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:warning: nt/find_coprime_pair.hpp

Depends on

Code

#include "ds/my_bitset.hpp"
#include "nt/lpf_table.hpp"
#include "nt/factor.hpp"

// A[i] と互いに素な A[j] を検出 / A[i] の削除
// N=1e5,A=1e7 連結成分分解 1030ms
// https://codeforces.com/contest/1148/problem/G
template <int thresh = 200>
struct Find_Coprime_Pair {
  // thresh 以上ある素数を bitset 管理
  using BS = My_Bitset;
  int N;
  vc<int> A;
  vc<int> lpf;
  vc<int> S;
  vc<int> ptr;
  vc<int> bidx;
  vc<BS> dat;
  BS remain;
  // 20 以下の素数の積
  const int prod = 9699690;

  Find_Coprime_Pair(vc<int> A) : A(A) {
    N = len(A);
    int ma = MAX(A);
    lpf = lpf_table(ma);
    vc<int> ptr1(ma + 1);
    vc<int> ids(N);
    for (auto& x : A) ptr1[x]++;
    ptr1 = cumsum<int>(ptr1);
    FOR(i, N) { ids[ptr1[A[i]]++] = i; }
    FOR_R(i, len(ptr1) - 1) ptr1[i + 1] = ptr1[i];

    ptr.resize(ma + 2);
    FOR(p, 23, ma + 1) {
      if (lpf[p] != p) continue;
      ptr[p] = len(S);
      for (int n = p; n <= ma; n += p) {
        FOR(k, ptr1[n], ptr1[n + 1]) S.eb(ids[k]);
      }
      ptr[p + 1] = len(S);
    }

    bidx.assign(ma + 1, -1);
    {
      vc<int> prime = {2, 3, 5, 7, 11, 13, 17, 19};
      vc<BS> tmp(1 << 8);
      tmp[0] = BS(N, 1);
      FOR(i, 8) {
        BS bs(N, 1);
        FOR(j, N) if (A[j] % prime[i] == 0) bs[j] = 0;
        FOR(s, 1 << i) tmp[s | 1 << i] = tmp[s] & bs;
      }
      FOR(s, 1 << 8) {
        int prd = 1;
        FOR(i, 8) if (s >> i & 1) prd *= prime[i];
        if (prd <= ma) {
          bidx[prd] = len(dat);
          dat.eb(tmp[s]);
        }
      }
    }

    FOR(p, 23, ma + 1) {
      if (lpf[p] != p) continue;
      int cnt = ptr[p + 1] - ptr[p];
      if (cnt < thresh) continue;
      BS bs(N, 1);
      FOR(i, ptr[p], ptr[p + 1]) bs[S[i]] = 0;
      bidx[p] = len(dat);
      dat.eb(bs);
    }
    remain = BS(N, 1);
  }

  void remove(int i) { remain[i] = 0; }

  // 自分自身は除いて
  template <typename F>
  void enumerate_all(int i, F f) {
    int d = gcd(A[i], prod);
    BS x = remain & dat[bidx[d]];
    for (auto& [p, e] : factor_by_lpf(A[i], lpf)) {
      if (p < 20) continue;
      if (bidx[p] == -1) {
        FOR(k, ptr[p], ptr[p + 1]) { x[S[k]] = 0; }
      } else {
        x &= dat[bidx[p]];
      }
    }
    x.enumerate(0, N, f);
  }
};
#line 2 "ds/my_bitset.hpp"

// https://codeforces.com/contest/914/problem/F
// https://yukicoder.me/problems/no/142
// わずかに普通の bitset より遅いときもあるようだが，
// 固定長にしたくないときや slice 操作が必要なときに使う
struct My_Bitset {
  using T = My_Bitset;
  int N;
  vc<u64> dat;

