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:heavy_check_mark: Verify/verify-yosupo-tree/point_set_tree_path_composite_sum_fixed_root.test.cpp

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Code

#define PROBLEM "https://judge.yosupo.jp/problem/point_set_tree_path_composite_sum_fixed_root"
#include "../../Graph/Graph.hpp"
#include "../../Modint/Modint.hpp"
#include "../../Template/Template.hpp"
#include "../../Tree/StaticTopTree.hpp"
using mint = Modint<MOD>;
using edge_type = array<ll, 4>;
using func_type = pair<mint, mint>;
void solve() {
    LL(N, Q);
    static VEC(mint, a, N);
    Graph<func_type> gr(N);
    rep(i, N - 1) {
        LL(u, v, b, c);
        gr.add_edge(v, u, {b, c});
    }
    stack<ll> vert;
    vert.push(0);
    static vec(func_type, func, N, {1, 0});
    vec(ll, change, N - 1, -1);
    while (!vert.empty()) {
        ll pos = vert.top();
        vert.pop();
        each(i, gr[pos]) {
            if (change[i.idx] == -1) {
                func[i] = i.cost;
                change[i.idx] = i;
                vert.push(i);
            }
        }
    }
    struct ops {
        using point = array<mint, 2>;
        using path = array<mint, 4>;
        static path vertex(int v) {
            return {1, a[v] * func[v].fi + func[v].se, func[v].fi, func[v].se};
        }
        static path compress(path p, path c) {
            return {p[0] + c[0], p[1] + c[1] * p[2] + c[0] * p[3], p[2] * c[2],
                    p[2] * c[3] + p[3]};
        }
        static path add_vertex(point t, int v) {
            return {t[0] + 1,
                    (a[v] + t[1]) * func[v].fi + (t[0] + 1) * func[v].se,
                    func[v].fi, func[v].se};
        }
        static point rake(point x, point y) {
            return {x[0] + y[0], x[1] + y[1]};
        }
        static point add_edge(path t) { return {t[0], t[1]}; }
    };
    StaticTopTree<ops> tree(gr, 0);
    rep(_, Q) {
        LL(t);
        if (t == 0) {
            LL(w, x);
            a[w] = x;
            tree.calc(w);
        } else {
            LL(e, y, z);
            func[change[e]] = {y, z};
            tree.calc(change[e]);
        }
        out(tree.root_value()[1]);
    }
}
int main() { solve(); }
#line 1 "Verify/verify-yosupo-tree/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"
#line 2 "Graph/Graph.hpp"
#include <cstdint>
#include <vector>
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 2 "Modint/Modint.hpp"
#include <assert.h>

#line 5 "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) noexcept {
        return os << b.x;
    }
    friend std::istream &operator>>(std::istream &is, Modint &b) noexcept {
        return is >> b.x;
    }
    constexpr uint64_t val() noexcept { return x; }
    constexpr Modint operator+() noexcept { return (*this); }
    constexpr Modint operator-() noexcept { return Modint() - (*this); }
    friend Modint operator+(const Modint lhs, const Modint rhs) noexcept {
        return Modint(lhs) += rhs;
    }
    friend Modint operator-(const Modint lhs, const Modint rhs) noexcept {
        return Modint(lhs) -= rhs;
    }
    friend Modint operator*(const Modint lhs, const Modint rhs) noexcept {
        return Modint(lhs) *= rhs;
    }
    friend Modint operator/(const Modint lhs, const Modint rhs) {
        return Modint(lhs) /= 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;
    }
    friend bool operator==(const Modint lhs, const Modint rhs) noexcept {
        return lhs.x == rhs.x;
    }
    friend bool operator!=(const Modint lhs, const Modint rhs) noexcept {
        return rhs.x != rhs.x;
    }
    constexpr Modint &operator/=(Modint rhs) { return (*this) *= rhs.inv(); }
    constexpr Modint inv() {
        int64_t a = (*this).x, b = get_mod();
        assert(a != 0);
        int64_t s = b, t = a;
        int64_t m0 = 0, m1 = 1;
        while (t) {
            int64_t u = s / t;
            s -= t * u;
            m0 -= m1 * u;
            int64_t tmp = s;
            s = t;
            t = tmp;
            tmp = m0;
            m0 = m1;
            m1 = tmp;
        }
        assert(s == 1);
        if (m0 < 0) m0 += b;
        return Modint(m0);
    }
    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) noexcept {
        return os << b.x;
    }
    friend std::istream &operator>>(std::istream &is,
                                    ArbitraryModint &b) noexcept {
        return is >> b.x;
    }
