結果
| 問題 |
No.1796 木上のクーロン
|
| コンテスト | |
| ユーザー |
 ebi_fly
|
| 提出日時 | 2024-05-22 12:13:33 |
| 言語 | C++23 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 776 ms / 10,000 ms |
| コード長 | 32,917 bytes |
| コンパイル時間 | 3,984 ms |
| コンパイル使用メモリ | 283,424 KB |
| 実行使用メモリ | 49,840 KB |
| 最終ジャッジ日時 | 2024-12-20 18:25:34 |
| 合計ジャッジ時間 | 13,735 ms |
|
ジャッジサーバーID （参考情報） |
judge5 / judge4 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 3 |
| other | AC * 34 |
ソースコード
#line 1 "test/yuki/yuki_1796.test.cpp"
#define PROBLEM "https://yukicoder.me/problems/no/1796"
#line 2 "fps/middle_product.hpp"
#include <algorithm>
#include <bit>
#include <cassert>
#include <ranges>
#include <vector>
#line 2 "convolution/ntt.hpp"
#line 4 "convolution/ntt.hpp"
#include <array>
#line 8 "convolution/ntt.hpp"
#line 2 "math/internal_math.hpp"
#line 4 "math/internal_math.hpp"
namespace ebi {
namespace internal {
constexpr int primitive_root_constexpr(int m) {
if (m == 2) return 1;
if (m == 167772161) return 3;
if (m == 469762049) return 3;
if (m == 754974721) return 11;
if (m == 998244353) return 3;
if (m == 880803841) return 26;
if (m == 924844033) return 5;
return -1;
}
template <int m> constexpr int primitive_root = primitive_root_constexpr(m);
} // namespace internal
} // namespace ebi
#line 2 "template/int_alias.hpp"
#include <cstdint>
namespace ebi {
using ld = long double;
using std::size_t;
using i8 = std::int8_t;
using u8 = std::uint8_t;
using i16 = std::int16_t;
using u16 = std::uint16_t;
using i32 = std::int32_t;
using u32 = std::uint32_t;
using i64 = std::int64_t;
using u64 = std::uint64_t;
using i128 = __int128_t;
using u128 = __uint128_t;
} // namespace ebi
#line 2 "modint/base.hpp"
#include <concepts>
#include <iostream>
#include <utility>
namespace ebi {
template <class T>
concept Modint = requires(T a, T b) {
a + b;
a - b;
a * b;
a / b;
a.inv();
a.val();
a.pow(std::declval<long long>());
T::mod();
};
template <Modint mint> std::istream &operator>>(std::istream &os, mint &a) {
long long x;
os >> x;
a = x;
return os;
}
template <Modint mint>
std::ostream &operator<<(std::ostream &os, const mint &a) {
return os << a.val();
}
} // namespace ebi
#line 12 "convolution/ntt.hpp"
namespace ebi {
namespace internal {
template <Modint mint, int g = internal::primitive_root<mint::mod()>>
struct ntt_info {
static constexpr int rank2 =
std::countr_zero((unsigned int)(mint::mod() - 1));
std::array<mint, rank2 + 1> root, inv_root;
ntt_info() {
root[rank2] = mint(g).pow((mint::mod() - 1) >> rank2);
inv_root[rank2] = root[rank2].inv();
for (int i = rank2 - 1; i >= 0; i--) {
root[i] = root[i + 1] * root[i + 1];
inv_root[i] = inv_root[i + 1] * inv_root[i + 1];
}
}
};
template <Modint mint> void fft2(std::vector<mint>& a) {
static const ntt_info<mint> info;
int n = int(a.size());
int bit_size = std::countr_zero(a.size());
assert(n == 1 << bit_size);
for (int bit = bit_size - 1; bit >= 0; bit--) {
int m = 1 << bit;
for (int i = 0; i < n; i += 2 * m) {
mint w = 1;
for (int j = 0; j < m; j++) {
mint p1 = a[i + j];
mint p2 = a[i + j + m];
a[i + j] = p1 + p2;
a[i + j + m] = (p1 - p2) * w;
w *= info.root[bit + 1];
}
}
}
}
template <Modint mint> void ifft2(std::vector<mint>& a) {
static const ntt_info<mint> info;
int n = int(a.size());
