compro-library

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:heavy_check_mark: test/graph/Tree-hld-vertex-3.test.cpp

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Code

#define PROBLEM "https://judge.yosupo.jp/problem/vertex_set_path_composite"

#include <vector>
#include <iostream>
#include <cassert>
#include <map>
#include <algorithm>
#include <stack>
#include <numeric>
#include <array>
using namespace std;
#include "../../lib/40-graph/Graph.cpp"
#include "../../lib/40-graph/StaticTree.cpp"
#include "../../lib/00-util/ModInt.cpp"
#include "../../lib/10-segment-tree/SegmentTree.cpp"
#include "../../lib/99-operator/monoid/MonoidRangeCompositePointUpdate.cpp"

//一次関数
template<class T> struct MonoidRangeRevCompositePointUpdate {
    using TypeNode = T;
    inline static constexpr TypeNode unit_node = make_pair(1,0);
    inline static constexpr TypeNode func_fold(TypeNode l,TypeNode r){return {l.first*r.first,l.first*r.second+l.second};}
    inline static constexpr TypeNode func_operate(TypeNode l,TypeNode r){return r;}
    inline static constexpr bool func_check(TypeNode nodeVal,TypeNode var){return var == nodeVal;}
};

using modint = ModInt<998244353>;
int main(void){
    cin.tie(0);ios::sync_with_stdio(false);
    int N,Q;
    cin >> N >> Q;
    SegmentTree<MonoidRangeCompositePointUpdate<pair<modint,modint>>> segLtoR(N,{1,0});
    SegmentTree<MonoidRangeRevCompositePointUpdate<pair<modint,modint>>> segRtoL(N,{1,0});
    vector<int> A(N),B(N);
    for(int i=0;i<N;++i) cin >> A[i] >> B[i];
    Graph<int> g(N);
    for(int i=0;i+1<N;++i) {
        int u,v; cin >> u >> v;
        g.make_bidirectional_edge(u,v,1);
    }
    auto tree = StaticTree<StaticTreeOperator<int>>::builder(g).root(0).parent().child().subtree_size().heavy_light_decomposition().build();
    for(int i=0;i<N;++i) {
        int j = tree.hld[i];
        segLtoR.operate(j,{A[i],B[i]});
        segRtoL.operate(j,{A[i],B[i]});
    }
    while(Q--) {
        int q; cin >> q;
        if(q==0) {
            int i,a,b; cin >> i >> a >> b;
            int j = tree.hld[i];
            segLtoR.operate(j,{a,b});
            segRtoL.operate(j,{a,b});
        }
        else {
            int l,r,x; cin >> l >> r >> x;
            auto tp = tree.vertex_ordered_set_on_path(l,r);

            pair<modint,modint> line = {1,0};
            for(auto& p:tp.first) {
                auto tmp = segRtoL.fold(p.first,p.second+1);
                line = {tmp.first*line.first,tmp.first*line.second+tmp.second};
            }
            for(auto& p:tp.second) {
                auto tmp = segLtoR.fold(p.first,p.second+1);
                line = {tmp.first*line.first,tmp.first*line.second+tmp.second};
            }
            cout << line.first*x+line.second << "\n";
        }
    }
    return 0; 
}
#line 1 "test/graph/Tree-hld-vertex-3.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/vertex_set_path_composite"

