#line 1 "verify/tree/LC_vertex_set_path_composite.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/vertex_set_path_composite"
#line 2 "template/template.hpp"
#include <bits/stdc++.h>
using namespace std;
#line 2 "template/macro.hpp"
#define rep(i, a, b) for (int i = (a); i < (int)(b); i++)
#define rrep(i, a, b) for (int i = (int)(b) - 1; i >= (a); i--)
#define ALL(v) (v).begin(), (v).end()
#define UNIQUE(v) sort(ALL(v)), (v).erase(unique(ALL(v)), (v).end())
#define SZ(v) (int)v.size()
#define MIN(v) *min_element(ALL(v))
#define MAX(v) *max_element(ALL(v))
#define LB(v, x) int(lower_bound(ALL(v), (x)) - (v).begin())
#define UB(v, x) int(upper_bound(ALL(v), (x)) - (v).begin())
#define YN(b) cout << ((b) ? "YES" : "NO") << "\n";
#define Yn(b) cout << ((b) ? "Yes" : "No") << "\n";
#define yn(b) cout << ((b) ? "yes" : "no") << "\n";
#line 6 "template/template.hpp"
#line 2 "template/util.hpp"
using uint = unsigned int;
using ll = long long int;
using ull = unsigned long long;
using i128 = __int128_t;
using u128 = __uint128_t;
template <class T>
using priority_queue_asc = priority_queue<T, vector<T>, greater<T>>;
template <class T, class S = T>
S SUM(const vector<T>& a) {
return accumulate(ALL(a), S(0));
}
template <class T1, class T2>
inline bool chmin(T1& a, T2 b) {
if (a > b) {
a = b;
return true;
}
return false;
}
template <class T1, class T2>
inline bool chmax(T1& a, T2 b) {
if (a < b) {
a = b;
return true;
}
return false;
}
template <class T1, class T2>
inline bool chmin_opt(optional<T1>& a, T2 b) {
if (!a || a > b) {
a = b;
return true;
}
return false;
}
template <class T1, class T2>
inline bool chmax_opt(optional<T1>& a, T2 b) {
if (!a || a < b) {
a = b;
return true;
}
return false;
}
template <class T>
int popcnt(T x) {
return __builtin_popcountll(x);
}
template <class T>
int topbit(T x) {
return (x == 0 ? -1 : 63 - __builtin_clzll(x));
}
template <class T>
int lowbit(T x) {
return (x == 0 ? -1 : __builtin_ctzll(x));
}
#line 8 "template/template.hpp"
#line 2 "template/inout.hpp"
struct Fast {
Fast() {
cin.tie(nullptr);
ios_base::sync_with_stdio(false);
cout << fixed << setprecision(15);
}
} fast;
ostream& operator<<(ostream& os, __uint128_t x) {
char buf[40];
size_t k = 0;
while (x > 0) buf[k++] = (char)(x % 10 + '0'), x /= 10;
if (k == 0) buf[k++] = '0';
while (k) os << buf[--k];
return os;
}
ostream& operator<<(ostream& os, __int128_t x) {
return x < 0 ? (os << '-' << (__uint128_t)(-x)) : (os << (__uint128_t)x);
}
template <class T, size_t N>
ostream& operator<<(ostream& os, const array<T, N>& a);
template <class T1, class T2>
istream& operator>>(istream& is, pair<T1, T2>& p) {
return is >> p.first >> p.second;
}
template <class T1, class T2>
ostream& operator<<(ostream& os, const pair<T1, T2>& p) {
return os << p.first << " " << p.second;
}
template <class T>
istream& operator>>(istream& is, vector<T>& a) {
for (auto& v : a) is >> v;
return is;
}
template <class T>
ostream& operator<<(ostream& os, const vector<T>& a) {
for (auto it = a.begin(); it != a.end();) {
os << *it;
if (++it != a.end()) os << " ";
}
