noya2_Library

This documentation is automatically generated by online-judge-tools/verification-helper

View the Project on GitHub noya2ruler/noya2_Library

:heavy_check_mark: test/tree/VertexSetPathComposite.test.cpp

Depends on

Code

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

#include"../../template/template.hpp"
#include"../../tree/heavy_light_decomposition.hpp"
#include"../../utility/modint.hpp"
#include"../../data_structure/segment_tree.hpp"

using mint = modint998244353;
using ar = array<mint,3>;

ar op(ar a, ar b){
    return {a[0] * b[0], b[0] * a[1] + b[1], a[0] * b[2] + a[2]};
}
ar e(){
    return {1, 0, 0};
}
ar flip(ar a){
    std::swap(a[1],a[2]);
    return a;
}

int main(){
    int n, q; cin >> n >> q;
    std::vector<std::pair<int, int>> ab(n);
    for (int i = 0; i < n; i++){
        cin >> ab[i].first >> ab[i].second;
    }
    hld_tree g(n);
    g.input_edges<0>();
    segtree<ar,op,e> seg([&]{
        std::vector<ar> a(n);
        for (int u = 0; u < n; u++){
            a[g.index(u)] = {ab[u].first, ab[u].second, ab[u].second};
        }
        return a;
    }());
    while (q--){
        int t; cin >> t;
        if (t == 0){
            int p, c, d; cin >> p >> c >> d;
            seg.set(g.index(p), {c, d, d});
        }
        if (t == 1){
            int u, v, x; cin >> u >> v >> x;
            ar sml = e(), smr = e();
            g.path_query(u, v, [&](int l, int r){
                if (l < r){
                    smr = op(seg.prod(l, r), smr);
                }
                else {
                    sml = op(sml, flip(seg.prod(r, l)));
                }
            });
            auto [a, b, revb] = op(sml, smr);
            mint ans = a * x + b;
            cout << ans.val() << '\n';
        }
    }
}
#line 1 "test/tree/VertexSetPathComposite.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/vertex_set_path_composite"

#line 2 "template/template.hpp"
using namespace std;

#include<bits/stdc++.h>
#line 1 "template/inout_old.hpp"
namespace noya2 {

template <typename T, typename U>
ostream &operator<<(ostream &os, const pair<T, U> &p){
    os << p.first << " " << p.second;
    return os;
}
template <typename T, typename U>
istream &operator>>(istream &is, pair<T, U> &p){
    is >> p.first >> p.second;
    return is;
}

template <typename T>
ostream &operator<<(ostream &os, const vector<T> &v){
    int s = (int)v.size();
    for (int i = 0; i < s; i++) os << (i ? " " : "") << v[i];
    return os;
}
template <typename T>
istream &operator>>(istream &is, vector<T> &v){
    for (auto &x : v) is >> x;
    return is;
}

void in() {}
template <typename T, class... U>
void in(T &t, U &...u){
    cin >> t;
    in(u...);
}

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<typename T>
void out(const vector<vector<T>> &vv){
    int s = (int)vv.size();
    for (int i = 0; i < s; i++) out(vv[i]);
}

struct IoSetup {
    IoSetup(){
        cin.tie(nullptr);
        ios::sync_with_stdio(false);
        cout << fixed << setprecision(15);
        cerr << fixed << setprecision(7);
    }
} iosetup_noya2;

} // namespace noya2
#line 1 "template/const.hpp"
namespace noya2{

const int iinf = 1'000'000'007;
const long long linf = 2'000'000'000'000'000'000LL;
const long long mod998 =  998244353;
const long long mod107 = 1000000007;
const long double pi = 3.14159265358979323;
const vector<int> dx = {0,1,0,-1,1,1,-1,-1};
const vector<int> dy = {1,0,-1,0,1,-1,-1,1};
const string ALP = "ABCDEFGHIJKLMNOPQRSTUVWXYZ";
const string alp = "abcdefghijklmnopqrstuvwxyz";
const string NUM = "0123456789";

void yes(){ cout << "Yes\n"; }
void no(){ cout << "No\n"; }
void YES(){ cout << "YES\n"; }
void NO(){ cout << "NO\n"; }
void yn(bool t){ t ? yes() : no(); }
void YN(bool t){ t ? YES() : NO(); }

} // namespace noya2
#line 2 "template/utils.hpp"

