結果
問題 | No.1956 猫の額 |
ユーザー |
|
提出日時 | 2022-05-24 00:26:54 |
言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
結果 |
MLE
|
実行時間 | - |
コード長 | 15,078 bytes |
コンパイル時間 | 5,019 ms |
コンパイル使用メモリ | 174,492 KB |
最終ジャッジ日時 | 2025-01-29 14:48:01 |
ジャッジサーバーID (参考情報) |
judge3 / judge4 |
(要ログイン)
ファイルパターン | 結果 |
---|---|
other | AC * 2 TLE * 4 MLE * 15 |
ソースコード
#include <array>#include <iostream>#include <vector>#include <atcoder/modint>#include <atcoder/convolution>using mint = atcoder::modint;#include <algorithm>#include <cassert>#include <iostream>#include <vector>namespace suisen {template <typename mint>class inv_mods {public:inv_mods() {}inv_mods(int n) { ensure(n); }const mint& operator[](int i) const {ensure(i);return invs[i];}static void ensure(int n) {int sz = invs.size();if (sz < 2) invs = {0, 1}, sz = 2;if (sz < n + 1) {invs.resize(n + 1);for (int i = sz; i <= n; ++i) invs[i] = mint(mod - mod / i) * invs[mod % i];}}private:static std::vector<mint> invs;static constexpr int mod = mint::mod();};template <typename mint>std::vector<mint> inv_mods<mint>::invs{};}namespace suisen {template <typename mint>using convolution_t = std::vector<mint> (*)(const std::vector<mint> &, const std::vector<mint> &);template <typename mint>class FPS : public std::vector<mint> {public:using std::vector<mint>::vector;FPS(const std::initializer_list<mint> l) : std::vector<mint>::vector(l) {}FPS(const std::vector<mint> &v) : std::vector<mint>::vector(v) {}FPS(std::vector<mint> &&v) : std::vector<mint>::vector(std::move(v)) {}static void set_multiplication(convolution_t<mint> multiplication) {FPS<mint>::mult = multiplication;}inline const mint operator[](int n) const noexcept { return n <= deg() ? unsafe_get(n) : 0; }inline mint& operator[](int n) noexcept { ensure_deg(n); return unsafe_get(n); }inline int size() const noexcept { return std::vector<mint>::size(); }inline int deg() const noexcept { return size() - 1; }inline int normalize() {while (this->size() and this->back() == 0) this->pop_back();return deg();}inline FPS& pre_inplace(int max_deg) noexcept {if (deg() > max_deg) this->resize(std::max(0, max_deg + 1));return *this;}inline FPS pre(int max_deg) const noexcept { return FPS(*this).pre_inplace(max_deg); }inline FPS operator+() const { return FPS(*this); }FPS operator-() const {FPS f(*this);for (auto &e : f) e = mint::mod() - e;return f;}inline FPS& operator++() { ++(*this)[0]; return *this; }inline FPS& operator--() { --(*this)[0]; return *this; }inline FPS& operator+=(const mint x) { (*this)[0] += x; return *this; }inline FPS& operator-=(const mint x) { (*this)[0] -= x; return *this; }FPS& operator+=(const FPS &g) {ensure_deg(g.deg());for (int i = 0; i <= g.deg(); ++i) unsafe_get(i) += g.unsafe_get(i);return *this;}FPS& operator-=(const FPS &g) {ensure_deg(g.deg());for (int i = 0; i <= g.deg(); ++i) unsafe_get(i) -= g.unsafe_get(i);return *this;}inline FPS& operator*=(const FPS &g) { return *this = FPS<mint>::mult(*this, g); }inline FPS& operator*=( FPS &&g) { return *this = FPS<mint>::mult(*this, g); }inline FPS& operator*=(const mint