結果
| 問題 |
No.650 行列木クエリ
|
| コンテスト | |
| ユーザー |
 rin204
|
| 提出日時 | 2024-07-20 00:07:10 |
| 言語 | C++23 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 191 ms / 2,000 ms |
| コード長 | 25,501 bytes |
| コンパイル時間 | 5,166 ms |
| コンパイル使用メモリ | 281,224 KB |
| 実行使用メモリ | 31,712 KB |
| 最終ジャッジ日時 | 2024-07-20 00:07:36 |
| 合計ジャッジ時間 | 5,622 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 * 1 |
| other | AC * 10 |
ソースコード
// #pragma GCC target("avx2")
// #pragma GCC optimize("O3")
// #pragma GCC optimize("unroll-loops")
// #define INTERACTIVE
#include <bits/stdc++.h>
using namespace std;
namespace templates {
// type
using ll = long long;
using ull = unsigned long long;
using Pii = pair<int, int>;
using Pil = pair<int, ll>;
using Pli = pair<ll, int>;
using Pll = pair<ll, ll>;
template <class T>
using pq = priority_queue<T>;
template <class T>
using qp = priority_queue<T, vector<T>, greater<T>>;
// clang-format off
#define vec(T, A, ...) vector<T> A(__VA_ARGS__);
#define vvec(T, A, h, ...) vector<vector<T>> A(h, vector<T>(__VA_ARGS__));
#define vvvec(T, A, h1, h2, ...) vector<vector<vector<T>>> A(h1, vector<vector<T>>(h2, vector<T>(__VA_ARGS__)));
// clang-format on
// for loop
#define fori1(a) for (ll _ = 0; _ < (a); _++)
#define fori2(i, a) for (ll i = 0; i < (a); i++)
#define fori3(i, a, b) for (ll i = (a); i < (b); i++)
#define fori4(i, a, b, c) for (ll i = (a); ((c) > 0 || i > (b)) && ((c) < 0 || i < (b)); i += (c))
#define overload4(a, b, c, d, e, ...) e
#define fori(...) overload4(__VA_ARGS__, fori4, fori3, fori2, fori1)(__VA_ARGS__)
// declare and input
// clang-format off
#define INT(...) int __VA_ARGS__; inp(__VA_ARGS__);
#define LL(...) ll __VA_ARGS__; inp(__VA_ARGS__);
#define STRING(...) string __VA_ARGS__; inp(__VA_ARGS__);
#define CHAR(...) char __VA_ARGS__; inp(__VA_ARGS__);
#define DOUBLE(...) double __VA_ARGS__; STRING(str___); __VA_ARGS__ = stod(str___);
#define VEC(T, A, n) vector<T> A(n); inp(A);
#define VVEC(T, A, n, m) vector<vector<T>> A(n, vector<T>(m)); inp(A);
// clang-format on
// const value
const ll MOD1 = 1000000007;
const ll MOD9 = 998244353;
const double PI = acos(-1);
// other macro
#if !defined(RIN__LOCAL) && !defined(INTERACTIVE)
#define endl "\n"
#endif
#define spa ' '
#define len(A) ll(A.size())
#define all(A) begin(A), end(A)
// function
vector<char> stoc(string &S) {
int n = S.size();
vector<char> ret(n);
for (int i = 0; i < n; i++) ret[i] = S[i];
return ret;
}
string ctos(vector<char> &S) {
int n = S.size();
string ret = "";
for (int i = 0; i < n; i++) ret += S[i];
return ret;
}
template <class T>
auto min(const T &a) {
return *min_element(all(a));
}
template <class T>
auto max(const T &a) {
return *max_element(all(a));
}
template <class T, class S>
auto clamp(T &a, const S &l, const S &r) {
return (a > r ? r : a < l ? l : a);
}
template <class T, class S>
inline bool chmax(T &a, const S &b) {
return (a < b ? a = b, 1 : 0);
}
template <class T, class S>
