#line 1 "verify/tree/LC_vertex_add_subtree_sum.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/vertex_add_subtree_sum"
#line 2 "template/template.hpp"
// repo: https://github.com/kumacs/library-cpp
// docs: https://kumacs.github.io/library-cpp
#include <bits/stdc++.h>
using namespace std;
#line 2 "template/macro.hpp"
#define rep(i, a, b) for (int i = (a); i < (int)(b); i++)
#define rrep(i, a, b) for (int i = (int)(b) - 1; i >= (a); i--)
#define ALL(v) (v).begin(), (v).end()
#define UNIQUE(v) sort(ALL(v)), (v).erase(unique(ALL(v)), (v).end())
#define SZ(v) (int)v.size()
#define MIN(v) *min_element(ALL(v))
#define MAX(v) *max_element(ALL(v))
#define LB(v, x) int(lower_bound(ALL(v), (x)) - (v).begin())
#define UB(v, x) int(upper_bound(ALL(v), (x)) - (v).begin())
#define YN(b) cout << ((b) ? "YES" : "NO") << "\n";
#define Yn(b) cout << ((b) ? "Yes" : "No") << "\n";
#define yn(b) cout << ((b) ? "yes" : "no") << "\n";
#line 10 "template/template.hpp"
#line 2 "template/util.hpp"
using uint = unsigned int;
using ll = long long int;
using ull = unsigned long long;
using i128 = __int128_t;
using u128 = __uint128_t;
template <class T>
using priority_queue_asc = priority_queue<T, vector<T>, greater<T>>;
template <class T, class S = T>
S SUM(const vector<T>& a) {
return accumulate(ALL(a), S(0));
}
template <class T1, class T2>
inline bool chmin(T1& a, T2 b) {
if (a > b) {
a = b;
return true;
}
return false;
}
template <class T1, class T2>
inline bool chmax(T1& a, T2 b) {
if (a < b) {
a = b;
return true;
}
return false;
}
template <class T1, class T2>
inline bool chmin_opt(optional<T1>& a, T2 b) {
if (!a || a > b) {
a = b;
return true;
}
return false;
}
template <class T1, class T2>
inline bool chmax_opt(optional<T1>& a, T2 b) {
if (!a || a < b) {
a = b;
return true;
}
return false;
}
template <class T>
int popcnt(T x) {
return __builtin_popcountll(x);
}
template <class T>
int topbit(T x) {
return (x == 0 ? -1 : 63 - __builtin_clzll(x));
}
template <class T>
int lowbit(T x) {
return (x == 0 ? -1 : __builtin_ctzll(x));
}
#line 12 "template/template.hpp"
#line 2 "template/inout.hpp"
struct Fast {
Fast() {
cin.tie(nullptr);
ios_base::sync_with_stdio(false);
cout << fixed << setprecision(15);
}
} fast;
ostream& operator<<(ostream& os, __uint128_t x) {
char buf[40];
size_t k = 0;
while (x > 0) buf[k++] = (char)(x % 10 + '0'), x /= 10;
if (k == 0) buf[k++] = '0';
while (k) os << buf[--k];
return os;
}
ostream& operator<<(ostream& os, __int128_t x) {
return x < 0 ? (os << '-' << (__uint128_t)(-x)) : (os << (__uint128_t)x);
}
template <class T, size_t N>
ostream& operator<<(ostream& os, const array<T, N>& a);
template <class T1, class T2>
istream& operator>>(istream& is, pair<T1, T2>& p) {
return is >> p.first >> p.second;
}
template <class T1, class T2>
ostream& operator<<(ostream& os, const pair<T1, T2>& p) {
return os << p.first << " " << p.second;
}
template <class T>
istream& operator>>(istream& is, vector<T>& a) {
for (auto& v : a) is >> v;
return is;
}
template <class T>
ostream& operator<<(ostream& os, const vector<T>& a) {
for (auto it = a.begin(); it != a.end();) {
os << *it;
if (++it != a.end()) os << " ";
}
return os;
}
template <class T, size_t N>
ostream& operator<<(ostream& os, const array<T, N>& a) {