return os;
}
template <class T, size_t N>
ostream& operator<<(ostream& os, const array<T, N>& a) {
for (auto it = a.begin(); it != a.end();) {
os << *it;
if (++it != a.end()) os << " ";
}
return os;
}
template <class T>
ostream& operator<<(ostream& os, const set<T>& st) {
os << "{";
for (auto it = st.begin(); it != st.end();) {
os << *it;
if (++it != st.end()) os << ",";
}
os << "}";
return os;
}
template <class T1, class T2>
ostream& operator<<(ostream& os, const map<T1, T2>& mp) {
os << "{";
for (auto it = mp.begin(); it != mp.end();) {
os << it->first << ":" << it->second;
if (++it != mp.end()) os << ",";
}
os << "}";
return os;
}
void in() {}
template <typename T, class... U>
void in(T& t, U&... u) {
cin >> t;
in(u...);
}
template <class... T>
void in_zip(int n, T&... t) {
assert(n >= 0 && ((size(t) >= static_cast<size_t>(n)) && ...));
for (int i = 0; i < n; i++) in(t[i]...);
}
void out() { cout << "\n"; }
template <typename T, class... U, char sep = ' '>
void out(const T& t, const U&... u) {
cout << t;
if (sizeof...(u)) cout << sep;
out(u...);
}
template <class T, class U>
void out_opt(const optional<T>& opt, const U& fallback, ostream& os = cout) {
if (opt.has_value())
os << opt.value();
else
os << fallback;
os << "\n";
}
template <class T, class U>
void out_opt(const vector<optional<T>>& vec, const U& fallback, ostream& os = cout) {
for (auto it = vec.begin(); it != vec.end();) {
if ((*it).has_value())
os << (*it).value();
else
os << fallback;
if (++it != vec.end()) os << " ";
}
os << "\n";
}
namespace IO {
template <class T, class... U>
T read(U&&... u) {
T t = T(forward<U>(u)...);
in(t);
return t;
}
namespace Graph {
vector<vector<int>> unweighted(int n, int m, bool directed = false, int offset = 1) {
vector<vector<int>> g(n);
for (int i = 0; i < m; i++) {
int u, v;
cin >> u >> v;
u -= offset, v -= offset;
g[u].push_back(v);
if (!directed) g[v].push_back(u);
}
return g;
}
template <class T>
vector<vector<pair<int, T>>> weighted(int n, int m, bool directed = false, int offset = 1) {
vector<vector<pair<int, T>>> g(n);
for (int i = 0; i < m; i++) {
int u, v;
T w;
cin >> u >> v >> w;
u -= offset, v -= offset;
g[u].push_back({v, w});
if (!directed) g[v].push_back({u, w});
}
return g;
}
} // namespace Graph
namespace Tree {
vector<vector<int>> unweighted(int n, bool directed = false, int offset = 1) {
return Graph::unweighted(n, n - 1, directed, offset);
}
template <class T>
vector<vector<pair<int, T>>> weighted(int n, bool directed = false, int offset = 1) {
return Graph::weighted<T>(n, n - 1, directed, offset);
}
vector<vector<int>> rooted(int n, bool to_root = true, bool to_leaf = true, int offset = 1) {
vector<vector<int>> g(n);
for (int i = 1; i < n; i++) {
int p;
cin >> p;
p -= offset;
if (to_root) g[i].push_back(p);
if (to_leaf) g[p].push_back(i);
}
return g;
}
} // namespace Tree
} // namespace IO
#line 10 "template/template.hpp"
#line 2 "template/debug.hpp"
#ifdef LOCAL
#define debug 1
#define show(...) _show(0, #__VA_ARGS__, __VA_ARGS__)
#else
#define debug 0
#define show(...) true
#endif
template <class T>
