結果
問題 | No.2959 Dolls' Tea Party |
ユーザー | kwm_t |
提出日時 | 2024-11-09 14:41:53 |
言語 | C++23 (gcc 12.3.0 + boost 1.83.0) |
結果 |
AC
|
実行時間 | 687 ms / 3,000 ms |
コード長 | 17,844 bytes |
コンパイル時間 | 7,113 ms |
コンパイル使用メモリ | 337,984 KB |
実行使用メモリ | 32,384 KB |
最終ジャッジ日時 | 2024-11-09 14:42:22 |
合計ジャッジ時間 | 26,452 ms |
ジャッジサーバーID (参考情報) |
judge3 / judge1 |
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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 | 25 ms
18,816 KB |
testcase_01 | AC | 24 ms
18,912 KB |
testcase_02 | AC | 25 ms
18,816 KB |
testcase_03 | AC | 24 ms
18,816 KB |
testcase_04 | AC | 25 ms
18,816 KB |
testcase_05 | AC | 26 ms
18,816 KB |
testcase_06 | AC | 687 ms
31,724 KB |
testcase_07 | AC | 632 ms
32,000 KB |
testcase_08 | AC | 656 ms
31,872 KB |
testcase_09 | AC | 587 ms
31,552 KB |
testcase_10 | AC | 607 ms
31,488 KB |
testcase_11 | AC | 587 ms
31,488 KB |
testcase_12 | AC | 634 ms
31,552 KB |
testcase_13 | AC | 595 ms
31,488 KB |
testcase_14 | AC | 642 ms
31,488 KB |
testcase_15 | AC | 633 ms
32,384 KB |
testcase_16 | AC | 616 ms
31,488 KB |
testcase_17 | AC | 617 ms
31,460 KB |
testcase_18 | AC | 634 ms
31,616 KB |
testcase_19 | AC | 607 ms
31,616 KB |
testcase_20 | AC | 625 ms
31,556 KB |
testcase_21 | AC | 633 ms
32,256 KB |
testcase_22 | AC | 662 ms
32,296 KB |
testcase_23 | AC | 627 ms
32,256 KB |
testcase_24 | AC | 25 ms
18,816 KB |
testcase_25 | AC | 24 ms
18,816 KB |
testcase_26 | AC | 23 ms
18,944 KB |
testcase_27 | AC | 609 ms
32,256 KB |
testcase_28 | AC | 584 ms
32,256 KB |
testcase_29 | AC | 627 ms
32,128 KB |
testcase_30 | AC | 584 ms
31,616 KB |
testcase_31 | AC | 602 ms
31,524 KB |
testcase_32 | AC | 553 ms
30,720 KB |
testcase_33 | AC | 613 ms
32,000 KB |
testcase_34 | AC | 582 ms
31,960 KB |
testcase_35 | AC | 620 ms
32,256 KB |
testcase_36 | AC | 558 ms
30,592 KB |
ソースコード
#include <bits/stdc++.h>#include <atcoder/all>using namespace std;using namespace atcoder;//using mint = modint1000000007;//const int mod = 1000000007;using mint = modint998244353;const int mod = 998244353;//const int INF = 1e9;//const long long LINF = 1e18;#define rep(i, n) for (int i = 0; i < (n); ++i)#define rep2(i,l,r)for(int i=(l);i<(r);++i)#define rrep(i, n) for (int i = (n) - 1; i >= 0; --i)#define rrep2(i,l,r)for(int i=(r) - 1;i>=(l);--i)#define all(x) (x).begin(),(x).end()#define allR(x) (x).rbegin(),(x).rend()#define P pair<int,int>template<typename A, typename B> inline bool chmax(A & a, const B & b) { if (a < b) { a = b; return true; } return false; }template<typename A, typename B> inline bool chmin(A & a, const B & b) { if (a > b) { a = b; return true; } return false; }// combination mod prime// https://www.youtube.com/watch?v=8uowVvQ_-Mo&feature=youtu.be&t=1619struct combination {std::vector<mint> fact, ifact;combination(int n) :fact(n + 1), ifact(n + 1) {assert(n < mod);fact[0] = 1;for (int i = 1; i <= n; ++i) fact[i] = fact[i - 1] * i;ifact[n] = fact[n].inv();for (int i = n; i >= 1; --i) ifact[i - 