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test/yosupo_primitive_root.test.cpp
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- Last update: 2026-03-22 19:39:35+09:00
- Problem: https://judge.yosupo.jp/problem/primitive_root
Depends on
- Miller-Rabin素数判定
(math/prime/miller_rabin.cpp)
- 素因数分解(Pollard Rho)
(math/prime/primefactor_ll.cpp)
- 原始根(Primitive Root)
(math/prime/primitive_root.cpp)
- 高速入出力(Fast IO)
(util/fastio.cpp)
Code
#define PROBLEM "https://judge.yosupo.jp/problem/primitive_root"
#include <algorithm>
#include <cstdint>
#include <numeric>
#include <random>
#include <vector>
static const int MOD = 1000000007;
using ll = long long;
using uint = unsigned;
using ull = unsigned long long;
#include <cstdio>
#include <cstring>
#include <string>
#include <type_traits>
#include "../util/fastio.cpp"
#include "../math/prime/primitive_root.cpp"
int main() {
Scanner in;
Printer out;
int q;
in.read(q);
while (q--) {
ll p;
in.read(p);
out.println(primitive_root(p));
}
return 0;
}#line 1 "test/yosupo_primitive_root.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/primitive_root"
#include <algorithm>
#include <cstdint>
#include <numeric>
#include <random>
#include <vector>
static const int MOD = 1000000007;
using ll = long long;
using uint = unsigned;
using ull = unsigned long long;
#include <cstdio>
#include <cstring>
#include <string>
#include <type_traits>
#line 1 "util/fastio.cpp"
using namespace std;
extern "C" int fileno(FILE *);
extern "C" int isatty(int);
template<class T, class = void>
struct is_fastio_range : false_type {};
template<class T>
struct is_fastio_range<T, void_t<decltype(declval<T &>().begin()), decltype(declval<T &>().end())>> : true_type {};
template<class T, class = void>
struct has_fastio_value : false_type {};
template<class T>
struct has_fastio_value<T, void_t<decltype(declval<const T &>().value())>> : true_type {};
struct FastIoDigitTable {
char num[40000];
constexpr FastIoDigitTable() : num() {
for (int i = 0; i < 10000; ++i) {
int x = i;
for (int j = 3; j >= 0; --j) {
num[i * 4 + j] = char('0' + x % 10);
x /= 10;
}
}
}
};
struct Scanner {
static constexpr int BUFSIZE = 1 << 17;
static constexpr int OFFSET = 64;
char buf[BUFSIZE + 1];
int idx, size;
bool interactive;
Scanner() : idx(0), size(0), interactive(isatty(fileno(stdin))) {}
inline void load() {
int len = size - idx;
memmove(buf, buf + idx, len);
if (interactive) {
if (fgets(buf + len, BUFSIZE + 1 - len, stdin)) size = len + (int)strlen(buf + len);
else size = len;
} else {
size = len + (int)fread(buf + len, 1, BUFSIZE - len, stdin);
}
idx = 0;
buf[size] = 0;
}
inline void ensure() {
if (idx + OFFSET > size) load();
}
inline void ensure_interactive() {
if (idx == size) load();
}
inline char skip() {
if (interactive) {
ensure_interactive();
while (buf[idx] && buf[idx] <= ' ') {
++idx;
ensure_interactive();
}
return buf[idx++];
}
ensure();
while (buf[idx] && buf[idx] <= ' ') {
++idx;
ensure();
}
return buf[idx++];
}
template<class T, typename enable_if<is_integral<T>::value, int>::type = 0>
void read(T &x) {
if (interactive) {
char c = skip();
bool neg = false;
if constexpr (is_signed<T>::value) {
if (c == '-') {
