Library

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:heavy_check_mark: test/tree/Vertex_Add_Range_Contour_Sum_on_Tree_2.test.cpp

Depends on

Code

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

#include "../../data_structure/segtree.hpp"
#include "../../graph/base.hpp"
#include "../../template/template.hpp"
#include "../../tree/contour_query_on_weighted_tree.hpp"

namespace ebi {

i64 op(i64 a, i64 b) {
    return a + b;
}

i64 e() {
    return 0;
}

void main_() {
    int n, q;
    std::cin >> n >> q;
    std::vector<i64> a(n);
    std::cin >> a;
    Graph<int> g(n);
    g.read_tree(0);
    contour_query_on_weighted_tree cq(g);
    std::vector<i64> data(cq.size(), 0);
    rep(v, 0, n) {
        for (auto i : cq.get_vertex(v)) {
            data[i] += a[v];
        }
    }
    segtree<i64, op, e> seg(data);
    while (q--) {
        int type;
        std::cin >> type;
        if (type == 0) {
            int p;
            i64 x;
            std::cin >> p >> x;
            a[p] += x;
            for (auto i : cq.get_vertex(p)) {
                seg.set(i, seg.get(i) + x);
            }
        } else {
            int p, l, r;
            std::cin >> p >> l >> r;
            i64 ans = 0;
            if (l == 0) ans += a[p];
            for (auto [il, ir] : cq.get_contour_from_vertex(p, l, r)) {
                ans += seg.prod(il, ir);
            }
            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/tree/Vertex_Add_Range_Contour_Sum_on_Tree_2.test.cpp"
#define PROBLEM \
    "https://judge.yosupo.jp/problem/vertex_add_range_contour_sum_on_tree"

#line 2 "data_structure/segtree.hpp"

#include <cassert>

#include <vector>


namespace ebi {

template <class S, S (*op)(S, S), S (*e)()> struct segtree {
  private:
    int n;
    int sz;
    std::vector<S> data;

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

  public:
    segtree(int n_) : segtree(std::vector<S>(n_, e())) {}
    segtree(const std::vector<S> &v) : n((int)v.size()), sz(1) {
        while (sz < n) sz *= 2;
        data = std::vector<S>(2 * sz, e());
        for (int i = 0; i < n; i++) {
            data[sz + i] = v[i];
        }
        for (int i = sz - 1; i >= 1; i--) update(i);
    }

    void set(int p, S x) {
        assert(0 <= p && p < n);
        p += sz;
        data[p] = x;
        while (p > 1) {
            p >>= 1;
            update(p);
        }
    }

    S get(int p) const {
        assert(0 <= p && p < n);
        return data[p + sz];
    }

    S prod(int l, int r) const {
        assert(0 <= l && l <= r && r <= n);
        S sml = e(), smr = e();
        l += sz;
        r += sz;
        while (l < r) {
            if (l & 1) sml = op(sml, data[l++]);
            if (r & 1) smr = op(data[--r], smr);
            l >>= 1;
            r >>= 1;
        }
        return op(sml, smr);
    }

    S all_prod() const {
        return data[1];
    }

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

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

    S operator[](int p) const {
        return data[sz + p];
    }
};

}  // namespace ebi

#line 2 "graph/base.hpp"

#line 4 "graph/base.hpp"
#include <iostream>
#include <ranges>
#line 7 "graph/base.hpp"

#line 2 "data_structure/simple_csr.hpp"

#line 4 "data_structure/simple_csr.hpp"
#include <utility>
#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 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 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 2 "tree/contour_query_on_weighted_tree.hpp"

#line 7 "tree/contour_query_on_weighted_tree.hpp"

#line 2 "tree/centroid_decomposition.hpp"

