結果
問題 | No.2264 Gear Coloring |
ユーザー |
![]() |
提出日時 | 2023-04-07 22:12:15 |
言語 | C++23 (gcc 13.3.0 + boost 1.87.0) |
結果 |
AC
|
実行時間 | 110 ms / 2,000 ms |
コード長 | 18,661 bytes |
コンパイル時間 | 2,647 ms |
コンパイル使用メモリ | 199,276 KB |
実行使用メモリ | 7,996 KB |
最終ジャッジ日時 | 2024-10-02 19:41:48 |
合計ジャッジ時間 | 3,588 ms |
ジャッジサーバーID (参考情報) |
judge3 / judge1 |
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ファイルパターン | 結果 |
---|---|
sample | AC * 4 |
other | AC * 18 |
ソースコード
#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 <numeric>#include <queue>#include <random>#include <set>#include <sstream>#include <stack>#include <string>#include <tuple>#include <type_traits>#include <unordered_map>#include <unordered_set>#include <utility>#include <vector>using namespace std;using lint = long long;using pint = pair<int, int>;using plint = pair<lint, lint>;struct fast_ios { fast_ios(){ cin.tie(nullptr), ios::sync_with_stdio(false), cout << fixed << setprecision(20); }; } fast_ios_;#define ALL(x) (x).begin(), (x).end()#define FOR(i, begin, end) for(int i=(begin),i##_end_=(end);i<i##_end_;i++)#define IFOR(i, begin, end) for(int i=(end)-1,i##_begin_=(begin);i>=i##_begin_;i--)#define REP(i, n) FOR(i,0,n)#define IREP(i, n) IFOR(i,0,n)template <typename T, typename V>void ndarray(vector<T>& vec, const V& val, int len) { vec.assign(len, val); }template <typename T, typename V, typename... Args> void ndarray(vector<T>& vec, const V& val, int len, Args... args) { vec.resize(len), for_each(begin(vec), end(vec), [&](T& v) { ndarray(v, val, args...); }); }template <typename T> bool chmax(T &m, const T q) { return m < q ? (m = q, true) : false; }template <typename T> bool chmin(T &m, const T q) { return m > q ? (m = q, true) : false; }const std::vector<std::pair<int, int>> grid_dxs{{1, 0}, {-1, 0}, {0, 1}, {0, -1}};int floor_lg(long long x) { return x <= 0 ? -1 : 63 - __builtin_clzll(x); }template <class T1, class T2> T1 floor_div(T1 num, T2 den) { return (num > 0 ? num / den : -((-num + den - 1) / den)); }template <class T1, class T2> std::pair<T1, T2> operator+(const std::pair<T1, T2> &l, const std::pair<T1, T2> &r) { return std::make_pair(l.first + r.first, l.second + r.second); }template <class T1, class T2> std::pair<T1, T2> operator-(const std::pair<T1, T2> &l, const std::pair<T1, T2> &r) { return std::make_pair(l.first - r.first, l.second - r.second); }template <class T> std::vector<T> sort_unique(std::vector<T> vec) { sort(vec.begin(), vec.end()), vec.erase(unique(vec.begin(), vec.end()), vec.end()); return vec; }template <class T> int arglb(const std::vector<T> &v, const T &x) { return std::distance(v.begin(), std::lower_bound(v.begin(), v.end(), x)); }template <class T> int argub(const std::vector<T> &v, const T &x) { return std::distance(v.begin(), std::upper_bound(v.begin(), v.end(), x)); }template <class IStream, class T> IStream &operator>>(IStream &is, std::vector<T> &vec) { for (auto &v : vec) is >> v; return is; }template <class OStream, class T> OStream &operator<<(OStream &os, const std::vector<T> &vec);template <class OStream, class T, size_t sz> OStream &operator<<(OStream &os, const std::array<T, sz> &arr);template <class OStream, class T, class TH> OStream &operator<<(OStream &os, const std::unordered_set<T, TH> &vec);template <class OStream, class T, class U> OStream &operator<<(OStream &os, const pair<T, U> &pa);template <class OStream, class T> OStream &operator<<(OStream &os, const std::deque<T> &vec);template <class OStream, class T> OStream &operator<<(OStream &os, const std::set<T> &vec);template <class OStream, class T> OStream &operator<<(OStream &os, const std::multiset<T> &vec);template <class OStream, class T> OStream &operator<<(OStream &os, const std::unordered_multiset<T> &vec);template <class OStream, class T, class U> OStream &operator<<(OStream &os, const std::pair<T, U> &pa);template <class OStream, class TK, class TV> OStream &operator<<(OStream &os, const std::map<TK, TV> &mp);template <class OStream, class TK, class TV, class TH> OStream &operator<<(OStream &os, const std::unordered_map<TK, TV, TH> &mp);template <class OStream, class... T> OStream &operator<<(OStream &os, const std::tuple<T...