#include <vector>
#include <iostream>
#include <cassert>
#include <map>
#include <algorithm>
#include <stack>
#include <numeric>
#include <array>
using namespace std;
#line 1 "lib/40-graph/Graph.cpp"
/*
 * @title Graph
 * @docs md/graph/Graph.md
 */
template<class T> class Graph{
private:
    const size_t N,H,W;
public:
    vector<vector<pair<size_t,T>>> edges;
    Graph(const size_t N):H(-1),W(-1),N(N), edges(N) {}
    Graph(const size_t H, const size_t W):H(H),W(W),N(H*W), edges(H*W) {}
    inline void make_edge(size_t from, size_t to, T w) {
        edges[from].emplace_back(to,w);
    }
    //{from_y,from_x} -> {to_y,to_x} 
    inline void make_edge(pair<size_t,size_t> from, pair<size_t,size_t> to, T w) {
        make_edge(from.first*W+from.second,to.first*W+to.second,w);
    }
    inline void make_bidirectional_edge(size_t from, size_t to, T w) {
        make_edge(from,to,w);
        make_edge(to,from,w);
    }
    inline void make_bidirectional_edge(pair<size_t,size_t> from, pair<size_t,size_t> to, T w) {
        make_edge(from.first*W+from.second,to.first*W+to.second,w);
        make_edge(to.first*W+to.second,from.first*W+from.second,w);
    }
    inline size_t size(){return N;}
    inline size_t idx(pair<size_t,size_t> yx){return yx.first*W+yx.second;}
};
#line 1 "lib/40-graph/StaticTree.cpp"
/*
 * @title StaticTree - 木
 * @docs md/graph/StaticTree.md
 */
template<class Operator> class StaticTreeBuilder;
template<class Operator> class StaticTree {
private:
    using TypeEdge = typename Operator::TypeEdge;
    size_t num;
    size_t ord;
    Graph<TypeEdge>& g;
    friend StaticTreeBuilder<Operator>;
    StaticTree(Graph<TypeEdge>& graph):
            g(graph),
            num(graph.size()),
            depth(graph.size(),-1),
            order(graph.size()),
            edge_dist(graph.size()){
    }
    //for make_depth
    void dfs(int curr, int prev){
        for(const auto& e:g.edges[curr]){
            const int& next = e.first;
            if(next==prev) continue;
            depth[next] = depth[curr] + 1;
            edge_dist[next]  = Operator::func_edge_merge(edge_dist[curr],e.second);
            dfs(next,curr);
            order[ord++] = next;
        }
    }
    //for make_eulertour
    void dfs(int from){
        eulertour.push_back(from);
        for(auto& e:child[from]){
            int to = e.first;
            dfs(to);
            eulertour.push_back(from);
        }
    }
    void make_root(const int root) {
        depth[root] = 0;
        edge_dist[root] = Operator::unit_edge;
        ord = 0;
        dfs(root,-1);
        order[ord++] = root;
        reverse_copy(order.begin(),order.end(),back_inserter(reorder));
    }
    void make_root() {
        ord = 0;
        for(int i=0;i<num;++i) {
            if(depth[i]!=-1) continue;
            depth[i] = 0;
            edge_dist[i] = Operator::unit_edge;
            dfs(i,-1);
            order[ord++] = i;
        }
        reverse_copy(order.begin(),order.end(),back_inserter(reorder));
    }
    void make_child(const int root = 0) {
        child.resize(num);
        for (size_t i = 0; i < num; ++i) for (auto& e : g.edges[i]) if (depth[i] < depth[e.first]) child[i].push_back(e);
    }
    void make_subtree_size() {
        subtree_size.resize(num,1);
        for (size_t i:order) for (auto e : child[i]) subtree_size[i] += subtree_size[e.first];
    }
    void make_parent() {
        parent.resize(num,make_pair(num,Operator::unit_edge));
        for (size_t i = 0; i < num; ++i) for (auto& e : g.edges[i]) if (depth[i] > depth[e.first]) parent[i] = e;
    }
    void make_ancestor() {
        ancestor.resize(num);
        for (size_t i = 0; i < num; ++i) ancestor[i][0] = (parent[i].first!=num?parent[i]:make_pair(i,Operator::unit_lca_edge));
