結果

問題 No.2959 Dolls' Tea Party
ユーザー KumaTachiRen
提出日時 2024-11-08 22:34:45
言語 C++23
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 918 ms / 3,000 ms
コード長 12,468 bytes
コンパイル時間 7,797 ms
コンパイル使用メモリ 346,204 KB
実行使用メモリ 13,568 KB
最終ジャッジ日時 2024-11-08 22:35:16
合計ジャッジ時間 25,335 ms
ジャッジサーバーID
(参考情報)
judge4 / judge5
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
sample AC * 4
other AC * 33
権限があれば一括ダウンロードができます
コンパイルメッセージ
In file included from /home/linuxbrew/.linuxbrew/Cellar/gcc@12/12.3.0/include/c++/12/x86_64-pc-linux-gnu/bits/c++allocator.h:33,
                 from /home/linuxbrew/.linuxbrew/Cellar/gcc@12/12.3.0/include/c++/12/bits/allocator.h:46,
                 from /home/linuxbrew/.linuxbrew/Cellar/gcc@12/12.3.0/include/c++/12/string:41,
                 from /home/linuxbrew/.linuxbrew/Cellar/gcc@12/12.3.0/include/c++/12/bits/locale_classes.h:40,
                 from /home/linuxbrew/.linuxbrew/Cellar/gcc@12/12.3.0/include/c++/12/bits/ios_base.h:41,
                 from /home/linuxbrew/.linuxbrew/Cellar/gcc@12/12.3.0/include/c++/12/ios:42,
                 from /home/linuxbrew/.linuxbrew/Cellar/gcc@12/12.3.0/include/c++/12/istream:38,
                 from /home/linuxbrew/.linuxbrew/Cellar/gcc@12/12.3.0/include/c++/12/sstream:38,
                 from /home/linuxbrew/.linuxbrew/Cellar/gcc@12/12.3.0/include/c++/12/complex:45,
                 from /home/linuxbrew/.linuxbrew/Cellar/gcc@12/12.3.0/include/c++/12/ccomplex:39,
                 from /home/linuxbrew/.linuxbrew/Cellar/gcc@12/12.3.0/include/c++/12/x86_64-pc-linux-gnu/bits/stdc++.h:54,
                 from main.cpp:3:
In member function 'void std::__new_allocator<_Tp>::deallocate(_Tp*, size_type) [with _Tp = atcoder::static_modint<998244353>]',
    inlined from 'constexpr void std::allocator< <template-parameter-1-1> >::deallocate(_Tp*, std::size_t) [with _Tp = atcoder::static_modint<998244353>]' at /home/linuxbrew/.linuxbrew/Cellar/gcc@12/12.3.0/include/c++/12/bits/allocator.h:200:35,
    inlined from 'static constexpr void std::allocator_traits<std::allocator<_CharT> >::deallocate(allocator_type&, pointer, size_type) [with _Tp = atcoder::static_modint<998244353>]' at /home/linuxbrew/.linuxbrew/Cellar/gcc@12/12.3.0/include/c++/12/bits/alloc_traits.h:496:23,
    inlined from 'constexpr void std::_Vector_base<_Tp, _Alloc>::_M_deallocate(pointer, std::size_t) [with _Tp = atcoder::static_modint<998244353>; _Alloc = std:

ソースコード

diff #
プレゼンテーションモードにする

#pragma GCC optimize("O3")
#include <bits/stdc++.h>
using namespace std;
#if __has_include(<atcoder/all>)
#include <atcoder/all>
using namespace atcoder;
using mint = modint998244353;
using vm = vector<mint>;
using vvm = vector<vm>;
inline ostream &operator<<(ostream &os, const mint x)
{
return os << x.val();
};
inline istream &operator>>(istream &is, mint &x)
{
long long v;
is >> v;
x = v;
return is;
};
#endif
struct Fast
{
Fast()
{
std::cin.tie(nullptr);
ios::sync_with_stdio(false);
