#include // #include using namespace std; using namespace numbers; template struct modular_unfixed_base{ static unsigned int _mod; static unsigned long long _inverse_mod; static unsigned int &mod(){ return _mod; } static void precalc_barrett(){ _inverse_mod = (unsigned long long)-1 / _mod + 1; } static void setup(unsigned int mod = 0){ if(!mod) cin >> mod; _mod = mod; assert(_mod >= 1); precalc_barrett(); } template static vector precalc_power(T base, int SZ){ vector res(SZ + 1, 1); for(auto i = 1; i <= SZ; ++ i) res[i] = res[i - 1] * base; return res; } static vector _INV; static void precalc_inverse(int SZ){ if(_INV.empty()) _INV.assign(2, 1); for(auto x = _INV.size(); x <= SZ; ++ x) _INV.push_back(_mod / x * -_INV[_mod % x]); } // _mod must be a prime static modular_unfixed_base _primitive_root; static modular_unfixed_base primitive_root(){ if(_primitive_root) return _primitive_root; if(_mod == 2) return _primitive_root = 1; if(_mod == 998244353) return _primitive_root = 3; unsigned int divs[20] = {}; divs[0] = 2; int cnt = 1; unsigned int x = (_mod - 1) / 2; while(x % 2 == 0) x /= 2; for(auto i = 3; 1LL * i * i <= x; i += 2){ if(x % i == 0){ divs[cnt ++] = i; while(x % i == 0) x /= i; } } if(x > 1) divs[cnt ++] = x; for(auto g = 2; ; ++ g){ bool ok = true; for(auto i = 0; i < cnt; ++ i){ if((modular_unfixed_base(g).power((_mod - 1) / divs[i])) == 1){ ok = false; break; } } if(ok) return _primitive_root = g; } } constexpr modular_unfixed_base(): data(){ } modular_unfixed_base(const double &x){ data = normalize(llround(x)); } modular_unfixed_base(const long double &x){ data = normalize(llround(x)); } template::value>::type* = nullptr> modular_unfixed_base(const T &x){ data = normalize(x); } template::value>::type* = nullptr> static unsigned int normalize(const T &x){ if(_mod == 1) return 0; assert(_inverse_mod); int sign = x >= 0 ? 1 : -1; unsigned int v = _mod <= sign * x ? sign * x - ((__uint128_t)(sign * x) * _inverse_mod >> 64) * _mod : sign * x; if(v >= _mod) v += _mod; if(sign == -1 && v) v = _mod - v; return v; } const unsigned int &operator()() const{ return data; } template operator T() const{ return data; } modular_unfixed_base &operator+=(const modular_unfixed_base &otr){ if((data += otr.data) >= _mod) data -= _mod; return *this; } modular_unfixed_base &operator-=(const modular_unfixed_base &otr){ if((data += _mod - otr.data) >= _mod) data -= _mod; return *this; } template::value>::type* = nullptr> modular_unfixed_base &operator+=(const T &otr){ return *this += modular_unfixed_base(otr); } template::value>::type* = nullptr> modular_unfixed_base &operator-=(const T &otr){ return *this -= modular_unfixed_base(otr); } modular_unfixed_base &operator++(){ return *this += 1; } modular_unfixed_base &operator--(){ return *this += _mod - 1; } modular_unfixed_base operator++(int){ modular_unfixed_base result(*this); *this += 1; return result; } modular_unfixed_base operator--(int){ modular_unfixed_base result(*this); *this += _mod - 1; return result; } modular_unfixed_base operator-() const{ return modular_unfixed_base(_mod - data); } modular_unfixed_base &operator*=(const modular_unfixed_base &rhs){ data = normalize((unsigned long long)data * rhs.data); return *this; } template::value>::type* = nullptr> modular_unfixed_base &inplace_power(T e){ if(e == 0) return *this = 1; if(data == 0) return *this = {}; if(data == 1) return *this; if(data == mod() - 1) return e % 2 ? *this : *this = -*this; if(e < 0) *this = 1 / *this, e = -e; modular_unfixed_base res = 1; for(; e; *this *= *this, e >>= 1) if(e & 1) res *= *this; return *this = res; } template::value>::type* = nullptr> modular_unfixed_base power(T e) const{ return modular_unfixed_base(*this).inplace_power(e); } modular_unfixed_base &operator/=(const modular_unfixed_base &otr){ int a = otr.data, m = _mod, u = 0, v = 1; if(a < _INV.size()) return *this *= _INV[a]; while(a){ int t = m / a; m -= t * a; swap(a, m); u -= t * v; swap(u, v); } assert(m == 1); return *this *= u; } unsigned int data; }; template unsigned int modular_unfixed_base::_mod; template unsigned long long modular_unfixed_base::_inverse_mod; template vector> modular_unfixed_base::_INV; template modular_unfixed_base modular_unfixed_base::_primitive_root; template bool operator==(const modular_unfixed_base &lhs, const modular_unfixed_base &rhs){ return lhs.data == rhs.data; } template::value>::type* = nullptr> bool operator==(const modular_unfixed_base &lhs, T rhs){ return lhs == modular_unfixed_base(rhs); } template::value>::type* = nullptr> bool operator==(T lhs, const modular_unfixed_base &rhs){ return modular_unfixed_base(lhs) == rhs; } template bool operator!