        for (size_t j = 1; j < Operator::bit; ++j) {
            for (size_t i = 0; i < num; ++i) {
                size_t k = ancestor[i][j - 1].first;
                ancestor[i][j] = Operator::func_lca_edge_merge(ancestor[k][j - 1],ancestor[i][j - 1]);
            }
        }
    }
    pair<size_t,TypeEdge> lca_impl(size_t l, size_t r) {
        if (depth[l] < depth[r]) swap(l, r);
        int diff = depth[l] - depth[r];
        auto ancl = make_pair(l,Operator::unit_lca_edge);
        auto ancr = make_pair(r,Operator::unit_lca_edge);
        for (int j = 0; j < Operator::bit; ++j) {
            if (diff & (1 << j)) ancl = Operator::func_lca_edge_merge(ancestor[ancl.first][j],ancl);
        }
        if(ancl.first==ancr.first) return ancl;
        for (int j = Operator::bit - 1; 0 <= j; --j) {
            if(ancestor[ancl.first][j].first!=ancestor[ancr.first][j].first) {
                ancl = Operator::func_lca_edge_merge(ancestor[ancl.first][j],ancl);
                ancr = Operator::func_lca_edge_merge(ancestor[ancr.first][j],ancr);
            }
        }
        ancl = Operator::func_lca_edge_merge(ancestor[ancl.first][0],ancl);
        ancr = Operator::func_lca_edge_merge(ancestor[ancr.first][0],ancr);
        return Operator::func_lca_edge_merge(ancl,ancr);
    }
    pair<TypeEdge,vector<size_t>> diameter_impl() {
        StaticTree tree = StaticTree::builder(g).build();
        size_t root = 0;
        {
            tree.make_root(0);
        }
        root = max_element(tree.edge_dist.begin(),tree.edge_dist.end()) - tree.edge_dist.begin();
        {
            tree.make_root(root);
        }
        size_t leaf = max_element(tree.edge_dist.begin(),tree.edge_dist.end()) - tree.edge_dist.begin();
        TypeEdge sz = tree.edge_dist[leaf];
        vector<size_t> st;
        {
            tree.make_parent();
            while(leaf != root) {
                st.push_back(leaf);
                leaf = tree.parent[leaf].first;
            }
            st.push_back(root);
        }
        return make_pair(sz,st);
    }
    template<class TypeReroot> vector<TypeReroot> rerooting_impl(vector<TypeReroot> rerootdp,vector<TypeReroot> rerootparent) {
        for(size_t pa:order) for(auto& e:child[pa]) rerootdp[pa] = Operator::func_reroot_dp(rerootdp[pa],rerootdp[e.first]);
        for(size_t pa:reorder) {
            if(depth[pa]) rerootdp[pa] = Operator::func_reroot_dp(rerootdp[pa],rerootparent[pa]);
            size_t m = child[pa].size();
            for(int j = 0; j < m && depth[pa]; ++j){
                size_t ch = child[pa][j].first;
                rerootparent[ch] = Operator::func_reroot_dp(rerootparent[ch],rerootparent[pa]);
            }
            if(m <= 1) continue;
            vector<TypeReroot> l(m),r(m);
            for(int j = 0; j < m; ++j) {
                size_t ch = child[pa][j].first;
                l[j] = rerootdp[ch];
                r[j] = rerootdp[ch];
            }
            for(int j = 1; j+1 < m; ++j) l[j] = Operator::func_reroot_merge(l[j],l[j-1]);
            for(int j = m-2; 0 <=j; --j) r[j] = Operator::func_reroot_merge(r[j],r[j+1]);
            size_t chl = child[pa].front().first;
            size_t chr = child[pa].back().first;
            rerootparent[chl] = Operator::func_reroot_dp(rerootparent[chl],r[1]);
            rerootparent[chr] = Operator::func_reroot_dp(rerootparent[chr],l[m-2]);
            for(int j = 1; j+1 < m; ++j) {
                size_t ch = child[pa][j].first;
                rerootparent[ch] = Operator::func_reroot_dp(rerootparent[ch],l[j-1]);
                rerootparent[ch] = Operator::func_reroot_dp(rerootparent[ch],r[j+1]);
            }
        }
        return rerootdp;
