結果
| 問題 |
No.3101 Range Eratosthenes Query
|
| ユーザー |
 hato336
|
| 提出日時 | 2025-04-12 08:54:35 |
| 言語 | C++23 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 2,947 ms / 3,000 ms |
| コード長 | 23,686 bytes |
| コンパイル時間 | 4,977 ms |
| コンパイル使用メモリ | 327,104 KB |
| 実行使用メモリ | 263,640 KB |
| 最終ジャッジ日時 | 2025-04-12 08:55:52 |
| 合計ジャッジ時間 | 73,347 ms |
|
ジャッジサーバーID （参考情報） |
judge4 / judge2 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 2 |
| other | AC * 24 |
ソースコード
#include <bits/stdc++.h>
using namespace std;
#define all(...) std::begin(__VA_ARGS__), std::end(__VA_ARGS__)
#define rall(...) std::rbegin(__VA_ARGS__), std::rend(__VA_ARGS__)
#define OVERLOAD_REP(_1, _2, _3, _4, name, ...) name
#define REP1(n) for(ll i=0;i<n;i++)
#define REP2(i, n) for (ll i=0;i<n;i++)
#define REP3(i, a, n) for (ll i=a;i<n;i++)
#define REP4(i, a, b, n) for(ll i=a;i<n;i+=b)
#define rep(...) OVERLOAD_REP(__VA_ARGS__, REP4, REP3, REP2, REP1)(__VA_ARGS__)
#define OVERLOAD_RREP(_1, _2, _3, _4, name, ...) name
#define RREP1(n) for(ll i=n-1;i>=0;i--)
#define RREP2(i, n) for(ll i=n-1;i>=0;i--)
#define RREP3(i, a, n) for(ll i=n-1;i>=a;i--)
#define RREP4(i, a, b, n) for(ll i=n-1;i>=a;i-=b)
#define rrep(...) OVERLOAD_RREP(__VA_ARGS__, RREP4, RREP3, RREP2, RREP1)(__VA_ARGS__)
#define foa(a,v) (auto& a : (v))
#define uniq(a) sort(all(a));a.erase(unique(all(a)),end(a))
#define len(n) (long long)(n).size()
#define pb push_back
using ll = long long;
using ld = long double;
using ull = unsigned long long;
using vi = vector<int>;
using vvi = vector<vi>;
using vvvi = vector<vvi>;
using vll = vector<ll>;
using vvll = vector<vll>;
using vvvll = vector<vvll>;
using vs = vector<string>;
using vvs = vector<vs>;
using vvvs = vector<vvs>;
using vld = vector<ld>;
using vvld = vector<vld>;
using vvvld = vector<vvld>;
using vc = vector<char>;
using vvc = vector<vc>;
using vvvc = vector<vvc>;
using pll = pair<ll,ll>;
using vpll = vector<pll>;
template<class... T>
constexpr auto min(T... a){
return min(initializer_list<common_type_t<T...>>{a...});
}
template<class... T>
void input(T&... a){
(cin >> ... >> a);
}
ll POW(ll a,ll b){
ll ans = 1;
while (b){
if (b & 1){
ans *= a;
}
a *= a;
b /= 2;
}
return ans;
}
ll MODPOW(ll a,ll b,ll c){
ll ans = 1;
while (b){
if (b & 1){
ans *= a;
ans %= c;
}
a *= a;
a %= c;
b /= 2;
}
return ans;
}
#define INT(...) int __VA_ARGS__; input(__VA_ARGS__)
#define LL(...) ll __VA_ARGS__; input(__VA_ARGS__)
#define ULL(...) ull __VA_ARGS__; input(__VA_ARGS__)
#define LD(...) ld __VA_ARGS__; input(__VA_ARGS__)
#define STR(...) string __VA_ARGS__; input(__VA_ARGS__)
#define CHA(...) char __VA_ARGS__; input(__VA_ARGS__)
#define VLL(name,length) vll name(length);rep(i,length){cin >> name[i];}
#define VVLL(name,h,w) vvll name(h,vll(w));rep(i,h)rep(j,w){cin >> name[i][j];}
#define VVVLL(name,a,b,c) vvvll name(a,vvll(b,vll(c)));rep(i,a)rep(j,b)rep(k,c){cin >> name[i][j][k];}
#define VI(name,length) vi name(length);rep(i,length){cin >> name[i];}
#define VVI(name,h,w) vvi name(h,vi(w));rep(i,h)rep(j,w){cin >> name[i][j];}