int bit_size = std::countr_zero(a.size());
assert(n == 1 << bit_size);
for (int bit = 0; bit < bit_size; bit++) {
for (int i = 0; i < n / (1 << (bit + 1)); i++) {
mint w = 1;
for (int j = 0; j < (1 << bit); j++) {
int idx = i * (1 << (bit + 1)) + j;
int jdx = idx + (1 << bit);
mint p1 = a[idx];
mint p2 = w * a[jdx];
a[idx] = p1 + p2;
a[jdx] = p1 - p2;
w *= info.inv_root[bit + 1];
}
}
}
}
template <Modint mint> void fft4(std::vector<mint>& a) {
static const ntt_info<mint> info;
const u32 mod = mint::mod();
const u64 iw = info.root[2].val();
int n = int(a.size());
int bit_size = std::countr_zero(a.size());
assert(n == 1 << bit_size);
int len = bit_size;
while (len > 0) {
if (len == 1) {
for (int i = 0; i < n; i += 2) {
mint p0 = a[i];
mint p1 = a[i + 1];
a[i] = p0 + p1;
a[i + 1] = p0 - p1;
}
len--;
} else {
int m = 1 << (len - 2);
u64 w1 = 1, w2 = 1, w3 = 1, iw1 = iw, iw3 = iw;
for (int i = 0; i < m; i++) {
for (int j = 0; j < n; j += 4 * m) {
int i0 = i + j, i1 = i0 + m, i2 = i1 + m, i3 = i2 + m;
u32 a0 = a[i0].val();
u32 a1 = a[i1].val();
u32 a2 = a[i2].val();
u32 a3 = a[i3].val();
u32 a0_plus_a2 = a0 + a2;
u32 a1_plus_a3 = a1 + a3;
u32 a0_minus_a2 = a0 + mod - a2;
u32 a1_minus_a3 = a1 + mod - a3;
a[i0] = a0_plus_a2 + a1_plus_a3;
a[i1] = a0_minus_a2 * w1 + a1_minus_a3 * iw1;
a[i2] = (a0_plus_a2 + 2 * mod - a1_plus_a3) * w2;
a[i3] = a0_minus_a2 * w3 + (2 * mod - a1_minus_a3) * iw3;
}
w1 = w1 * info.root[len].val() % mod;
w2 = w1 * w1 % mod;
w3 = w2 * w1 % mod;
iw1 = iw * w1 % mod;
iw3 = iw * w3 % mod;
}
len -= 2;
}
}
}
template <Modint mint> void ifft4(std::vector<mint>& a) {
static const ntt_info<mint> info;
const u32 mod = mint::mod();
const u64 mod2 = u64(mod) * mod;
const u64 iw = info.inv_root[2].val();
int n = int(a.size());
int bit_size = std::countr_zero(a.size());
assert(n == 1 << bit_size);
int len = (bit_size & 1 ? 1 : 2);
while (len <= bit_size) {
if (len == 1) {
for (int i = 0; i < n; i += 2) {
mint a0 = a[i];
mint a1 = a[i + 1];
a[i] = a0 + a1;
a[i + 1] = a0 - a1;
}
} else {
int m = 1 << (len - 2);
u64 w1 = 1, w2 = 1, w3 = 1, iw1 = iw, iw3 = iw;
for (int i = 0; i < m; i++) {
for (int j = 0; j < n; j += 4 * m) {
int i0 = i + j, i1 = i0 + m, i2 = i1 + m, i3 = i2 + m;
u64 a0 = a[i0].val();
u64 a1 = w1 * a[i1].val();
u64 a2 = w2 * a[i2].val();
u64 a3 = w3 * a[i3].val();
u64 b1 = iw1 * a[i1].val();
u64 b3 = iw3 * a[i3].val();
u64 a0_plus_a2 = a0 + a2;
u64 a1_plus_a3 = a1 + a3;
u64 a0_minus_a2 = a0 + mod2 - a2;
u64 b1_minus_b3 = b1 + mod2 - b3;
a[i0] = a0_plus_a2 + a1_plus_a3;
a[i1] = a0_minus_a2 + b1_minus_b3;
a[i2] = a0_plus_a2 + mod2 * 2 - a1_plus_a3;
a[i3] = a0_minus_a2 + mod2 * 2 - b1_minus_b3;
}
w1 = w1 * info.inv_root[len].val() % mod;
w2 = w1 * w1 % mod;
w3 = w2 * w1 % mod;
iw1 = iw * w1 % mod;
iw3 = iw * w3 % mod;
}
}
len += 2;
}
}
} // namespace internal
} // namespace ebi
#line 11 "fps/middle_product.hpp"
namespace ebi {
template <Modint mint>
std::vector<mint> middle_product(const std::vector<mint> &a,
const std::vector<mint> &b) {
assert(a.size() >= b.size());
if (std::min(a.size() - b.size() + 1, b.size()) <= 60) {
return middle_product_naive<mint>(a, b);
}
int n = std::bit_ceil(a.size());
std::vector<mint> fa(n), fb(n);
std::copy(a.begin(), a.end(), fa.begin());
