This documentation is automatically generated by online-judge-tools/verification-helper
#define PROBLEM "https://judge.yosupo.jp/problem/tree_path_composite_sum"
#include "../../../src/template/template.hpp"
#include "../../../src/graph/graph_template.hpp"
#include "../../../src/tree/rerooting.hpp"
#include "../../../src/template/static_modint.hpp"
using mint = modint998244353;
int main(void) {
int n;
cin >> n;
vector<mint> a(n);
rep(i, 0, n) cin >> a[i];
Graph<int> g(n);
map<pair<int, int>, pair<mint, mint>> mp;
rep(i, 0, n - 1) {
int u, v, b, c;
cin >> u >> v >> b >> c;
g.add_edge(u, v);
mp[minmax(u, v)] = {b, c};
}
using DP = pair<mint, int>;
auto f1 = [&](const DP& x, const DP& y) -> DP {
return {x.first + y.first, x.second + y.second};
};
auto f2 = [&](const DP& x, const int child, const int parent) -> DP {
auto [b, c] = mp[minmax(child, parent)];
return {(x.first + a[child]) * b + c * (x.second + 1), x.second + 1};
};
const DP id = {0, 0};
vector<DP> dp = rerooting(g, f1, f2, id);
rep(i, 0, n) {
cout << dp[i].first + a[i] << " \n"[i + 1 == n];
}
}
#line 1 "verify/library_checker/tree/tree_path_composite_sum.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/tree_path_composite_sum"
#line 2 "src/template/template.hpp"
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using P = pair<long long, long long>;
#define rep(i, a, b) for(long long i = (a); i < (b); ++i)
#define rrep(i, a, b) for(long long i = (a); i >= (b); --i)
constexpr long long inf = 4e18;
struct SetupIO {
SetupIO() {
ios::sync_with_stdio(0);
cin.tie(0);
cout << fixed << setprecision(30);
}
} setup_io;
#line 3 "src/graph/graph_template.hpp"
template <typename T>
struct Edge {
int from, to;
T cost;
int idx;
Edge()
: from(-1), to(-1), cost(-1), idx(-1) {}
Edge(const int from, const int to, const T& cost = 1, const int idx = -1)
: from(from), to(to), cost(cost), idx(idx) {}
operator int() const {
return to;
}
};
template <typename T>
struct Graph {
Graph(const int N)
: n(N), es(0), g(N) {}
int size() const {
return n;
}
int edge_size() const {
return es;
}
void add_edge(const int from, const int to, const T& cost = 1) {
assert(0 <= from and from < n);
assert(0 <= to and to < n);
g[from].emplace_back(from, to, cost, es);
g[to].emplace_back(to, from, cost, es++);
}
void add_directed_edge(const int from, const int to, const T& cost = 1) {
assert(0 <= from and from < n);
assert(0 <= to and to < n);
g[from].emplace_back(from, to, cost, es++);
}
inline vector<Edge<T>>& operator[](const int& k) {
assert(0 <= k and k < n);
return g[k];
}
inline const vector<Edge<T>>& operator[](const int& k) const {
assert(0 <= k and k < n);
return g[k];
}
private:
int n, es;
vector<vector<Edge<T>>> g;
};
template <typename T>
using Edges = vector<Edge<T>>;
#line 4 "src/tree/rerooting.hpp"
template <typename DP, typename T, typename F1, typename F2>
vector<DP> rerooting(const Graph<T>& g, const F1& f1, const F2& f2, const DP& id) {
const int n = g.size();
vector<DP> memo(n, id), dp(n, id);
auto dfs = [&](const auto& dfs, const int cur, const int par) -> void {
for(const Edge<T>& e : g[cur]) {
if(e.to == par) continue;
dfs(dfs, e.to, cur);
memo[cur] = f1(memo[cur], f2(memo[e.to], e.to, cur));
}
};
auto efs = [&](const auto& efs, const int cur, const int par, const DP& pval) -> void {
vector<DP> buf;
for(const Edge<T>& e : g[cur]) {
if(e.to == par) continue;
buf.emplace_back(f2(memo[e.to], e.to, cur));
}
vector<DP> head(buf.size() + 1), tail(buf.size() + 1);
head[0] = tail[buf.size()] = id;
for(int i = 0; i < (int)buf.size(); ++i) head[i + 1] = f1(head[i], buf[i]);
for(int i = (int)buf.size() - 1; i >= 0; --i) {
tail[i] = f1(tail[i + 1], buf[i]);
}
dp[cur] = par == -1 ? head.back() : f1(pval, head.back());
int idx = 0;
for(const Edge<T>& e : g[cur]) {
if(e.to == par) continue;
efs(efs, e.to, cur, f2(f1(pval, f1(head[idx], tail[idx + 1])), cur, e));
