結果
| 問題 | No.2588 Increasing Record |
| ユーザー |
 noya2
|
| 提出日時 | 2024-12-24 02:26:42 |
| 言語 | C++23 (gcc 12.3.0 + boost 1.83.0) |
| 結果 |
AC
|
| 実行時間 | 193 ms / 3,000 ms |
| コード長 | 50,964 bytes |
| コンパイル時間 | 7,499 ms |
| コンパイル使用メモリ | 337,300 KB |
| 実行使用メモリ | 19,740 KB |
| 最終ジャッジ日時 | 2024-12-24 02:27:00 |
| 合計ジャッジ時間 | 15,252 ms |
|
ジャッジサーバーID （参考情報） |
judge1 / judge4 |
（要ログイン）
テストケース
テストケース表示| 入力 | 結果 | 実行時間 実行使用メモリ |
|---|---|---|
| testcase_00 | AC | 2 ms
5,248 KB |
| testcase_01 | AC | 3 ms
5,248 KB |
| testcase_02 | AC | 3 ms
5,248 KB |
| testcase_03 | AC | 2 ms
5,248 KB |
| testcase_04 | AC | 2 ms
5,248 KB |
| testcase_05 | AC | 2 ms
5,248 KB |
| testcase_06 | AC | 2 ms
5,248 KB |
| testcase_07 | AC | 2 ms
5,248 KB |
| testcase_08 | AC | 3 ms
5,248 KB |
| testcase_09 | AC | 3 ms
5,248 KB |
| testcase_10 | AC | 3 ms
5,248 KB |
| testcase_11 | AC | 2 ms
5,248 KB |
| testcase_12 | AC | 69 ms
5,248 KB |
| testcase_13 | AC | 59 ms
5,248 KB |
| testcase_14 | AC | 51 ms
5,248 KB |
| testcase_15 | AC | 60 ms
5,248 KB |
| testcase_16 | AC | 91 ms
7,808 KB |
| testcase_17 | AC | 148 ms
10,752 KB |
| testcase_18 | AC | 141 ms
14,120 KB |
| testcase_19 | AC | 168 ms
16,728 KB |
| testcase_20 | AC | 158 ms
17,280 KB |
| testcase_21 | AC | 183 ms
17,384 KB |
| testcase_22 | AC | 158 ms
17,324 KB |
| testcase_23 | AC | 153 ms
17,408 KB |
| testcase_24 | AC | 193 ms
17,408 KB |
| testcase_25 | AC | 116 ms
10,752 KB |
| testcase_26 | AC | 129 ms
13,824 KB |
| testcase_27 | AC | 141 ms
16,604 KB |
| testcase_28 | AC | 141 ms
16,512 KB |
| testcase_29 | AC | 142 ms
16,768 KB |
| testcase_30 | AC | 100 ms
11,520 KB |
| testcase_31 | AC | 124 ms
15,528 KB |
| testcase_32 | AC | 152 ms
18,844 KB |
| testcase_33 | AC | 140 ms
19,584 KB |
| testcase_34 | AC | 136 ms
19,684 KB |
| testcase_35 | AC | 141 ms
19,688 KB |
| testcase_36 | AC | 143 ms
19,740 KB |
| testcase_37 | AC | 149 ms
17,408 KB |
| testcase_38 | AC | 118 ms
10,752 KB |
| testcase_39 | AC | 86 ms
14,464 KB |
| testcase_40 | AC | 92 ms
14,864 KB |
| testcase_41 | AC | 111 ms
15,684 KB |
| testcase_42 | AC | 92 ms
16,080 KB |
| testcase_43 | AC | 93 ms
18,112 KB |
| testcase_44 | AC | 103 ms
11,540 KB |
| testcase_45 | AC | 117 ms
13,632 KB |
| testcase_46 | AC | 122 ms
16,000 KB |
ソースコード
#line 2 "/Users/noya2/Desktop/Noya2_library/template/template.hpp"
using namespace std;
#include<bits/stdc++.h>
#line 1 "/Users/noya2/Desktop/Noya2_library/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 "/Users/noya2/Desktop/Noya2_library/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 "/Users/noya2/Desktop/Noya2_library/template/utils.hpp"
#line 6 "/Users/noya2/Desktop/Noya2_library/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 "/Users/noya2/Desktop/Noya2_library/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 "hld_test.cpp"
