結果
| 問題 | No.650 行列木クエリ |
| ユーザー |
 hirayuu_yc
|
| 提出日時 | 2024-05-14 21:32:58 |
| 言語 | C++23(gcc13) (gcc 13.2.0 + boost 1.83.0) |
| 結果 |
AC
|
| 実行時間 | 107 ms / 2,000 ms |
| コード長 | 23,478 bytes |
| コンパイル時間 | 6,270 ms |
| コンパイル使用メモリ | 303,864 KB |
| 実行使用メモリ | 33,656 KB |
| 最終ジャッジ日時 | 2024-05-14 21:33:06 |
| 合計ジャッジ時間 | 6,019 ms |
|
ジャッジサーバーID （参考情報） |
judge5 / judge4 |
（要ログイン）
テストケース
テストケース表示| 入力 | 結果 | 実行時間 実行使用メモリ |
|---|---|---|
| testcase_00 | AC | 2 ms
6,816 KB |
| testcase_01 | AC | 39 ms
6,944 KB |
| testcase_02 | AC | 107 ms
20,160 KB |
| testcase_03 | AC | 2 ms
6,940 KB |
| testcase_04 | AC | 40 ms
6,940 KB |
| testcase_05 | AC | 103 ms
20,160 KB |
| testcase_06 | AC | 2 ms
6,944 KB |
| testcase_07 | AC | 2 ms
6,940 KB |
| testcase_08 | AC | 41 ms
9,344 KB |
| testcase_09 | AC | 92 ms
33,656 KB |
| testcase_10 | AC | 2 ms
6,940 KB |
ソースコード
#line 2 "/root/AtCoder/Halc-Library/DataStructure/SegmentTree.hpp"
#include <cstdint>
#include <queue>
#include <stack>
#include <vector>
template <class M>
struct SegmentTree {
using T = typename M::T;
int32_t siz;
std::vector<T> tree;
SegmentTree(int32_t sz) {
siz = sz;
tree = std::vector<T>(siz << 1, M::e);
}
SegmentTree(std::vector<T> def) {
siz = def.size();
tree = std::vector<T>(siz << 1, M::e);
for (int32_t i = 0; i < siz; i++) {
tree[i + siz] = def[i];
}
for (int32_t i = siz - 1; i > 0; i--) {
tree[i] = M::op(tree[i << 1], tree[(i << 1) + 1]);
}
}
void set(int32_t p, T v) {
p += siz;
tree[p] = v;
p >>= 1;
while (p > 0) {
tree[p] = M::op(tree[p << 1], tree[(p << 1) + 1]);
p >>= 1;
}
}
T get(int32_t p) { return tree[p + siz]; }
T prod(int32_t lf, int32_t ri) {
lf += siz;
ri += siz;
T rel = M::e;
T rer = M::e;
while (lf < ri) {
if (lf & 1) {
rel = M::op(rel, tree[lf]);
lf++;
}
if (ri & 1) {
ri--;
rer = M::op(tree[ri], rer);
}
lf >>= 1;
ri >>= 1;
}
return M::op(rel, rer);
}
template <bool (*f)(T)>
int32_t max_right(int lf) {
return max_right(lf, [](T x) { return f(x); });
}
template <class F>
int32_t max_right(int32_t lf, F f) {
lf += siz;
int32_t ri = siz << 1;
std::queue<int32_t> lfp;
std::stack<int32_t> rip;
while (lf < ri) {
if (lf & 1) {
lfp.push(lf);
lf++;
}
if (ri & 1) {
ri--;
rip.push(ri);
}
lf >>= 1;
ri >>= 1;
}
T val = M::e;
while (!lfp.empty()) {
int32_t i = lfp.front();
lfp.pop();
if (!f(M::op(val, tree[i]))) {
while (i < siz) {
i <<= 1;
if (f(M::op(val, tree[i]))) {
val = M::op(val, tree[i]);
i++;
}
}
return i - siz;
}
val = M::op(val, tree[i]);
}
while (!rip.empty()) {
int32_t i = rip.top();
rip.pop();
if (!f(M::op(val, tree[i]))) {
while (i < siz) {
i <<= 1;
if (f(M::op(val, tree[i]))) {
val = M::op(val, tree[i]);
i++;
}
}
return i - siz;
}
val = M::op(val, tree[i]);
}
return siz;
}
template <bool (*f)(T)>
int32_t min_left(int ri) {
return min_left(ri, [](T x) { return f(x); });
}
template <class F>
int32_t min_left(int32_t ri, F f) {
ri += siz;
int32_t lf = siz;
std::queue<int32_t> rip;
std::stack<int32_t> lfp;
while (lf < ri) {
if (lf & 1) {
lfp.push(lf);
lf++;
}
if (ri & 1) {
ri--;
rip.push(ri);
}
lf >>= 1;
ri >>= 1;
}
T val = M::e;
while (!rip.empty()) {
int32_t i = rip.front();
rip.pop();
if (!f(M::op(val, tree[i]))) {
while (i < siz) {
i <<= 1;
i++;
if (f(M::op(tree[i], val))) {
val = M::op(tree[i], val);
i--;
}
}
return i - siz + 1;
}
val = M::op(tree[i], val);
}
while (!lfp.empty()) {