neg = true;
ensure_interactive();
c = buf[idx++];
}
}
x = 0;
while (c >= '0') {
x = x * 10 + (c & 15);
ensure_interactive();
c = buf[idx++];
}
if constexpr (is_signed<T>::value) {
if (neg) x = -x;
}
return;
}
char c = skip();
bool neg = false;
if constexpr (is_signed<T>::value) {
if (c == '-') {
neg = true;
c = buf[idx++];
}
}
x = 0;
while (c >= '0') {
x = x * 10 + (c & 15);
c = buf[idx++];
}
if constexpr (is_signed<T>::value) {
if (neg) x = -x;
}
}
template<class T, typename enable_if<!is_integral<T>::value && !is_fastio_range<T>::value && !is_same<typename decay<T>::type, string>::value && has_fastio_value<T>::value, int>::type = 0>
void read(T &x) {
long long v;
read(v);
x = T(v);
}
template<class Head, class Next, class... Tail>
void read(Head &head, Next &next, Tail &...tail) {
read(head);
read(next, tail...);
}
template<class T, class U>
void read(pair<T, U> &p) {
read(p.first, p.second);
}
template<class T, typename enable_if<is_fastio_range<T>::value && !is_same<typename decay<T>::type, string>::value, int>::type = 0>
void read(T &a) {
for (auto &x : a) read(x);
}
void read(char &c) {
c = skip();
}
void read(string &s) {
s.clear();
if (interactive) {
ensure_interactive();
while (buf[idx] && buf[idx] <= ' ') {
++idx;
ensure_interactive();
}
while (true) {
int start = idx;
while (idx < size && buf[idx] > ' ') ++idx;
s.append(buf + start, idx - start);
if (idx < size) break;
load();
if (size == 0) break;
}
if (idx < size) ++idx;
return;
}
ensure();
while (buf[idx] && buf[idx] <= ' ') {
++idx;
ensure();
}
while (true) {
int start = idx;
while (idx < size && buf[idx] > ' ') ++idx;
s.append(buf + start, idx - start);
if (idx < size) break;
load();
}
if (idx < size) ++idx;
}
};
struct Printer {
static constexpr int BUFSIZE = 1 << 17;
static constexpr int OFFSET = 64;
char buf[BUFSIZE];
int idx;
bool interactive;
inline static constexpr FastIoDigitTable table{};
Printer() : idx(0), interactive(isatty(fileno(stdout))) {}
~Printer() { flush(); }
inline void flush() {
if (idx) {
fwrite(buf, 1, idx, stdout);
idx = 0;
}
}
inline void pc(char c) {
if (idx > BUFSIZE - OFFSET) flush();
buf[idx++] = c;
if (interactive && c == '\n') flush();
}
inline void print_range(const char *s, size_t n) {
size_t pos = 0;
while (pos < n) {
if (idx == BUFSIZE) flush();
size_t chunk = min(n - pos, (size_t)(BUFSIZE - idx));
memcpy(buf + idx, s + pos, chunk);
idx += (int)chunk;
pos += chunk;
}
}
void print(const char *s) {
print_range(s, strlen(s));
}
void print(const string &s) {
print_range(s.data(), s.size());
}
void print(char c) {
pc(c);
}
void print(bool b) {
pc(char('0' + (b ? 1 : 0)));
}
template<class T, typename enable_if<is_integral<T>::value && !is_same<T, bool>::value, int>::type = 0>
void print(T x) {
if (idx > BUFSIZE - 100) flush();
using U = typename make_unsigned<T>::type;
U y;
if constexpr (is_signed<T>::value) {
if (x < 0) {
buf[idx++] = '-';
y = U(0) - static_cast<U>(x);
} else {
y = static_cast<U>(x);
}
} else {
y = x;
}
if (y == 0) {
buf[idx++] = '0';
return;
}
static constexpr int TMP_SIZE = sizeof(U) * 10 / 4;
char tmp[TMP_SIZE];
int pos = TMP_SIZE;
while (y >= 10000) {
pos -= 4;
memcpy(tmp + pos, table.num + (y % 10000) * 4, 4);