#line 2 "/Users/noya2/Desktop/Noya2_library/tree/heavy_light_decomposition.hpp"
#line 2 "/Users/noya2/Desktop/Noya2_library/tree/simple_tree.hpp"
#line 2 "/Users/noya2/Desktop/Noya2_library/data_structure/csr.hpp"
#line 4 "/Users/noya2/Desktop/Noya2_library/data_structure/csr.hpp"
#include<ranges>
#line 7 "/Users/noya2/Desktop/Noya2_library/data_structure/csr.hpp"
namespace noya2::internal {
template<class E>
struct csr {
csr () {}
csr (int _n) : n(_n) {}
csr (int _n, int m) : n(_n){
start.reserve(m);
elist.reserve(m);
}
// ACL style constructor (do not have to call build)
csr (int _n, const std::vector<std::pair<int,E>> &idx_elem) : n(_n), start(_n + 2), elist(idx_elem.size()) {
for (auto &[i, e] : idx_elem){
start[i + 2]++;
}
for (int i = 1; i < n; i++){
start[i + 2] += start[i + 1];
}
for (auto &[i, e] : idx_elem){
elist[start[i + 1]++] = e;
}
prepared = true;
}
int add(int idx, E elem){
int eid = start.size();
start.emplace_back(idx);
elist.emplace_back(elem);
return eid;
}
void build(){
if (prepared) return ;
int m = start.size();
std::vector<E> nelist(m);
std::vector<int> nstart(n + 2, 0);
for (int i = 0; i < m; i++){
nstart[start[i] + 2]++;
}
for (int i = 1; i < n; i++){
nstart[i + 2] += nstart[i + 1];
}
for (int i = 0; i < m; i++){
nelist[nstart[start[i] + 1]++] = elist[i];
}
swap(elist,nelist);
swap(start,nstart);
prepared = true;
}
const auto operator[](int idx) const {
return std::ranges::subrange(elist.begin()+start[idx],elist.begin()+start[idx+1]);
}
auto operator[](int idx){
return std::ranges::subrange(elist.begin()+start[idx],elist.begin()+start[idx+1]);
}
const auto operator()(int idx, int l, int r) const {
return std::ranges::subrange(elist.begin()+start[idx]+l,elist.begin()+start[idx]+r);
}
auto operator()(int idx, int l, int r){
return std::ranges::subrange(elist.begin()+start[idx]+l,elist.begin()+start[idx]+r);
}
size_t size() const {
return n;
}
int n;
std::vector<int> start;
std::vector<E> elist;
bool prepared = false;
};
} // namespace noya2::internal
#line 5 "/Users/noya2/Desktop/Noya2_library/tree/simple_tree.hpp"
namespace noya2 {
struct simple_tree {
internal::csr<int> g;
simple_tree () {}
simple_tree (int _n) : g(_n, (_n - 1)*2) {
if (_n == 1){
g.build();
}
}
void add_edge(int u, int v){
g.add(u, v);
int id = g.add(v, u);
if (id + 1 == (g.n - 1)*2) g.build();
}
void input(int indexed = 1){
for (int i = 0; i < g.n - 1; i++){
int u, v; cin >> u >> v;
u -= indexed, v -= indexed;
add_edge(u, v);
}
}
void input_parents(int indexed = 1){
for (int i = 0; i < g.n - 1; i++){
int v; cin >> v;
v -= indexed;
add_edge(i + 1, v);
}
}
const auto operator[](int v) const {
return g[v];
}
auto operator[](int v){
return g[v];
}
size_t size() const {
return g.size();
}
};
} // namespace noya2
