結果
問題 | No.1066 #いろいろな色 / Red and Blue and more various colors (Easy) |
ユーザー |
![]() |
提出日時 | 2020-05-29 21:35:54 |
言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
結果 |
AC
|
実行時間 | 97 ms / 2,000 ms |
コード長 | 22,101 bytes |
コンパイル時間 | 1,642 ms |
コンパイル使用メモリ | 136,000 KB |
最終ジャッジ日時 | 2025-01-10 16:39:52 |
ジャッジサーバーID (参考情報) |
judge2 / judge1 |
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ファイルパターン | 結果 |
---|---|
sample | AC * 3 |
other | AC * 24 |
ソースコード
//#pragma GCC optimize("Ofast")//#pragma GCC target("avx")//#undef LOCAL#include <algorithm>#include <array>#include <bitset>#include <cassert>#include <complex>#include <cstdio>#include <cstring>#include <iostream>#include <map>#include <numeric>#include <queue>#include <set>#include <string>#include <unordered_map>#include <unordered_set>#include <vector>using namespace std;using uint = unsigned int;using ll = long long;using ull = unsigned long long;constexpr ll TEN(int n) { return (n == 0) ? 1 : 10 * TEN(n - 1); }template <class T> using V = vector<T>;template <class T> using VV = V<V<T>>;#include <unistd.h>struct Scanner {int fd = -1;char line[(1 << 15) + 1];size_t st = 0, ed = 0;void reread() {memmove(line, line + st, ed - st);ed -= st;st = 0;ed += ::read(fd, line + ed, (1 << 15) - ed);line[ed] = '\0';}bool succ() {while (true) {if (st == ed) {reread();if (st == ed) return false;}while (st != ed && isspace(line[st])) st++;if (st != ed) break;}if (ed - st <= 50) {bool sep = false;for (size_t i = st; i < ed; i++) {if (isspace(line[i])) {sep = true;break;}}if (!sep) reread();}return true;}template <class T, enable_if_t<is_same<T, string>::value, int> = 0>bool read_single(T& ref) {if (!succ()) return false;while (true) {size_t sz = 0;while (st + sz < ed && !isspace(line[st + sz])) sz++;ref.append(line + st, sz);st += sz;if (!sz || st != ed) break;reread();}return true;}template <class T, enable_if_t<is_integral<T>::value, int> = 0>bool read_single(T& ref) {if (!succ()) return false;bool neg = false;if (line[st] == '-') {neg = true;st++;}ref = T(0);while (isdigit(line[st])) {ref = 10 * ref + (line[st++] & 0xf);}if (neg) ref = -ref;return true;}template <class T> bool read_single(V<T>& ref) {for (auto& d : ref) {if (!read_single(d)) return false;}return true;}void read() {}template <class H, class... T> void read(H& h, T&... t) {bool f = read_single(h);assert(f);read(t...);}Scanner(FILE* fp) : fd(fileno(fp)) {}};struct Printer {public:template <bool F = false> void write() {}template <bool F = false, class H, class... T>void write(const H& h, const T&... t) {if (F) write_single(' ');write_single(h);write<true>(t...);}template <class... T> void writeln(const T&... t) {write(t...);write_single('\n');}Printer(FILE* _fp) : fp(_fp) {}~Printer() { flush(); }private:static constexpr size_t SIZE = 1 << 15;FILE* fp;char line[SIZE], small[50];size_t pos = 0;void flush() {fwrite(line, 1, pos, fp);pos = 0;}void write_single(const char& val) {if (pos == SIZE) flush();line[pos++] = val;}template <class T, enable_if_t<is_integral<T>::value, int> = 0>void write_single(T val) {if (pos > (1 << 15) - 50) flush();if (val == 0) {write_single('0');return;}if (val < 0) {write_single('-');val = -val; // todo min}size_t len = 0;while (val) {small[len++] = char(0x30 | (val % 10));val /= 10;}for (size_t i = 0; i < len; i++) {line[pos + i] = small[len - 1 - i];}pos += len;}void