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graph/test/point_set_tree_path_composite_sum_fixed_root.test.cpp
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- Last update: 2026-04-09 11:45:48+09:00
- Problem: https://judge.yosupo.jp/problem/point_set_tree_path_composite_sum_fixed_root
Depends on
- graph/dynamic_tree_dp.hpp
- graph/graph.hpp
- graph/static_top_tree.hpp
- number_theory/mod_int.hpp
- number_theory/utils.hpp
- template/fastio.hpp
- template/template.hpp
Code
#define PROBLEM "https://judge.yosupo.jp/problem/point_set_tree_path_composite_sum_fixed_root"
#define FAST_IO
#include "../../graph/dynamic_tree_dp.hpp"
#include "../../number_theory/mod_int.hpp"
#include "../../template/template.hpp"
#include "../../template/fastio.hpp"
using M = ModInt<998244353>;
struct TreeDP {
using Value = pair<M, M>;
using Func = tuple<M, M, M, M>;
V<M> as;
V<pair<M, M>> fs;
Value id() const {
return Value(0, M());
}
Value op(Value x, Value y) const {
return Value(x.first + y.first, x.second + y.second);
}
Func composite(Func f, Func g) const {
auto [f0, f1, f2, f3] = f;
auto [g0, g1, g2, g3] = g;
M h0 = f0 * g0;
M h1 = f0 * g1 + f1;
M h2 = f0 * g2 + f1 * g3 + f2;
M h3 = f3 + g3;
return Func(h0, h1, h2, h3);
}
Value apply(Func f, Value x) const {
x.first = get<0>(f) * x.first + get<1>(f) * x.second;
x.first += get<2>(f);
x.second += get<3>(f);
return x;
}
Func lift(i32 vtx, Value val) const {
val.first += as[vtx];
val.second += M::raw(1);
val.first = fs[vtx].first * val.first + fs[vtx].second * val.second;
return Func(fs[vtx].first, fs[vtx].second, val.first, val.second);
}
};
void solve() {
i32 n, q;
rd.read(n, q);
TreeDP dp;
dp.as.resize(n);
REP(i, n) {
rd.read(dp.as[i].val);
}
Graph<pair<M, M>> g(n);
REP(i, n - 1) {
i32 u, v;
M a, b;
rd.read(u, v, a.val, b.val);
g.add_edge(u, v, pair<M, M>(a, b));
}
g.build();
dp.fs.resize(n);
dp.fs[0] = pair<M, M>(M::raw(1), M());
V<i32> es(n - 1);
{
queue<pi> que;
que.emplace(0, -1);
while (!que.empty()) {
auto [v, p] = que.front();
que.pop();
for (const auto &e : g[v]) {
if (e.to != p) {
es[e.id] = e.to;
dp.fs[e.to] = e.weight;
que.emplace(e.to, v);
}
}
}
}
DynamicTreeDP<TreeDP> tree(g, dp);
REP(qi, q) {
i32 ty;
rd.read(ty);
if (ty == 0) {
i32 w;
M x;
rd.read(w, x.val);
dp.as[w] = x;
wr.writeln(tree.update(w).first.val);
} else {
i32 e;
M y, z;
rd.read(e, y.val, z.val);
dp.fs[es[e]] = pair<M, M>(y, z);
wr.writeln(tree.update(es[e]).first.val);
}
}
}
int main() {
i32 t = 1;
// cin >> t;
while (t--) {
solve();
}
}#line 1 "graph/test/point_set_tree_path_composite_sum_fixed_root.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/point_set_tree_path_composite_sum_fixed_root"
#define FAST_IO
#line 2 "graph/static_top_tree.hpp"
#include <algorithm>
#include <queue>
#line 2 "graph/graph.hpp"
#include <iostream>
#include <cassert>
#include <vector>
template <typename T>
struct Edge {
using W = T;
int from, to, id;
W weight;