#line 6 "template/utils.hpp"

namespace noya2{

unsigned long long inner_binary_gcd(unsigned long long a, unsigned long long b){
    if (a == 0 || b == 0) return a + b;
    int n = __builtin_ctzll(a); a >>= n;
    int m = __builtin_ctzll(b); b >>= m;
    while (a != b) {
        int mm = __builtin_ctzll(a - b);
        bool f = a > b;
        unsigned long long c = f ? a : b;
        b = f ? b : a;
        a = (c - b) >> mm;
    }
    return a << std::min(n, m);
}

template<typename T> T gcd_fast(T a, T b){ return static_cast<T>(inner_binary_gcd(std::abs(a),std::abs(b))); }

long long sqrt_fast(long long n) {
    if (n <= 0) return 0;
    long long x = sqrt(n);
    while ((x + 1) * (x + 1) <= n) x++;
    while (x * x > n) x--;
    return x;
}

template<typename T> T floor_div(const T n, const T d) {
    assert(d != 0);
    return n / d - static_cast<T>((n ^ d) < 0 && n % d != 0);
}

template<typename T> T ceil_div(const T n, const T d) {
    assert(d != 0);
    return n / d + static_cast<T>((n ^ d) >= 0 && n % d != 0);
}

template<typename T> void uniq(std::vector<T> &v){
    std::sort(v.begin(),v.end());
    v.erase(unique(v.begin(),v.end()),v.end());
}

template <typename T, typename U> inline bool chmin(T &x, U y) { return (y < x) ? (x = y, true) : false; }

template <typename T, typename U> inline bool chmax(T &x, U y) { return (x < y) ? (x = y, true) : false; }

template<typename T> inline bool range(T l, T x, T r){ return l <= x && x < r; }

} // namespace noya2
#line 8 "template/template.hpp"

#define rep(i,n) for (int i = 0; i < (int)(n); i++)
#define repp(i,m,n) for (int i = (m); i < (int)(n); i++)
#define reb(i,n) for (int i = (int)(n-1); i >= 0; i--)
#define all(v) (v).begin(),(v).end()

using ll = long long;
using ld = long double;
using uint = unsigned int;
using ull = unsigned long long;
using pii = pair<int,int>;
using pll = pair<ll,ll>;
using pil = pair<int,ll>;
using pli = pair<ll,int>;

namespace noya2{

/*　~ (. _________ . /)　*/

}

using namespace noya2;


#line 2 "tree/heavy_light_decomposition.hpp"

#line 6 "tree/heavy_light_decomposition.hpp"
#include <ranges>
#line 9 "tree/heavy_light_decomposition.hpp"

// #include "data_structure/csr.hpp"

namespace noya2 {

struct hld_tree {
    int n, root;
    std::vector<int> down, nxt, sub, tour;
	// noya2::internal::csr<int> childs;

    // default constructor (nop)
    hld_tree () {}

    // tree with _n node
    // after construct, call input_edges / input_parents / add_edge _n - 1 times
    hld_tree (int _n, int _root = 0) : n(_n), root(_root), down(n), nxt(n), sub(n, 1), tour(n) {
        if (n == 1){
            nxt[0] = -1;
            down[0] = -1;
            build_from_parents();
        }
    }

    // par[i] < i, par[0] == -1
    hld_tree (const std::vector<int> &par) : n(par.size()), root(0), down(n, -1), nxt(par), sub(n, 1), tour(n){
        build_from_parents();
    }

    // par[i] < i, par[0] == -1
    hld_tree (std::vector<int> &&par) : n(par.size()), root(0), down(n, -1), sub(n, 1), tour(n) {
        nxt.swap(par);
        build_from_parents();
    }

    // distinct unweighted undirected n - 1 edges of tree 
    hld_tree (const std::vector<std::pair<int, int>> &es, int _root = 0) : n(es.size() + 1), root(_root), down(n), nxt(n), sub(n, 1), tour(n) {
        for (auto &[u, v] : es){
            down[u]++;
            down[v]++;
            nxt[u] ^= v;
            nxt[v] ^= u;
        }
        build_from_edges();
    }

    // input parents from cin
    template<int indexed = 1>
    void input_parents(){
        // using std::cin;
        nxt[0] = -1;
        for (int u = 1; u < n; u++){
            cin >> nxt[u];
            nxt[u] -= indexed;
        }
        build_from_parents();
    }

