This documentation is automatically generated by online-judge-tools/verification-helper
#define PROBLEM "https://judge.yosupo.jp/problem/range_parallel_unionfind"
#include "../../data_structure/range_parallel_dsu.hpp"
#include "../../modint/modint.hpp"
#include "../../template/template.hpp"
namespace ebi {
using mint = modint998244353;
void main_() {
int n, q;
std::cin >> n >> q;
std::vector<mint> x(n);
std::cin >> x;
range_parallel_dsu uf(n);
mint ans = 0;
while (q--) {
int k, a, b;
std::cin >> k >> a >> b;
uf.merge(a, b, k, [&](int i, int j) -> void {
ans += x[i] * x[j];
x[i] += x[j];
});
std::cout << ans << '\n';
}
}
} // namespace ebi
int main() {
ebi::fast_io();
int t = 1;
// std::cin >> t;
while (t--) {
ebi::main_();
}
return 0;
}
#line 1 "test/data_structure/Range_Parallel_Unionfind.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/range_parallel_unionfind"
#line 2 "data_structure/range_parallel_dsu.hpp"
#include <bit>
#include <cassert>
#include <vector>
#line 2 "data_structure/dsu.hpp"
#include <algorithm>
#line 5 "data_structure/dsu.hpp"
namespace ebi {
struct dsu {
private:
std::vector<int> par;
int c;
public:
dsu(int n = 0) : par(n, -1), c(n) {}
bool same(int x, int y) {
return leader(x) == leader(y);
}
bool merge(int x, int y) {
x = leader(x);
y = leader(y);
if (x == y) return false;
if (par[x] > par[y]) std::swap(x, y);
par[x] += par[y];
par[y] = x;
c--;
return true;
}
int leader(int x) {
if (par[x] < 0)
return x;
else
return par[x] = leader(par[x]);
}
int size(int x) {
return -par[leader(x)];
}
int count_group() const {
return c;
}
std::vector<std::vector<int>> groups() {
int n = par.size();
std::vector result(n, std::vector<int>());
for (int i = 0; i < n; i++) {
result[leader(i)].emplace_back(i);
}
result.erase(std::remove_if(result.begin(), result.end(),
[](const std::vector<int> &v) -> bool {
return v.empty();
}),
result.end());
return result;
}
void clear() {
for (int i = 0; i < int(par.size()); i++) {
par[i] = -1;
}
}
};
} // namespace ebi
#line 8 "data_structure/range_parallel_dsu.hpp"
namespace ebi {
struct range_parallel_dsu {
private:
void merge_(int u, int v, int d) {
if (uf[d].same(u, v)) return;
uf[d].merge(u, v);
if (d > 0) {
merge_(u, v, d - 1);
merge_(u + (1 << (d - 1)), v + (1 << (d - 1)), d - 1);
}
}
template <class F> void merge_(int u, int v, int d, F f) {
if (d == 0) {
u = uf[0].leader(u);
v = uf[0].leader(v);
if (u == v) return;
uf[0].merge(u, v);
int leader = uf[0].leader(u);
f(leader, u ^ v ^ leader);
return;
} else if (d > 0) {
if (!uf[d].merge(u, v)) return;
merge_(u, v, d - 1, f);
merge_(u + (1 << (d - 1)), v + (1 << (d - 1)), d - 1, f);
} else
assert(0);
}
public:
range_parallel_dsu(int n_)
: n(n_), uf(std::bit_width((unsigned int)n), dsu(n)) {}
void merge(int u, int v, int w) {
if (u > v) std::swap(u, v);
w = std::min(w, n - v);
if (w == 0 || u == v) return;
int lg2 = std::bit_width((unsigned int)w) - 1;
merge_(u, v, lg2);
merge_(u + w - (1 << lg2), v + w - (1 << lg2), lg2);
}
template <class F> void merge(int u, int v, int w, F f) {
if (u > v) std::swap(u, v);
w = std::min(w, n - v);
if (w == 0 || u == v) return;
int lg2 = std::bit_width((unsigned int)w) - 1;
merge_(u, v, lg2, f);
merge_(u + w - (1 << lg2), v + w - (1 << lg2), lg2, f);
}
bool same(int u, int v) {
return uf[0].same(u, v);
}
int size(int u) {
return uf[0].size(u);
}
int leader(int u) {
return uf[0].leader(u);
}
std::vector<std::vector<int>> groups() {
return uf[0].groups();
}
int count_group() {
return uf[0].count_group();
