution");vector<T> za = zeta_divisor(a), zb = zeta_divisor(b);vector<T> zc(a.size());for (int i = 1; i < (int)a.size(); i++)zc[i] = za[i] * zb[i];return mobius_divisor(zc);}// |a| = |b| を仮定// a[0], b[0] は用いないtemplate <class T>vector<T> gcd_convolution(const vector<T> &a, const vector<T> &b){assert(a.size() == b.size() && "gcd_convolution");vector<T> za = zeta_multiple(a), zb = zeta_multiple(b);vector<T> zc(a.size());for (int i = 1; i < (int)a.size(); i++)zc[i] = za[i] * zb[i];return mobius_multiple(zc);}};using namespace zeta_mobius_small;namespace multiplicative{// 完全乗法的関数: f(1) = 1, f(p1^e1 ... pk^ek) = f(p1)^e1 ... f(pk)^ek// f(p) が O(t) 時間で計算できるとき f(1), ..., f(n) を O(n + nt/log n) 時間で計算// f_primepower の引数は PrimePower 型 (なお f(p) 部分しか用いない)template <class T>vector<T> enumerate_completely_multiplicative(int n, const auto &f_primepower){LinearSieve::extend(n);vector<T> res(n + 1);if (n >= 1)res[1] = 1;for (int d = 2; d <= n; d++){int p = LinearSieve::_lpf[d].p;if (d == p)res[d] = f_primepower(PrimePower<int>(p, 1, p));elseres[d] = res[p] * res[d / p];}return res;}// 乗法的関数: f(1) = 1, f(p1^e1 ... pk^ek) = f(p1^e1) ... f(pk^ek)// f(p^e) が O(1) 時間で計算できるとき f(1), ..., f(n) を O(n) 時間で列挙// f_primepower の引数は PrimePower 型template <class T>vector<T> enumerate_multiplicative(int n, const auto &f_primepower){LinearSieve::extend(n);vector<T> res(n + 1);if (n >= 1)res[1] = 1;for (int d = 2; d <= n; d++){const PrimePower<int> &lpf_d = LinearSieve::_lpf[d];int pe = lpf_d.pe;if (d == pe)res[d] = f_primepower(lpf_d);elseres[d] = res[d / pe] * res[pe];}return res;}// ------ 完全乗法的 -----// 単位元: ε(1) = 1, otherwise 0template <class T, class P = ll>const auto e_primepower = [](const PrimePower<P> &q) -> T{ return q.pe == 1 ? 1 : 0; };// ゼータ関数 ζ(s): 1(n) = 1template <class T, class P = ll>const auto zeta_primepower = [](const PrimePower<P> &q) -> T{ return 1; };// 恒等写像 ζ(s-1): id(n) = ntemplate <class T, class P = ll>const auto id_primepower = [](const PrimePower<P> &q) -> T{ return q.pe; };// f(n) = n^k (k >= 0)// T は modint を想定// 1 から n までの列挙にかかる計算量: O(n log k / log n)template <class T, class P = ll>const auto pow_primepower = [](ll k){return [&](const PrimePower<P> &q) -> T{ return T(q.pe).pow(k); };};// f(n) = n^{-k} (k >= 0)// 逆元がないときは 0 とする// T は modint を想定// 1 から n までの列挙にかかる計算量: O(n log k)template <class T, class P = ll>const auto pow_inv_primepower = [](ll k){return [&](const PrimePower<P> &q) -> T{if (internal::is_prime_constexpr(T::mod()))return T(q.pe).pow(safemod(-k, T::mod() - 1));elsereturn T::mod() % q.p == 0 ? T(0) : T(q.pe).inv().pow(k);};};// ----- 乗法的 -----// メビウス関数: μ(s) = 1/ζ(s) = prod_{p} (1-p)// 重複する素因数があれば 0、相異なる素因数の積のとき、素因数が偶数個なら 1、奇数個なら -1template <class T, class P = ll>const auto mobius_primepower = [](const PrimePower<P> &q) -> T{ return q.e == 0 ? 