> &tpl);template <class OStream, class T> OStream &operator<<(OStream &os, const std::vector<T> &vec) { os << '['; for (auto v : vec) os << v << ','; os <<']'; return os; }template <class OStream, class T, size_t sz> OStream &operator<<(OStream &os, const std::array<T, sz> &arr) { os << '['; for (auto v : arr) os << v<< ','; os << ']'; return os; }template <class... T> std::istream &operator>>(std::istream &is, std::tuple<T...> &tpl) { std::apply([&is](auto &&... args) { ((is >> args), ...);},tpl); return is; }template <class OStream, class... T> OStream &operator<<(OStream &os, const std::tuple<T...> &tpl) { os << '('; std::apply([&os](auto &&... args) {((os << args << ','), ...);}, tpl); return os << ')'; }template <class OStream, class T, class TH> OStream &operator<<(OStream &os, const std::unordered_set<T, TH> &vec) { os << '{'; for (auto v : vec) os<< v << ','; os << '}'; return os; }template <class OStream, class T> OStream &operator<<(OStream &os, const std::deque<T> &vec) { os << "deq["; for (auto v : vec) os << v << ','; os <<']'; return os; }template <class OStream, class T> OStream &operator<<(OStream &os, const std::set<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}';return os; }template <class OStream, class T> OStream &operator<<(OStream &os, const std::multiset<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os <<'}'; return os; }template <class OStream, class T> OStream &operator<<(OStream &os, const std::unordered_multiset<T> &vec) { os << '{'; for (auto v : vec) os << v <<','; os << '}'; return os; }template <class OStream, class T, class U> OStream &operator<<(OStream &os, const std::pair<T, U> &pa) { return os << '(' << pa.first << ',' << pa.second << ')'; }template <class OStream, class TK, class TV> OStream &operator<<(OStream &os, const std::map<TK, TV> &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; }template <class OStream, class TK, class TV, class TH> OStream &operator<<(OStream &os, const std::unordered_map<TK, TV, TH> &mp) { os << '{'; for(auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; }#ifdef HITONANODE_LOCALconst string COLOR_RESET = "\033[0m", BRIGHT_GREEN = "\033[1;32m", BRIGHT_RED = "\033[1;31m", BRIGHT_CYAN = "\033[1;36m", NORMAL_CROSSED = "\033[0;9;37m", RED_BACKGROUND = "\033[1;41m", NORMAL_FAINT = "\033[0;2m";#define dbg(x) std::cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET<< std::endl#define dbgif(cond, x) ((cond) ? std::cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " <<__FILE__ << COLOR_RESET << std::endl : std::cerr)#else#define dbg(x) ((void)0)#define dbgif(cond, x) ((void)0)#endif// Linear sieve algorithm for fast prime factorization// Complexity: O(N) time, O(N) space:// - MAXN = 10^7: ~44 MB, 80~100 ms (Codeforces / AtCoder GCC, C++17)// - MAXN = 10^8: ~435 MB, 810~980 ms (Codeforces / AtCoder GCC, C++17)// Reference:// [1] D. Gries, J. Misra, "A Linear Sieve Algorithm for Finding Prime Numbers,"// Communications of the ACM, 21(12), 999-1003, 1978.// - https://cp-algorithms.com/algebra/prime-sieve-linear.html// - https://37zigen.com/linear-sieve/struct Sieve {std::vector<int> min_factor;std::vector<int> primes;Sieve(int MAXN) : min_factor(MAXN + 1) {for (int d = 2; d <= MAXN; d++) {if (!min_factor[d]) {min_factor[d] = d;primes.emplace_back(d);}for (const auto &p : primes) {if (p > min_factor[d] or d * p > MAXN) break;min_factor[d * p] = p;}}}// Prime factorization for 1 <= x <= MAXN^2// Complexity: O(log x) (x <= MAXN)// O(MAXN / log MAXN) (MAXN < x <= MAXN^2)template <class T> std::map<T, int> factorize(T x) const {std::map<T, int> ret;assert(x > 0 andx <= ((long long)min_factor.size() - 1) * ((long long)min_factor.size() - 1));for (const auto &p : primes) {if (x < T(min_factor.size())) break;while (!