Edge<T> rev() const {
return Edge<T>{to, from, id, weight};
}
};
template <typename T>
void debug(const Edge<T> &e) {
std::cerr << e.from << " -> " << e.to << " id = " << e.id << std::cerr << " weight = ";
debug(e.weight);
}
template <typename T = int, bool DIR = false>
class Graph {
public:
using E = Edge<T>;
using W = T;
static constexpr bool DIRECTED = DIR;
struct Adjacency {
using Iter = typename std::vector<E>::iterator;
Iter be, en;
Iter begin() const { return be; }
Iter end() const { return en; }
int size() const { return (int)std::distance(be, en); }
E &operator[](int idx) const { return be[idx]; }
};
struct ConstAdjacency {
using Iter = typename std::vector<E>::const_iterator;
Iter be, en;
Iter begin() const { return be; }
Iter end() const { return en; }
int size() const { return (int)std::distance(be, en); }
const E &operator[](int idx) const { return be[idx]; }
};
private:
int n, m;
std::vector<E> edges, csr;
std::vector<int> sep;
bool built;
public:
Graph(int n) : n(n), m(0), built(false) {}
int v() const { return n; }
int e() const { return m; }
int add_vertex() {
return n++;
}
void add_edge(int from, int to, W weight = 1) {
assert(0 <= from && from < n && 0 <= to && to < n);
edges.emplace_back(E{from, to, m++, weight});
}
void build() {
sep.assign(n + 1, 0);
csr.resize(DIRECTED ? m : 2 * m);
for (const E &e : edges) {
++sep[e.from + 1];
if (!DIRECTED) {
++sep[e.to + 1];
}
}
for (int i = 0; i < n; ++i) {
sep[i + 1] += sep[i];
}
std::vector<int> c = sep;
for (const E &e : edges) {
csr[c[e.from]++] = e;
if (!DIRECTED) {
csr[c[e.to]++] = e.rev();
}
}
built = true;
}
Adjacency operator[](int v) {
assert(built && 0 <= v && v < n);
return Adjacency{csr.begin() + sep[v], csr.begin() + sep[v + 1]};
}
ConstAdjacency operator[](int v) const {
assert(built && 0 <= v && v < n);
return ConstAdjacency{csr.begin() + sep[v], csr.begin() + sep[v + 1]};
}
};
#line 5 "graph/static_top_tree.hpp"
class StaticTopTree {
public:
enum class NodeType {
AddEdge,
AddVertex,
Compress,
Rake
};
struct Node {
NodeType ty;
int par, lch, rch;
};
std::vector<Node> nodes;
int stt_root;
template <typename T, bool DIR>
StaticTopTree(Graph<T, DIR> &g, int root = 0) {
assert(0 <= root && root < g.v());
nodes.reserve(3 * g.v());
dfs(g, root, -1);
nodes.resize(g.v(), Node{NodeType::AddVertex, -1, -1, -1});
stt_root = compress(g, root, -1).second;
}
private:
template <typename T, bool DIR>
int dfs(Graph<T, DIR> &g, int v, int p) {
int sz = 1, mx = 0;
for (Edge<T> &e : g[v]) {
if (e.to == p) {
continue;
}
int t = dfs(g, e.to, v);
if (mx < t) {
mx = t;
swap(g[v][0], e);
}
sz += t;
}
return sz;
}
int make_node(NodeType ty, int lch, int rch) {
int v = (int)nodes.size();
nodes.emplace_back(Node{ty, -1, lch, rch});
if (lch != -1) {
nodes[lch].par = v;
}
if (rch != -1) {
nodes[rch].par = v;
}
return v;
}
void merge(std::vector<std::pair<int, int>> &path) {
auto [xf, xs] = path.back();
path.pop_back();