cout << setprecision(10);
}
} fast;
#define all(a) (a).begin(), (a).end()
#define contains(a, x) ((a).find(x) != (a).end())
#define rep(i, a, b) for (int i = (a); i < (int)(b); i++)
#define rrep(i, a, b) for (int i = (int)(b) - 1; i >= (a); i--)
#define YN(b) cout << ((b) ? "YES" : "NO") << "\n";
#define Yn(b) cout << ((b) ? "Yes" : "No") << "\n";
#define yn(b) cout << ((b) ? "yes" : "no") << "\n";
template <class T>
inline bool chmin(T &a, T b)
{
if (a > b)
{
a = b;
return true;
}
return false;
}
template <class T>
inline bool chmax(T &a, T b)
{
if (a < b)
{
a = b;
return true;
}
return false;
}
using ll = long long;
using vb = vector<bool>;
using vvb = vector<vb>;
using vi = vector<int>;
using vvi = vector<vi>;
using vl = vector<ll>;
using vvl = vector<vl>;
template <typename T1, typename T2>
ostream &operator<<(ostream &os, pair<T1, T2> &p)
{
os << "(" << p.first << "," << p.second << ")";
return os;
}
template <typename T>
ostream &operator<<(ostream &os, vector<T> &vec)
{
for (int i = 0; i < (int)vec.size(); i++)
{
os << vec[i] << (i + 1 == (int)vec.size() ? "" : " ");
}
return os;
}
template <typename T>
istream &operator>>(istream &is, vector<T> &vec)
{
for (int i = 0; i < (int)vec.size(); i++)
is >> vec[i];
return is;
}
ll floor(ll a, ll b) { return a >= 0 ? a / b : (a + 1) / b - 1; }
ll ceil(ll a, ll b) { return a > 0 ? (a - 1) / b + 1 : a / b; }
template <typename mint>
struct FormalPowerSeries : vector<mint>
{
using vector<mint>::vector;
using FPS = FormalPowerSeries;
FPS &operator+=(const FPS &r)
{
if (r.size() > this->size())
this->resize(r.size());
for (int i = 0; i < (int)r.size(); i++)
(*this)[i] += r[i];
return *this;
}
FPS &operator+=(const mint &r)
{
if (this->empty())
this->resize(1);
(*this)[0] += r;
return *this;
}
FPS &operator-=(const FPS &r)
{
if (r.size() > this->size())
this->resize(r.size());
for (int i = 0; i < (int)r.size(); i++)
(*this)[i] -= r[i];
return *this;
}
FPS &operator-=(const mint &r)
{
if (this->empty())
this->resize(1);
(*this)[0] -= r;
return *this;
}
FPS &operator*=(const mint &v)
{
for (int k = 0; k < (int)this->size(); k++)
(*this)[k] *= v;
return *this;
}
FPS &operator*=(const FPS &r)
{
auto c = atcoder::convolution<mint>((*this), r);
this->resize(c.size());
for (int i = 0; i < (int)c.size(); i++)
(*this)[i] = c[i];
return *this;
}
FPS &operator/=(const FPS &r)
{
if (this->size() < r.size())
{
this->clear();
return *this;
}
int n = this->size() - r.size() + 1;
if ((int)r.size() <= 64)
{
FPS f(*this), g(r);
g.shrink();
mint coeff = g.at(g.size() - 1).inv();
for (auto &x : g)
x *= coeff;
int deg = (int)f.size() - (int)g.size() + 1;
int gs = g.size();
FPS quo(deg);
for (int i = deg - 1; i >= 0; i--)
{
quo[i] = f[i + gs - 1];
for (int j = 0; j < gs; j++)
f[i + j] -= quo[i] * g[j];
}
*this = quo * coeff;
this->resize(n, mint(0));
return *this;
}
return *this = ((*this).rev().pre(n) * r.rev().inv(n)).pre(n).rev();
}
FPS &operator%=(const FPS &r)
{
