結果

問題 No.2305 [Cherry 5th Tune N] Until That Day...
ユーザー 👑 emthrmemthrm
提出日時 2023-05-20 00:00:02
言語 C++23
(gcc 13.3.0 + boost 1.87.0)
結果
WA  
実行時間 -
コード長 18,692 bytes
コンパイル時間 5,648 ms
コンパイル使用メモリ 319,440 KB
実行使用メモリ 6,824 KB
最終ジャッジ日時 2024-12-20 03:09:09
合計ジャッジ時間 14,320 ms
ジャッジサーバーID
(参考情報)
judge5 / judge3
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ファイルパターン 結果
other AC * 1 WA * 20
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ソースコード

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プレゼンテーションモードにする

#include <bits/stdc++.h>
using namespace std;
#define FOR(i,m,n) for(int i=(m);i<(n);++i)
#define REP(i,n) FOR(i,0,n)
#define ALL(v) (v).begin(),(v).end()
using ll = long long;
constexpr int INF = 0x3f3f3f3f;
constexpr long long LINF = 0x3f3f3f3f3f3f3f3fLL;
constexpr double EPS = 1e-8;
constexpr int MOD = 998244353;
// constexpr int MOD = 1000000007;
constexpr int DY4[]{1, 0, -1, 0}, DX4[]{0, -1, 0, 1};
constexpr int DY8[]{1, 1, 0, -1, -1, -1, 0, 1};
constexpr int DX8[]{0, -1, -1, -1, 0, 1, 1, 1};
template <typename T, typename U>
inline bool chmax(T& a, U b) { return a < b ? (a = b, true) : false; }
template <typename T, typename U>
inline bool chmin(T& a, U b) { return a > b ? (a = b, true) : false; }
struct IOSetup {
IOSetup() {
std::cin.tie(nullptr);
std::ios_base::sync_with_stdio(false);
std::cout << fixed << setprecision(20);
}
} iosetup;
template <unsigned int M>
struct MInt {
unsigned int v;
constexpr MInt() : v(0) {}
constexpr MInt(const long long x) : v(x >= 0 ? x % M : x % M + M) {}
static constexpr MInt raw(const int x) {
MInt x_;
x_.v = x;
return x_;
}
static constexpr int get_mod() { return M; }
static constexpr void set_mod(const int divisor) {
assert(std::cmp_equal(divisor, M));
}
static void init(const int x) {
inv<true>(x);
fact(x);
fact_inv(x);
}
template <bool MEMOIZES = false>
static MInt inv(const int n) {
// assert(0 <= n && n < M && std::gcd(n, M) == 1);
static std::vector<MInt> inverse{0, 1};
const int prev = inverse.size();
if (n < prev) return inverse[n];
if constexpr (MEMOIZES) {
// "n!" and "M" must be disjoint.
inverse.resize(n + 1);
for (int i = prev; i <= n; ++i) {
inverse[i] = -inverse[M % i] * raw(M / i);
}
return inverse[n];
}
int u = 1, v = 0;
for (unsigned int a = n, b = M; b;) {
const unsigned int q = a / b;
std::swap(a -= q * b, b);
std::swap(u -= q * v, v);
}
return u;
}
static MInt fact(const int n) {
static std::vector<MInt> factorial{1};
if (const int prev = factorial.size(); n >= prev) {
factorial.resize(n + 1);
for (int i = prev; i <= n; ++i) {
factorial[i] = factorial[i - 1] * i;
}
}
return factorial[n];
}
static MInt fact_inv(const int n) {
static std::vector<MInt> f_inv{1};
if (const int prev = f_inv.size(); n >= prev) {
f_inv.resize(n + 1);
f_inv[n] = inv(fact(n).v);
for (int i = n; i > prev; --i) {
f_inv[i - 1] = f_inv[i] * i;
}
}
return f_inv[n];
}
static MInt nCk(const int n, const int k) {
if (n < 0 || n < k || k < 0) [[unlikely]] return MInt();
return fact(n) * (n - k < k ? fact_inv(k) * fact_inv(n - k) :
fact_inv(n - k) * fact_inv(k));
}
static MInt nPk(const int n, const int k) {
return n < 0 || n < k || k < 0 ? MInt() : fact(n) * fact_inv(n - k);
}
static MInt nHk(const int n, const int k) {
return n < 0 || k < 0 ? MInt() : (k == 0 ? 1 : nCk(n + k - 1, k));
}
static MInt large_nCk(long long n, const int k) {