  // x で埋める
  My_Bitset(int N = 0, int x = 0) : N(N) {
    assert(x == 0 || x == 1);
    u64 v = (x == 0 ? 0 : -1);
    dat.assign((N + 63) >> 6, v);
    if (N) dat.back() >>= (64 * len(dat) - N);
  }

  int size() { return N; }

  void resize(int size) {
    dat.resize((size + 63) >> 6);
    int remainingBits = size & 63;
    if (remainingBits != 0) {
      u64 mask = (u64(1) << remainingBits) - 1;
      dat.back() &= mask;
    }
    N = size;
  }

  void append(int idx, bool b) {
    assert(N == idx);
    resize(idx + 1), (*this)[idx] = b;
  }

  static T from_string(string &S) {
    int N = len(S);
    T ANS(N);
    FOR(i, N) ANS[i] = (S[i] == '1');
    return ANS;
  }

  // thanks to chatgpt!
  class Proxy {
  public:
    Proxy(vc<u64> &d, int i) : dat(d), index(i) {}
    operator bool() const { return (dat[index >> 6] >> (index & 63)) & 1; }

    Proxy &operator=(u64 value) {
      dat[index >> 6] &= ~(u64(1) << (index & 63));
      dat[index >> 6] |= (value & 1) << (index & 63);
      return *this;
    }
    void flip() {
      dat[index >> 6] ^= (u64(1) << (index & 63)); // XOR to flip the bit
    }

  private:
    vc<u64> &dat;
    int index;
  };

  Proxy operator[](int i) { return Proxy(dat, i); }

  bool operator==(const T &p) {
    assert(N == p.N);
    FOR(i, len(dat)) if (dat[i] != p.dat[i]) return false;
    return true;
  }

  T &operator&=(const T &p) {
    assert(N == p.N);
    FOR(i, len(dat)) dat[i] &= p.dat[i];
    return *this;
  }
  T &operator|=(const T &p) {
    assert(N == p.N);
    FOR(i, len(dat)) dat[i] |= p.dat[i];
    return *this;
  }
  T &operator^=(const T &p) {
    assert(N == p.N);
    FOR(i, len(dat)) dat[i] ^= p.dat[i];
    return *this;
  }
  T operator&(const T &p) const { return T(*this) &= p; }
  T operator|(const T &p) const { return T(*this) |= p; }
  T operator^(const T &p) const { return T(*this) ^= p; }
  T operator~() const {
    T p = (*this);
    p.flip_range(0, N);
    return p;
  }

  void set_minus_inplace(T &other) {
    assert(N == other.N);
    FOR(i, len(dat)) dat[i] = dat[i] & (~other.dat[i]);
  }

  T set_minus(T other) {
    assert(N == other.N);
    FOR(i, len(dat)) other.dat[i] = dat[i] & (~other.dat[i]);
    return other;
  }

  int count() {
    int ans = 0;
    for (u64 val: dat) ans += popcnt(val);
    return ans;
  }

  int dot(T &p) {
    assert(N == p.N);
    int ans = 0;
    FOR(i, len(dat)) ans += popcnt(dat[i] & p.dat[i]);
    return ans;
  }

  int next(int i) {
    chmax(i, 0);
    if (i >= N) return N;
    int k = i >> 6;
    {
      u64 x = dat[k];
      int s = i & 63;
      x = (x >> s) << s;
      if (x) return (k << 6) | lowbit(x);
    }
    FOR(idx, k + 1, len(dat)) {
      if (dat[idx] == 0) continue;
      return (idx << 6) | lowbit(dat[idx]);
    }
    return N;
  }

  int prev(int i) {
    chmin(i, N - 1);
    if (i <= -1) return -1;
    int k = i >> 6;
    if ((i & 63) < 63) {
      u64 x = dat[k];
      x &= (u64(1) << ((i & 63) + 1)) - 1;
      if (x) return (k << 6) | topbit(x);
      --k;
    }
    FOR_R(idx, k + 1) {
      if (dat[idx] == 0) continue;
      return (idx << 6) | topbit(dat[idx]);
    }
    return -1;
  }