1 : q.e == 1 ? -1 : 0; };// 約数個数関数: σ_0(s) = ζ(s)ζ(s)template <class T, class P = ll>const auto divisor_count_primepower = [](const PrimePower<P> &q) -> T{ return 1 + q.e; };// 約数総和関数: σ_1(s) = ζ(s)ζ(s-1)template <class T, class P = ll>const auto divisor_sum_primepower = [](const PrimePower<P> &q) -> T{ return (q.pe * q.p - 1) / (q.p - 1); };// 約数の k 乗和: σ_k(s) = ζ(s)ζ(s-k)// f(p^e) = 1 + p^k + (p^k)^2 + ... + (p^k)^e// T は modint を想定// 素べき部分の計算量: O(log k + e)template <class T, class P = ll>const auto divisor_k_primepower = [](ll k){return [&](const PrimePower<P> &q) -> T{T pk = T(q.p).pow(k);T r = 1, res = 0;for (int i = 0; i <= q.e; i++){res += r;r *= pk;}return res;};};// オイラー関数 (トーシェント関数): φ(s) = ζ(s-1)/ζ(s)// n と互いに素な 1 以上 n 以下の整数の個数// n * prod_{p}(1 - 1/p)template <class T, class P = ll>const auto totient_primepower = [](const PrimePower<P> &q) -> T{ return q.pe - q.pe / q.p; };// ----- 累積和が簡単に求まるもの -----// 単位元: ε(1) = 1, otherwise 0template <class T>const auto e_prefix_sum = [](ll n) -> T{ return 1; };// ゼータ関数 ζ(s): 1(n) = 1template <class T>const auto zeta_prefix_sum = [](ll n) -> T{ return n; };// 恒等写像 ζ(s-1): id(n) = ntemplate <class T>const auto id_prefix_sum = [](ll n) -> T{ return n % 2 == 0 ? T(n / 2) * T(n + 1) : T(n) * T((n + 1) / 2); };};using namespace multiplicative;// 同じ数で何回も割るとき、modint 等で毎回 log がつかないようにしつつ、整数でも動くようにするtemplate <class T, const bool use_inv = numeric_limits<T>::is_integer>struct Div{T val, inv;Div() {}Div(const T &val) : val(val), inv(1 / val) {}T ÷(T &x) { return use_inv ? x *= inv : x /= val; }T divided(T x) { return x /= val; }};// prefix 形式// f(1), ..., f(k) のテーブルを保持template <class T>struct DirichletP{public:int k;vector<T> f;bool is_multiplicative;DirichletP() {}// 乗法的関数の場合DirichletP(const int &k, const auto &f_primepower, const bool &is_completely_multiplicative = false): k(k), is_multiplicative(true){if (is_completely_multiplicative)f = multiplicative::enumerate_completely_multiplicative<T>(k, f_primepower);elsef = multiplicative::enumerate_multiplicative<T>(k, f_primepower);}DirichletP(const vector<T> &f, const bool &is_multiplicative = false): k((int)f.size() - 1), f(f), is_multiplicative(is_multiplicative){}private:static vector<T> prod_arbitrary(const vector<T> &a, const vector<T> &b){assert(a.size() == b.size() && "DirichletP::prod_arbitrary");const int _k = (int)a.size() - 1;vector<T> c(_k + 1);for (int i = 1; i <= _k; i++)for (int j = 1; i * j <= _k; j++)c[i * j] += a[i] * b[j];return c;};static vector<T> prod_half_multiplicative(const vector<T> &a, const vector<T> &b){assert(a.size() == b.size() && "DirichletP::prod_half_multiplicative");const int _k = (int)a.size() - 1;LinearSieve::extend(_k);vector<T> c(b);for (const int &p : LinearSieve::primes){if (p > _k)break;for (int i = _k / p; i > 0; i--){int j = i * p;ll q = p; // q = p^eint m = i; // j = p^e * mwhile (q <= _k){c[j] += a[q] * c[m];if (m % p != 0)break;q *= p, m /= p;}}}return c;};static vector<T> prod_multiplicative(const vector<T> &a, const vector<T> &b){assert(a.size() == b.size() && "DirichletP::prod_multiplicative");const int _k = (int)a.size() - 1;auto f_primepower = [&](const PrimePower<ll> &q){T res = 0;for (int r = q.pe, s = 1; r >= 1; r /= q.p, s *= q.p)res += a[r] * b[s];return res;};return multiplicative::enumerate_multiplicative<T>(_k, f_primepower);};static vector<T> div_multiplicative(const vector<T> &c, const vector<T> &a){assert(a.size() == c.size() && "DirichletP::div_multiplicative");const int _k = (int)a.size() - 1;if (_k == 0)return vector<T>(1);vector<T> b(_k + 1);b[1] = 1;for (const int &p : LinearSieve::primes){for (ll pe = p; pe <= _k; pe *= p){b[pe] = c[pe];for (int q = 1, r = pe; q < pe; q *= p, r /= p)b[pe] -= b[q] * a[r];}}return multiplicative::enumerate_multiplicative<T>(_k, [&](const PrimePower<ll> &q) -> T{ return b[q.pe]; });}static vector<T> div_arbitrary(const vector<T> &c, const vector<T> &a){assert(a.size() == c.size() && "DirichletP::div_arbitrary");const int _k = (int)a.size() - 1;if (_k == 0)return vector<T>(1);assert(a[1] != 0 && "div_arbitrary");vector<T> b(c.begin(), c.end());Div<T> div_a1(a[1]);for (int i = 1; i <= _k; i++){div_a1.divide(b[i]);for (int j = 2; i * j <= _k; j++)b[i * j] -= a[j] * b[i];}return b;}public:// 乗算// 両方が乗法的なら O(k)// 一方が乗法的なら O(k loglog k)// それ以外なら O(k log k)DirichletP operator*(const DirichletP<T> &other) const{vector<T> res_f;if (this->is_multiplicative && other.is_multiplicative)res_f = prod_multiplicative(this->f, other.f);else if (this->is_multiplicative)res_f = prod_half_multiplicative(this->f, other.f);else if (other.is_multiplicative)res_f = prod_half_multiplicative(other.f, this->f);elseres_f = prod_arbitrary(this->f, other.f);bool res_is_multiplicative= this->is_multiplicative && other.is_multiplicative;return DirichletP(res_f, res_is_multiplicative);}DirichletP &operator*=(const DirichletP<T> &other) { return *this = *this * other; }// 逆元// 乗法的なら O(k), そうでない場合 O(k log k)DirichletP inv() const{DirichletP e(k, multiplicative::e_primepower<T>, true);return e / *this;}// 除算 c/a// a, c ともに乗法的なら O(k)// a のみ乗法的なら O(k loglog k)// それ以外なら O(k log k)DirichletP operator/(const DirichletP<T> &other) const{vector<T> res_f;if (this->is_multiplicative && other.is_multiplicative)res_f = div_multiplicative(this->f, other.f);else if (other.is_multiplicative)res_f = prod_half_multiplicative(other.inv().f, this->f);elseres_f = div_arbitrary(this->f, other.f);bool