if (n < 0 || n < k || k < 0) [[unlikely]] return MInt();
inv<true>(k);
MInt res = 1;
for (int i = 1; i <= k; ++i) {
res *= inv(i) * n--;
}
return res;
}
constexpr MInt pow(long long exponent) const {
MInt res = 1, tmp = *this;
for (; exponent > 0; exponent >>= 1) {
if (exponent & 1) res *= tmp;
tmp *= tmp;
}
return res;
}
constexpr MInt& operator+=(const MInt& x) {
if ((v += x.v) >= M) v -= M;
return *this;
}
constexpr MInt& operator-=(const MInt& x) {
if ((v += M - x.v) >= M) v -= M;
return *this;
}
constexpr MInt& operator*=(const MInt& x) {
v = (unsigned long long){v} * x.v % M;
return *this;
}
MInt& operator/=(const MInt& x) { return *this *= inv(x.v); }
constexpr auto operator<=>(const MInt& x) const = default;
constexpr MInt& operator++() {
if (++v == M) [[unlikely]] v = 0;
return *this;
}
constexpr MInt operator++(int) {
const MInt res = *this;
++*this;
return res;
}
constexpr MInt& operator--() {
v = (v == 0 ? M - 1 : v - 1);
return *this;
}
constexpr MInt operator--(int) {
const MInt res = *this;
--*this;
return res;
}
constexpr MInt operator+() const { return *this; }
constexpr MInt operator-() const { return raw(v ? M - v : 0); }
constexpr MInt operator+(const MInt& x) const { return MInt(*this) += x; }
constexpr MInt operator-(const MInt& x) const { return MInt(*this) -= x; }
constexpr MInt operator*(const MInt& x) const { return MInt(*this) *= x; }
MInt operator/(const MInt& x) const { return MInt(*this) /= x; }
friend std::ostream& operator<<(std::ostream& os, const MInt& x) {
return os << x.v;
}
friend std::istream& operator>>(std::istream& is, MInt& x) {
long long v;
is >> v;
x = MInt(v);
return is;
}
};
using ModInt = MInt<MOD>;
#include <atcoder/convolution>
template <unsigned int T>
struct NumberTheoreticTransform {
using ModInt = MInt<T>;
NumberTheoreticTransform() = default;
template <typename U>
std::vector<ModInt> dft(const std::vector<U>& a);
void idft(std::vector<ModInt>* a);
template <typename U>
std::vector<ModInt> convolution(const std::vector<U>& a,
const std::vector<U>& b) {
const int a_size = a.size(), b_size = b.size();
std::vector<atcoder::static_modint<T>> c(a_size), d(b_size);
for (int i = 0; i < a_size; ++i) {
c[i] = atcoder::static_modint<T>::raw(ModInt(a[i]).v);
}
for (int i = 0; i < b_size; ++i) {
d[i] = atcoder::static_modint<T>::raw(ModInt(b[i]).v);
}
c = atcoder::convolution(c, d);
const int c_size = c.size();
std::vector<ModInt> res(c_size);
for (int i = 0; i < c_size; ++i) {
res[i] = ModInt::raw(c[i].val());
}
return res;
}
};
template <typename T>
struct FormalPowerSeries {
std::vector<T> coef;
explicit FormalPowerSeries(const int deg = 0) : coef(deg + 1, 0) {}
explicit FormalPowerSeries(const std::vector<T>& coef) : coef(coef) {}
FormalPowerSeries(const std::initializer_list<T> init)
: coef(init.begin(), init.end()) {}
template <typename InputIter>
explicit FormalPowerSeries(const InputIter first, const InputIter last)
: coef(first, last) {}
inline const T& operator[](const int term) const { return coef[term]; }
inline T& operator[](const int term) { return coef[term]; }
using Mult = std::function<std::vector<T>(const std::vector<T>&,
const std::vector<T>&)>;
using Sqrt = std::function<bool(const T&, T*)>;
static void set_mult(const Mult mult) { get_mult() = mult; }
static void set_sqrt(const Sqrt sqrt) { get_sqrt() = sqrt; }
void resize(const int deg) { coef.resize(deg + 1, 0); }