#define VVVI(name,a,b,c) vvvi name(a,vvll(b,vi(c)));rep(i,a)rep(j,b)rep(k,c){cin >> name[i][j][k];}
#define VLD(name,length) vld name(length);rep(i,length){cin >> name[i];}
#define VVLD(name,h,w) vvld name(h,vld(w));rep(i,h)rep(j,w){cin >> name[i][j];}
#define VVVLD(name,a,b,c) vvvld name(a,vvld(b,vld(c)));rep(i,a)rep(j,b)rep(k,c){cin >> name[i][j][k];}
#define VC(name,length) vc name(length);rep(i,length){cin >> name[i];}
#define VVC(name,h,w) vvc name(h,vc(w));rep(i,h)rep(j,w){cin >> name[i][j];}
#define VVVC(name,a,b,c) vvvc name(a,vvc(b,vc(c)));rep(i,a)rep(j,b)rep(k,c){cin >> name[i][j][k];}
#define VS(name,length) vs name(length);rep(i,length){cin >> name[i];}
#define VVS(name,h,w) vvs name(h,vs(w));rep(i,h)rep(j,w){cin >> name[i][j];}
#define VVVS(name,a,b,c) vvvs name(a,vvs(b,vs(c)));rep(i,a)rep(j,b)rep(k,c){cin >> name[i][j][k];}
#define PLL(name) pll name;cin>>name.first>>name.second;
#define VPLL(name,length) vpll name(length);rep(i,length){cin>>name[i].first>>name[i].second;}
void print(){cout << "\n";}
template<class T, class... Ts>
void print(const T& a, const Ts&... b){cout << a;(cout << ... << (cout << ' ', b));cout << '\n';}
void print(vll x){rep(i,len(x)){cout << x[i];if(i!=len(x)-1){cout << " ";}else{cout << '\n';}}}
void print(vvll x){rep(i,len(x))rep(j,len(x[i])){cout << x[i][j];if(j!=len(x[i])-1){cout << " ";}else{cout << '\n';}}}
void print(vi x){rep(i,len(x)){cout << x[i];if(i!=len(x)-1){cout << " ";}else{cout << '\n';}}}
void print(vvi x){rep(i,len(x))rep(j,len(x[i])){cout << x[i][j];if(j!=len(x[i])-1){cout << " ";}else{cout << '\n';}}}
void print(vvvi x){rep(i,len(x))rep(j,len(x[i]))rep(k,len(x[i][j])){cout << x[i][j][k];if(k!=len(x[i][j])-1){cout << " ";}else if(j!=len(x[i])-1){cout << " | ";}else{cout << '\n';}}}
void print(vld x){rep(i,len(x)){cout << x[i];if(i!=len(x)-1){cout << " ";}else{cout << '\n';}}}
void print(vvld x){rep(i,len(x))rep(j,len(x[i])){cout << x[i][j];if(j!=len(x[i])-1){cout << " ";}else{cout << '\n';}}}
void print(vvvld x){rep(i,len(x))rep(j,len(x[i]))rep(k,len(x[i][j])){cout << x[i][j][k];if(k!=len(x[i][j])-1){cout << " ";}else if(j!=len(x[i])-1){cout << " | ";}else{cout << '\n';}}}
void print(vc x){rep(i,len(x)){cout << x[i];if(i!=len(x)-1){cout << " ";}else{cout << '\n';}}}
void print(vvc x){rep(i,len(x))rep(j,len(x[i])){cout << x[i][j];if(j!=len(x[i])-1){cout << " ";}else{cout << '\n';}}}
void print(vvvc x){rep(i,len(x))rep(j,len(x[i]))rep(k,len(x[i][j])){cout << x[i][j][k];if(k!=len(x[i][j])-1){cout << " ";}else if(j!=len(x[i])-1){cout << " | ";}else{cout << '\n';}}}
void print(vs x){rep(i,len(x)){cout << x[i];if(i!=len(x)-1){cout << " ";}else{cout << '\n';}}}
void print(vvs x){rep(i,len(x))rep(j,len(x[i])){cout << x[i][j];if(j!=len(x[i])-1){cout << " ";}else{cout << '\n';}}}
void print(vvvs x){rep(i,len(x))rep(j,len(x[i]))rep(k,len(x[i][j])){cout << x[i][j][k];if(k!=len(x[i][j])-1){cout << " ";}else if(j!=len(x[i])-1){cout << " | ";}else{cout << '\n';}}}
void print(pll x){cout << x.first << x.second << '\n';}
void print(vpll x){rep(i,len(x)){cout << x[i].first << x[i].second << '\n';}}
