結果
問題 | No.754 畳み込みの和 |
ユーザー |
|
提出日時 | 2023-10-09 00:38:34 |
言語 | C++23 (gcc 13.3.0 + boost 1.87.0) |
結果 |
AC
|
実行時間 | 223 ms / 5,000 ms |
コード長 | 20,425 bytes |
コンパイル時間 | 2,845 ms |
コンパイル使用メモリ | 218,740 KB |
実行使用メモリ | 18,524 KB |
最終ジャッジ日時 | 2024-07-26 18:18:12 |
合計ジャッジ時間 | 4,790 ms |
ジャッジサーバーID (参考情報) |
judge4 / judge5 |
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ファイルパターン | 結果 |
---|---|
other | AC * 3 |
ソースコード
// #define Q__OPTIMIZE// #define Q__INCLUDE_ATCODER_LIB// #define Q__INTERACTIVE#if !__INCLUDE_LEVEL__#include __FILE__struct Solver {void solve() {INT(n);VEC(ll,a,n+1); VEC(ll,b,n+1);Polynomial<ll> P,Q;P.coef = a;Q.coef = b;auto C = P * Q;DUMP(C.coef);ll ans = 0;REP(i,n+1) ans = safe_mod(ans+C[i],MOD);print(ans);}void naive() {}} solver;signed main(void){NO_SYNC_STD;V<string> options;#ifdef Q__OPTIMIZEoptions.push_back("OPTIMIZE");#endif#ifdef Q__INTERACTIVEoptions.push_back("INTERACTIVE");#endif#ifdef Q__INCLUDE_ATCODER_LIBoptions.push_back("INCLUDE_ATCODER_LIB");#endifDUMP(options);#ifndef Q__NAIVEsolver.solve();#elseDUMP("naive");solver.naive();#endifreturn 0;}#else#define _GLIBCXX_DEQUE_BUF_SIZE 64#ifdef Q__OPTIMIZE#pragma GCC target("avx")#pragma GCC optimize("O3")#pragma GCC optimize("unroll-loops")#endif#include <algorithm>#include <array>#include <bitset>#include <cassert>#include <chrono>#include <cmath>#include <complex>#include <deque>#include <forward_list>#include <fstream>#include <functional>#include <iomanip>#include <ios>#include <iostream>#include <limits>#include <list>#include <map>#include <memory>#include <numeric>#include <optional>#include <queue>#include <random>#include <set>#include <sstream>#include <stack>#include <string>#include <thread>#include <tuple>#include <type_traits>#include <unordered_map>#include <unordered_set>#include <utility>#include <vector>#ifdef Q__INCLUDE_ATCODER_LIB#include <atcoder/all>using namespace atcoder;//using mint = modint1000000007;using mint = modint998244353;std::istream &operator>>(std::istream& is, mint& a) { long long tmp; is >> tmp; a = tmp; return is; }std::ostream &operator<<(std::ostream& os, const mint& a) {os << a.val(); return os;}#endifusing namespace std;#define MOD 1000000007#define OVERLOAD4(a, b, c, d, e, ...) e#define REP1(a) for(decltype(a) i = 0, i##_len = (a); i < i##_len; ++i)#define REP2(i, a) for(decltype(a) i = 0, i##_len = (a); i < i##_len; ++i)#define REP3(i, a, b) for(decltype(b) i = (a), i##_len = (b); i < i##_len; ++i)#define REP4(i, a, b, c) for(decltype(b) i = (a), i##_len = (b); i < i##_len; i += (c))#define REP(...) OVERLOAD4(__VA_ARGS__, REP4, REP3, REP2, REP1)(__VA_ARGS__)#define RREP1(a) for(decltype(a) i = (a); i--;)#define RREP2(i, a) for(decltype(a) i = (a); i--;)#define RREP3(i, a, b) for(decltype(a) i = (b), i##_len = (a); i-- > i##_len;)#define RREP4(i, a, b, c) for(decltype(a) i = (a)+((b)-(a)-1)/(c)*(c), i##_len = (a); i >= i##_len; i -= c)#define RREP(...) OVERLOAD4(__VA_ARGS__, RREP4, RREP3, RREP2, RREP1)(__VA_ARGS__)#define MREP(v,...) for(auto v:make_enum_vec({__VA_ARGS__}))#define QREP(q, l, r, n) for (ll q = 1, l = n / (q + 1) + 1, r = n / q + 1; q <= n; q = (q == n ? n + 1 : n / (n / (q + 1))), l = n / (q + 1) + 1, r= n / q + 1)#define COMB_REP(i,n,k) for (ll t, i = POW2(k) - 1; i < POW2(n); t=i|(i-1), i = (t+1)|(((~t & - ~t)-1) >> (__builtin_ctzll(i)+1)))#define SUBSET_ENUM_REP(i,s) for (ll i = (1LL << 60) - 1; i >= 0, i &= s; --i)#define SUBSET_INCLUDE_REP(i,n,s) for (int i = s; i < POW2(n); i=(++i)|s)#define POPONLY_REP(i,s) for (ll i=s&-s; i; i=s&(~s+(i << 1)))#define ALL(x) (x).begin(), (x).end()#define RALL(x) (x).rbegin(), (x).rend()#define SZ(x) ((int)(x).size())#define POW2(n) (1LL << ((int)(n)))#define GET1BIT(x,n) (((x) >> (int)(n)) & 1)#define INF ((1 << 30) - 1)#define INFL (1LL << 60)#define PRECISION std::setprecision(16)#define SLEEP(n) std::this_thread::sleep_for(std::chrono::seconds(n))#define INT(...) int __VA_ARGS__; input(__VA_ARGS__)#define LL(...) ll __VA_ARGS__; input(__VA_ARGS__)#define STR(...) string __VA_ARGS__; input(__VA_ARGS__)#define LD(...) ld __VA_ARGS__; input(__VA_ARGS__)#define VEC(type, name, size) vector<type> name(size); input(name)#ifdef Q__INTERACTIVE#define NO_SYNC_STD#define ENDL std::endl#else#define NO_SYNC_STD std::cin.tie(nullptr);ios::sync_with_stdio(false)#define ENDL "\n"#endif#ifdef Q__LOCAL#include <dump.hpp>#define DUMP(...) DUMPOUT << " " << string(#__VA_ARGS__) << ": " << "[" << to_string(__LINE__) << ":" << __FUNCTION__ << "]" << endl ,dump_func(__VA_ARGS__)#define VDUMP(...) DUMPOUT << " " << string(#__VA_ARGS__) << ": " << "[" << to_string(__LINE__) << ":" << __FUNCTION__ << "]" << endl, vdump_func(__VA_ARGS__)#else#define DUMP(...)#define VDUMP(...)#endifusing ll=long long;using ull=unsigned long long;using ld=long double;template<class T> using V=vector<T>;template<class T> using VV=vector<vector<T>>;template<class T> using PQ=priority_queue<T,V<T>,greater<T>>;template<class T> istream &operator>>(istream &is,V<T> &v){for(auto&& e:v)is >> e;return is;}template<class T> istream &operator>>(istream &is,complex<T> &v){T x,y; is >> x >> y;v.real(x);v.imag(y);return is;}template<class T,class U> istream &operator>>(istream &is,pair<T,U> &v){is >> v.first >> v.second;return is;}template<class T,size_t n> istream &operator>>(istream &is,array<T,n> &v){for(auto&& e:v)is >> e;return is;}template<class... A> void input(A&&... args){(cin >> ... >> args);}template<class... A> void print_rest(){cout << ENDL;}template<class T,class... A> void print_rest(const T& first,const A&... rest){cout << " " << first;print_rest(rest...);}template<class T,class... A> void print(const T& first,const A&... rest){cout << fixed << PRECISION << first;print_rest(rest...);}template<class T,class... A> void die(const T& first,const A&... rest){cout << fixed << PRECISION << first;print_rest(rest...);exit(0);}template <typename ... Args> string fmt(const string& fmt, Args ... args ){size_t len = snprintf( nullptr, 0, fmt.c_str(), args ... );vector<char>buf(len + 1);snprintf(&buf[0], len + 1, fmt.c_str(), args ... );return string(&buf[0], &buf[0] + len);}template<class T> inline string join(const T& v,string sep=" "){if(!SZ(v))return "";stringstream ss;for(auto&& e:v)ss << sep << e;return ss.str().substr(SZ(sep));}V<string> split(const string &s,char sep=' ') {V<string> ret;stringstream ss(s);string buf;while(getline(ss,buf,sep))ret.push_back(buf);return ret;}template<class T> inline string padding(const T& v,int len,char pad=' ',bool l=false){stringstream ss;ss << (l?std::left:std::right) << setw(len) <<setfill(pad) << v;return ss.str();}template<class T> V<T> make_vec(size_t n,T a){return V<T>(n,a);}template<class... Ts> auto make_vec(size_t n,Ts... ts){return V<decltype(make_vec(ts...))