int32_t i = lfp.top();
lfp.pop();
if (!f(M::op(val, tree[i]))) {
while (i < siz) {
i <<= 1;
i++;
if (f(M::op(tree[i], val))) {
val = M::op(tree[i], val);
i--;
}
}
return i - siz + 1;
}
val = M::op(tree[i], val);
}
return 0;
}
int32_t size() { return siz; }
};
#line 4 "/root/AtCoder/Halc-Library/Graph/Graph.hpp"
template <class T = int32_t>
struct Edge {
int32_t from, to;
T cost;
int32_t idx;
Edge() = default;
Edge(int32_t from, int32_t to, T cost = 1, int32_t idx = -1)
: from(from), to(to), cost(cost), idx(idx) {}
operator int32_t() { return to; }
void reverse() { std::swap(from, to); }
};
template <class T = int32_t>
struct Graph {
std::vector<std::vector<Edge<T>>> gr;
int32_t eds = 0;
Graph() = default;
Graph(int32_t n) { gr.resize(n); }
void add_edge(int32_t from, int32_t to, T cost = 1, bool directed = false) {
gr[from].emplace_back(from, to, cost, eds);
if (!directed) {
gr[to].emplace_back(to, from, cost, eds);
}
eds++;
}
void add_directed_edge(int32_t from, int32_t to, T cost = 1) {
gr[from].emplace_back(from, to, cost, eds);
eds++;
}
inline std::vector<Edge<T>> &operator[](const int32_t &p) { return gr[p]; }
int32_t size() { return gr.size(); }
};
template <class T>
Graph<T> reverse_edges(Graph<T> &gr) {
Graph<T> ret(gr.size());
for (int32_t i = 0; i < gr.size(); i++) {
for (Edge<T> j : gr[i]) {
ret[j].emplace_back(j);
ret[j].back().reverse();
}
}
return ret;
}
#line 3 "/root/AtCoder/Halc-Library/Modint/Modint.hpp"
#include <iostream>
template <uint64_t Mod>
struct Modint {
uint64_t x;
constexpr Modint() noexcept { x = 0; }
constexpr Modint(int64_t val) noexcept {
x = (val < 0 ? val % (int64_t)(Mod) + Mod : val % Mod);
}
inline uint64_t _get_mod(uint64_t val) noexcept {
const static uint64_t m_inv = (-1ULL) / Mod + 1;
uint64_t ret = ((unsigned __int128)(val)*m_inv) >> 64;
uint64_t pro = ret * Mod;
return (val - pro + (val < pro ? Mod : 0));
}
friend std::ostream &operator<<(std::ostream &os, Modint &b) {
return os << b.x;
}
friend std::istream &operator>>(std::istream &is, Modint &b) {
return is >> b.x;
}
constexpr uint64_t val() noexcept { return x; }
constexpr Modint operator+() noexcept { return (*this); }
constexpr Modint operator-() noexcept { return Modint() - (*this); }
constexpr Modint operator+(const Modint rhs) noexcept {
return Modint(*this) += rhs;
}
constexpr Modint operator-(const Modint rhs) noexcept {
return Modint(*this) -= rhs;
}
constexpr Modint operator*(const Modint rhs) noexcept {
return Modint(*this) *= rhs;
}
constexpr Modint operator/(const Modint rhs) noexcept {
return Modint(*this) /= rhs;
}
constexpr Modint &operator+=(const Modint rhs) noexcept {
x += rhs.x;
if (x >= Mod) x -= Mod;
return *this;
}
constexpr Modint &operator-=(const Modint rhs) noexcept {
if (x < rhs.x) x += Mod;
x -= rhs.x;
return *this;
}
constexpr Modint &operator*=(const Modint rhs) noexcept {
x = _get_mod(x * rhs.x);
return *this;
}
constexpr bool operator==(Modint rhs) noexcept { return x == rhs.x; }
constexpr bool operator!=(Modint rhs) noexcept { return x != rhs.x; }
constexpr Modint &operator/=(Modint rhs) noexcept {
return (*this) *= rhs.inv();
}
constexpr Modint inv() noexcept { return (*this).pow(Mod - 2); }
constexpr Modint pow(uint64_t x) noexcept {
Modint ret = 1;
Modint bin = (*this);
while (x) {
if (x & 1) ret *= bin;