std::copy(b.rbegin(), b.rend(), fb.begin());
internal::fft4(fa);
internal::fft4(fb);
for (int i = 0; i < n; i++) {
fa[i] *= fb[i];
}
internal::ifft4(fa);
mint inv_n = mint(n).inv();
for (auto &x : fa) {
x *= inv_n;
}
fa.resize(a.size());
fa.erase(fa.begin(), fa.begin() + b.size() - 1);
return fa;
}
template <Modint mint>
std::vector<mint> middle_product_naive(const std::vector<mint> &a,
const std::vector<mint> &b) {
int n = (int)a.size();
int m = (int)b.size();
assert(n >= m);
std::vector<mint> c(n - m + 1, 0);
for (int i : std::views::iota(0, n - m + 1)) {
for (int j : std::views::iota(0, m)) {
c[i] += b[j] * a[i + j];
}
}
return c;
}
} // namespace ebi
#line 2 "graph/base.hpp"
#line 7 "graph/base.hpp"
#line 2 "data_structure/simple_csr.hpp"
#line 6 "data_structure/simple_csr.hpp"
namespace ebi {
template <class E> struct simple_csr {
simple_csr() = default;
simple_csr(int n, const std::vector<std::pair<int, E>>& elements)
: start(n + 1, 0), elist(elements.size()) {
for (auto e : elements) {
start[e.first + 1]++;
}
for (auto i : std::views::iota(0, n)) {
start[i + 1] += start[i];
}
auto counter = start;
for (auto [i, e] : elements) {
elist[counter[i]++] = e;
}
}
simple_csr(const std::vector<std::vector<E>>& es)
: start(es.size() + 1, 0) {
int n = es.size();
for (auto i : std::views::iota(0, n)) {
start[i + 1] = (int)es[i].size() + start[i];
}
elist.resize(start.back());
for (auto i : std::views::iota(0, n)) {
std::copy(es[i].begin(), es[i].end(), elist.begin() + start[i]);
}
}
int size() const {
return (int)start.size() - 1;
}
const auto operator[](int i) const {
return std::ranges::subrange(elist.begin() + start[i],
elist.begin() + start[i + 1]);
}
auto operator[](int i) {
return std::ranges::subrange(elist.begin() + start[i],
elist.begin() + start[i + 1]);
}
const auto operator()(int i, int l, int r) const {
return std::ranges::subrange(elist.begin() + start[i] + l,
elist.begin() + start[i + 1] + r);
}
auto operator()(int i, int l, int r) {
return std::ranges::subrange(elist.begin() + start[i] + l,
elist.begin() + start[i + 1] + r);
}
private:
std::vector<int> start;
std::vector<E> elist;
};
} // namespace ebi
#line 9 "graph/base.hpp"
namespace ebi {
template <class T> struct Edge {
int from, to;
T cost;
int id;
};
template <class E> struct Graph {
using cost_type = E;
using edge_type = Edge<cost_type>;
Graph(int n_) : n(n_) {}
Graph() = default;
void add_edge(int u, int v, cost_type c) {
buff.emplace_back(u, edge_type{u, v, c, m});
edges.emplace_back(edge_type{u, v, c, m++});
}
void add_undirected_edge(int u, int v, cost_type c) {
buff.emplace_back(u, edge_type{u, v, c, m});
buff.emplace_back(v, edge_type{v, u, c, m});
edges.emplace_back(edge_type{u, v, c, m});
m++;
}
void read_tree(int offset = 1, bool is_weighted = false) {
read_graph(n - 1, offset, false, is_weighted);
}
void read_parents(int offset = 1) {
for (auto i : std::views::iota(1, n)) {
int p;
std::cin >> p;
p -= offset;
add_undirected_edge(p, i, 1);
}
build();
}
void read_graph(int e, int offset = 1, bool is_directed = false,
bool is_weighted = false) {
for (int i = 0; i < e; i++) {
int u, v;
std::cin >> u >> v;
u -= offset;
v -= offset;
if (is_weighted) {
cost_type c;
std::cin >> c;
if (is_directed) {
add_edge(u, v, c);
} else {