*this -= *this / r * r;
shrink();
return *this;
}
FPS operator+(const FPS &r) const { return FPS(*this) += r; }
FPS operator+(const mint &v) const { return FPS(*this) += v; }
FPS operator-(const FPS &r) const { return FPS(*this) -= r; }
FPS operator-(const mint &v) const { return FPS(*this) -= v; }
FPS operator*(const FPS &r) const { return FPS(*this) *= r; }
FPS operator*(const mint &v) const { return FPS(*this) *= v; }
FPS operator/(const FPS &r) const { return FPS(*this) /= r; }
FPS operator%(const FPS &r) const { return FPS(*this) %= r; }
FPS operator-() const
{
FPS ret(this->size());
for (int i = 0; i < (int)this->size(); i++)
ret[i] = -(*this)[i];
return ret;
}
void shrink()
{
while (this->size() && this->back() == mint(0))
this->pop_back();
}
FPS rev() const
{
FPS ret(*this);
reverse(begin(ret), end(ret));
return ret;
}
FPS dot(FPS r) const
{
FPS ret(min(this->size(), r.size()));
for (int i = 0; i < (int)ret.size(); i++)
ret[i] = (*this)[i] * r[i];
return ret;
}
FPS pre(int sz) const
{
return FPS(begin(*this), begin(*this) + min((int)this->size(), sz));
}
FPS operator>>=(int sz)
{
assert(sz >= 0);
if ((int)this->size() <= sz)
return {};
this->erase(this->begin(), this->begin() + sz);
return *this;
}
FPS operator>>(int sz) const
{
if ((int)this->size() <= sz)
return {};
FPS ret(*this);
ret.erase(ret.begin(), ret.begin() + sz);
return ret;
}
FPS operator<<=(int sz)
{
assert(sz >= 0);
this->insert(this->begin(), sz, mint(0));
return *this;
}
FPS operator<<(int sz) const
{
FPS ret(*this);
ret.insert(ret.begin(), sz, mint(0));
return ret;
}
FPS diff() const
{
const int n = (int)this->size();
FPS ret(max(0, n - 1));
mint one(1), coeff(1);
for (int i = 1; i < n; i++)
{
ret[i - 1] = (*this)[i] * coeff;
coeff += one;
}
return ret;
}
FPS integral() const
{
const int n = (int)this->size();
FPS ret(n + 1);
ret[0] = mint(0);
if (n > 0)
ret[1] = mint(1);
auto mod = mint::mod();
for (int i = 2; i <= n; i++)
ret[i] = (-ret[mod % i]) * (mod / i);
for (int i = 0; i < n; i++)
ret[i + 1] *= (*this)[i];
return ret;
}
mint eval(mint x) const
{
mint r = 0, w = 1;
for (auto &v : *this)
r += w * v, w *= x;
return r;
}
FPS log(int deg = -1) const
{
assert((*this)[0] == mint(1));
if (deg == -1)
deg = (int)this->size();
return (this->diff() * this->inv(deg)).pre(deg - 1).integral();
}
FPS pow(int64_t k, int deg = -1) const
{
const int n = (int)this->size();
if (deg == -1)
deg = n;
if (k == 0)
{
FPS ret(deg);
if (deg)
ret[0] = 1;
return ret;
}
for (int i = 0; i < n; i++)
{
if ((*this)[i] != mint(0))
{
mint rev = mint(1) / (*this)[i];
FPS ret = (((*this * rev) >> i).log(deg) * k).exp(deg);
ret *= (*this)[i].pow(k);
ret = (ret << (i * k)).pre(deg);
if ((int)ret.size() < deg)
ret.resize(deg, mint(0));
return ret;
}
if (__int128_t(i + 1) * k >= deg)
return FPS(deg, mint(0));
}
return FPS(deg, mint(0));
}
FPS inv(int deg = -1) const
{
assert((*this)[0] != mint(0));
if (deg == -1)
deg = (*this).size();
FPS ret{mint(1) / (*this)[0]};