#line 2 "misc/mo.hpp"
struct Mo {
int width;
vector<int> left, right, order;
Mo(int N, int Q) : order(Q) {
width = max<int>(1, 1.0 * N / max<double>(1.0, sqrt(Q * 2.0 / 3.0)));
iota(begin(order), end(order), 0);
}
void insert(int l, int r) { /* [l, r) */
left.emplace_back(l);
right.emplace_back(r);
}
template <typename AL, typename AR, typename DL, typename DR, typename REM>
void run(const AL &add_left, const AR &add_right, const DL &delete_left,
const DR &delete_right, const REM &rem) {
assert(left.size() == order.size());
sort(begin(order), end(order), [&](int a, int b) {
int ablock = left[a] / width, bblock = left[b] / width;
if (ablock != bblock) return ablock < bblock;
if (ablock & 1) return right[a] < right[b];
return right[a] > right[b];
});
int nl = 0, nr = 0;
for (auto idx : order) {
while (nl > left[idx]) add_left(--nl);
while (nr < right[idx]) add_right(nr++);
while (nl < left[idx]) delete_left(nl++);
while (nr > right[idx]) delete_right(--nr);
rem(idx);
}
}
};
/**
* @brief Mo's algorithm
* @docs docs/misc/mo.md
*/
// CUT begin
// Count elements in $[A_\mathrm{begin}, ..., A_{\mathrm{end}-1}]$ which satisfy $A_i < \mathrm{query}$
// Complexity: $O(N \log N)$ for initialization, $O(\log^2 N)$ for each query
// Verified: https://codeforces.com/contest/1288/submission/68865506
template <typename T> struct merge_sort_tree {
int N;
std::vector<std::vector<T>> x;
merge_sort_tree() = default;
merge_sort_tree(const std::vector<T> &vec) : N(vec.size()) {
x.resize(N * 2);
for (int i = 0; i < N; i++) x[N + i] = {vec[i]};
for (int i = N - 1; i; i--) {
std::merge(x[i * 2].begin(), x[i * 2].end(), x[i * 2 + 1].begin(), x[i * 2 + 1].end(),
std::back_inserter(x[i]));
}
}
int cntLess(int l, int r, T query) const {
l += N, r += N;
int ret = 0;
while (l < r) {
if (l & 1)
ret += std::lower_bound(x[l].begin(), x[l].end(), query) - x[l].begin(), l++;
if (r & 1)
r--, ret += std::lower_bound(x[r].begin(), x[r].end(), query) - x[r].begin();
l >>= 1, r >>= 1;
}
return ret;
}
int cntLesseq(int l, int r, T query) const {
l += N, r += N;
int ret = 0;
while (l < r) {
if (l & 1)
ret += std::upper_bound(x[l].begin(), x[l].end(), query) - x[l].begin(), l++;
if (r & 1)
r--, ret += std::upper_bound(x[r].begin(), x[r].end(), query) - x[r].begin();
l >>= 1, r >>= 1;
}
return ret;
}
int cntMore(int begin, int end, T query) const {
int tot = std::max(0, std::min(end, N) - std::max(begin, 0));
return tot - cntLesseq(begin, end, query);
}
int cntMoreeq(int begin, int end, T query) const {
int tot = std::max(0, std::min(end, N) - std::max(begin, 0));
return tot - cntLess(begin, end, query);
}
template <class OStream> friend OStream &operator<<(OStream &os, const merge_sort_tree &clt) {
os << '[';
for (int i = 0; i < clt.N; i++) os << clt.x[clt.N + i][0] << ',';
return os << ']';
}
};
// N の約数をすべて求める関数
vector<long long> calc_divisors(long long N) {
// 答えを表す集合
vector<long long> res;
// 各整数 i が N の約数かどうかを調べる
for (long long i = 1; i * i <= N; ++i) {
// i が N の約数でない場合はスキップ
if (N % i != 0) continue;
// i は約数である
