結果
| 問題 |
No.2688 Cell Proliferation (Hard)
|
| コンテスト | |
| ユーザー |
 momohara
|
| 提出日時 | 2024-04-13 16:19:32 |
| 言語 | C++23 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 639 ms / 4,000 ms |
| コード長 | 21,812 bytes |
| コンパイル時間 | 5,788 ms |
| コンパイル使用メモリ | 328,236 KB |
| 実行使用メモリ | 18,572 KB |
| 最終ジャッジ日時 | 2024-10-03 00:13:20 |
| 合計ジャッジ時間 | 17,253 ms |
|
ジャッジサーバーID （参考情報） |
judge1 / judge5 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 3 |
| other | AC * 26 |
ソースコード
#include <atcoder/all>
#include <bits/stdc++.h>
using namespace std;
using namespace atcoder;
using ll = long long;
using ull = unsigned long long;
using ld = long double;
using P = pair<ll, ll>;
using tp = tuple<ll, ll, ll>;
template <class T>
using vec = vector<T>;
template <class T>
using vvec = vector<vec<T>>;
#define all(hoge) (hoge).begin(), (hoge).end()
#define en '\n'
#define rep(i, m, n) for(ll i = (ll)(m); i < (ll)(n); ++i)
#define rep2(i, m, n) for(ll i = (ll)(n)-1; i >= (ll)(m); --i)
#define REP(i, n) rep(i, 0, n)
#define REP2(i, n) rep2(i, 0, n)
constexpr long long INF = 1LL << 60;
constexpr int INF_INT = 1 << 25;
// constexpr long long MOD = (ll)1e9 + 7;
constexpr long long MOD = 998244353LL;
static const ld pi = 3.141592653589793L;
#pragma GCC target("avx2")
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
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;
}
struct Edge {
int to, rev;
ll cap;
Edge(int _to, int _rev, ll _cap) : to(_to), rev(_rev), cap(_cap) {}
};
typedef vector<Edge> Edges;
typedef vector<Edges> Graph;
void add_edge(Graph &G, int from, int to, ll cap, bool revFlag, ll revCap) {
G[from].push_back(Edge(to, (int)G[to].size(), cap));
if(revFlag)
G[to].push_back(Edge(from, (int)G[from].size() - 1, revCap));
}
template <int mod>
struct ModInt {
int x;
ModInt() : x(0) {}
ModInt(int64_t y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {}
ModInt &operator+=(const ModInt &p) {
if((x += p.x) >= mod)
x -= mod;
return *this;
}
ModInt &operator-=(const ModInt &p) {
if((x += mod - p.x) >= mod)
x -= mod;
return *this;
}
ModInt &operator*=(const ModInt &p) {
x = (int)(1LL * x * p.x % mod);
return *this;
}
ModInt &operator/=(const ModInt &p) {
*this *= p.inverse();
return *this;
}
ModInt operator-() const { return ModInt(-x); }
ModInt operator+() const { return ModInt(*this); }
ModInt operator+(const ModInt &p) const { return ModInt(*this) += p; }
ModInt operator-(const ModInt &p) const { return ModInt(*this) -= p; }
ModInt operator*(const ModInt &p) const { return ModInt(*this) *= p; }
ModInt operator/(const ModInt &p) const { return ModInt(*this) /= p; }
bool operator==(const ModInt &p) const { return x == p.x; }
bool operator!=(const ModInt &p) const { return x != p.x; }
ModInt inverse() const {
int a = x, b = mod, u = 1, v = 0, t;
while(b > 0) {
t = a / b;
swap(a -= t * b, b);
swap(u -= t * v, v);
}
return ModInt(u);
}
ModInt pow(int64_t n) const {
ModInt ret(1), mul(x);
while(n > 0) {
if(n & 1)
ret *= mul;
mul *= mul;
n >>= 1;
}
return ret;
}
friend ostream &operator<<(ostream &os, const ModInt &p) { return os << p.x; }
friend istream &operator>>(istream &is, ModInt &a) {
int64_t t;
is >> t;
a = ModInt<mod>(t);
return (is);
}
int get() const { return x; }