    // input n - 1 edges from cin
    template<int indexed = 1>
    void input_edges(){
        // using std::cin;
        for (int i = 1; i < n; i++){
            int u, v; cin >> u >> v;
            u -= indexed;
            v -= indexed;
            down[u]++;
            down[v]++;
            nxt[u] ^= v;
            nxt[v] ^= u;
        }
        build_from_edges();
    }

    void add_edge(int u, int v){
        down[u]++;
        down[v]++;
        nxt[u] ^= v;
        nxt[v] ^= u;
        // use tour[0] as counter
        if (++tour[0] == n - 1){
            build_from_edges();
        }
    }

    size_t size() const {
        return n;
    }

    // top vertex of heavy path which contains v
    int leader(int v) const {
        return nxt[v] < 0 ? v : nxt[v];
    }

    // level ancestor
    // ret is ancestor of v, dist(ret, v) == d
    // if d > depth(v), return -1
    int la(int v, int d) const {
        while (v != -1){
            int u = leader(v);
            if (down[v] - d >= down[u]){
                v = tour[down[v] - d];
                break;
            }
            d -= down[v] - down[u] + 1;
            v = (u == root ? -1 : ~nxt[u]);
        }
        return v;
    }

    // lowest common ancestor of u and v
    int lca(int u, int v) const {
        int du = down[u], dv = down[v];
        if (du > dv){
            std::swap(du, dv);
            std::swap(u, v);
        }
        if (dv < du + sub[u]){
            return u;
        }
        while (du < dv){
            v = ~nxt[leader(v)];
            dv = down[v];
        }
        return v;
    }

    // distance from u to v
    int dist(int u, int v) const {
        int _dist = 0;
        while (leader(u) != leader(v)){
            if (down[u] > down[v]) std::swap(u, v);
            _dist += down[v] - down[leader(v)] + 1;
            v = ~nxt[leader(v)];
        }
        _dist += std::abs(down[u] - down[v]);
        return _dist;
    }

    // d times move from to its neighbor (direction of to)
    // if d > dist(from, to), return -1
    int jump(int from, int to, int d) const {
        int _from = from, _to = to;
        int dist_from_lca = 0, dist_to_lca = 0;
        while (leader(_from) != leader(_to)){
            if (down[_from] > down[_to]){
                dist_from_lca += down[_from] - down[leader(_from)] + 1;
                _from = ~nxt[leader(_from)];
            }
            else {
                dist_to_lca += down[_to] - down[leader(_to)] + 1;
                _to = ~nxt[leader(_to)];
            }
        }
        if (down[_from] > down[_to]){
            dist_from_lca += down[_from] - down[_to];
        }
        else {
            dist_to_lca += down[_to] - down[_from];
        }
        if (d <= dist_from_lca){
            return la(from, d);
        }
        d -= dist_from_lca;
        if (d <= dist_to_lca){
            return la(to, dist_to_lca - d);
        }
        return -1;
    }

    // parent of v (if v is root, return -1)
    int parent(int v) const {
        if (v == root) return -1;
        return (nxt[v] < 0 ? ~nxt[v] : tour[down[v] - 1]);
    }

    // visiting time in euler tour
    // usage : seg.set(index(v), X[v])
    int index(int vertex) const {
        return down[vertex];
    }
    // usage : seg.set(index_edge(e.u, e.v), e.val)
    int index(int vertex1, int vertex2) const {
        return std::max(down[vertex1], down[vertex2]);
    }

    // subtree size of v
    int subtree_size(int v) const {
        return sub[v];
    }

    // prod in subtree v : seg.prod(subtree_l(v), subtree_r(v))
    int subtree_l(int v) const {
        return down[v];
    }
    int subtree_r(int v) const {
        return down[v] + sub[v];
    }

    // v is in subtree r
    bool is_in_subtree(int r, int v) const {
        return subtree_l(r) <= subtree_l(v) && subtree_r(v) <= subtree_r(r);
    }
    
    // distance table from s
    std::vector<int> dist_table(int s) const {
        std::vector<int> table(n, -1);
        table[s] = 0;
        while (s != root){
            table[parent(s)] = table[s] + 1;
            s = parent(s);
        }
        for (int v : tour){
            if (table[v] == -1){
                table[v] = table[parent(v)] + 1;
            }
        }
        return table;
    }