1] = ifact[i] * i;}mint operator()(int n, int k) { return com(n, k); }mint com(int n, int k) {//負の二項係数を考慮する場合にコメントアウトを外す//if (n < 0) return com(-n, k) * (k % 2 ? -1 : 1);if (k < 0 || k > n) return 0;return fact[n] * ifact[k] * ifact[n - k];}mint comsub(long long n, long long k) {if (n - k < k) k = n - k;assert(k < (int)fact.size());mint val = ifact[k];for (int i = 0; i < k; ++i) val *= n - i;return val;}template <typename ...Ms, std::enable_if_t<std::conjunction_v<std::is_integral<Ms>...>, std::nullptr_t> = nullptr>mint polynom(const int n, const Ms & ...ms) {mint res = fact[n];int sum = 0;for (int m : { ms... }) {if (m < 0 or m > n) return 0;res *= ifact[m];sum += m;}if (sum > n)return 0;res *= ifact[n - sum];return res;}mint div(int x) {if (x >= (int)fact.size())return mint(x).inv();return fact[x - 1] * ifact[x];}mint inv(int n, int k) {//if (n < 0) return inv(-n, k) * (k % 2 ? -1 : 1);if (k < 0 || k > n) return 0;return ifact[n] * fact[k] * fact[n - k];}mint p(int n, int k) { return fact[n] * ifact[n - k]; }}com(2000006);#include <algorithm>#include <iostream>#include <vector>// https://opt-cp.com/fps-implementation/// verified by:// https://judge.yosupo.jp/problem/convolution_mod// https://judge.yosupo.jp/problem/inv_of_formal_power_series// https://judge.yosupo.jp/problem/log_of_formal_power_series// https://judge.yosupo.jp/problem/exp_of_formal_power_series// https://judge.yosupo.jp/problem/pow_of_formal_power_series// https://judge.yosupo.jp/problem/polynomial_taylor_shift// https://judge.yosupo.jp/problem/bernoulong longi_number// https://judge.yosupo.jp/problem/sharp_p_subset_sum//using mint = modint998244353;template<typename T> struct Factorial {int MAX;std::vector<T> fac, finv;Factorial(int m = 0) : MAX(m), fac(m + 1, 1), finv(m + 1, 1) {for (int i = 2; i < MAX + 1; ++i) fac[i] = fac[i - 1] * i;finv[MAX] /= fac[MAX];for (int i = MAX; i >= 3; --i)finv[i - 1] = finv[i] * i;}T binom(int n, int k) {if (k < 0 || n < k) return 0;return fac[n] * finv[k] * finv[n - k];}T perm(int n, int k) {if (k < 0 || n < k) return 0;return fac[n] * finv[n - k];}};Factorial<mint> fc;std::istream &operator>>(std::istream &is, modint998244353 &a) { long long v; is >> v; a = v; return is; }std::ostream &operator<<(std::ostream &os, const modint998244353 &a) { return os << a.val(); }std::istream &operator>>(std::istream &is, modint1000000007 &a) { long long v; is >> v; a = v; return is; }std::ostream &operator<<(std::ostream &os, const modint1000000007 &a) { return os << a.val(); }template<int m> std::istream &operator>>(std::istream &is, static_modint<m> &a) { long long v; is >> v; a = v; return is; }template<int m> std::istream &operator>>(std::istream &is, dynamic_modint<m> &a) { long long v; is >> v; a = v; return is; }template<int m> std::ostream &operator<<(std::ostream &os, const static_modint<m> &a) { return os << a.val(); }template<int m> std::ostream &operator<<(std::ostream &os, const dynamic_modint<m> &a) { return os << a.val(); }template<class T> std::istream &operator>>(std::istream &is, std::vector<T> &v) { for (auto &e : v) is >> e; return is; }template<class T> std::ostream &operator<<(std::ostream &os, const std::vector<T> &v) { for (auto &e : v) os << e << ' '; return os; }template<class T>struct FormalPowerSeries : std::vector<T> {using std::vector<T>::vector;using std::vector<T>::operator=;using F = FormalPowerSeries;F operator-() const {F res(*this);for (auto &e : res) e = -e;return res;}F &operator*=(const T &g) {for (auto &e : *this) e *= g;return *this;}F &operator/=(const T &g) {assert(g != T(0));*this *= g.inv();return *this;}F &operator+=(const F &g) {int n = this->size(), m = g.size();for (int i = 0; i < std::min(n, m); ++i) (*this)[i] += g[i];return *this;}F &operator-=(const F &g) {int n = this->size(), m = g.size();for (int i = 0; i < std::min(n, m); ++i)(*this)[i] -= g[i];return *this;}F &operator<<=(const int d) {int n = this->size();if (d >= n) *this = F(n);this->insert(this->begin(), d, 0);this->resize(n);return *this;}F &operator>>=(const int d) {int n = this->size();this->erase(this->begin(), this->begin() + min(n, d));this->resize(n);return *this;}// O(n log n)F inv(int d = -1) const {int n = this->size();assert(n != 0 && (*this)[0] != 0);if (d == -1) d = n;assert(d >= 0);F res{ (*this)[0].inv() };for (int m = 1; m < d; m *= 2) {F f(this->begin(), this->begin() + std::min(n, 2 * m));F g(res);f.resize(2 * m), internal::butterfly(f);g.resize(2 * m), internal::butterfly(g);for (int i = 0; i < 2 * m; ++i) f[i] *= g[i];internal::butterfly_inv(f);f.erase(f.begin(), f.begin() + m);f.resize(2 * m), internal::butterfly(f);for (int i = 0; i < 2 * m; ++i) f[i] *= g[i];internal::butterfly_inv(f);T iz = T(2 * m).inv(); iz *= -iz;for (int i = 0; i < m; ++i) f[i] *= iz;res.insert(res.end(), f.begin(), f.begin() + m);}res.resize(d);return res;}// fast: FMT-friendly modulus only// O(n log n)F &multiply_inplace(const F &g, int d = -1) {int n = this->size();if (d == -1) d = n;assert(d >= 0);*this = convolution(move(*this), g);this->resize(d);return *this;}F multiply(const F &g, const int d = -1) const { return F(*this).multiply_inplace(g, d); }// O(n log n)F ÷_inplace(const F &g, int d = -1) {int n = this->size();if (d == -1) d = n;assert(d >= 0);*this = convolution(move(*this), g.inv(d));this->resize(d);return *this;}F divide(const F &g, const int d = -1) const { return F(*this).divide_inplace(g, d); }// // naive// // O(n^2)// F &multiply_inplace(const F &g) {// int n = this->size(), m = g.size();// rrep(i, n) {// (*this)[i] *= g[0];// rep2(j, 1, min(i+1, m)) (*this)[i] += (*this)[i-j] * g[j];// }// return *this;// }// F multiply(const F &g) const { return F(*this).multiply_inplace(g); }// // O(n^2)// F ÷_inplace(const F &g) {// assert(g[0] != T(0));// T ig0 = g[0].inv();// int n = this->size(), m = g.size();// rep(i, n) {// rep2(j, 1, min(i+1, m)) (*this)[i] -= (*this)[i-j] * g[j];// (*this)[i] *= ig0;// }// return *this;// }// F divide(const