x) {for (auto &e : *this) e *= x;return *this;}FPS& operator/=(FPS &&g) {const int fd = normalize(), gd = g.normalize();assert(gd >= 0);if (fd < gd) { this->clear(); return *this; }if (gd == 0) return *this *= g.unsafe_get(0).inv();static constexpr int THRESHOLD_NAIVE_POLY_QUOTIENT = 256;if (gd <= THRESHOLD_NAIVE_POLY_QUOTIENT) {*this = std::move(naive_div_inplace(std::move(g), gd).first);return *this;}std::reverse(this->begin(), this->end()), std::reverse(g.begin(), g.end());const int k = fd - gd;*this *= g.inv_inplace(k), this->resize(k + 1);std::reverse(this->begin(), this->end());return *this;}FPS& operator%=(FPS &&g) {int fd = normalize(), gd = g.normalize();assert(gd >= 0);if (fd < gd) return *this;if (gd == 0) { this->clear(); return *this; }static constexpr int THRESHOLD_NAIVE_REMAINDER = 256;if (gd <= THRESHOLD_NAIVE_REMAINDER) return naive_div_inplace(std::move(g), gd).second;*this -= g * (*this / g);return pre_inplace(gd - 1);}inline FPS& operator/=(const FPS &g) { return *this /= FPS(g); }inline FPS& operator%=(const FPS &g) { return *this %= FPS(g); }FPS& operator<<=(const int shamt) {this->insert(this->begin(), shamt, 0);return *this;}FPS& operator>>=(const int shamt) {if (shamt > size()) this->clear();else this->erase(this->begin(), this->begin() + shamt);return *this;}inline FPS operator+(FPS &&g) const { return FPS(*this) += std::move(g); }inline FPS operator-(FPS &&g) const { return FPS(*this) -= std::move(g); }inline FPS operator*(FPS &&g) const { return FPS(*this) *= std::move(g); }inline FPS operator/(FPS &&g) const { return FPS(*this) /= std::move(g); }inline FPS operator%(FPS &&g) const { return FPS(*this) %= std::move(g); }inline FPS operator+(const FPS &g) const { return FPS(*this) += g; }inline FPS operator+(const mint x) const { return FPS(*this) += x; }inline FPS operator-(const FPS &g) const { return FPS(*this) -= g; }inline FPS operator-(const mint x) const { return FPS(*this) -= x; }inline FPS operator*(const FPS &g) const { return FPS(*this) *= g; }inline FPS operator*(const mint x) const { return FPS(*this) *= x; }inline FPS operator/(const FPS &g) const { return FPS(*this) /= g; }inline FPS operator%(const FPS &g) const { return FPS(*this) %= g; }inline friend FPS operator*(const mint x, const FPS &f) { return f * x; }inline friend FPS operator*(const mint x, FPS &&f) { return f *= x; }inline FPS operator<<(const int shamt) { return FPS(*this) <<= shamt; }inline FPS operator>>(const int shamt) { return FPS(*this) >>= shamt; }friend bool operator==(const FPS &f, const FPS &g) {int n = f.size(), m = g.size();if (n < m) return g == f;for (int i = 0; i < m; ++i) if (f.unsafe_get(i) != g.unsafe_get(i)) return false;for (int i = m; i < n; ++i) if (f.unsafe_get(i) != 0) return false;return true;}FPS& diff_inplace() {if (this->size() == 0) return *this;for (int i = 1; i <= deg(); ++i) unsafe_get(i - 1) = unsafe_get(i) * i;this->pop_back();return *this;}FPS& intg_inplace() {int d = deg();ensure_deg(d + 1);for (int i = d; i >= 0; --i) unsafe_get(i + 1) = unsafe_get(i) * invs[i + 1];unsafe_get(0) = 