#line 1 "template/template.hpp" #include #define rep(i, a, n) for (int i = (int)(a); i < (int)(n); i++) #define rrep(i, a, n) for (int i = ((int)(n)-1); i >= (int)(a); i--) #define Rep(i, a, n) for (i64 i = (i64)(a); i < (i64)(n); i++) #define RRep(i, a, n) for (i64 i = ((i64)(n)-i64(1)); i >= (i64)(a); i--) #define all(v) (v).begin(), (v).end() #define rall(v) (v).rbegin(), (v).rend() #line 2 "template/int_alias.hpp" #line 4 "template/int_alias.hpp" namespace ebi { using ld = long double; using std::size_t; using i8 = std::int8_t; using u8 = std::uint8_t; using i16 = std::int16_t; using u16 = std::uint16_t; using i32 = std::int32_t; using u32 = std::uint32_t; using i64 = std::int64_t; using u64 = std::uint64_t; using i128 = __int128_t; using u128 = __uint128_t; } // namespace ebi #line 2 "template/io.hpp" #line 5 "template/io.hpp" #include #line 7 "template/io.hpp" namespace ebi { template std::ostream &operator<<(std::ostream &os, const std::pair &pa) { return os << pa.first << " " << pa.second; } template std::istream &operator>>(std::istream &os, std::pair &pa) { return os >> pa.first >> pa.second; } template std::ostream &operator<<(std::ostream &os, const std::vector &vec) { for (std::size_t i = 0; i < vec.size(); i++) os << vec[i] << (i + 1 == vec.size() ? "" : " "); return os; } template std::istream &operator>>(std::istream &os, std::vector &vec) { for (T &e : vec) std::cin >> e; return os; } template std::ostream &operator<<(std::ostream &os, const std::optional &opt) { if (opt) { os << opt.value(); } else { os << "invalid value"; } return os; } void fast_io() { std::cout << std::fixed << std::setprecision(15); std::cin.tie(nullptr); std::ios::sync_with_stdio(false); } } // namespace ebi #line 2 "template/utility.hpp" #line 5 "template/utility.hpp" #line 2 "graph/base.hpp" #line 5 "graph/base.hpp" #include #line 7 "graph/base.hpp" #line 2 "data_structure/simple_csr.hpp" #line 6 "data_structure/simple_csr.hpp" namespace ebi { template struct simple_csr { simple_csr() = default; simple_csr(int n, const std::vector>& elements) : start(n + 1, 0), elist(elements.size()) { for (auto e : elements) { start[e.first + 1]++; } for (auto i : std::views::iota(0, n)) { start[i + 1] += start[i]; } auto counter = start; for (auto [i, e] : elements) { elist[counter[i]++] = e; } } simple_csr(const std::vector>& es) : start(es.size() + 1, 0) { int n = es.size(); for (auto i : std::views::iota(0, n)) { start[i + 1] = (int)es[i].size() + start[i]; } elist.resize(start.back()); for (auto i : std::views::iota(0, n)) { std::copy(es[i].begin(), es[i].end(), elist.begin() + start[i]); } } int size() const { return (int)start.size() - 1; } const auto operator[](int i) const { return std::ranges::subrange(elist.begin() + start[i], elist.begin() + start[i + 1]); } auto operator[](int i) { return std::ranges::subrange(elist.begin() + start[i], elist.begin() + start[i + 1]); } const auto operator()(int i, int l, int r) const { return std::ranges::subrange(elist.begin() + start[i] + l, elist.begin() + start[i + 1] + r); } auto operator()(int i, int l, int r) { return std::ranges::subrange(elist.begin() + start[i] + l, elist.begin() + start[i + 1] + r); } private: std::vector start; std::vector elist; }; } // namespace ebi #line 9 "graph/base.hpp" namespace ebi { template struct Edge { int from, to; T cost; int id; }; template struct Graph { using cost_type = E; using edge_type = Edge; Graph(int n_) : n(n_) {} Graph() = default; void add_edge(int u, int v, cost_type c) { assert(!prepared && u < n && v < n); buff.emplace_back(u, edge_type{u, v, c, m}); edges.emplace_back(edge_type{u, v, c, m++}); } void add_undirected_edge(int u, int v, cost_type c) { assert(!prepared && u < n && v < n); buff.emplace_back(u, edge_type{u, v, c, m}); buff.emplace_back(v, edge_type{v, u, c, m}); edges.emplace_back(edge_type{u, v, c, m}); m++; } void read_tree(int offset = 1, bool is_weighted = false) { read_graph(n - 1, offset, false, is_weighted); } void read_parents(int offset = 1) { for (auto i : std::views::iota(1, n)) { int p; std::cin >> p; p -= offset; add_undirected_edge(p, i, 1); } build(); } void read_graph(int e, int offset = 1, bool is_directed = false, bool is_weighted = false) { for (int i = 0; i < e; i++) { int u, v; std::cin >> u >> v; u -= offset; v -= offset; if (is_weighted) { cost_type c; std::cin >> c; if (is_directed) { add_edge(u, v, c); } else { add_undirected_edge(u, v, c); } } else { if (is_directed) { add_edge(u, v, 1); } else { add_undirected_edge(u, v, 1); } } } build(); } void build() { assert(!prepared); csr = simple_csr(n, buff); buff.clear(); prepared = true; } int size() const { return n; } int node_number() const { return n; } int edge_number() const { return m; } edge_type get_edge(int i) const { assert(prepared); return edges[i]; } std::vector get_edges() const { assert(prepared); return edges; } const auto operator[](int i) const { assert(prepared); return csr[i]; } auto operator[](int i) { assert(prepared); return csr[i]; } private: int n, m = 0; std::vector> buff; std::vector edges; simple_csr csr; bool prepared = false; }; } // namespace ebi #line 8 "template/utility.hpp" namespace ebi { template inline bool chmin(T &a, T b) { if (a > b) { a = b; return true; } return false; } template inline bool chmax(T &a, T b) { if (a < b) { a = b; return true; } return false; } template T safe_ceil(T a, T b) { if (a % b == 0) return a / b; else if (a >= 0) return (a / b) + 1; else return -((-a) / b); } template T safe_floor(T a, T b) { if (a % b == 0) return a / b; else if (a >= 0) return a / b; else return -((-a) / b) - 1; } constexpr i64 LNF = std::numeric_limits::max() / 4; constexpr int INF = std::numeric_limits::max() / 2; const std::vector dy = {1, 0, -1, 0, 1, 1, -1, -1}; const std::vector dx = {0, 1, 0, -1, 1, -1, 1, -1}; } // namespace ebi #line 2 "template/debug_template.hpp" #line 4 "template/debug_template.hpp" namespace ebi { #ifdef LOCAL #define debug(...) \ std::cerr << "LINE: " << __LINE__ << " [" << #__VA_ARGS__ << "]:", \ debug_out(__VA_ARGS__) #else #define debug(...) #endif void debug_out() { std::cerr << std::endl; } template void debug_out(Head h, Tail... t) { std::cerr << " " << h; if (sizeof...