write_single(const string& s) {for (char c : s) write_single(c);}void write_single(const char* s) {size_t len = strlen(s);for (size_t i = 0; i < len; i++) write_single(s[i]);}template <class T> void write_single(const V<T>& val) {auto n = val.size();for (size_t i = 0; i < n; i++) {if (i) write_single(' ');write_single(val[i]);}}};template <uint MD> struct ModInt {using M = ModInt;static constexpr uint get_mod() { return MD; }const static M G;uint v;ModInt(ll _v = 0) { set_v(uint(_v % MD + MD)); }M& set_v(uint _v) {v = (_v < MD) ? _v : _v - MD;return *this;}explicit operator bool() const { return v != 0; }M operator-() const { return M() - *this; }M operator+(const M& r) const { return M().set_v(v + r.v); }M operator-(const M& r) const { return M().set_v(v + MD - r.v); }M operator*(const M& r) const { return M().set_v(uint(ull(v) * r.v % MD)); }M operator/(const M& r) const { return *this * r.inv(); }M& operator+=(const M& r) { return *this = *this + r; }M& operator-=(const M& r) { return *this = *this - r; }M& operator*=(const M& r) { return *this = *this * r; }M& operator/=(const M& r) { return *this = *this / r; }bool operator==(const M& r) const { return v == r.v; }M pow(ll n) const {M x = *this, r = 1;while (n) {if (n & 1) r *= x;x *= x;n >>= 1;}return r;}M inv() const { return pow(MD - 2); }friend ostream& operator<<(ostream& os, const M& r) { return os << r.v; }};// using Mint = ModInt<998244353>;// template<> const Mint Mint::G = Mint(3);using Mint = ModInt<998244353>;template<> const Mint Mint::G = Mint(3);// bit opint popcnt(uint x) { return __builtin_popcount(x); }int popcnt(ull x) { return __builtin_popcountll(x); }int bsr(uint x) { return 31 - __builtin_clz(x); }int bsr(ull x) { return 63 - __builtin_clzll(x); }int bsf(uint x) { return __builtin_ctz(x); }int bsf(ull x) { return __builtin_ctzll(x); }template <class Mint> void nft(bool type, V<Mint>& a) {int n = int(a.size()), s = 0;while ((1 << s) < n) s++;assert(1 << s == n);static V<Mint> ep, iep;while (int(ep.size()) <= s) {ep.push_back(Mint::G.pow(Mint(-1).v / (1 << ep.size())));iep.push_back(ep.back().inv());}V<Mint> b(n);for (int i = 1; i <= s; i++) {int w = 1 << (s - i);Mint base = type ? iep[i] : ep[i], now = 1;for (int y = 0; y < n / 2; y += w) {for (int x = 0; x < w; x++) {auto l = a[y << 1 | x];auto r = now * a[y << 1 | x | w];b[y | x] = l + r;b[y | x | n >> 1] = l - r;}now *= base;}swap(a, b);}}template <class Mint> V<Mint> multiply_nft(const V<Mint>& a, const V<Mint>& b) {int n = int(a.size()), m = int(b.size());if (!n || !m) return {};if (min(n, m) <= 8) {V<Mint> ans(n + m - 1);for (int i = 0; i < n; i++)for (int j = 0; j < m; j++) ans[i + j] += a[i] * b[j];return ans;}int lg = 0;while ((1 << lg) < n + m - 1) lg++;int z = 1 << lg;auto a2 = a, b2 = b;a2.resize(z);b2.resize(z);nft(false, a2);nft(false, b2);for (int i = 0; i < z; i++) a2[i] *= b2[i];nft(true, a2);a2.resize(n + m - 1);Mint iz = Mint(z).inv();for (int i = 0; i < n + m - 1; i++) a2[i] *= iz;return a2;}// Cooley-Tukey: input -> butterfly -> bit reversing -> output から// bit reversingを抜いたもの 直接使うなtemplate <class Mint> void butterfly(bool type, V<Mint>& a) {int n = int(a.size()), h = 0;while ((1 << h) < n) h++;assert(1 << h == n);if (n == 1) return;static V<Mint> snow, sinow;if (snow.empty()) {Mint sep = Mint(1), siep = Mint(1);uint mod = Mint(-1).v;uint di = 4;while (mod % di == 0) {Mint ep = Mint::G.pow(mod / di);Mint iep = ep.inv();snow.push_back(siep * ep);sinow.push_back(sep * iep);sep *= ep;siep *= iep;di *= 2;}}if (!type) {// fftfor (int ph = 1; ph <= h; ph++) {// phase ph: size w -> 2w の FFT, p 並列int w = 1 << (ph - 1), p = 1 << (h - ph);Mint now = Mint(1);for (int s = 0; s < w; s++) {int offset = s << (h - ph + 1);for (int i = 0; i < p; i++) {auto l = a[i + offset];auto r = a[i + offset + p] * now;a[i + offset] = l + r;a[i + offset + p] = l - r;}int u = bsf(~uint(s));now *= snow[u];}}} else {// ifftfor (int ph = h; ph >= 1; ph--) {int w = 1 << (ph - 1), p = 1 << (h - ph);Mint inow = Mint(1);for (int s = 0; s < w; s++) {int offset = s << (h - ph + 1);for (int i = 0; i < p; i++) {auto l = a[i + offset];auto r = a[i + offset + p];a[i + offset] = l + r;a[i + offset + p] = (l - r) * inow;}int u = bsf(~uint(s));inow *= sinow[u];}}}}template <class Mint> V<Mint> multiply(const V<Mint>& a, const V<Mint>& b) {int n = int(a.size()), m = int(b.size());if (!n || !m) return {};if (min(n, m) < 8) {V<Mint> ans(n + m - 1);for (int i = 0; i < n; i++)for (int j = 0; j < m; j++) ans[i + j] += a[i] * b[j];return ans;}int lg = 0;while ((1 << lg) < n + m - 1) lg++;int z = 1 << lg;auto a2 = a;a2.resize(z);butterfly(false, a2);if (a == b) {for (int i = 0; i < z; i++) a2[i] *= a2[i];} else {auto b2 = b;b2.resize(z);butterfly(false, b2);for (int i = 0; i < z; i++) a2[i] *= b2[i];}butterfly(true, a2);a2.resize(n + m - 1);Mint iz = Mint(z).inv();for (int i = 0; i < n + m - 1; i++) a2[i] *= iz;return a2;}#include <chrono>#include <cstdint>#include <random>struct Random {private:// Use xoshiro256**// Refereces: http://xoshiro.di.unimi.it/xoshiro256starstar.cstatic uint64_t rotl(const uint64_t x, int k) {return (x << k) | (x >> (64 - k));}std::array<uint64_t, 4> s;uint64_t next() {const uint64_t result_starstar = rotl(s[1] * 5, 7) * 9;const uint64_t t = s[1] << 17;s[2] ^= s[0];s[3] ^= s[1];s[1] ^= s[2];s[0] ^= s[3];s[2] ^= t;s[3] = rotl(s[3], 45);return result_starstar;}// random choice from [0, upper]uint64_t next(uint64_t upper) {if (!(upper & (upper + 1))) {// b = 00..0011..11return next() & upper;}int lg = 63 - __builtin_clzll(upper);uint64_t mask = (lg == 63) ? ~0ULL : (1ULL << (lg + 1)) - 1;while (true) {uint64_t r = next() & mask;if (r <= upper) return r;}}public:Random(uint64_t seed = 0) {// Use splitmix64// Reference: http://xoshiro.di.unimi.it/splitmix64.cfor (int i = 0; i < 4; i++) {uint64_t z = (seed += 0x9e3779b97f4a7c15);z = (z ^ (z >> 30)) * 0xbf58476d1ce4e5b9;z = (z ^ (z >> 27)) * 0x94d049bb133111eb;s[i] = z ^ (z >> 31);}}// random choice from [lower, upper]template <class T> T uniform(T lower, T upper) {assert(lower <= upper);return T(lower + next(uint64_t(upper - lower)));}bool uniform_bool() { return uniform(0, 1) == 1; }double uniform01() {uint64_t v = next(1ULL << 63);return double(v) / (1ULL << 63);}template <class T> std::pair<T, T> uniform_pair(T lower, T upper) {assert(upper - lower >= 1);T a, b;do {a = uniform(lower, upper);b = uniform(lower, upper);} while (a == b);if (a > b) std::swap(a, b);return {a, b};}// generate random lower string that length = nstd::string lower_string(size_t n) {std::string res = "";for (size_t i = 0; i < n; i++) {res += uniform('a', 'z');}return res;}// random shuffletemplate <class Iter> void shuffle(Iter first, Iter last) {if (first == last) return;// Reference and edit:// cpprefjp - C++日本語リファレンス// (https://cpprefjp.github.io/reference/algorithm/shuffle.html)int len = 1;for (auto it = first + 1; it != last; it++) {len++;int j = uniform(0, len - 1);if (j != len - 1) iter_swap(it, first + j);}}// generate random permutation that length = ntemplate <class T> std::vector<T> perm(size_t n) {std::vector<T> idx(n);std::iota(idx.begin(), idx.end(), T(0));shuffle(idx.begin(), idx.end());return idx;}template <class T> std::vector<T> choice(size_t n, T lower, T upper) {assert(n <= upper - lower + 1);std::set<T> res;while (res.size() < n) res.insert(uniform(lower, upper));return {res.begin(), res.end()};}};Random& global_gen() {static Random gen;return gen;}Random get_random_gen() {return Random(chrono::steady_clock::now().time_since_epoch().count());}Random& global_runtime_gen() {static Random gen = get_random_gen();return gen;}template <class D> struct Poly {V<D> v;Poly(const V<D>& _v = {}) : v(_v) { shrink(); }void shrink() {while (v.size() && !v.back()) v.pop_back();}int size() const { return int(v.size()); }D freq(int p) const { return (p < size()) ? v[p] : D(0); }Poly operator+(const Poly& r) const {auto n = max(size(), r.size());V<D> res(n);for (int i = 0; i < n; i++) res[i] = freq(i) + r.freq(i);return res;}Poly operator-(const Poly& r) const {int n = max(size(), r.size());V<D> res(n);for (int i = 0; i < n; i++) res[i] = freq(i) - r.freq(i);return res;}Poly operator*(const Poly& r) const { return {multiply(v, r.v)}; }Poly operator*(const D& r) const {int n = size();V<D> res(n);for (int i = 0; i < n; i++) res[i] = v[i] * r;return res;}Poly operator/(const D &r) const{return *this * r.inv();}Poly operator/(const Poly& r) const {if (size() < r.size()) return {{}};int n = size() - r.size() + 1;return (rev().pre(n) * r.rev().inv(n)).pre(n).rev(n);}Poly operator%(const Poly& r) const { return *this - *this / r * r; }Poly operator<<(int s) const {V<D> res(size() + s);for (int i = 0; i < size(); i++) res[i + s] = v[i];return res;}Poly operator>>(int s) const {if (size() <= s) return Poly();V<D> res(size() - s);for (int i = 0; i < size() - s; i++) res[i] = v[i + s];return res;}Poly& operator+=(const Poly& r) { return *this = *this + r; }Poly& operator-=(const Poly& r) { return *this = *this - r; }Poly& operator*=(const Poly& r) { return *this = *this * r; }Poly& operator*=(const D& r) { return *this = *this * r; }Poly& operator/=(const Poly& r) { return *this = *this / r; }Poly& operator/=(const D &r) {return *this = *this/r;}Poly& operator%=(const Poly& r) { return *this = *this % r; }Poly& operator<<=(const size_t& n) { return *this = *this << n; }Poly& operator>>=(const size_t& n) { return *this = *this >> n; }Poly pre(int le) const {return {{v.begin(), v.begin() + min(size(), le)}};}Poly rev(int n = -1) const {V<D> res = v;if (n != -1) res.resize(n);reverse(res.begin(), res.end());return res;}Poly diff() const {V<D> res(max(0, size() - 1));for (int i = 1; i < size(); i++) res[i - 1] = freq(i) * i;return res;}Poly inte() const {V<D> res(size() + 1);for (int i = 0; i < size(); i++) res[i + 1] = freq(i) / (i + 1);return res;}// f * f.inv() = 1 + g(x)x^mPoly inv(int m) const {Poly res = Poly({D(1) / freq(0)});for (int i = 1; i < m; i *= 2) {res = (res * D(2) - res * res * pre(2 * i)).pre(2 * i);}return res.pre(m);}Poly exp(int n) const {assert(freq(0) == 0);Poly f({1}), g({1});for (int i = 1; i < n; i *= 2) {g = (g * 2 - f * g * g).pre(i);Poly q = diff().pre(i - 1);Poly w = (q + g * (f.diff() - f * q)).pre(2 * i - 1);f = (f + f * (*this - w.inte()).pre(2 * i)).pre(2 * i);}return f.pre(n);}Poly log(int n) const {assert(freq(0) == 1);auto f = pre(n);return (f.diff() * f.inv(n - 1)).pre(n - 1).inte();}Poly sqrt(int n) const {assert(freq(0) == 1);Poly f = pre(n + 1);Poly g({1});for (int i = 1; i < n; i *= 2) {g = (g + f.pre(2 * i) * g.inv(2 * i)) / 2;}return g.pre(n + 1);}Poly pow_mod(ll n, const Poly& mod) {Poly x = *this, r = {{1}};while (n) {if (n & 1) r = r * x % mod;x = x * x % mod;n >>= 1;}return r;}friend ostream& operator<<(ostream& os, const Poly& p) {if (p.size() == 0) return os << "0";for (auto i = 0; i < p.size(); i++) {if (p.v[i]) {os << p.v[i] << "x^" << i;if (i != p.size() - 1) os << "+";}}return os;}};template <class Mint> struct MultiEval {using NP = MultiEval*;NP l, r;V<Mint> que;int sz;Poly<Mint> mul;MultiEval(const V<Mint>& _que, int off, int _sz) : sz(_sz) {if (sz <= 100) {que = {_que.begin() + off, _que.begin() + off + sz};mul = {{1}};for (auto x : que) mul *= {{-x, 1}};return;}l = new MultiEval(_que, off, sz / 2);r = new MultiEval(_que, off + sz / 2, sz - sz / 2);mul = l->mul * r->mul;}MultiEval(const V<Mint>& _que) : MultiEval(_que, 0, int(_que.size())) {}void query(const Poly<Mint>& _pol, V<Mint>& res) const {if (sz <= 100) {for (auto x : que) {Mint sm = 0, base = 1;for (int i = 0; i < _pol.size(); i++) {sm += base * _pol.freq(i);base *= x;}res.push_back(sm);}return;}auto pol = _pol % mul;l->query(pol, res);r->query(pol, res);}V<Mint> query(const Poly<Mint>& pol) const {V<Mint> res;query(pol, res);return res;}};template <class Mint> Poly<Mint> berlekamp_massey(const V<Mint>& s) {int n = int(s.size());V<Mint> b = {Mint(-1)}, c = {Mint(-1)};Mint y = Mint(1);for (int ed = 1; ed <= n; ed++) {int l = int(c.size()), m = int(b.size());Mint x = 0;for (int i = 0; i < l; i++) {x += c[i] * s[ed - l + i];}b.push_back(0);m++;if (!x) continue;Mint freq = x / y;if (l < m) {// use bauto tmp = c;c.insert(begin(c), m - l, Mint(0));for (int i = 0; i < m; i++) {c[m - 1 - i] -= freq * b[m - 1 - i];}b = tmp;y = x;} else {// use cfor (int i = 0; i < m; i++) {c[l - 1 - i] -= freq * b[m - 1 - i];}}}return c;}template <class E, class Mint = decltype(E().f)>Mint sparse_det(const VV<E>& g) {int n = int(g.size());if (n == 0) return 1;auto rand_v = [&]() {V<Mint> res(n);for (int i = 0; i < n; i++) {res[i] = Mint(global_gen().uniform<int>(1, Mint::get_mod() - 1));}return res;};V<Mint> c = rand_v(), l = rand_v(), r = rand_v();// l * mat * rV<Mint> buf(2 * n);for (int fe = 0; fe < 2 * n; fe++) {for (int i = 0; i < n; i++) {buf[fe] += l[i] * r[i];}for (int i = 0; i < n; i++) {r[i] *= c[i];}V<Mint> tmp(n);for (int i = 0; i < n; i++) {for (auto e : g[i]) {tmp[i] += r[e.to] * e.f;}}r = tmp;}auto u = berlekamp_massey(buf);if (u.size() != n + 1) return sparse_det(g);auto acdet = u.freq(0) * Mint(-1);if (n % 2) acdet *= Mint(-1);if (!acdet) return 0;Mint cdet = 1;for (int i = 0; i < n; i++) cdet *= c[i];return acdet / cdet;}using MPol = Poly<Mint>;Scanner sc = Scanner(stdin);Printer pr = Printer(stdout);int main() {int n, q;sc.read(n, q);MPol ans = {{Mint(1)}};for (int i = 0; i < n; i++) {int a;sc.read(a);MPol f = {{Mint(a - 1), Mint(1)}};ans = ans * f;}for (int i = 0; i < q; i++) {int b;sc.read(b);pr.writeln(ans.freq(b).v);}return 0;}