inline bool chmin(T &a, const S &b) {
return (a > b ? a = b, 1 : 0);
}
template <class T, class S>
inline bool chclamp(T &a, const S &l, const S &r) {
auto b = clamp(a, l, r);
return (a != b ? a = b, 1 : 0);
}
template <typename T>
T sum(vector<T> &A) {
T tot = 0;
for (auto a : A) tot += a;
return tot;
}
template <typename T>
vector<T> compression(vector<T> X) {
sort(all(X));
X.erase(unique(all(X)), X.end());
return X;
}
// input and output
namespace io {
// __int128_t
std::ostream &operator<<(std::ostream &dest, __int128_t value) {
std::ostream::sentry s(dest);
if (s) {
__uint128_t tmp = value < 0 ? -value : value;
char buffer[128];
char *d = std::end(buffer);
do {
--d;
*d = "0123456789"[tmp % 10];
tmp /= 10;
} while (tmp != 0);
if (value < 0) {
--d;
*d = '-';
}
int len = std::end(buffer) - d;
if (dest.rdbuf()->sputn(d, len) != len) {
dest.setstate(std::ios_base::badbit);
}
}
return dest;
}
// vector<T>
template <typename T>
istream &operator>>(istream &is, vector<T> &A) {
for (auto &a : A) is >> a;
return is;
}
template <typename T>
ostream &operator<<(ostream &os, vector<T> &A) {
for (size_t i = 0; i < A.size(); i++) {
os << A[i];
if (i != A.size() - 1) os << ' ';
}
return os;
}
// vector<vector<T>>
template <typename T>
istream &operator>>(istream &is, vector<vector<T>> &A) {
for (auto &a : A) is >> a;
return is;
}
template <typename T>
ostream &operator<<(ostream &os, vector<vector<T>> &A) {
for (size_t i = 0; i < A.size(); i++) {
os << A[i];
if (i != A.size() - 1) os << endl;
}
return os;
}
// pair<S, T>
template <typename S, typename T>
istream &operator>>(istream &is, pair<S, T> &A) {
is >> A.first >> A.second;
return is;
}
template <typename S, typename T>
ostream &operator<<(ostream &os, pair<S, T> &A) {
os << A.first << ' ' << A.second;
return os;
}
// vector<pair<S, T>>
template <typename S, typename T>
istream &operator>>(istream &is, vector<pair<S, T>> &A) {
for (size_t i = 0; i < A.size(); i++) {
is >> A[i];
}
return is;
}
template <typename S, typename T>
ostream &operator<<(ostream &os, vector<pair<S, T>> &A) {
for (size_t i = 0; i < A.size(); i++) {
os << A[i];
if (i != A.size() - 1) os << endl;
}
return os;
}
// tuple
template <typename T, size_t N>
struct TuplePrint {
static ostream &print(ostream &os, const T &t) {
TuplePrint<T, N - 1>::print(os, t);
os << ' ' << get<N - 1>(t);
return os;
}
};
template <typename T>
struct TuplePrint<T, 1> {
static ostream &print(ostream &os, const T &t) {
os << get<0>(t);
return os;
}
};
template <typename... Args>
ostream &operator<<(ostream &os, const tuple<Args...> &t) {
TuplePrint<decltype(t), sizeof...(Args)>::print(os, t);
return os;
}
// io functions
void FLUSH() {
cout << flush;
}
void print() {
cout << endl;
}
template <class Head, class... Tail>
void print(Head &&head, Tail &&...tail) {
cout << head;
if (sizeof...(Tail)) cout << spa;
print(std::forward<Tail>(tail)...);
}
template <typename T, typename S>