#line 7 "tree/centroid_decomposition.hpp"

namespace ebi {

namespace internal {

template <class F>
void centroid_decomposition_dfs_naive(const std::vector<int> &par,
                                      const std::vector<int> &original_vs,
                                      F f) {
    const int n = (int)par.size();
    assert(par.size() == original_vs.size());
    int center = -1;
    std::vector<int> sz(n, 1);
    for (const int v : std::views::iota(0, n) | std::views::reverse) {
        if (sz[v] >= (n + 1) / 2) {
            center = v;
            break;
        }
        sz[par[v]] += sz[v];
    }
    std::vector<int> color(n, -1);
    std::vector<int> vs = {center};
    color[center] = 0;
    int c = 1;
    for (const int v : std::views::iota(1, n)) {
        if (par[v] == center) {
            vs.emplace_back(v);
            color[v] = c++;
        }
    }
    if (center > 0) {
        for (int v = par[center]; v != -1; v = par[v]) {
            vs.emplace_back(v);
            color[v] = c;
        }
        c++;
    }
    for (const int v : std::views::iota(0, n)) {
        if (color[v] == -1) {
            vs.emplace_back(v);
            color[v] = color[par[v]];
        }
    }
    std::vector<int> index_ptr(c + 1, 0);
    for (const int v : std::views::iota(0, n)) {
        index_ptr[color[v] + 1]++;
    }
    for (const int i : std::views::iota(0, c)) {
        index_ptr[i + 1] += index_ptr[i];
    }
    auto counter = index_ptr;
    std::vector<int> ord(n);
    for (auto v : vs) {
        ord[counter[color[v]]++] = v;
    }
    std::vector<int> relabel(n);
    for (const int v : std::views::iota(0, n)) {
        relabel[ord[v]] = v;
    }
    std::vector<int> original_vs2(n);
    for (const int v : std::views::iota(0, n)) {
        original_vs2[relabel[v]] = original_vs[v];
    }
    std::vector<int> relabel_par(n, -1);
    for (int v : std::views::iota(1, n)) {
        int a = relabel[v];
        int b = relabel[par[v]];
        if (a > b) std::swap(a, b);
        relabel_par[b] = a;
    }
    f(relabel_par, original_vs2, index_ptr);
    for (const int i : std::views::iota(1, c)) {
        int l = index_ptr[i], r = index_ptr[i + 1];
        std::vector<int> par1(r - l, -1);
        std::vector<int> original_vs1(r - l, -1);
        for (int v : std::views::iota(l, r)) {
            par1[v - l] = (relabel_par[v] == 0 ? -1 : relabel_par[v] - l);
            original_vs1[v - l] = original_vs2[v];
        }
        centroid_decomposition_dfs_naive(par1, original_vs1, f);
    }
    return;
}

template <class F>
void one_third_centroid_decomposition(const std::vector<int> &par,
                                      const std::vector<int> &original_vs,
                                      F f) {
    const int n = (int)par.size();
    assert(n > 1);
    if (n == 2) return;
    int center = -1;
    std::vector<int> sz(n, 1);

    for (const int v : std::views::iota(0, n) | std::views::reverse) {
        if (sz[v] >= (n + 1) / 2) {
            center = v;
            break;
        }
        sz[par[v]] += sz[v];
    }

