結果
問題 | No.1781 LCM |
ユーザー | NyaanNyaan |
提出日時 | 2021-12-10 09:36:19 |
言語 | C++17 (gcc 12.3.0 + boost 1.83.0) |
結果 |
AC
|
実行時間 | 627 ms / 5,000 ms |
コード長 | 16,874 bytes |
コンパイル時間 | 2,868 ms |
コンパイル使用メモリ | 259,976 KB |
実行使用メモリ | 9,816 KB |
最終ジャッジ日時 | 2024-11-15 22:21:36 |
合計ジャッジ時間 | 7,736 ms |
ジャッジサーバーID (参考情報) |
judge3 / judge4 |
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テストケース
テストケース表示入力 | 結果 | 実行時間 実行使用メモリ |
---|---|---|
testcase_00 | AC | 2 ms
6,816 KB |
testcase_01 | AC | 2 ms
6,816 KB |
testcase_02 | AC | 2 ms
6,820 KB |
testcase_03 | AC | 1 ms
6,816 KB |
testcase_04 | AC | 2 ms
6,820 KB |
testcase_05 | AC | 2 ms
6,816 KB |
testcase_06 | AC | 2 ms
6,816 KB |
testcase_07 | AC | 2 ms
6,820 KB |
testcase_08 | AC | 2 ms
6,820 KB |
testcase_09 | AC | 2 ms
6,816 KB |
testcase_10 | AC | 2 ms
6,816 KB |
testcase_11 | AC | 2 ms
6,820 KB |
testcase_12 | AC | 2 ms
6,820 KB |
testcase_13 | AC | 2 ms
6,816 KB |
testcase_14 | AC | 2 ms
6,820 KB |
testcase_15 | AC | 2 ms
6,816 KB |
testcase_16 | AC | 2 ms
6,816 KB |
testcase_17 | AC | 1 ms
6,820 KB |
testcase_18 | AC | 2 ms
6,816 KB |
testcase_19 | AC | 2 ms
6,816 KB |
testcase_20 | AC | 2 ms
6,820 KB |
testcase_21 | AC | 619 ms
9,568 KB |
testcase_22 | AC | 623 ms
9,600 KB |
testcase_23 | AC | 2 ms
6,816 KB |
testcase_24 | AC | 2 ms
6,820 KB |
testcase_25 | AC | 620 ms
9,816 KB |
testcase_26 | AC | 627 ms
9,472 KB |
testcase_27 | AC | 611 ms
9,564 KB |
testcase_28 | AC | 517 ms
8,832 KB |
testcase_29 | AC | 129 ms
6,820 KB |
testcase_30 | AC | 135 ms
6,816 KB |
testcase_31 | AC | 2 ms
6,816 KB |
testcase_32 | AC | 2 ms
6,820 KB |
ソースコード
/*** date : 2021-12-10 09:36:13*/#define NDEBUGusing namespace std;// intrinstic#include <immintrin.h>#include <algorithm>#include <array>#include <bitset>#include <cassert>#include <cctype>#include <cfenv>#include <cfloat>#include <chrono>#include <cinttypes>#include <climits>#include <cmath>#include <complex>#include <cstdarg>#include <cstddef>#include <cstdint>#include <cstdio>#include <cstdlib>#include <cstring>#include <deque>#include <fstream>#include <functional>#include <initializer_list>#include <iomanip>#include <ios>#include <iostream>#include <istream>#include <iterator>#include <limits>#include <list>#include <map>#include <memory>#include <new>#include <numeric>#include <ostream>#include <queue>#include <random>#include <set>#include <sstream>#include <stack>#include <streambuf>#include <string>#include <tuple>#include <type_traits>#include <typeinfo>#include <unordered_map>#include <unordered_set>#include <utility>#include <vector>// utilitynamespace Nyaan {using ll = long long;using i64 = long long;using u64 = unsigned long long;using i128 = __int128_t;using u128 = __uint128_t;template <typename T>using V = vector<T>;template <typename T>using VV = vector<vector<T>>;using vi = vector<int>;using vl = vector<long long>;using vd = V<double>;using vs = V<string>;using vvi = vector<vector<int>>;using vvl = vector<vector<long long>>;template <typename T, typename U>struct P : pair<T, U> {template <typename... Args>P(Args... args) : pair<T, U>(args...) {}using pair<T, U>::first;using pair<T, U>::second;T &x() { return first; }const T &x() const { return first; }U &y() { return second; }const U &y() const { return second; }P &operator+=(const