add_undirected_edge(u, v, c);
}
} else {
if (is_directed) {
add_edge(u, v, 1);
} else {
add_undirected_edge(u, v, 1);
}
}
}
build();
}
void build() {
assert(!prepared);
csr = simple_csr<edge_type>(n, buff);
buff.clear();
prepared = true;
}
int size() const {
return n;
}
int node_number() const {
return n;
}
int edge_number() const {
return m;
}
edge_type get_edge(int i) const {
return edges[i];
}
std::vector<edge_type> get_edges() const {
return edges;
}
const auto operator[](int i) const {
return csr[i];
}
auto operator[](int i) {
return csr[i];
}
private:
int n, m = 0;
std::vector<std::pair<int,edge_type>> buff;
std::vector<edge_type> edges;
simple_csr<edge_type> csr;
bool prepared = false;
};
} // namespace ebi
#line 2 "math/binomial.hpp"
#line 9 "math/binomial.hpp"
#line 11 "math/binomial.hpp"
namespace ebi {
template <Modint mint> struct Binomial {
private:
static void extend(int len = -1) {
int sz = (int)fact.size();
if (len < 0)
len = 2 * sz;
else if (len <= sz)
return;
else
len = std::max(2 * sz, (int)std::bit_ceil(std::uint32_t(len)));
len = std::min(len, mint::mod());
assert(sz <= len);
fact.resize(len);
inv_fact.resize(len);
for (int i : std::views::iota(sz, len)) {
fact[i] = fact[i - 1] * i;
}
inv_fact[len - 1] = fact[len - 1].inv();
for (int i : std::views::iota(sz, len) | std::views::reverse) {
inv_fact[i - 1] = inv_fact[i] * i;
}
}
public:
Binomial() = default;
Binomial(int n) {
extend(n + 1);
}
static mint f(int n) {
if (n >= (int)fact.size()) [[unlikely]] {
extend(n + 1);
}
return fact[n];
}
static mint inv_f(int n) {
if (n >= (int)fact.size()) [[unlikely]] {
extend(n + 1);
}
return inv_fact[n];
}
static mint c(int n, int r) {
if (r < 0 || n < r) return 0;
return f(n) * inv_f(r) * inv_f(n - r);
}
static mint neg_c(int k, int d) {
assert(d > 0);
return c(k + d - 1, d - 1);
}
static mint p(int n, int r) {
if (r < 0 || n < r) return 0;
return f(n) * inv_f(n - r);
}
static mint inv(int n) {
return inv_f(n) * f(n - 1);
}
static void reserve(int n) {
extend(n + 1);
}
private:
static std::vector<mint> fact, inv_fact;
};
template <Modint mint>
std::vector<mint> Binomial<mint>::fact = std::vector<mint>(2, 1);
template <Modint mint>
std::vector<mint> Binomial<mint>::inv_fact = std::vector<mint>(2, 1);
} // namespace ebi
#line 2 "modint/modint.hpp"
#line 5 "modint/modint.hpp"
#line 7 "modint/modint.hpp"
namespace ebi {
template <int m> struct static_modint {
private:
using modint = static_modint;
public:
static constexpr int mod() {
return m;
}
static constexpr modint raw(int v) {
modint x;
x._v = v;
return x;
}
constexpr static_modint() : _v(0) {}
template<std::signed_integral T>
constexpr static_modint(T v) {
long long x = (long long)(v % (long long)(umod()));
if (x < 0) x += umod();
_v = (unsigned int)(x);
}
template<std::unsigned_integral T>
constexpr static_modint(T v) {
_v = v % umod();
}
constexpr unsigned int val() const {
return _v;
}
constexpr unsigned int value() const {
return val();
}
constexpr modint &operator++() {
_v++;
if (_v == umod()) _v = 0;
return *this;
}
constexpr modint &operator--() {
if (_v == 0) _v = umod();
_v--;
return *this;
}
constexpr modint operator++(int) {
modint res = *this;
++*this;
return res;
}
constexpr modint operator--(int) {
modint res = *this;
--*this;