for (auto it = a.begin(); it != a.end();) {
os << *it;
if (++it != a.end()) os << " ";
}
return os;
}
template <class T>
ostream& operator<<(ostream& os, const set<T>& st) {
os << "{";
for (auto it = st.begin(); it != st.end();) {
os << *it;
if (++it != st.end()) os << ",";
}
os << "}";
return os;
}
template <class T1, class T2>
ostream& operator<<(ostream& os, const map<T1, T2>& mp) {
os << "{";
for (auto it = mp.begin(); it != mp.end();) {
os << it->first << ":" << it->second;
if (++it != mp.end()) os << ",";
}
os << "}";
return os;
}
void in() {}
template <typename T, class... U>
void in(T& t, U&... u) {
cin >> t;
in(u...);
}
template <class... T>
void in_zip(int n, T&... t) {
assert(n >= 0 && ((size(t) >= static_cast<size_t>(n)) && ...));
for (int i = 0; i < n; i++) in(t[i]...);
}
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 <class T, class U>
void out_opt(const optional<T>& opt, const U& fallback, ostream& os = cout) {
if (opt.has_value())
os << opt.value();
else
os << fallback;
os << "\n";
}
template <class T, class U>
void out_opt(const vector<optional<T>>& vec, const U& fallback, ostream& os = cout) {
for (auto it = vec.begin(); it != vec.end();) {
if ((*it).has_value())
os << (*it).value();
else
os << fallback;
if (++it != vec.end()) os << " ";
}
os << "\n";
}
namespace IO {
template <class T, class... U>
T read(U&&... u) {
T t = T(forward<U>(u)...);
in(t);
return t;
}
namespace Graph {
vector<vector<int>> unweighted(int n, int m, bool directed = false, int offset = 1) {
vector<vector<int>> g(n);
for (int i = 0; i < m; i++) {
int u, v;
cin >> u >> v;
u -= offset, v -= offset;
g[u].push_back(v);
if (!directed) g[v].push_back(u);
}
return g;
}
template <class T>
vector<vector<pair<int, T>>> weighted(int n, int m, bool directed = false, int offset = 1) {
vector<vector<pair<int, T>>> g(n);
for (int i = 0; i < m; i++) {
int u, v;
T w;
cin >> u >> v >> w;
u -= offset, v -= offset;
g[u].push_back({v, w});
if (!directed) g[v].push_back({u, w});
}
return g;
}
} // namespace Graph
namespace Tree {
vector<vector<int>> unweighted(int n, bool directed = false, int offset = 1) {
return Graph::unweighted(n, n - 1, directed, offset);
}
template <class T>
vector<vector<pair<int, T>>> weighted(int n, bool directed = false, int offset = 1) {
return Graph::weighted<T>(n, n - 1, directed, offset);
}
vector<vector<int>> rooted(int n, bool to_root = true, bool to_leaf = true, int offset = 1) {
vector<vector<int>> g(n);
for (int i = 1; i < n; i++) {
int p;
cin >> p;
p -= offset;
if (to_root) g[i].push_back(p);
if (to_leaf) g[p].push_back(i);
}
return g;
}
} // namespace Tree
} // namespace IO
#line 14 "template/template.hpp"
#line 2 "template/debug.hpp"
#ifdef LOCAL
#define debug 1
#define show(...) _show(0, #__VA_ARGS__, __VA_ARGS__)
#else
#define debug 0
#define show(...) true
#endif
template <class T>
void _show(int, T) {
cerr << '\n';
}
template <class T1, class T2, class... T3>
void _show(int i, const T1& a, const T2& b, const T3&... c) {
for (; a[i] != ',' && a[i] != '\0'; i++) cerr << a[i];
cerr << ":" << b << " ";
_show(i + 1, a, c...);
}
#line 2 "algebraic-structure/util.hpp"
#ifdef __cpp_concepts
#define REQUIRES(...) requires __VA_ARGS__
#else
#define REQUIRES(...)