P &r) {first += r.first;second += r.second;return *this;}P &operator-=(const P &r) {first -= r.first;second -= r.second;return *this;}P &operator*=(const P &r) {first *= r.first;second *= r.second;return *this;}P operator+(const P &r) const { return P(*this) += r; }P operator-(const P &r) const { return P(*this) -= r; }P operator*(const P &r) const { return P(*this) *= r; }P operator*(int r) const { return {first * r, second * r}; }P operator-() const { return P{-first, -second}; }};using pl = P<ll, ll>;using pi = P<int, int>;using vp = V<pl>;constexpr int inf = 1001001001;constexpr long long infLL = 4004004004004004004LL;template <typename T>int sz(const T &t) {return t.size();}template <typename T, typename U>inline bool amin(T &x, U y) {return (y < x) ? (x = y, true) : false;}template <typename T, typename U>inline bool amax(T &x, U y) {return (x < y) ? (x = y, true) : false;}template <typename T>inline T Max(const vector<T> &v) {return *max_element(begin(v), end(v));}template <typename T>inline T Min(const vector<T> &v) {return *min_element(begin(v), end(v));}template <typename T>inline long long Sum(const vector<T> &v) {return accumulate(begin(v), end(v), 0LL);}template <typename T>int lb(const vector<T> &v, const T &a) {return lower_bound(begin(v), end(v), a) - begin(v);}template <typename T>int ub(const vector<T> &v, const T &a) {return upper_bound(begin(v), end(v), a) - begin(v);}constexpr long long TEN(int n) {long long ret = 1, x = 10;for (; n; x *= x, n >>= 1) ret *= (n & 1 ? x : 1);return ret;}template <typename T, typename U>pair<T, U> mkp(const T &t, const U &u) {return make_pair(t, u);}template <typename T>vector<T> mkrui(const vector<T> &v, bool rev = false) {vector<T> ret(v.size() + 1);if (rev) {for (int i = int(v.size()) - 1; i >= 0; i--) ret[i] = v[i] + ret[i + 1];} else {for (int i = 0; i < int(v.size()); i++) ret[i + 1] = ret[i] + v[i];}return ret;};template <typename T>vector<T> mkuni(const vector<T> &v) {vector<T> ret(v);sort(ret.begin(), ret.end());ret.erase(unique(ret.begin(), ret.end()), ret.end());return ret;}template <typename F>vector<int> mkord(int N, F f) {vector<int> ord(N);iota(begin(ord), end(ord), 0);sort(begin(ord), end(ord), f);return ord;}template <typename T>vector<int> mkinv(vector<T> &v) {int max_val = *max_element(begin(v), end(v));vector<int> inv(max_val + 1, -1);for (int i = 0; i < (int)v.size(); i++) inv[v[i]] = i;return inv;}} // namespace Nyaan// bit operationnamespace Nyaan {__attribute__((target("popcnt"))) inline int popcnt(const u64 &a) {return _mm_popcnt_u64(a);}inline int lsb(const u64 &a) { return a ? __builtin_ctzll(a) : 64; }inline int ctz(const u64 &a) { return a ? __builtin_ctzll(a) : 64; }inline int msb(const u64 &a) { return a ? 63 - __builtin_clzll(a) : -1; }template <typename T>inline int gbit(const T &a, int i) {return (a >> i) & 1;}template <typename T>inline void sbit(T &a, int i, bool b) {if (gbit(a, i) != b) a ^= T(1) << i;}constexpr long long PW(int n) { return 1LL << n; }constexpr long long MSK(int n) { return (1LL << n) - 1; }} // namespace Nyaan// inoutnamespace Nyaan {template <typename T, typename U>ostream &operator<<(ostream &os, const pair<T, U> &p) {os << p.first << " " << p.second;return os;}template <typename T, typename U>istream &operator>>(istream &is, pair<T, U> &p) {is >> p.first >> p.second;return is;}template <typename T>ostream &operator<<(ostream &os, const vector<T> &v) {int s = (int)v.size();for (int i = 0; i < s; i++) os << (i ? " " : "") << v[i];return os;}template <typename T>istream &operator>>(istream &is, vector<T> &v) {for (auto &x : v) is >> x;return is;}void in() {}template <typename T, class... U>void in(T &t, U &... u) {cin >> t;in(u...);}void out() { cout << "\n"; }template <typename T, class... U, char sep = ' '>void out(const T &t, const U &... u) {cout << t;if (sizeof...(u)) cout << sep;out(u...);}void outr() {}template <typename T, class... U, char sep = ' '>void outr(const T &t, const U &... u) {cout << t;outr(u...);}struct IoSetupNya {IoSetupNya() {cin.tie(nullptr);ios::sync_with_stdio(false);cout << fixed << setprecision(15);cerr << fixed << setprecision(7);}} iosetupnya;} // namespace Nyaan// debugnamespace DebugImpl {template <typename U, typename = void>struct is_specialize : false_type {};template <typename U>struct is_specialize<U, typename conditional<false, typename U::iterator, void>::type>: true_type {};template <typename U>struct is_specialize<U, typename conditional<false, decltype(U::first), void>::type>: true_type {};template <typename U>struct is_specialize<U, enable_if_t<is_integral<U>::value, void>> : true_type {};void dump(const char& t) { cerr << t; }void dump(const string& t) { cerr << t; }void dump(const bool& t) { cerr << (t ? "true" : "false"); }template <typename U,enable_if_t<!is_specialize<U>::value, nullptr_t> = nullptr>void dump(const U& t) {cerr << t;}template <typename T>void dump(const T& t, enable_if_t<is_integral<T>::value>* = nullptr) {string res;if (t == Nyaan::inf) res = "inf";if constexpr (is_signed<T>::value) {if (t == -Nyaan::inf) res = "-inf";}if constexpr (sizeof(T) == 8) {if (t == Nyaan::infLL) res = "inf";if constexpr (is_signed<T>::value) {if (t == -Nyaan::infLL) res = "-inf";}}if (res.empty()) res = to_string(t);cerr << res;}template <typename T, typename U>void dump(const pair<T, U>&);template <typename T>void dump(const pair<T*, int>&);template <typename T>void dump(const T& t,enable_if_t<!is_void<typename T::iterator>::value>* = nullptr) {cerr << "[ ";for (auto it = t.begin(); it != t.end();) {dump(*it);cerr << (++it == t.end() ? "" : ", ");}cerr << " ]";}template <typename T, typename U>void dump(const pair<T, U>& t) {cerr << "( ";dump(t.first);cerr << ", ";dump(t.second);cerr << " )";}template <typename T>void dump(const pair<T*, int>& t) {cerr << "[ ";for (int i = 0; i < t.second; i++) {dump(t.first[i]);cerr << (i == t.second - 1 ? "" : ", ");}cerr << " ]";}void trace() { cerr << endl; }template <typename Head, typename... Tail>void trace(Head&& head, Tail&&... tail) {cerr << " ";dump(head);if (sizeof...(tail) != 0) cerr << ",";trace(forward<Tail>(tail)...);}} // namespace DebugImpl#ifdef NyaanDebug#define trc(...) \do { \cerr << "## " << #__VA_ARGS__ << " = "; \DebugImpl::trace(__VA_ARGS__); \} while (0)#else#define trc(...) (void(0))#endif// macro#define each(x, v) for (auto&& x : v)#define each2(x, y, v) for (auto&& [x, y] : v)#define all(v) (v).begin(), (v).end()#define rep(i, N) for (long long i = 0; i < (long long)(N); i++)#define repr(i, N) for (long long i = (long long)(N)-1; i >= 