auto [yf, ys] = path.back();
path.pop_back();
path.emplace_back(std::max(xf, yf) + 1, make_node(NodeType::Compress, ys, xs));
}
template <typename T, bool DIR>
std::pair<int, int> compress(const Graph<T, DIR> &g, int v, int p) {
std::vector<std::pair<int, int>> path;
while (true) {
path.emplace_back(rake(g, v, p));
while (true) {
int l = (int)path.size();
if (l >= 3 && (path[l - 3].first == path[l - 2].first || path[l - 3].first <= path[l - 1].first)) {
std::pair<int, int> t = path.back();
path.pop_back();
merge(path);
path.emplace_back(t);
} else if (l >= 2 && path[l - 2].first <= path[l - 1].first) {
merge(path);
} else {
break;
}
}
if (g[v].size() == 0 || g[v][0].to == p) {
break;
}
p = v;
v = g[v][0].to;
}
while (path.size() >= 2) {
merge(path);
}
auto [xf, xs] = path.back();
int z = make_node(NodeType::AddEdge, xs, -1);
return std::pair<int, int>(xf + 1, z);
}
template <typename T, bool DIR>
std::pair<int, int> rake(const Graph<T, DIR> &g, int v, int p) {
std::priority_queue<std::pair<int, int>, std::vector<std::pair<int, int>>, std::greater<>> pq;
for (int i = 1; i < (int)g[v].size(); ++i) {
const Edge<T> &e = g[v][i];
if (e.to == p) {
continue;
}
pq.emplace(compress(g, e.to, v));
}
if (pq.empty()) {
return std::pair<int, int>(0, v);
}
while (pq.size() >= 2) {
auto [xf, xs] = pq.top();
pq.pop();
auto [yf, ys] = pq.top();
pq.pop();
pq.emplace(std::max(xf, yf) + 1, make_node(NodeType::Rake, xs, ys));
}
auto [rf, rs] = pq.top();
nodes[v].lch = rs;
nodes[rs].par = v;
return std::pair<int, int>(rf + 1, v);
}
};
#line 3 "graph/dynamic_tree_dp.hpp"
template <typename TreeDP>
struct DynamicTreeDP {
using Value = typename TreeDP::Value;
using Func = typename TreeDP::Func;
TreeDP &dp;
StaticTopTree stt;
std::vector<Value> value;
std::vector<Func> func;
template <typename T, bool DIR>
DynamicTreeDP(Graph<T, DIR> &g, TreeDP &dp, int root = 0) : dp(dp), stt(g, root), value(stt.nodes.size()), func(stt.nodes.size()) {
init(stt.stt_root);
}
Value update(int v) {
while (v != -1) {
update_single(v);
v = stt.nodes[v].par;
}
return value[stt.stt_root];
}
Value get() const {
return value[stt.stt_root];
}
private:
void init(int v) {
const StaticTopTree::Node &node = stt.nodes[v];
if (node.lch != -1) {
init(node.lch);
}
if (node.rch != -1) {
init(node.rch);
}
update_single(v);
}
void update_single(int v) {
const StaticTopTree::Node &node = stt.nodes[v];
if (node.ty == StaticTopTree::NodeType::AddEdge) {
value[v] = dp.apply(func[node.lch], dp.id());
} else if (node.ty == StaticTopTree::NodeType::AddVertex) {
func[v] = dp.lift(v, node.lch == -1 ? dp.id() : value[node.lch]);
} else if (node.ty == StaticTopTree::NodeType::Compress) {
func[v] = dp.composite(func[node.lch], func[node.rch]);
} else {
value[v] = dp.op(value[node.lch], value[node.rch]);
}
}
};
#line 2 "number_theory/mod_int.hpp"
#line 5 "number_theory/mod_int.hpp"
#include <type_traits>
#line 2 "number_theory/utils.hpp"
#include <utility>