return res;
}
constexpr modint &operator+=(const modint &rhs) {
_v += rhs._v;
if (_v >= umod()) _v -= umod();
return *this;
}
constexpr modint &operator-=(const modint &rhs) {
_v -= rhs._v;
if (_v >= umod()) _v += umod();
return *this;
}
constexpr modint &operator*=(const modint &rhs) {
unsigned long long x = _v;
x *= rhs._v;
_v = (unsigned int)(x % (unsigned long long)umod());
return *this;
}
constexpr modint &operator/=(const modint &rhs) {
return *this = *this * rhs.inv();
}
constexpr modint operator+() const {
return *this;
}
constexpr modint operator-() const {
return modint() - *this;
}
constexpr modint pow(long long n) const {
assert(0 <= n);
modint x = *this, res = 1;
while (n) {
if (n & 1) res *= x;
x *= x;
n >>= 1;
}
return res;
}
constexpr modint inv() const {
assert(_v);
return pow(umod() - 2);
}
friend modint operator+(const modint &lhs, const modint &rhs) {
return modint(lhs) += rhs;
}
friend modint operator-(const modint &lhs, const modint &rhs) {
return modint(lhs) -= rhs;
}
friend modint operator*(const modint &lhs, const modint &rhs) {
return modint(lhs) *= rhs;
}
friend modint operator/(const modint &lhs, const modint &rhs) {
return modint(lhs) /= rhs;
}
friend bool operator==(const modint &lhs, const modint &rhs) {
return lhs.val() == rhs.val();
}
friend bool operator!=(const modint &lhs, const modint &rhs) {
return !(lhs == rhs);
}
private:
unsigned int _v = 0;
static constexpr unsigned int umod() {
return m;
}
};
using modint998244353 = static_modint<998244353>;
using modint1000000007 = static_modint<1000000007>;
} // namespace ebi
#line 1 "template/template.hpp"
#include <bits/stdc++.h>
#define rep(i, a, n) for (int i = (int)(a); i < (int)(n); i++)
#define rrep(i, a, n) for (int i = ((int)(n)-1); i >= (int)(a); i--)
#define Rep(i, a, n) for (i64 i = (i64)(a); i < (i64)(n); i++)
#define RRep(i, a, n) for (i64 i = ((i64)(n)-i64(1)); i >= (i64)(a); i--)
#define all(v) (v).begin(), (v).end()
#define rall(v) (v).rbegin(), (v).rend()
#line 2 "template/debug_template.hpp"
#line 4 "template/debug_template.hpp"
namespace ebi {
#ifdef LOCAL
#define debug(...) \
std::cerr << "LINE: " << __LINE__ << " [" << #__VA_ARGS__ << "]:", \
debug_out(__VA_ARGS__)
#else
#define debug(...)
#endif
void debug_out() {
std::cerr << std::endl;
}
template <typename Head, typename... Tail> void debug_out(Head h, Tail... t) {
std::cerr << " " << h;
if (sizeof...(t) > 0) std::cerr << " :";
debug_out(t...);
}
} // namespace ebi
#line 2 "template/io.hpp"
#line 5 "template/io.hpp"
#include <optional>
#line 7 "template/io.hpp"
namespace ebi {
template <typename T1, typename T2>
std::ostream &operator<<(std::ostream &os, const std::pair<T1, T2> &pa) {
return os << pa.first << " " << pa.second;
}
template <typename T1, typename T2>
std::istream &operator>>(std::istream &os, std::pair<T1, T2> &pa) {
return os >> pa.first >> pa.second;
}
template <typename T>
std::ostream &operator<<(std::ostream &os, const std::vector<T> &vec) {
for (std::size_t i = 0; i < vec.size(); i++)
os << vec[i] << (i + 1 == vec.size() ? "" : " ");
return os;
}
template <typename T>
std::istream &operator>>(std::istream &os, std::vector<T> &vec) {
for (T &e : vec) std::cin >> e;
return os;
}
template <typename T>