void shrink() {
while (coef.size() > 1 && coef.back() == 0) coef.pop_back();
}
int degree() const { return std::ssize(coef) - 1; }
FormalPowerSeries& operator=(const std::vector<T>& coef_) {
coef = coef_;
return *this;
}
FormalPowerSeries& operator=(const FormalPowerSeries& x) = default;
FormalPowerSeries& operator+=(const FormalPowerSeries& x) {
const int deg_x = x.degree();
if (deg_x > degree()) resize(deg_x);
for (int i = 0; i <= deg_x; ++i) {
coef[i] += x[i];
}
return *this;
}
FormalPowerSeries& operator-=(const FormalPowerSeries& x) {
const int deg_x = x.degree();
if (deg_x > degree()) resize(deg_x);
for (int i = 0; i <= deg_x; ++i) {
coef[i] -= x[i];
}
return *this;
}
FormalPowerSeries& operator*=(const T x) {
for (T& e : coef) e *= x;
return *this;
}
FormalPowerSeries& operator*=(const FormalPowerSeries& x) {
return *this = get_mult()(coef, x.coef);
}
FormalPowerSeries& operator/=(const T x) {
assert(x != 0);
return *this *= static_cast<T>(1) / x;
}
FormalPowerSeries& operator/=(const FormalPowerSeries& x) {
const int n = degree() - x.degree() + 1;
if (n <= 0) return *this = FormalPowerSeries();
const std::vector<T> tmp = get_mult()(
std::vector<T>(coef.rbegin(), std::next(coef.rbegin(), n)),
FormalPowerSeries(
x.coef.rbegin(),
std::next(x.coef.rbegin(), std::min(x.degree() + 1, n)))
.inv(n - 1).coef);
return *this = FormalPowerSeries(std::prev(tmp.rend(), n), tmp.rend());
}
FormalPowerSeries& operator%=(const FormalPowerSeries& x) {
if (x.degree() == 0) return *this = FormalPowerSeries{0};
*this -= *this / x * x;
resize(x.degree() - 1);
return *this;
}
FormalPowerSeries& operator<<=(const int n) {
coef.insert(coef.begin(), n, 0);
return *this;
}
FormalPowerSeries& operator>>=(const int n) {
if (degree() < n) return *this = FormalPowerSeries();
coef.erase(coef.begin(), coef.begin() + n);
return *this;
}
bool operator==(FormalPowerSeries x) const {
x.shrink();
FormalPowerSeries y = *this;
y.shrink();
return x.coef == y.coef;
}
FormalPowerSeries operator+() const { return *this; }
FormalPowerSeries operator-() const {
FormalPowerSeries res = *this;
for (T& e : res.coef) e = -e;
return res;
}
FormalPowerSeries operator+(const FormalPowerSeries& x) const {
return FormalPowerSeries(*this) += x;
}
FormalPowerSeries operator-(const FormalPowerSeries& x) const {
return FormalPowerSeries(*this) -= x;
}
FormalPowerSeries operator*(const T x) const {
return FormalPowerSeries(*this) *= x;
}
FormalPowerSeries operator*(const FormalPowerSeries& x) const {
return FormalPowerSeries(*this) *= x;
}
FormalPowerSeries operator/(const T x) const {
return FormalPowerSeries(*this) /= x;
}
FormalPowerSeries operator/(const FormalPowerSeries& x) const {
return FormalPowerSeries(*this) /= x;
}
FormalPowerSeries operator%(const FormalPowerSeries& x) const {
return FormalPowerSeries(*this) %= x;
}
FormalPowerSeries operator<<(const int n) const {
return FormalPowerSeries(*this) <<= n;
}
FormalPowerSeries operator>>(const int n) const {
return FormalPowerSeries(*this) >>= n;
}
T horner(const T x) const {
return std::accumulate(
coef.rbegin(), coef.rend(), static_cast<T>(0),
[x](const T l, const T r) -> T { return l * x + r; });
}
FormalPowerSeries differential() const {
const int deg = degree();
assert(deg >= 0);
FormalPowerSeries res(std::max(deg - 1, 0));
for (int i = 1; i <= deg; ++i) {
res[i - 1] = coef[i] * i;
}