    std::vector<int> color(n, -1);
    std::vector<int> ord(n, -1);
    ord[center] = 0;
    int t = 1;
    int red = n - sz[center];
    for (int v = par[center]; v != -1; v = par[v]) {
        ord[v] = t++;
        color[v] = 0;
    }
    for (const int v : std::views::iota(1, n)) {
        if (par[v] == center && 3 * (red + sz[v]) <= 2 * (n - 1)) {
            red += sz[v];
            ord[v] = t++;
            color[v] = 0;
        }
    }
    for (const int v : std::views::iota(1, n)) {
        if (v != center && color[v] == -1 && color[par[v]] == 0) {
            ord[v] = t++;
            color[v] = 0;
        }
    }
    const int n0 = t - 1;
    for (const int v : std::views::iota(1, n)) {
        if (v != center && color[v] == -1) {
            ord[v] = t++;
            color[v] = 1;
        }
    }
    assert(t == n);
    const int n1 = n - 1 - n0;
    std::vector<int> par0(n0 + 1, -1), par1(n1 + 1, -1), par2(n, -1);
    std::vector<int> original_vs0(n0 + 1), original_vs1(n1 + 1),
        original_vs2(n);
    for (const int i : std::views::iota(0, n)) {
        int v = ord[i];
        original_vs2[v] = original_vs[i];
        if (color[i] != 1) {
            original_vs0[v] = original_vs[i];
        }
        if (color[i] != 0) {
            int idx = std::max(v - n0, 0);
            original_vs1[idx] = original_vs[i];
        }
    }
    for (const int v : std::views::iota(1, n)) {
        int a = ord[v], b = ord[par[v]];
        if (a > b) std::swap(a, b);
        par2[b] = a;
        if (color[v] != 1 && color[par[v]] != 1) {
            par0[b] = a;
        }
        if (color[v] != 0 && color[par[v]] != 0) {
            par1[b - n0] = std::max(a - n0, 0);
        }
    }
    f(par2, original_vs2, n0, n1);
    one_third_centroid_decomposition(par0, original_vs0, f);
    one_third_centroid_decomposition(par1, original_vs1, f);
    return;
}

template <class F>
void one_third_centroid_decomposition_virtual_real(
    const std::vector<int> &par, const std::vector<int> &original_vs,
    const std::vector<int> &is_real, F f) {
    const int n = (int)par.size();
    assert(n > 1);
    if (n == 2) {
        if (is_real[0] && is_real[1]) {
            f(par, original_vs, {0, 1});
        }
        return;
    }
    int center = -1;
    std::vector<int> sz(n, 1);

    for (const int v : std::views::iota(0, n) | std::views::reverse) {
        if (sz[v] >= (n + 1) / 2) {
            center = v;
            break;
        }
        sz[par[v]] += sz[v];
    }

    std::vector<int> color(n, -1);
    std::vector<int> ord(n, -1);
    ord[center] = 0;
    int t = 1;
    int red = n - sz[center];
    for (int v = par[center]; v != -1; v = par[v]) {
        ord[v] = t++;
        color[v] = 0;
    }
    for (const int v : std::views::iota(1, n)) {
        if (par[v] == center && 3 * (red + sz[v]) <= 2 * (n - 1)) {
            red += sz[v];
            ord[v] = t++;
            color[v] = 0;
        }
    }
    for (const int v : std::views::iota(1, n)) {
        if (v != center && color[v] == -1 && color[par[v]] == 0) {
            ord[v] = t++;
            color[v] = 0;
        }
    }
    const int n0 = t - 1;
    for (const int v : std::views::iota(1, n)) {
        if (v != center && color[v] == -1) {
            ord[v] = t++;
            color[v] = 1;
        }
    }
    assert(t == n);
    const int n1 = n - 1 - n0;
    std::vector<int> par0(n0 + 1, -1), par1(n1 + 1, -1), par2(n, -1);
    std::vector<int> original_vs0(n0 + 1), original_vs1(n1 + 1),
        original_vs2(n);
    std::vector<int> is_real0(n0 + 1), is_real1(n1 + 1), is_real2(n);
    for (const int i : std::views::iota(0, n)) {
        int v = ord[i];
        original_vs2[v] = original_vs[i];
        is_real2[v] = is_real[i];
        if (color[i] != 1) {
            original_vs0[v] = original_vs[i];
            is_real0[v] = is_real[i];
        }
        if (color[i] != 0) {
            int idx = std::max(v - n0, 0);
            original_vs1[idx] = original_vs[i];
            is_real1[idx] = is_real[i];
        }
    }
    for (const int v : std::views::iota(1, n)) {
        int a = ord[v], b = ord[par[v]];
        if (a > b) std::swap(a, b);
        par2[b] = a;
        if (color[v] != 1 && color[par[v]] != 1) {
            par0[b] = a;
        }
        if (color[v] != 0 && color[par[v]] != 0) {
            par1[b - n0] = std::max(a - n0, 0);
        }
    }
    if (is_real[center]) {
        color.assign(n, -1);
        color[0] = 0;
        for (const int v : std::views::iota(1, n)) {
            if (is_real2[v]) color[v] = 1;
        }
        f(par2, original_vs2, color);
        is_real0[0] = is_real1[0] = is_real2[0] = 0;
    }
    color.assign(n, -1);
    for (const int v : std::views::iota(1, n)) {
        if (is_real2[v]) {
            color[v] = int(v > n0);
        }
    }
    f(par2, original_vs2, color);
    one_third_centroid_decomposition_virtual_real(par0, original_vs0, is_real0,
                                                  f);
    one_third_centroid_decomposition_virtual_real(par1, original_vs1, is_real1,
                                                  f);
    return;
}