(x % p)) x /= p, ret[p]++;}if (x >= T(min_factor.size())) ret[x]++, x = 1;while (x > 1) ret[min_factor[x]]++, x /= min_factor[x];return ret;}// Enumerate divisors of 1 <= x <= MAXN^2// Be careful of highly composite numbers https://oeis.org/A002182/list// https://gist.github.com/dario2994/fb4713f252ca86c1254d#file-list-txt (n, (# of div. of n)):// 45360->100, 735134400(<1e9)->1344, 963761198400(<1e12)->6720template <class T> std::vector<T> divisors(T x) const {std::vector<T> ret{1};for (const auto p : factorize(x)) {int n = ret.size();for (int i = 0; i < n; i++) {for (T a = 1, d = 1; d <= p.second; d++) {a *= p.first;ret.push_back(ret[i] * a);}}}return ret; // NOT sorted}// Euler phi functions of divisors of given x// Verified: ABC212 G https://atcoder.jp/contests/abc212/tasks/abc212_g// Complexity: O(sqrt(x) + d(x))template <class T> std::map<T, T> euler_of_divisors(T x) const {assert(x >= 1);std::map<T, T> ret;ret[1] = 1;std::vector<T> divs{1};for (auto p : factorize(x)) {int n = ret.size();for (int i = 0; i < n; i++) {ret[divs[i] * p.first] = ret[divs[i]] * (p.first - 1);divs.push_back(divs[i] * p.first);for (T a = divs[i] * p.first, d = 1; d < p.second; a *= p.first, d++) {ret[a * p.first] = ret[a] * p.first;divs.push_back(a * p.first);}}}return ret;}// Moebius function Table, (-1)^{# of different prime factors} for square-free x// return: [0=>0, 1=>1, 2=>-1, 3=>-1, 4=>0, 5=>-1, 6=>1, 7=>-1, 8=>0, ...] https://oeis.org/A008683std::vector<int> GenerateMoebiusFunctionTable() const {std::vector<int> ret(min_factor.size());for (unsigned i = 1; i < min_factor.size(); i++) {if (i == 1) {ret[i] = 1;} else if ((i / min_factor[i]) % min_factor[i] == 0) {ret[i] = 0;} else {ret[i] = -ret[i / min_factor[i]];}}return ret;}// Calculate [0^K, 1^K, ..., nmax^K] in O(nmax)// Note: **0^0 == 1**template <class MODINT> std::vector<MODINT> enumerate_kth_pows(long long K, int nmax) const {assert(nmax < int(min_factor.size()));assert(K >= 0);if (K == 0) return std::vector<MODINT>(nmax + 1, 1);std::vector<MODINT> ret(nmax + 1);ret[0] = 0, ret[1] = 1;for (int n = 2; n <= nmax; n++) {if (min_factor[n] == n) {ret[n] = MODINT(n).pow(K);} else {ret[n] = ret[n / min_factor[n]] * ret[min_factor[n]];}}return ret;}};Sieve sieve((1 << 20));template <int md> struct ModInt {#if __cplusplus >= 201402L#define MDCONST constexpr#else#define MDCONST#endifusing lint = long long;MDCONST static int mod() { return md; }static int get_primitive_root() {static int primitive_root = 0;if (!primitive_root) {primitive_root = [&]() {std::set<int> fac;int v = md - 1;for (lint i = 2; i * i <= v; i++)while (v % i == 0) fac.insert(i), v /= i;if (v > 1) fac.insert(v);for (int g = 1; g < md; g++) {bool ok = true;for (auto i : fac)if (ModInt(g).pow((md - 1) / i) == 1) {ok = false;break;}if (ok) return g;}return -1;}();}return primitive_root;}int val_;int val() const noexcept { return val_; }MDCONST ModInt() : val_(0) {}MDCONST ModInt &_setval(lint v) { return val_ = (v >= md ? v - md : v), *this; }MDCONST ModInt(lint v) { _setval(v % md + md); }MDCONST explicit operator bool() const { return val_ != 0; }MDCONST ModInt operator+(const ModInt &x) const {return ModInt()._setval((lint)val_ + x.val_);}MDCONST ModInt operator-(const ModInt &x) const {return ModInt()._setval((lint)val_ - x.val_ + md);}MDCONST ModInt operator*(const ModInt &x) const {return ModInt()._setval((lint)val_ * x.val_ % md);}MDCONST ModInt operator/(const ModInt &x) const {return ModInt()._setval((lint)val_ * x.inv().val() % md);}MDCONST ModInt operator-() const { return ModInt()._setval(md - val_); }MDCONST ModInt &operator+=(const ModInt &x) { return *this = *this + x; }MDCONST ModInt &operator-=(const ModInt &x) { return *this = *this - x; }MDCONST ModInt &operator*=(const ModInt &x) { return *this = *this * x; }MDCONST ModInt &operator/=(const ModInt &x) { return *this = *this / x; }friend MDCONST ModInt operator+(lint a, const ModInt &x) {return ModInt()._setval(a % md + x.val_);}friend MDCONST ModInt operator-(lint a, const ModInt &x) {return ModInt()._setval(a % md - x.val_ + md);}friend MDCONST ModInt operator*(lint a, const ModInt &x) {return ModInt()._setval(a % md * x.val_ % md);}friend MDCONST ModInt operator/(lint a, const ModInt &x) {return ModInt()._setval(a % md * x.inv().val() % md);}MDCONST bool operator==(const ModInt &x) const { return val_ == x.val_; }MDCONST bool operator!