void _show(int, T) {
cerr << '\n';
}
template <class T1, class T2, class... T3>
void _show(int i, const T1& a, const T2& b, const T3&... c) {
for (; a[i] != ',' && a[i] != '\0'; i++) cerr << a[i];
cerr << ":" << b << " ";
_show(i + 1, a, c...);
}
#line 2 "graph/graph.hpp"
#line 4 "graph/graph.hpp"
template <class E>
struct GraphBase {
public:
GraphBase() : GraphBase(0) {}
GraphBase(int size) : n(size) {
assert(size >= 0);
g.resize(size);
}
size_t size() const { return n; }
const vector<E>& operator[](int x) const {
assert(0 <= x && x < n);
return g[x];
}
vector<E>& operator[](int x) {
assert(0 <= x && x < n);
return g[x];
}
protected:
int n;
vector<vector<E>> g;
};
struct EdgeUnweighted {
int to;
};
struct GraphUnweighted : GraphBase<EdgeUnweighted> {
using base = GraphBase<EdgeUnweighted>;
public:
GraphUnweighted() : base(0) {}
GraphUnweighted(int size) : base(size) {}
GraphUnweighted(const vector<vector<int>>& graph) : base(graph.size()) {
for (int x = 0; x < n; x++) {
base::g[x].reserve(graph[x].size());
for (int y : graph[x]) base::g[x].push_back({y});
}
}
void add_edge(int x, int y) {
(*this)[x].push_back({y});
(*this)[y].push_back({x});
}
void add_edge_directed(int from, int to) { (*this)[from].push_back({to}); }
};
template <class T>
struct EdgeWeighted {
int to;
T weight;
};
template <class T>
struct GraphWeighted : GraphBase<EdgeWeighted<T>> {
using base = GraphBase<EdgeWeighted<T>>;
public:
GraphWeighted() : base(0) {}
GraphWeighted(int size) : base(size) {}
GraphWeighted(const vector<vector<pair<int, T>>>& graph) : base(graph.size()) {
for (int x = 0; x < base::n; x++) {
base::g[x].reserve(graph[x].size());
for (const auto& [y, w] : graph[x]) base::g[x].push_back({y, w});
}
}
void add_edge(int x, int y, T w) {
(*this)[x].push_back({y, w});
(*this)[y].push_back({x, w});
}
void add_edge_directed(int from, int to, T w) { (*this)[from].push_back({to, w}); }
};
inline GraphWeighted<int> GraphUnweightedToWeighted(const GraphUnweighted& g) {
GraphWeighted<int> h(g.size());
for (int x = 0; x < static_cast<int>(g.size()); x++) {
h[x].reserve(g[x].size());
for (const auto& e : g[x]) h[x].push_back({e.to, 1});
}
return h;
}
/**
* @brief Graph
* @docs docs/graph/graph.md
*/
#line 2 "math/util.hpp"
namespace Math {
template <class T>
T safe_mod(T a, T b) {
assert(b != 0);
if (b < 0) a = -a, b = -b;
a %= b;
return a >= 0 ? a : a + b;
}
template <class T>
T floor(T a, T b) {
assert(b != 0);
if (b < 0) a = -a, b = -b;
return a >= 0 ? a / b : (a + 1) / b - 1;
}
template <class T>
T ceil(T a, T b) {
assert(b != 0);
if (b < 0) a = -a, b = -b;
return a > 0 ? (a - 1) / b + 1 : a / b;
}
long long isqrt(long long n) {
if (n <= 0) return 0;
long long x = sqrt(n);
while ((__int128)(x + 1) * (x + 1) <= n) x++;
while ((__int128)x * x > n) x--;
return x;
}
long long floor_root(long long n, int k) {
assert(n >= 0);
if (n == 0) return 0;
assert(k >= 1);
if (k == 1) return n;
if (k > 64) return 1;
long long x = round(pow((long double)n, 1.0L / k));
auto check = [&](long long a) {
if (a <= 0) return true;
__int128_t p = 1;
for (int i = 0; i < k; ++i)