    constexpr uint64_t val() noexcept { return x; }
    constexpr ArbitraryModint operator+() noexcept { return (*this); }
    constexpr ArbitraryModint operator-() noexcept {
        return ArbitraryModint() - (*this);
    }
    friend ArbitraryModint operator+(const ArbitraryModint lhs,
                                     const ArbitraryModint rhs) noexcept {
        return ArbitraryModint(lhs) += rhs;
    }
    friend ArbitraryModint operator-(const ArbitraryModint lhs,
                                     const ArbitraryModint rhs) noexcept {
        return ArbitraryModint(lhs) -= rhs;
    }
    friend ArbitraryModint operator*(const ArbitraryModint lhs,
                                     const ArbitraryModint rhs) noexcept {
        return ArbitraryModint(lhs) *= rhs;
    }
    friend ArbitraryModint operator/(const ArbitraryModint lhs,
                                     const ArbitraryModint rhs) {
        return ArbitraryModint(lhs) /= rhs;
    }
    constexpr ArbitraryModint &operator+=(const ArbitraryModint rhs) noexcept {
        x += rhs.x;
        if (x >= mod()) x -= mod();
        return *this;
    }
    constexpr ArbitraryModint &operator-=(const ArbitraryModint rhs) noexcept {
        if (x < rhs.x) x += mod();
        x -= rhs.x;
        return *this;
    }
    constexpr ArbitraryModint &operator*=(const ArbitraryModint rhs) noexcept {
        x = _get_mod(x * rhs.x);
        return *this;
    }
    friend bool operator==(const ArbitraryModint lhs,
                           const ArbitraryModint rhs) noexcept {
        return lhs.x == rhs.x;
    }
    friend bool operator!=(const ArbitraryModint lhs,
                           const ArbitraryModint rhs) noexcept {
        return rhs.x != rhs.x;
    }
    constexpr ArbitraryModint &operator/=(ArbitraryModint rhs) {
        return (*this) *= rhs.inv();
    }
    constexpr ArbitraryModint inv() {
        int64_t a = (*this).x, b = get_mod();
        assert(a != 0);
        int64_t s = b, t = a;
        int64_t m0 = 0, m1 = 1;
        while (t) {
            int64_t u = s / t;
            s -= t * u;
            m0 -= m1 * u;
            int64_t tmp = s;
            s = t;
            t = tmp;
            tmp = m0;
            m0 = m1;
            m1 = tmp;
        }
        assert(s == 1);
        if (m0 < 0) m0 += b;
        return ArbitraryModint(m0);
    }
    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 2 "Template/Template.hpp"
#include <bits/stdc++.h>
using namespace std;

#line 8 "Template/InOut.hpp"
inline void scan() {}
inline void scan(int32_t &a) { std::cin >> a; }
inline void scan(uint32_t &a) { std::cin >> a; }
inline void scan(int64_t &a) { std::cin >> a; }
inline void scan(uint64_t &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 int32_t &a) { std::cout << a; }
inline void print(const uint32_t &a) { std::cout << a; }
inline void print(const int64_t &a) { std::cout << a; }
inline void print(const uint64_t &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"); }
inline void Takahashi(bool i = true) { out(i ? "Takahashi" : "Aoki"); }
inline void Aoki(bool i = true) { out(i ? "Aoki" : "Takahashi"); }
inline void Alice(bool i = true) { out(i ? "Alice" : "Bob"); }
inline void Bob(bool i = true) { out(i ? "Bob" : "Alice"); }
inline void First(bool i = true) { out(i ? "First" : "Second"); }
inline void Second(bool i = true) { out(i ? "Second" : "First"); }
inline void Possible(bool i = true) { out(i ? "Possible" : "Impossible"); }
inline void Impossible(bool i = true) { out(i ? "Impossible" : "Possible"); }
inline void fls() { std::flush(std::cout); }
struct IOsetup {
    IOsetup() {
        std::ios::sync_with_stdio(false);
        std::cin.tie(nullptr);
        std::cout << std::fixed << std::setprecision(16);
    }
} iosetup;
#line 9 "Template/Util.hpp"
using ll = int64_t;
using ld = long double;
using ull = uint64_t;
using uint = uint32_t;
using pll = std::pair<ll, ll>;
using pii = std::pair<int32_t, int32_t>;
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 "Template/Macro.hpp"
#define _overload3(_1, _2, _3, name, ...) name
#define _overload4(_1, _2, _3, _4, name, ...) name
#define _rep1(i, n) for (int64_t i = 0; i < (n); i++)
#define _rep2(i, a, b) for (int64_t i = (a); i < (b); i++)
#define _rep3(i, a, b, c) for (int64_t i = (a); i < (b); i += (c))
#define rep(...) _overload4(__VA_ARGS__, _rep3, _rep2, _rep1)(__VA_ARGS__)