  My_Bitset range(int L, int R) {
    assert(L <= R);
    My_Bitset p(R - L);
    int rm = (R - L) & 63;
    FOR(rm) {
      p[R - L - 1] = bool((*this)[R - 1]);
      --R;
    }
    int n = (R - L) >> 6;
    int hi = L & 63;
    int lo = 64 - hi;
    int s = L >> 6;
    if (hi == 0) {
      FOR(i, n) { p.dat[i] ^= dat[s + i]; }
    } else {
      FOR(i, n) { p.dat[i] ^= (dat[s + i] >> hi) ^ (dat[s + i + 1] << lo); }
    }
    return p;
  }

  My_Bitset slice(int L, int R) { return range(L, R); }

  int count_range(int L, int R) {
    assert(L <= R);
    int cnt = 0;
    while ((L < R) && (L & 63)) cnt += (*this)[L++];
    while ((L < R) && (R & 63)) cnt += (*this)[--R];
    int l = L >> 6, r = R >> 6;
    FOR(i, l, r) cnt += popcnt(dat[i]);
    return cnt;
  }

  // [L,R) に p を代入
  void assign_to_range(int L, int R, My_Bitset &p) {
    assert(p.N == R - L);
    int a = 0, b = p.N;
    while (L < R && (L & 63)) { (*this)[L++] = bool(p[a++]); }
    while (L < R && (R & 63)) { (*this)[--R] = bool(p[--b]); }
    // p[a:b] を [L:R] に
    int l = L >> 6, r = R >> 6;
    int s = a >> 6, t = b >> t;
    int n = r - l;
    if (!(a & 63)) {
      FOR(i, n) dat[l + i] = p.dat[s + i];
    } else {
      int hi = a & 63;
      int lo = 64 - hi;
      FOR(i, n) dat[l + i] = (p.dat[s + i] >> hi) | (p.dat[1 + s + i] << lo);
    }
  }

  // [L,R) に p を xor
  void xor_to_range(int L, int R, My_Bitset &p) {
    assert(p.N == R - L);
    int a = 0, b = p.N;
    while (L < R && (L & 63)) {
      dat[L >> 6] ^= u64(p[a]) << (L & 63);
      ++a, ++L;
    }
    while (L < R && (R & 63)) {
      --b, --R;
      dat[R >> 6] ^= u64(p[b]) << (R & 63);
    }
    // p[a:b] を [L:R] に
    int l = L >> 6, r = R >> 6;
    int s = a >> 6, t = b >> t;
    int n = r - l;
    if (!(a & 63)) {
      FOR(i, n) dat[l + i] ^= p.dat[s + i];
    } else {
      int hi = a & 63;
      int lo = 64 - hi;
      FOR(i, n) dat[l + i] ^= (p.dat[s + i] >> hi) | (p.dat[1 + s + i] << lo);
    }
  }

  // 行列基本変形で使うやつ
  // p は [i:N) にしかないとして p を xor する
  void xor_suffix(int i, My_Bitset &p) {
    assert(N == p.N && 0 <= i && i < N);
    FOR(k, i / 64, len(dat)) { dat[k] ^= p.dat[k]; }
  }

  // [L,R) に p を and
  void and_to_range(int L, int R, My_Bitset &p) {
    assert(p.N == R - L);
    int a = 0, b = p.N;
    while (L < R && (L & 63)) {
      if (!p[a]) (*this)[L] = 0;
      a++, L++;
    }
    while (L < R && (R & 63)) {
      --b, --R;
      if (!p[b]) (*this)[R] = 0;
    }
    // p[a:b] を [L:R] に
    int l = L >> 6, r = R >> 6;
    int s = a >> 6, t = b >> t;
    int n = r - l;
    if (!(a & 63)) {
      FOR(i, n) dat[l + i] &= p.dat[s + i];
    } else {
      int hi = a & 63;
      int lo = 64 - hi;
      FOR(i, n) dat[l + i] &= (p.dat[s + i] >> hi) | (p.dat[1 + s + i] << lo);
    }
  }