#line 5 "/Users/noya2/Desktop/Noya2_library/tree/heavy_light_decomposition.hpp"
namespace noya2 {
using namespace std;
struct hld_tree {
internal::csr<int> g;
hld_tree () {}
hld_tree (int _n, int _root = 0) : g(_n,(_n - 1)*2), n(_n), root(_root) {
if (_n == 1){
build();
}
}
hld_tree (simple_tree _g, int _root = 0) : g(_g.g), n(_g.g.n), root(_root){
build();
}
size_t size() const {
return g.n;
}
int root_v() const {
return root;
}
void add_edge(int u, int v){
g.add(u, v);
int id = g.add(v, u);
if (id + 1 == (n - 1)*2) build();
}
void input(int indexed = 1){
for (int i = 0; i < n - 1; i++){
int u, v; cin >> u >> v;
u -= indexed, v -= indexed;
add_edge(u, v);
}
}
void input_parents(int indexed = 1){
for (int i = 0; i < n - 1; i++){
int v; cin >> v;
v -= indexed;
add_edge(i + 1, v);
}
}
int depth(int v) const {
return dep[v];
}
int parent(int v) const {
if (v == root) return -1;
return g[v].back();
}
int degree(int v) const {
return g[v].size();
}
int subtree_size(int v) const {
return sub[v];
}
// if d > dep[v], return -1
int la(int v, int d) const {
while (v != -1){
int u = nxt[v];
if (down[v] - d >= down[u]){
v = tour[down[v] - d];
break;
}
d -= down[v] - down[u] + 1;
v = parent(u);
}
return v;
}
int lca(int u, int v) const {
while (nxt[u] != nxt[v]){
if (down[u] < down[v]) swap(u,v);
u = parent(nxt[u]);
}
return dep[u] < dep[v] ? u : v;
}
int dist(int u, int v) const {
return dep[u] + dep[v] - 2*dep[lca(u,v)];
}
// if d > dist(from, to), return -1
int jump(int from, int to, int d) const {
int l = lca(from,to);
if (d <= dep[from] - dep[l]){
return la(from, d);
}
d -= dep[from] - dep[l];
if (d <= dep[to] - dep[l]){
return la(to, dep[to] - dep[l] - d);
}
return -1;
}
// seg.set(index(v), X[v]);
int index(int vertex) const {
return down[vertex];
}
int index_from_edge(int u, int v) const {
return (dep[u] < dep[v] ? down[v] : down[u]);
}
// X[vertex(i)] = seg.get(i);
int vertex(int index) const {
return tour[index];
}
int subtree_l(int v) const {
return down[v];
}
int subtree_r(int v) const {
return down[v] + sub[v];
}
// if r == v, return true
bool is_in_subtree(int r, int v) const {
return subtree_l(r) <= subtree_l(v) && subtree_l(v) < subtree_r(r);
}
bool is_in_path(int lv, int mv, int rv) const {
return dist(lv,mv) + dist(mv,rv) == dist(lv,rv);
}
// dist, v1, v2
tuple<int,int,int> diameter(){
int v1 = max_element(dep.begin(),dep.end()) - dep.begin();
vector<int> dist_from_v1(n,numeric_limits<int>::max());
queue<int> que;
que.push(v1);
dist_from_v1[v1] = 0;
while (!que.empty()){
int v = que.front(); que.pop();
for (int u : g[v]){
if (dist_from_v1[u] > dist_from_v1[v]+1){
dist_from_v1[u] = dist_from_v1[v]+1;
que.push(u);
}
}
}
int v2 = max_element(dist_from_v1.begin(),dist_from_v1.end()) - dist_from_v1.begin();
return make_tuple(dist_from_v1[v2],v1,v2);