return res;
}
FormalPowerSeries exp(const int deg) const {
assert(coef[0] == 0);
const int n = coef.size();
const FormalPowerSeries one{1};
FormalPowerSeries res = one;
for (int i = 1; i <= deg; i <<= 1) {
res *= FormalPowerSeries(coef.begin(),
std::next(coef.begin(), std::min(n, i << 1)))
- res.log((i << 1) - 1) + one;
res.coef.resize(i << 1);
}
res.resize(deg);
return res;
}
FormalPowerSeries exp() const { return exp(degree()); }
FormalPowerSeries inv(const int deg) const {
assert(coef[0] != 0);
const int n = coef.size();
FormalPowerSeries res{static_cast<T>(1) / coef[0]};
for (int i = 1; i <= deg; i <<= 1) {
res = res + res - res * res * FormalPowerSeries(
coef.begin(), std::next(coef.begin(), std::min(n, i << 1)));
res.coef.resize(i << 1);
}
res.resize(deg);
return res;
}
FormalPowerSeries inv() const { return inv(degree()); }
FormalPowerSeries log(const int deg) const {
assert(coef[0] == 1);
FormalPowerSeries integrand = differential() * inv(deg - 1);
integrand.resize(deg);
for (int i = deg; i > 0; --i) {
integrand[i] = integrand[i - 1] / i;
}
integrand[0] = 0;
return integrand;
}
FormalPowerSeries log() const { return log(degree()); }
FormalPowerSeries pow(long long exponent, const int deg) const {
const int n = coef.size();
if (exponent == 0) {
FormalPowerSeries res(deg);
if (deg != -1) [[unlikely]] res[0] = 1;
return res;
}
assert(deg >= 0);
for (int i = 0; i < n; ++i) {
if (coef[i] == 0) continue;
if (i > deg / exponent) break;
const long long shift = exponent * i;
T tmp = 1, base = coef[i];
for (long long e = exponent; e > 0; e >>= 1) {
if (e & 1) tmp *= base;
base *= base;
}
const FormalPowerSeries res = ((*this >> i) / coef[i]).log(deg - shift);
return ((res * exponent).exp(deg - shift) * tmp) << shift;
}
return FormalPowerSeries(deg);
}
FormalPowerSeries pow(const long long exponent) const {
return pow(exponent, degree());
}
FormalPowerSeries mod_pow(long long exponent,
const FormalPowerSeries& md) const {
const int deg = md.degree() - 1;
if (deg < 0) [[unlikely]] return FormalPowerSeries(-1);
const FormalPowerSeries inv_rev_md =
FormalPowerSeries(md.coef.rbegin(), md.coef.rend()).inv();
const auto mod_mult = [&md, &inv_rev_md, deg](
FormalPowerSeries* multiplicand, const FormalPowerSeries& multiplier)
-> void {
*multiplicand *= multiplier;
if (deg < multiplicand->degree()) {
const int n = multiplicand->degree() - deg;
const FormalPowerSeries quotient =
FormalPowerSeries(multiplicand->coef.rbegin(),
std::next(multiplicand->coef.rbegin(), n))
* FormalPowerSeries(
inv_rev_md.coef.begin(),
std::next(inv_rev_md.coef.begin(), std::min(deg + 2, n)));
*multiplicand -=
FormalPowerSeries(std::prev(quotient.coef.rend(), n),
quotient.coef.rend()) * md;
multiplicand->resize(deg);
}
multiplicand->shrink();
};
FormalPowerSeries res{1}, base = *this;
for (; exponent > 0; exponent >>= 1) {
if (exponent & 1) mod_mult(&res, base);
mod_mult(&base, base);
}
return res;
}
FormalPowerSeries sqrt(const int deg) const {
const int n = coef.size();
if (coef[0] == 0) {
for (int i = 1; i < n; ++i) {
if (coef[i] == 0) continue;
if (i & 1) return FormalPowerSeries(-1);
const int shift = i >> 1;
if (deg < shift) break;
FormalPowerSeries res = (*this >> i).sqrt(deg - shift);
if (res.coef.empty()) return FormalPowerSeries(-1);
res <<= shift;
res.resize(deg);
return res;
}
return FormalPowerSeries(deg);
}
T s;