(t) > 0) std::cerr << " :"; debug_out(t...); } } // namespace ebi #line 2 "data_structure/static_rectangle_sum.hpp" #line 6 "data_structure/static_rectangle_sum.hpp" #line 2 "data_structure/compress.hpp" #line 6 "data_structure/compress.hpp" namespace ebi { template struct compress { private: std::vector cp; public: compress() = default; compress(std::vector cp_) : cp(cp_) { build(); } void build() { std::sort(cp.begin(), cp.end()); cp.erase(std::unique(cp.begin(), cp.end()), cp.end()); } void add(const T &val) { cp.emplace_back(val); } int get(const T &val) const { return std::lower_bound(cp.begin(), cp.end(), val) - cp.begin(); } int size() const { return cp.size(); } bool find(const T &val) const { auto itr = std::lower_bound(cp.begin(), cp.end(), val); if (itr == cp.end()) return false; else return *itr == val; } T val(int idx) const { assert(0 <= idx && idx < (int)cp.size()); return cp[idx]; } }; } // namespace ebi #line 2 "data_structure/fenwick_tree.hpp" #line 5 "data_structure/fenwick_tree.hpp" namespace ebi { template struct fenwick_tree { private: int n; std::vector data; public: fenwick_tree(int _n) : n(_n), data(std::vector(_n + 1, T(0))) {} void add(int i, T val) { i++; for (int x = i; x <= n; x += x & -x) { data[x] += val; } } T prefix_sum(int i) const { assert(0 <= i && i <= n); T ret = 0; for (int x = i; x > 0; x -= x & -x) { ret += data[x]; } return ret; } T sum(int l, int r) const { return prefix_sum(r) - prefix_sum(l); } T all_sum() const { return prefix_sum(n); } // prefix_sum(x) >= key となる最小のxを返す関数 O(log N) int lower_bound(T key) { if (key <= 0) return 0; int x = 0; int max = 1; while ((max << 1) <= n) max <<= 1; for (int k = max; k > 0; k >>= 1) { if (x + k <= n && data[x + k] < key) { x += k; key -= data[x]; } } return x + 1; } }; } // namespace ebi #line 9 "data_structure/static_rectangle_sum.hpp" namespace ebi { template struct static_rectangle_sum { private: public: static_rectangle_sum() = default; void add_point(S x, S y, T val) { p.emplace_back(x, y, val); cp_x.add(x); cp_y.add(y); } void add_query(S l, S d, S r, S u) { q.push_back({l, d, r, u}); cp_x.add(l); cp_x.add(r); cp_y.add(d); cp_y.add(u); } std::vector run() { assert(is_first); is_first = false; cp_x.build(); cp_y.build(); std::vector ptable(cp_x.size(), std::vector()); std::vector qtable(cp_x.size(), std::vector(2, std::vector())); for (int i = 0; auto [x, y, val] : p) { ptable[cp_x.get(x)].emplace_back(i); i++; } for (int i = 0; auto [l, d, r, u] : q) { qtable[cp_x.get(l)][0].emplace_back(i); qtable[cp_x.get(r)][1].emplace_back(i); i++; } std::vector res(q.size(), 0); fenwick_tree ftree(cp_y.size()); for (int i = 0; i < cp_x.size(); i++) { for (int j = 0; j < 2; j++) { for (auto idx : qtable[i][j]) { int d = q[idx][1], u = q[idx][3]; res[idx] += (j == 0 ? -1 : 1) * ftree.sum(cp_y.get(d), cp_y.get(u)); } } for (auto idx : ptable[i]) { auto [x, y, val] = p[idx]; ftree.add(cp_y.get(y), val); } } return res; } private: bool is_first = true; std::vector> p; std::vector> q; compress cp_x, cp_y; }; } // namespace ebi #line 3 "a.cpp" namespace ebi { void main_() { int q; std::cin >> q; const int n = 1'000'010; std::vector table(n, -1); table[0] = 0; table[1] = 0; rep(i,1,n) { for(int j = 2 * i; j < n; j += i) { chmax(table[j], i); } } static_rectangle_sum rec; rep(i,1,n) { rec.add_point(i, table[i], 1); } rep(i,0,q) { int l,r; std::cin >> l >> r; r++; rec.add_query(l, 0, r, l); } auto ans = rec.run(); for(auto x: ans) std::cout << x << '\n'; } } // namespace ebi int main() { ebi::fast_io(); int t = 1; // std::cin >> t; while (t--) { ebi::main_(); } return 0; }