constexpr bool is_prime(unsigned n) {
if (n == 0 || n == 1) {
return false;
}
for (unsigned i = 2; i * i <= n; ++i) {
if (n % i == 0) {
return false;
}
}
return true;
}
constexpr unsigned mod_pow(unsigned x, unsigned y, unsigned mod) {
unsigned ret = 1, self = x;
while (y != 0) {
if (y & 1) {
ret = (unsigned)((unsigned long long)ret * self % mod);
}
self = (unsigned)((unsigned long long)self * self % mod);
y /= 2;
}
return ret;
}
template <unsigned mod>
constexpr unsigned primitive_root() {
static_assert(is_prime(mod), "`mod` must be a prime number.");
if (mod == 2) {
return 1;
}
unsigned primes[32] = {};
int it = 0;
{
unsigned m = mod - 1;
for (unsigned i = 2; i * i <= m; ++i) {
if (m % i == 0) {
primes[it++] = i;
while (m % i == 0) {
m /= i;
}
}
}
if (m != 1) {
primes[it++] = m;
}
}
for (unsigned i = 2; i < mod; ++i) {
bool ok = true;
for (int j = 0; j < it; ++j) {
if (mod_pow(i, (mod - 1) / primes[j], mod) == 1) {
ok = false;
break;
}
}
if (ok) return i;
}
return 0;
}
// y >= 1
template <typename T>
constexpr T safe_mod(T x, T y) {
x %= y;
if (x < 0) {
x += y;
}
return x;
}
// y != 0
template <typename T>
constexpr T floor_div(T x, T y) {
if (y < 0) {
x *= -1;
y *= -1;
}
if (x >= 0) {
return x / y;
} else {
return -((-x + y - 1) / y);
}
}
// y != 0
template <typename T>
constexpr T ceil_div(T x, T y) {
if (y < 0) {
x *= -1;
y *= -1;
}
if (x >= 0) {
return (x + y - 1) / y;
} else {
return -(-x / y);
}
}
// b >= 1
// returns (g, x) s.t. g = gcd(a, b), a * x = g (mod b), 0 <= x < b / g
// from ACL
template <typename T>
std::pair<T, T> extgcd(T a, T b) {
a = safe_mod(a, b);
T s = b, t = a, m0 = 0, m1 = 1;
while (t) {
T u = s / t;
s -= t * u;
m0 -= m1 * u;
std::swap(s, t);
std::swap(m0, m1);
}
if (m0 < 0) {
m0 += b / s;
}
return std::pair<T, T>(s, m0);
}
// b >= 1
// returns (g, x, y) s.t. g = gcd(a, b), a * x + b * y = g, 0 <= x < b / g, |y| < max(2, |a| / g)
template <typename T>
std::tuple<T, T, T> extgcd2(T a, T b) {
T _a = safe_mod(a, b);
T quot = (a - _a) / b;
T x00 = 0, x01 = 1, y0 = b;
T x10 = 1, x11 = -quot, y1 = _a;
while (y1) {
T u = y0 / y1;
x00 -= u * x10;
x01 -= u * x11;
y0 -= u * y1;
std::swap(x00, x10);
std::swap(x01, x11);
std::swap(y0, y1);
}
if (x00 < 0) {
x00 += b / y0;
x01 -= a / y0;
}
return std::tuple<T, T, T>(y0, x00, x01);
}
// gcd(x, m) == 1
template <typename T>
T inv_mod(T x, T m) {
return extgcd(x, m).second;
}
#line 7 "number_theory/mod_int.hpp"
template <unsigned mod>
struct ModInt {
static_assert(mod != 0, "`mod` must not be equal to 0.");
static_assert(mod < (1u << 31),
"`mod` must be less than (1u << 31) = 2147483648.");
unsigned val;
static constexpr unsigned get_mod() { return mod; }
constexpr ModInt() : val(0) {}
template <typename T, std::enable_if_t<std::is_signed_v<T>> * = nullptr>
constexpr ModInt(T x)
: val((unsigned)((long long)x % (long long)mod + (x < 0 ? mod : 0))) {}
template <typename T, std::enable_if_t<std::is_unsigned_v<T>> * = nullptr>