res.push_back(i);
// N ÷ i も約数である (重複に注意)
if (N / i != i) res.push_back(N / i);
}
// 約数を小さい順に並び替えて出力
sort(res.begin(), res.end());
return res;
}
#line 2 "prime/fast-factorize.hpp"
#include <cstdint>
#include <numeric>
#include <vector>
using namespace std;
#line 2 "internal/internal-math.hpp"
#line 2 "internal/internal-type-traits.hpp"
#include <type_traits>
using namespace std;
namespace internal {
template <typename T>
using is_broadly_integral =
typename conditional_t<is_integral_v<T> || is_same_v<T, __int128_t> ||
is_same_v<T, __uint128_t>,
true_type, false_type>::type;
template <typename T>
using is_broadly_signed =
typename conditional_t<is_signed_v<T> || is_same_v<T, __int128_t>,
true_type, false_type>::type;
template <typename T>
using is_broadly_unsigned =
typename conditional_t<is_unsigned_v<T> || is_same_v<T, __uint128_t>,
true_type, false_type>::type;
#define ENABLE_VALUE(x) \
template <typename T> \
constexpr bool x##_v = x<T>::value;
ENABLE_VALUE(is_broadly_integral);
ENABLE_VALUE(is_broadly_signed);
ENABLE_VALUE(is_broadly_unsigned);
#undef ENABLE_VALUE
#define ENABLE_HAS_TYPE(var) \
template <class, class = void> \
struct has_##var : false_type {}; \
template <class T> \
struct has_##var<T, void_t<typename T::var>> : true_type {}; \
template <class T> \
constexpr auto has_##var##_v = has_##var<T>::value;
#define ENABLE_HAS_VAR(var) \
template <class, class = void> \
struct has_##var : false_type {}; \
template <class T> \
struct has_##var<T, void_t<decltype(T::var)>> : true_type {}; \
template <class T> \
constexpr auto has_##var##_v = has_##var<T>::value;
} // namespace internal
#line 4 "internal/internal-math.hpp"
namespace internal {
#include <cassert>
#include <utility>
#line 10 "internal/internal-math.hpp"
using namespace std;
// a mod p
template <typename T>
T safe_mod(T a, T p) {
a %= p;
if constexpr (is_broadly_signed_v<T>) {
if (a < 0) a += p;
}
return a;
}
// 返り値：pair(g, x)
// s.t. g = gcd(a, b), xa = g (mod b), 0 <= x < b/g
template <typename T>
pair<T, T> inv_gcd(T a, T p) {
static_assert(is_broadly_signed_v<T>);
a = safe_mod(a, p);
if (a == 0) return {p, 0};
T b = p, x = 1, y = 0;
while (a != 0) {
T q = b / a;
swap(a, b %= a);
swap(x, y -= q * x);
}
if (y < 0) y += p / b;
return {b, y};
}
// 返り値 : a^{-1} mod p
// gcd(a, p) != 1 が必要
template <typename T>
T inv(T a, T p) {
static_assert(is_broadly_signed_v<T>);
a = safe_mod(a, p);
T b = p, x = 1, y = 0;
while (a != 0) {
T q = b / a;
swap(a, b %= a);
swap(x, y -= q * x);
}
assert(b == 1);
return y < 0 ? y + p : y;
}
// T : 底の型
// U : T*T がオーバーフローしない かつ 指数の型
template <typename T, typename U>
T modpow(T a, U n, T p) {
a = safe_mod(a, p);
T ret = 1 % p;
while (n != 0) {
if (n % 2 == 1) ret = U(ret) * a % p;
a = U(a) * a % p;
n /= 2;
}
return ret;
}
// 返り値 : pair(rem, mod)
// 解なしのときは {0, 0} を返す
template <typename T>
pair<T, T> crt(const vector<T>& r, const vector<T>& m) {
static_assert(is_broadly_signed_v<T>);
assert(r.size() == m.size());
int n = int(r.size());
T r0 = 0, m0 = 1;
for (int i = 0; i < n; i++) {
assert(1 <= m[i]);