    // dist, v1, v2
    std::tuple<int, int, int> diameter() const {
        std::vector<int> dep = dist_table(root);
        int v1 = std::ranges::max_element(dep) - dep.begin();
        std::vector<int> fromv1 = dist_table(v1);
        int v2 = std::ranges::max_element(fromv1) - fromv1.begin();
        return {fromv1[v2], v1, v2};
    }

    // vertex array {from, ..., to}
    std::vector<int> path(int from, int to) const {
        int d = dist(from, to);
        std::vector<int> _path(d + 1);
        int front = 0, back = d;
        while (from != to){
            if (down[from] > down[to]){
                _path[front++] = from;
                from = parent(from);
            }
            else {
                _path[back--] = to;
                to = parent(to);
            }
        }
        _path[front] = from;
        return _path;
    }

    // path decomposition and query (vertex weighted)
    // if l < r, decsending order tour[l, r)
    // if l > r, acsending order tour(l, r]
    template<bool vertex = true>
    void path_query(int u, int v, auto f) const {
        while (leader(u) != leader(v)){
            if (down[u] < down[v]){
                f(down[leader(v)], down[v] + 1);
                v = ~nxt[leader(v)];
            }
            else {
                f(down[u] + 1, down[leader(u)]);
                u = ~nxt[leader(u)];
            }
        }
        if constexpr (vertex){
            if (down[u] < down[v]){
                f(down[u], down[v] + 1);
            }
            else {
                f(down[u] + 1, down[v]);
            }
        }
        else {
            if (down[u] != down[v]){
                f(down[u] + 1, down[v] + 1);
            }
        }
    }

    // {parent, mapping} : cptree i is correspond to tree mapping[i]. parent[i] is parent of i in cptree.
    // parent[i] < i, parent[0] == -1
	std::pair<std::vector<int>, std::vector<int>> compressed_tree(std::vector<int> vs) const {
        if (vs.empty()){
            return {{},{}};
        }
        auto comp = [&](int l, int r){
            return down[l] < down[r];
        };
		std::ranges::sort(vs, comp);
		int sz = vs.size(); vs.reserve(2*sz);
        for (int i = 0; i < sz-1; i++){
            vs.emplace_back(lca(vs[i], vs[i+1]));
        }
        std::sort(vs.begin() + sz, vs.end(), comp);
        std::ranges::inplace_merge(vs, vs.begin() + sz, comp);
        auto del = std::ranges::unique(vs);
        vs.erase(del.begin(), del.end());
        sz = vs.size();
        std::stack<int> st;
        std::vector<int> par(sz);
        par[0] = -1;
        st.push(0);
        for (int i = 1; i < sz; i++){
            while (!is_in_subtree(vs[st.top()], vs[i])) st.pop();
            par[i] = st.top();
            st.push(i);
        }
        return {par, vs};
	}

/*  CSR

	// build csr for using operator()
	void build_csr(){
		childs = noya2::internal::csr<int>(n, n - 1);
		for (int v = 0; v < n; v++){
			if (v == root) continue;
			childs.add(parent(v), v);
		}
		childs.build();
	}
	const auto operator()(int v) const {
		return childs[v];
	}
	auto operator()(int v){
		return childs[v];
	}
*/

    // hld_tree g;
    // euler tour order : `for (int v : g)`
    // with range_adaptor : `for (int v : g | std::views::reverse)`
    // bottom-up DP : `for (int v : g | std::views::drop(1) | std::views::reverse){ update dp[g.parent(v)] by dp[v] }`
    auto begin() const {
        return tour.begin();
    }
    auto end() const {
        return tour.end();
    }

  private:
    // nxt[v] : parent of v, nxt[0] == -1
    void build_from_parents(){
        for (int u = n - 1; u >= 1; u--){
            int v = nxt[u];
            sub[v] += sub[u];
            down[v] = std::max(down[v], sub[u]);
        }
        for (int u = n - 1; u >= 1; u--){
            int v = nxt[u];
            if (down[v] == sub[u]){
                sub[u] = ~sub[u];
                down[v] = ~down[v];
            }
        }

        sub[0] = ~down[0] + 1;
        down[0] = 0;
        for (int u = 1; u < n; u++){
            int v = nxt[u];
            int nsub = ~down[u] + 1;
            if (sub[u] < 0){
                down[u] = down[v] + 1;
                nxt[u] = (nxt[v] < 0 ? v : nxt[v]);
            }
            else {
                down[u] = down[v] + sub[v];
                sub[v] += sub[u];
                nxt[u] = ~v;
            }
            sub[u] = nsub;
        }