bin *= bin;
x >>= 1;
}
return ret;
}
static uint64_t get_mod() noexcept { return Mod; }
};
template <int64_t id>
struct ArbitraryModint {
uint64_t x;
static uint64_t &mod() noexcept {
static uint64_t Mod = 0;
return Mod;
}
constexpr ArbitraryModint() noexcept { x = 0; }
constexpr ArbitraryModint(int64_t val) noexcept {
x = (val < 0 ? val % (int64_t)(get_mod()) + get_mod()
: val % get_mod());
}
inline uint64_t _get_mod(uint64_t val) noexcept {
const static uint64_t m_inv = (-1ULL) / get_mod() + 1;
uint64_t ret = ((unsigned __int128)(val)*m_inv) >> 64;
uint64_t pro = ret * get_mod();
return (val - pro + (val < pro ? get_mod() : 0));
}
friend std::ostream &operator<<(std::ostream &os, ArbitraryModint &b) {
return os << b.x;
}
friend std::istream &operator>>(std::istream &is, ArbitraryModint &b) {
return is >> b.x;
}
constexpr uint64_t val() noexcept { return x; }
constexpr ArbitraryModint operator+() noexcept { return (*this); }
constexpr ArbitraryModint operator-() noexcept {
return ArbitraryModint() - (*this);
}
constexpr ArbitraryModint operator+(const ArbitraryModint rhs) noexcept {
return ArbitraryModint(*this) += rhs;
}
constexpr ArbitraryModint operator-(const ArbitraryModint rhs) noexcept {
return ArbitraryModint(*this) -= rhs;
}
constexpr ArbitraryModint operator*(const ArbitraryModint rhs) noexcept {
return ArbitraryModint(*this) *= rhs;
}
constexpr ArbitraryModint operator/(const ArbitraryModint rhs) noexcept {
return ArbitraryModint(*this) /= rhs;
}
constexpr ArbitraryModint &operator+=(const ArbitraryModint rhs) noexcept {
x += rhs.x;
if (x >= get_mod()) x -= get_mod();
return *this;
}
constexpr ArbitraryModint &operator-=(const ArbitraryModint rhs) noexcept {
if (x < rhs.x) x += get_mod();
x -= rhs.x;
return *this;
}
constexpr ArbitraryModint &operator*=(const ArbitraryModint rhs) noexcept {
x = _get_mod(x * rhs.x);
return *this;
}
constexpr ArbitraryModint &operator/=(ArbitraryModint rhs) noexcept {
return (*this) *= rhs.inv();
}
constexpr bool operator==(ArbitraryModint rhs) noexcept {
return x == rhs.x;
}
constexpr bool operator!=(ArbitraryModint rhs) noexcept {
return x != rhs.x;
}
constexpr ArbitraryModint inv() noexcept {
return (*this).pow(get_mod() - 2);
}
constexpr ArbitraryModint pow(uint64_t x) noexcept {
ArbitraryModint ret = 1;
ArbitraryModint bin = (*this);
while (x) {
if (x & 1) ret *= bin;
bin *= bin;
x >>= 1;
}
return ret;
}
static void set_mod(const uint64_t x) noexcept { mod() = x; }
static uint64_t get_mod() noexcept { return mod(); }
};
template <uint64_t N>
inline void scan(Modint<N> &a) {
std::cin >> a.x;
}
template <int64_t id>
inline void scan(ArbitraryModint<id> &a) {
std::cin >> a.x;
}
template <uint64_t N>
inline void print(Modint<N> a) {
std::cout << a.x;
}
template <int64_t id>
inline void print(ArbitraryModint<id> a) {
std::cout << a.x;
}
#line 5 "/root/AtCoder/Halc-Library/Tree/HLDecomposition.hpp"
#line 7 "/root/AtCoder/Halc-Library/Tree/HLDecomposition.hpp"
struct HLDecomposition {
struct Segment {
int32_t lf, ri;
bool rev;
};
int32_t sz;
std::vector<int32_t> tree_sz;
std::vector<int32_t> depth;
std::vector<int32_t> order;
std::vector<int32_t> path_roots;
std::vector<int32_t> parent;
std::vector<int32_t> out;
template <class T>
void _build(int32_t pos, Graph<T> &tree) {
order[pos] = sz;
sz++;