void prisep(vector<T> &A, S sep) {
int n = A.size();
for (int i = 0; i < n; i++) {
cout << A[i];
if (i != n - 1) cout << sep;
}
cout << endl;
}
template <typename T, typename S>
void priend(T A, S end) {
cout << A << end;
}
template <typename T>
void prispa(T A) {
priend(A, spa);
}
template <typename T, typename S>
bool printif(bool f, T A, S B) {
if (f)
print(A);
else
print(B);
return f;
}
template <class... T>
void inp(T &...a) {
(cin >> ... >> a);
}
} // namespace io
using namespace io;
// read graph
vector<vector<int>> read_edges(int n, int m, bool direct = false, int indexed = 1) {
vector<vector<int>> edges(n, vector<int>());
for (int i = 0; i < m; i++) {
INT(u, v);
u -= indexed;
v -= indexed;
edges[u].push_back(v);
if (!direct) edges[v].push_back(u);
}
return edges;
}
vector<vector<int>> read_tree(int n, int indexed = 1) {
return read_edges(n, n - 1, false, indexed);
}
template <typename T = long long>
vector<vector<pair<int, T>>> read_wedges(int n, int m, bool direct = false, int indexed = 1) {
vector<vector<pair<int, T>>> edges(n, vector<pair<int, T>>());
for (int i = 0; i < m; i++) {
INT(u, v);
T w;
inp(w);
u -= indexed;
v -= indexed;
edges[u].push_back({v, w});
if (!direct) edges[v].push_back({u, w});
}
return edges;
}
template <typename T = long long>
vector<vector<pair<int, T>>> read_wtree(int n, int indexed = 1) {
return read_wedges<T>(n, n - 1, false, indexed);
}
// yes / no
namespace yesno {
// yes
inline bool yes(bool f = true) {
cout << (f ? "yes" : "no") << endl;
return f;
}
inline bool Yes(bool f = true) {
cout << (f ? "Yes" : "No") << endl;
return f;
}
inline bool YES(bool f = true) {
cout << (f ? "YES" : "NO") << endl;
return f;
}
// no
inline bool no(bool f = true) {
cout << (!f ? "yes" : "no") << endl;
return f;
}
inline bool No(bool f = true) {
cout << (!f ? "Yes" : "No") << endl;
return f;
}
inline bool NO(bool f = true) {
cout << (!f ? "YES" : "NO") << endl;
return f;
}
// possible
inline bool possible(bool f = true) {
cout << (f ? "possible" : "impossible") << endl;
return f;
}
inline bool Possible(bool f = true) {
cout << (f ? "Possible" : "Impossible") << endl;
return f;
}
inline bool POSSIBLE(bool f = true) {
cout << (f ? "POSSIBLE" : "IMPOSSIBLE") << endl;
return f;
}
// impossible
inline bool impossible(bool f = true) {
cout << (!f ? "possible" : "impossible") << endl;
return f;
}
inline bool Impossible(bool f = true) {
cout << (!f ? "Possible" : "Impossible") << endl;
return f;
}
inline bool IMPOSSIBLE(bool f = true) {
cout << (!f ? "POSSIBLE" : "IMPOSSIBLE") << endl;
return f;
}
// Alice Bob
inline bool Alice(bool f = true) {
cout << (f ? "Alice" : "Bob") << endl;
return f;
}
inline bool Bob(bool f = true) {
cout << (f ? "Bob" : "Alice") << endl;
return f;
}
// Takahashi Aoki
inline bool Takahashi(bool f = true) {
cout << (f ? "Takahashi" : "Aoki") << endl;
return f;
}
inline bool Aoki(bool f = true) {