std::ostream &operator<<(std::ostream &os, const std::optional<T> &opt) {
if (opt) {
os << opt.value();
} else {
os << "invalid value";
}
return os;
}
void fast_io() {
std::cout << std::fixed << std::setprecision(15);
std::cin.tie(nullptr);
std::ios::sync_with_stdio(false);
}
} // namespace ebi
#line 2 "template/utility.hpp"
#line 5 "template/utility.hpp"
#line 8 "template/utility.hpp"
namespace ebi {
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;
}
template <class T> T safe_ceil(T a, T b) {
if (a % b == 0)
return a / b;
else if (a >= 0)
return (a / b) + 1;
else
return -((-a) / b);
}
template <class T> T safe_floor(T a, T b) {
if (a % b == 0)
return a / b;
else if (a >= 0)
return a / b;
else
return -((-a) / b) - 1;
}
constexpr i64 LNF = std::numeric_limits<i64>::max() / 4;
constexpr int INF = std::numeric_limits<int>::max() / 2;
const std::vector<int> dy = {1, 0, -1, 0, 1, 1, -1, -1};
const std::vector<int> dx = {0, 1, 0, -1, 1, -1, 1, -1};
} // namespace ebi
#line 2 "tree/centroid_decomposition.hpp"
#line 7 "tree/centroid_decomposition.hpp"
namespace ebi {
namespace internal {
template <class F>
void centroid_decomposition_dfs_naive(const std::vector<int> &par,
const std::vector<int> &original_vs,
F f) {
const int n = (int)par.size();
assert(par.size() == original_vs.size());
int center = -1;
std::vector<int> sz(n, 1);
for (const int v : std::views::iota(0, n) | std::views::reverse) {
if (sz[v] >= (n + 1) / 2) {
center = v;
break;
}
sz[par[v]] += sz[v];
}
std::vector<int> color(n, -1);
std::vector<int> vs = {center};
color[center] = 0;
int c = 1;
for (const int v : std::views::iota(1, n)) {
if (par[v] == center) {
vs.emplace_back(v);
color[v] = c++;
}
}
if (center > 0) {
for (int v = par[center]; v != -1; v = par[v]) {
vs.emplace_back(v);
color[v] = c;
}
c++;
}
for (const int v : std::views::iota(0, n)) {
if (color[v] == -1) {
vs.emplace_back(v);
color[v] = color[par[v]];
}
}
std::vector<int> index_ptr(c + 1, 0);
for (const int v : std::views::iota(0, n)) {
index_ptr[color[v] + 1]++;
}
for (const int i : std::views::iota(0, c)) {
index_ptr[i + 1] += index_ptr[i];
}
auto counter = index_ptr;
std::vector<int> ord(n);
for (auto v : vs) {
ord[counter[color[v]]++] = v;
}
std::vector<int> relabel(n);
for (const int v : std::views::iota(0, n)) {
relabel[ord[v]] = v;
}
std::vector<int> original_vs2(n);
for (const int v : std::views::iota(0, n)) {
original_vs2[relabel[v]] = original_vs[v];
}
std::vector<int> relabel_par(n, -1);
for (int v : std::views::iota(1, n)) {
int a = relabel[v];
int b = relabel[par[v]];
if (a > b) std::swap(a, b);
relabel_par[b] = a;
}
f(relabel_par, original_vs2, index_ptr);
for (const int i : std::views::iota(1, c)) {
int l = index_ptr[i], r = index_ptr[i + 1];
std::vector<int> par1(r - l, -1);
std::vector<int> original_vs1(r - l, -1);
for (int v : std::views::iota(l, r)) {
par1[v - l] = (relabel_par[v] == 0 ? -1 : relabel_par[v] - l);
original_vs1[v - l] = original_vs2[v];
}
centroid_decomposition_dfs_naive(par1, original_vs1, f);
}
return;
}
template <class F>
void one_third_centroid_decomposition(const std::vector<int> &par,
const std::vector<int> &original_vs,
F f) {
const int n = (int)par.size();
assert(n > 1);
if (n == 2) return;
int center = -1;
std::vector<int> sz(n, 1);