static constexpr int get_mod() { return mod; }
};
using mint = ModInt<MOD>;
template <typename mint>
struct NTT {
static constexpr uint32_t get_pr() {
uint32_t _mod = mint::get_mod();
using u64 = uint64_t;
u64 ds[32] = {};
int idx = 0;
u64 m = _mod - 1;
for(u64 i = 2; i * i <= m; ++i) {
if(m % i == 0) {
ds[idx++] = i;
while(m % i == 0)
m /= i;
}
}
if(m != 1)
ds[idx++] = m;
uint32_t _pr = 2;
while(1) {
int flg = 1;
for(int i = 0; i < idx; ++i) {
u64 a = _pr, b = (_mod - 1) / ds[i], r = 1;
while(b) {
if(b & 1)
r = r * a % _mod;
a = a * a % _mod;
b >>= 1;
}
if(r == 1) {
flg = 0;
break;
}
}
if(flg == 1)
break;
++_pr;
}
return _pr;
};
static constexpr uint32_t mod = mint::get_mod();
static constexpr uint32_t pr = get_pr();
static constexpr int level = __builtin_ctzll(mod - 1);
mint dw[level], dy[level];
void setwy(int k) {
mint w[level], y[level];
w[k - 1] = mint(pr).pow((mod - 1) / (1 << k));
y[k - 1] = w[k - 1].inverse();
for(int i = k - 2; i > 0; --i)
w[i] = w[i + 1] * w[i + 1], y[i] = y[i + 1] * y[i + 1];
dw[1] = w[1], dy[1] = y[1], dw[2] = w[2], dy[2] = y[2];
for(int i = 3; i < k; ++i) {
dw[i] = dw[i - 1] * y[i - 2] * w[i];
dy[i] = dy[i - 1] * w[i - 2] * y[i];
}
}
NTT() { setwy(level); }
void fft4(vector<mint> &a, int k) {
if((int)a.size() <= 1)
return;
if(k == 1) {
mint a1 = a[1];
a[1] = a[0] - a[1];
a[0] = a[0] + a1;
return;
}
if(k & 1) {
int v = 1 << (k - 1);
for(int j = 0; j < v; ++j) {
mint ajv = a[j + v];
a[j + v] = a[j] - ajv;
a[j] += ajv;
}
}
int u = 1 << (2 + (k & 1));
int v = 1 << (k - 2 - (k & 1));
mint one = mint(1);
mint imag = dw[1];
while(v) {
// jh = 0
{
int j0 = 0;
int j1 = v;
int j2 = j1 + v;
int j3 = j2 + v;
for(; j0 < v; ++j0, ++j1, ++j2, ++j3) {
mint t0 = a[j0], t1 = a[j1], t2 = a[j2], t3 = a[j3];
mint t0p2 = t0 + t2, t1p3 = t1 + t3;
mint t0m2 = t0 - t2, t1m3 = (t1 - t3) * imag;
a[j0] = t0p2 + t1p3, a[j1] = t0p2 - t1p3;
a[j2] = t0m2 + t1m3, a[j3] = t0m2 - t1m3;
}
}
// jh >= 1
mint ww = one, xx = one * dw[2], wx = one;
for(int jh = 4; jh < u;) {
ww = xx * xx, wx = ww * xx;
int j0 = jh * v;
int je = j0 + v;
int j2 = je + v;
for(; j0 < je; ++j0, ++j2) {
mint t0 = a[j0], t1 = a[j0 + v] * xx, t2 = a[j2] * ww,
t3 = a[j2 + v] * wx;
mint t0p2 = t0 + t2, t1p3 = t1 + t3;
mint t0m2 = t0 - t2, t1m3 = (t1 - t3) * imag;
a[j0] = t0p2 + t1p3, a[j0 + v] = t0p2 - t1p3;
a[j2] = t0m2 + t1m3, a[j2 + v] = t0m2 - t1m3;
}
xx *= dw[__builtin_ctzll((jh += 4))];
}
u <<= 2;
v >>= 2;
}
}
void ifft4(vector<mint> &a, int k) {
if((int)a.size() <= 1)
return;
if(k == 1) {
mint a1 = a[1];
a[1] = a[0] - a[1];
a[0] = a[0] + a1;
return;
}
int u = 1 << (k - 2);
int v = 1;
mint one = mint(1);
mint imag = dy[1];
while(u) {
// jh = 0
{
int j0 = 0;
int j1 = v;
int j2 = v + v;
int j3 = j2 + v;
for(; j0 < v; ++j0, ++j1, ++j2, ++j3) {
mint t0 = a[j0], t1 = a[j1], t2 = a[j2], t3 = a[j3];
mint t0p1 = t0 + t1, t2p3 = t2 + t3;
mint t0m1 = t0 - t1, t2m3 = (t2 - t3) * imag;
a[j0] = t0p1 + t2p3, a[j2] = t0p1 - t2p3;
a[j1] = t0m1 + t2m3, a[j3] = t0m1 - t2m3;
}
}
// jh >= 1
mint ww = one, xx = one * dy[2], yy = one;
u <<= 2;
for(int jh = 4; jh < u;) {
ww = xx * xx, yy = xx * imag;
int j0 = jh * v;
int je = j0 + v;
int j2 = je + v;
for(; j0 < je; ++j0, ++j2) {
mint t0 = a[j0], t1 = a[j0 + v], t2 = a[j2], t3 = a[j2 + v];