cout << (f ? "Aoki" : "Takahashi") << endl;
return f;
}
} // namespace yesno
using namespace yesno;
} // namespace templates
using namespace templates;
template <class S, S (*op)(S, S), S (*e)()>
struct segtree {
public:
segtree() : segtree(0) {}
explicit segtree(int n) : segtree(std::vector<S>(n, e())) {};
explicit segtree(const std::vector<S> &v) : _n(int(v.size())) {
size = 1;
log = 0;
while (size < _n) {
log++;
size <<= 1;
}
d = std::vector<S>(2 * size, e());
for (int i = 0; i < _n; i++) d[size + i] = v[i];
for (int i = size - 1; i >= 1; i--) update(i);
}
void set(int p, S x) {
assert(0 <= p && p < _n);
p += size;
d[p] = x;
for (int i = 1; i <= log; i++) update(p >> i);
}
S get(int p) {
assert(0 <= p && p < _n);
return d[p + size];
}
S prod(int l, int r) {
assert(0 <= l && l <= r && r <= _n);
S sml = e(), smr = e();
l += size;
r += size;
while (l < r) {
if (l & 1) sml = op(sml, d[l++]);
if (r & 1) smr = op(d[--r], smr);
l >>= 1;
r >>= 1;
}
return op(sml, smr);
}
private:
int _n, size, log;
std::vector<S> d;
void update(int k) {
d[k] = op(d[2 * k], d[2 * k + 1]);
}
};
template <int MOD>
struct Modint {
int x;
Modint() : x(0) {}
Modint(int64_t y) {
if (y >= 0)
x = y % MOD;
else
x = (y % MOD + MOD) % MOD;
}
Modint &operator+=(const Modint &p) {
x += p.x;
if (x >= MOD) x -= MOD;
return *this;
}
Modint &operator-=(const Modint &p) {
x -= p.x;
if (x < 0) x += MOD;
return *this;
}
Modint &operator*=(const Modint &p) {
x = int(1LL * x * p.x % MOD);
return *this;
}
Modint &operator/=(const Modint &p) {
*this *= p.inverse();
return *this;
}
Modint &operator%=(const Modint &p) {
assert(p.x == 0);
return *this;
}
Modint operator-() const {
return Modint(-x);
}
Modint &operator++() {
x++;
if (x == MOD) x = 0;
return *this;
}
Modint &operator--() {
if (x == 0) x = MOD;
x--;
return *this;
}
Modint operator++(int) {
Modint result = *this;
++*this;
return result;
}
Modint operator--(int) {
Modint result = *this;
--*this;
return result;
}
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 Modint operator%(const Modint &lhs, const Modint &rhs) {
assert(rhs.x == 0);
return Modint(lhs);
}
bool operator==(const Modint &p) const {
return x == p.x;
}
bool operator!=(const Modint &p) const {
return x != p.x;
}
bool operator<(const Modint &rhs) const {
return x < rhs.x;
}
bool operator<=(const Modint &rhs) const {
return x <= rhs.x;
}
bool operator>(const Modint &rhs) const {
return x > rhs.x;
}
bool operator>=(const Modint &rhs) const {
return x >= rhs.x;
}
Modint inverse() const {
int a = x, b = MOD, u = 1, v = 0, t;
while (b > 0) {
t = a / b;
a -= t * b;
u -= t * v;
std::swap(a, b);
std::swap(u, v);
}
return Modint(u);
}
Modint pow(int64_t k) const {
Modint ret(1);
Modint y(x);
while (k > 0) {
if (k & 1) ret *= y;
y *= y;
k >>= 1;
}
return ret;
}
std::pair<int, int> to_frac(int max_n = 1000) const {
int y = x;
for (int i = 1; i <= max_n; i++) {
if (y <= max_n) {
return {y, i};
} else if (MOD - y <= max_n) {