if (!get_sqrt()(coef.front(), &s)) return FormalPowerSeries(-1);
FormalPowerSeries res{s};
const T half = static_cast<T>(1) / 2;
for (int i = 1; i <= deg; i <<= 1) {
res = (FormalPowerSeries(coef.begin(),
std::next(coef.begin(), std::min(n, i << 1)))
* res.inv((i << 1) - 1) + res) * half;
}
res.resize(deg);
return res;
}
FormalPowerSeries sqrt() const { return sqrt(degree()); }
FormalPowerSeries translate(const T c) const {
const int n = coef.size();
std::vector<T> fact(n, 1), inv_fact(n, 1);
for (int i = 1; i < n; ++i) {
fact[i] = fact[i - 1] * i;
}
inv_fact[n - 1] = static_cast<T>(1) / fact[n - 1];
for (int i = n - 1; i > 0; --i) {
inv_fact[i - 1] = inv_fact[i] * i;
}
std::vector<T> g(n), ex(n);
for (int i = 0; i < n; ++i) {
g[i] = coef[i] * fact[i];
}
std::reverse(g.begin(), g.end());
T pow_c = 1;
for (int i = 0; i < n; ++i) {
ex[i] = pow_c * inv_fact[i];
pow_c *= c;
}
const std::vector<T> conv = get_mult()(g, ex);
FormalPowerSeries res(n - 1);
for (int i = 0; i < n; ++i) {
res[i] = conv[n - 1 - i] * inv_fact[i];
}
return res;
}
private:
static Mult& get_mult() {
static Mult mult = [](const std::vector<T>& a, const std::vector<T>& b)
-> std::vector<T> {
const int n = a.size(), m = b.size();
std::vector<T> res(n + m - 1, 0);
for (int i = 0; i < n; ++i) {
for (int j = 0; j < m; ++j) {
res[i + j] += a[i] * b[j];
}
}
return res;
};
return mult;
}
static Sqrt& get_sqrt() {
static Sqrt sqrt = [](const T&, T*) -> bool { return false; };
return sqrt;
}
};
template <typename T>
T bostan_mori(FormalPowerSeries<T> p, FormalPowerSeries<T> q, long long n) {
q.shrink();
const int d = q.degree();
assert(d >= 0 && q[0] != 0);
T res = 0;
p.shrink();
if (p.degree() >= d) {
const FormalPowerSeries<T> quotient = p / q;
p -= quotient * q;
p.shrink();
if (n <= quotient.degree()) res += quotient[n];
}
if (d == 0 || (p.degree() == 0 && p[0] == 0)) return res;
p.resize(d - 1);
for (; n > 0; n >>= 1) {
FormalPowerSeries<T> tmp = q;
for (int i = 1; i <= d; i += 2) {
tmp[i] = -tmp[i];
}
p *= tmp;
if (n & 1) {
for (int i = 0; i < d; ++i) {
p[i] = p[(i << 1) + 1];
}
} else {
for (int i = 1; i < d; ++i) {
p[i] = p[i << 1];
}
}
p.resize(d - 1);
q *= tmp;
for (int i = 1; i <= d; ++i) {
q[i] = q[i << 1];
}
q.resize(d);
}
return res + p[0] / q[0];
}
int main() {
FormalPowerSeries<ModInt>::set_mult(
[](const vector<ModInt>& a, const vector<ModInt>& b) -> vector<ModInt> {
static NumberTheoreticTransform<MOD> ntt;
return ntt.convolution(a, b);
});
const FormalPowerSeries<ModInt> one{1};
int n; cin >> n;
vector<vector<int>> graph(n + 1);
FOR(i, 1, n + 1) {
int p; cin >> p;
graph[p].emplace_back(i);
}
vector<int> w(n + 1, 0); FOR(i, 1, n + 1) cin >> w[i];
int q; cin >> q;
while (q--) {
int a, k; cin >> a >> k;
FormalPowerSeries<ModInt> f(n + 1), fy(n + 1), h(n), hy(n);
const auto dfs = [&](auto dfs, const int node, const ModInt& prob, const int depth, const bool is_passed) -> void {
if (graph[node].empty()) {
(is_passed ? fy : f)[depth + 1] += prob;
return;
}
(is_passed ? hy : h)[depth] += prob;
ll den = 0;
for (const int e : graph[node]) den += w[e];
for (const int e : graph[node]) {
dfs(dfs, e, prob * w[e] / den, depth + 1, is_passed || (e == a));
}
};
dfs(dfs, 0, 1, 0, a == 0);
cout << bostan_mori((h + hy) * fy + (one - f - fy) * hy, (one - f - fy) * (one - f - fy), k) << '\n';
}
return 0;
}
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