}
private:
int n;
std::vector<dsu> uf;
};
} // namespace ebi
#line 2 "modint/modint.hpp"
#line 4 "modint/modint.hpp"
#include <iostream>
#line 2 "modint/base.hpp"
#include <concepts>
#line 5 "modint/base.hpp"
#include <utility>
namespace ebi {
template <class T>
concept Modint = requires(T a, T b) {
a + b;
a - b;
a * b;
a / b;
a.inv();
a.val();
a.pow(std::declval<long long>());
T::mod();
};
template <Modint mint> std::istream &operator>>(std::istream &os, mint &a) {
long long x;
os >> x;
a = x;
return os;
}
template <Modint mint>
std::ostream &operator<<(std::ostream &os, const mint &a) {
return os << a.val();
}
} // namespace ebi
#line 7 "modint/modint.hpp"
namespace ebi {
template <int m> struct static_modint {
private:
using modint = static_modint;
public:
static constexpr int mod() {
return m;
}
static constexpr modint raw(int v) {
modint 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;
}
constexpr unsigned int value() const {
return val();
}
constexpr modint &operator++() {
_v++;
if (_v == umod()) _v = 0;
return *this;
}
constexpr modint &operator--() {
if (_v == 0) _v = umod();
_v--;
return *this;
}
constexpr modint operator++(int) {
modint res = *this;
++*this;
return res;
}
constexpr modint operator--(int) {
modint res = *this;
--*this;
return res;
}
constexpr modint &operator+=(const modint &rhs) {
_v += rhs._v;
if (_v >= umod()) _v -= umod();
return *this;
}
constexpr modint &operator-=(const modint &rhs) {
_v -= rhs._v;
if (_v >= umod()) _v += umod();
return *this;
}
constexpr modint &operator*=(const modint &rhs) {
unsigned long long x = _v;
x *= rhs._v;
_v = (unsigned int)(x % (unsigned long long)umod());
return *this;
}
constexpr modint &operator/=(const modint &rhs) {
return *this = *this * rhs.inv();
}
constexpr modint operator+() const {
return *this;
}
constexpr modint operator-() const {
return modint() - *this;
}
constexpr modint pow(long long n) const {
assert(0 <= n);
modint x = *this, res = 1;
while (n) {
if (n & 1) res *= x;
x *= x;
n >>= 1;
}
return res;
}
constexpr modint inv() const {
assert(_v);
return pow(umod() - 2);
}
friend modint operator+(const modint &lhs, const modint &rhs) {
return modint(lhs) += rhs;
}
friend modint operator-(const modint &lhs, const modint &rhs) {
return modint(lhs) -= rhs;
}
friend modint operator*(const modint &lhs, const modint &rhs) {
return modint(lhs) *= rhs;
}
friend modint operator/(const modint &lhs, const modint &rhs) {
return modint(lhs) /= rhs;
}
friend bool operator==(const modint &lhs, const modint &rhs) {
return lhs.val() == rhs.val();
}
friend bool operator!=(const modint &lhs, const modint &rhs) {
return !(lhs == rhs);
}
private:
unsigned int _v = 0;
static constexpr unsigned int umod() {
return m;
}
};
using modint998244353 = static_modint<998244353>;
using modint1000000007 = static_modint<1000000007>;
} // namespace ebi
#line 1 "template/template.hpp"
#include <bits/stdc++.h>
#define rep(i, a, n) for (int i = (int)(a); i < (int)(n); i++)
#define rrep(i, a, n) for (int i = ((int)(n)-1); i >= (int)(a); i--)
#define Rep(i, a, n) for (i64 i = (i64)(a); i < (i64)(n); i++)
#define RRep(i, a, n) for (i64 i = ((i64)(n)-i64(1)); i >= (i64)(a); i--)
#define all(v) (v).begin(), (v).end()
#define rall(v) (v).rbegin(), (v).rend()
#line 2 "template/debug_template.hpp"
#line 4 "template/debug_template.hpp"
namespace ebi {
#ifdef LOCAL
#define debug(...) \
std::cerr << "LINE: " << __LINE__ << " [" << #__VA_ARGS__ << "]:", \
debug_out(__VA_ARGS__)
#else
#define debug(...)