return {-(MOD - y), i};
}
y = (y + x) % MOD;
}
return {-1, -1};
}
friend std::ostream &operator<<(std::ostream &os, const Modint &p) {
return os << p.x;
}
friend std::istream &operator>>(std::istream &is, Modint &p) {
int64_t y;
is >> y;
p = Modint<MOD>(y);
return (is);
}
static int get_mod() {
return MOD;
}
};
struct Arbitrary_Modint {
int x;
static int MOD;
static void set_mod(int mod) {
MOD = mod;
}
Arbitrary_Modint() : x(0) {}
Arbitrary_Modint(int64_t y) {
if (y >= 0)
x = y % MOD;
else
x = (y % MOD + MOD) % MOD;
}
Arbitrary_Modint &operator+=(const Arbitrary_Modint &p) {
x += p.x;
if (x >= MOD) x -= MOD;
return *this;
}
Arbitrary_Modint &operator-=(const Arbitrary_Modint &p) {
x -= p.x;
if (x < 0) x += MOD;
return *this;
}
Arbitrary_Modint &operator*=(const Arbitrary_Modint &p) {
x = int(1LL * x * p.x % MOD);
return *this;
}
Arbitrary_Modint &operator/=(const Arbitrary_Modint &p) {
*this *= p.inverse();
return *this;
}
Arbitrary_Modint &operator%=(const Arbitrary_Modint &p) {
assert(p.x == 0);
return *this;
}
Arbitrary_Modint operator-() const {
return Arbitrary_Modint(-x);
}
Arbitrary_Modint &operator++() {
x++;
if (x == MOD) x = 0;
return *this;
}
Arbitrary_Modint &operator--() {
if (x == 0) x = MOD;
x--;
return *this;
}
Arbitrary_Modint operator++(int) {
Arbitrary_Modint result = *this;
++*this;
return result;
}
Arbitrary_Modint operator--(int) {
Arbitrary_Modint result = *this;
--*this;
return result;
}
friend Arbitrary_Modint operator+(const Arbitrary_Modint &lhs, const Arbitrary_Modint &rhs) {
return Arbitrary_Modint(lhs) += rhs;
}
friend Arbitrary_Modint operator-(const Arbitrary_Modint &lhs, const Arbitrary_Modint &rhs) {
return Arbitrary_Modint(lhs) -= rhs;
}
friend Arbitrary_Modint operator*(const Arbitrary_Modint &lhs, const Arbitrary_Modint &rhs) {
return Arbitrary_Modint(lhs) *= rhs;
}
friend Arbitrary_Modint operator/(const Arbitrary_Modint &lhs, const Arbitrary_Modint &rhs) {
return Arbitrary_Modint(lhs) /= rhs;
}
friend Arbitrary_Modint operator%(const Arbitrary_Modint &lhs, const Arbitrary_Modint &rhs) {
assert(rhs.x == 0);
return Arbitrary_Modint(lhs);
}
bool operator==(const Arbitrary_Modint &p) const {
return x == p.x;
}
bool operator!=(const Arbitrary_Modint &p) const {
return x != p.x;
}
bool operator<(const Arbitrary_Modint &rhs) {
return x < rhs.x;
}
bool operator<=(const Arbitrary_Modint &rhs) {
return x <= rhs.x;
}
bool operator>(const Arbitrary_Modint &rhs) {
return x > rhs.x;
}
bool operator>=(const Arbitrary_Modint &rhs) {
return x >= rhs.x;
}
Arbitrary_Modint inverse() const {
int a = x, b = MOD, u = 1, v = 0, t;
while (b > 0) {
t = a / b;
a -= t * b;
u -= t * v;
std::swap(a, b);
std::swap(u, v);
}
return Arbitrary_Modint(u);
}
Arbitrary_Modint pow(int64_t k) const {
Arbitrary_Modint ret(1);
Arbitrary_Modint y(x);
while (k > 0) {
if (k & 1) ret *= y;
y *= y;
k >>= 1;
}
return ret;
}
friend std::ostream &operator<<(std::ostream &os, const Arbitrary_Modint &p) {