0;return *this;}FPS& inv_inplace(const int max_deg) {FPS res { unsafe_get(0).inv() };for (int k = 1; k <= max_deg; k *= 2) {FPS tmp(this->pre(k * 2) * (res * res));res *= 2, res -= tmp.pre_inplace(2 * k);}return *this = std::move(res), pre_inplace(max_deg);}FPS& log_inplace(const int max_deg) {FPS f_inv = inv(max_deg);diff_inplace(), *this *= f_inv, pre_inplace(max_deg - 1), intg_inplace();return *this;}FPS& exp_inplace(const int max_deg) {FPS res {1};for (int k = 1; k <= max_deg; k *= 2) res *= ++(pre(k * 2) - res.log(k * 2)), res.pre_inplace(k * 2);return *this = std::move(res), pre_inplace(max_deg);}FPS& pow_inplace(const long long k, const int max_deg) {int tlz = 0;while (tlz <= deg() and unsafe_get(tlz) == 0) ++tlz;if (tlz * k > max_deg) { this->clear(); return *this; }*this >>= tlz;mint base = (*this)[0];*this *= base.inv(), log_inplace(max_deg), *this *= k, exp_inplace(max_deg), *this *= base.pow(k);return *this <<= tlz * k, pre_inplace(max_deg);}inline FPS diff() const { return FPS(*this).diff_inplace(); }inline FPS intg() const { return FPS(*this).intg_inplace(); }inline FPS inv(const int max_deg) const { return FPS(*this).inv_inplace(max_deg); }inline FPS log(const int max_deg) const { return FPS(*this).log_inplace(max_deg); }inline FPS exp(const int max_deg) const { return FPS(*this).exp_inplace(max_deg); }inline FPS pow(const long long k, const int max_deg) const { return FPS(*this).pow_inplace(k, max_deg); }mint eval(mint x) const {mint y = 0;for (int i = size() - 1; i >= 0; --i) y = y * x + unsafe_get(i);return y;}private:static inline inv_mods<mint> invs;static convolution_t<mint> mult;inline void ensure_deg(int d) { if (deg() < d) this->resize(d + 1, 0); }inline const mint& unsafe_get(int i) const { return std::vector<mint>::operator[](i); }inline mint& unsafe_get(int i) { return std::vector<mint>::operator[](i); }std::pair<FPS, FPS&> naive_div_inplace(FPS &&g, const int gd) {const int k = deg() - gd;mint head_inv = g.unsafe_get(gd).inv();FPS q(k + 1);for (int i = k; i >= 0; --i) {mint div = this->unsafe_get(i + gd) * head_inv;q.unsafe_get(i) = div;for (int j = 0; j <= gd; ++j) this->unsafe_get(i + j) -= div * g.unsafe_get(j);}return {q, pre_inplace(gd - 1)};}};template <typename mint>convolution_t<mint> FPS<mint>::mult = [](const auto &, const auto &) {std::cerr << "convolution function is not available." << std::endl;assert(false);return std::vector<mint>{};};} // namespace suisentemplate <typename mint>auto sqrt(suisen::FPS<mint> a) -> decltype(mint::mod(), suisen::FPS<mint>{}) {assert(false);}template <typename mint>auto log(suisen::FPS<mint> a) -> decltype(mint::mod(), suisen::FPS<mint>{}) {return a.log(a.deg());}template <typename mint>auto exp(suisen::FPS<mint> a) -> decltype(mint::mod(), mint()) {return a.exp(a.deg());}template <typename mint, typename T>auto pow(suisen::FPS<mint> a, T b) -> decltype(mint::mod(), mint()) {return a.pow(b, a.deg());}template <typename mint>auto inv(suisen::FPS<mint> a) -> decltype(mint::mod(), suisen::FPS<mint>{}) {return a.inv(a.deg());}namespace suisen {template <typename mint>FPS<mint> polynomial_interpolation(const std::vector<mint>& xs, const std::vector<mint>& ys) {assert(xs.size() == ys.size());int n = xs.size();std::vector<FPS<mint>> seg(2 * n), g(2 * n);for (int i = 0; i < n; ++i) seg[n + i] = FPS<mint>{ -xs[i], 1 };for (int i = n - 1; i > 0; --i) {seg[i] = seg[i * 2] * seg[i * 2 + 1];}g[1] = std::move(seg[1].diff_inplace());for (int i = 1; i < n; ++i) {int l = 2 * i, r = l + 1;g[l] = g[i] % seg[l], g[r] = g[i] % seg[r];}for (int i = 0; i < n; ++i) g[n + i] = FPS<mint>{ ys[i] / g[n + i][0] };for (int i = n - 1; i > 0; --i) {int l = 2 * i, r = l + 1;g[i] = g[l] * seg[r] + g[r] * seg[l];}return g[1];}} // namespace suisenconstexpr int N = 100000;constexpr long long MOD1 = 1107296257;constexpr long long MOD2 = 1711276033;constexpr long long MOD3 = 1224736769;constexpr long long M1M2 = MOD1 * MOD2;constexpr long long INV_M1_MOD2 = atcoder::internal::inv_gcd(MOD1, MOD2).second;constexpr long long INV_M1M2_MOD3 = atcoder::internal::inv_gcd(M1M2, MOD3).second;using mint1 = atcoder::static_modint<MOD1>;using mint2 = atcoder::static_modint<MOD2>;using mint3 = atcoder::static_modint<MOD3>;mint garner(mint1 c1, mint2 c2, mint3 c3) {const long long m1m2 = mint(M1M2).val();long long x1 = c1.val();long long x2 = (atcoder::static_modint<MOD2>(c2.val() - x1) * INV_M1_MOD2).val();long long x3 = (atcoder::static_modint<MOD3>(c3.val() - x1 - x2 * MOD1) * INV_M1M2_MOD3).val();return x1 + x2 * MOD1 + x3 * m1m2;}template <typename T>std::vector<T> solve(int n, int c, int s, std::array<int, N + 1> cnt) {suisen::FPS<T>::set_multiplication([](const auto& a, const auto& b) { return atcoder::convolution(a, b); });std::vector<std::vector<T>> binom(n + 1);for (int i = 0; i <= n; ++i) {binom[i].resize(i + 1);binom[i][0] = binom[i][i] = 1;for (int j = 1; j < i; ++j) {binom[i][j] = binom[i - 1][j - 1] + binom[i - 1][j];}}std::vector<T> ans(s + 1);const int ml = s / 3, mr = s - ml;std::array<int, 4> sep{ 0, ml, mr, s + 1 };for (int sep_i = 0; sep_i < 3; ++sep_i) {const int l = sep[sep_i], r = sep[sep_i + 1];std::vector<T> xs(n + 1);std::vector<std::vector<T>> ys(r - l, std::vector<T>(n + 1));for (int x = 0; x <= n; ++x) {xs[x] = x;std::vector<T> dp(s + 1);dp[0] = 1;for (int val = N; val >= 1; --val) if (const int p = cnt[val]; p != 0) {for (int sum = s; sum >= 0; --sum) {const int max_num = std::min(p, sum / val);T pow_x = 1;for (int num = 1; num <= max_num; ++num) {pow_x *= x;dp[sum] += dp[sum - val * num] * binom[p][num] * pow_x;}}}for (int sum = l; sum < r; ++sum) {ys[sum - l][x] = dp[sum];}}for (int sum = l; sum < r; ++sum) {ans[sum] = suisen::polynomial_interpolation(xs, ys[sum - l])[c];}}return ans;}int main() {int n, m, c;std::cin >> n >> m >> c;mint::set_mod(m);int s = 0;std::array<int, N + 1> cnt{};for (int i = 0; i < n; ++i) {int e;std::cin >> e;s += e;++cnt[e];}auto ans1 = solve<mint1>(n, c, s, cnt);auto ans2 = solve<mint2>(n, c, s, cnt);auto ans3 = solve<mint3>(n, c, s, cnt);for (int sum = 1; sum <= s; ++sum) {std::cout << garner(ans1[sum], ans2[sum], ans3[sum]).val() << " \n"[s == sum];}return 0;}