#line 1 "test/yuki/No3030.test.cpp" #define PROBLEM "https://yukicoder.me/problems/no/3030" #include #line 2 "src/math/dynamic_modint.hpp" #include #line 2 "src/internal/barrett.hpp" #include namespace kyopro { namespace internal { /** * @brief Barrett Reduction */ class barrett { using u32 = uint32_t; using u64 = uint64_t; using u128 = __uint128_t; u32 m; u64 im; public: constexpr explicit barrett() : m(0), im(0) {} constexpr explicit barrett(u32 m) : m(m), im(static_cast(-1) / m + 1) {} constexpr u32 get_mod() const { return m; } constexpr u32 reduce(u32 a) const { return mul(1, a); } constexpr u32 mul(u32 a, u32 b) const { u64 z = (u64)a * b; u64 x = (u64)(((u128)(z)*im) >> 64); u64 y = x * m; return (u32)(z - y + (z < y ? m : 0)); } }; }; // namespace internal }; // namespace kyopro /** * @ref * https://github.com/atcoder/ac-library/blob/master/atcoder/internal_math.hpp */ #line 3 "src/internal/montgomery.hpp" #include #include #line 5 "src/internal/type_traits.hpp" #include namespace kyopro { namespace internal { /* * @ref https://qiita.com/kazatsuyu/items/f8c3b304e7f8b35263d8 */ template struct first_enabled {}; template struct first_enabled, Args...> { using type = T; }; template struct first_enabled, Args...> : first_enabled {}; template struct first_enabled { using type = T; }; template using first_enabled_t = typename first_enabled::type; template struct int_least { static_assert(dgt <= 128); using type = first_enabled_t, std::enable_if, std::enable_if, std::enable_if, std::enable_if >; }; template struct uint_least { static_assert(dgt <= 128); using type = first_enabled_t, std::enable_if, std::enable_if, std::enable_if, std::enable_if >; }; template using int_least_t = typename int_least::type; template using uint_least_t = typename uint_least::type; template using double_size_uint_t = uint_least_t<2 * std::numeric_limits::digits>; template using double_size_int_t = int_least_t<2 * std::numeric_limits::digits>; }; // namespace internal }; // namespace kyopro #line 6 "src/internal/montgomery.hpp" namespace kyopro { namespace internal { using u32 = uint32_t; using u64 = uint64_t; using i32 = int32_t; using i64 = int64_t; using u128 = __uint128_t; using i128 = __int128_t; /** * @brief Montgomery Reduction */ template class Montgomery { static constexpr int lg = std::numeric_limits::digits; using LargeT = internal::double_size_uint_t; T mod, r, r2, minv; T inv() { T t = 0, res = 0; for (int i = 0; i < lg; ++i) { if (~t & 1) { t += mod; res += static_cast(1) << i; } t >>= 1; } return res; } public: Montgomery() = default; constexpr T get_mod() { return mod; } void set_mod(T m) { assert(m); assert(m & 1); mod = m; r = (-static_cast(mod)) % mod; r2 = (-static_cast(mod)) % mod; minv = inv(); } T reduce(LargeT x) const { u64 res = (x + static_cast(static_cast(x) * minv) * mod) >> lg; if (res >= mod) res -= mod; return res; } T generate(LargeT x) { return reduce(x * r2); } T mul(T x, T y) { return reduce((LargeT)x * y); } }; }; // namespace internal }; // namespace kyopro #line 6 "src/math/dynamic_modint.hpp" namespace kyopro { template class barrett_modint { using mint = barrett_modint; using u32 = uint32_t; using u64 = uint64_t; using i32 = int32_t; using i64 = int64_t; using br = internal::barrett; static br brt; u32 v; public: static void set_mod(u32 mod_) { brt = br(mod_); } public: explicit constexpr barrett_modint() : v(0) { assert(mod()); } explicit constexpr barrett_modint(i64 v_) : v() { assert(mod()); if (v_ < 0) v_ = (i64)mod() - v_; v = brt.reduce(v_); } u32 val() const { return v; } static u32 mod() { return