return os << p.x;
}
friend std::istream &operator>>(std::istream &is, Arbitrary_Modint &p) {
int64_t y;
is >> y;
p = Arbitrary_Modint(y);
return (is);
}
static int get_mod() {
return MOD;
}
};
int Arbitrary_Modint::MOD = 998244353;
using modint9 = Modint<998244353>;
using modint1 = Modint<1000000007>;
using modint = Arbitrary_Modint;
struct HLD {
int n, path;
std::vector<std::vector<int>> edges;
std::vector<int> siz;
std::vector<int> par;
std::vector<int> depth;
std::vector<int> path_ind;
std::vector<int> path_root;
std::vector<int> heavy_child;
std::vector<bool> isheavy;
std::vector<int> L;
std::vector<int> R;
HLD(int n) : n(n) {
edges.resize(n);
siz.assign(n, -1);
par.assign(n, -1);
depth.assign(n, -1);
path_ind.assign(n, -1);
heavy_child.assign(n, -1);
isheavy.assign(n, false);
L.assign(n, -1);
R.assign(n, -1);
}
void read_edges(int indexed = 1) {
int u, v;
for (int i = 0; i < n - 1; i++) {
std::cin >> u >> v;
u -= indexed;
v -= indexed;
edges[u].push_back(v);
edges[v].push_back(u);
}
}
void add_edge(int u, int v) {
edges[u].push_back(v);
edges[v].push_back(u);
}
void build(int root = 0) {
depth[root] = 0;
std::stack<int> st;
std::vector<int> route;
st.push(root);
route.push_back(root);
while (!st.empty()) {
int pos = st.top();
st.pop();
for (auto npos : edges[pos]) {
if (depth[npos] == -1) {
depth[npos] = depth[pos] + 1;
par[npos] = pos;
st.push(npos);
route.push_back(npos);
}
}
}
reverse(route.begin(), route.end());
for (auto pos : route) {
siz[pos] = 1;
int ma = -1;
for (auto npos : edges[pos]) {
if (depth[npos] > depth[pos]) siz[pos] += siz[npos];
if (siz[npos] > ma) {
ma = siz[npos];
heavy_child[pos] = npos;
}
}
if (heavy_child[pos] != -1) isheavy[heavy_child[pos]] = true;
}
isheavy[root] = true;
path = 0;
st.push(~root);
st.push(root);
path_root.push_back(root);
int cc = 0;
while (!st.empty()) {
int pos = st.top();
st.pop();
if (pos >= 0) {
L[pos] = cc++;
if (!isheavy[pos]) {
path++;
path_root.push_back(pos);
}
path_ind[pos] = path;
for (auto npos : edges[pos]) {
if (npos == par[pos] || npos == heavy_child[pos]) continue;
st.push(~npos);
st.push(npos);
}
if (heavy_child[pos] != -1) {
int npos = heavy_child[pos];
st.push(~npos);
st.push(npos);
}
} else {
pos = ~pos;
R[pos] = cc;
}
}
}
std::vector<std::pair<int, int>> get_path(int u, int v) {
std::vector<int> ll;
std::vector<int> rr;
ll.push_back(u);
rr.push_back(v);
while (path_ind[u] != path_ind[v]) {
if (depth[path_root[path_ind[u]]] >= depth[path_root[path_ind[v]]]) {
u = path_root[path_ind[u]];
ll.push_back(u);
u = par[u];
ll.push_back(u);
} else {
v = path_root[path_ind[v]];
rr.push_back(v);
v = par[v];
rr.push_back(v);
}
}
reverse(rr.begin(), rr.end());
ll.insert(ll.end(), rr.begin(), rr.end());
int n = ll.size();
std::vector<std::pair<int, int>> res(n / 2);
for (int i = 0; i < n; i += 2) {
res[i / 2] = {ll[i], ll[i + 1]};
}
return res;
}
int lca(int u, int v) {