    }
    void make_eulertour() {
        dfs(reorder.front());
        eulertour_range.resize(num);
        for(int i = 0; i < eulertour.size(); ++i) eulertour_range[eulertour[i]].second = i+1;
        for(int i = eulertour.size()-1; 0 <= i; --i) eulertour_range[eulertour[i]].first = i;
    }
    void make_heavy_light_decomposition(){
        head.resize(num);
        hld.resize(num);
        iota(head.begin(),head.end(),0);
        for(size_t& pa:reorder) {
            pair<size_t,size_t> maxi = {0,num};
            for(auto& p:child[pa]) maxi = max(maxi,{subtree_size[p.first],p.first});
            if(maxi.first) head[maxi.second] = head[pa];
        }
        stack<size_t> st_head,st_sub;
        size_t cnt = 0;
        //根に近い方から探索
        for(size_t& root:reorder){
            if(depth[root]) continue;
            //根をpush
            st_head.push(root);
            while(st_head.size()){
                size_t h = st_head.top();
                st_head.pop();
                //部分木の根をpush
                st_sub.push(h);
                while (st_sub.size()){
                    size_t pa = st_sub.top();
                    st_sub.pop();
                    //部分木をカウントしていく
                    hld[pa] = cnt++;
                    //子を探索
                    for(auto& p:child[pa]) {
                        //子のheadが親と同じなら、そのまま進む
                        if(head[p.first]==head[pa]) st_sub.push(p.first);
                            //そうじゃない場合は、そこから新しく部分木としてみなす
                        else st_head.push(p.first);
                    }
                }
            }
        }
    }
    //type 0: vertex, 1: edge
    vector<pair<size_t,size_t>> path_impl(size_t u,size_t v,int type = 0) {
        vector<pair<size_t,size_t>> path;
        while(1){
            if(hld[u]>hld[v]) swap(u,v);
            if(head[u]!=head[v]) {
                path.push_back({hld[head[v]],hld[v]});
                v=parent[head[v]].first;
            }
            else {
                path.push_back({hld[u],hld[v]});
                break;
            }
        }
        reverse(path.begin(),path.end());
        if(type) path.front().first++;
        return path;
    }
    pair<vector<pair<size_t,size_t>>,vector<pair<size_t,size_t>>> ordered_path_impl(size_t u,size_t v,int type = 0) {
        vector<pair<size_t,size_t>> path_lca_to_u;
        vector<pair<size_t,size_t>> path_lca_to_v;
        while(1){
            if(head[u] == head[v]) {
                if(depth[u] < depth[v]) path_lca_to_v.emplace_back(hld[u]+type,hld[v]);
                else path_lca_to_u.emplace_back(hld[v]+type,hld[u]);
                break;
            }
            else if(hld[u] < hld[v]) {
                path_lca_to_v.emplace_back(hld[head[v]],hld[v]);
                v = parent[head[v]].first;
            }
            else if(hld[u] > hld[v]) {
                path_lca_to_u.emplace_back(hld[head[u]],hld[u]);
                u = parent[head[u]].first;
            }
        }
        reverse(path_lca_to_v.begin(),path_lca_to_v.end());
        return {path_lca_to_u,path_lca_to_v};
    }
    size_t lca_idx_impl(size_t u,size_t v){
        while(1){
            if(hld[u]>hld[v]) swap(u,v);
            if(head[u]==head[v]) return u;
            v=parent[head[v]].first;
        }
    }
    vector<size_t> head;
public:
    vector<size_t> depth;
    vector<size_t> order;
    vector<size_t> reorder;
    vector<size_t> subtree_size;
    vector<pair<size_t,TypeEdge>> parent;
    vector<vector<pair<size_t,TypeEdge>>> child;
    vector<TypeEdge> edge_dist;
    vector<array<pair<size_t,TypeEdge>,Operator::bit>> ancestor;
    vector<size_t> eulertour;
    vector<pair<size_t,size_t>> eulertour_range;
    vector<size_t> hld;