        for (int u = 0; u < n; u++){
            tour[down[u]] = u;
        }
    }

    // down[v] : degree of v
    // nxt[v] : xor prod of neighbor of v
    void build_from_edges(){
        // use tour as queue
        int back = 0;
        for (int u = 0; u < n; u++){
            if (u != root && down[u] == 1){
                tour[back++] = u;
            }
        }
        for (int front = 0; front < n - 1; front++){
            int u = tour[front];
            down[u] = -1;
            int v = nxt[u]; // parent of v
            nxt[v] ^= u;
            if (--down[v] == 1 && v != root){
                tour[back++] = v;
            }
        }
        // check : now, tour is reverse of topological order

        tour.pop_back();

        // check : now, down[*] <= 1
        for (int u : tour){
            int v = nxt[u];
            // subtree size (initialized (1,1,...,1))
            sub[v] += sub[u];
            // heaviest subtree of its child
            down[v] = std::max(down[v], sub[u]);
        }
        for (int u : tour){
            int v = nxt[u];
            // whether u is not the top of heavy path
            if (down[v] == sub[u]){
                sub[u] = ~sub[u];
                down[v] = ~down[v];
            }
        }

        // after appearing v as u (or v == root), 
        // down[v] is the visiting time of euler tour
        // nxt[v] is the lowest vertex of heavy path which contains v
        //   (if v itself, nxt[v] is ~(parent of v))
        // sub[v] + down[v] is the light child's starting time of euler tour
        // note : heavy child's visiting time of euler tour is (the time of its parent) + 1
        sub[root] = ~down[root] + 1;
        down[root] = 0;
        nxt[root] = -1;
        for (int u : tour | std::views::reverse){
            int v = nxt[u];
            int nsub = ~down[u] + 1;
            // heavy child
            if (sub[u] < 0){
                down[u] = down[v] + 1;
                nxt[u] = (nxt[v] < 0 ? v : nxt[v]);
            }
            // light child
            else {
                down[u] = down[v] + sub[v];
                sub[v] += sub[u];
                nxt[u] = ~v;
            }
            sub[u] = nsub;
        }

        // tour is inverse permutation of down
        tour.push_back(0);
        for (int u = 0; u < n; u++){
            tour[down[u]] = u;
        }
    }
};

} // namespace noya2
#line 2 "utility/modint.hpp"

#line 4 "utility/modint.hpp"

#line 2 "math/prime.hpp"

#line 4 "math/prime.hpp"
namespace noya2 {

constexpr long long safe_mod(long long x, long long m) {
    x %= m;
    if (x < 0) x += m;
    return x;
}

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 = safe_mod(x, 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_flag = is_prime_constexpr(n);

constexpr std::pair<long long, long long> inv_gcd(long long a, long long b) {
    a = safe_mod(a, b);
    if (a == 0) return {b, 0};
    long long s = b, t = a;
    long long m0 = 0, m1 = 1;
    while (t) {
        long long u = s / t;
        s -= t * u;
        m0 -= m1 * u; 
        auto tmp = s;
        s = t;
        t = tmp;
        tmp = m0;
        m0 = m1;
        m1 = tmp;
    }
    if (m0 < 0) m0 += b / s;
    return {s, m0};
}

constexpr int primitive_root_constexpr(int m) {
    if (m == 2) return 1;
    if (m == 167772161) return 3;
    if (m == 469762049) return 3;
    if (m == 754974721) return 11;
    if (m == 998244353) return 3;
    int divs[20] = {};
    divs[0] = 2;
    int cnt = 1;
    int x = (m - 1) / 2;
    while (x % 2 == 0) x /= 2;
    for (int i = 3; (long long)(i)*i <= x; i += 2) {
        if (x % i == 0) {
            divs[cnt++] = i;
            while (x % i == 0) {
                x /= i;
            }
        }
    }
    if (x > 1) {
        divs[cnt++] = x;
    }
    for (int g = 2;; g++) {
        bool ok = true;
        for (int i = 0; i < cnt; i++) {
            if (pow_mod_constexpr(g, (m - 1) / divs[i], m) == 1) {
                ok = false;
                break;
            }
        }
        if (ok) return g;
    }
}
template <int m> constexpr int primitive_root_flag = primitive_root_constexpr(m);

