/* preprocessor start */ #ifdef LOCAL //* #define _GLIBCXX_DEBUG // gcc /*/ #define _LIBCPP_DEBUG 0 // clang //*/ #define __clock__ // #define __buffer_check__ #else #pragma GCC optimize("Ofast") /* #define _GLIBCXX_DEBUG // gcc /*/ // #define _LIBCPP_DEBUG 0 // clang //*/ // #define __buffer_check__ // #define NDEBUG #endif #define __precision__ 10 #define iostream_untie true #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #define __all(v) std::begin(v), std::end(v) #define __rall(v) std::rbegin(v), std::rend(v) #define __popcount(n) __builtin_popcountll(n) #define __clz32(n) __builtin_clz(n) #define __clz64(n) __builtin_clzll(n) #define __ctz32(n) __builtin_ctz(n) #define __ctz64(n) __builtin_ctzll(n) /* preprocessor end */ namespace std { // hash template size_t hash_combine(size_t seed, T const &key) { return seed ^ (hash()(key) + 0x9e3779b9 + (seed << 6) + (seed >> 2)); } template struct hash> { size_t operator()(pair const &pr) const { return hash_combine(hash_combine(0, pr.first), pr.second); } }; template ::value - 1> struct tuple_hash_calc { static size_t apply(size_t seed, tuple_t const &t) { return hash_combine(tuple_hash_calc::apply(seed, t), get(t)); } }; template struct tuple_hash_calc { static size_t apply(size_t seed, tuple_t const &t) { return hash_combine(seed, get<0>(t)); } }; template struct hash> { size_t operator()(tuple const &t) const { return tuple_hash_calc>::apply(0, t); } }; // iostream template istream &operator>>(istream &is, pair &p) { return is >> p.first >> p.second; } template ostream &operator<<(ostream &os, const pair &p) { return os << p.first << ' ' << p.second; } template struct tupleis { static istream &apply(istream &is, tuple_t &t) { tupleis::apply(is, t); return is >> get(t); } }; template struct tupleis { static istream &apply(istream &is, tuple_t &t) { return is; } }; template istream &operator>>(istream &is, tuple &t) { return tupleis, tuple_size>::value - 1>::apply(is, t); } template <> istream &operator>>(istream &is, tuple<> &t) { return is; } template struct tupleos { static ostream &apply(ostream &os, const tuple_t &t) { tupleos::apply(os, t); return os << ' ' << get(t); } }; template struct tupleos { static ostream &apply(ostream &os, const tuple_t &t) { return os << get<0>(t); } }; template ostream &operator<<(ostream &os, const tuple &t) { return tupleos, tuple_size>::value - 1>::apply(os, t); } template <> ostream &operator<<(ostream &os, const tuple<> &t) { return os; } template , string>::value, nullptr_t> = nullptr> istream& operator>>(istream& is, Container &cont) { for(auto&& e : cont) is >> e; return is; } template , string>::value, nullptr_t> = nullptr> ostream& operator<<(ostream& os, const Container &cont) { bool flag = 1; for(auto&& e : cont) flag ? flag = 0 : (os << ' ', 0), os << e; return os; } } // namespace std namespace setting { using namespace std; using namespace chrono; system_clock::time_point start_time, end_time; long long get_elapsed_time() { end_time = system_clock::now(); return duration_cast(end_time - start_time).count(); } void print_elapsed_time() { cerr << "\n----- Exec time : " << get_elapsed_time() << " ms -----\n\n"; } void buffer_check() { char bufc; if(cin >> bufc) cerr << "\n\033[1;35mwarning\033[0m: buffer not empty.\n"; } struct setupper { setupper() { if(iostream_untie) ios::sync_with_stdio(false), cin.tie(nullptr); cout << fixed << setprecision(__precision__); #ifdef stderr_path if(freopen(stderr_path, "a", stderr)) cerr << fixed << setprecision(__precision__); #endif #ifdef LOCAL cerr << boolalpha << "\n----- stderr at LOCAL -----\n\n"; #endif #ifdef __buffer_check__ atexit(buffer_check); #endif #ifdef __clock__ start_time = system_clock::now(); atexit(print_elapsed_time); #endif } } __setupper; // struct setupper } // namespace setting #ifdef __clock__ #include "C:\Users\euler\OneDrive\Documents\Competitive_Programming\Library\local\clock.hpp" #else #define build_clock() ((void)0) #define set_clock() ((void)0) #define get_clock() ((void)0) #endif #ifdef LOCAL #include "C:\Users\euler\OneDrive\Documents\Competitive_Programming\Library\local\dump.hpp" #else #define dump(...) ((void)0) #endif /* function utility start */ template T read(types... args) noexcept { typename std::remove_const::type obj(args...); std::cin >> obj; return obj; } #define input(type, var, ...) type var{read(__VA_ARGS__)} // substitute y for x if x > y. template inline bool chmin(T &x, const T &y) { return x > y ? x = y, true : false; } // substitute y for x if x < y. template inline bool chmax(T &x, const T &y) { return x < y ? x = y, true : false; } // binary search on discrete range. template iter_type binary(iter_type __ok, iter_type __ng, pred_type pred) { std::ptrdiff_t dist(__ng - __ok); while(std::abs(dist) > 1) { iter_type mid(__ok + dist / 2); if(pred(mid)) __ok = mid, dist -= dist / 2; else __ng = mid, dist /= 2; } return __ok; } // binary search on real numbers. template long double binary(long double __ok, long double __ng, const long double eps, pred_type pred) { while(std::abs(__ok - __ng) > eps) { long double mid{(__ok + __ng) / 2}; (pred(mid) ? __ok : __ng) = mid; } return __ok; } // size of array. template size_t size(A (&array)[N]) { return N; } // be careful that val is type-sensitive. template void init(A (&array)[N], const T &val) { std::fill((T*)array, (T*)(array + N), val); } /* functon utility end */ /* using alias start */ using namespace std; using i32 = int_least32_t; using i64 = int_least64_t; using u32 = uint_least32_t; using u64 = uint_least64_t; using p32 = pair; using p64 = pair; template > using heap = priority_queue, Comp>; template using hashset = unordered_set; template using hashmap = unordered_map; /* using alias end */ /* library start */ class modint_runtime { long long val; friend std::ostream &operator<<(std::ostream &os, const modint_runtime &other) noexcept { return os << other.val; } friend std::istream &operator>>(std::istream &is, modint_runtime &other) noexcept { long long val; other = modint_runtime((is >> val, val)); return is; } public: static long long &mod() noexcept { static long long mod{}; return mod; } modint_runtime(long long x = 0) : val{(x %= mod()) < 0 ? x + mod() : x} {} long long value() const noexcept { return val; } modint_runtime operator++(int) noexcept { modint_runtime t = *this; return ++val, t; } modint_runtime &operator++() noexcept { return ++val, *this; } modint_runtime operator--(int) noexcept { modint_runtime t = *this; return --val, t; } modint_runtime &operator--() noexcept { return --val, *this; } modint_runtime &operator=(long long other) noexcept { return val = (other %= mod()) < 0 ? other + mod() : other, *this; } modint_runtime &operator+=(long long other) noexcept { return (val += other % mod()) < mod() ? 0 : val -= mod(), *this; } modint_runtime &operator+=(const modint_runtime &other) noexcept { return (val += other.val) < mod() ? 0 : val -= mod(), *this; } modint_runtime &operator-=(long long other) noexcept { return (val += mod() - other % mod()) < mod() ? 0 : val -= mod(), *this; } modint_runtime &operator-=(const modint_runtime &other) noexcept { return (val += mod() - other.val) < mod() ? 0 : val -= mod(), *this; } modint_runtime &operator*=(long long other) noexcept { return (val *= other % mod()) %= mod(), *this; } modint_runtime &operator*=(const modint_runtime &other) noexcept { return (val *= other.val) %= mod(), *this; } modint_runtime &operator/=(long long other) noexcept { return *this *= inverse(other); } modint_runtime &operator/=(const modint_runtime &other) noexcept { return *this *= inverse(other); } modint_runtime operator-() const noexcept { return modint_runtime(-val); } modint_runtime operator+(const modint_runtime &other) const noexcept { return modint_runtime{*this} += other; } modint_runtime operator-(const modint_runtime &other) const noexcept { return modint_runtime{*this} -= other; } modint_runtime operator*(const modint_runtime &other) const noexcept { return modint_runtime{*this} *= other; } modint_runtime operator/(const modint_runtime &other) const noexcept { return modint_runtime{*this} /= other; } bool operator==(const modint_runtime &other) const noexcept { return val == other.val; } bool operator!=(const modint_runtime &other) const noexcept { return val != other.val; } bool operator!() const noexcept { return !val; } friend modint_runtime operator+(long long x, modint_runtime y) noexcept { return {x + y.val}; } friend modint_runtime operator-(long long x, modint_runtime y) noexcept { return {x - y.val}; } friend modint_runtime operator*(long long x, modint_runtime y) noexcept { return {x % mod() * y.val}; } friend modint_runtime operator/(long long x, modint_runtime y) noexcept { return {x % mod() * inverse(y).val}; } static modint_runtime inverse(const modint_runtime &other) noexcept { assert(mod() && other.val); long long a{mod()}, b{other.val}, u{}, v{1}, t{}; while(b) t = a / b, a ^= b ^= (a -= t * b) ^= b, u ^= v ^= (u -= t * v) ^= v; return {u}; } static modint_runtime pow(modint_runtime other, long long e) noexcept { if(e < 0) e = e % (mod() - 1) + mod() - 1; modint_runtime res{1}; while(e) { if(e & 1) res *= other; other *= other, e >>= 1; } return res; } }; // class modint_runtime /* library end */ /* The main code follows. */ template void _main(); struct solver; int main() { _main(); } template void _main() { unsigned t; #ifdef LOCAL t = 1; #else t = 1; // single test case #endif // t = -1; // infinite loop // cin >> t; // case number given while(t--) solver(); } struct solver { solver() { i64 P; cin>>P; modint_runtime::mod()=P; modint_runtime n; cin>>n; i64 ord=P-1; for(i64 i=1; i*i