constexpr ModInt(T x) : val((unsigned)(x % mod)) {}
static constexpr ModInt raw(unsigned x) {
ModInt<mod> ret;
ret.val = x;
return ret;
}
constexpr unsigned get_val() const { return val; }
constexpr ModInt operator+() const { return *this; }
constexpr ModInt operator-() const { return ModInt<mod>(0u) - *this; }
constexpr ModInt &operator+=(const ModInt &rhs) {
val += rhs.val;
if (val >= mod) val -= mod;
return *this;
}
constexpr ModInt &operator-=(const ModInt &rhs) {
val -= rhs.val;
if (val >= mod) val += mod;
return *this;
}
constexpr ModInt &operator*=(const ModInt &rhs) {
val = (unsigned long long)val * rhs.val % mod;
return *this;
}
constexpr ModInt &operator/=(const ModInt &rhs) {
val = (unsigned long long)val * rhs.inv().val % mod;
return *this;
}
friend constexpr ModInt operator+(const ModInt &lhs, const ModInt &rhs) {
return ModInt<mod>(lhs) += rhs;
}
friend constexpr ModInt operator-(const ModInt &lhs, const ModInt &rhs) {
return ModInt<mod>(lhs) -= rhs;
}
friend constexpr ModInt operator*(const ModInt &lhs, const ModInt &rhs) {
return ModInt<mod>(lhs) *= rhs;
}
friend constexpr ModInt operator/(const ModInt &lhs, const ModInt &rhs) {
return ModInt<mod>(lhs) /= rhs;
}
constexpr ModInt pow(unsigned long long x) const {
ModInt<mod> ret = ModInt<mod>::raw(1);
ModInt<mod> self = *this;
while (x != 0) {
if (x & 1) ret *= self;
self *= self;
x >>= 1;
}
return ret;
}
constexpr ModInt inv() const {
static_assert(is_prime(mod), "`mod` must be a prime number.");
assert(val != 0);
return this->pow(mod - 2);
}
friend std::istream &operator>>(std::istream &is, ModInt<mod> &x) {
long long val;
is >> val;
x.val = val % mod + (val < 0 ? mod : 0);
return is;
}
friend std::ostream &operator<<(std::ostream &os, const ModInt<mod> &x) {
os << x.val;
return os;
}
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.val != rhs.val;
}
};
template <unsigned mod>
void debug(ModInt<mod> x) {
std::cerr << x.val;
}
#line 2 "template/template.hpp"
#include <bits/stdc++.h>
#define OVERRIDE(a, b, c, d, ...) d
#define REP2(i, n) for (i32 i = 0; i < (i32)(n); ++i)
#define REP3(i, m, n) for (i32 i = (i32)(m); i < (i32)(n); ++i)
#define REP(...) OVERRIDE(__VA_ARGS__, REP3, REP2)(__VA_ARGS__)
#define PER2(i, n) for (i32 i = (i32)(n)-1; i >= 0; --i)
#define PER3(i, m, n) for (i32 i = (i32)(n)-1; i >= (i32)(m); --i)
#define PER(...) OVERRIDE(__VA_ARGS__, PER3, PER2)(__VA_ARGS__)
#define ALL(x) begin(x), end(x)
#define LEN(x) (i32)(x.size())
using namespace std;
using u32 = unsigned int;
using u64 = unsigned long long;
using i32 = signed int;
using i64 = signed long long;
using f64 = double;
using f80 = long double;
using pi = pair<i32, i32>;
using pl = pair<i64, i64>;
template <typename T>
using V = vector<T>;
template <typename T>
using VV = V<V<T>>;
template <typename T>
using VVV = V<V<V<T>>>;
template <typename T>
using VVVV = V<V<V<V<T>>>>;
template <typename T>