++idx;
}
};
dfs(dfs, 0, -1);
efs(efs, 0, -1, id);
return dp;
}
#line 3 "src/template/static_modint.hpp"
template <uint32_t m>
struct StaticModint {
using mint = StaticModint;
static constexpr uint32_t mod() {
return m;
}
static constexpr mint raw(const uint32_t v) {
mint a;
a._v = v;
return a;
}
constexpr StaticModint()
: _v(0) {}
template <class T>
constexpr StaticModint(const T& v) {
static_assert(is_integral_v<T>);
if constexpr(is_signed_v<T>) {
int64_t x = int64_t(v % int64_t(m));
if(x < 0) x += m;
_v = uint32_t(x);
} else _v = uint32_t(v % m);
}
constexpr uint32_t val() const {
return _v;
}
constexpr mint& operator++() {
return *this += 1;
}
constexpr mint& operator--() {
return *this -= 1;
}
constexpr mint operator++(int) {
mint res = *this;
++*this;
return res;
}
constexpr mint operator--(int) {
mint res = *this;
--*this;
return res;
}
constexpr mint& operator+=(mint rhs) {
if(_v >= m - rhs._v) _v -= m;
_v += rhs._v;
return *this;
}
constexpr mint& operator-=(mint rhs) {
if(_v < rhs._v) _v += m;
_v -= rhs._v;
return *this;
}
constexpr mint& operator*=(mint rhs) {
return *this = *this * rhs;
}
constexpr mint& operator/=(mint rhs) {
return *this *= rhs.inv();
}
constexpr mint operator+() const {
return *this;
}
constexpr mint operator-() const {
return mint{} - *this;
}
constexpr mint pow(long long n) const {
assert(0 <= n);
if(n == 0) return 1;
mint x = *this, r = 1;
while(1) {
if(n & 1) r *= x;
n >>= 1;
if(n == 0) return r;
x *= x;
}
}
constexpr mint inv() const {
if constexpr(prime) {
assert(_v);
return pow(m - 2);
} else {
const auto eg = inv_gcd(_v, m);
assert(eg.first == 1);
return eg.second;
}
}
friend constexpr mint operator+(mint lhs, mint rhs) {
return lhs += rhs;
}
friend constexpr mint operator-(mint lhs, mint rhs) {
return lhs -= rhs;
}
friend constexpr mint operator*(mint lhs, mint rhs) {
return uint64_t(lhs._v) * rhs._v;
}
friend constexpr mint operator/(mint lhs, mint rhs) {
return lhs /= rhs;
}
friend constexpr bool operator==(mint lhs, mint rhs) {
return lhs._v == rhs._v;
}
friend constexpr bool operator!=(mint lhs, mint rhs) {
return lhs._v != rhs._v;
}
friend istream& operator>>(istream& in, mint& x) {
long long a;
in >> a;
x = a;
return in;
}
friend ostream& operator<<(ostream& out, const mint& x) {
return out << x.val();
}
private:
uint32_t _v = 0;
static constexpr bool prime = []() -> bool {
if(m == 1) return 0;
if(m == 2 or m == 7 or m == 61) return 1;
if(m % 2 == 0) return 0;
uint32_t d = m - 1;
while(d % 2 == 0) d /= 2;
for(uint32_t a : {2, 7, 61}) {
uint32_t t = d;
mint y = mint(a).pow(t);
while(t != m - 1 && y != 1 && y != m - 1) {
y *= y;
t <<= 1;
}
if(y != m - 1 && t % 2 == 0) return 0;
}
return 1;
}();
static constexpr pair<int32_t, int32_t> inv_gcd(const int32_t a, const int32_t b) {
if(a == 0) return {b, 0};
int32_t s = b, t = a, m0 = 0, m1 = 1;
while(t) {
const int32_t u = s / t;
s -= t * u;
m0 -= m1 * u;
swap(s, t);
swap(m0, m1);
}
if(m0 < 0) m0 += b / s;
return {s, m0};
}
};
using modint998244353 = StaticModint<998244353>;
using modint1000000007 = StaticModint<1000000007>;
#line 6 "verify/library_checker/tree/tree_path_composite_sum.test.cpp"
using mint = modint998244353;
int main(void) {
int n;
cin >> n;
vector<mint> a(n);
rep(i, 0, n) cin >> a[i];
Graph<int> g(n);
map<pair<int, int>, pair<mint, mint>> mp;
rep(i, 0, n - 1) {
int u, v, b, c;
cin >> u >> v >> b >> c;
g.add_edge(u, v);
mp[minmax(u, v)] = {b, c};
}
using DP = pair<mint, int>;
auto f1 = [&](const DP& x, const DP& y) -> DP {
return {x.first + y.first, x.second + y.second};
};
auto f2 = [&](const DP& x, const int child, const int parent) -> DP {
auto [b, c] = mp[minmax(child, parent)];
return {(x.first + a[child]) * b + c * (x.second + 1), x.second + 1};
};
const DP id = {0, 0};
vector<DP> dp = rerooting(g, f1, f2, id);
rep(i, 0, n) {
cout << dp[i].first + a[i] << " \n"[i + 1 == n];
}
}