for (const int v : std::views::iota(0, n) | std::views::reverse) {
if (sz[v] >= (n + 1) / 2) {
center = v;
break;
}
sz[par[v]] += sz[v];
}
std::vector<int> color(n, -1);
std::vector<int> ord(n, -1);
ord[center] = 0;
int t = 1;
int red = n - sz[center];
for (int v = par[center]; v != -1; v = par[v]) {
ord[v] = t++;
color[v] = 0;
}
for (const int v : std::views::iota(1, n)) {
if (par[v] == center && 3 * (red + sz[v]) <= 2 * (n - 1)) {
red += sz[v];
ord[v] = t++;
color[v] = 0;
}
}
for (const int v : std::views::iota(1, n)) {
if (v != center && color[v] == -1 && color[par[v]] == 0) {
ord[v] = t++;
color[v] = 0;
}
}
const int n0 = t - 1;
for (const int v : std::views::iota(1, n)) {
if (v != center && color[v] == -1) {
ord[v] = t++;
color[v] = 1;
}
}
assert(t == n);
const int n1 = n - 1 - n0;
std::vector<int> par0(n0 + 1, -1), par1(n1 + 1, -1), par2(n, -1);
std::vector<int> original_vs0(n0 + 1), original_vs1(n1 + 1),
original_vs2(n);
for (const int i : std::views::iota(0, n)) {
int v = ord[i];
original_vs2[v] = original_vs[i];
if (color[i] != 1) {
original_vs0[v] = original_vs[i];
}
if (color[i] != 0) {
int idx = std::max(v - n0, 0);
original_vs1[idx] = original_vs[i];
}
}
for (const int v : std::views::iota(1, n)) {
int a = ord[v], b = ord[par[v]];
if (a > b) std::swap(a, b);
par2[b] = a;
if (color[v] != 1 && color[par[v]] != 1) {
par0[b] = a;
}
if (color[v] != 0 && color[par[v]] != 0) {
par1[b - n0] = std::max(a - n0, 0);
}
}
f(par2, original_vs2, n0, n1);
one_third_centroid_decomposition(par0, original_vs0, f);
one_third_centroid_decomposition(par1, original_vs1, f);
return;
}
template <class F>
void one_third_centroid_decomposition_virtual_real(
const std::vector<int> &par, const std::vector<int> &original_vs,
const std::vector<int> &is_real, F f) {
const int n = (int)par.size();
assert(n > 1);
if (n == 2) {
if (is_real[0] && is_real[1]) {
f(par, original_vs, {0, 1});
}
return;
}
int center = -1;
std::vector<int> sz(n, 1);
for (const int v : std::views::iota(0, n) | std::views::reverse) {
if (sz[v] >= (n + 1) / 2) {
center = v;
break;
}
sz[par[v]] += sz[v];
}
std::vector<int> color(n, -1);
std::vector<int> ord(n, -1);
ord[center] = 0;
int t = 1;
int red = n - sz[center];
for (int v = par[center]; v != -1; v = par[v]) {
ord[v] = t++;
color[v] = 0;
}
for (const int v : std::views::iota(1, n)) {
if (par[v] == center && 3 * (red + sz[v]) <= 2 * (n - 1)) {
red += sz[v];
ord[v] = t++;
color[v] = 0;
}
}
for (const int v : std::views::iota(1, n)) {
if (v != center && color[v] == -1 && color[par[v]] == 0) {
ord[v] = t++;
color[v] = 0;
}
}
const int n0 = t - 1;
for (const int v : std::views::iota(1, n)) {
if (v != center && color[v] == -1) {
ord[v] = t++;
color[v] = 1;
}
}
assert(t == n);
const int n1 = n - 1 - n0;
std::vector<int> par0(n0 + 1, -1), par1(n1 + 1, -1), par2(n, -1);
std::vector<int> original_vs0(n0 + 1), original_vs1(n1 + 1),
original_vs2(n);
std::vector<int> is_real0(n0 + 1), is_real1(n1 + 1), is_real2(n);
for (const int i : std::views::iota(0, n)) {
int v = ord[i];
original_vs2[v] = original_vs[i];
is_real2[v] = is_real[i];
if (color[i] != 1) {
original_vs0[v] = original_vs[i];
is_real0[v] = is_real[i];
}
if (color[i] != 0) {
int idx = std::max(v - n0, 0);
original_vs1[idx] = original_vs[i];