if ((p *= a) > n) return false;
return true;
};
while (check(x + 1)) x++;
while (!check(x)) x--;
return x;
}
unsigned long long floor_root_unsigned(unsigned long long n, int k) {
assert(k >= 1);
if (n <= 1 || k == 1) return n;
if (k >= 64) return 1;
int bits = (64 + k - 1) / k;
unsigned long long ok = 1, ng = min(n, 1ULL << bits);
auto check = [&](unsigned long long a) {
__uint128_t p = 1;
for (int i = 0; i < k; i++) {
p *= a;
if (p > n) return false;
}
return true;
};
while (ok + 1 < ng) {
unsigned long long mid = ok + (ng - ok) / 2;
(check(mid) ? ok : ng) = mid;
}
return ok;
}
// return g=gcd(a,b)
// a*x+b*y=g
// - b!=0 -> 0<=x<|b|/g
// - b=0 -> ax=g
template <class T>
T ext_gcd(T a, T b, T& x, T& y) {
T a0 = a, b0 = b;
bool sgn_a = a < 0, sgn_b = b < 0;
if (sgn_a) a = -a;
if (sgn_b) b = -b;
if (b == 0) {
x = sgn_a ? -1 : 1;
y = 0;
return a;
}
T x00 = 1, x01 = 0, x10 = 0, x11 = 1;
while (b != 0) {
T q = a / b, r = a - b * q;
x00 -= q * x01;
x10 -= q * x11;
swap(x00, x01);
swap(x10, x11);
a = b, b = r;
}
x = x00, y = x10;
if (sgn_a) x = -x;
if (sgn_b) y = -y;
if (b0 != 0) {
a0 /= a, b0 /= a;
if (b0 < 0) a0 = -a0, b0 = -b0;
T q = x >= 0 ? x / b0 : (x + 1) / b0 - 1;
x -= b0 * q;
y += a0 * q;
}
return a;
}
constexpr long long inv_mod(long long x, long long m) {
x %= m;
if (x < 0) x += m;
long long a = m, b = x;
long long y0 = 0, y1 = 1;
while (b > 0) {
long long q = a / b;
swap(a -= q * b, b);
swap(y0 -= q * y1, y1);
}
if (y0 < 0) y0 += m / a;
return y0;
}
long long pow_mod(long long x, long long n, long long m) {
if (m == 1) return 0;
x = (x % m + m) % m;
long long y = 1;
while (n) {
if (n & 1) y = y * x % m;
x = x * x % m;
n >>= 1;
}
return y;
}
constexpr long long pow_mod_constexpr(long long x, long long n, int m) {
if (m == 1) return 0;
unsigned int _m = (unsigned int)(m);
unsigned long long r = 1;
unsigned long long y = x % m;
if (y >= m) y += m;
while (n) {
if (n & 1) r = (r * y) % _m;
y = (y * y) % _m;
n >>= 1;
}
return r;
}
constexpr bool is_prime_constexpr(int n) {
if (n <= 1) return false;
if (n == 2 || n == 7 || n == 61) return true;
if (n % 2 == 0) return false;
long long d = n - 1;
while (d % 2 == 0) d /= 2;
constexpr long long bases[3] = {2, 7, 61};
for (long long a : bases) {
long long t = d;
long long y = pow_mod_constexpr(a, t, n);
while (t != n - 1 && y != 1 && y != n - 1) {
y = y * y % n;
t <<= 1;
}
if (y != n - 1 && t % 2 == 0) {
return false;
}
}
return true;
}
template <int n>
constexpr bool is_prime = is_prime_constexpr(n);
}; // namespace Math
#line 3 "modint/modint.hpp"
template <unsigned int m = 998244353>
struct ModInt {
using mint = ModInt;
static constexpr unsigned int get_mod() { return m; }
static mint raw(int v) {
mint x;
x._v = v;
return x;
}
ModInt() : _v(0) {}
ModInt(int64_t v) {
long long x = (long long)(v % (long long)(umod()));
if (x < 0) x += umod();
_v = (unsigned int)(x);
}
unsigned int val() const { return _v; }
mint& operator++() {
_v++;
if (_v == umod()) _v = 0;
return *this;
}
mint& operator--() {
if (_v == 0) _v = umod();
_v--;
return *this;
}
mint operator++(int) {