T r1 = safe_mod(r[i], m[i]), m1 = m[i];
if (m0 < m1) swap(r0, r1), swap(m0, m1);
if (m0 % m1 == 0) {
if (r0 % m1 != r1) return {0, 0};
continue;
}
auto [g, im] = inv_gcd(m0, m1);
T u1 = m1 / g;
if ((r1 - r0) % g) return {0, 0};
T x = (r1 - r0) / g % u1 * im % u1;
r0 += x * m0;
m0 *= u1;
if (r0 < 0) r0 += m0;
}
return {r0, m0};
}
} // namespace internal
#line 2 "misc/rng.hpp"
#line 2 "internal/internal-seed.hpp"
#include <chrono>
using namespace std;
namespace internal {
unsigned long long non_deterministic_seed() {
unsigned long long m =
chrono::duration_cast<chrono::nanoseconds>(
chrono::high_resolution_clock::now().time_since_epoch())
.count();
m ^= 9845834732710364265uLL;
m ^= m << 24, m ^= m >> 31, m ^= m << 35;
return m;
}
unsigned long long deterministic_seed() { return 88172645463325252UL; }
// 64 bit の seed 値を生成 (手元では seed 固定)
// 連続で呼び出すと同じ値が何度も返ってくるので注意
// #define RANDOMIZED_SEED するとシードがランダムになる
unsigned long long seed() {
#if defined(NyaanLocal) && !defined(RANDOMIZED_SEED)
return deterministic_seed();
#else
return non_deterministic_seed();
#endif
}
} // namespace internal
#line 4 "misc/rng.hpp"
namespace my_rand {
using i64 = long long;
using u64 = unsigned long long;
// [0, 2^64 - 1)
u64 rng() {
static u64 _x = internal::seed();
return _x ^= _x << 7, _x ^= _x >> 9;
}
// [l, r]
i64 rng(i64 l, i64 r) {
assert(l <= r);
return l + rng() % u64(r - l + 1);
}
// [l, r)
i64 randint(i64 l, i64 r) {
assert(l < r);
return l + rng() % u64(r - l);
}
// choose n numbers from [l, r) without overlapping
vector<i64> randset(i64 l, i64 r, i64 n) {
assert(l <= r && n <= r - l);
unordered_set<i64> s;
for (i64 i = n; i; --i) {
i64 m = randint(l, r + 1 - i);
if (s.find(m) != s.end()) m = r - i;
s.insert(m);
}
vector<i64> ret;
for (auto& x : s) ret.push_back(x);
sort(begin(ret), end(ret));
return ret;
}
// [0.0, 1.0)
double rnd() { return rng() * 5.42101086242752217004e-20; }
// [l, r)
double rnd(double l, double r) {
assert(l < r);
return l + rnd() * (r - l);
}
template <typename T>
void randshf(vector<T>& v) {
int n = v.size();
for (int i = 1; i < n; i++) swap(v[i], v[randint(0, i + 1)]);
}
} // namespace my_rand
using my_rand::randint;
using my_rand::randset;
using my_rand::randshf;
using my_rand::rnd;
using my_rand::rng;
#line 2 "modint/arbitrary-montgomery-modint.hpp"
#include <iostream>
using namespace std;
template <typename Int, typename UInt, typename Long, typename ULong, int id>
struct ArbitraryLazyMontgomeryModIntBase {
using mint = ArbitraryLazyMontgomeryModIntBase;
inline static UInt mod;
inline static UInt r;
inline static UInt n2;
static constexpr int bit_length = sizeof(UInt) * 8;
static UInt get_r() {
UInt ret = mod;
while (mod * ret != 1) ret *= UInt(2) - mod * ret;
return ret;
}
static void set_mod(UInt m) {
assert(m < (UInt(1u) << (bit_length - 2)));
assert((m & 1) == 1);
mod = m, n2 = -ULong(m) % m, r = get_r();
}
UInt a;
ArbitraryLazyMontgomeryModIntBase() : a(0) {}
ArbitraryLazyMontgomeryModIntBase(const Long &b)
: a(reduce(ULong(b % mod + mod) * n2)){};
static UInt reduce(const ULong &b) {
