This documentation is automatically generated by online-judge-tools/verification-helper
#include "nt/find_coprime_pair.hpp"
#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);
}
};