}  // namespace internal

template <int MODE, class T, class F>
void centroid_decomposition(const Graph<T> &tree, F f) {
    int n = (int)tree.size();
    if (n == 1) return;
    std::vector<int> bfs_order(n), par(n, -1);
    bfs_order[0] = 0;
    int l = 0, r = 1;
    while (l < r) {
        int v = bfs_order[l++];
        for (auto e : tree[v]) {
            int nv = e.to;
            if (nv == par[v]) continue;
            bfs_order[r++] = nv;
            par[nv] = v;
        }
    }
    assert(l == n && r == n);
    {
        std::vector<int> relabel(n);
        for (int i : std::views::iota(0, n)) {
            relabel[bfs_order[i]] = i;
        }
        std::vector<int> relabel_par(n, -1);
        for (int i : std::views::iota(1, n)) {
            relabel_par[relabel[i]] = relabel[par[i]];
        }
        std::swap(par, relabel_par);
    }
    static_assert(MODE == 0 || MODE == 1 || MODE == 2);
    if constexpr (MODE == 0) {
        internal::centroid_decomposition_dfs_naive(par, bfs_order, f);
    } else if constexpr (MODE == 1) {
        internal::one_third_centroid_decomposition(par, bfs_order, f);
    } else {
        internal::one_third_centroid_decomposition_virtual_real(
            par, bfs_order, std::vector<int>(n, 1), f);
    }
}

}  // namespace ebi
#line 10 "tree/contour_query_on_weighted_tree.hpp"

namespace ebi {

template <class T> struct contour_query_on_weighted_tree {
    contour_query_on_weighted_tree(const Graph<T> &tree) : n(int(tree.size())) {
        int t = 0;
        labels.resize(n);
        range = {0};
        std::vector<int> rev(n, -1);
        auto f = [&](const std::vector<int> &par, const std::vector<int> &vs,
                     const std::vector<int> &color) -> void {
            int sz = (int)par.size();
            std::vector<T> depth(sz, -1);
            depth[0] = 0;
            for (int i : std::views::iota(0, sz)) {
                rev[vs[i]] = i;
            }
            for (int i : std::views::iota(0, sz)) {
                int v = vs[i];
                for (auto e : tree[v]) {
                    if (rev[e.to] == -1) continue;
                    depth[rev[e.to]] = depth[rev[v]] + e.cost;
                }
                rev[v] = -1;
            }
            std::vector<int> red, blue;
            for (const int v : std::views::iota(0, sz)) {
                if (color[v] == 0) {
                    red.emplace_back(v);
                } else if (color[v] == 1) {
                    blue.emplace_back(v);
                } else {
                    assert(color[v] == -1);
                }
            }
            if (red.empty() || blue.empty()) return;

            auto update = [&](std::vector<int> &s) -> void {
                std::sort(s.begin(), s.end(), [&](int i, int j) -> bool {
                    return depth[i] < depth[j];
                });
                for (int i = 0; const int v : s) {
                    dist.emplace_back(depth[v]);
                    labels[vs[v]].emplace_back(t, i, depth[v]);
                    i++;
                }
                range.emplace_back(dist.size());
                t++;
            };
            update(red);
            update(blue);
        };
        centroid_decomposition<2>(tree, f);
    }

