#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(!data) 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){ #if defined(LOCAL) && defined(_SHOW_FRACTION) out << number(); cerr << "("; for(auto d = 1; ; ++ d){ if((number * d).data <= 1000000){ cerr << (number * d).data << "/" << d; break; } else if((-number * d).data <= 1000000){ cerr << "-" << (-number * d).data << "/" << d; break; } } cerr << ")"; return out; #else return out << number(); #endif } #undef _SHOW_FRACTION using modular = modular_unfixed_base<0>; template struct segment_tree_base{ #define ifQ if constexpr(HAS_QUERY) #define ifU if constexpr(HAS_UPDATE) int n, size, log; vector data; vector data_action; F1 TT; // monoid operation (always adjacent) T T_id; // monoid identity F2 UU; // monoid operation (superset, subset) U U_id; // monoid identity F3 UT; // action of U on T (superset, subset) // O(n) segment_tree_base(F1 TT, T T_id, F2 UU, U U_id, F3 UT): TT(TT), T_id(T_id), UU(UU), U_id(U_id), UT(UT){ } segment_tree_base &operator=(const segment_tree_base &seg){ n = seg.n; size = seg.size; log = seg.log; data = seg.data; data_action = seg.data_action; } // O(n) void build(int n){ this->n = n; size = 1; while(size < n) size <<= 1; log = __lg(size); ifQ data.assign(size << 1, T_id); ifU data_action.assign(HAS_QUERY ? size : size << 1, U_id); } // O(n) void build(int n, T x){ static_assert(HAS_QUERY); this->n = n; size = 1; while(size < n) size <<= 1; log = __lg(size); data.assign(size << 1, T_id); fill(data.begin() + size, data.begin() + size + n, x); for(auto i = size - 1; i >= 1; -- i) refresh(i); ifU data_action.assign(size, U_id); } // O(n) void build(const vector &a){ static_assert(HAS_QUERY); n = (int)a.size(); size = 1; while(size < n) size <<= 1; log = __lg(size); data.assign(size << 1, T_id); copy(a.begin(), a.end(), data.begin() + size); for(auto i = size - 1; i >= 1; -- i) refresh(i); ifU data_action.assign(size, U_id); } // O(n) void build_action(int n){ static_assert(!HAS_QUERY && HAS_UPDATE); build(n); } // O(n) void build_action(int n, U f){ static_assert(!HAS_QUERY && HAS_UPDATE); this->n = n; size = 1; while(size < n) size <<= 1; log = __lg(size); data_action.assign(size << 1, U_id); fill(data_action.begin() + size, data_action.begin() + size + n, f); } // O(n) void build_action(const vector &a){ static_assert(!HAS_QUERY && HAS_UPDATE); n = (int)a.size(); size = 1; while(size < n) size <<= 1; log = __lg(size); data_action.assign(size << 1, U_id); copy(a.begin(), a.end(), data_action.begin() + size); } // O(1) void refresh(int i){ static_assert(HAS_QUERY); data[i] = TT(data[i << 1], data[i << 1 | 1]); } // O(1) void apply(int i, U f){ static_assert(HAS_UPDATE); ifQ data[i] = UT(f, data[i]); if(!HAS_QUERY || i < size) data_action[i] = UU(f, data_action[i]); } // O(1) void push(int i){ static_assert(HAS_UPDATE); apply(i << 1, data_action[i]), apply(i << 1 | 1, data_action[i]); data_action[i] = U_id; } // O(log(n)) if HAS_UPDATE, O(1) otherwise. T query(int p){ static_assert(HAS_QUERY); assert(0 <= p && p < n); p += size; ifU for(auto i = log; i >= 1; -- i) push(p >> i); return data[p]; } // O(log(n)) U query_action(int p){ static_assert(!HAS_QUERY && HAS_UPDATE); p += size; ifU for(auto i = log; i >= 1; -- i) push(p >> i); return data_action[p]; } // O(log(n)) T query(int l, int r){ static_assert(HAS_QUERY); assert(0 <= l && l <= r && r <= n); if(l == r) return T_id; l += size, r += size; ifU for(auto i = log; i >= 1; -- i){ if(l >> i << i != l) push(l >> i); if(r >> i << i != r) push(r - 1 >> i); } T res_left = T_id, res_right = T_id; for(; l < r; l >>= 1, r >>= 1){ if(l & 1) res_left = TT(res_left, data[l ++]); if(r & 1) res_right = TT(data[-- r], res_right); } return TT(res_left, res_right); } // O(1) T query_all() const{ static_assert(HAS_QUERY); return data[1]; } // O(n) vector to_array(){ static_assert(HAS_QUERY); ifU for(auto i = 1; i < size; ++ i) push(i); return vector(data.begin() + size, data.begin() + size + n); } // O(n) vector to_array_of_updates(){ static_assert(!HAS_QUERY && HAS_UPDATE); for(auto i = 1; i < size; ++ i) push(i); return vector(data_action.begin() + size, data_action.begin() + size + n); } // O(log(n)) void set(int p, T x){ static_assert(HAS_QUERY); assert(0 <= p && p < n); p += size; ifU for(auto i = log; i >= 1; -- i) push(p >> i); data[p] = x; for(auto i = 1; i <= log; ++ i) refresh(p >> i); } // O(log(n)) void set_action(int p, U f){ static_assert(!HAS_QUERY && HAS_UPDATE); assert(0 <= p && p < n); p += size; for(auto i = log; i >= 1; -- i) push(p >> i); data_action[p] = f; } // O(log(n)) void update(int p, U f){ static_assert(HAS_UPDATE); assert(0 <= p && p < n); p += size; for(auto i = log; i >= 1; -- i) push(p >> i); ifQ{ data[p] = UT(f, data[p]); for(auto i = 1; i <= log; ++ i) refresh(p >> i); } else data_action[p] = UU(f, data_action[p]); } // O(log(n)) void update(int l, int r, U f){ static_assert(HAS_UPDATE); assert(0 <= l && l <= r && r <= n); if(l == r) return; l += size, r += size; for(auto i = log; i >= 1; -- i){ if(l >> i << i != l) push(l >> i); if(r >> i << i != r) push(r - 1 >> i); } int l2 = l, r2 = r; for(; l < r; l >>= 1, r >>= 1){ if(l & 1) apply(l ++, f); if(r & 1) apply(-- r, f); } l = l2, r = r2; ifQ for(auto i = 1; i <= log; ++ i){ if(l >> i << i != l) refresh(l >> i); if(r >> i << i != r) refresh(r - 1 >> i); } } // pred(sum[l, r)) is T, T, ..., T, F, F, ..., F // Returns max r with T // O(log(n)) int max_pref(int l, auto pred){ static_assert(HAS_QUERY); assert(0 <= l && l <= n && pred(T_id)); if(l == n) return n; l += size; ifU for(auto i = log; i >= 1; -- i) push(l >> i); T sum = T_id; do{ while(~l & 1) l >>= 1; if(!pred(TT(sum, data[l]))){ while(l < size){ ifU push(l); l = l << 1; if(pred(TT(sum, data[l]))) sum = TT(sum, data[l ++]); } return l - size; } sum = TT(sum, data[l]); ++ l; }while((l & -l) != l); return n; } // pred(sum[l, r)) is F, F, ..., F, T, T, ..., T // Returns min l with T // O(log(n)) int min_suff(int r, auto pred){ static_assert(HAS_QUERY); assert(0 <= r && r <= n && pred(T_id)); if(r == 0) return 0; r += size; ifU for(auto i = log; i >= 1; -- i) push(r - 1 >> i); T sum = T_id; do{ -- r; while(r > 1 && r & 1) r >>= 1; if(!pred(TT(data[r], sum))){ while(r < size){ ifU push(r); r = r << 1 | 1; if(pred(TT(data[r], sum))) sum = TT(data[r --], sum); } return r + 1 - size; } sum = TT(data[r], sum); }while((r & -r) != r); return 0; } template friend output_stream &operator<<(output_stream &out, segment_tree_base seg){ out << "{"; for(auto i = 0; i < seg.n; ++ i){ HAS_QUERY ? out << seg.query(i) : out << seg.query_action(i); if(i != seg.n - 1) out << ", "; } return out << '}'; } }; // Supports query template auto make_Q_segment_tree(F TT, T T_id){ using U = int; auto _UU = [&](U, U)->U{ return U{}; }; auto _UT = [&](U, T)->T{ return T{}; }; return segment_tree_base(TT, T_id, _UU, U{}, _UT); } // Supports update template auto make_U_segment_tree(F UU, U U_id){ using T = int; auto _TT = [&](T, T)->T{ return T{}; }; auto _UT = [&](U, T)->T{ return T{}; }; return segment_tree_base(_TT, T{}, UU, U_id, _UT); } // Supports query and update template auto make_Q_segment_tree(F1 TT, T T_id, F2 UU, U U_id, F3 UT){ return segment_tree_base(TT, T_id, UU, U_id, UT); } int main(){ cin.tie(0)->sync_with_stdio(0); cin.exceptions(ios::badbit | ios::failbit); int n, qn; cin >> n; modular::setup(); cin >> qn; auto seg = make_U_segment_tree(plus<>(), 0); seg.build_action(n); vector x(qn + 1), y(qn + 1), z(qn + 1); iota(x.begin(), x.end(), 1); z = modular::precalc_power(3, qn); y[0] = 1; for(auto i = 1; i <= qn; ++ i){ y[i] = 3 * y[i - 1] + 2 * x[i] * z[i - 1]; } for(auto qi = 0; qi < qn; ++ qi){ int l, p, r; cin >> l >> p >> r, -- l, -- p; seg.update(l, r, 1); int cnt = seg.query_action(p); cout << x[cnt] << " " << y[cnt] << " " << z[cnt] << "\n"; } return 0; } /* */ //////////////////////////////////////////////////////////////////////////////////////// // // // Coded by Aeren // // // ////////////////////////////////////////////////////////////////////////////////////////