F &g) const { return F(*this).divide_inplace(g); }// sparse// O(nk)F &multiply_inplace(std::vector<std::pair<int, T>> g) {int n = this->size();auto[d, c] = g.front();if (d == 0) g.erase(g.begin());else c = 0;for (int i = (n - 1); i >= 0; --i) {(*this)[i] *= c;for (auto &[j, b] : g) {if (j > i) break;(*this)[i] += (*this)[i - j] * b;}}return *this;}F multiply(const std::vector<std::pair<int, T>> &g) const { return F(*this).multiply_inplace(g); }// O(nk)F ÷_inplace(std::vector<std::pair<int, T>> g) {int n = this->size();auto[d, c] = g.front();assert(d == 0 && c != T(0));T ic = c.inv();g.erase(g.begin());for (int i = 0; i < n; ++i) {for (auto &[j, b] : g) {if (j > i) break;(*this)[i] -= (*this)[i - j] * b;}(*this)[i] *= ic;}return *this;}F divide(const std::vector<std::pair<int, T>> &g) const { return F(*this).divide_inplace(g); }// multiply and divide (1 + cz^d)// O(n)void multiply_inplace(const int d, const T c) {int n = this->size();if (c == T(1)) for (int i = (n - d - 1); i >= 0; --i) (*this)[i + d] += (*this)[i];else if (c == T(-1)) for (int i = (n - d - 1); i >= 0; --i) (*this)[i + d] -= (*this)[i];else for (int i = (n - d - 1); i >= 0; --i) (*this)[i + d] += (*this)[i] * c;}// O(n)void divide_inplace(const int d, const T c) {int n = this->size();if (c == T(1)) for (int i = 0; i < n - d; ++i) (*this)[i + d] -= (*this)[i];else if (c == T(-1)) for (int i = 0; i < n - d; ++i) (*this)[i + d] += (*this)[i];else for (int i = 0; i < n - d; ++i) (*this)[i + d] -= (*this)[i] * c;}// O(n)T eval(const T &a) const {T x(1), res(0);for (auto e : *this) res += e * x, x *= a;return res;}// O(n)F &integ_inplace() {int n = this->size();assert(n > 0);if (n == 1) return *this = F{ 0 };this->insert(this->begin(), 0);this->pop_back();std::vector<T> inv(n);inv[1] = 1;int p = T::mod();for (int i = 2; i < n; ++i) inv[i] = -inv[p%i] * (p / i);for (int i = 2; i < n; ++i) (*this)[i] *= inv[i];return *this;}F integ() const { return F(*this).integ_inplace(); }// O(n)F &deriv_inplace() {int n = this->size();assert(n > 0);for (int i = 2; i < n; ++i) (*this)[i] *= i;this->erase(this->begin());this->push_back(0);return *this;}F deriv() const { return F(*this).deriv_inplace(); }// O(n log n)F &log_inplace(int d = -1) {int n = this->size();assert(n > 0 && (*this)[0] == 1);if (d == -1) d = n;assert(d >= 0);if (d < n) this->resize(d);F f_inv = this->inv();this->deriv_inplace();this->multiply_inplace(f_inv);this->integ_inplace();return *this;}F log(const int d = -1) const { return F(*this).log_inplace(d); }// O(n log n)// https://arxiv.org/abs/1301.5804 (Figure 1, right)F &exp_inplace(int d = -1) {int n = this->size();assert(n > 0 && (*this)[0] == 0);if (d == -1) d = n;assert(d >= 0);F g{ 1 }, g_fft{ 1, 1 };(*this)[0] = 1;this->resize(d);F h_drv(this->deriv());for (int m = 2; m < d; m *= 2) {// prepareF f_fft(this->begin(), this->begin() + m);f_fft.resize(2 * m), internal::butterfly(f_fft);// Step 2.a'// {F _g(m);for (int i = 0; i < m; ++i) _g[i] = f_fft[i] * g_fft[i];internal::butterfly_inv(_g);_g.erase(_g.begin(), _g.begin() + m / 2);_g.resize(m), internal::butterfly(_g);for (int i = 0; i < m; ++i) _g[i] *= g_fft[i];internal::butterfly_inv(_g);_g.resize(m / 2);_g /= T(-m) * m;g.insert(g.end(), _g.begin(), _g.begin() + m / 2);// }// Step 2.b'--d'F t(this->begin(), this->begin() + m);t.deriv_inplace();// {// Step 2.b'F r{ h_drv.begin(), h_drv.begin() + m - 1 };// Step 2.c'r.resize(m); internal::butterfly(r);for (int i = 0; i < m; ++i) r[i] *= f_fft[i];internal::butterfly_inv(r);r /= -m;// Step 2.d't += r;t.insert(t.begin(), t.back()); t.pop_back();// }// Step 2.e'if (2 * m < d) {t.resize(2 * m); internal::butterfly(t);g_fft = g; g_fft.resize(2 * m); internal::butterfly(g_fft);for (int i = 0; i < 2 * m; ++i) t[i] *= g_fft[i];internal::butterfly_inv(t);t.resize(m);t /= 2 * m;}else { // この場合分けをしても数パーセントしか速くならないF g1(g.begin() + m / 2, g.end());F s1(t.begin() + m / 2, t.end());t.resize(m / 2);g1.resize(m), internal::butterfly(g1);t.resize(m), internal::butterfly(t);s1.resize(m), internal::butterfly(s1);for (int i = 0; i < m; ++i) s1[i] = g_fft[i] * s1[i] + g1[i] * t[i];for (int i = 0; i < m; ++i) t[i] *= g_fft[i];internal::butterfly_inv(t);internal::butterfly_inv(s1);for (int i = 0; i < m / 2; ++i) t[i + m / 2] += s1[i];t /= m;}// Step 2.f'F v(this->begin() + m, this->begin() + std::min<int>(d, 2 * m)); v.resize(m);t.insert(t.begin(), m - 1, 0); t.push_back(0);t.integ_inplace();for (int i = 0; i < m; ++i) v[i] -= t[m + i];// Step 2.g'v.resize(2 * m); internal::butterfly(v);for (int i = 0; i < 2 * m; ++i) v[i] *= f_fft[i];internal::butterfly_inv(v);v.resize(m);v /= 2 * m;// Step 2.h'for (int i = 0; i < std::min(d - m, m); ++i)(*this)[m + i] = v[i];}return *this;}F exp(const int d = -1) const { return F(*this).exp_inplace(d); }// O(n log n)F &pow_inplace(const long long k, int d = -1) {int n = this->size();if (d == -1) d = n;assert(d >= 0 && k >= 0);if (k == 0) {*this = F(d);if (d > 0) (*this)[0] = 1;return *this;}int l = 0;while (l < n && (*this)[l] == 0) ++l;if (l > (d - 1) / k || l == n) return *this = F(d);T c = (*this)[l];this->erase(this->begin(), this->begin() + l);*this /= c;this->log_inplace(d - l * k);*this *= k;this->exp_inplace();*this *= c.pow(k);this->insert(this->begin(), l*k, 0);return *this;}F pow(const long long k, const int d = -1) const { return F(*this).pow_inplace(k, d); }// O(n log n)F &shift_inplace(const T c) {int n = this->size();fc = Factorial<T>(n);for (int i = 0; i < n; ++i) (*this)[i] *= fc.fac[i];reverse(this->begin(), this->end());F g(n);T cp = 1;for (int i = 0; i < n; ++i) g[i] = cp * fc.finv[i], cp *= c;this->multiply_inplace(g, n);reverse(this->begin(), this->end());for (int i = 0; i < n; ++i) (*this)[i] *= fc.finv[i];return *this;}F shift(const T c) const { return F(*this).shift_inplace(c); }F operator*(const T &g) const { return F(*this) *= g; }F operator/(const T &g) const { return F(*this) /= g; }F operator+(const F &g) const { return