}
// vertex array : vector<int> {from, v1, v2, ... , to}
vector<int> path(int from, int to){
int l = lca(from,to);
const int sizf = dep[from]-dep[l], sizt = dep[to]-dep[l];
vector<int> pf = {from}, pt;
pf.reserve(sizf+1); pt.reserve(sizt);
for (int i = 0; i < sizf; i++){
from = parent(from);
pf.push_back(from);
}
for (int i = 0; i < sizt; i++){
pt.push_back(to);
to = parent(to);
}
pf.insert(pf.end(),pt.rbegin(),pt.rend());
return pf;
}
template<typename F>
void path_query(int u, int v, bool vertex, const F &f){
int l = lca(u,v);
for (auto [s, t] : ascend(u, l)){
f(t, s + 1);
}
if (vertex) f(down[l], down[l] + 1);
for (auto [s, t] : descend(l, v)){
f(s, t + 1);
}
}
template<typename F>
void path_noncommutative_query(int u, int v, bool vertex, const F &f){
int l = lca(u,v);
for (auto [s, t] : ascend(u, l)){
f(s + 1, t); // l > r ok
}
if (vertex) f(down[l],down[l] + 1);
for (auto [s, t] : descend(l, v)){
f(s, t + 1); // l > r ok
}
}
template<typename F>
void subtree_query(int v, bool vertex, const F &f){
f(down[v] + (vertex ? 0 : 1), down[v] + sub[v]);
}
// adjacent to v
const auto operator[](int v) const {
return g[v];
}
auto operator[](int v){
return g[v];
}
// only child
const auto operator()(int v) const {
return g(v, 0, degree(v) - (v == root ? 0 : 1));
}
auto operator()(int v){
return g(v, 0, degree(v) - (v == root ? 0 : 1));
}
private:
int n, root;
vector<int> dep, sub, down, tour, nxt;
// v is ancestor of u.
// enumerate [closed] intervals of down ( interval [l, r] may hold l > r ).
vector<pair<int,int>> ascend(int u, int v){
vector<pair<int,int>> res;
while (nxt[u] != nxt[v]){
res.emplace_back(down[u], down[nxt[u]]);
u = parent(nxt[u]);
}
if (u != v) res.emplace_back(down[u], down[v]+1);
return res;
}
// u is ancestor of v.
// enumerate [closed] intervals of down ( interval [l, r] may hold l > r ).
vector<pair<int,int>> descend(int u, int v){
if (u == v) return {};
if (nxt[u] == nxt[v]){
return {pair<int,int>(down[u]+1, down[v])};
}
vector<pair<int,int>> res = descend(u, parent(nxt[v]));
res.emplace_back(down[nxt[v]], down[v]);
return res;
}
void build(){
g.build();
init_sz();
init_hld();
}
/*
setup dep, sub
if v is not root, g[v].back() is parent of v.
if v is not leaf (i.e. v has child), g[v].front() is heavy child of v.
*/
void init_sz(){
dep.resize(n, 0);
sub.resize(n, 1);
auto dfs = [&](auto sfs, int v, int f) -> void {
for (int &u : g[v]){
// only one chance to take parent as u.
if (u == f) swap(g[v].back(), u);
// twice means u is the last element of g[v], i.e. parent of v.
if (u == f) break;
dep[u] = dep[v]+1;
sfs(sfs, u, v);
sub[v] += sub[u];
if (sub[g[v].front()] < sub[u]){
swap(g[v].front(), u);
}
}
};
dfs(dfs, root, -1);
}
/*
setup down, tour, nxt
only heavy child c of v, nxt[c] = nxt[v]. for other child c, nxt[c] = c.
