#line 1 "test/yj_vertex_add_path_sum.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/vertex_add_path_sum"
#include <cstdint>
#include <cstdio>
#include <utility>
#include <vector>
#line 1 "Graph/hl_decomposition.cpp"
/**
* @brief HL 分解
* @author えびちゃん
* @see https://codeforces.com/blog/entry/53170
*/
#include <cstddef>
#include <tuple>
#include <type_traits>
#line 15 "Graph/hl_decomposition.cpp"
struct value_on_directed_edge_tag {};
struct value_on_undirected_edge_tag {};
struct value_on_vertex_tag {};
template <typename RangeQuery, typename ValueAttribute>
class hl_decomposed_tree {
public:
using size_type = size_t;
using range_query_type = RangeQuery;
using value_type = typename range_query_type::value_type;
using attribute = ValueAttribute;
private:
size_type M_n = 0;
std::vector<size_type> M_p, M_hp; // parent, heavy path root
std::vector<size_type> M_in;
range_query_type M_fa, M_fd;
void M_dfs_size(
std::vector<std::vector<size_type>>& al, std::vector<size_type>& ss,
size_type v, size_type p
) {
ss[v] = 1;
M_p[v] = p;
if (al[v][0] == p) std::swap(al[v][0], al[v].back());
for (auto& u: al[v]) {
if (u == p) continue;
M_dfs_size(al, ss, u, v);
ss[v] += ss[u];
if (ss[u] > ss[al[v][0]]) std::swap(u, al[v][0]);
}
}
void M_dfs_heavy_path(
std::vector<std::vector<size_type>> const& al, std::vector<size_type> const& ss,
size_type v, size_type& t
) {
M_in[v] = t++;
for (auto u: al[v]) {
if (u == M_p[v]) continue;
M_hp[u] = ((u == al[v][0])? M_hp[v]: u);
M_dfs_heavy_path(al, ss, u, t);
}
}
void M_decompose(std::vector<std::vector<size_type>>& al, size_type r = 0) {
std::vector<size_type> ss(M_n, 0);
M_dfs_size(al, ss, r, M_n);
size_type in = 0;
M_dfs_heavy_path(al, ss, r, in);
}
size_type M_lca(size_type u, size_type v) const {
if (M_in[u] > M_in[v]) std::swap(u, v);
if (M_hp[u] == M_hp[v]) return u;
return M_lca(u, M_p[M_hp[v]]);
}
static void S_fold(value_type& this_, value_type that, bool foldl) {
if (foldl) {
this_ += that;
} else {
this_ = that + std::move(this_);
}
}
value_type M_fold_one_way(size_type u, size_type v, bool asc) {
value_type res{};
if (asc) {
while (M_hp[u] != M_hp[v]) {
size_type l = M_n-1 - M_in[u];
size_type r = M_n-1 - M_in[M_hp[u]];
S_fold(res, M_fa.fold(l, r+1), true);
u = M_p[M_hp[u]];
}
size_type l = M_n-1 - M_in[u];
size_type r = M_n-1 - M_in[v];
S_fold(res, M_fa.fold(l, r), true);
} else {
while (M_hp[u] != M_hp[v]) {
size_type l = M_in[M_hp[u]];
size_type r = M_in[u];
S_fold(res, M_fd.fold(l, r+1), false);
u = M_p[M_hp[u]];
}
size_type l = M_in[v]+1;
size_type r = M_in[u]+1;
S_fold(res, M_fd.fold(l, r), false);
}
return res;
}
template <typename Tp>
void M_act_one_way(size_type u, size_type v, Tp x, bool asc) {
if (asc) {
while (M_hp[u] != M_hp[v]) {
size_type l = M_n-1 - M_in[u];
size_type r = M_n-1 - M_in[M_hp[u]];
M_fa.act(l, r+1, x);
u = M_p[M_hp[u]];
}
size_type l = M_n-1 - M_in[u];
size_type r = M_n-1 - M_in[v];
M_fa.act(l, r, x);
} else {
while (M_hp[u] != M_hp[v]) {
size_type l = M_in[M_hp[u]];
size_type r = M_in[u];
M_fd.act(l, r+1, x);
u = M_p[M_hp[u]];
}
size_type l = M_in[v]+1;
size_type r = M_in[u]+1;
M_fd.act(l, r, x);
}
}
value_type M_fold(size_type u, size_type v) {
size_type w = M_lca(u, v);
value_type resl = M_fold_one_way(u, w, true);