y /= 10000;
}
if (y >= 1000) {
memcpy(buf + idx, table.num + (y << 2), 4);
idx += 4;
} else if (y >= 100) {
memcpy(buf + idx, table.num + (y << 2) + 1, 3);
idx += 3;
} else if (y >= 10) {
unsigned q = (unsigned(y) * 205) >> 11;
buf[idx] = char('0' + q);
buf[idx + 1] = char('0' + (unsigned(y) - q * 10));
idx += 2;
} else {
buf[idx++] = char('0' + y);
}
memcpy(buf + idx, tmp + pos, TMP_SIZE - pos);
idx += TMP_SIZE - pos;
}
template<class T, typename enable_if<!is_integral<T>::value && !is_fastio_range<T>::value && !is_same<typename decay<T>::type, string>::value && has_fastio_value<T>::value, int>::type = 0>
void print(const T &x) {
print(x.value());
}
template<class T, typename enable_if<is_fastio_range<T>::value && !is_same<typename decay<T>::type, string>::value, int>::type = 0>
void print(const T &a) {
bool first = true;
for (auto &&x : a) {
if (!first) pc(' ');
first = false;
print(x);
}
}
template<class T>
void println(const T &x) {
print(x);
pc('\n');
}
template<class Head, class... Tail>
void println(const Head &head, const Tail &...tail) {
print(head);
((pc(' '), print(tail)), ...);
pc('\n');
}
void println() {
pc('\n');
}
};
template<class T>
Scanner &operator>>(Scanner &in, T &x) {
in.read(x);
return in;
}
template<class T>
Printer &operator<<(Printer &out, const T &x) {
out.print(x);
return out;
}
/**
* @brief 高速入出力(Fast IO)
*/
#line 1 "math/prime/miller_rabin.cpp"
using u128 = __uint128_t;
struct mod64 {
unsigned long long n;
static unsigned long long mod, inv, r2;
mod64() : n(0) {}
mod64(unsigned long long x) : n(init(x)) {}
static unsigned long long init(unsigned long long w) {
return reduce(u128(w) * r2);
}
static void set_mod(unsigned long long m) {
mod = inv = m;
for (int i = 0; i < 5; ++i) inv *= 2 - inv * m;
r2 = -u128(m) % m;
}
static unsigned long long reduce(u128 x) {
unsigned long long y =
static_cast<unsigned long long>(x >> 64)
- static_cast<unsigned long long>((u128(static_cast<unsigned long long>(x) * inv) * mod) >> 64);
return (long long)y < 0 ? y + mod : y;
}
mod64& operator*=(mod64 x) {
n = reduce(u128(n) * x.n);
return *this;
}
mod64 operator*(mod64 x) const {
return mod64(*this) *= x;
}
mod64& operator+=(mod64 x) {
n += x.n - mod;
if((long long)n < 0) n += mod;
return *this;
}
mod64 operator+(mod64 x) const {
return mod64(*this) += x;
}
unsigned long long val() const {
return reduce(n);
}
};
unsigned long long mod64::mod, mod64::inv, mod64::r2;
bool suspect(unsigned long long a, unsigned long long s, unsigned long long d, unsigned long long n){
if(mod64::mod != n) mod64::set_mod(n);
mod64 x(1), xx(a), one(1), minusone(n - 1);
while(d > 0){
if(d & 1) x *= xx;
xx *= xx;
d >>= 1;
}
if (x.n == one.n) return true;
for (unsigned long long r = 0; r < s; ++r) {
if(x.n == minusone.n) return true;
x *= x;
}
return false;
}
template<class T>
bool miller_rabin(T m){
unsigned long long n = m;
if (n <= 1 || (n > 2 && n % 2 == 0)) return false;
if (n == 2 || n == 3 || n == 5 || n == 7) return true;
if (n % 3 == 0 || n % 5 == 0 || n % 7 == 0) return false;
unsigned long long d = n - 1, s = 0;
while (!(d & 1)) { ++s; d >>= 1; }
static constexpr unsigned long long small[] = {2, 7, 61};