    /**
     * O(N) builder
     */
    static StaticTreeBuilder<Operator> builder(Graph<TypeEdge>& graph) { return StaticTreeBuilder<Operator>(graph);}
    /**
     * O(logN) after make_ancestor
     * return {lca,lca_dist} l and r must be connected
     */
    pair<size_t,TypeEdge> lca(size_t l, size_t r) {return lca_impl(l,r);}
    /**
     * O(N) anytime
     * return {diameter size,diameter set}
     */
    pair<TypeEdge,vector<size_t>> diameter(void){return diameter_impl();}
    /**
     * O(N) after make_child
     */
    template<class TypeReroot> vector<TypeReroot> rerooting(const vector<TypeReroot>& rerootdp,const vector<TypeReroot>& rerootparent) {return rerooting_impl(rerootdp,rerootparent);}
    /**
     * O(logN)
     */
    vector<pair<size_t,size_t>> vertex_set_on_path(size_t u, size_t v) {return path_impl(u,v,0);}
    /**
    /**
     * O(logN)
     */
    vector<pair<size_t,size_t>> edge_set_on_path(size_t u, size_t v) {return path_impl(u,v,1);}
    /**
     * O(logN)
     * {lca to u path,lca to v path}
     */
    pair<vector<pair<size_t,size_t>>,vector<pair<size_t,size_t>>> vertex_ordered_set_on_path(size_t u, size_t v) {return ordered_path_impl(u,v,0);}
    /**
     * O(logN)
     * {lca to u path,lca to v path}
     */
    pair<vector<pair<size_t,size_t>>,vector<pair<size_t,size_t>>> edge_ordered_set_on_path(size_t u, size_t v) {return ordered_path_impl(u,v,1);}
    /**
     * O(logN) ancestorのlcaより定数倍軽め。idxだけ
     */
    size_t lca_idx(size_t u, size_t v) {return lca_idx_impl(u,v);}
};