=(const modular_unfixed_base &lhs, const modular_unfixed_base &rhs){ return !(lhs == rhs); } template::value>::type* = nullptr> bool operator!=(const modular_unfixed_base &lhs, T rhs){ return !(lhs == rhs); } template::value>::type* = nullptr> bool operator!=(T lhs, const modular_unfixed_base &rhs){ return !(lhs == rhs); } template bool operator<(const modular_unfixed_base &lhs, const modular_unfixed_base &rhs){ return lhs.data < rhs.data; } template bool operator>(const modular_unfixed_base &lhs, const modular_unfixed_base &rhs){ return lhs.data > rhs.data; } template bool operator<=(const modular_unfixed_base &lhs, const modular_unfixed_base &rhs){ return lhs.data <= rhs.data; } template bool operator>=(const modular_unfixed_base &lhs, const modular_unfixed_base &rhs){ return lhs.data >= rhs.data; } template modular_unfixed_base operator+(const modular_unfixed_base &lhs, const modular_unfixed_base &rhs){ return modular_unfixed_base(lhs) += rhs; } template::value>::type* = nullptr> modular_unfixed_base operator+(const modular_unfixed_base &lhs, T rhs){ return modular_unfixed_base(lhs) += rhs; } template::value>::type* = nullptr> modular_unfixed_base operator+(T lhs, const modular_unfixed_base &rhs){ return modular_unfixed_base(lhs) += rhs; } template modular_unfixed_base operator-(const modular_unfixed_base &lhs, const modular_unfixed_base &rhs){ return modular_unfixed_base(lhs) -= rhs; } template::value>::type* = nullptr> modular_unfixed_base operator-(const modular_unfixed_base &lhs, T rhs){ return modular_unfixed_base(lhs) -= rhs; } template::value>::type* = nullptr> modular_unfixed_base operator-(T lhs, const modular_unfixed_base &rhs){ return modular_unfixed_base(lhs) -= rhs; } template modular_unfixed_base operator*(const modular_unfixed_base &lhs, const modular_unfixed_base &rhs){ return modular_unfixed_base(lhs) *= rhs; } template::value>::type* = nullptr> modular_unfixed_base operator*(const modular_unfixed_base &lhs, T rhs){ return modular_unfixed_base(lhs) *= rhs; } template::value>::type* = nullptr> modular_unfixed_base operator*(T lhs, const modular_unfixed_base &rhs){ return modular_unfixed_base(lhs) *= rhs; } template modular_unfixed_base operator/(const modular_unfixed_base &lhs, const modular_unfixed_base &rhs) { return modular_unfixed_base(lhs) /= rhs; } template::value>::type* = nullptr> modular_unfixed_base operator/(const modular_unfixed_base &lhs, T rhs) { return modular_unfixed_base(lhs) /= rhs; } template::value>::type* = nullptr> modular_unfixed_base operator/(T lhs, const modular_unfixed_base &rhs) { return modular_unfixed_base(lhs) /= rhs; } template istream &operator>>(istream &in, modular_unfixed_base &number){ long long x; in >> x; number.data = modular_unfixed_base::normalize(x); return in; } // #define _SHOW_FRACTION template ostream &operator<<(ostream &out, const modular_unfixed_base &number){ out << number(); #if defined(LOCAL) && defined(_SHOW_FRACTION) cerr << "("; for(auto d = 1; ; ++ d){ if((number * d).data <= 1000000){ cerr << (number * d).data; if(d != 1) cerr << "/" << d; break; } else if((-number * d).data <= 1000000){ cerr << "-" << (-number * d).data; if(d != 1) cerr << "/" << d; break; } } cerr << ")"; #endif return out; } #undef _SHOW_FRACTION using modular = modular_unfixed_base<0>; int main(){ cin.tie(0)->sync_with_stdio(0); cin.exceptions(ios::badbit | ios::failbit); int n; cin >> n; modular::setup(); set appear; modular cur = 0; int rem = n; for(auto i = 0; i < n; ++ i){ int x; cin >> x; cur *= 2; if(appear.insert(x).second){ ++ cur; -- rem; } cout << cur * modular(2).power(rem) << "\n"; } return 0; } /* */ //////////////////////////////////////////////////////////////////////////////////////// // // // Coded by Aeren // // // ////////////////////////////////////////////////////////////////////////////////////////