mint result = *this;
++*this;
return result;
}
mint operator--(int) {
mint result = *this;
--*this;
return result;
}
mint& operator+=(const mint& rhs) {
_v += rhs._v;
if (_v >= umod()) _v -= umod();
return *this;
}
mint& operator-=(const mint& rhs) {
_v -= rhs._v;
if (_v >= umod()) _v += umod();
return *this;
}
mint& operator*=(const mint& rhs) {
unsigned long long z = _v;
z *= rhs._v;
_v = (unsigned int)(z % umod());
return *this;
}
mint& operator/=(const mint& rhs) { return *this *= rhs.inv(); }
mint operator+() const { return *this; }
mint operator-() const { return mint() - *this; }
mint pow(long long n) const {
assert(0 <= n);
mint x = *this, r = 1;
while (n) {
if (n & 1) r *= x;
x *= x;
n >>= 1;
}
return r;
}
mint inv() const {
if (is_prime) {
assert(_v);
return pow(umod() - 2);
} else {
auto inv = Math::inv_mod(_v, umod());
return raw(inv);
}
}
friend mint operator+(const mint& lhs, const mint& rhs) { return mint(lhs) += rhs; }
friend mint operator-(const mint& lhs, const mint& rhs) { return mint(lhs) -= rhs; }
friend mint operator*(const mint& lhs, const mint& rhs) { return mint(lhs) *= rhs; }
friend mint operator/(const mint& lhs, const mint& rhs) { return mint(lhs) /= rhs; }
friend bool operator==(const mint& lhs, const mint& rhs) { return lhs._v == rhs._v; }
friend bool operator!=(const mint& lhs, const mint& rhs) { return lhs._v != rhs._v; }
friend istream& operator>>(istream& is, mint& x) {
int64_t v;
is >> v;
x = mint(v);
return is;
}
friend ostream& operator<<(ostream& os, const mint& x) { return os << x.val(); }
private:
unsigned int _v;
static constexpr unsigned int umod() { return m; }
static constexpr bool is_prime = Math::is_prime<m>;
};
using ModInt998244353 = ModInt<998244353>;
using ModInt1000000007 = ModInt<1000000007>;
#line 2 "algebraic-structure/util.hpp"
#ifdef __cpp_concepts
#define REQUIRES(...) requires __VA_ARGS__
#else
#define REQUIRES(...)
#endif
#line 3 "algebraic-structure/magma.hpp"
#ifdef __cpp_concepts
template <class M>
concept Magma = requires(typename M::value_type x, typename M::value_type y) {
typename M::value_type;
{ M::op(x, y) } -> same_as<typename M::value_type>;
};
#endif
template <class T>
struct AddMagma {
using value_type = T;
static T op(T x, T y) { return x + y; }
};
template <class T>
struct MulMagma {
using value_type = T;
static T op(T x, T y) { return x * y; }
};
template <class T, T id>
struct MaxMagma {
using value_type = T;
static T op(T x, T y) { return x > y ? x : y; }
};
template <class T, T id>
struct MinMagma {
using value_type = T;
static T op(T x, T y) { return x < y ? x : y; }
};
#line 3 "algebraic-structure/monoid.hpp"
#ifdef __cpp_concepts
template <class M>
concept Monoid = Magma<M> && requires {
{ M::e() } -> same_as<typename M::value_type>;
};
#endif
template <class T>
struct AddMonoid {
using value_type = T;
static T op(T x, T y) { return x + y; }
static T e() { return T(0); }
};
template <class T>
struct MulMonoid {
using value_type = T;
static T op(T x, T y) { return x * y; }
static T e() { return T(1); }
};
template <class T, T id>
struct MaxMonoid {
