#include #if __has_include() #include std::istream &operator>>(std::istream &is, atcoder::modint &v) { long long value; is >> value; v = value; return is; } std::ostream &operator<<(std::ostream &os, const atcoder::modint &v) { os << v.val(); return os; } std::ostream &operator<<(std::ostream &os, const atcoder::modint998244353 &v) { os << v.val(); return os; } std::istream &operator>>(std::istream &is, atcoder::modint998244353 &v) { long long x; is >> x; v = x; return is; } std::ostream &operator<<(std::ostream &os, const atcoder::modint1000000007 &v) { os << v.val(); return os; } std::istream &operator>>(std::istream &is, atcoder::modint1000000007 &v) { long long x; is >> x; v = x; return is; } #endif using namespace std; using ll = long long; using lint = __int128_t; using pll = pair; #define newl '\n'; #define rep(i, s, t) for (ll i = s; i < (ll)(t); i++) #define rrep(i, s, t) for (ll i = (ll)(t) - 1; i >= (ll)(s); i--) #define all(x) begin(x), end(x) #define SZ(x) ll(x.size()) #define eb emplace_back #define pb push_back #define TT template TT using vec = vector; TT using vvec = vec>; TT using vvvec = vec>; TT using minheap = priority_queue, greater>; TT using maxheap = priority_queue; TT bool chmin(T &x, T y) { return x > y ? (x = y, true) : false; } TT bool chmax(T &x, T y) { return x < y ? (x = y, true) : false; } TT T smod(T x, T mod) { x %= mod; if (x < 0) x += mod; return x; } TT bool rng(T l, T x, T r) { return l <= x && x < r; } TT T flr(T a, T b) { if (b < 0) a = -a, b = -b; return a >= 0 ? a / b : (a + 1) / b - 1; } TT T cil(T a, T b) { if (b < 0) a = -a, b = -b; return a > 0 ? (a - 1) / b + 1 : a / b; } TT T sqr(T x) { return x * x; } //{0, 1, ... } -> {p[0], p[1], ...} template void rearrange(vector &A, vector const &p) { assert(p.size() == A.size()); vector a = A; for (int i = 0; i < ssize(A); ++i) { a[i] = A[p[i]]; } swap(a, A); } template void rearrange(vector &A, vector p, vector &...rest) { rearrange(A, p); (rearrange(rest, p), ...); } template void rearrange(vector &A, Compare cmp, vector &...rest) { vector p(ssize(A)); iota(p.begin(), p.end(), 0); sort(p.begin(), p.end(), cmp); rearrange(A, p); (rearrange(rest, p), ...); } struct io_setup { io_setup() { ios::sync_with_stdio(false); std::cin.tie(nullptr); cout << fixed << setprecision(15); } } io_setup; template ostream &operator<<(ostream &os, const pair &p) { os << p.first << " " << p.second; return os; } TT ostream &operator<<(ostream &os, const vector &v) { for (size_t i = 0; i < v.size(); i++) { os << v[i] << (i + 1 != v.size() ? " " : ""); } return os; } template ostream &operator<<(ostream &os, const array &v) { for (size_t i = 0; i < n; i++) { os << v[i] << (i + 1 != n ? " " : ""); } return os; } template ostream &operator<<(ostream &os, const vvec &v) { for (size_t i = 0; i < v.size(); i++) { os << v[i] << (i + 1 != v.size() ? "\n" : ""); } return os; } TT istream &operator>>(istream &is, vector &v) { for (size_t i = 0; i < v.size(); i++) { is >> v[i]; } return is; } #if __has_include() #include #else #define dbg(...) true #define DBG(...) true #define OUT(...) true #endif struct notlinear_sieve { int n; vector sm; notlinear_sieve(int max_n) : n(max_n), sm(max_n + 1) { assert(1 <= n); iota(sm.begin(), sm.end(), 0); if (n >= 2) sm[2] = 2; for (int j = 4; j <= n; j += 2) sm[j] = 2; for (int i = 3; i * i <= n; i += 2) { if (sm[i] != i) continue; for (int j = i * 2; j <= n; j += i) { if (sm[j] == j) sm[j] = i; } } } bool is_prime(int v) const noexcept { assert(v <= n); if (v <= 1) return false; return sm[v] == v; } vector primes(int max_n) const noexcept { assert(1 <= max_n && max_n <= n); vector ret; for (int i = 2; i <= max_n; i++) if (is_prime(i)) ret.push_back(i); return ret; } // sorted vector> factorize(int v) const noexcept { assert(1 <= v && v <= n); vector> ret; while (sm[v] != v) { int tmp = v; int c = 0; while (tmp % sm[v] == 0) c++, tmp /= sm[v]; ret.emplace_back(sm[v], c); v = tmp; } if (v != 1) ret.emplace_back(v, 1); return ret; } int divcnt(int v) const noexcept { assert(1 <= v && v <= n); auto ps = factorize(v); int ret = 1; for (auto [p, c] : ps) ret *= (c + 1); return ret; } // not sorted vector divs(int v) const noexcept { assert(1 <= v && v <= n); auto ps = factorize(v); int sz = 1; for (auto [p, c] : ps) sz *= (c + 1); vector ret(sz); ret[0] = 1; int r = 1; for (auto [p, c] : ps) { int nr = r; for (int j = 0; j < c; j++) { for (int k = 0; k < r; k++) { ret[nr] = p * ret[nr - r]; nr++; } } r = nr; } return ret; } // 偶数...+1 奇数...-1 p^2...0 template vector mobius(int N) const { assert(N <= n); vector ret(N + 1, 1); for (int p = 2; p <= N; p++) if (is_prime(p)) { for (int q = p; q <= N; q += p) { if ((q / p) % p == 0) ret[q] = 0; else ret[q] = -ret[q]; } } return ret; } // 以下4つは素因数ごとの累積和と思うと良い。計算量はO(nloglogn) // zeta_transform... 結合則 + 交換則 ならなんでも乗る // mobius_transform ... 結合 + 交換 + 逆元の存在 ならなんでも乗る // f -> F 約数の添字をadd template vector divisor_zeta_transform(vector A) const { int N = int(A.size()) - 1; assert(N <= n); for (int p = 2; p <= N; p++) { if (is_prime(p)) { for (int k = 1; k * p <= N; k++) { A[k * p] += A[k]; } } } return A; } // F -> f template vector divisor_mobius_transform(vector A) const { int N = int(A.size()) - 1; assert(N <= n); for (int p = 2; p <= N; p++) { if (is_prime(p)) { for (int k = N / p; k >= 1; k--) { A[k * p] -= A[k]; } } } return A; } // f -> F 倍数の添字をadd template vector multiple_zeta_transform(vector A) const { int N = int(A.size()) - 1; assert(N <= n); for (int p = 2; p <= N; p++) { if (is_prime(p)) { for (int k = N / p; k >= 1; k--) { A[k] += A[k * p]; } } } return A; } // F -> f template vector multiple_mobius_transform(vector A) const { int N = int(A.size()) - 1; assert(N <= n); for (int p = 2; p <= N; p++) { if (is_prime(p)) { for (int k = 1; k <= N / p; k++) { A[k] -= A[k * p]; } } } return A; } }; template struct fenwick_tree { public: fenwick_tree() : n(0) { } explicit fenwick_tree(int n) : n(n), data(n), raw(n, T()), S(T()) { } void add(int p, T x) { assert(0 <= p && p < n); raw[p] += x; S += x; p++; while (p <= n) { data[p - 1] += x; p += p & -p; } } T sum(int r) const { T s = 0; while (r > 0) { s += data[r - 1]; r -= r & -r; } return s; } T prod(int l, int r) const { assert(0 <= l && l <= r && r <= n); return sum(r) - sum(l); } T all_prod() const { return S; } T get(int p) const { return raw[p]; } template int max_right(F f) const { assert(f(0)); T s = 0; int p = 0; for (int i = 32 - __builtin_clz(n) - 1; i >= 0; i--) { int k = p + (1 << i); if (k <= n && f(s + data[k - 1])) { s += data[k - 1]; p = k; } } return p; } private: int n; vector data; vector raw; T S; }; const ll M = 1'000'000; notlinear_sieve sieve(M+10); int main() { ll q; cin >> q; fenwick_tree fen(M+10); vector ls(M + 10, vector()); vector ans(q, -1); rep(qi, 0, q) { ll l, r; cin >> l >> r; r++; ls[r].eb(l, qi); } rep(r, 1, M + 2) { for (auto [l, i] : ls[r]) { ans[i] = fen.prod(l, r); } fen.add(r, 1); // rの最大の約数は? if(r==1) continue; auto ds = sieve.divs(r); sort(all(ds)); reverse(all(ds)); fen.add(ds[1], -1); } for(auto v : ans) cout << v << newl; } /* 同じ議論を繰り返さない do smth instead of nothing and stay organized WRITE STUFF DOWN DON'T GET STUCK ON ONE APPROACH */