結果

問題 No.1956 猫の額
ユーザー suisen
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
このコードへのチャレンジ
(要ログイン)
ファイルパターン 結果
other AC * 2 TLE * 4 MLE * 15
権限があれば一括ダウンロードができます

ソースコード

diff #
プレゼンテーションモードにする

#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 suisen
template <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 suisen
constexpr 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;
}
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