int32_t mx = -1, mp = -1;
for (int32_t i : tree[pos]) {
if (i == parent[pos]) continue;
if (mx < tree_sz[i]) {
mx = tree_sz[i];
mp = i;
}
}
if (mx == -1) {
out[pos] = sz;
return;
}
path_roots[mp] = path_roots[pos];
_build(mp, tree);
for (int32_t i : tree[pos]) {
if (i == parent[pos]) continue;
if (i == mp) continue;
path_roots[i] = i;
_build(i, tree);
}
out[pos] = sz;
}
template <class T>
int32_t _calc_sz(int32_t pos, Graph<T> &tree) {
if (tree_sz[pos] != -1) return tree_sz[pos];
tree_sz[pos] = 1;
for (int32_t i : tree[pos]) {
if (parent[pos] != i) {
parent[i] = pos;
depth[i] = depth[pos] + 1;
tree_sz[pos] += _calc_sz(i, tree);
}
}
return tree_sz[pos];
}
template <class T>
HLDecomposition(Graph<T> &tree, int32_t root = 0) {
sz = tree.size();
tree_sz.resize(sz, -1);
depth.resize(sz, -1);
parent.resize(sz, -1);
depth[root] = 0;
_calc_sz(root, tree);
order.resize(sz, -1);
out.resize(sz, -1);
path_roots.resize(sz, -1);
sz = 0;
path_roots[root] = root;
_build(root, tree);
}
int32_t operator[](int32_t p) { return order[p]; }
Segment subtree(int32_t pos) { return {order[pos], out[pos], false}; }
std::vector<Segment> path(int32_t s, int32_t t) {
std::vector<Segment> ret;
std::stack<Segment> right;
while (path_roots[s] != path_roots[t]) {
if (depth[path_roots[s]] > depth[path_roots[t]]) {
ret.emplace_back(
Segment{order[path_roots[s]], order[s] + 1, true});
s = parent[path_roots[s]];
} else {
right.push({order[path_roots[t]], order[t] + 1, false});
t = parent[path_roots[t]];
}
}
if (depth[s] < depth[t]) {
ret.emplace_back(Segment{order[s], order[t] + 1, false});
} else {
ret.emplace_back(Segment{order[t], order[s] + 1, true});
}
while (!right.empty()) {
ret.push_back(right.top());
right.pop();
}
return ret;
}
int32_t lca(int32_t s, int32_t t) {
while (path_roots[s] != path_roots[t]) {
if (depth[path_roots[s]] > depth[path_roots[t]]) {
s = parent[path_roots[s]];
} else {
t = parent[path_roots[t]];
}
}
if (depth[s] < depth[t]) return s;
return t;
}
};
#line 2 "/root/AtCoder/Halc-Library/Template/Template.hpp"
#include <bits/stdc++.h>
using namespace std;
#line 8 "/root/AtCoder/Halc-Library/Template/InOut.hpp"
inline void scan() {}
inline void scan(int &a) { std::cin >> a; }
inline void scan(unsigned &a) { std::cin >> a; }
inline void scan(long &a) { std::cin >> a; }
inline void scan(long long &a) { std::cin >> a; }
inline void scan(unsigned long long &a) { std::cin >> a; }
inline void scan(char &a) { std::cin >> a; }
inline void scan(float &a) { std::cin >> a; }
inline void scan(double &a) { std::cin >> a; }
inline void scan(long double &a) { std::cin >> a; }
inline void scan(std::vector<bool> &vec) {
for (int32_t i = 0; i < vec.size(); i++) {
int a;
scan(a);
vec[i] = a;
}
}
inline void scan(std::string &a) { std::cin >> a; }
template <class T>
inline void scan(std::vector<T> &vec);
template <class T, size_t size>
inline void scan(std::array<T, size> &vec);
template <class T, class L>
inline void scan(std::pair<T, L> &p);
template <class T, size_t size>
inline void scan(T (&vec)[size]);
template <class T>
inline void scan(std::vector<T> &vec) {
for (auto &i : vec) scan(i);
}
template <class T>
inline void scan(std::deque<T> &vec) {
for (auto &i : vec) scan(i);
}
template <class T, size_t size>
inline void scan(std::array<T, size> &vec) {