template<class Operator> class StaticTreeBuilder {
    bool is_root_made =false;
    bool is_child_made =false;
    bool is_parent_made=false;
    bool is_subtree_size_made=false;
public:
    using TypeEdge = typename Operator::TypeEdge;
    StaticTreeBuilder(Graph<TypeEdge>& g):tree(g){}
    StaticTreeBuilder& root(const int rt) { is_root_made=true; tree.make_root(rt); return *this;}
    StaticTreeBuilder& root() { is_root_made=true; tree.make_root(); return *this;}
    StaticTreeBuilder& child() { assert(is_root_made); is_child_made=true;  tree.make_child();  return *this;}
    StaticTreeBuilder& parent() { assert(is_root_made); is_parent_made=true; tree.make_parent(); return *this;}
    StaticTreeBuilder& subtree_size() { assert(is_child_made); is_subtree_size_made=true; tree.make_subtree_size(); return *this;}
    StaticTreeBuilder& ancestor() { assert(is_parent_made); tree.make_ancestor(); return *this;}
    StaticTreeBuilder& eulertour() { assert(is_child_made); tree.make_eulertour(); return *this;}
    StaticTreeBuilder& heavy_light_decomposition() { assert(is_subtree_size_made); assert(is_parent_made); tree.make_heavy_light_decomposition(); return *this;}
    StaticTree<Operator>&& build() {return move(tree);}
private:
    StaticTree<Operator> tree;
};
template<class T> struct StaticTreeOperator{
    using TypeEdge = T;
    inline static constexpr size_t bit = 20;
    inline static constexpr TypeEdge unit_edge = 0;
    inline static constexpr TypeEdge unit_lca_edge = 0;
    inline static constexpr TypeEdge func_edge_merge(const TypeEdge& parent,const TypeEdge& w){return parent+w;}
    inline static constexpr pair<size_t,TypeEdge> func_lca_edge_merge(const pair<size_t,TypeEdge>& l,const pair<size_t,TypeEdge>& r){return make_pair(l.first,l.second+r.second);}
    template<class TypeReroot> inline static constexpr TypeReroot func_reroot_dp(const TypeReroot& l,const TypeReroot& r) {return {l.first+r.first+r.second,l.second+r.second};}
    template<class TypeReroot> inline static constexpr TypeReroot func_reroot_merge(const TypeReroot& l,const TypeReroot& r) {return {l.first+r.first,l.second+r.second};}
};
//auto tree = StaticTree<StaticTreeOperator<int>>::builder(g).build();
#line 1 "lib/00-util/ModInt.cpp"
/*
 * @title ModInt
 * @docs md/util/ModInt.md
 */
template<long long mod> class ModInt {
public:
    long long x;
    constexpr ModInt():x(0) {}
    constexpr ModInt(long long y) : x(y>=0?(y%mod): (mod - (-y)%mod)%mod) {}
    constexpr ModInt &operator+=(const ModInt &p) {if((x += p.x) >= mod) x -= mod;return *this;}
    constexpr ModInt &operator+=(const long long y) {ModInt p(y);if((x += p.x) >= mod) x -= mod;return *this;}
    constexpr ModInt &operator+=(const int y) {ModInt p(y);if((x += p.x) >= mod) x -= mod;return *this;}
    constexpr ModInt &operator-=(const ModInt &p) {if((x += mod - p.x) >= mod) x -= mod;return *this;}
    constexpr ModInt &operator-=(const long long y) {ModInt p(y);if((x += mod - p.x) >= mod) x -= mod;return *this;}
    constexpr ModInt &operator-=(const int y) {ModInt p(y);if((x += mod - p.x) >= mod) x -= mod;return *this;}
    constexpr ModInt &operator*=(const ModInt &p) {x = (x * p.x % mod);return *this;}
    constexpr ModInt &operator*=(const long long y) {ModInt p(y);x = (x * p.x % mod);return *this;}
    constexpr ModInt &operator*=(const int y) {ModInt p(y);x = (x * p.x % mod);return *this;}
    constexpr ModInt &operator^=(const ModInt &p) {x = (x ^ p.x) % mod;return *this;}
    constexpr ModInt &operator^=(const long long y) {ModInt p(y);x = (x ^ p.x) % mod;return *this;}
    constexpr ModInt &operator^=(const int y) {ModInt p(y);x = (x ^ p.x) % mod;return *this;}
    constexpr ModInt &operator/=(const ModInt &p) {*this *= p.inv();return *this;}
    constexpr ModInt &operator/=(const long long y) {ModInt p(y);*this *= p.inv();return *this;}
    constexpr ModInt &operator/=(const int y) {ModInt p(y);*this *= p.inv();return *this;}
    constexpr ModInt operator=(const int y) {ModInt p(y);*this = p;return *this;}
    constexpr ModInt operator=(const long long y) {ModInt p(y);*this = p;return *this;}
    constexpr ModInt operator-() const {return ModInt(-x); }
    constexpr ModInt operator++() {x++;if(x>=mod) x-=mod;return *this;}
    constexpr ModInt operator--() {x--;if(x<0) x+=mod;return *this;}
    constexpr ModInt operator+(const ModInt &p) const { return ModInt(*this) += p; }
    constexpr ModInt operator-(const ModInt &p) const { return ModInt(*this) -= p; }
    constexpr ModInt operator*(const ModInt &p) const { return ModInt(*this) *= p; }
    constexpr ModInt operator/(const ModInt &p) const { return ModInt(*this) /= p; }
    constexpr ModInt operator^(const ModInt &p) const { return ModInt(*this) ^= p; }
    constexpr bool operator==(const ModInt &p) const { return x == p.x; }
    constexpr bool operator!=(const ModInt &p) const { return x != p.x; }
    // ModInt inv() const {int a=x,b=mod,u=1,v=0,t;while(b > 0) {t = a / b;swap(a -= t * b, b);swap(u -= t * v, v);} return ModInt(u);}
    constexpr ModInt inv() const {int a=x,b=mod,u=1,v=0,t=0,tmp=0;while(b > 0) {t = a / b;a-=t*b;tmp=a;a=b;b=tmp;u-=t*v;tmp=u;u=v;v=tmp;} return ModInt(u);}
    constexpr ModInt pow(long long n) const {ModInt ret(1), mul(x);for(;n > 0;mul *= mul,n >>= 1) if(n & 1) ret *= mul;return ret;}
    friend ostream &operator<<(ostream &os, const ModInt &p) {return os << p.x;}
    friend istream &operator>>(istream &is, ModInt &a) {long long t;is >> t;a = ModInt<mod>(t);return (is);}
};
constexpr long long MOD_998244353 = 998244353;
constexpr long long MOD_1000000007 = 1'000'000'000LL + 7; //'
#line 1 "lib/10-segment-tree/SegmentTree.cpp"
/*
 * @title SegmentTree - 非再帰抽象化セグメント木
 * @docs md/segment-tree/SegmentTree.md
 */
template<class Monoid> class SegmentTree {
    using TypeNode = typename Monoid::TypeNode;
    size_t length;
    size_t num;
    vector<TypeNode> node;
    vector<pair<int,int>> range;
    inline void build() {
        for (int i = length - 1; i >= 0; --i) node[i] = Monoid::func_fold(node[(i<<1)+0],node[(i<<1)+1]);
        range.resize(2 * length);
        for (int i = 0; i < length; ++i) range[i+length] = make_pair(i,i+1);
        for (int i = length - 1; i >= 0; --i) range[i] = make_pair(range[(i<<1)+0].first,range[(i<<1)+1].second);
    }
public:

    //unitで初期化
    SegmentTree(const size_t num): num(num) {
        for (length = 1; length <= num; length *= 2);
        node.resize(2 * length, Monoid::unit_node);
        build();
    }

    //vectorで初期化
    SegmentTree(const vector<TypeNode> & vec) : num(vec.size()) {
        for (length = 1; length <= vec.size(); length *= 2);
        node.resize(2 * length, Monoid::unit_node);
        for (int i = 0; i < vec.size(); ++i) node[i + length] = vec[i];
        build();
    }

    //同じinitで初期化
    SegmentTree(const size_t num, const TypeNode init) : num(num) {
        for (length = 1; length <= num; length *= 2);
        node.resize(2 * length, Monoid::unit_node);
        for (int i = 0; i < length; ++i) node[i+length] = init;
        build();
    }

    //[idx,idx+1)
    void operate(size_t idx, const TypeNode var) {
        if(idx < 0 || length <= idx) return;
        idx += length;
        node[idx] = Monoid::func_operate(node[idx],var);
        while(idx >>= 1) node[idx] = Monoid::func_fold(node[(idx<<1)+0],node[(idx<<1)+1]);
    }

    //[l,r)
    TypeNode fold(int l, int r) {
        if (l < 0 || length <= l || r < 0 || length < r) return Monoid::unit_node;
        TypeNode vl = Monoid::unit_node, vr = Monoid::unit_node;
        for(l += length, r += length; l < r; l >>=1, r >>=1) {
            if(l&1) vl = Monoid::func_fold(vl,node[l++]);
            if(r&1) vr = Monoid::func_fold(node[--r],vr);
        }
        return Monoid::func_fold(vl,vr);
    }

    //range[l,r) return [l,r] search max right
    int prefix_binary_search(int l, int r, TypeNode var) {
        assert(0 <= l && l < length && 0 < r && r <= length);
        TypeNode ret = Monoid::unit_node;
        size_t off = l;
        for(size_t idx = l+length; idx < 2*length && off < r; ){
            if(range[idx].second<=r && !Monoid::func_check(Monoid::func_fold(ret,node[idx]),var)) {
                ret = Monoid::func_fold(ret,node[idx]);
                off = range[idx++].second;
                if(!(idx&1)) idx >>= 1;
            }
            else{
                idx <<=1;
            }
        }
        return off;
    }