0; i--)#define rep1(i, N) for (long long i = 1; i <= (long long)(N); i++)#define repr1(i, N) for (long long i = (N); (long long)(i) > 0; i--)#define reg(i, a, b) for (long long i = (a); i < (b); i++)#define regr(i, a, b) for (long long i = (b)-1; i >= (a); i--)#define fi first#define se second#define ini(...) \int __VA_ARGS__; \in(__VA_ARGS__)#define inl(...) \long long __VA_ARGS__; \in(__VA_ARGS__)#define ins(...) \string __VA_ARGS__; \in(__VA_ARGS__)#define in2(s, t) \for (int i = 0; i < (int)s.size(); i++) { \in(s[i], t[i]); \}#define in3(s, t, u) \for (int i = 0; i < (int)s.size(); i++) { \in(s[i], t[i], u[i]); \}#define in4(s, t, u, v) \for (int i = 0; i < (int)s.size(); i++) { \in(s[i], t[i], u[i], v[i]); \}#define die(...) \do { \Nyaan::out(__VA_ARGS__); \return; \} while (0)namespace Nyaan {void solve();}int main() { Nyaan::solve(); }//template <uint32_t mod>struct LazyMontgomeryModInt {using mint = LazyMontgomeryModInt;using i32 = int32_t;using u32 = uint32_t;using u64 = uint64_t;static constexpr u32 get_r() {u32 ret = mod;for (i32 i = 0; i < 4; ++i) ret *= 2 - mod * ret;return ret;}static constexpr u32 r = get_r();static constexpr u32 n2 = -u64(mod) % mod;static_assert(r * mod == 1, "invalid, r * mod != 1");static_assert(mod < (1 << 30), "invalid, mod >= 2 ^ 30");static_assert((mod & 1) == 1, "invalid, mod % 2 == 0");u32 a;constexpr LazyMontgomeryModInt() : a(0) {}constexpr LazyMontgomeryModInt(const int64_t &b): a(reduce(u64(b % mod + mod) * n2)){};static constexpr u32 reduce(const u64 &b) {return (b + u64(u32(b) * u32(-r)) * mod) >> 32;}constexpr mint &operator+=(const mint &b) {if (i32(a += b.a - 2 * mod) < 0) a += 2 * mod;return *this;}constexpr mint &operator-=(const mint &b) {if (i32(a -= b.a) < 0) a += 2 * mod;return *this;}constexpr mint &operator*=(const mint &b) {a = reduce(u64(a) * b.a);return *this;}constexpr mint &operator/=(const mint &b) {*this *= b.inverse();return *this;}constexpr mint operator+(const mint &b) const { return mint(*this) += b; }constexpr mint operator-(const mint &b) const { return mint(*this) -= b; }constexpr mint operator*(const mint &b) const { return mint(*this) *= b; }constexpr mint operator/(const mint &b) const { return mint(*this) /= b; }constexpr bool operator==(const mint &b) const {return (a >= mod ? a - mod : a) == (b.a >= mod ? b.a - mod : b.a);}constexpr bool operator!=(const mint &b) const {return (a >= mod ? a - mod : a) != (b.a >= mod ? b.a - mod : b.a);}constexpr mint operator-() const { return mint() - mint(*this); }constexpr mint pow(u64 n) const {mint ret(1), mul(*this);while (n > 0) {if (n & 1) ret *= mul;mul *= mul;n >>= 1;}return ret;}constexpr mint inverse() const { return pow(mod - 2); }friend ostream &operator<<(ostream &os, const mint &b) {return os << b.get();}friend istream &operator>>(istream &is, mint &b) {int64_t t;is >> t;b = LazyMontgomeryModInt<mod>(t);return (is);}constexpr u32 get() const {u32 ret = reduce(a);return ret >= mod ? ret - mod : ret;}static constexpr u32 get_mod() { return mod; }};template <typename T>struct Binomial {vector<T> f, g, h;Binomial(int MAX = 0) : f(1, T(1)), g(1, T(1)), h(1, T(1)) {while (MAX >= (int)f.size()) extend();}void extend() {int n = f.size();int m = n * 2;f.resize(m);g.resize(m);h.resize(m);for (int i = n; i < m; i++) f[i] = f[i - 1] * T(i);g[m - 1] = f[m - 1].inverse();h[m - 1] = g[m - 1] * f[m - 2];for (int i = m - 2; i >= n; i--) {g[i] = g[i + 1] * T(i + 1);h[i] = g[i] * f[i - 1];}}T fac(int i) {if (i < 0) return T(0);while (i >= (int)f.size()) extend();return f[i];}T finv(int i) {if (i < 0) return T(0);while (i >= (int)g.size()) extend();return g[i];}T inv(int i) {if (i < 0) return -inv(-i);while (i >= (int)h.size()) extend();return h[i];}T C(int n, int r) {if (n < 0 || n < r || r < 0) return T(0);return fac(n) * finv(n - r) * finv(r);}inline T operator()(int n, int r) { return C(n, r); }template <typename I>T multinomial(const vector<I>& r) {static_assert(is_integral<I>::value == true);int n = 0;for (auto& x : r) {if(x < 0) return T(0);n += x;}T res = fac(n);for (auto& x : r) res *= finv(x);return res;}template <typename I>T operator()(const vector<I>& r) {return multinomial(r);}T C_naive(int n, int r) {if (n < 0 || n < r || r < 0) return T(0);T ret = T(1);r = min(r, n - r);for (int i = 1; i <= r; ++i) ret *= inv(i) * (n--);return ret;}T P(int n, int r) {if (n < 0 || n < r || r < 0) return T(0);return fac(n) * finv(n - r);}T H(int n, int r) {if (n < 0 || r < 0) return T(0);return r == 0 ? 1 : C(n + r - 1, r);}};// Prime Sieve {2, 3, 5, 7, 11, 13, 17, ...}vector<int> prime_enumerate(int N) {vector<bool> sieve(N / 3 + 1, 1);for (int p = 5, d = 4, i = 1, sqn = sqrt(N); p <= sqn; p += d = 6 - d, i++) {if (!sieve[i]) continue;for (int q = p * p / 3, r = d * p / 3 + (d * p % 3 == 2), s = 2 * p,qe = sieve.size();q < qe; q += r = s - r)sieve[q] = 0;}vector<int> ret{2, 3};for (int p = 5, d = 4, i = 1; p <= N; p += d = 6 - d, i++)if (sieve[i]) ret.push_back(p);while (!ret.empty() && ret.back() > N) ret.pop_back();return ret;}//using namespace Nyaan;using mint = LazyMontgomeryModInt<998244353>;// using mint = LazyMontgomeryModInt<1000000007>;using vm = vector<mint>;using vvm = vector<vm>;using namespace Nyaan;i64 my_div(i64 n, i64 p) { return double(n) / p; };void Nyaan::solve() {inl(N, M);vm cmemo, buf;i64 s = 0, sq = sqrt(M);auto idx = [&](i64 n) { return n <= sq ? s - n : my_div(M, n); };auto p = prime_enumerate(sq);{i64 Ndsq = my_div(M, sq);vector<i64> hl(Ndsq);for (int i = 1; i < Ndsq; i++) hl[i] = my_div(M, i) - 1;if (hl.back() == sq - 1) Ndsq--, hl.pop_back();vector<int> hs(sq + 1);iota(begin(hs), end(hs), -1);int pi = 0;for (auto& x : p) {i64 x2 = i64(x) * x;i64 imax = min<i64>(Ndsq, my_div(M, x2) + 1);i64 ix = x;for (i64 i = 1; i < imax; ++i) {hl[i] -= (ix < Ndsq ? hl[ix] : hs[my_div(M, ix)]) - pi;ix += x;}for (int n = sq; n >= x2; n--) {hs[n] -= hs[my_div(n, x)] - pi;}pi++;}buf.reserve(2 * sq + 10);mint coe = mint{2}.pow(N);for (auto& x : hl) buf.push_back(coe * x);for (int i = hs.size(); --i;) buf.push_back(coe * hs[i]);s = buf.size();}rep(i, 50) cmemo.push_back(mint{i}.pow(N));mint ans = buf[idx(M)] + 1;auto d = [&](auto r, int i, int c, i64 v, i64 lim, mint cur) -> void {ans += cur * cmemo[c + 2];if (lim >= 1LL * p[i] * p[i])r(r, i, c + 1, p[i] * v, my_div(lim, p[i]), cur);cur *= cmemo[c + 1];ans += cur * (buf[idx(lim)] - buf[idx(p[i])]);for (int j = i + 1; j < (int)p.size() && 1LL * p[j] * p[j] <= lim; j++) {r(r, j, 1, p[j], my_div(lim, p[j]), cur);}};for (int i = 0; i < (int)p.size(); i++) d(d, i, 1, p[i], my_div(M, p[i]), 1);out(ans);}