res_is_multiplicative= this->is_multiplicative && other.is_multiplicative;return DirichletP(res_f, res_is_multiplicative);}DirichletP &operator/=(const DirichletP<T> &other) { return *this = *this / other; }DirichletP pow(ll x) const{DirichletP res(k, multiplicative::e_primepower<T>, true);DirichletP tmp(*this);while (x > 0){if (x & 1)res *= tmp;tmp *= tmp;x >>= 1;}return res;}};// prefix-quotient 形式// f(1), ..., f(k) のテーブルに加え、// F(1), ..., F(k) および F(⌊n/1⌋), ..., F(⌊n/l⌋) のテーブルも保持// d に 2 以上を指定した場合は F(⌊(n/j)^{1/d}⌋) を保持// k >= l および ⌊(n/(l+1))^{1/d}⌋ <= k を仮定template <class T, const int d = 1>struct DirichletPQ{public:DirichletP<T> pre;ll n;int l;vector<T> F, qF;// F(⌊(n/i)^{1/d}⌋) を得るT &getqF(ll i){assert(1 <= i && i <= n);if (i <= l)return qF[i];elsereturn F[iroot(n / i, d)];}DirichletPQ() {}DirichletPQ(const DirichletP<T> &pre, const ll &n, const int &l, const auto &getF): pre(pre), n(n), l(l), F(pre.k + 1), qF(l + 1){assert(pre.k >= l && "DirichletPQ");assert(iroot(n / (l + 1), d) <= pre.k && "DirichletPQ");for (int i = 1; i <= pre.k; i++)F[i] = F[i - 1] + pre.f[i];for (int i = 1; i <= l; i++)qF[i] = getF(iroot(n / i, d));}DirichletPQ(const DirichletP<T> &pre, const ll &n, const vector<T> &qF): pre(pre), n(n), l((int)qF.size() - 1), F(pre.k + 1), qF(qF){assert(pre.k >= l && "DirichletPQ");assert(iroot(n / (l + 1), d) <= pre.k && "DirichletPQ");for (int i = 1; i <= pre.k; i++)F[i] = F[i - 1] + pre.f[i];}// 乗算// - いずれも乗法的なら O(k + √(nl))// - このとき k = O(n^{2/3}), l = O(n^{1/3}) が最適// - 一方のみ乗法的なら O(k loglog k + √(nl))// - このとき k = O((n/loglog n)^{2/3}), l = O(n^{1/3}(loglog n)^{2/3}) が最適// - 乗法的でないなら O(k log k + √(nl))// - このとき k = O((n/log n)^{2/3}), l = O(n^{1/3}(log n)^{2/3}) が最適// 一般の d では、O(k + (nl)^{1/2d}) 等で、k = O(n^{2/(2d+1)}), l = O(n^{1/(2d+1)})DirichletPQ operator*(const DirichletPQ &other) const{assert(n == other.n && pre.k == other.pre.k && l == other.l && "DirichletPQ::operator*");DirichletP<T> res_pre = pre * other.pre;vector<T> res_qF(l + 1);for (ll j = 1; j <= l; j++){const int m = iroot(n / j, 2 * d);for (ll i = 1; i <= m; i++)res_qF[j] += pre.f[i] * other.getqF(ipow(i, d) * j) + other.pre.f[i] * (getqF(ipow(i, d) * j) - F[m]);}return DirichletPQ(res_pre, n, res_qF);}DirichletPQ &operator*=(const DirichletPQ &other) { return *this = *this * other; }// 除算// - いずれも乗法的なら O(k + √(nl))// - このとき k = O(n^{2/3}), l = O(n^{1/3}) が最適// - 一方のみ乗法的なら O(k loglog k + √(nl))// - このとき k = O((n/loglog n)^{2/3}), l = O(n^{1/3}(loglog n)^{2/3}) が最適// - 乗法的でないなら O(k log k + √(nl))// - このとき k = O((n/log n)^{2/3}), l = O(n^{1/3}(log n)^{2/3}) が最適// 一般の d では、O(k + (nl)^{1/2d}) 等で、k = O(n^{2/(2d+1)}), l = O(n^{1/(2d+1)})DirichletPQ operator/(const DirichletPQ &other) const{assert(n == other.n && pre.k == other.pre.k && l == other.l && "DirichletPQ::operator/");if (pre.k == 0)return DirichletPQ(DirichletP<T>(vector<T>(1)), n, vector<T>(l + 1));assert(other.pre.f[1] != 0 && "DirichletPQ::operator/");DirichletPQ res(pre / other.pre, n, qF);Div<T> div_a1(other.pre.f[1]);for (ll j = l; j >= 1; j--){const int m = iroot(n / j, 2 * d);for (ll i = 1; i <= m; i++)res.qF[j] -= res.pre.f[i] * (other.getqF(ipow(i, d) * j) - other.F[m]);for (ll i = 2; i <= m; i++)res.qF[j] -= other.pre.f[i] * res.getqF(ipow(i, d) * j);div_a1.divide(res.qF[j]);}return res;}DirichletPQ &operator/=(const DirichletPQ<T> &other) { return *this = *this / other; }// 逆元DirichletPQ inv() const{DirichletPQ e(DirichletP<T>(pre.k, multiplicative::e_primepower<T>, true), n, l, multiplicative::e_prefix_sum<T>);return e / *this;}DirichletPQ pow(ll x) const{DirichletPQ res(DirichletP<T>(pre.k, multiplicative::e_primepower<T>, true), n, l, multiplicative::e_prefix_sum<T>);DirichletPQ tmp(*this);while (x > 0){if (x & 1)res *= tmp;tmp *= tmp;x >>= 1;}return res;}};// 積 c = a * b について C(n) ひとつを求める// 計算量: O(k + l)// k = l = ⌊√n⌋ がオーダー最適で O(√n)template <class T>T prodFn(const DirichletPQ<T> &a, const DirichletPQ<T> &b){assert(a.n == b.n && a.pre.k == b.pre.k && a.l == b.l && "prodFn");T ans = 0;for (int i = 1; i <= a.l; i++)ans += a.pre.f[i] * b.getqF(i);for (int j = 1; j <= a.pre.k; j++)ans += b.pre.f[j] * (a.getqF(j) - a.F[a.l]);return ans;}// 入力: **完全**乗法的関数 f について、PQ 形式および素数部分の値 f(p)// 出力: f の素数部分のみを取り出した関数の PQ 形式// 計算量: k = l = ⌊√n⌋ とするとき O(n^{3/4} / log n)template <class T>DirichletPQ<T> lucy_dp(const DirichletPQ<T> &f_pq, const auto &f_primepower){// dp_i(v) := 2 以上 v 以下の整数のうち i 以下の素数でふるわれない整数に対する f の和// i が素数でないか、v < i^2 の場合、dp_i(v) = dp_{i-1}(v)// それ以外の場合、dp_i(v) = dp_{i-1}(v) - f(i) ( dp_{i-1}(⌊v/i⌋) - dp_{i-1}(i-1) )vector<T> res_qF(f_pq.l + 1);for (int j = 1; j <= f_pq.l; j++)res_qF[j] = f_pq.qF[j] - 1;DirichletPQ<T> res(f_pq.pre, f_pq.n, res_qF);for (int v = 1; v <= f_pq.pre.k; v++)res.F[v] -= 1;for (ll i = 2; i * i <= f_pq.n; i++){// この時点で dp_{i-1} が入っているif (!LinearSieve::is_prime(i))continue;T fi = f_primepower(PrimePower<ll>(i, 1, i));T dp_i_minus_1 = res.F[i - 1];for (int j = 1; j <= f_pq.l; j++){dump(i, j, f_pq.n / j, res.getqF(j));// dp(⌊n/j⌋) を更新if (f_pq.n / j < i * i)break;res.getqF(j) -= fi * (res.getqF(i * j) - dp_i_minus_1);}for (int v = f_pq.pre.k; v >= 1; v--){// dp(v) を更新if (v < i * i)break;res.F[v] -= fi * (res.F[v / i] - dp_i_minus_1);}}for (int i = 2; i <= f_pq.pre.k; i++){if (!LinearSieve::is_prime(i))res.pre.f[i] = 0;}return res;}void init() {}void main2(){/* segmented sieve https://atcoder.jp/contests/abc227/tasks/abc227_gLL(N, K);SegmentedSieve ssv(N - K + 1, N);vl cnt(max(K, (ll)sqrtl(N)) + 1, 0);mint ans = 1;rep(x, 