F(*this) += g; }F operator-(const F &g) const { return F(*this) -= g; }F operator<<(const int d) const { return F(*this) <<= d; }F operator>>(const int d) const { return F(*this) >>= d; }F operator*(std::vector<std::pair<int, T>> g) const { return F(*this) *= g; }F operator/(std::vector<std::pair<int, T>> g) const { return F(*this) /= g; }};using fps = FormalPowerSeries<mint>;using sfps = std::vector<std::pair<int, mint>>;// https://judge.yosupo.jp/problem/inv_of_formal_power_series// f(x)に対して 1/f(x)の先頭n項を求めるvoid yosupo_inv() {int n; std::cin >> n;fps a(n); std::cin >> a;std::cout << a.inv() << '\n';}// https://judge.yosupo.jp/problem/log_of_formal_power_series// f(x)に対して log(f(x))の先頭n項を求めるvoid yosupo_log() {int n; std::cin >> n;fps a(n); std::cin >> a;std::cout << a.log_inplace() << '\n';}// https://judge.yosupo.jp/problem/exp_of_formal_power_series// f(x)に対して exp(f(x))の先頭n項を求めるvoid yosupo_exp() {int n; std::cin >> n;fps a(n); std::cin >> a;std::cout << a.exp_inplace() << '\n';}// https://judge.yosupo.jp/problem/pow_of_formal_power_series// f(x)に対してf(x)^mの先頭n項を求めるvoid yosupo_pow() {int n, m; std::cin >> n >> m;fps a(n); std::cin >> a;std::cout << a.pow_inplace(m) << '\n';}// https://judge.yosupo.jp/problem/polynomial_taylor_shift// f(x)に対してf(x+c)の先頭n項を求めるvoid yosupo_shift() {int n, c; std::cin >> n >> c;fps a(n); std::cin >> a;std::cout << a.shift_inplace(c) << '\n';}// https://judge.yosupo.jp/problem/bernoulli_number// ベルヌーイ数の先頭n項を求めるvoid yosupo_bernoulli() {int n; std::cin >> n;++n;fc = Factorial<mint>(n);fps f((fc.finv).begin() + 1, (fc.finv).end());f = f.inv();for (int i = 0; i < n; ++i) f[i] *= fc.fac[i];std::cout << f << '\n';}// https://judge.yosupo.jp/problem/sharp_p_subset_sum// Π(1+x^a)の先頭t+1項を求めるvoid yosupo_count_subset_sum() {int n, t; std::cin >> n >> t;++t;std::vector<int> c(t);for (int i = 0; i < n; ++i) {int s; std::cin >> s;++c[s];}std::vector<mint> inv(t);inv[1] = 1;int p = mint::mod();for (int i = 2; i < t; ++i) inv[i] = -inv[p%i] * (p / i);fps f(t);for (int i = 0; i < t; ++i) {if (c[i] == 0) continue;for (int j = 1, d = i; d < t; ++j, d += i) {if (j & 1) f[d] += c[i] * inv[j];else f[d] -= c[i] * inv[j];}}f.exp_inplace();f.erase(f.begin());std::cout << f << '\n';}int main() {ios::sync_with_stdio(false);cin.tie(nullptr);int n, k; cin >> n >> k;vector<int>cnt(k + 1);rep(i, n) {int a; cin >> a;chmin(a, k);cnt[a]++;}// gcd周期になるvector<int>g_cnt(k + 1);rep(i, k) {int g = gcd(i, k);g_cnt[g]++;}vector<fps>f(k + 1, fps(k + 1));rep(i, k + 1) {if (i != 0)f[i] = f[i - 1];f[i][i] = com.ifact[i];}vector<fps>log_f(k + 1, fps(k + 1));rep(i, k + 1) {log_f[i] = f[i].log();}mint ans = 0;for (int p = 0; p < k + 1; ++p) {int c = g_cnt[p];if (c == 0)continue;int q = k / p;vector<int>s_cnt(p + 1);rep(i, k + 1) s_cnt[i / q] += cnt[i];mint tmp = 0;{// exp^log(f) = ffps log(p + 1);rep(i, p + 1) log += log_f[i] * s_cnt[i];log.exp_inplace();tmp += log[p];}ans += tmp * com.fact[p] * c;}ans /= k;cout << ans.val() << endl;return 0;}