using PQR = priority_queue<T, V<T>, greater<T>>;
template <typename T>
bool chmin(T &x, const T &y) {
if (x > y) {
x = y;
return true;
}
return false;
}
template <typename T>
bool chmax(T &x, const T &y) {
if (x < y) {
x = y;
return true;
}
return false;
}
template <typename T>
i32 lob(const V<T> &arr, const T &v) {
return (i32)(lower_bound(ALL(arr), v) - arr.begin());
}
template <typename T>
i32 upb(const V<T> &arr, const T &v) {
return (i32)(upper_bound(ALL(arr), v) - arr.begin());
}
template <typename T>
V<i32> argsort(const V<T> &arr) {
V<i32> ret(arr.size());
iota(ALL(ret), 0);
sort(ALL(ret), [&](i32 i, i32 j) -> bool {
if (arr[i] == arr[j]) {
return i < j;
} else {
return arr[i] < arr[j];
}
});
return ret;
}
#ifdef INT128
using u128 = __uint128_t;
using i128 = __int128_t;
#endif
[[maybe_unused]] constexpr i32 INF = 1000000100;
[[maybe_unused]] constexpr i64 INF64 = 3000000000000000100;
struct SetUpIO {
SetUpIO() {
#ifdef FAST_IO
ios::sync_with_stdio(false);
cin.tie(nullptr);
#endif
cout << fixed << setprecision(15);
}
} set_up_io;
void scan(char &x) { cin >> x; }
void scan(u32 &x) { cin >> x; }
void scan(u64 &x) { cin >> x; }
void scan(i32 &x) { cin >> x; }
void scan(i64 &x) { cin >> x; }
void scan(f64 &x) { cin >> x; }
void scan(string &x) { cin >> x; }
template <typename T>
void scan(V<T> &x) {
for (T &ele : x) {
scan(ele);
}
}
void read() {}
template <typename Head, typename... Tail>
void read(Head &head, Tail &...tail) {
scan(head);
read(tail...);
}
#define CHAR(...) \
char __VA_ARGS__; \
read(__VA_ARGS__);
#define U32(...) \
u32 __VA_ARGS__; \
read(__VA_ARGS__);
#define U64(...) \
u64 __VA_ARGS__; \
read(__VA_ARGS__);
#define I32(...) \
i32 __VA_ARGS__; \
read(__VA_ARGS__);
#define I64(...) \
i64 __VA_ARGS__; \
read(__VA_ARGS__);
#define F64(...) \
f64 __VA_ARGS__; \
read(__VA_ARGS__);
#define STR(...) \
string __VA_ARGS__; \
read(__VA_ARGS__);
#define VEC(type, name, size) \
V<type> name(size); \
read(name);
#define VVEC(type, name, size1, size2) \
VV<type> name(size1, V<type>(size2)); \
read(name);
#line 6 "template/fastio.hpp"
// unable to read INT_MIN (int), LLONG_MIN (long long)
class Reader {
FILE *fp;
static constexpr int BUF = 1 << 18;
char buf[BUF];
char *pl, *pr;
void reread() {
int wd = pr - pl;
std::memcpy(buf, pl, wd);
pl = buf;
pr = buf + wd;
pr += std::fread(pr, 1, BUF - wd, fp);
}
char skip() {
char ch = *pl++;
while (ch <= ' ') {
ch = *pl++;
}
return ch;
}
template <typename T>
void read_unsigned(T &x) {
if (pr - pl < 64) {
reread();
}
x = 0;
char ch = skip();
while ('0' <= ch) {
x = 10 * x + (0xf & ch);
ch = *pl++;
}
}
template <typename T>
void read_signed(T &x) {
if (pr - pl < 64) {
reread();
}
x = 0;
bool neg = false;
char ch = skip();
if (ch == '-') {
ch = *pl++;
neg = true;
}
while ('0' <= ch) {
x = 10 * x + (0xf & ch);
ch = *pl++;
}
if (neg) {
x = -x;
}
}
void read_single(int &x) { read_signed(x); }
void read_single(unsigned &x) { read_unsigned(x); }