#define _rrep1(i, n) for (int64_t i = (n) - 1; i >= 0; i--)
#define _rrep2(i, a, b) for (int64_t i = (b) - 1; i >= (a); i--)
#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) ((int64_t)(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(...) int32_t __VA_ARGS__; in(__VA_ARGS__)
#define LL(...) int64_t __VA_ARGS__; in(__VA_ARGS__)
#define ULL(...) uint64_t __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 5 "Tree/StaticTopTree.hpp"

#line 7 "Tree/StaticTopTree.hpp"
template <class M>
struct StaticTopTree {
    using point = typename M::point;
    using path = typename M::path;
    struct Node {
        bool is_path;
        point point_val;
        path path_val;
        int32_t pos;
        int32_t left;
        int32_t right;
        int32_t parent;
        Node(bool pat, int32_t po = -1, int32_t lf = -1, int32_t ri = -1) {
            is_path = pat;
            pos = po;
            left = lf;
            right = ri;
            parent = -1;
        }
    };
    int32_t sz;
    std::vector<int32_t> node_pos;
    std::vector<Node> nodes;
    int32_t rt;
    template <class T>
    StaticTopTree(Graph<T> gr, int32_t root) {
        sz = gr.size();
        node_pos.resize(sz);
        _build(root, gr);
    }
    template <class T>
    int32_t _path_cluster(int32_t pos, std::vector<int32_t> &tree_sz,
                          Graph<T> &tree) {
        if (tree[pos].empty()) {
            node_pos[pos] = nodes.size();
            nodes.emplace_back(Node(1, pos));
            _calc_val(nodes.size() - 1);
            return nodes.size() - 1;
        }
        std::vector<int32_t> address;
        std::vector<int32_t> sizes;
        while (!tree[pos].empty()) {
            int32_t max_size = -1;
            int32_t next_pos = -1;
            for (int i = 0; i < tree[pos].size(); i++) {
                if (tree_sz[tree[pos][i]] > max_size) {
                    max_size = tree_sz[tree[pos][i]];
                    next_pos = i;
                }
            }
            std::swap(tree[pos][next_pos], tree[pos].back());
            next_pos = tree[pos].back();
            tree[pos].pop_back();
            tree_sz[pos] -= tree_sz[next_pos];
            sizes.emplace_back(tree_sz[pos]);
            address.emplace_back(_point_cluster(pos, tree_sz, tree));
            pos = next_pos;
        }
        address.emplace_back(_point_cluster(pos, tree_sz, tree));
        sizes.emplace_back(tree_sz[pos]);
        return _merge(address, sizes, 0, address.size(), 1);
    }
    template <class T>
    int32_t _point_cluster(int32_t pos, std::vector<int32_t> &tree_sz,
                           Graph<T> &tree) {
        if (tree[pos].empty()) {
            node_pos[pos] = nodes.size();
            nodes.emplace_back(Node(1, pos));
            _calc_val(nodes.size() - 1);
            return nodes.size() - 1;
        }
        std::vector<int32_t> address;
        std::vector<int32_t> sizes;
        for (int32_t i : tree[pos]) {
            sizes.emplace_back(tree_sz[i]);
            int32_t vert = _path_cluster(i, tree_sz, tree);
            nodes.emplace_back(Node(0, -1, vert));
            nodes[vert].parent = nodes.size() - 1;
            address.emplace_back(nodes.size() - 1);
            _calc_val(nodes.size() - 1);
        }
        int32_t vert = _merge(address, sizes, 0, address.size(), 0);
        node_pos[pos] = nodes.size();
        nodes.emplace_back(Node(1, pos, vert));
        nodes[vert].parent = nodes.size() - 1;
        _calc_val(nodes.size() - 1);
        return nodes.size() - 1;
    }
    int32_t _merge(std::vector<int32_t> &address, std::vector<int32_t> &sizes,
                   int32_t lf, int32_t ri, bool pat) {
        if (lf + 1 == ri) return address[lf];
        int32_t add = 0;
        for (int32_t i = lf; i < ri; i++) {
            add += sizes[i];
        }
        int32_t now = 0;
        int32_t bef = add + 1;
        for (int32_t i = lf; i < ri; i++) {
            now += sizes[i];
            if (now > add - now) {
                if (now + now - add > bef) i--;
                int32_t left = _merge(address, sizes, lf, i + 1, pat);
                int32_t right = _merge(address, sizes, i + 1, ri, pat);
                nodes.emplace_back(Node(pat, -1, left, right));
                nodes[left].parent = nodes.size() - 1;
                nodes[right].parent = nodes.size() - 1;
                _calc_val(nodes.size() - 1);
                return nodes.size() - 1;