    std::size_t size() {
        return dist.size();
    }

    // [0, k)
    std::vector<std::pair<std::size_t, std::size_t>>
    get_range_less_than_k_from_v(int v, T k) const {
        std::vector<std::pair<std::size_t, std::size_t>> res;
        for (auto [t, i, d] : labels[v]) {
            t ^= 1;
            std::size_t id_l = range[t];
            std::size_t id_r =
                std::lower_bound(dist.begin() + range[t],
                                 dist.begin() + range[t + 1], k - d) -
                dist.begin();
            res.emplace_back(id_l, id_r);
        }
        return res;
    }

    // [k, infty)
    std::vector<std::pair<std::size_t, std::size_t>> get_range_k_or_more_from_v(
        int v, T k) const {
        std::vector<std::pair<std::size_t, std::size_t>> res;
        for (auto [t, i, d] : labels[v]) {
            t ^= 1;
            std::size_t id_l =
                std::lower_bound(dist.begin() + range[t],
                                 dist.begin() + range[t + 1], k - d) -
                dist.begin();
            std::size_t id_r = range[t + 1];
            res.emplace_back(id_l, id_r);
        }
        return res;
    }

    // [l, r)
    std::vector<std::pair<std::size_t, std::size_t>> get_contour_from_vertex(
        int v, T l, T r) const {
        std::vector<std::pair<std::size_t, std::size_t>> res;
        for (auto [t, i, d] : labels[v]) {
            t ^= 1;
            std::size_t id_l =
                std::lower_bound(dist.begin() + range[t],
                                 dist.begin() + range[t + 1], l - d) -
                dist.begin();
            std::size_t id_r =
                std::lower_bound(dist.begin() + range[t],
                                 dist.begin() + range[t + 1], r - d) -
                dist.begin();
            res.emplace_back(id_l, id_r);
        }
        return res;
    }

    std::vector<std::size_t> get_vertex(int v) const {
        assert(0 <= v && v < n);
        std::vector<std::size_t> res;
        for (auto [t, i, _] : labels[v]) {
            res.emplace_back(range[t] + i);
        }
        return res;
    }

    std::pair<int, int> sub_range(int i) const {
        return {range[i], range[i + 1]};
    }

  private:
    int n;
    std::vector<T> dist;
    std::vector<int> range;
    std::vector<std::vector<std::tuple<int, int, T>>> labels;
};

}  // namespace ebi
#line 8 "test/tree/Vertex_Add_Range_Contour_Sum_on_Tree_2.test.cpp"

namespace ebi {

i64 op(i64 a, i64 b) {
    return a + b;
}

i64 e() {
    return 0;
}

void main_() {
    int n, q;
    std::cin >> n >> q;
    std::vector<i64> a(n);
    std::cin >> a;
    Graph<int> g(n);
    g.read_tree(0);
    contour_query_on_weighted_tree cq(g);
    std::vector<i64> data(cq.size(), 0);
    rep(v, 0, n) {
        for (auto i : cq.get_vertex(v)) {
            data[i] += a[v];
        }
    }
    segtree<i64, op, e> seg(data);
    while (q--) {
        int type;
        std::cin >> type;
        if (type == 0) {
            int p;
            i64 x;
            std::cin >> p >> x;
            a[p] += x;
            for (auto i : cq.get_vertex(p)) {
                seg.set(i, seg.get(i) + x);
            }
        } else {
            int p, l, r;
            std::cin >> p >> l >> r;
            i64 ans = 0;
            if (l == 0) ans += a[p];
            for (auto [il, ir] : cq.get_contour_from_vertex(p, l, r)) {
                ans += seg.prod(il, ir);
            }
            std::cout << ans << '\n';
        }
    }
}

}  // namespace ebi

int main() {
    ebi::fast_io();
    int t = 1;
    // std::cin >> t;
    while (t--) {
        ebi::main_();
    }
    return 0;
}
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