  // [L,R) に p を or
  void or_to_range(int L, int R, My_Bitset &p) {
    assert(p.N == R - L);
    int a = 0, b = p.N;
    while (L < R && (L & 63)) {
      dat[L >> 6] |= u64(p[a]) << (L & 63);
      ++a, ++L;
    }
    while (L < R && (R & 63)) {
      --b, --R;
      dat[R >> 6] |= u64(p[b]) << (R & 63);
    }
    // p[a:b] を [L:R] に
    int l = L >> 6, r = R >> 6;
    int s = a >> 6, t = b >> t;
    int n = r - l;
    if (!(a & 63)) {
      FOR(i, n) dat[l + i] |= p.dat[s + i];
    } else {
      int hi = a & 63;
      int lo = 64 - hi;
      FOR(i, n) dat[l + i] |= (p.dat[s + i] >> hi) | (p.dat[1 + s + i] << lo);
    }
  }
  // 行列基本変形で使うやつ
  // p は [i:N) にしかないとして p を or する
  void or_suffix(int i, My_Bitset &p) {
    assert(N == p.N && 0 <= i && i < N);
    FOR(k, i / 64, len(dat)) { dat[k] |= p.dat[k]; }
  }

  // [L,R) を 1 に変更
  void set_range(int L, int R) {
    while (L < R && (L & 63)) { set(L++); }
    while (L < R && (R & 63)) { set(--R); }
    FOR(i, L >> 6, R >> 6) dat[i] = u64(-1);
  }

  // [L,R) を 1 に変更
  void reset_range(int L, int R) {
    while (L < R && (L & 63)) { reset(L++); }
    while (L < R && (R & 63)) { reset(--R); }
    FOR(i, L >> 6, R >> 6) dat[i] = u64(0);
  }

  // [L,R) を flip
  void flip_range(int L, int R) {
    while (L < R && (L & 63)) { flip(L++); }
    while (L < R && (R & 63)) { flip(--R); }
    FOR(i, L >> 6, R >> 6) dat[i] ^= u64(-1);
  }

  // bitset に仕様を合わせる
  void set(int i) { (*this)[i] = 1; }
  void reset(int i) { (*this)[i] = 0; }
  void flip(int i) { (*this)[i].flip(); }
  void set() {
    fill(all(dat), u64(-1));
    resize(N);
  }
  void reset() { fill(all(dat), 0); }
  void flip() {
    FOR(i, len(dat) - 1) { dat[i] = u64(-1) ^ dat[i]; }
    int i = len(dat) - 1;
    FOR(k, 64) {
      if (64 * i + k >= size()) break;
      flip(64 * i + k);
    }
  }
  bool any() {
    FOR(i, len(dat)) {
      if (dat[i]) return true;
    }
    return false;
  }

  bool ALL() {
    dat.resize((N + 63) >> 6);
    int r = N & 63;
    if (r != 0) {
      u64 mask = (u64(1) << r) - 1;
      if (dat.back() != mask) return 0;
    }
    for (int i = 0; i < N / 64; ++i)
      if (dat[i] != u64(-1)) return false;
    return true;
  }
  // bs[i]==true であるような i 全体
  vc<int> collect_idx() {
    vc<int> I;
    FOR(i, N) if ((*this)[i]) I.eb(i);
    return I;
  }

  bool is_subset(T &other) {
    assert(len(other) == N);
    FOR(i, len(dat)) {
      u64 a = dat[i], b = other.dat[i];
      if ((a & b) != a) return false;
    }
    return true;
  }

  int _Find_first() { return next(0); }
  int _Find_next(int p) { return next(p + 1); }