*/
void init_hld(){
down.resize(n);
tour.resize(n);
nxt.resize(n);
nxt[root] = root;
int clock = 0;
auto dfs = [&](auto sfs, int v) -> void {
down[v] = clock++;
tour[down[v]] = v;
// in case of no child, nothing to do
if ((*this)(v).empty()) return ;
// heavy child
nxt[(*this)(v).front()] = nxt[v];
sfs(sfs, (*this)(v).front());
// other child
for (int u : (*this)(v).next()){
nxt[u] = u;
sfs(sfs, u);
}
};
dfs(dfs, root);
}
public:
struct compressed_tree : public simple_tree {
using simple_tree::simple_tree;
using simple_tree::operator=;
hld_tree &g;
compressed_tree (hld_tree &g_, vector<int> vs) : g(g_){
auto comp = [&](int lv, int rv){
return g.index(lv) < g.index(rv);
};
sort(vs.begin(),vs.end(),comp);
int sz = vs.size();
for (int i = 0; i < sz-1; i++){
vs.emplace_back(g.lca(vs[i],vs[i+1]));
}
sort(vs.begin(),vs.end(),comp);
vs.erase(unique(vs.begin(),vs.end()),vs.end());
sz = vs.size();
(*this) = simple_tree(sz);
real_vertex = vs;
for (int i = 0; i < sz; i++){
g.virtual_vertex[real_vertex[i]] = i;
}
stack<int> st;
st.push(0);
for (int i = 1; i < sz; i++){
while (!g.is_in_subtree(real_vertex[st.top()], real_vertex[i])) st.pop();
(*this).add_edge(st.top(),i);
st.push(i);
}
}
vector<int> real_vertex;
int real_v(int virtual_v) const {
return real_vertex[virtual_v];
}
int virtual_v(int real_v) const {
return g.virtual_vertex[real_v];
}
size_t size() const {
return real_vertex.size();
}
};
compressed_tree compressed_tree_gen(const vector<int> &vs){
if ((int)virtual_vertex.size() != n) virtual_vertex.resize(n);
return compressed_tree(*this, vs);
}
vector<int> virtual_vertex;
};
} // namespace noya2
#line 2 "/Users/noya2/Desktop/Noya2_library/misc/random_tree.hpp"
#line 4 "/Users/noya2/Desktop/Noya2_library/misc/random_tree.hpp"
#line 2 "/Users/noya2/Desktop/Noya2_library/misc/rng.hpp"
#line 4 "/Users/noya2/Desktop/Noya2_library/misc/rng.hpp"
namespace noya2 {
// [0, 2^64 - 1)
ull rng() {
static ull _x = 88172645463325252UL;
return _x ^= _x << 7, _x ^= _x >> 9;
}
// [l, r]
ll rng(ll l, ll r) {
assert(l <= r);
return l + rng() % ull(r - l + 1);
}
// [l, r)
ll randint(ll l, ll r) {
assert(l < r);
return l + rng() % ull(r - l);
}
// [0.0, 1.0)
ld rnd() { return rng() * 5.42101086242752217004e-20; }
// [l, r)
ld rnd(ld l, ld r) {
assert(l < r);
return l + rnd() * (r - l);
}
} // namespace noya2
#line 6 "/Users/noya2/Desktop/Noya2_library/misc/random_tree.hpp"
namespace noya2 {
// input: [c \in [0, n)] * (n-2), n >= 3
vector<vector<int>> pruefer_code(const vector<int>& code) {
int n = code.size() + 2;
assert(n > 2);
vector<vector<int>> g(n);
vector<int> deg(n, 1);
int e = 0;
for (auto& x : code) deg[x]++;
set<int> ps;
for (int j = 0; j < n; j++) {
if (deg[j] == 1) ps.insert(j);
}
for (auto& i : code) {
if (ps.empty()) break;
int j = *begin(ps);
ps.erase(j);
g[i].push_back(j);
g[j].push_back(i);
if (deg[i] == 1) ps.erase(i);
deg[i]--, deg[j]--;
if (deg[i] == 1) ps.insert(i);
e++;
}
int u = -1, v = -1;
for (int i = 0; i < n; i++) {
if (deg[i] == 1) (u == -1 ? u : v) = i;
}
assert(u != -1 and v != -1);
g[u].push_back(v);