>(n,make_vec(ts...));}template<class T> inline bool chmax(T& a,T b){if(a<b){a=b;return 1;} return 0;}template<class T> inline bool chmin(T& a,T b){if(a>b){a=b;return 1;} return 0;}template<class T,class F> pair<T,T> binarysearch(T ng,T ok,T eps,F f,bool sign=false){while(abs(ng-ok)>eps){auto mid=ng+(ok-ng)/2;if(sign^f(mid)){ok=mid;}else{ng=mid;}}return{ng,ok};}template<class T> constexpr T cdiv(T x,T y){return (x+y-1)/y;}template<class T> constexpr bool between(T a,T x,T b){return(a<=x&&x<b);}template<class T> constexpr T pos1d(T y,T x,T h,T w){assert(between(T(0),y,h));assert(between(T(0),x,w));return y*w+x;}template<class T> constexpr pair<T,T> pos2d(T p,T h,T w){T y=p/w,x=p-y*w;assert(between(T(0),y,h));assert(between(T(0),x,w));return{y,x};}template<class T> constexpr T sign(T n) {return (n > 0) - (n < 0);}template<class T> inline V<T> transposed(V<T>& A){int h=SZ(A),w=SZ(A[0]);V<T> tA(w);REP(i,h)REP(j,w)tA[j].push_back(A[i][j]);return tA;}template<class T> inline V<T> ruiseki(V<T>& a){auto ret = a; ret.push_back(T(0));exclusive_scan(ALL(ret), ret.begin(), 0);return ret;}template<class T> inline V<T> kaisa(V<T>& a){V<T> ret(a.size());adjacent_difference(ALL(a), ret.begin());return ret;}template<class T> inline int g_index(V<T> &s, T x) {if (s.empty()) return -2;auto it = upper_bound(ALL(s), x);if (it == s.end()) return -1;return (int)distance(s.begin(), it);}template<class T> inline int ge_index(V<T> &s, T x) {if (s.empty()) return -2;auto it = lower_bound(ALL(s), x);if (it == s.end()) return -1;return (int)distance(s.begin(), it);}template<class T> inline int l_index(V<T> &s, T x) {if (s.empty()) return -2;auto it = lower_bound(ALL(s), x);if (it == s.begin()) return -1;return (int)distance(s.begin(), prev(it));}template<class T> inline int le_index(V<T> &s, T x) {if (s.empty()) return -2;auto it = upper_bound(ALL(s), x);if (it == s.begin()) return -1;return (int)distance(s.begin(), prev(it));}template<class T> inline pair<typename set<T>::iterator,bool> g_it(set<T> &s, T x) {if (s.empty()) return {s.end(), false};auto it = s.upper_bound(x);if (it == s.end()) return {it, false};return {it, true};}template<class T> inline pair<typename set<T>::iterator,bool> ge_it(set<T> &s, T x) {if (s.empty()) return {s.end(), false};auto it = s.lower_bound(x);if (it == s.end()) return {it, false};return {it, true};}template<class T> inline pair<typename set<T>::iterator,bool> l_it(set<T> &s, T x) {if (s.empty()) return {s.end(), false};auto it = s.lower_bound(x);if (it == s.begin()) return {it, false};return {prev(it), true};}template<class T> inline pair<typename set<T>::iterator,bool> le_it(set<T> &s, T x) {if (s.empty()) return {s.end(), false};auto it = s.upper_bound(x);if (it == s.begin()) return {it, false};return {prev(it), true};}template<class T> inline V<T> it_range(set<T> &st, int l, int r) {auto startIt = st.lower_bound(l); auto endIt = st.upper_bound(r); V<T> ret;for(auto itr = startIt; itr != endIt; itr++) ret.emplace_back(*itr);return ret;}template<class T> inline pair<typename multiset<T>::iterator,bool> g_it(multiset<T> &s, T x) {if (s.empty()) return {s.end(), false};auto it = s.upper_bound(x);if (it == s.end()) return {it, false};return {it, true};}template<class T> inline pair<typename multiset<T>::iterator,bool> ge_it(multiset<T> &s, T x) {if (s.empty()) return {s.end(), false};auto it = s.lower_bound(x);if (it == s.end()) return {it, false};return {it, true};}template<class T> inline pair<typename multiset<T>::iterator,bool> l_it(multiset<T> &s, T x) {if (s.empty()) return {s.end(), false};auto it = s.lower_bound(x);if (it == s.begin()) return {it, false};return {prev(it), true};}template<class T> inline pair<typename multiset<T>::iterator,bool> le_it(multiset<T> &s, T x) {if (s.empty()) return {s.end(), false};auto it = s.upper_bound(x);if (it == s.begin()) return {it, false};return {prev(it), true};}template<class T> inline V<T> it_range(multiset<T> &st, int l, int r) {auto startIt = st.lower_bound(l); auto endIt = st.upper_bound(r); V<T> ret;for(auto itr = startIt; itr != endIt; itr++) ret.emplace_back(*itr);return ret;}constexpr ll modpow(ll x,ll n,ll m=1152921504606846976LL){ll ret=1;for(;n>0;x=x*x%m,n>>=1)if(n&1)ret=ret*x%m;return ret;}constexpr ll safe_mod(ll x, ll m) {x%=m;if(x<0)x+=m;return x;}constexpr ll keta(ll n, ll base = 10LL) {ll ret = 0; while(n > 0) {n /= base, ret++;} return ret;}constexpr int pcnt(ll x) {return __builtin_popcountll(x);}constexpr int log2f(ll x) {return 63 - __builtin_clzll(x);}constexpr int log2c(ll x) {return (x==1LL)?0:(64-__builtin_clzll(x-1LL));}constexpr ll nC2(ll n) {return n*(n-1)/2;}constexpr ld deg2rad(ll degree){return (ld)degree * M_PI/180;}mt19937 rnd_engine{random_device{}()};inline int rand(int l, int r) {uniform_int_distribution<> ret(l, r);return ret(rnd_engine);}inline ld lrand(ld l, ld r) {uniform_real_distribution<> ret(l, r);return ret(rnd_engine);}inline ld nrand(ld ave, ld var) {normal_distribution<> ret(ave, var);return ret(rnd_engine);}inline void yes(bool cond) {cout << (cond?"Yes":"No") << ENDL;}inline bool is_palindrome(const string& s){return equal(ALL(s), s.rbegin());}inline string make_palindrome(const string& s, bool odd = true) {string t = s.substr(0, SZ(s)-odd);reverse(ALL(t));return s + t;}VV<int> make_enum_vec(V<int> v){if(v.empty()) return VV<int>(1,V<int>());int n=v.back(); v.pop_back();VV<int> ret,tmp=make_enum_vec(v);for(auto e:tmp)for(int i=0;i<n;++i){ret.push_back(e);ret.back().push_back(i);}return ret;}V<int> restore_path(V<int>& to, int goal, bool to1indexed = true) {V<int> ret;int x = goal;while(x >= 0) {ret.push_back(x);x = to[x];}reverse(ALL(ret));if (to1indexed) for(auto&& e: ret) e++;return ret;}const int dx4[4] = {1, 0, -1, 0};const int dy4[4] = {0, 1, 0, -1};const int dx6[6] = {1, 0, -1, 0, 1, -1};const int dy6[6] = {0, 1, 0, -1, 1, -1};const int dx8[8] = {1, 0, -1, 0, 1, -1, -1, 1};const int dy8[8] = {0, 