brt.get_mod(); } static mint raw(u32 v) { mint x; x.v = v; return x; } constexpr mint& operator++() { ++v; if (v == mod()) v = 0; return (*this); } constexpr mint& operator--() { if (v == 0) v = mod(); --v; return (*this); } constexpr mint operator++(int) { mint res(*this); ++(*this); return res; } constexpr mint operator--(int) { mint res(*this); --(*this); return res; } constexpr mint& operator+=(const mint& r) { v += r.v; if (v >= mod()) v -= mod(); return (*this); } constexpr mint& operator-=(const mint& r) { v += mod() - r.v; if (v >= mod()) { v -= mod(); } return (*this); } constexpr mint& operator*=(const mint& r) { v = brt.mul(v, r.v); return (*this); } constexpr mint& operator/=(const mint& r) { return (*this) *= r.inv(); } friend mint operator+(const mint& lhs, const mint& rhs) { return mint(lhs) += rhs; } friend mint operator-(const mint& lhs, const mint& rhs) { return mint(lhs) -= rhs; } friend mint operator*(const mint& lhs, const mint& rhs) { return mint(lhs) *= rhs; } friend mint operator/(const mint& lhs, const mint& rhs) { return mint(lhs) /= rhs; } friend bool operator==(const mint& lhs, const mint& rhs) { return lhs._v == rhs._v; } friend bool operator!=(const mint& lhs, const mint& rhs) { return lhs._v != rhs._v; } constexpr mint& operator+=(i64 r) { return (*this) += mint(r); } constexpr mint& operator-=(i64 r) { return (*this) -= mint(r); } constexpr mint& operator*=(i64 r) { return (*this) *= mint(r); } friend mint operator+(i64 l, const mint& r) { return mint(l) += r; } friend mint operator+(const mint& l, i64 r) { return mint(l) += r; } friend mint operator-(i64 l, const mint& r) { return mint(l) -= r; } friend mint operator-(const mint& l, i64 r) { return mint(l) -= r; } friend mint operator*(i64 l, const mint& r) { return mint(l) *= r; } friend mint operator*(const mint& l, i64 r) { return mint(l) *= r; } constexpr mint operator+() const { return *this; } constexpr mint operator-() const { return mint() - *this; } friend std::ostream& operator<<(std::ostream& os, const mint& mt) { os << mt.val(); return os; } friend std::istream& operator>>(std::istream& is, mint& mt) { i64 v_; is >> v_; mt = mint(v_); return is; } template mint pow(T e) const { mint res(1), base(*this); while (e) { if (e & 1) { res *= base; } e >>= 1; base *= base; } return res; } constexpr mint inv() const { return pow(mod() - 2); } }; }; // namespace kyopro template typename kyopro::barrett_modint::br kyopro::barrett_modint::brt; namespace kyopro { template class dynamic_modint { using LargeT = internal::double_size_uint_t; static T _mod; static internal::Montgomery mr; public: static void set_mod(T mod_) { mr.set_mod(mod_); _mod = mod_; } static T mod() { return _mod; } private: T v; public: dynamic_modint(T v_ = 0) { assert(_mod); v = mr.generate(v_); } T val() const { return mr.reduce(v); } using mint = dynamic_modint; mint& operator+=(const mint& r) { v += r.v; if (v >= mr.get_mod()) { v -= mr.get_mod(); } return (*this); } mint& operator-=(const mint& r) { v += mr.get_mod() - r.v; if (v >= mr.get_mod) { v -= mr.get_mod(); } return (*this); } mint& operator*=(const mint& r) { v = mr.mul(v, r.v); return (*this); } mint operator+(const mint& r) { return mint(*this) += r; } mint operator-(const mint& r) { return mint(*this) -= r; } mint operator*(const mint& r) { return mint(*this) *= r; } mint& operator=(const T& v_) { (*this) = mint(v_); return (*this); } friend std::ostream& operator<<(std::ostream& os, const mint& mt) { os << mt.val(); return os; } friend std::istream& operator>>(std::istream& is, mint& mt) { T v_; is >> v_; mt = v_; return