for (auto &i : vec) scan(i);
}
template <class T, class L>
inline void scan(std::pair<T, L> &p) {
scan(p.first);
scan(p.second);
}
template <class T, size_t size>
inline void scan(T (&vec)[size]) {
for (auto &i : vec) scan(i);
}
template <class T>
inline void scan(T &a) {
std::cin >> a;
}
inline void in() {}
template <class Head, class... Tail>
inline void in(Head &head, Tail &...tail) {
scan(head);
in(tail...);
}
inline void print() { std::cout << ' '; }
inline void print(const bool &a) { std::cout << a; }
inline void print(const int &a) { std::cout << a; }
inline void print(const unsigned &a) { std::cout << a; }
inline void print(const long &a) { std::cout << a; }
inline void print(const long long &a) { std::cout << a; }
inline void print(const unsigned long long &a) { std::cout << a; }
inline void print(const char &a) { std::cout << a; }
inline void print(const char a[]) { std::cout << a; }
inline void print(const float &a) { std::cout << a; }
inline void print(const double &a) { std::cout << a; }
inline void print(const long double &a) { std::cout << a; }
inline void print(const std::string &a) {
for (auto &&i : a) print(i);
}
template <class T>
inline void print(const std::vector<T> &vec);
template <class T, size_t size>
inline void print(const std::array<T, size> &vec);
template <class T, class L>
inline void print(const std::pair<T, L> &p);
template <class T, size_t size>
inline void print(const T (&vec)[size]);
template <class T>
inline void print(const std::vector<T> &vec) {
if (vec.empty()) return;
print(vec[0]);
for (auto i = vec.begin(); ++i != vec.end();) {
std::cout << ' ';
print(*i);
}
}
template <class T>
inline void print(const std::deque<T> &vec) {
if (vec.empty()) return;
print(vec[0]);
for (auto i = vec.begin(); ++i != vec.end();) {
std::cout << ' ';
print(*i);
}
}
template <class T, size_t size>
inline void print(const std::array<T, size> &vec) {
print(vec[0]);
for (auto i = vec.begin(); ++i != vec.end();) {
std::cout << ' ';
print(*i);
}
}
template <class T, class L>
inline void print(const std::pair<T, L> &p) {
print(p.first);
std::cout << ' ';
print(p.second);
}
template <class T, size_t size>
inline void print(const T (&vec)[size]) {
print(vec[0]);
for (auto i = vec; ++i != end(vec);) {
std::cout << ' ';
print(*i);
}
}
template <class T>
inline void print(const T &a) {
std::cout << a;
}
inline void out() { std::cout << '\n'; }
template <class T>
inline void out(const T &t) {
print(t);
std::cout << '\n';
}
template <class Head, class... Tail>
inline void out(const Head &head, const Tail &...tail) {
print(head);
std::cout << ' ';
out(tail...);
}
inline void Yes(bool i = true) { out(i ? "Yes" : "No"); }
inline void No(bool i = true) { out(i ? "No" : "Yes"); }
struct IOsetup {
IOsetup() {
std::ios::sync_with_stdio(false);
std::cin.tie(nullptr);
std::cout << std::setprecision(10);
}
} iosetup;
#line 8 "/root/AtCoder/Halc-Library/Template/Util.hpp"
using ll = long long;
using ld = long double;
using ull = unsigned long long;
using uint = unsigned int;
using pll = std::pair<ll, ll>;
using pii = std::pair<int, int>;
using vl = std::vector<ll>;
using vvl = std::vector<std::vector<ll>>;
using pdd = std::pair<ld, ld>;
using tuplis = std::array<ll, 3>;
template <class T>
using pq = std::priority_queue<T, std::vector<T>, std::greater<T>>;