g[v].push_back(u);
e++;
assert(e == n - 1);
return g;
}
vector<vector<int>> random_tree(int n) {
if (n <= 2) {
vector<vector<int>> g(n);
if (n == 2) {
g[0].push_back(1);
g[1].push_back(0);
}
return g;
}
vector<int> pruefer(n - 2);
for (auto& x : pruefer) x = randint(0,n);
return pruefer_code(pruefer);
}
} // namespace noya2
#line 5 "hld_test.cpp"
#line 2 "hld_new.hpp"
#line 10 "hld_new.hpp"
namespace hld_new {
struct hld_tree {
int n, root;
std::vector<int> down, nxt, sub, tour;
noya2::internal::csr<int> adjacent;
// 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();
}
}
// 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];
}
// 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]
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 (down[u] < down[v]){
f(down[u], down[v] + 1);
}
else {
f(down[u] + 1, down[v]);
}
}
// {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};
}
// build csr for using operator[], operator()
void build_csr(){
adjacent = noya2::internal::csr<int>(n, n - 1);
for (int v = 0; v < n; v++){
if (v == root) continue;
adjacent.add(parent(v), v);
}
adjacent.build();
}
const auto operator[](int v) const {
return adjacent[v];
}
auto operator[](int v){
return adjacent[v];
}
// 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 hld_new
#line 7 "hld_test.cpp"
void jikken1(int n){
auto g = random_tree(n);
int root = randint(0,n);
noya2::hld_tree tr1(n,root);
hld_new::hld_tree tr2(n,root);
rep(i,n){
for (int j : g[i]){
if (i < j){
tr1.add_edge(i, j);
tr2.add_edge(i, j);
}
}
}
// subtree size
rep(i,n){
assert(tr1.subtree_size(i) == tr2.subtree_size(i));
}
cout << "subtree ok" << endl;
// parent
rep(i,n){
assert(tr1.parent(i) == tr2.parent(i));
}
cout << "parent ok" << endl;
// diameter
{
assert(get<0>(tr1.diameter()) == get<0>(tr2.diameter()));
}
cout << "diameter ok" << endl;
// lca
rep(i,n) rep(j,n){
assert(tr1.lca(i,j) == tr2.lca(i,j));
}
cout << "lca ok" << endl;
// la
rep(i,n) rep(j,n){
assert(tr1.la(i,j) == tr2.la(i,j));
}
cout << "la ok" << endl;
// path
rep(i,n) rep(j,n){
assert(tr1.path(i,j) == tr2.path(i,j));
}
cout << "path ok" << endl;
// dist
rep(i,n) rep(j,n){
assert(tr1.dist(i,j) == tr2.dist(i,j));
}
cout << "dist ok" << endl;
}
void jikken2(){
int n; in(n);
int t; in(t);
while (t--){
jikken1(n);
}
cout << "jikken2 done" << endl;
}
void jikken3(int n){
auto g = random_tree(n);
vector<int> par = [&]{
vector<int> ret(n);
noya2::hld_tree tr(n);
rep(i,n) for (int j : g[i]){
if (i < j){
tr.add_edge(i, j);
}
}
ret[0] = -1;
repp(i,1,n){
ret[tr.index(i)] = tr.index(tr.parent(i));
}
return ret;
}();
noya2::hld_tree tr1(n);
hld_new::hld_tree tr2(par);
repp(i,1,n){
tr1.add_edge(i, par[i]);
}
// subtree size
rep(i,n){
assert(tr1.subtree_size(i) == tr2.subtree_size(i));
}
cout << "subtree ok" << endl;
// parent
rep(i,n){
assert(tr1.parent(i) == tr2.parent(i));
}
cout << "parent ok" << endl;
// diameter
{
assert(get<0>(tr1.diameter()) == get<0>(tr2.diameter()));
}
cout << "diameter ok" << endl;
// lca
rep(i,n) rep(j,n){
assert(tr1.lca(i,j) == tr2.lca(i,j));
}
cout << "lca ok" << endl;
// la
