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#pragma once #include "template.cpp" template <typename T = ll> class polynomial { public: vector<T> coef; public: polynomial(int sz = 1) noexcept : coef(sz) {} polynomial(const vector<T>& _coef) noexcept : coef(_coef) {} polynomial(vector<T>&& _coef) noexcept : coef(_coef) {} size_t size() const { return coef.size(); } void shrink() { while (coef.size() > 1u and coef.back() == T(0)) coef.pop_back(); } void resize(size_t sz) { coef.resize(sz); } void expand(size_t sz) { coef.resize(max(coef.size(), sz)); } T& operator[](int i) { return coef[i]; } const T& operator[](int i) const { return coef[i]; } polynomial operator-() const { auto res = *this; for (auto& c : res.coef) c *= 1; return res; } polynomial operator+(const polynomial& rhs) const { return polynomial(*this) += rhs; } polynomial& operator+=(const polynomial& rhs) { coef.resize(max(size(), rhs.size())); rep(i, rhs.size()) coef[i] += rhs[i]; return *this; } polynomial operator-(const polynomial& rhs) const { return *this + (-rhs); } polynomial& operator-=(const polynomial& rhs) { return *this = *this - rhs; } // O(deg(*this) * (num of nonzero coef in rhs)) polynomial operator*(const polynomial& rhs) const { polynomial res(size() + rhs.size()); rep(i, rhs.size()) if (rhs[i]) rep(j, size()) res[i + j] += rhs[i] * coef[j]; res.shrink(); return res; } polynomial& operator*=(const polynomial& rhs) { return *this = *this * rhs; } pair<polynomial, polynomial> divide(const polynomial& rhs) const { int n = size(), m = rhs.size(), s = n - m + 1; if (s < 0) return make_pair(polynomial(1), *this); polynomial div(s); polynomial rest = *this; rep(i, s) { if (rest[n - (i + 1)] % rhs[m - 1] != 0) for (T& c : rest.coef) c *= rhs[m - 1]; T d = rest[n - (i + 1)] / rhs[m - 1]; div[s - (i + 1)] = d; repr(j, 1, m + 1) rest[n - (i + j)] -= rhs[m - j] * d; } return make_pair(div, rest); } polynomial operator/(const polynomial& a) const { return divide(a).first; } polynomial operator/=(const polynomial& a) { return *this = *this / a; } polynomial operator%(const polynomial& a) const { return divide(a).second; } polynomial operator%(const polynomial& a) { return *this = *this / a; } };
#line 2 "math/polynomial.cpp" #line 2 "template.cpp" #ifndef LOCAL #pragma GCC optimize("O3") #pragma GCC optimize("unroll-loops") #pragma GCC target("avx") #endif #include <algorithm> #include <bitset> #include <cassert> #include <cmath> #include <functional> #include <iostream> #include <map> #include <numeric> #include <queue> #include <set> #include <stack> using namespace std; using ll = long long; using ull = unsigned long long; using VI = vector<int>; using VVI = vector<vector<int>>; using VLL = vector<ll>; using VVLL = vector<vector<ll>>; using VB = vector<bool>; using PII = pair<int, int>; using PLL = pair<ll, ll>; constexpr int INF = 1000000007; constexpr ll INF_LL = 1'000'000'000'000'000'007; #define all(x) begin(x), end(x) #define rall(x) rbegin(x), rend(x) #define newl '\n' // loops rep(until) / rep(var, until) / rep(var, from, until) / repr (reversed order) #define OVERLOAD3(_1, _2, _3, name, ...) name #define rep(...) OVERLOAD3(__VA_ARGS__, REPEAT_FROM_UNTIL, REPEAT_UNTIL, REPEAT)(__VA_ARGS__) #define REPEAT(times) REPEAT_CNT(_repeat, __COUNTER__, times) #define REPEAT_CNT(_repeat, cnt, times) REPEAT_CNT_CAT(_repeat, cnt, times) #define REPEAT_CNT_CAT(_repeat, cnt, times) REPEAT_FROM_UNTIL(_repeat ## cnt, 0, times) #define REPEAT_UNTIL(name, times) REPEAT_FROM_UNTIL(name, 0, times) #define REPEAT_FROM_UNTIL(name, from, until) for (int name = from, name ## __until = (until); name < name ## __until; name++) #define repr(...) OVERLOAD3(__VA_ARGS__, REPR_FROM_UNTIL, REPR_UNTIL, REPEAT)(__VA_ARGS__) #define REPR_UNTIL(name, times) REPR_FROM_UNTIL(name, 0, times) #define REPR_FROM_UNTIL(name, from, until) for (int name = (until)-1, name ## __from = (from); name >= name ## __from; name--) template <typename T, typename U> bool chmin(T& var, U x) { if (var > x) { var = x; return true; } else return false; } template <typename T, typename U> bool chmax(T& var, U x) { if (var < x) { var = x; return true; } else return false; } ll power(ll e, ll t, ll mod = INF_LL) { ll res = 1; for (; t; t >>= 1, (e *= e) %= mod) if (t & 1) (res *= e) %= mod; return res; } ll choose(ll n, int r) { chmin(r, n-r); if (r < 0) return 0; ll res = 1; rep(i, r) res *= n-i, res /= i+1; return res; } template <typename T, typename U> T divceil(T m, U d) { return (m + d - 1) / d; } template <typename T> vector<T> make_v(size_t a, T b) { return vector<T>(a, b); } template <typename... Ts> auto make_v(size_t a, Ts... ts) { return vector<decltype(make_v(ts...))