} // namespace noya2
#line 6 "utility/modint.hpp"

namespace noya2{

struct barrett {
    unsigned int _m;
    unsigned long long im;
    explicit barrett(unsigned int m) : _m(m), im((unsigned long long)(-1) / m + 1) {}
    unsigned int umod() const { return _m; }
    unsigned int mul(unsigned int a, unsigned int b) const {
        unsigned long long z = a;
        z *= b;
        unsigned long long x = (unsigned long long)((__uint128_t(z) * im) >> 64);
        unsigned int v = (unsigned int)(z - x * _m);
        if (_m <= v) v += _m;
        return v;
    }
};

template <int m>
struct static_modint {
    using mint = static_modint;
  public:
    static constexpr int mod() { return m; }
    static mint raw(int v) {
        mint x;
        x._v = v;
        return x;
    }
    constexpr static_modint() : _v(0) {}
    template<std::signed_integral T>
    constexpr static_modint(T v){
        long long x = (long long)(v % (long long)(umod()));
        if (x < 0) x += umod();
        _v = (unsigned int)(x);
    }
    template<std::unsigned_integral T>
    constexpr static_modint(T v){
        _v = (unsigned int)(v % umod());
    }
    constexpr 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;
    }
    constexpr mint& operator+=(const mint& rhs) {
        _v += rhs._v;
        if (_v >= umod()) _v -= umod();
        return *this;
    }
    constexpr mint& operator-=(const mint& rhs) {
        _v -= rhs._v;
        if (_v >= umod()) _v += umod();
        return *this;
    }
    constexpr mint& operator*=(const mint& rhs) {
        unsigned long long z = _v;
        z *= rhs._v;
        _v = (uint)(z % umod());
        return *this;
    }
    constexpr mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); }
    constexpr mint operator+() const { return *this; }
    constexpr mint operator-() const { return mint() - *this; }
    constexpr 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;
    }
    constexpr mint inv() const {
        if (prime) {
            assert(_v);
            return pow(umod() - 2);
        } else {
            auto eg = inv_gcd(_v, m);
            assert(eg.first == 1);
            return eg.second;
        }
    }
    friend constexpr mint operator+(const mint& lhs, const mint& rhs) {
        return mint(lhs) += rhs;
    }
    friend constexpr mint operator-(const mint& lhs, const mint& rhs) {
        return mint(lhs) -= rhs;
    }
    friend constexpr mint operator*(const mint& lhs, const mint& rhs) {
        return mint(lhs) *= rhs;
    }
    friend constexpr mint operator/(const mint& lhs, const mint& rhs) {
        return mint(lhs) /= rhs;
    }
    friend constexpr bool operator==(const mint& lhs, const mint& rhs) {
        return lhs._v == rhs._v;
    }
    friend constexpr bool operator!=(const mint& lhs, const mint& rhs) {
        return lhs._v != rhs._v;
    }
    friend std::ostream &operator<<(std::ostream &os, const mint& p) {
        return os << p.val();
    }
    friend std::istream &operator>>(std::istream &is, mint &a) {
        long long t; is >> t;
        a = mint(t);
        return (is);
    }

  private:
    unsigned int _v;
    static constexpr unsigned int umod() { return m; }
    static constexpr bool prime = is_prime_flag<m>;
};


template <int id> struct dynamic_modint {
    using mint = dynamic_modint;
  public:
    static int mod() { return (int)(bt.umod()); }
    static void set_mod(int m) {
        assert(1 <= m);
        bt = barrett(m);
    }
    static mint raw(int v) {
        mint x;
        x._v = v;
        return x;
    }

    dynamic_modint() : _v(0) {}
    template<std::signed_integral T>
    dynamic_modint(T v){
        long long x = (long long)(v % (long long)(umod()));
        if (x < 0) x += umod();
        _v = (unsigned int)(x);
    }
    template<std::unsigned_integral T>
    dynamic_modint(T v){
        _v = (unsigned int)(v % umod());
    }
    uint 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 += mod() - rhs._v;
        if (_v >= umod()) _v -= umod();
        return *this;
    }
    mint& operator*=(const mint& rhs) {
        _v = bt.mul(_v, rhs._v);
        return *this;
    }
    mint& operator/=(const mint& rhs) { return *this = *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 {
        auto eg = noya2::inv_gcd(_v, mod());
        assert(eg.first == 1);
        return eg.second;
    }
    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 std::ostream &operator<<(std::ostream &os, const mint& p) {
        return os << p.val();
    }
    friend std::istream &operator>>(std::istream &is, mint &a) {
        long long t; is >> t;
        a = mint(t);
        return (is);
    }