1, 0, -1, 1, 1, -1, -1};template<class T> T extgcd(T a, T b, T& x, T& y) { for (T u = y = 1, v = x = 0; a;) { T q = b / a; swap(x -= q * u, u); swap(y -= q * v, v); swap(b-= q * a, a); } return b; }template<class T> T mod_inv(T a, T m) { T x, y; extgcd(a, m, x, y); return (m + x % m) % m; }template<int mod, int primitive_root>class NTT {public:int get_mod() const { return mod; }void _ntt(vector<ll>& a, int sign) {const int n = SZ(a);assert((n ^ (n&-n)) == 0); //n = 2^kconst int g = 3; //g is primitive root of modint h = (int)modpow(g, (mod - 1) / n, mod); // h^n = 1if (sign == -1) h = (int)mod_inv(h, mod); //h = h^-1 % mod//bit reverseint i = 0;for (int j = 1; j < n - 1; ++j) {for (int k = n >> 1; k >(i ^= k); k >>= 1);if (j < i) swap(a[i], a[j]);}for (int m = 1; m < n; m *= 2) {const int m2 = 2 * m;const ll base = modpow(h, n / m2, mod);ll w = 1;REP(x, m) {for (int s = x; s < n; s += m2) {ll u = a[s];ll d = a[s + m] * w % mod;a[s] = u + d;if (a[s] >= mod) a[s] -= mod;a[s + m] = u - d;if (a[s + m] < 0) a[s + m] += mod;}w = w * base % mod;}}for (auto& x : a) if (x < 0) x += mod;}void ntt(vector<ll>& input) {_ntt(input, 1);}void intt(vector<ll>& input) {_ntt(input, -1);const int n_inv = mod_inv(SZ(input), mod);for (auto& x : input) x = x * n_inv % mod;}vector<ll> convolution(const vector<ll>& a, const vector<ll>& b){int ntt_size = 1;while (ntt_size < SZ(a) + SZ(b)) ntt_size *= 2;vector<ll> _a = a, _b = b;_a.resize(ntt_size); _b.resize(ntt_size);ntt(_a);ntt(_b);REP(i, ntt_size) (_a[i] *= _b[i]) %= mod;intt(_a);return _a;}};using NTT_1 = NTT<167772161, 3>;using NTT_2 = NTT<469762049, 3>;using NTT_3 = NTT<1224736769, 3>;vector<ll> fast_int32mod_convolution(vector<ll> a, vector<ll> b, int mod){for (auto& x : a) x %= mod;for (auto& x : b) x %= mod;NTT_1 ntt1; NTT_2 ntt2; NTT_3 ntt3;assert(ntt1.get_mod() < ntt2.get_mod() && ntt2.get_mod() < ntt3.get_mod());auto x = ntt1.convolution(a, b);auto y = ntt2.convolution(a, b);auto z = ntt3.convolution(a, b);const ll m1 = ntt1.get_mod(), m2 = ntt2.get_mod(), m3 = ntt3.get_mod();const ll m1_inv_m2 = mod_inv<ll>(m1, m2);const ll m12_inv_m3 = mod_inv<ll>(m1 * m2, m3);const ll m12_mod = m1 * m2 % mod;vector<ll> ret(SZ(x));REP(i, SZ(x)){ll v1 = (y[i] - x[i]) * m1_inv_m2 % m2;if (v1 < 0) v1 += m2;ll v2 = (z[i] - (x[i] + m1 * v1) % m3) * m12_inv_m3 % m3;if (v2 < 0) v2 += m3;ll constants3 = (x[i] + m1 * v1 + m12_mod * v2) % mod;if (constants3 < 0) constants3 += mod;ret[i] = constants3;}return ret;}template<class T> class Polynomial {public:std::vector<T> coef;Polynomial() : coef(1, 0) {}Polynomial(int N) : coef(N + 1, 0) {}Polynomial(std::initializer_list<T> a) : coef(a) {}Polynomial(std::string s) {using Pit = std::string::const_iterator;auto next = [&](Pit& it) {do { ++it; } while (it != s.cend() && *it == ' ');};auto num = [&](Pit& it) -> int {int res = 0;while (it != s.cend() && std::isdigit(*it)) {res = res * 10 + (*it - '0');next(it);}return res;};auto atom = [&](Pit& it) -> Polynomial<T> {if (std::isdigit(*it)) {int c = num(it);return { c }; // c}else if (*it == 'x') {next(it);if (it != s.cend() && *it == '^') {next(it);int t = num(it);Polynomial<T> r(t);r[t] = 1;return