while (path_ind[u] != path_ind[v]) {
if (depth[path_root[path_ind[u]]] >= depth[path_root[path_ind[v]]])
u = par[path_root[path_ind[u]]];
else
v = par[path_root[path_ind[v]]];
}
return (depth[u] <= depth[v]) ? u : v;
}
int dist(int u, int v) {
int p = lca(u, v);
return depth[u] + depth[v] - 2 * depth[p];
}
template <typename T>
std::vector<T> reorder(std::vector<T> &A, bool rev = false) {
assert(int(A.size()) == n);
std::vector<T> ret(n);
for (int i = 0; i < n; i++) {
ret[L[i]] = A[i];
}
if (rev) reverse(ret.begin(), ret.end());
return ret;
}
};
using mint = modint1;
struct S {
mint x00;
mint x01;
mint x10;
mint x11;
};
S op(S l, S r) {
return S{l.x00 * r.x00 + l.x01 * r.x10, l.x00 * r.x01 + l.x01 * r.x11,
l.x10 * r.x00 + l.x11 * r.x10, l.x10 * r.x01 + l.x11 * r.x11};
}
S e() {
return S{1, 0, 0, 1};
}
void solve() {
INT(n);
HLD hld(2 * n - 1);
fori(i, n - 1) {
INT(u, v);
hld.add_edge(u, i + n);
hld.add_edge(v, i + n);
}
hld.build(0);
segtree<S, op, e> seg(2 * n - 1);
INT(Q);
fori(Q) {
CHAR(t);
if (t == 'x') {
INT(i, x00, x01, x10, x11);
i += n;
seg.set(hld.L[i], S{x00, x01, x10, x11});
} else {
INT(i, j);
S ans = e();
for (auto [u, v] : hld.get_path(i, j)) {
u = hld.L[u];
v = hld.L[v];
ans = op(ans, seg.prod(u, v + 1));
auto res = seg.prod(u, v + 1);
}
print(ans.x00, ans.x01, ans.x10, ans.x11);
}
}
}
int main() {
#ifndef INTERACTIVE
std::cin.tie(0)->sync_with_stdio(0);
#endif
// std::cout << std::fixed << std::setprecision(12);
int t;
t = 1;
// std::cin >> t;
while (t--) solve();
return 0;
}
// // #pragma GCC target("avx2")
// // #pragma GCC optimize("O3")
// // #pragma GCC optimize("unroll-loops")
// // #define INTERACTIVE
//
// #include "kyopro-cpp/template.hpp"
//
// #include "data_structure/segTree.hpp"
// #include "misc/Modint.hpp"
// #include "tree/HLD.hpp"
// using mint = modint1;
//
// struct S {
// mint x00;
// mint x01;
// mint x10;
// mint x11;
// };
// S op(S l, S r) {
// return S{l.x00 * r.x00 + l.x01 * r.x10, l.x00 * r.x01 + l.x01 * r.x11,
// l.x10 * r.x00 + l.x11 * r.x10, l.x10 * r.x01 + l.x11 * r.x11};
// }
// S e() {
// return S{1, 0, 0, 1};
// }
//
// void solve() {
// INT(n);
// HLD hld(2 * n - 1);
// fori(i, n - 1) {
// INT(u, v);
// hld.add_edge(u, i + n);
// hld.add_edge(v, i + n);
// }
// hld.build(0);
// segtree<S, op, e> seg(2 * n - 1);
// INT(Q);
// fori(Q) {
// CHAR(t);
// if (t == 'x') {
// INT(i, x00, x01, x10, x11);
// i += n;
// seg.set(hld.L[i], S{x00, x01, x10, x11});
// } else {
// INT(i, j);
// S ans = e();
// for (auto [u, v] : hld.get_path(i, j)) {
// u = hld.L[u];
// v = hld.L[v];
//
// ans = op(ans, seg.prod(u, v + 1));
// auto res = seg.prod(u, v + 1);
// }
// print(ans.x00, ans.x01, ans.x10, ans.x11);
// }
// }
// }
//
// int main() {
// #ifndef INTERACTIVE
// std::cin.tie(0)->sync_with_stdio(0);
// #endif
// // std::cout << std::fixed << std::setprecision(12);
// int t;
// t = 1;
// // std::cin >> t;
// while (t--) solve();
// return 0;
// }