value_type resr = M_fold_one_way(v, w, false);
if (std::is_same<attribute, value_on_vertex_tag>::value) {
resl += M_fd.fold(M_in[w], M_in[w]+1);
}
return resl += resr;
}
void M_set(size_type v, value_type x, bool asc) {
// on directed edges or on vertices
bool dir = std::is_same<ValueAttribute, value_on_directed_edge_tag>::value;
if (asc || !dir) M_fa.set(M_n-1 - M_in[v], x);
if (!asc || !dir) M_fd.set(M_in[v], x);
}
template <typename Tp>
void M_act(size_type u, size_type v, Tp x) {
size_type w = M_lca(u, v);
M_act_one_way(u, w, x, true);
M_act_one_way(v, w, x, false);
if (!std::is_same<attribute, value_on_directed_edge_tag>::value) {
M_act_one_way(v, w, x, true);
M_act_one_way(u, w, x, false);
if (std::is_same<attribute, value_on_vertex_tag>::value) {
M_act_one_way(w, M_p[w], x, true);
M_act_one_way(w, M_p[w], x, false);
}
}
}
public:
hl_decomposed_tree() = default;
template <
typename Va = ValueAttribute,
typename Tp = typename std::enable_if<std::is_same<Va, value_on_vertex_tag>::value, value_type>::type
>
hl_decomposed_tree(
std::vector<Tp> const& vs,
std::vector<std::pair<size_type, size_type>> const& es, size_type r = 0
): M_n(vs.size()+1), M_p(M_n, M_n), M_hp(M_n, r), M_in(M_n) {
size_type n = M_n-1;
std::vector<std::vector<size_type>> al(M_n);
for (auto const& [u, v]: es) {
al[u].push_back(v);
al[v].push_back(u);
}
al[r].push_back(n);
al[n].push_back(r);
M_decompose(al, n);
std::vector<value_type> a(M_n), d(M_n);
for (size_type i = 0; i < n; ++i) a[M_in[i]] = d[M_in[i]] = vs[i];
M_fa.assign(a.rbegin(), a.rend());
M_fd.assign(d.begin(), d.end());
}
template <
typename Va = ValueAttribute,
typename Sz = typename std::enable_if<!std::is_same<Va, value_on_vertex_tag>::value, size_type>::type
>
hl_decomposed_tree(
Sz n, std::vector<std::tuple<size_type, size_type, value_type>> const& es,
size_type r = 0
): M_n(n), M_p(n, n), M_hp(n, r), M_in(n) {
std::vector<std::vector<size_type>> al(n);
bool undir = std::is_same<Va, value_on_undirected_edge_tag>::value;
for (auto const& e: es) {
size_type u, v;
std::tie(u, v, std::ignore) = e;
al[u].push_back(v);
if (undir) al[v].push_back(u);
}
M_decompose(al);
std::vector<value_type> a(n), d(n);
for (auto const& [u, v, w]: es) {
if (u == M_p[v]) {
d[M_in[v]] = w;
if (undir) a[M_in[v]] = w;
} else {
a[M_in[u]] = w;
if (undir) d[M_in[u]] = w;
}
}
M_fa.assign(a.rbegin(), a.rend());
M_fd.assign(d.begin(), d.end());
}
value_type fold(size_type u, size_type v) { return M_fold(u, v); }
void set(size_type v, value_type x, bool asc = true) { M_set(v, x, asc); }
template <typename Rq = RangeQuery, typename Ta = typename Rq::action_type>
void act(size_type u, size_type v, Ta x) { M_act(u, v, x); }
};
#line 1 "DataStructure/basic_segment_tree.cpp"
/**
* @brief 単一更新セグメント木
* @author えびちゃん
* @docs docs/basic_segment_tree.md
*/
#line 11 "DataStructure/basic_segment_tree.cpp"
#include <algorithm>
#line 13 "DataStructure/basic_segment_tree.cpp"
template <typename Monoid>
class basic_segment_tree {
public:
using value_type = Monoid;
using size_type = size_t;
private:
std::vector<value_type> M_c;
size_type M_n;
public:
basic_segment_tree() = default;
explicit basic_segment_tree(size_type n): M_c(n+n), M_n(n) {}
explicit basic_segment_tree(size_type n, value_type const& x):