#endif
#line 3 "algebraic-structure/magma.hpp"
#ifdef __cpp_concepts
template <class M>
concept Magma = requires(typename M::value_type x, typename M::value_type y) {
typename M::value_type;
{ M::op(x, y) } -> same_as<typename M::value_type>;
};
#endif
template <class T>
struct AddMagma {
using value_type = T;
static T op(T x, T y) { return x + y; }
};
template <class T>
struct MulMagma {
using value_type = T;
static T op(T x, T y) { return x * y; }
};
template <class T, T id>
struct MaxMagma {
using value_type = T;
static T op(T x, T y) { return x > y ? x : y; }
};
template <class T, T id>
struct MinMagma {
using value_type = T;
static T op(T x, T y) { return x < y ? x : y; }
};
#line 3 "algebraic-structure/monoid.hpp"
#ifdef __cpp_concepts
template <class M>
concept Monoid = Magma<M> && requires {
{ M::e() } -> same_as<typename M::value_type>;
};
#endif
template <class T>
struct AddMonoid {
using value_type = T;
static T op(T x, T y) { return x + y; }
static T e() { return T(0); }
};
template <class T>
struct MulMonoid {
using value_type = T;
static T op(T x, T y) { return x * y; }
static T e() { return T(1); }
};
template <class T, T id>
struct MaxMonoid {
using value_type = T;
static T op(T x, T y) { return x > y ? x : y; }
static T e() { return id; }
};
template <class T, T id>
struct MinMonoid {
using value_type = T;
static T op(T x, T y) { return x < y ? x : y; }
static T e() { return id; }
};
#line 2 "graph/graph.hpp"
template <class E>
struct GraphBase {
public:
GraphBase() : GraphBase(0) {}
GraphBase(int size) : n(size) {
assert(size >= 0);
g.resize(size);
}
size_t size() const { return n; }
const vector<E>& operator[](int x) const {
assert(0 <= x && x < n);
return g[x];
}
vector<E>& operator[](int x) {
assert(0 <= x && x < n);
return g[x];
}
protected:
int n;
vector<vector<E>> g;
};
struct EdgeUnweighted {
int to;
};
struct GraphUnweighted : GraphBase<EdgeUnweighted> {
using base = GraphBase<EdgeUnweighted>;
public:
GraphUnweighted() : base(0) {}
GraphUnweighted(int size) : base(size) {}
GraphUnweighted(const vector<vector<int>>& graph) : base(graph.size()) {
for (int x = 0; x < n; x++) {
base::g[x].reserve(graph[x].size());
for (int y : graph[x]) base::g[x].push_back({y});
}
}
void add_edge(int x, int y) {
(*this)[x].push_back({y});
(*this)[y].push_back({x});
}
void add_edge_directed(int from, int to) { (*this)[from].push_back({to}); }
};
struct EdgeUnweightedIndexed {
int to, id;
};
struct GraphUnweightedIndexed : GraphBase<EdgeUnweightedIndexed> {
using base = GraphBase<EdgeUnweightedIndexed>;
public:
GraphUnweightedIndexed() : GraphUnweightedIndexed(0) {}
GraphUnweightedIndexed(int size) : base(size), m(0) {}
int edge_count() const { return m; }
int add_edge(int x, int y) {
int id = m++;
(*this)[x].push_back({y, id});
(*this)[y].push_back({x, id});
return id;
}
int add_edge_directed(int from, int to) {
int id = m++;
(*this)[from].push_back({to, id});
return id;
}
private:
int m;
};
template <class T>
struct EdgeWeighted {
int to;
T weight;
};
template <class T>
struct GraphWeighted : GraphBase<EdgeWeighted<T>> {
using base = GraphBase<EdgeWeighted<T>>;
public:
GraphWeighted() : base(0) {}
GraphWeighted(int size) : base(size) {}
GraphWeighted(const vector<vector<pair<int, T>>>& graph) : base(graph.size()) {
for (int x = 0; x < base::n; x++) {
base::g[x].reserve(graph[x].size());
for (const auto& [y, w] : graph[x]) base::g[x].push_back({y, w});
}
}
void add_edge(int x, int y, T w) {
(*this)[x].push_back({y, w});
(*this)[y].push_back({x, w});
}
void add_edge_directed(int from, int to, T w) { (*this)[from].push_back({to, w}); }
};
inline GraphWeighted<int> GraphUnweightedToWeighted(const GraphUnweighted& g) {
GraphWeighted<int> h(g.size());
for (int x = 0; x < static_cast<int>(g.size()); x++) {
h[x].reserve(g[x].size());
for (const auto& e : g[x]) h[x].push_back({e.to, 1});
}
return h;
}
/**
* @brief Graph
* @docs docs/graph/graph.md
*/
#line 2 "tree/tree-vertex-set-subtree-prod.hpp"
#line 2 "tree/euler-tour.hpp"
template <class G>
pair<vector<int>, vector<int>> EulerTour(const G& g, int root = 0) {
int n = g.size();
assert(n > 0);
assert(0 <= root && root < n);