  template <typename F>
  void enumerate(int L, int R, F f) {
    if (L >= size()) return;
    int p = ((*this)[L] ? L : _Find_next(L));
    while (p < R) {
      f(p);
      p = _Find_next(p);
    }
  }

  static string TO_STR[256];
  string to_string() const {
    if (TO_STR[0].empty()) precompute();
    string S;
    for (auto &x: dat) { FOR(i, 8) S += TO_STR[(x >> (8 * i) & 255)]; }
    S.resize(N);
    return S;
  }

  static void precompute() {
    FOR(s, 256) {
      string x;
      FOR(i, 8) x += '0' + (s >> i & 1);
      TO_STR[s] = x;
    }
  }
};
string My_Bitset::TO_STR[256];
#line 2 "nt/primetable.hpp"

template <typename T = int>
vc<T> primetable(int LIM) {
  ++LIM;
  const int S = 32768;
  static int done = 2;
  static vc<T> primes = {2}, sieve(S + 1);

  if (done < LIM) {
    done = LIM;

    primes = {2}, sieve.assign(S + 1, 0);
    const int R = LIM / 2;
    primes.reserve(int(LIM / log(LIM) * 1.1));
    vc<pair<int, int>> cp;
    for (int i = 3; i <= S; i += 2) {
      if (!sieve[i]) {
        cp.eb(i, i * i / 2);
        for (int j = i * i; j <= S; j += 2 * i) sieve[j] = 1;
      }
    }
    for (int L = 1; L <= R; L += S) {
      array<bool, S> block{};
      for (auto& [p, idx]: cp)
        for (int i = idx; i < S + L; idx = (i += p)) block[i - L] = 1;
      FOR(i, min(S, R - L)) if (!block[i]) primes.eb((L + i) * 2 + 1);
    }
  }
  int k = LB(primes, LIM + 1);
  return {primes.begin(), primes.begin() + k};
}
#line 3 "nt/lpf_table.hpp"

// [0, LIM], 0, 1 には -1 が入る。
vc<int> lpf_table(ll LIM) {
  auto primes = primetable(LIM);
  vc<int> res(LIM + 1, -1);
  FOR_R(i, len(primes)) {
    auto p = primes[i];
    FOR3(j, 1, LIM / p + 1) res[p * j] = p;
  }
  return res;
}
#line 2 "nt/factor.hpp"

#line 2 "random/base.hpp"

u64 RNG_64() {
  static u64 x_ = u64(chrono::duration_cast<chrono::nanoseconds>(chrono::high_resolution_clock::now().time_since_epoch()).count()) * 10150724397891781847ULL;
  x_ ^= x_ << 7;
  return x_ ^= x_ >> 9;
}

u64 RNG(u64 lim) { return RNG_64() % lim; }

ll RNG(ll l, ll r) { return l + RNG_64() % (r - l); }
#line 2 "mod/mongomery_modint.hpp"

// odd mod.
// x の代わりに rx を持つ
template <int id, typename U1, typename U2>
struct Mongomery_modint {
  using mint = Mongomery_modint;
  inline static U1 m, r, n2;
  static constexpr int W = numeric_limits<U1>::digits;

  static void set_mod(U1 mod) {
    assert(mod & 1 && mod <= U1(1) << (W - 2));
    m = mod, n2 = -U2(m) % m, r = m;
    FOR(5) r *= 2 - m * r;
    r = -r;
    assert(r * m == U1(-1));
  }
  static U1 reduce(U2 b) { return (b + U2(U1(b) * r) * m) >> W; }