#endif
void debug_out() {
std::cerr << std::endl;
}
template <typename Head, typename... Tail> void debug_out(Head h, Tail... t) {
std::cerr << " " << h;
if (sizeof...(t) > 0) std::cerr << " :";
debug_out(t...);
}
} // namespace ebi
#line 2 "template/int_alias.hpp"
#line 4 "template/int_alias.hpp"
namespace ebi {
using ld = long double;
using std::size_t;
using i8 = std::int8_t;
using u8 = std::uint8_t;
using i16 = std::int16_t;
using u16 = std::uint16_t;
using i32 = std::int32_t;
using u32 = std::uint32_t;
using i64 = std::int64_t;
using u64 = std::uint64_t;
using i128 = __int128_t;
using u128 = __uint128_t;
} // namespace ebi
#line 2 "template/io.hpp"
#line 5 "template/io.hpp"
#include <optional>
#line 7 "template/io.hpp"
namespace ebi {
template <typename T1, typename T2>
std::ostream &operator<<(std::ostream &os, const std::pair<T1, T2> &pa) {
return os << pa.first << " " << pa.second;
}
template <typename T1, typename T2>
std::istream &operator>>(std::istream &os, std::pair<T1, T2> &pa) {
return os >> pa.first >> pa.second;
}
template <typename T>
std::ostream &operator<<(std::ostream &os, const std::vector<T> &vec) {
for (std::size_t i = 0; i < vec.size(); i++)
os << vec[i] << (i + 1 == vec.size() ? "" : " ");
return os;
}
template <typename T>
std::istream &operator>>(std::istream &os, std::vector<T> &vec) {
for (T &e : vec) std::cin >> e;
return os;
}
template <typename T>
std::ostream &operator<<(std::ostream &os, const std::optional<T> &opt) {
if (opt) {
os << opt.value();
} else {
os << "invalid value";
}
return os;
}
void fast_io() {
std::cout << std::fixed << std::setprecision(15);
std::cin.tie(nullptr);
std::ios::sync_with_stdio(false);
}
} // namespace ebi
#line 2 "template/utility.hpp"
#line 5 "template/utility.hpp"
#line 2 "graph/base.hpp"
#line 5 "graph/base.hpp"
#include <ranges>
#line 7 "graph/base.hpp"
#line 2 "data_structure/simple_csr.hpp"
#line 6 "data_structure/simple_csr.hpp"
namespace ebi {
template <class E> struct simple_csr {
simple_csr() = default;
simple_csr(int n, const std::vector<std::pair<int, E>>& elements)
: start(n + 1, 0), elist(elements.size()) {
for (auto e : elements) {
start[e.first + 1]++;
}
for (auto i : std::views::iota(0, n)) {
start[i + 1] += start[i];
}
auto counter = start;
for (auto [i, e] : elements) {
elist[counter[i]++] = e;
}
}
simple_csr(const std::vector<std::vector<E>>& es)
: start(es.size() + 1, 0) {
int n = es.size();
for (auto i : std::views::iota(0, n)) {
start[i + 1] = (int)es[i].size() + start[i];
}
elist.resize(start.back());
for (auto i : std::views::iota(0, n)) {
std::copy(es[i].begin(), es[i].end(), elist.begin() + start[i]);
}
}
int size() const {
return (int)start.size() - 1;
}
const auto operator[](int i) const {
return std::ranges::subrange(elist.begin() + start[i],
elist.begin() + start[i + 1]);
}
auto operator[](int i) {
return std::ranges::subrange(elist.begin() + start[i],
elist.begin() + start[i + 1]);
}
const auto operator()(int i, int l, int r) const {
return std::ranges::subrange(elist.begin() + start[i] + l,
elist.begin() + start[i + 1] + r);
}
auto operator()(int i, int l, int r) {
return std::ranges::subrange(elist.begin() + start[i] + l,
elist.begin() + start[i + 1] + r);