vector<int> in_time(n), out_time(n);
vector<int> parent(n, -2), iter(n);
parent[root] = -1;
int t = 0;
vector<int> st = {root};
while (!st.empty()) {
int x = st.back();
if (iter[x] == 0) in_time[x] = t++;
if (iter[x] == (int)g[x].size()) {
out_time[x] = t;
st.pop_back();
continue;
}
int y = g[x][iter[x]++].to;
if (y == parent[x]) continue;
assert(parent[y] == -2);
parent[y] = x;
st.push_back(y);
}
assert(t == n);
return {in_time, out_time};
}
/**
* @brief Euler Tour of Tree
* @docs docs/tree/euler-tour.md
*/
#line 3 "segment-tree/segment-tree.hpp"
template <class M>
REQUIRES(Monoid<M>)
struct SegmentTree {
using T = typename M::value_type;
private:
int _n, size, log;
vector<T> d;
void update(int p) { d[p] = M::op(d[2 * p], d[2 * p + 1]); }
public:
SegmentTree() : SegmentTree(0) {}
explicit SegmentTree(int sz) : SegmentTree(vector<T>(sz, M::e())) {}
explicit SegmentTree(const vector<T>& v) : _n(v.size()) {
size = 1, log = 0;
while (size < _n) size <<= 1, log++;
d.assign(2 * size, M::e());
for (int i = 0; i < _n; i++) d[size + i] = v[i];
for (int i = size - 1; i > 0; i--) update(i);
}
void clear() { fill(d.begin(), d.end(), M::e()); }
void set_without_update(int p, T v) { d[p + size] = v; }
void all_update() {
for (int i = size - 1; i > 0; i--) update(i);
}
T get(int p) {
assert(0 <= p && p <= _n);
return d[p + size];
}
void set(int p, T v) {
assert(0 <= p && p <= _n);
p += size;
d[p] = v;
for (int i = 1; i <= log; i++) update(p >> i);
}
void apply(int p, T v) {
assert(0 <= p && p <= _n);
p += size;
d[p] = M::op(d[p], v);
for (int i = 1; i <= log; i++) update(p >> i);
}
T all_prod() { return d[1]; }
T prod(int l, int r) {
if (l >= r) return M::e();
assert(0 <= l && l <= r && r <= _n);
T sl = M::e(), sr = M::e();
l += size, r += size;
while (l < r) {
if ((l & 1) != 0) sl = M::op(sl, d[l++]);
if ((r & 1) != 0) sr = M::op(d[--r], sr);
l >>= 1, r >>= 1;
}
return M::op(sl, sr);
}
template <bool (*f)(T)>
int max_right(int l) const {
return max_right(l, [](T x) { return f(x); });
}
template <class F>
int max_right(int l, F f) const {
assert(0 <= l && l <= size);
assert(f(M::e()));
if (l == _n) return _n;
l += size;
T s = M::e();
do {
while (l % 2 == 0) l >>= 1;
if (!f(M::op(s, d[l]))) {
while (l < size) {
l <<= 1;
if (f(M::op(s, d[l]))) s = M::op(s, d[l++]);
}
return l - size;
}
s = M::op(s, d[l++]);
} while ((l & -l) != l);
return _n;
}
template <bool (*f)(T)>
int min_left(int r) const {
return min_left(r, [](T x) { return f(x); });
}
template <class F>
int min_left(int r, F f) const {
assert(0 <= r && r <= _n);
assert(f(M::e()));
if (r == 0) return 0;
r += size;
T s = M::e();
do {
r--;
while (r > 1 && (r % 2)) r >>= 1;
if (!f(M::op(d[r], s))) {
while (r < size) {
r <<= 1, r++;
if (f(M::op(d[r], s))) s = M::op(d[r--], s);
}
return r + 1 - size;
}
s = M::op(d[r], s);
} while ((r & -r) != r);
return 0;
}
};
/**
* @brief Segment Tree
* @docs docs/segment-tree/segment-tree.md
*/
#line 6 "tree/tree-vertex-set-subtree-prod.hpp"
template <class M>
REQUIRES(Monoid<M>)
struct TreeVertexSetSubtreeProd {
using T = M::value_type;
TreeVertexSetSubtreeProd() {}
template <class G>
TreeVertexSetSubtreeProd(const G& g, const vector<T>& vertex_value, int root = 0) : n(g.size()) {
assert((int)vertex_value.size() == n);
tie(in_time, out_time) = EulerTour(g, root);
vector<T> data(n);
for (int x = 0; x < n; x++) data[in_time[x]] = vertex_value[x];
seg = SegmentTree<M>(data);
}
void set(int x, T v) { seg.set(in_time[x], v); }
void apply(int x, T v) { seg.apply(in_time[x], v); }
T prod(int x) { return seg.prod(in_time[x], out_time[x]); }
private:
int n;
vector<int> in_time, out_time;
SegmentTree<M> seg;
};
/**
* @brief Tree Vertex Set Subtree Product
* @docs docs/tree/tree-vertex-set-subtree-prod.md
*/
#line 7 "verify/tree/LC_vertex_add_subtree_sum.test.cpp"
int main() {
int n, q;
in(n, q);
vector<long long> a(n);
in(a);
GraphUnweighted g(n);
rep(x, 1, n) {
int p;
in(p);
g.add_edge(p, x);
}
TreeVertexSetSubtreeProd<AddMonoid<long long>> ds(g, a);
while (q--) {
int type, x;
in(type, x);
if (type == 0) {
long long v;
in(v);
ds.apply(x, v);
} else {
out(ds.prod(x));
}
}
}
verify/tree/LC_vertex_add_subtree_sum.test.cpp