is_real1[idx] = is_real[i];
}
}
for (const int v : std::views::iota(1, n)) {
int a = ord[v], b = ord[par[v]];
if (a > b) std::swap(a, b);
par2[b] = a;
if (color[v] != 1 && color[par[v]] != 1) {
par0[b] = a;
}
if (color[v] != 0 && color[par[v]] != 0) {
par1[b - n0] = std::max(a - n0, 0);
}
}
if (is_real[center]) {
color.assign(n, -1);
color[0] = 0;
for (const int v : std::views::iota(1, n)) {
if (is_real2[v]) color[v] = 1;
}
f(par2, original_vs2, color);
is_real0[0] = is_real1[0] = is_real2[0] = 0;
}
color.assign(n, -1);
for (const int v : std::views::iota(1, n)) {
if (is_real2[v]) {
color[v] = int(v > n0);
}
}
f(par2, original_vs2, color);
one_third_centroid_decomposition_virtual_real(par0, original_vs0, is_real0,
f);
one_third_centroid_decomposition_virtual_real(par1, original_vs1, is_real1,
f);
return;
}
} // namespace internal
template <int MODE, class T, class F>
void centroid_decomposition(const Graph<T> &tree, F f) {
int n = (int)tree.size();
if (n == 1) return;
std::vector<int> bfs_order(n), par(n, -1);
bfs_order[0] = 0;
int l = 0, r = 1;
while (l < r) {
int v = bfs_order[l++];
for (auto e : tree[v]) {
int nv = e.to;
if (nv == par[v]) continue;
bfs_order[r++] = nv;
par[nv] = v;
}
}
assert(l == n && r == n);
{
std::vector<int> relabel(n);
for (int i : std::views::iota(0, n)) {
relabel[bfs_order[i]] = i;
}
std::vector<int> relabel_par(n, -1);
for (int i : std::views::iota(1, n)) {
relabel_par[relabel[i]] = relabel[par[i]];
}
std::swap(par, relabel_par);
}
static_assert(MODE == 0 || MODE == 1 || MODE == 2);
if constexpr (MODE == 0) {
internal::centroid_decomposition_dfs_naive(par, bfs_order, f);
} else if constexpr (MODE == 1) {
internal::one_third_centroid_decomposition(par, bfs_order, f);
} else {
internal::one_third_centroid_decomposition_virtual_real(
par, bfs_order, std::vector<int>(n, 1), f);
}
}
} // namespace ebi
#line 9 "test/yuki/yuki_1796.test.cpp"
namespace ebi {
using mint = modint998244353;
void main_() {
Binomial<mint> binom(300000);
int n;
std::cin >> n;
std::vector<mint> q(n);
std::cin >> q;
Graph<int> tree(n);
auto ans = q;
rep(i, 0, n - 1) {
int u, v;
std::cin >> u >> v;
u--;
v--;
tree.add_edge(u, v, 1);
tree.add_edge(v, u, 1);
ans[u] += q[v] * binom.inv(4);
ans[v] += q[u] * binom.inv(4);
}
tree.build();
auto calc = [&](const std::vector<int> &par, const std::vector<int> &vs,
int n0, int n1) {
int sz = (int)par.size();
std::vector<int> depth(sz, 0);
rep(i, 1, sz) {
depth[i] = depth[par[i]] + 1;
}
auto calc2 = [&](int l0, int r0, int l1, int r1) -> void {
int sz0 = *std::max_element(depth.begin() + l0, depth.begin() + r0);
int sz1 = *std::max_element(depth.begin() + l1, depth.begin() + r1);
std::vector<mint> f(sz0 + sz1 + 1), g(sz1 + 1);
rep(i, 0, f.size()) {
f[i] = binom.inv(i + 1) * binom.inv(i + 1);
}
rep(i, l1, r1) {
g[depth[i]] += q[vs[i]];
}
auto h = middle_product<mint>(f, g);
assert((int)h.size() == sz0 + 1);
rep(i, l0, r0) {
ans[vs[i]] += h[depth[i]];
}
};
calc2(1, 1 + n0, 1 + n0, 1 + n0 + n1);
calc2(1 + n0, 1 + n0 + n1, 1, 1 + n0);
};
centroid_decomposition<1>(tree, calc);
rep(i, 0, n) {
ans[i] *= binom.f(n) * binom.f(n);
std::cout << ans[i] << '\n';
}
}
} // namespace ebi
int main() {
ebi::fast_io();
int t = 1;
// std::cin >> t;
while (t--) {
ebi::main_();
}
return 0;
}