return (b + ULong(UInt(b) * UInt(-r)) * mod) >> bit_length;
}
mint &operator+=(const mint &b) {
if (Int(a += b.a - 2 * mod) < 0) a += 2 * mod;
return *this;
}
mint &operator-=(const mint &b) {
if (Int(a -= b.a) < 0) a += 2 * mod;
return *this;
}
mint &operator*=(const mint &b) {
a = reduce(ULong(a) * b.a);
return *this;
}
mint &operator/=(const mint &b) {
*this *= b.inverse();
return *this;
}
mint operator+(const mint &b) const { return mint(*this) += b; }
mint operator-(const mint &b) const { return mint(*this) -= b; }
mint operator*(const mint &b) const { return mint(*this) *= b; }
mint operator/(const mint &b) const { return mint(*this) /= b; }
bool operator==(const mint &b) const {
return (a >= mod ? a - mod : a) == (b.a >= mod ? b.a - mod : b.a);
}
bool operator!=(const mint &b) const {
return (a >= mod ? a - mod : a) != (b.a >= mod ? b.a - mod : b.a);
}
mint operator-() const { return mint(0) - mint(*this); }
mint operator+() const { return mint(*this); }
mint pow(ULong n) const {
mint ret(1), mul(*this);
while (n > 0) {
if (n & 1) ret *= mul;
mul *= mul, n >>= 1;
}
return ret;
}
friend ostream &operator<<(ostream &os, const mint &b) {
return os << b.get();
}
friend istream &operator>>(istream &is, mint &b) {
Long t;
is >> t;
b = ArbitraryLazyMontgomeryModIntBase(t);
return (is);
}
mint inverse() const {
Int x = get(), y = get_mod(), u = 1, v = 0;
while (y > 0) {
Int t = x / y;
swap(x -= t * y, y);
swap(u -= t * v, v);
}
return mint{u};
}
UInt get() const {
UInt ret = reduce(a);
return ret >= mod ? ret - mod : ret;
}
static UInt get_mod() { return mod; }
};
// id に適当な乱数を割り当てて使う
template <int id>
using ArbitraryLazyMontgomeryModInt =
ArbitraryLazyMontgomeryModIntBase<int, unsigned int, long long,
unsigned long long, id>;
template <int id>
using ArbitraryLazyMontgomeryModInt64bit =
ArbitraryLazyMontgomeryModIntBase<long long, unsigned long long, __int128_t,
__uint128_t, id>;
#line 2 "prime/miller-rabin.hpp"
#line 4 "prime/miller-rabin.hpp"
using namespace std;
#line 8 "prime/miller-rabin.hpp"
namespace fast_factorize {
template <typename T, typename U>
bool miller_rabin(const T& n, vector<T> ws) {
if (n <= 2) return n == 2;
if (n % 2 == 0) return false;
T d = n - 1;
while (d % 2 == 0) d /= 2;
U e = 1, rev = n - 1;
for (T w : ws) {
if (w % n == 0) continue;
T t = d;
U y = internal::modpow<T, U>(w, t, n);
while (t != n - 1 && y != e && y != rev) y = y * y % n, t *= 2;
if (y != rev && t % 2 == 0) return false;
}
return true;
}
bool miller_rabin_u64(unsigned long long n) {
return miller_rabin<unsigned long long, __uint128_t>(
n, {2, 325, 9375, 28178, 450775, 9780504, 1795265022});
}
template <typename mint>
bool miller_rabin(unsigned long long n, vector<unsigned long long> ws) {
if (n <= 2) return n == 2;
if (n % 2 == 0) return false;
if (mint::get_mod() != n) mint::set_mod(n);
unsigned long long d = n - 1;
while (~d & 1) d >>= 1;
mint e = 1, rev = n - 1;
for (unsigned long long w : ws) {
if (w % n == 0) continue;
unsigned long long t = d;
mint y = mint(w).pow(t);
while (t != n - 1 && y != e && y != rev) y *= y, t *= 2;