rep(i,n) rep(j,n){
assert(tr1.la(i,j) == tr2.la(i,j));
}
cout << "la ok" << endl;
// path
rep(i,n) rep(j,n){
assert(tr1.path(i,j) == tr2.path(i,j));
}
cout << "path ok" << endl;
// dist
rep(i,n) rep(j,n){
assert(tr1.dist(i,j) == tr2.dist(i,j));
}
cout << "dist ok" << endl;
}
void jikken4(){
int n; in(n);
int t; in(t);
while (t--){
jikken3(n);
}
cout << "jikken4 done" << endl;
}
#line 2 "/Users/noya2/Desktop/Noya2_library/misc/timer.hpp"
#line 5 "/Users/noya2/Desktop/Noya2_library/misc/timer.hpp"
namespace noya2{
struct Timer {
private:
std::chrono::high_resolution_clock::time_point start, end;
public:
Timer() { set(); }
void set() { start = std::chrono::high_resolution_clock::now(); }
int time() {
end = std::chrono::high_resolution_clock::now();
return std::chrono::duration_cast<std::chrono::milliseconds>(end - start).count();
}
double dtime(){
return (double)(time()) / 1000;
}
bool before(double T) { return time() < (int)(T * 1000); }
void print() { std::cerr << "elapsed time: " << (double)time() / 1000 << " sec" << std::endl; }
};
} // namespace noya2
#line 135 "hld_test.cpp"
void jikken5(int n){
auto g = random_tree(n);
vector<pii> es; es.reserve(n-1);
rep(i,n) for (int j : g[i]){
if (i < j){
es.emplace_back(i, j);
}
}
vector<pii> a(n);
rep(i,n){
a[i] = {randint(0,n),randint(0,n)};
}
Timer tm;
tm.set();
noya2::hld_tree tr1(n);
for (auto [u, v] : es){
tr1.add_edge(u, v);
}
tm.print();
tm.set();
int val = 0;
for (auto [u, v] : a){
val ^= tr1.lca(u, v);
}
tm.print();
tm.set();
hld_new::hld_tree tr2(n);
for (auto [u, v] : es){
tr2.add_edge(u, v);
}
tm.print();
tm.set();
for (auto [u, v] : a){
val ^= tr2.lca(u, v);
}
tm.print();
assert(val == 0);
}
void jikken6(){
int n; in(n);
int t; in(t);
while (t--){
jikken5(n);
}
}
void jikken7(int n){
auto g = random_tree(n);
vector<int> par = [&]{
vector<int> ret(n);
noya2::hld_tree tr(n);
rep(i,n) for (int j : g[i]){
if (i < j){
tr.add_edge(i, j);
}
}
ret[0] = -1;
repp(i,1,n){
ret[tr.index(i)] = tr.index(tr.parent(i));
}
return ret;
}();
vector<pii> a(n);
rep(i,n){
a[i] = {randint(0,n),randint(0,n)};
}
Timer tm;
tm.set();
noya2::hld_tree tr1(n);
repp(i,1,n){
tr1.add_edge(i, par[i]);
}
tm.print();
tm.set();
int val = 0;
for (auto [u, v] : a){
val ^= tr1.dist(u, v);
}
tm.print();
tm.set();
hld_new::hld_tree tr2(par);
tm.print();
tm.set();
for (auto [u, v] : a){
val ^= tr2.dist(u, v);
}
tm.print();
assert(val == 0);
}
void jikken8(){
int n; in(n);
int t; in(t);
while (t--){
jikken7(n);
}
}
#line 2 "/Users/noya2/Desktop/Noya2_library/data_structure/dsu.hpp"
#line 6 "/Users/noya2/Desktop/Noya2_library/data_structure/dsu.hpp"
namespace noya2{
struct dsu {
public:
dsu() : _n(0) {}
dsu(int n) : _n(n), parent_or_size(n, -1) {}
int merge(int a, int b) {
assert(0 <= a && a < _n);
assert(0 <= b && b < _n);
int x = leader(a), y = leader(b);
if (x == y) return x;
if (-parent_or_size[x] < -parent_or_size[y]) std::swap(x, y);
parent_or_size[x] += parent_or_size[y];
parent_or_size[y] = x;
return x;
}
bool same(int a, int b) {
assert(0 <= a && a < _n);
assert(0 <= b && b < _n);