  U1 x;
  Mongomery_modint() : x(0) {}
  Mongomery_modint(U1 x) : x(reduce(U2(x) * n2)){};
  U1 val() const {
    U1 y = reduce(x);
    return y >= m ? y - m : y;
  }
  mint &operator+=(mint y) {
    x = ((x += y.x) >= m ? x - m : x);
    return *this;
  }
  mint &operator-=(mint y) {
    x -= (x >= y.x ? y.x : y.x - m);
    return *this;
  }
  mint &operator*=(mint y) {
    x = reduce(U2(x) * y.x);
    return *this;
  }
  mint operator+(mint y) const { return mint(*this) += y; }
  mint operator-(mint y) const { return mint(*this) -= y; }
  mint operator*(mint y) const { return mint(*this) *= y; }
  bool operator==(mint y) const {
    return (x >= m ? x - m : x) == (y.x >= m ? y.x - m : y.x);
  }
  bool operator!=(mint y) const { return not operator==(y); }
  mint pow(ll n) const {
    assert(n >= 0);
    mint y = 1, z = *this;
    for (; n; n >>= 1, z *= z)
      if (n & 1) y *= z;
    return y;
  }
};

template <int id>
using Mongomery_modint_32 = Mongomery_modint<id, u32, u64>;
template <int id>
using Mongomery_modint_64 = Mongomery_modint<id, u64, u128>;
#line 3 "nt/primetest.hpp"

bool primetest(const u64 x) {
  assert(x < u64(1) << 62);
  if (x == 2 or x == 3 or x == 5 or x == 7) return true;
  if (x % 2 == 0 or x % 3 == 0 or x % 5 == 0 or x % 7 == 0) return false;
  if (x < 121) return x > 1;
  const u64 d = (x - 1) >> lowbit(x - 1);

  using mint = Mongomery_modint_64<202311020>;

  mint::set_mod(x);
  const mint one(u64(1)), minus_one(x - 1);
  auto ok = [&](u64 a) -> bool {
    auto y = mint(a).pow(d);
    u64 t = d;
    while (y != one && y != minus_one && t != x - 1) y *= y, t <<= 1;
    if (y != minus_one && t % 2 == 0) return false;
    return true;
  };
  if (x < (u64(1) << 32)) {
    for (u64 a: {2, 7, 61})
      if (!ok(a)) return false;
  } else {
    for (u64 a: {2, 325, 9375, 28178, 450775, 9780504, 1795265022}) {
      if (!ok(a)) return false;
    }
  }
  return true;
}
#line 5 "nt/factor.hpp"

template <typename mint>
ll rho(ll n, ll c) {
  assert(n > 1);
  const mint cc(c);
  auto f = [&](mint x) { return x * x + cc; };
  mint x = 1, y = 2, z = 1, q = 1;
  ll g = 1;
  const ll m = 1LL << (__lg(n) / 5);
  for (ll r = 1; g == 1; r <<= 1) {
    x = y;
    FOR(r) y = f(y);
    for (ll k = 0; k < r && g == 1; k += m) {
      z = y;
      FOR(min(m, r - k)) y = f(y), q *= x - y;
      g = gcd(q.val(), n);
    }
  }
  if (g == n) do {
      z = f(z);
      g = gcd((x - z).val(), n);
    } while (g == 1);
  return g;
}

ll find_prime_factor(ll n) {
  assert(n > 1);
  if (primetest(n)) return n;
  FOR(100) {
    ll m = 0;
    if (n < (1 << 30)) {
      using mint = Mongomery_modint_32<20231025>;
      mint::set_mod(n);
      m = rho<mint>(n, RNG(0, n));
    } else {
      using mint = Mongomery_modint_64<20231025>;
      mint::set_mod(n);
      m = rho<mint>(n, RNG(0, n));
    }
    if (primetest(m)) return m;
    n = m;
  }
  assert(0);
  return -1;
}