if (y != rev && t % 2 == 0) return false;
}
return true;
}
bool is_prime(unsigned long long n) {
using mint32 = ArbitraryLazyMontgomeryModInt<96229631>;
using mint64 = ArbitraryLazyMontgomeryModInt64bit<622196072>;
if (n <= 2) return n == 2;
if (n % 2 == 0) return false;
if (n < (1uLL << 30)) {
return miller_rabin<mint32>(n, {2, 7, 61});
} else if (n < (1uLL << 62)) {
return miller_rabin<mint64>(
n, {2, 325, 9375, 28178, 450775, 9780504, 1795265022});
} else {
return miller_rabin_u64(n);
}
}
} // namespace fast_factorize
using fast_factorize::is_prime;
/**
* @brief Miller-Rabin primality test
*/
#line 12 "prime/fast-factorize.hpp"
namespace fast_factorize {
using u64 = uint64_t;
template <typename mint, typename T>
T pollard_rho(T n) {
if (~n & 1) return 2;
if (is_prime(n)) return n;
if (mint::get_mod() != n) mint::set_mod(n);
mint R, one = 1;
auto f = [&](mint x) { return x * x + R; };
auto rnd_ = [&]() { return rng() % (n - 2) + 2; };
while (1) {
mint x, y, ys, q = one;
R = rnd_(), y = rnd_();
T g = 1;
constexpr int m = 128;
for (int r = 1; g == 1; r <<= 1) {
x = y;
for (int i = 0; i < r; ++i) y = f(y);
for (int k = 0; g == 1 && k < r; k += m) {
ys = y;
for (int i = 0; i < m && i < r - k; ++i) q *= x - (y = f(y));
g = gcd(q.get(), n);
}
}
if (g == n) do
g = gcd((x - (ys = f(ys))).get(), n);
while (g == 1);
if (g != n) return g;
}
exit(1);
}
using i64 = long long;
vector<i64> inner_factorize(u64 n) {
using mint32 = ArbitraryLazyMontgomeryModInt<452288976>;
using mint64 = ArbitraryLazyMontgomeryModInt64bit<401243123>;
if (n <= 1) return {};
u64 p;
if (n <= (1LL << 30)) {
p = pollard_rho<mint32, uint32_t>(n);
} else if (n <= (1LL << 62)) {
p = pollard_rho<mint64, uint64_t>(n);
} else {
exit(1);
}
if (p == n) return {i64(p)};
auto l = inner_factorize(p);
auto r = inner_factorize(n / p);
copy(begin(r), end(r), back_inserter(l));
return l;
}
vector<i64> factorize(u64 n) {
auto ret = inner_factorize(n);
sort(begin(ret), end(ret));
return ret;
}
map<i64, i64> factor_count(u64 n) {
map<i64, i64> mp;
for (auto &x : factorize(n)) mp[x]++;
return mp;
}
vector<i64> divisors(u64 n) {
if (n == 0) return {};
vector<pair<i64, i64>> v;
for (auto &p : factorize(n)) {
if (v.empty() || v.back().first != p) {
v.emplace_back(p, 1);
} else {
v.back().second++;
}
}
vector<i64> ret;
auto f = [&](auto rc, int i, i64 x) -> void {
if (i == (int)v.size()) {
ret.push_back(x);
return;
}
rc(rc, i + 1, x);
for (int j = 0; j < v[i].second; j++) rc(rc, i + 1, x *= v[i].first);
};
f(f, 0, 1);
sort(begin(ret), end(ret));
return ret;
}
} // namespace fast_factorize
using fast_factorize::divisors;
using fast_factorize::factor_count;
using fast_factorize::factorize;
/**
* @brief 高速素因数分解(Miller Rabin/Pollard's Rho)
* @docs docs/prime/fast-factorize.md
*/
int main(){
ios::sync_with_stdio(false);
std::cin.tie(nullptr);
LL(q);
ll m = 1000000+10;
vll a(m,0);
a[1] = 0;
rep(i,2,m){
auto x = factorize(i);
a[i] = i / x[0];
}
merge_sort_tree<ll> st(a);
rep(i,q){
LL(l,r);
ll x = st.cntMoreeq(l,r+1,l);
print(r-l+1-x);
}
}