            }
            bef = add - now - now;
        }
        assert(false);
    }
    void _calc_val(int32_t pos) {
        if (nodes[pos].is_path) {
            if ((nodes[pos].left == -1) && (nodes[pos].right == -1)) {
                nodes[pos].path_val = M::vertex(nodes[pos].pos);
            } else if ((nodes[pos].left != -1) && (nodes[pos].right != -1)) {
                nodes[pos].path_val =
                    M::compress(nodes[nodes[pos].left].path_val,
                                nodes[nodes[pos].right].path_val);
            } else {
                nodes[pos].path_val = M::add_vertex(
                    nodes[nodes[pos].left].point_val, nodes[pos].pos);
            }
        } else {
            if ((nodes[pos].left != -1) && (nodes[pos].right != -1)) {
                nodes[pos].point_val =
                    M::rake(nodes[nodes[pos].left].point_val,
                            nodes[nodes[pos].right].point_val);
            } else {
                nodes[pos].point_val =
                    M::add_edge(nodes[nodes[pos].left].path_val);
            }
        }
    }
    template <class T>
    void _build(int32_t root, Graph<T> &tree) {
        std::vector<int32_t> vert(sz);
        std::vector<int32_t> tree_sz(sz, -1);
        vert[0] = root;
        tree_sz[root] = 0;
        int32_t cnt = 1;
        for (int32_t i = 0; i < sz; i++) {
            for (int32_t j : tree[vert[i]]) {
                if (tree_sz[j]) {
                    tree_sz[j] = 0;
                    vert[cnt] = j;
                    cnt++;
                }
            }
        }
        for (int32_t i = sz - 1; i >= 0; i--) {
            int32_t parent = 0;
            for (int32_t j : tree[vert[i]]) {
                if (tree_sz[j] == 0) {
                    parent = -parent - 1;
                }
                if (parent >= 0) parent++;
                tree_sz[vert[i]] += tree_sz[j];
            }
            if (parent < 0) {
                std::swap(tree[vert[i]][-parent - 1], tree[vert[i]].back());
                tree[vert[i]].pop_back();
            }
            tree_sz[vert[i]]++;
        }
        rt = _path_cluster(root, tree_sz, tree);
    }
    path root_value() { return nodes[rt].path_val; }
    void calc(int32_t pos) {
        int32_t change = node_pos[pos];
        while (nodes[change].parent != -1) {
            _calc_val(change);
            change = nodes[change].parent;
        }
        _calc_val(change);
    }
    int32_t size() { return sz; }
};
#line 6 "Verify/verify-yosupo-tree/point_set_tree_path_composite_sum_fixed_root.test.cpp"
using mint = Modint<MOD>;
using edge_type = array<ll, 4>;
using func_type = pair<mint, mint>;
void solve() {
    LL(N, Q);
    static VEC(mint, a, N);
    Graph<func_type> gr(N);
    rep(i, N - 1) {
        LL(u, v, b, c);
        gr.add_edge(v, u, {b, c});
    }
    stack<ll> vert;
    vert.push(0);
    static vec(func_type, func, N, {1, 0});
    vec(ll, change, N - 1, -1);
    while (!vert.empty()) {
        ll pos = vert.top();
        vert.pop();
        each(i, gr[pos]) {
            if (change[i.idx] == -1) {
                func[i] = i.cost;
                change[i.idx] = i;
                vert.push(i);
            }
        }
    }
    struct ops {
        using point = array<mint, 2>;
        using path = array<mint, 4>;
        static path vertex(int v) {
            return {1, a[v] * func[v].fi + func[v].se, func[v].fi, func[v].se};
        }
        static path compress(path p, path c) {
            return {p[0] + c[0], p[1] + c[1] * p[2] + c[0] * p[3], p[2] * c[2],
                    p[2] * c[3] + p[3]};
        }
        static path add_vertex(point t, int v) {
            return {t[0] + 1,
                    (a[v] + t[1]) * func[v].fi + (t[0] + 1) * func[v].se,
                    func[v].fi, func[v].se};
        }
        static point rake(point x, point y) {
            return {x[0] + y[0], x[1] + y[1]};
        }
        static point add_edge(path t) { return {t[0], t[1]}; }
    };
    StaticTopTree<ops> tree(gr, 0);
    rep(_, Q) {
        LL(t);
        if (t == 0) {
            LL(w, x);
            a[w] = x;
            tree.calc(w);
        } else {
            LL(e, y, z);
            func[change[e]] = {y, z};
            tree.calc(change[e]);
        }
        out(tree.root_value()[1]);
    }
}
int main() { solve(); }
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