r; // x^e}else {return {0, 1}; // x}}return {};};std::function<Polynomial<T>(Pit&)> expr;auto mono = [&](Pit& it) -> Polynomial<T> {if (*it == '(') {next(it);auto r = expr(it);next(it);if (it != s.cend() && *it == '^') {next(it);r ^= num(it);}return r;}else {return atom(it);}};auto prod = [&](Pit& it) -> Polynomial<T> {Polynomial<T> r({ 1 });r *= mono(it);while (it != s.cend()) {if (*it == '*') {next(it);r *= mono(it);}else if (*it == '(' || *it == 'x' || std::isdigit(*it)) {r *= mono(it);}else break;}return r;};expr = [&](Pit& it) -> Polynomial<T> {Polynomial<T> r = prod(it);while (it != s.cend() && *it != ')') {bool neg = false;if (*it == '-') neg = true;next(it);if (neg) r -= prod(it);else r += prod(it);}return r;};if (!s.empty() && (s.front() == '+' || s.front() == '-')) s = '0' + s;Pit it = s.cbegin();*this = expr(it);}Polynomial(const char* s) : Polynomial(std::string(s)) {}Polynomial& operator+=(const Polynomial& r) {if (SZ(coef) < SZ(r.coef)) coef.resize(SZ(r.coef));REP(i,SZ(r.coef)) coef[i] = safe_mod(coef[i]+r.coef[i],MOD);return *this;}Polynomial& operator-=(const Polynomial& r) {if (SZ(coef) < SZ(r.coef)) coef.resize(SZ(r.coef));REP(i,SZ(r.coef)) coef[i] = safe_mod(coef[i]-r.coef[i],MOD);return *this;}//Polynomial& operator*=(const Polynomial & r) { // O(N^2)// std::vector<T> c(this->SZ(coef) + SZ(r.coef) - 1);// REP(i, this->SZ(coef)) REP(j, SZ(r.coef)) c[i + j] += this->coef[i] * r.coef[j];// coef = c;// return *this;//}Polynomial& operator*=(const Polynomial& r) { // O(NlogN)this->coef = fast_int32mod_convolution(this->coef, r.coef, MOD);return *this;}Polynomial operator*(const Polynomial& r) { Polynomial res(*this); return res *= r; }Polynomial& mul_sparse(const std::map<int, T>& r, int sizeLimit = -1) {size_t sz = SZ(coef);size_t rsz = r.rbegin()->first;coef.resize(sz + rsz, 0);for (int i = sz + rsz - 1; i >= 0; --i) {for (const auto& p : r) if (p.first != 0) {if (i >= p.first) {coef[i] = safe_mod(coef[i] + safe_mod(p.second,MOD) * safe_mod(coef[i - p.first],MOD), MOD);}}}if (sizeLimit > 0 && SZ(coef) > sizeLimit) {coef.resize(sizeLimit);}return *this;}Polynomial& div_sparse(const std::map<int, T>& r, int sz = -1) {if (sz == -1) sz = SZ(coef);REP(i,sz) {for (const auto& p : r) if (p.first != 0) {if (i >= p.first) {coef[i] = safe_mod(coef[i] - safe_mod(p.second,MOD) * safe_mod(coef[i - p.first],MOD), MOD);}}}return *this;}Polynomial& operator^=(long long p) {Polynomial x(*this);*this = Polynomial(0);coef[0] = 1;while (p) {if (p & 1) (*this) *= x;x *= x;p >>= 1;}return *this;}Polynomial operator^(long long p) { Polynomial res(*this); return res ^= p; }T& operator[](size_t i) { return coef[i]; }std::vector<T> getCoef() const { return coef; }};// get [X^N]P(X)/Q(X) in O(k logk logN) where k=deg(Q)template<class T> T coef_of_rational_polynomial(ll N, Polynomial<T> P, Polynomial<T> Q) {for (; N; N >>= 1) {Polynomial<T> Q1(Q);for (int i = 1; i < SZ(Q.coef); i += 2) Q1[i] = MOD-Q[i];P *= Q1;int j = 0;for (int i = N & 1; i < SZ(P.coef); i += 2) P.coef[j++] = P.coef[i];P.coef.resize(j);Q *= Q1;j = 0;for (int i = 0; i < SZ(Q.coef); i += 2) Q.coef[j++] = Q.coef[i];Q.coef.resize(j);}return safe_mod(P[0],MOD);}#endif