for (int i = 1; i < deg; i <<= 1)
ret = (ret + ret - ret * ret * (*this).pre(i << 1)).pre(i << 1);
return ret.pre(deg);
}
FPS exp(int deg = -1) const
{
assert((*this)[0] == mint(0));
if (deg == -1)
deg = (*this).size();
FPS ret{mint(1)};
for (int i = 1; i < deg; i <<= 1)
ret = (ret * ((*this).pre(i << 1) - ret.log(i << 1) + 1)).pre(i << 1);
return ret.pre(deg);
}
};
using fps = FormalPowerSeries<mint>;
template <typename mint>
struct factorial
{
vector<mint> f, g, h;
factorial(int MAX = 0)
{
f.resize(1, mint{1});
g.resize(1, mint{1});
h.resize(1, mint{1});
if (MAX > 0)
extend(MAX + 1);
}
void extend(int m = -1)
{
int n = f.size();
if (m == -1)
m = n * 2;
if (n >= m)
return;
f.resize(m);
g.resize(m);
h.resize(m);
for (int i = n; i < m; i++)
f[i] = f[i - 1] * mint(i);
g[m - 1] = f[m - 1].inv();
h[m - 1] = g[m - 1] * f[m - 2];
for (int i = m - 2; i >= n; i--)
{
g[i] = g[i + 1] * mint(i + 1);
h[i] = g[i] * f[i - 1];
}
}
mint fact(int i)
{
if (i < 0)
return mint(0);
while (i >= (int)f.size())
extend();
return f[i];
}
mint fact_inv(int i)
{
if (i < 0)
return mint(0);
while (i >= (int)g.size())
extend();
return g[i];
}
mint inv(int i)
{
if (i < 0)
return -inv(-i);
while (i >= (int)h.size())
extend();
return h[i];
}
mint binom(int n, int r)
{
if (n < 0 || n < r || r < 0)
return mint(0);
return fact(n) * fact_inv(n - r) * fact_inv(r);
}
mint multinom(const vector<int> &r)
{
int n = 0;
for (auto &x : r)
{
if (x < 0)
return mint(0);
n += x;
}
mint res = fact(n);
for (auto &x : r)
res *= fact_inv(x);
return res;
}
mint binom_naive(int n, int r)
{
if (n < 0 || n < r || r < 0)
return mint(0);
mint ret = mint(1);
r = min(r, n - r);
for (int i = 1; i <= r; ++i)
ret *= inv(i) * (n--);
return ret;
}
mint P(int n, int r)
{
if (n < 0 || n < r || r < 0)
return mint(0);
return fact(n) * fact_inv(n - r);
}
mint H(int n, int r)
{
if (n < 0 || r < 0)
return mint(0);
return r == 0 ? 1 : binom(n + r - 1, r);
}
};
int gcd(int a, int b) { return b == 0 ? a : gcd(b, a % b); }
void solve()
{
int n, k;
cin >> n >> k;
vi a(n);
rep(i, 0, n) cin >> a[i];
vi b(k + 1, 0);
for (auto v : a)
b[min(v, k)]++;
vi c(k + 1, 0);
rep(i, 0, k) c[gcd(i, k)]++;
factorial<mint> fact(100000);
map<int, vm> log_memo;
mint ans = 0;
for (int w = k; w > 0; w--)
{
if (c[w] == 0) continue;
int d = k / w;
int s = 0;
vi cnt(w + 1, 0);
for (int i = 0; i <= k; i++)
{
if (b[i] == 0) continue;
int m = min(w, i / d);
s += m * b[i];
cnt[m] += b[i];
}
if (s < w) continue;
fps f(w + 1, 0);
for (int i = 1; i <= w; i++)
{
if (cnt[i] == 0) continue;
if (!contains(log_memo, i))
{
fps g(i + 1, 0);
rep(j, 0, i + 1) g[j] = fact.fact_inv(j);
log_memo[i] = g.log(w + 1);
}
{
auto g = log_memo[i];
for (int j = 0; j <= w; j++)
f[j] += g[j] * cnt[i];
}
}
f = f.exp();
ans += f[w] * fact.fact(w) * c[w];
}
ans *= fact.inv(k);
cout << ans.val() << "\n";
}
int main()
{
int t = 1;
// cin >> t;
while (t--)
solve();
}
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