M_c(n+n, x), M_n(n)
{
for (size_type i = n; i--;) M_c[i] = M_c[i<<1|0] + M_c[i<<1|1];
}
template <typename InputIt>
basic_segment_tree(InputIt first, InputIt last) {
std::vector<value_type> tmp(first, last);
M_n = tmp.size();
M_c.resize(M_n);
M_c.insert(M_c.end(), tmp.begin(), tmp.end());
for (size_type i = M_n; i--;) M_c[i] = M_c[i<<1|0] + M_c[i<<1|1];
}
void assign(size_type n, value_type const& x) {
M_c.assign(n+n, x);
M_n = n;
for (size_type i = n; i--;) M_c[i] = M_c[i<<1|0] + M_c[i<<1|1];
}
template <typename InputIt>
void assign(InputIt first, InputIt last) {
std::vector<value_type> tmp(first, last);
M_n = tmp.size();
M_c.resize(M_n);
M_c.insert(M_c.end(), tmp.begin(), tmp.end());
for (size_type i = M_n; i--;) M_c[i] = M_c[i<<1|0] + M_c[i<<1|1];
}
void set(size_type i, value_type const& x) {
i += M_n;
M_c[i] = x;
while (i > 1) {
i >>= 1;
M_c[i] = M_c[i<<1|0] + M_c[i<<1|1];
}
}
void set(size_type i, value_type&& x) {
i += M_n;
M_c[i] = std::move(x);
while (i > 1) {
i >>= 1;
M_c[i] = M_c[i<<1|0] + M_c[i<<1|1];
}
}
value_type const& operator [](size_type i) const { return M_c[i + M_n]; }
value_type fold(size_type l, size_type r) const {
value_type resl{}, resr{};
l += M_n;
r += M_n;
while (l < r) {
if (l & 1) resl += M_c[l++];
if (r & 1) resr = M_c[--r] + std::move(resr);
l >>= 1;
r >>= 1;
}
return resl += resr;
}
template <typename Predicate>
size_type foldl_bisect(size_type l, Predicate pred) const {
size_type r = M_n+M_n;
value_type x{};
size_type h = 0;
if (l == M_n) return pred(x)? -1: l;
l += M_n;
auto bisect = [&](size_type v) -> size_type {
while (v < M_n) {
v <<= 1;
if (pred(x + M_c[v])) x += M_c[v++];
}
return v - M_n;
};
for (; l < r; ++h, l >>= 1, r >>= 1) {
if (l & 1) {
if (!pred(x + M_c[l])) return bisect(l);
x += M_c[l];
++l;
}
if (r & 1) --r;
}
while (r <<= 1, h--) {
if (((r+1) << h) <= M_n+M_n) {
if (!pred(x + M_c[r])) return bisect(r);
x += M_c[r];
++r;
}
}
return -1;
}
template <typename Predicate>
size_type foldr_bisect(size_type r, Predicate pred) const {
size_type l = M_n;
value_type x{};
size_type h = 0;
if (r == 0) return pred(x)? -1: 0;
r += M_n;
auto bisect = [&](size_type v) -> size_type {
while (v < M_n) {
v = (v << 1 | 1);
if (pred(M_c[v] + x)) x = M_c[v--] + std::move(x);
}
return v - M_n;
};
for (; l < r; ++h, l >>= 1, r >>= 1) {
if (l & 1) ++l;
if (r & 1) {
--r;
if (!pred(M_c[r] + x)) return bisect(r);
x = M_c[r] + std::move(x);
}
}
while (l <<= 1, h--) {
if (((l-1) << h) >= M_n) {
--l;
if (!pred(M_c[l] + x)) return bisect(l);
x = M_c[l] + std::move(x);
}
}
return -1;
}
};
#line 10 "test/yj_vertex_add_path_sum.test.cpp"
int main() {
size_t n, q;
scanf("%zu %zu", &n, &q);
std::vector<intmax_t> a(n);
for (auto& ai: a) scanf("%jd", &ai);
std::vector<std::pair<size_t, size_t>> es;
es.reserve(n-1);
for (size_t i = 1; i < n; ++i) {
size_t u, v;
scanf("%zu %zu", &u, &v);
es.emplace_back(u, v);
}
hl_decomposed_tree<basic_segment_tree<intmax_t>, value_on_vertex_tag> g(a, es);
for (size_t i = 0; i < q; ++i) {
int t;
scanf("%d", &t);
if (t == 0) {
size_t p;
intmax_t x;
scanf("%zu %jd", &p, &x);
a[p] += x;
g.set(p, a[p]);
} else if (t == 1) {
size_t u, v;
scanf("%zu %zu", &u, &v);
printf("%jd\n", g.fold(u, v));
}
}
}
test/yj_vertex_add_path_sum.test.cpp