// ソートしてくれる
vc<pair<ll, int>> factor(ll n) {
  assert(n >= 1);
  vc<pair<ll, int>> pf;
  FOR(p, 2, 100) {
    if (p * p > n) break;
    if (n % p == 0) {
      ll e = 0;
      do { n /= p, e += 1; } while (n % p == 0);
      pf.eb(p, e);
    }
  }
  while (n > 1) {
    ll p = find_prime_factor(n);
    ll e = 0;
    do { n /= p, e += 1; } while (n % p == 0);
    pf.eb(p, e);
  }
  sort(all(pf));
  return pf;
}

vc<pair<ll, int>> factor_by_lpf(ll n, vc<int>& lpf) {
  vc<pair<ll, int>> res;
  while (n > 1) {
    int p = lpf[n];
    int e = 0;
    while (n % p == 0) {
      n /= p;
      ++e;
    }
    res.eb(p, e);
  }
  return res;
}
#line 4 "nt/find_coprime_pair.hpp"

// A[i] と互いに素な A[j] を検出 / A[i] の削除
// N=1e5,A=1e7 連結成分分解 1030ms
// https://codeforces.com/contest/1148/problem/G
template <int thresh = 200>
struct Find_Coprime_Pair {
  // thresh 以上ある素数を bitset 管理
  using BS = My_Bitset;
  int N;
  vc<int> A;
  vc<int> lpf;
  vc<int> S;
  vc<int> ptr;
  vc<int> bidx;
  vc<BS> dat;
  BS remain;
  // 20 以下の素数の積
  const int prod = 9699690;

  Find_Coprime_Pair(vc<int> A) : A(A) {
    N = len(A);
    int ma = MAX(A);
    lpf = lpf_table(ma);
    vc<int> ptr1(ma + 1);
    vc<int> ids(N);
    for (auto& x : A) ptr1[x]++;
    ptr1 = cumsum<int>(ptr1);
    FOR(i, N) { ids[ptr1[A[i]]++] = i; }
    FOR_R(i, len(ptr1) - 1) ptr1[i + 1] = ptr1[i];

    ptr.resize(ma + 2);
    FOR(p, 23, ma + 1) {
      if (lpf[p] != p) continue;
      ptr[p] = len(S);
      for (int n = p; n <= ma; n += p) {
        FOR(k, ptr1[n], ptr1[n + 1]) S.eb(ids[k]);
      }
      ptr[p + 1] = len(S);
    }

    bidx.assign(ma + 1, -1);
    {
      vc<int> prime = {2, 3, 5, 7, 11, 13, 17, 19};
      vc<BS> tmp(1 << 8);
      tmp[0] = BS(N, 1);
      FOR(i, 8) {
        BS bs(N, 1);
        FOR(j, N) if (A[j] % prime[i] == 0) bs[j] = 0;
        FOR(s, 1 << i) tmp[s | 1 << i] = tmp[s] & bs;
      }
      FOR(s, 1 << 8) {
        int prd = 1;
        FOR(i, 8) if (s >> i & 1) prd *= prime[i];
        if (prd <= ma) {
          bidx[prd] = len(dat);
          dat.eb(tmp[s]);
        }
      }
    }

    FOR(p, 23, ma + 1) {
      if (lpf[p] != p) continue;
      int cnt = ptr[p + 1] - ptr[p];
      if (cnt < thresh) continue;
      BS bs(N, 1);
      FOR(i, ptr[p], ptr[p + 1]) bs[S[i]] = 0;
      bidx[p] = len(dat);
      dat.eb(bs);
    }
    remain = BS(N, 1);
  }

  void remove(int i) { remain[i] = 0; }

  // 自分自身は除いて
  template <typename F>
  void enumerate_all(int i, F f) {
    int d = gcd(A[i], prod);
    BS x = remain & dat[bidx[d]];
    for (auto& [p, e] : factor_by_lpf(A[i], lpf)) {
      if (p < 20) continue;
      if (bidx[p] == -1) {
        FOR(k, ptr[p], ptr[p + 1]) { x[S[k]] = 0; }
      } else {
        x &= dat[bidx[p]];
      }
    }
    x.enumerate(0, N, f);
  }
};
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