  private:
    unsigned int _v;
    static barrett bt;
    static unsigned int umod() { return bt.umod(); }
};
template <int id> noya2::barrett dynamic_modint<id>::bt(998244353);

using modint998244353 = static_modint<998244353>;
using modint1000000007 = static_modint<1000000007>;
using modint = dynamic_modint<-1>;

template<typename T>
concept Modint = requires (T &a){
    T::mod();
    a.inv();
    a.val();
    a.pow(declval<int>());
};

} // namespace noya2
#line 2 "data_structure/segment_tree.hpp"

namespace noya2{

template <class S, S (*op)(S, S), S (*e)()> struct segtree {
  public:
    segtree() : segtree(0) {}
    segtree(int n) : segtree(std::vector<S>(n, e())) {}
    segtree(const std::vector<S>& v) : _n(int(v.size())) {
        log = 0;
        size = 1;
        while (size < _n) size <<= 1, log++;

        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);
    }

    S all_prod() { return d[1]; }

    template <bool (*f)(S)> int max_right(int l) {
        return max_right(l, [](S x) { return f(x); });
    }
    template <class F> int max_right(int l, F f) {
        assert(0 <= l && l <= _n);
        assert(f(e()));
        if (l == _n) return _n;
        l += size;
        S sm = e();
        do {
            while (l % 2 == 0) l >>= 1;
            if (!f(op(sm, d[l]))) {
                while (l < size) {
                    l = (2 * l);
                    if (f(op(sm, d[l]))) {
                        sm = op(sm, d[l]);
                        l++;
                    }
                }
                return l - size;
            }
            sm = op(sm, d[l]);
            l++;
        } while ((l & -l) != l);
        return _n;
    }

    template <bool (*f)(S)> int min_left(int r) {
        return min_left(r, [](S x) { return f(x); });
    }
    template <class F> int min_left(int r, F f) {
        assert(0 <= r && r <= _n);
        assert(f(e()));
        if (r == 0) return 0;
        r += size;
        S sm = e();
        do {
            r--;
            while (r > 1 && (r % 2)) r >>= 1;
            if (!f(op(d[r], sm))) {
                while (r < size) {
                    r = (2 * r + 1);
                    if (f(op(d[r], sm))) {
                        sm = op(d[r], sm);
                        r--;
                    }
                }
                return r + 1 - size;
            }
            sm = op(d[r], sm);
        } while ((r & -r) != r);
        return 0;
    }

  private:
    int _n, size, log;
    std::vector<S> d;

    void update(int k) { d[k] = op(d[2 * k], d[2 * k + 1]); }
};

} // namespace noya2
#line 7 "test/tree/VertexSetPathComposite.test.cpp"

using mint = modint998244353;
using ar = array<mint,3>;

ar op(ar a, ar b){
    return {a[0] * b[0], b[0] * a[1] + b[1], a[0] * b[2] + a[2]};
}
ar e(){
    return {1, 0, 0};
}
ar flip(ar a){
    std::swap(a[1],a[2]);
    return a;
}

int main(){
    int n, q; cin >> n >> q;
    std::vector<std::pair<int, int>> ab(n);
    for (int i = 0; i < n; i++){
        cin >> ab[i].first >> ab[i].second;
    }
    hld_tree g(n);
    g.input_edges<0>();
    segtree<ar,op,e> seg([&]{
        std::vector<ar> a(n);
        for (int u = 0; u < n; u++){
            a[g.index(u)] = {ab[u].first, ab[u].second, ab[u].second};
        }
        return a;
    }());
    while (q--){
        int t; cin >> t;
        if (t == 0){
            int p, c, d; cin >> p >> c >> d;
            seg.set(g.index(p), {c, d, d});
        }
        if (t == 1){
            int u, v, x; cin >> u >> v >> x;
            ar sml = e(), smr = e();
            g.path_query(u, v, [&](int l, int r){
                if (l < r){
                    smr = op(seg.prod(l, r), smr);
                }
                else {
                    sml = op(sml, flip(seg.prod(r, l)));
                }
            });
            auto [a, b, revb] = op(sml, smr);
            mint ans = a * x + b;
            cout << ans.val() << '\n';
        }
    }
}
Back to top page