mint t0p1 = t0 + t1, t2p3 = t2 + t3;
mint t0m1 = (t0 - t1) * xx, t2m3 = (t2 - t3) * yy;
a[j0] = t0p1 + t2p3, a[j2] = (t0p1 - t2p3) * ww;
a[j0 + v] = t0m1 + t2m3, a[j2 + v] = (t0m1 - t2m3) * ww;
}
xx *= dy[__builtin_ctzll(jh += 4)];
}
u >>= 4;
v <<= 2;
}
if(k & 1) {
u = 1 << (k - 1);
for(int j = 0; j < u; ++j) {
mint ajv = a[j] - a[j + u];
a[j] += a[j + u];
a[j + u] = ajv;
}
}
}
void ntt(vector<mint> &a) {
if((int)a.size() <= 1)
return;
fft4(a, __builtin_ctz(a.size()));
}
void intt(vector<mint> &a) {
if((int)a.size() <= 1)
return;
ifft4(a, __builtin_ctz(a.size()));
mint iv = mint(a.size()).inverse();
for(auto &x : a)
x *= iv;
}
vector<mint> multiply(const vector<mint> &a, const vector<mint> &b) {
int l = a.size() + b.size() - 1;
if(min<int>(a.size(), b.size()) <= 40) {
vector<mint> s(l);
for(int i = 0; i < (int)a.size(); ++i)
for(int j = 0; j < (int)b.size(); ++j)
s[i + j] += a[i] * b[j];
return s;
}
int k = 2, M = 4;
while(M < l)
M <<= 1, ++k;
setwy(k);
vector<mint> s(M);
for(int i = 0; i < (int)a.size(); ++i)
s[i] = a[i];
fft4(s, k);
if(a.size() == b.size() && a == b) {
for(int i = 0; i < M; ++i)
s[i] *= s[i];
} else {
vector<mint> t(M);
for(int i = 0; i < (int)b.size(); ++i)
t[i] = b[i];
fft4(t, k);
for(int i = 0; i < M; ++i)
s[i] *= t[i];
}
ifft4(s, k);
s.resize(l);
mint invm = mint(M).inverse();
for(int i = 0; i < l; ++i)
s[i] *= invm;
return s;
}
void ntt_doubling(vector<mint> &a) {
int M = (int)a.size();
auto b = a;
intt(b);
mint r = 1, zeta = mint(pr).pow((mint::get_mod() - 1) / (M << 1));
for(int i = 0; i < M; i++)
b[i] *= r, r *= zeta;
ntt(b);
copy(begin(b), end(b), back_inserter(a));
}
};
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) {
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.back().inverse();
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;
}
// 前 sz 項を取ってくる。sz に足りない項は 0 埋めする
FPS pre(int sz) const {
FPS ret(begin(*this), begin(*this) + min((int)this->size(), sz));
if((int)ret.size() < sz)
ret.resize(sz);
return ret;
}
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) 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::get_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).empty() && (*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));
}
static void *ntt_ptr;
static void set_fft();
FPS &operator*=(const FPS &r);
void ntt();
void intt();
void ntt_doubling();
static int ntt_pr();
FPS inv(int deg = -1) const;
FPS exp(int deg = -1) const;
};
template <typename mint>
void *FormalPowerSeries<mint>::ntt_ptr = nullptr;
template <typename mint>
void FormalPowerSeries<mint>::set_fft() {
if(!ntt_ptr)
ntt_ptr = new NTT<mint>;
}
template <typename mint>
FormalPowerSeries<mint> &FormalPowerSeries<mint>::operator*=(
const FormalPowerSeries<mint> &r) {
if(this->empty() || r.empty()) {
this->clear();
return *this;
}
set_fft();
auto ret = static_cast<NTT<mint> *>(ntt_ptr)->multiply(*this, r);
return *this = FormalPowerSeries<mint>(ret.begin(), ret.end());
}
template <typename mint>
void FormalPowerSeries<mint>::ntt() {
set_fft();
static_cast<NTT<mint> *>(ntt_ptr)->ntt(*this);
}
template <typename mint>
void FormalPowerSeries<mint>::intt() {
set_fft();
static_cast<NTT<mint> *>(ntt_ptr)->intt(*this);
}
template <typename mint>
void FormalPowerSeries<mint>::ntt_doubling() {