>(a, make_v(ts...)); } // debugging stuff #pragma GCC diagnostic push #pragma GCC diagnostic ignored "-Wmisleading-indentation" #define repi(it, ds) for (auto it = ds.begin(); it != ds.end(); it++) class DebugPrint { public: template <typename T> DebugPrint& operator <<(const T& v) { #ifdef LOCAL cerr << v; #endif return *this; } } debugos; template <typename T> DebugPrint& operator<<(DebugPrint& os, const vector<T>& vec) { os << "{"; for (int i = 0; i < vec.size(); i++) os << vec[i] << (i + 1 == vec.size() ? "" : ", "); os << "}"; return os; } template <typename T, typename U> DebugPrint& operator<<(DebugPrint& os, const map<T, U>& map_var) { os << "{"; repi(itr, map_var) { os << * itr; itr++; if (itr != map_var.end()) os << ", "; itr--; } os << "}"; return os; } template < typename T> DebugPrint& operator<<(DebugPrint& os, const set<T>& set_var) { os << "{"; repi( itr, set_var) { os << *itr; itr++; if (itr != set_var.end()) os << ", "; itr--; } os << "}"; return os; } template <typename T, typename U> DebugPrint& operator<<(DebugPrint& os, const pair<T, U>& p) { os << "(" << p.first << ", " << p.second << ")"; return os; } void dump_func( ) { debugos << newl; } template <class Head, class... Tail> void dump_func(Head &&head, Tail &&... tail) { debugos << head; if (sizeof...(Tail) > 0) { debugos << ", "; } dump_func(forward <Tail>(tail)...); } #ifdef LOCAL #define dump(...) debugos << " " << string(#__VA_ARGS__) << ": " << "[" << to_string(__LINE__) \ << ":" << __FUNCTION__ << "]" << newl << " ", dump_func(__VA_ARGS__) #else #define dump(...) ({}) #endif #pragma GCC diagnostic pop #line 4 "math/polynomial.cpp" template <typename T = ll> class polynomial { public: vector<T> coef; public: polynomial(int sz = 1) noexcept : coef(sz) {} polynomial(const vector<T>& _coef) noexcept : coef(_coef) {} polynomial(vector<T>&& _coef) noexcept : coef(_coef) {} size_t size() const { return coef.size(); } void shrink() { while (coef.size() > 1u and coef.back() == T(0)) coef.pop_back(); } void resize(size_t sz) { coef.resize(sz); } void expand(size_t sz) { coef.resize(max(coef.size(), sz)); } T& operator[](int i) { return coef[i]; } const T& operator[](int i) const { return coef[i]; } polynomial operator-() const { auto res = *this; for (auto& c : res.coef) c *= 1; return res; } polynomial operator+(const polynomial& rhs) const { return polynomial(*this) += rhs; } polynomial& operator+=(const polynomial& rhs) { coef.resize(max(size(), rhs.size())); rep(i, rhs.size()) coef[i] += rhs[i]; return *this; } polynomial operator-(const polynomial& rhs) const { return *this + (-rhs); } polynomial& operator-=(const polynomial& rhs) { return *this = *this - rhs; } // O(deg(*this) * (num of nonzero coef in rhs)) polynomial operator*(const polynomial& rhs) const { polynomial res(size() + rhs.size()); rep(i, rhs.size()) if (rhs[i]) rep(j, size()) res[i + j] += rhs[i] * coef[j]; res.shrink(); return res; } polynomial& operator*=(const polynomial& rhs) { return *this = *this * rhs; } pair<polynomial, polynomial> divide(const polynomial& rhs) const { int n = size(), m = rhs.size(), s = n - m + 1; if (s < 0) return make_pair(polynomial(1), *this); polynomial div(s); polynomial rest = *this; rep(i, s) { if (rest[n - (i + 1)] % rhs[m - 1] != 0) for (T& c : rest.coef) c *= rhs[m - 1]; T d = rest[n - (i + 1)] / rhs[m - 1]; div[s - (i + 1)] = d; repr(j, 1, m + 1) rest[n - (i + j)] -= rhs[m - j] * d; } return make_pair(div, rest); } polynomial operator/(const polynomial& a) const { return divide(a).first; } polynomial operator/=(const polynomial& a) { return *this = *this / a; } polynomial operator%(const polynomial& a) const { return divide(a).second; } polynomial operator%(const polynomial& a) { return *this = *this / a; } };