using value_type = T;
static T op(T x, T y) { return x > y ? x : y; }
static T e() { return id; }
};
template <class T, T id>
struct MinMonoid {
using value_type = T;
static T op(T x, T y) { return x < y ? x : y; }
static T e() { return id; }
};
#line 3 "segment-tree/segment-tree.hpp"
template <class M>
REQUIRES(Monoid<M>)
struct SegmentTree {
using T = typename M::value_type;
private:
int _n, size, log;
vector<T> d;
void update(int p) { d[p] = M::op(d[2 * p], d[2 * p + 1]); }
public:
SegmentTree() : SegmentTree(0) {}
explicit SegmentTree(int sz) : SegmentTree(vector<T>(sz, M::e())) {}
explicit SegmentTree(const vector<T>& v) : _n(v.size()) {
size = 1, log = 0;
while (size < _n) size <<= 1, log++;
d.assign(2 * size, M::e());
for (int i = 0; i < _n; i++) d[size + i] = v[i];
for (int i = size - 1; i > 0; i--) update(i);
}
void clear() { fill(d.begin(), d.end(), M::e()); }
void set_without_update(int p, T v) { d[p + size] = v; }
void all_update() {
for (int i = size - 1; i > 0; i--) update(i);
}
T get(int p) {
assert(0 <= p && p <= _n);
return d[p + size];
}
void set(int p, T v) {
assert(0 <= p && p <= _n);
p += size;
d[p] = v;
for (int i = 1; i <= log; i++) update(p >> i);
}
void apply(int p, T v) {
assert(0 <= p && p <= _n);
p += size;
d[p] = M::op(d[p], v);
for (int i = 1; i <= log; i++) update(p >> i);
}
T all_prod() { return d[1]; }
T prod(int l, int r) {
if (l >= r) return M::e();
assert(0 <= l && l <= r && r <= _n);
T sl = M::e(), sr = M::e();
l += size, r += size;
while (l < r) {
if ((l & 1) != 0) sl = M::op(sl, d[l++]);
if ((r & 1) != 0) sr = M::op(d[--r], sr);
l >>= 1, r >>= 1;
}
return M::op(sl, sr);
}
template <bool (*f)(T)>
int max_right(int l) const {
return max_right(l, [](T x) { return f(x); });
}
template <class F>
int max_right(int l, F f) const {
assert(0 <= l && l <= size);
assert(f(M::e()));
if (l == _n) return _n;
l += size;
T s = M::e();
do {
while (l % 2 == 0) l >>= 1;
if (!f(M::op(s, d[l]))) {
while (l < size) {
l <<= 1;
if (f(M::op(s, d[l]))) s = M::op(s, d[l++]);
}
return l - size;
}
s = M::op(s, d[l++]);
} while ((l & -l) != l);
return _n;
}
template <bool (*f)(T)>
int min_left(int r) const {
return min_left(r, [](T x) { return f(x); });
}
template <class F>
int min_left(int r, F f) const {
assert(0 <= r && r <= _n);
assert(f(M::e()));
if (r == 0) return 0;
r += size;
T s = M::e();
do {
r--;
while (r > 1 && (r % 2)) r >>= 1;
if (!f(M::op(d[r], s))) {
while (r < size) {
r <<= 1, r++;
if (f(M::op(d[r], s))) s = M::op(d[r--], s);
}
return r + 1 - size;
}
s = M::op(d[r], s);
} while ((r & -r) != r);
return 0;
}
};
/**
* @brief Segment Tree
* @docs docs/segment-tree/segment-tree.md
*/
#line 2 "tree/heavy-light-decomposition.hpp"
struct HeavyLightDecomposition {
vector<int> vertices, pos, parent, depth, heavy_root;
HeavyLightDecomposition() {}
template <class G>
HeavyLightDecomposition(const G& g, int root = 0) { build(g, root); }
template <class F>
void path(int x, int y, F f) const {
int n = parent.size();
assert(0 <= x && x < n);
assert(0 <= y && y < n);
array<pair<int, int>, numeric_limits<unsigned int>::digits> right;