1, K + 1){auto facs = ssv.factorize(x);dump(x, facs);for (cauto &fac : facs)cnt.at(fac.p) -= fac.e;}rep(x, N - K + 1, N + 1){auto facs = ssv.factorize(x);dump(x, facs);for (cauto &fac : facs){if (fac.p < (int)cnt.size())cnt.at(fac.p) += fac.e;elseans *= 2;}}rep(x, cnt.size()) ans *= 1 + cnt.at(x);PRINT(ans);//*//* gcd convolution https://judge.yosupo.jp/problem/gcd_convolutionINT(N);VEC(mint, N, A, B);A.insert(A.begin(), 0), B.insert(B.begin(), 0);auto C = gcd_convolution(A, B);C.erase(C.begin());PRINTVEC(C);//*//* lcm convolution https://judge.yosupo.jp/problem/lcm_convolutionINT(N);VEC(mint, N, A, B);A.insert(A.begin(), 0), B.insert(B.begin(), 0);auto C = lcm_convolution(A, B);C.erase(C.begin());PRINTVEC(C);//*//* enumerate multiplicativeLL(N);dump(enumerate_completely_multiplicative<mint>(N, e_primepower<mint>) | cp::index());dump(enumerate_completely_multiplicative<mint>(N, zeta_primepower<mint>) | cp::index());dump(enumerate_completely_multiplicative<mint>(N, id_primepower<mint>) | cp::index());dump(enumerate_completely_multiplicative<static_modint<10000>>(N, pow_primepower<static_modint<10000>>(3)) | cp::index());dump(enumerate_completely_multiplicative<static_modint<10000>>(N, pow_inv_primepower<static_modint<10000>>(3)) | cp::index());dump(enumerate_multiplicative<mint>(N, mobius_primepower<mint>) | cp::index());dump(enumerate_multiplicative<mint>(N, divisor_count_primepower<mint>) | cp::index());dump(enumerate_multiplicative<mint>(N, divisor_sum_primepower<mint>) | cp::index());dump(enumerate_multiplicative<mint>(N, divisor_k_primepower<mint>(2)) | cp::index());dump(enumerate_multiplicative<mint>(N, totient_primepower<mint>) | cp::index());//*//* dirichletP// declared as multiplicativeDirichletP<mint> mobius_p(100, mobius_primepower<mint>);DirichletP<mint> totient_p(100, totient_primepower<mint>);DirichletP<mint> zeta_p(100, zeta_primepower<mint>);DirichletP<mint> id_p(100, id_primepower<mint>);// declared as non-multiplicativeDirichletP<mint> mobius_p_nm(mobius_p.f);DirichletP<mint> totient_p_nm(totient_p.f);DirichletP<mint> zeta_p_nm(zeta_p.f);DirichletP<mint> id_p_nm(id_p.f);// totient * zeta = iddump(id_p.f | cp::index());for (cauto &T : {totient_p, totient_p_nm}){for (cauto &Z : {zeta_p, zeta_p_nm}){dump(T.f | cp::index(), Z.f | cp::index(), (T * Z).f | cp::index(), T.is_multiplicative, Z.is_multiplicative);assert((T * Z).f == id_p.f);}}for (cauto &T : {totient_p, totient_p_nm}){for (cauto &M : {mobius_p, mobius_p_nm}){dump(T.f | cp::index(), M.f | cp::index(), (T * M).f | cp::index(), T.is_multiplicative, M.is_multiplicative);assert((T / M).f == id_p.f);}}exit(0);//*//* https://atcoder.jp/contests/abc172/tasks/abc172_d// prodFn// sum[ij <= N] ijLL(N);ll M = sqrtl(N);DirichletPQ<ll> id(DirichletP<ll>(M, id_primepower<ll>), N, M, id_prefix_sum<ll>);ll ans = prodFn(id, id);PRINT(ans);//*//* https://atcoder.jp/contests/arc116/tasks/arc116_c// pow// sum((zeta)^N)[M]LL(N, M);ll L = pow(M, 1.0 / 3.0), K = divceil(M, L);DirichletPQ<mint> zeta(DirichletP<mint>(K, zeta_primepower<mint>), M, L, zeta_prefix_sum<mint>);mint ans = zeta.pow(N).getqF(1);PRINT(ans);//*//* sum of totient https://judge.yosupo.jp/problem/sum_of_totient_function// zeta * phi = idLL(N);ll L = pow(N, 1.0 / 3.0), K = divceil(N, L);DirichletPQ<mint> zeta(DirichletP<mint>(K, zeta_primepower<mint>), N, L, zeta_prefix_sum<mint>);DirichletPQ<mint> id(DirichletP<mint>(K, id_primepower<mint>), N, L, id_prefix_sum<mint>);DirichletPQ<mint> phi = id / zeta;PRINT(phi.getqF(1));//*//* counting square-frees https://judge.yosupo.jp/problem/counting_squarefrees// ζ(s)/ζ(2s) の累積和なので sum[ij <= N, j は平方数] μ(√j)// = sum[k^2 <= N] μ(k) ⌊N/k^2⌋// = sum[x: ∃k, x = ⌊N/k^2⌋] x( M(⌊√(N/x)⌋) - M(⌊√(N/(x+1))⌋) )LL(N);ll L = 3 * pow(N, 1.0 / 5.0), K = max(L, (ll)sqrtl(divceil(N, L)));dump(N, K, L);DirichletPQ<ll, 2> zeta(DirichletP<ll>(K, zeta_primepower<ll>), N, L, zeta_prefix_sum<ll>);auto mobius = zeta.inv();ll ans = 0;for (ll k = 1; k * k <= N;){ll x = N / (k * k);dump(k, x);ans += x * (mobius.getqF(x) - (x == N ? 0 : mobius.getqF(x + 1)));k = sqrtl(N / x) + 1;}PRINT(ans);//*//* counting primes https://judge.yosupo.jp/problem/counting_primesLL(N);ll M = sqrtl(N);DirichletPQ<ll> zeta(DirichletP<ll>(M, zeta_primepower<ll>), N, M, zeta_prefix_sum<ll>);auto zeta_prime = lucy_dp(zeta, zeta_primepower<ll>);PRINT(zeta_prime.getqF(1));//*///* sum of primes https://yukicoder.me/problems/no/713LL(N);ll M = sqrtl(N);DirichletPQ<ll> id(DirichletP<ll>(M, id_primepower<ll>), N, M, id_prefix_sum<ll>);auto id_prime = lucy_dp(id, id_primepower<ll>);PRINT(id_prime.getqF(1));//*/}void test(){/*#ifdef LOCALrep(t, 100000){dump(t);// ----- generate cases -----ll N = 1 + rand() % 5;ll K = -10 + rand() % 21;vl A(N);rep(i, N) A.at(i) = -10 + rand() % 21;// --------------------------// ------ check output ------auto god = naive(K, A);auto ans = solve(K, A);if (god != ans){dump(N, K, A);dump(god, ans);exit(0);}// --------------------------}dump("ok");#endif//*/}int main(){cauto CERR = [](cauto &val){#ifndef BOJcerr << val;#endif};#if defined FAST_IO and not defined LOCALCERR("[FAST_IO]\n\n");cin.tie(0);ios::sync_with_stdio(false);#endifcout << fixed << setprecision(20);test();init();#if defined AOJ_TESTCASE or (defined LOCAL and defined SINGLE_TESTCASE)CERR("[AOJ_TESTCASE]\n\n");while (true) main2();#elif defined SINGLE_TESTCASECERR("[SINGLE_TESTCASE]\n\n");main2();#elif defined MULTI_TESTCASECERR("[MULTI_TESTCASE]\n\n");int T;cin >> T;while (T--) main2();#endif}