=(const ModInt &x) const { return val_ != x.val_; }MDCONST bool operator<(const ModInt &x) const {return val_ < x.val_;} // To use std::map<ModInt, T>friend std::istream &operator>>(std::istream &is, ModInt &x) {lint t;return is >> t, x = ModInt(t), is;}MDCONST friend std::ostream &operator<<(std::ostream &os, const ModInt &x) {return os << x.val_;}MDCONST ModInt pow(lint n) const {ModInt ans = 1, tmp = *this;while (n) {if (n & 1) ans *= tmp;tmp *= tmp, n >>= 1;}return ans;}static std::vector<ModInt> facs, facinvs, invs;MDCONST static void _precalculation(int N) {int l0 = facs.size();if (N > md) N = md;if (N <= l0) return;facs.resize(N), facinvs.resize(N), invs.resize(N);for (int i = l0; i < N; i++) facs[i] = facs[i - 1] * i;facinvs[N - 1] = facs.back().pow(md - 2);for (int i = N - 2; i >= l0; i--) facinvs[i] = facinvs[i + 1] * (i + 1);for (int i = N - 1; i >= l0; i--) invs[i] = facinvs[i] * facs[i - 1];}MDCONST ModInt inv() const {if (this->val_ < std::min(md >> 1, 1 << 21)) {if (facs.empty()) facs = {1}, facinvs = {1}, invs = {0};while (this->val_ >= int(facs.size())) _precalculation(facs.size() * 2);return invs[this->val_];} else {return this->pow(md - 2);}}MDCONST ModInt fac() const {while (this->val_ >= int(facs.size())) _precalculation(facs.size() * 2);return facs[this->val_];}MDCONST ModInt facinv() const {while (this->val_ >= int(facs.size())) _precalculation(facs.size() * 2);return facinvs[this->val_];}MDCONST ModInt doublefac() const {lint k = (this->val_ + 1) / 2;return (this->val_ & 1) ? ModInt(k * 2).fac() / (ModInt(2).pow(k) * ModInt(k).fac()): ModInt(k).fac() * ModInt(2).pow(k);}MDCONST ModInt nCr(const ModInt &r) const {return (this->val_ < r.val_) ? 0 : this->fac() * (*this - r).facinv() * r.facinv();}MDCONST ModInt nPr(const ModInt &r) const {return (this->val_ < r.val_) ? 0 : this->fac() * (*this - r).facinv();}ModInt sqrt() const {if (val_ == 0) return 0;if (md == 2) return val_;if (pow((md - 1) / 2) != 1) return 0;ModInt b = 1;while (b.pow((md - 1) / 2) == 1) b += 1;int e = 0, m = md - 1;while (m % 2 == 0) m >>= 1, e++;ModInt x = pow((m - 1) / 2), y = (*this) * x * x;x *= (*this);ModInt z = b.pow(m);while (y != 1) {int j = 0;ModInt t = y;while (t != 1) j++, t *= t;z = z.pow(1LL << (e - j - 1));x *= z, z *= z, y *= z;e = j;}return ModInt(std::min(x.val_, md - x.val_));}};template <int md> std::vector<ModInt<md>> ModInt<md>::facs = {1};template <int md> std::vector<ModInt<md>> ModInt<md>::facinvs = {1};template <int md> std::vector<ModInt<md>> ModInt<md>::invs = {0};using mint = ModInt<998244353>;int main() {int N, M;cin >> N >> M;vector<int> A(N);cin >> A;dbg(A);int l = 1;for (int x : A) l = std::lcm(x, l);dbg(l);auto fc = sieve.factorize(l);dbg(fc);vector<int> ps;for (auto [p, deg] : fc) ps.push_back(p);vector<pint> val_weights;REP(s, 1 << ps.size()) {int tmp = 1;int w = 1;REP(i, ps.size()) {if ((s >> i) & 1) {tmp *= ps.at(i);w = -w;}}val_weights.emplace_back(tmp, w);}dbg(val_weights);auto ds = sieve.divisors(l);sort(ALL(ds));dbg(ds);vector<int> weight(ds.size());IREP(j, ds.size()) {const int d = ds.at(j);int tmp = 0;for (auto [pro, pw] : val_weights) {lint xn = lint(d) * pro;if (l % xn == 0) {int k = arglb(ds, int(xn));tmp += (l / xn) * pw;}}weight.at(j) = tmp;}dbg(weight);mint ret = 0;REP(j, ds.size()) {const int d = ds.at(j);mint tmp = weight.at(j);for (int a : A) {int g = std::gcd(a, d);tmp *= mint(M).pow(g);}ret += tmp;}cout << ret / l << '\n';}