int right_size = 0;
while (heavy_root[x] != heavy_root[y]) {
int hx = heavy_root[x], hy = heavy_root[y];
if (depth[hx] >= depth[hy]) {
f(pos[hx], pos[x] + 1, true);
x = parent[hx];
} else {
assert(right_size < static_cast<int>(right.size()));
right[right_size++] = {pos[hy], pos[y] + 1};
y = parent[hy];
}
}
if (pos[x] <= pos[y])
f(pos[x], pos[y] + 1, false);
else
f(pos[y], pos[x] + 1, true);
for (int i = right_size - 1; i >= 0; i--) f(right[i].first, right[i].second, false);
}
template <class G>
void build(const G& g, int root = 0) {
int n = g.size();
assert(n > 0);
assert(0 <= root && root < n);
parent.assign(n, -2);
depth.assign(n, 0);
parent[root] = -1;
vertices.clear();
vertices.reserve(n);
stack<int> st;
st.push(root);
while (!st.empty()) {
int x = st.top();
st.pop();
vertices.push_back(x);
for (const auto& e : g[x]) {
int y = e.to;
if (parent[y] != -2) continue;
parent[y] = x;
depth[y] = depth[x] + 1;
st.push(y);
}
}
assert(static_cast<int>(vertices.size()) == n);
vector<int> subtree_size(n, 1), heavy(n, -1);
for (auto it = vertices.rbegin(); it != vertices.rend(); it++) {
int x = *it, p = parent[x];
if (p != -1) {
subtree_size[p] += subtree_size[x];
if (heavy[p] == -1 || subtree_size[x] > subtree_size[heavy[p]]) heavy[p] = x;
}
}
vertices.clear();
pos.resize(n);
heavy_root.resize(n);
stack<pair<int, int>> paths;
paths.push({root, root});
while (!paths.empty()) {
auto [start, head] = paths.top();
paths.pop();
for (int x = start; x != -1; x = heavy[x]) {
pos[x] = static_cast<int>(vertices.size());
vertices.push_back(x);
heavy_root[x] = head;
for (const auto& e : g[x]) {
int y = e.to;
if (parent[y] == x && y != heavy[x]) paths.push({y, y});
}
}
}
}
};
/**
* @brief Heavy Light Decomposition
* @docs docs/tree/heavy-light-decomposition.md
*/
#line 8 "verify/tree/LC_vertex_set_path_composite.test.cpp"
using mint = ModInt998244353;
struct F {
mint a, b;
mint eval(mint x) const { return a * x + b; }
};
struct CompositeMonoid {
using value_type = F;
static F op(F f, F g) { return {f.a * g.a, f.b * g.a + g.b}; }
static F e() { return {1, 0}; }
};
struct ReverseCompositeMonoid {
using value_type = F;
static F op(F f, F g) { return CompositeMonoid::op(g, f); }
static F e() { return CompositeMonoid::e(); }
};
int main() {
int n, q;
in(n, q);
vector<F> f(n);
rep(x, 0, n) in(f[x].a, f[x].b);
GraphUnweighted g(n);
rep(i, 0, n - 1) {
int u, v;
in(u, v);
g.add_edge(u, v);
}
HeavyLightDecomposition hld(g);
vector<F> arranged(n);
rep(x, 0, n) arranged[hld.pos[x]] = f[x];
SegmentTree<CompositeMonoid> seg(arranged);
SegmentTree<ReverseCompositeMonoid> rseg(arranged);
while (q--) {
int type;
in(type);
if (type == 0) {
int p;
F value;
in(p, value.a, value.b);
seg.set(hld.pos[p], value);
rseg.set(hld.pos[p], value);
} else {
int u, v;
mint x;
in(u, v, x);
F prod = CompositeMonoid::e();
hld.path(u, v, [&](int l, int r, bool rev) {
F part = rev ? rseg.prod(l, r) : seg.prod(l, r);
prod = CompositeMonoid::op(prod, part);
});
out(prod.eval(x));
}
}
}
verify/tree/LC_vertex_set_path_composite.test.cpp
algebraic-structure/magma.hpp