constexpr ll LINF = (1LL << 62) - (1LL << 31);
constexpr int32_t INF = INT_MAX >> 1;
constexpr ll MINF = 1LL << 40;
constexpr ld DINF = std::numeric_limits<ld>::infinity();
constexpr int32_t MODD = 1000000007;
constexpr int32_t MOD = 998244353;
constexpr ld EPS = 1e-9;
constexpr ld PI = 3.1415926535897932;
const ll four[] = {0, 1, 0, -1, 0};
const ll eight[] = {0, 1, 1, 0, -1, -1, 1, -1, 0};
template <class T>
bool chmin(T &a, const T &b) {
if (a > b) {
a = b;
return true;
} else
return false;
}
template <class T>
bool chmax(T &a, const T &b) {
if (a < b) {
a = b;
return true;
} else
return false;
}
template <class T>
ll sum(const T &a) {
return accumulate(std::begin(a), std::end(a), 0LL);
}
template <class T>
ld dsum(const T &a) {
return accumulate(std::begin(a), std::end(a), 0.0L);
}
template <class T>
auto min(const T &a) {
return *min_element(std::begin(a), std::end(a));
}
template <class T>
auto max(const T &a) {
return *max_element(std::begin(a), std::end(a));
}
#line 1 "/root/AtCoder/Halc-Library/Template/Macro.hpp"
#define _overload3(_1, _2, _3, name, ...) name
#define _overload4(_1, _2, _3, _4, name, ...) name
#define _rep1(i, n) for (ll i = 0; i < (n); i++)
#define _rep2(i, a, b) for (ll i = (a); i < (b); i++)
#define _rep3(i, a, b, c) for (ll i = (a); i < (b); i += (c))
#define rep(...) _overload4(__VA_ARGS__, _rep3, _rep2, _rep1)(__VA_ARGS__)
#define _rrep1(i, n) for (ll i = (n); i-- > 0;)
#define _rrep2(i, a, b) for (ll i = (b); i-- > (a);)
#define rrep(...) _overload3(__VA_ARGS__, _rrep2, _rrep1)(__VA_ARGS__)
#define each(i, ...) for (auto&& i : __VA_ARGS__)
#define all(i) std::begin(i), std::end(i)
#define rall(i) std::rbegin(i), std::rend(i)
#define len(x) ((int)(x).size())
#define fi first
#define se second
#define uniq(x) x.erase(unique(all(x)), std::end(x))
#define vec(type, name, ...) vector<type> name(__VA_ARGS__);
#define vv(type, name, h, ...) std::vector<std::vector<type>> name(h, std::vector<type>(__VA_ARGS__));
#define INT(...) int __VA_ARGS__; in(__VA_ARGS__)
#define LL(...) long long __VA_ARGS__; in(__VA_ARGS__)
#define ULL(...) unsigned long long __VA_ARGS__; in(__VA_ARGS__)
#define STR(...) std::string __VA_ARGS__; in(__VA_ARGS__)
#define CHR(...) char __VA_ARGS__; in(__VA_ARGS__)
#define LD(...) long double __VA_ARGS__; in(__VA_ARGS__)
#define VEC(type, name, size) std::vector<type> name(size); in(name)
#define VV(type, name, h, w) std::vector<std::vector<type>> name(h, std::vector<type>(w)); in(name)
#line 6 "main.cpp"
using mint = Modint<MODD>;
struct mat {
using T = array<mint, 4>;
static T op(T x, T y) {
return {
x[0] * y[0] + x[1] * y[2], x[0] * y[1] + x[1] * y[3],
x[2] * y[0] + x[3] * y[2], x[2] * y[1] + x[3] * y[3]
};
}
static inline T e = {1, 0, 0, 1};
};
void solve() {
LL(n);
Graph gr(n);
rep(i, n - 1) {
LL(u, v);
gr.add_edge(u, v);
}
HLDecomposition hld(gr);
SegmentTree<mat> seg(n);
vec(ll,change,n-1);
rep(i,n){
each(j,gr[i]){
if(hld.depth[i]<hld.depth[j]){
change[j.idx]=j;
}
}
}
LL(q);
rep(_,q){
CHR(t);
if(t=='x'){
LL(i);
mat::T x;
in(x);
seg.set(hld[change[i]],x);
}
else{
LL(i,j);
ll lca=hld.lca(i,j);
mat::T x=seg.get(hld[lca]);
seg.set(hld[lca],mat::e);
mat::T ans=mat::e;
for(auto &[lf, ri, _]:hld.path(i,j)){
ans=mat::op(ans,seg.prod(lf,ri));
}
out(ans);
seg.set(hld[lca],x);
}
}
}
int main() { solve(); }