}
private:
std::vector<int> start;
std::vector<E> elist;
};
} // namespace ebi
#line 9 "graph/base.hpp"
namespace ebi {
template <class T> struct Edge {
int from, to;
T cost;
int id;
};
template <class E> struct Graph {
using cost_type = E;
using edge_type = Edge<cost_type>;
Graph(int n_) : n(n_) {}
Graph() = default;
void add_edge(int u, int v, cost_type c) {
buff.emplace_back(u, edge_type{u, v, c, m});
edges.emplace_back(edge_type{u, v, c, m++});
}
void add_undirected_edge(int u, int v, cost_type c) {
buff.emplace_back(u, edge_type{u, v, c, m});
buff.emplace_back(v, edge_type{v, u, c, m});
edges.emplace_back(edge_type{u, v, c, m});
m++;
}
void read_tree(int offset = 1, bool is_weighted = false) {
read_graph(n - 1, offset, false, is_weighted);
}
void read_parents(int offset = 1) {
for (auto i : std::views::iota(1, n)) {
int p;
std::cin >> p;
p -= offset;
add_undirected_edge(p, i, 1);
}
build();
}
void read_graph(int e, int offset = 1, bool is_directed = false,
bool is_weighted = false) {
for (int i = 0; i < e; i++) {
int u, v;
std::cin >> u >> v;
u -= offset;
v -= offset;
if (is_weighted) {
cost_type c;
std::cin >> c;
if (is_directed) {
add_edge(u, v, c);
} else {
add_undirected_edge(u, v, c);
}
} else {
if (is_directed) {
add_edge(u, v, 1);
} else {
add_undirected_edge(u, v, 1);
}
}
}
build();
}
void build() {
assert(!prepared);
csr = simple_csr<edge_type>(n, buff);
buff.clear();
prepared = true;
}
int size() const {
return n;
}
int node_number() const {
return n;
}
int edge_number() const {
return m;
}
edge_type get_edge(int i) const {
return edges[i];
}
std::vector<edge_type> get_edges() const {
return edges;
}
const auto operator[](int i) const {
return csr[i];
}
auto operator[](int i) {
return csr[i];
}
private:
int n, m = 0;
std::vector<std::pair<int,edge_type>> buff;
std::vector<edge_type> edges;
simple_csr<edge_type> csr;
bool prepared = false;
};
} // namespace ebi
#line 8 "template/utility.hpp"
namespace ebi {
template <class T> inline bool chmin(T &a, T b) {
if (a > b) {
a = b;
return true;
}
return false;
}
template <class T> inline bool chmax(T &a, T b) {
if (a < b) {
a = b;
return true;
}
return false;
}
template <class T> T safe_ceil(T a, T b) {
if (a % b == 0)
return a / b;
else if (a >= 0)
return (a / b) + 1;
else
return -((-a) / b);
}
template <class T> T safe_floor(T a, T b) {
if (a % b == 0)
return a / b;
else if (a >= 0)
return a / b;
else
return -((-a) / b) - 1;
}
constexpr i64 LNF = std::numeric_limits<i64>::max() / 4;
constexpr int INF = std::numeric_limits<int>::max() / 2;
const std::vector<int> dy = {1, 0, -1, 0, 1, 1, -1, -1};
const std::vector<int> dx = {0, 1, 0, -1, 1, -1, 1, -1};
} // namespace ebi
#line 6 "test/data_structure/Range_Parallel_Unionfind.test.cpp"
namespace ebi {
using mint = modint998244353;
void main_() {
int n, q;
std::cin >> n >> q;
std::vector<mint> x(n);
std::cin >> x;
range_parallel_dsu uf(n);
mint ans = 0;
while (q--) {
int k, a, b;
std::cin >> k >> a >> b;
uf.merge(a, b, k, [&](int i, int j) -> void {
ans += x[i] * x[j];
x[i] += x[j];
});
std::cout << ans << '\n';
}
}
} // namespace ebi
int main() {
ebi::fast_io();
int t = 1;
// std::cin >> t;
while (t--) {
ebi::main_();
}
return 0;
}