set_fft();
static_cast<NTT<mint> *>(ntt_ptr)->ntt_doubling(*this);
}
template <typename mint>
int FormalPowerSeries<mint>::ntt_pr() {
set_fft();
return static_cast<NTT<mint> *>(ntt_ptr)->pr;
}
template <typename mint>
FormalPowerSeries<mint> FormalPowerSeries<mint>::inv(int deg) const {
assert((*this)[0] != mint(0));
if(deg == -1)
deg = (int)this->size();
FormalPowerSeries<mint> res(deg);
res[0] = {mint(1) / (*this)[0]};
for(int d = 1; d < deg; d <<= 1) {
FormalPowerSeries<mint> f(2 * d), g(2 * d);
for(int j = 0; j < min((int)this->size(), 2 * d); j++)
f[j] = (*this)[j];
for(int j = 0; j < d; j++)
g[j] = res[j];
f.ntt();
g.ntt();
for(int j = 0; j < 2 * d; j++)
f[j] *= g[j];
f.intt();
for(int j = 0; j < d; j++)
f[j] = 0;
f.ntt();
for(int j = 0; j < 2 * d; j++)
f[j] *= g[j];
f.intt();
for(int j = d; j < min(2 * d, deg); j++)
res[j] = -f[j];
}
return res.pre(deg);
}
template <typename mint>
FormalPowerSeries<mint> FormalPowerSeries<mint>::exp(int deg) const {
using fps = FormalPowerSeries<mint>;
assert((*this).size() == 0 || (*this)[0] == mint(0));
if(deg == -1)
deg = this->size();
fps inv;
inv.reserve(deg + 1);
inv.push_back(mint(0));
inv.push_back(mint(1));
auto inplace_integral = [&](fps &F) -> void {
const int n = (int)F.size();
auto mod = mint::get_mod();
while((int)inv.size() <= n) {
int i = inv.size();
inv.push_back((-inv[mod % i]) * (mod / i));
}
F.insert(begin(F), mint(0));
for(int i = 1; i <= n; i++)
F[i] *= inv[i];
};
auto inplace_diff = [](fps &F) -> void {
if(F.empty())
return;
F.erase(begin(F));
mint coeff = 1, one = 1;
for(int i = 0; i < (int)F.size(); i++) {
F[i] *= coeff;
coeff += one;
}
};
fps b{1, 1 < (int)this->size() ? (*this)[1] : 0}, c{1}, z1, z2{1, 1};
for(int m = 2; m < deg; m *= 2) {
auto y = b;
y.resize(2 * m);
y.ntt();
z1 = z2;
fps z(m);
for(int i = 0; i < m; ++i)
z[i] = y[i] * z1[i];
z.intt();
fill(begin(z), begin(z) + m / 2, mint(0));
z.ntt();
for(int i = 0; i < m; ++i)
z[i] *= -z1[i];
z.intt();
c.insert(end(c), begin(z) + m / 2, end(z));
z2 = c;
z2.resize(2 * m);
z2.ntt();
fps x(begin(*this), begin(*this) + min<int>(this->size(), m));
x.resize(m);
inplace_diff(x);
x.push_back(mint(0));
x.ntt();
for(int i = 0; i < m; ++i)
x[i] *= y[i];
x.intt();
x -= b.diff();
x.resize(2 * m);
for(int i = 0; i < m - 1; ++i)
x[m + i] = x[i], x[i] = mint(0);
x.ntt();
for(int i = 0; i < 2 * m; ++i)
x[i] *= z2[i];
x.intt();
x.pop_back();
inplace_integral(x);
for(int i = m; i < min<int>(this->size(), 2 * m); ++i)
x[i] += (*this)[i];
fill(begin(x), begin(x) + m, mint(0));
x.ntt();
for(int i = 0; i < 2 * m; ++i)
x[i] *= y[i];
x.intt();
b.insert(end(b), begin(x) + m, end(x));
}
return fps{begin(b), begin(b) + deg};
}
void solve() {
ll p1, p2, q1, q2, t;
cin >> p1 >> p2 >> q1 >> q2 >> t;
mint p = mint(p1) / p2;
mint q = mint(q1) / q2;
FormalPowerSeries<mint> g(t + 1, mint(0));
g[0] = 1;
rep(i, 1, t + 1) {
g[i] -= p * q.pow(i * (i - 1) / 2);
}
FormalPowerSeries<mint> f = g.inv();
mint ans = 0;
REP(i, t + 1) {
ans += f[i] * q.pow((t - i) * (t - i + 1) / 2);
}
cout << ans << en;
}
int main() {
ios::sync_with_stdio(false);
cin.tie(0);
cout.tie(0);
// cout << fixed << setprecision(10);
// ll t;
// cin >> t;
// REP(i, t - 1) {
// solve();
// }
solve();
return 0;
}