void read_single(long &x) { read_signed(x); }
void read_single(unsigned long &x) { read_signed(x); }
void read_single(long long &x) { read_signed(x); }
void read_single(unsigned long long &x) { read_unsigned(x); }
public:
Reader(FILE *fp) : fp(fp), pl(buf), pr(buf) { reread(); }
void read() {}
template <typename Head, typename... Tail>
void read(Head &head, Tail &...tail) {
read_single(head);
read(tail...);
}
};
struct NumberToString {
char buf[10000][4];
constexpr NumberToString() : buf() {
for (int i = 0; i < 10000; ++i) {
int n = i;
for (int j = 3; j >= 0; --j) {
buf[i][j] = '0' + n % 10;
n /= 10;
}
}
}
} constexpr number_to_string_precalc;
class Writer {
FILE *fp;
static constexpr int BUF = 1 << 18;
char buf[BUF];
char *ptr;
void write_u32(unsigned x) {
if ((buf + BUF - ptr) < 32) {
flush();
}
static char sml[12];
int t = 8;
while (x >= 10000) {
unsigned n = x % 10000;
x /= 10000;
std::memcpy(sml + t, number_to_string_precalc.buf[n], 4);
t -= 4;
}
if (x >= 1000) {
std::memcpy(ptr, number_to_string_precalc.buf[x], 4);
ptr += 4;
} else if (x >= 100) {
std::memcpy(ptr, number_to_string_precalc.buf[x] + 1, 3);
ptr += 3;
} else if (x >= 10) {
unsigned q = (x * 103) >> 10;
*ptr++ = q | '0';
*ptr++ = (x - 10 * q) | '0';
} else {
*ptr++ = '0' | x;
}
std::memcpy(ptr, sml + (t + 4), 8 - t);
ptr += 8 - t;
}
void write_u64(unsigned long long x) {
if ((buf + BUF - ptr) < 32) {
flush();
}
if (x >= 10000000000000000) {
unsigned long long z = x % 100000000;
x /= 100000000;
unsigned long long y = x % 100000000;
x /= 100000000;
if (x >= 1000) {
std::memcpy(ptr, number_to_string_precalc.buf[x], 4);
ptr += 4;
} else if (x >= 100) {
std::memcpy(ptr, number_to_string_precalc.buf[x] + 1, 3);
ptr += 3;
} else if (x >= 10) {
unsigned q = (x * 103) >> 10;
*ptr++ = q | '0';
*ptr++ = (x - 10 * q) | '0';
} else {
*ptr++ = '0' | x;
}
std::memcpy(ptr, number_to_string_precalc.buf[y / 10000], 4);
std::memcpy(ptr + 4, number_to_string_precalc.buf[y % 10000], 4);
std::memcpy(ptr + 8, number_to_string_precalc.buf[z / 10000], 4);
std::memcpy(ptr + 12, number_to_string_precalc.buf[z % 10000], 4);
ptr += 16;
} else {
static char sml[12];
int t = 8;
while (x >= 10000) {
unsigned long long n = x % 10000;
x /= 10000;
std::memcpy(sml + t, number_to_string_precalc.buf[n], 4);
t -= 4;
}
if (x >= 1000) {
std::memcpy(ptr, number_to_string_precalc.buf[x], 4);
ptr += 4;
} else if (x >= 100) {
std::memcpy(ptr, number_to_string_precalc.buf[x] + 1, 3);
ptr += 3;
} else if (x >= 10) {
unsigned q = (x * 103) >> 10;
*ptr++ = q | '0';
*ptr++ = (x - 10 * q) | '0';
} else {
*ptr++ = '0' | x;
}
std::memcpy(ptr, sml + (t + 4), 8 - t);
ptr += 8 - t;
}
}
void write_char(char c) {
if (ptr == buf + BUF) {
flush();
}
*ptr++ = c;
}
template <typename T>
void write_unsigned(T x) {
if constexpr (std::is_same_v<T, unsigned long long> ||
std::is_same_v<T, unsigned long>) {
write_u64(x);
} else {
write_u32(x);
}
}