    //range(l,r] return [l,r] search max left
    int suffix_binary_search(const int l, const int r, const TypeNode var) {
        assert(-1 <= l && l < (int)length-1 && 0 <= r && r < length);
        TypeNode ret = Monoid::unit_node;
        int off = r;
        for(size_t idx = r+length; idx < 2*length && l < off; ){
            if(l < range[idx].first && !Monoid::func_check(Monoid::func_fold(node[idx],ret),var)) {
                ret = Monoid::func_fold(node[idx],ret);
                off = range[idx--].first-1;
                if(idx&1) idx >>= 1;
            }
            else{
                idx = (idx<<1)+1;
            }
        }
        return off;
    }

    void print(){
        // cout << "node" << endl;
        // for(int i = 1,j = 1; i < 2*length; ++i) {
        // 	cout << node[i] << " ";
        // 	if(i==((1<<j)-1) && ++j) cout << endl;
        // }
        cout << "vector" << endl;
        cout << "{ " << fold(0,1);
        for(int i = 1; i < length; ++i) cout << ", " << fold(i,i+1);
        cout << " }" << endl;
    }
};
#line 1 "lib/99-operator/monoid/MonoidRangeCompositePointUpdate.cpp"
/*
 * @title MonoidRangeCompositePointUpdate - [区間一次関数, 点更新]
 * @docs md/operator/monoid/MonoidRangeCompositePointUpdate.md
 */
template<class T> struct MonoidRangeCompositePointUpdate {
    using TypeNode = T;
    inline static constexpr TypeNode unit_node = make_pair(1,0);
    inline static constexpr TypeNode func_fold(TypeNode l,TypeNode r){return {r.first*l.first,r.first*l.second+r.second};}
    inline static constexpr TypeNode func_operate(TypeNode l,TypeNode r){return r;}
    inline static constexpr bool func_check(TypeNode nodeVal,TypeNode var){return var == nodeVal;}
};
#line 17 "test/graph/Tree-hld-vertex-3.test.cpp"

//一次関数
template<class T> struct MonoidRangeRevCompositePointUpdate {
    using TypeNode = T;
    inline static constexpr TypeNode unit_node = make_pair(1,0);
    inline static constexpr TypeNode func_fold(TypeNode l,TypeNode r){return {l.first*r.first,l.first*r.second+l.second};}
    inline static constexpr TypeNode func_operate(TypeNode l,TypeNode r){return r;}
    inline static constexpr bool func_check(TypeNode nodeVal,TypeNode var){return var == nodeVal;}
};

using modint = ModInt<998244353>;
int main(void){
    cin.tie(0);ios::sync_with_stdio(false);
    int N,Q;
    cin >> N >> Q;
    SegmentTree<MonoidRangeCompositePointUpdate<pair<modint,modint>>> segLtoR(N,{1,0});
    SegmentTree<MonoidRangeRevCompositePointUpdate<pair<modint,modint>>> segRtoL(N,{1,0});
    vector<int> A(N),B(N);
    for(int i=0;i<N;++i) cin >> A[i] >> B[i];
    Graph<int> g(N);
    for(int i=0;i+1<N;++i) {
        int u,v; cin >> u >> v;
        g.make_bidirectional_edge(u,v,1);
    }
    auto tree = StaticTree<StaticTreeOperator<int>>::builder(g).root(0).parent().child().subtree_size().heavy_light_decomposition().build();
    for(int i=0;i<N;++i) {
        int j = tree.hld[i];
        segLtoR.operate(j,{A[i],B[i]});
        segRtoL.operate(j,{A[i],B[i]});
    }
    while(Q--) {
        int q; cin >> q;
        if(q==0) {
            int i,a,b; cin >> i >> a >> b;
            int j = tree.hld[i];
            segLtoR.operate(j,{a,b});
            segRtoL.operate(j,{a,b});
        }
        else {
            int l,r,x; cin >> l >> r >> x;
            auto tp = tree.vertex_ordered_set_on_path(l,r);

            pair<modint,modint> line = {1,0};
            for(auto& p:tp.first) {
                auto tmp = segRtoL.fold(p.first,p.second+1);
                line = {tmp.first*line.first,tmp.first*line.second+tmp.second};
            }
            for(auto& p:tp.second) {
                auto tmp = segLtoR.fold(p.first,p.second+1);
                line = {tmp.first*line.first,tmp.first*line.second+tmp.second};
            }
            cout << line.first*x+line.second << "\n";
        }
    }
    return 0; 
}
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