is; } template mint pow(P e) const { assert(e >= 0); mint res(1), base(*this); while (e) { if (e & 1) { res *= base; } e >>= 1; base *= base; } return res; } mint inv() const { return pow(mod() - 2); } mint& operator/=(const mint& r) { return (*this) *= r.inv(); } mint operator/(const mint& r) const { return mint(*this) *= r.inv(); } mint& operator/=(T r) { return (*this) /= mint(r); } friend mint operator/(const mint& l, T r) { return mint(l) /= r; } friend mint operator/(T l, const mint& r) { return mint(l) /= r; } }; }; // namespace kyopro template T kyopro::dynamic_modint::_mod; template kyopro::internal::Montgomery kyopro::dynamic_modint::mr; /** * @brief 動的modint * @docs docs/math/dynamic_modint.md */ #line 3 "src/math/miller.hpp" namespace kyopro { /** * @brief MillerRabin素数判定法 */ class miller { using i128 = __int128_t; using u128 = __uint128_t; using u64 = uint64_t; using u32 = uint32_t; template static constexpr bool miller_rabin(T n) { T d = n - 1; while (~d & 1) { d >>= 1; } const T rev = n - 1; if (mint::mod() != n) { mint::set_mod(n); } for (int i = 0; i < length; ++i) { if (n <= bases[i]) { return true; } T t = d; mint y = mint(bases[i]).pow(t); while (t != n - 1 && y.val() != 1 && y.val() != rev) { y *= y; t <<= 1; } if (y.val() != rev && (~t & 1)) return false; } return true; } // 底 static constexpr int bases_int[3] = {2, 7, 61}; static constexpr int bases_ll[7] = {2, 325, 9375, 28178, 450775, 9780504, 1795265022}; public: template static constexpr bool is_prime(T n) { if (n < 2) { return false; } else if (n == 2) { return true; } else if (~n & 1) { return false; }; if (std::numeric_limits::digits < 32 || n <= 1 << 30) { return miller_rabin>, bases_int, 3>(n); } else { return miller_rabin>, bases_ll, 7>(n); } return false; } }; }; // namespace kyopro /** * @docs docs/math/miller.md */ #line 2 "src/stream.hpp" #include #include #include #line 6 "src/stream.hpp" namespace kyopro { // read void single_read(char& c) { c = getchar_unlocked(); while (isspace(c)) c = getchar_unlocked(); } template ::value || std::is_same::value || std::is_same::value>* = nullptr> void single_read(T& a) { a = 0; bool is_negative = false; char c = getchar_unlocked(); while (isspace(c)) { c = getchar_unlocked(); } if (c == '-') is_negative = true, c = getchar_unlocked(); while (isdigit(c)) { a = 10 * a + (c - '0'); c = getchar_unlocked(); } if (is_negative) a *= -1; } void single_read(std::string& str) { char c = getchar_unlocked(); while (isspace(c)) c = getchar_unlocked(); while (!isspace(c)) { str += c; c = getchar_unlocked(); } } void read() {} template void read(Head& head, Tail&... tail) { single_read(head), read(tail...); } // write void single_write(char c) { putchar_unlocked(c); } template ::value || std::is_same::value || std::is_same::value>* = nullptr> void single_write(T a) { if (!a) { putchar_unlocked('0'); putchar_unlocked('\n'); return; } if (a < 0) putchar_unlocked('-'), a *= -1; char s[37]; int now = 37; while (a) { s[--now] = (char)'0' + a % 10; a /= 10; } while (now < 37) putchar_unlocked(s[now++]); } void single_write(const std::string& str) { for (auto c : str) { putchar_unlocked(c); } } void write() {} template void write(Head head, Tail... tail) { single_write(head); putchar_unlocked(' '); write(tail...); } template void put(Args... x) { write(x...); putchar_unlocked('\n'); } }; // namespace kyopro /** * @brief fastIO */ #line 5 "test/yuki/No3030.test.cpp" int main() { int n; kyopro::read(n); for (int i = 0; i < n; ++i) { long long x; kyopro::read(x); kyopro::put(x, kyopro::miller::is_prime(x) ? '1' : '0'); } }