return leader(a) == leader(b);
}
int leader(int a) {
assert(0 <= a && a < _n);
if (parent_or_size[a] < 0) return a;
return parent_or_size[a] = leader(parent_or_size[a]);
}
int size(int a) {
assert(0 <= a && a < _n);
return -parent_or_size[leader(a)];
}
std::vector<std::vector<int>> groups() {
std::vector<int> leader_buf(_n), group_size(_n);
for (int i = 0; i < _n; i++) {
leader_buf[i] = leader(i);
group_size[leader_buf[i]]++;
}
std::vector<std::vector<int>> result(_n);
for (int i = 0; i < _n; i++) {
result[i].reserve(group_size[i]);
}
for (int i = 0; i < _n; i++) {
result[leader_buf[i]].push_back(i);
}
result.erase(
std::remove_if(result.begin(), result.end(),
[&](const std::vector<int>& v) { return v.empty(); }),
result.end());
return result;
}
private:
int _n;
// root node: -1 * component size
// otherwise: parent
std::vector<int> parent_or_size;
};
} // namespace noya2
#line 2 "/Users/noya2/Desktop/Noya2_library/data_structure/fenwick_tree.hpp"
#line 4 "/Users/noya2/Desktop/Noya2_library/data_structure/fenwick_tree.hpp"
namespace noya2{
template <class T> struct fenwick_tree {
public:
fenwick_tree() : _n(0) {}
explicit fenwick_tree(int n_) : _n(n_), data(n_) {}
void add(int p, T x) {
assert(0 <= p && p < _n);
p++;
while (p <= _n) {
data[p - 1] += x;
p += p & -p;
}
}
T sum(int l, int r) {
assert(0 <= l && l <= r && r <= _n);
return sum(r) - sum(l);
}
private:
int _n;
vector<T> data;
T sum(int r) {
T s = 0;
while (r > 0) {
s += data[r - 1];
r -= r & -r;
}
return s;
}
};
} // namespace noya2
#line 2 "/Users/noya2/Desktop/Noya2_library/utility/modint.hpp"
#line 4 "/Users/noya2/Desktop/Noya2_library/utility/modint.hpp"
#line 2 "/Users/noya2/Desktop/Noya2_library/math/prime.hpp"
#line 4 "/Users/noya2/Desktop/Noya2_library/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);
// constexpr long long primitive_root_constexpr(long long m){
// if (m == (1LL << 47) - (1LL << 24) + 1) return 3;
// return primitive_root_constexpr(static_cast<int>(m));
// }
} // namespace noya2
#line 6 "/Users/noya2/Desktop/Noya2_library/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 238 "hld_test.cpp"
using mint = modint998244353;
void jikken9(){
int n, m; in(n,m);
vector<vector<int>> to(n);
rep(i,m){
int u, v; in(u,v); u--, v--;
to[v].emplace_back(u);
}
dsu d(n);
vector<int> top(n); iota(all(top),0);
hld_new::hld_tree g(n,n-1);
rep(v,n){
for (int u : to[v]){
if (d.same(u,v)) continue;
g.add_edge(top[d.leader(u)],v);
top[d.merge(u,v)] = v;
}
}
fenwick_tree<mint> fen(n);
mint ans = 0;
rep(v,n){
auto [par, mapping] = g.compressed_tree(to[v]);
mint dp = 1;
if (!par.empty()){
g.path_query(mapping[0],v,[&](int l, int r){
if (l > r) swap(l,r);
dp += fen.sum(l,r);
});
}
repp(i,1,par.size()){
g.path_query(mapping[i],g.jump(mapping[par[i]],mapping[i],1),[&](int l, int r){
if (l > r) swap(l,r);
dp += fen.sum(l,r);
});
}
fen.add(g.index(v),dp);
// out(v,dp);
ans += dp;
}
out(ans);
}
void solve(){
// jikken2();
// jikken4();
// jikken6();
// jikken8();
jikken9();
}
int main(){
std::cin.tie(0)->sync_with_stdio(0);
int t = 1; //in(t);
while (t--) { solve(); }
}