template <typename T>
void write_signed(T x) {
std::make_unsigned_t<T> y = x;
if (x < 0) {
write_char('-');
y = -y;
}
write_unsigned(y);
}
void write_string(const std::string &s) {
for (char c : s) {
write_char(c);
}
}
void write_single(int x) { write_signed(x); }
void write_single(unsigned x) { write_unsigned(x); }
void write_single(long x) { write_signed(x); }
void write_single(unsigned long x) { write_unsigned(x); }
void write_single(long long x) { write_signed(x); }
void write_single(unsigned long long x) { write_unsigned(x); }
void write_single(char c) { write_char(c); }
void write_single(const std::string &s) { write_string(s); }
public:
Writer(FILE *fp) : fp(fp), ptr(buf) {}
~Writer() { flush(); }
void flush() {
std::fwrite(buf, 1, ptr - buf, fp);
ptr = buf;
}
void write() {}
template <typename Head, typename... Tail>
void write(Head &&head, Tail &&...tail) {
write_single(head);
if (sizeof...(Tail)) {
write_char(' ');
}
write(std::forward<Tail>(tail)...);
}
template <typename... T>
void writeln(T &&...t) {
write(std::forward<T>(t)...);
write_char('\n');
}
};
Reader rd(stdin);
Writer wr(stdout);
#line 7 "graph/test/point_set_tree_path_composite_sum_fixed_root.test.cpp"
using M = ModInt<998244353>;
struct TreeDP {
using Value = pair<M, M>;
using Func = tuple<M, M, M, M>;
V<M> as;
V<pair<M, M>> fs;
Value id() const {
return Value(0, M());
}
Value op(Value x, Value y) const {
return Value(x.first + y.first, x.second + y.second);
}
Func composite(Func f, Func g) const {
auto [f0, f1, f2, f3] = f;
auto [g0, g1, g2, g3] = g;
M h0 = f0 * g0;
M h1 = f0 * g1 + f1;
M h2 = f0 * g2 + f1 * g3 + f2;
M h3 = f3 + g3;
return Func(h0, h1, h2, h3);
}
Value apply(Func f, Value x) const {
x.first = get<0>(f) * x.first + get<1>(f) * x.second;
x.first += get<2>(f);
x.second += get<3>(f);
return x;
}
Func lift(i32 vtx, Value val) const {
val.first += as[vtx];
val.second += M::raw(1);
val.first = fs[vtx].first * val.first + fs[vtx].second * val.second;
return Func(fs[vtx].first, fs[vtx].second, val.first, val.second);
}
};
void solve() {
i32 n, q;
rd.read(n, q);
TreeDP dp;
dp.as.resize(n);
REP(i, n) {
rd.read(dp.as[i].val);
}
Graph<pair<M, M>> g(n);
REP(i, n - 1) {
i32 u, v;
M a, b;
rd.read(u, v, a.val, b.val);
g.add_edge(u, v, pair<M, M>(a, b));
}
g.build();
dp.fs.resize(n);
dp.fs[0] = pair<M, M>(M::raw(1), M());
V<i32> es(n - 1);
{
queue<pi> que;
que.emplace(0, -1);
while (!que.empty()) {
auto [v, p] = que.front();
que.pop();
for (const auto &e : g[v]) {
if (e.to != p) {
es[e.id] = e.to;
dp.fs[e.to] = e.weight;
que.emplace(e.to, v);
}
}
}
}
DynamicTreeDP<TreeDP> tree(g, dp);
REP(qi, q) {
i32 ty;
rd.read(ty);
if (ty == 0) {
i32 w;
M x;
rd.read(w, x.val);
dp.as[w] = x;
wr.writeln(tree.update(w).first.val);
} else {
i32 e;
M y, z;
rd.read(e, y.val, z.val);
dp.fs[es[e]] = pair<M, M>(y, z);
wr.writeln(tree.update(es[e]).first.val);
}
}
}
int main() {
i32 t = 1;
// cin >> t;
while (t--) {
solve();
}
}