static constexpr unsigned long long large[] = {2, 325, 9375, 28178, 450775, 9780504, 1795265022};
if(n < 4759123141ULL) {
for (auto p : small) {
if(p >= n) break;
if(!suspect(p, s, d, n)) return false;
}
} else {
for (auto p : large) {
if(p >= n) break;
if(!suspect(p, s, d, n)) return false;
}
}
return true;
}
/**
* @brief Miller-Rabin素数判定
*/
#line 2 "math/prime/primefactor_ll.cpp"
template<typename T>
struct ExactDiv {
T t, i, val;
ExactDiv() {}
ExactDiv(T n) : t(T(-1) / n), i(mul_inv(n)) , val(n) {};
T mul_inv(T n) {
T x = n;
for (int i = 0; i < 5; ++i) x *= 2 - n * x;
return x;
}
bool divide(T n) const {
if(val == 2) return !(n & 1);
return n * this->i <= this->t;
}
};
vector<ExactDiv<ull>> get_prime(int n){
if(n <= 1) return vector<ExactDiv<ull>>();
vector<bool> is_prime(n+1, true);
vector<ExactDiv<ull>> prime;
is_prime[0] = is_prime[1] = false;
for (int i = 2; i <= n; ++i) {
if(is_prime[i]) prime.emplace_back(i);
for (auto &&j : prime){
ull v = (ull)i * j.val;
if(v > (ull)n) break;
is_prime[v] = false;
if(j.divide(i)) break;
}
}
return prime;
}
const auto primes = get_prime(50000);
mt19937_64 rng(0x8a5cd789635d2dffULL);
template<class T>
T pollard_rho2(T n) {
ull nn = n;
if ((nn & 1) == 0) return 2;
uniform_int_distribution<ull> ra(1, nn - 1);
mod64::set_mod(nn);
while(true){
ull c_ = ra(rng), g = 1, r = 1, m = 500;
while(c_ == nn - 2) c_ = ra(rng);
mod64 y(ra(rng)), xx(0), c(c_), ys(0), q(1);
while(g == 1){
xx.n = y.n;
for (ull i = 0; i < r; ++i) {
y *= y; y += c;
}
ull k = 0; g = 1;
while(k < r && g == 1){
ull lim = min(m, r - k);
for (ull i = 0; i < lim; ++i) {
ys.n = y.n;
y *= y; y += c;
ull xxx = xx.val(), yyy = y.val();
q *= mod64(xxx > yyy ? xxx - yyy : yyy - xxx);
}
g = gcd<ull>(q.val(), nn);
k += m;
}
r *= 2;
}
if(g == nn) g = 1;
while (g == 1){
ys *= ys; ys += c;
ull xxx = xx.val(), yyy = ys.val();
g = gcd<ull>(xxx > yyy ? xxx - yyy : yyy - xxx, nn);
}
if (g != nn && miller_rabin(g)) return (T)g;
}
}
template<class T>
void prime_factor_impl(T n, vector<T> &res, bool trial){
if(trial) {
for (auto &&i : primes) {
while (i.divide(n)){
res.emplace_back(i.val);
n /= i.val;
}
}
}
if(n == 1) return;
if(miller_rabin(n)) {
res.emplace_back(n);
return;
}
T x = pollard_rho2(n);
prime_factor_impl(x, res, false);
prime_factor_impl(n / x, res, false);
}
template<class T>
vector<T> prime_factor(T n){
vector<T> res;
prime_factor_impl(n, res, true);
sort(res.begin(),res.end());
return res;
}
/**
* @brief 素因数分解(Pollard Rho)
*/
#line 2 "math/prime/primitive_root.cpp"
ll primitive_root(ll m) {
if (m == 2) return 1;
auto divs = prime_factor(m - 1);
divs.erase(unique(divs.begin(), divs.end()), divs.end());
auto mod_pow = [&](ll x, ll n) {
ull a = x, r = 1, mod = m;
while (n > 0) {
if (n & 1) r = (u128)r * a % mod;
a = (u128)a * a % mod;
n >>= 1;
}
return (ll)r;
};
for (ll g = 2;; g++) {
bool ok = true;
for (auto &&d : divs) {
if (mod_pow(g, (m - 1) / d) == 1) {
ok = false;
break;
}
}
if (ok) return g;
}
}
/**
* @brief 原始根(Primitive Root)
*/
#line 21 "test/yosupo_primitive_root.test.cpp"
int main() {
Scanner in;
Printer out;
int q;
in.read(q);
while (q--) {
ll p;
in.read(p);
out.println(primitive_root(p));
}
return 0;
}