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:heavy_check_mark: verify/graph/tree/vertex_add_range_contour_sum_on_tree.test.cpp

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Code

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

#include "../../../graph/tree/range_contour_query.hpp"
#include "../../../monoid/xor.hpp"

#include <cassert>
#include <cstdint>
#include "../../../utilities/fast_io.hpp"
#include <queue>
#include <vector>

namespace {

std::vector<std::vector<int>> distances(
    const m1une::graph::Graph<>& graph
) {
    const int n = graph.size();
    std::vector<std::vector<int>> result(n, std::vector<int>(n, -1));
    for (int start = 0; start < n; start++) {
        std::queue<int> queue;
        result[start][start] = 0;
        queue.push(start);
        while (!queue.empty()) {
            int vertex = queue.front();
            queue.pop();
            for (const auto& edge : graph[vertex]) {
                if (result[start][edge.to] != -1) continue;
                result[start][edge.to] = result[start][vertex] + 1;
                queue.push(edge.to);
            }
        }
    }
    return result;
}

void randomized_test() {
    std::uint64_t state = 311;
    auto random = [&state]() {
        state ^= state << 7;
        state ^= state >> 9;
        return state;
    };

    for (int trial = 0; trial < 250; trial++) {
        int n = int(random() % 20) + 1;
        m1une::graph::Graph<> graph(n);
        for (int vertex = 1; vertex < n; vertex++) {
            graph.add_edge(vertex, int(random() % std::uint64_t(vertex)));
        }
        auto distance = distances(graph);
        std::vector<long long> value(n);
        for (long long& element : value) {
            element = static_cast<long long>(random() % 21) - 10;
        }

        m1une::tree::VertexAddRangeContourSum<long long> contour(graph, value);
        assert(contour.size() == n);
        assert(!contour.empty());
        for (int query = 0; query < 250; query++) {
            int vertex = int(random() % std::uint64_t(n));
            int type = int(random() % 4);
            if (type == 0) {
                long long delta = static_cast<long long>(random() % 21) - 10;
                contour.add(vertex, delta);
                value[vertex] += delta;
            } else if (type == 1) {
                long long replacement =
                    static_cast<long long>(random() % 21) - 10;
                contour.set(vertex, replacement);
                value[vertex] = replacement;
            } else if (type == 2) {
                assert(contour.get(vertex) == value[vertex]);
            } else {
                int left = int(random() % std::uint64_t(n + 3));
                int right = int(random() % std::uint64_t(n + 3));
                if (right < left) std::swap(left, right);
                long long expected = 0;
                for (int other = 0; other < n; other++) {
                    if (left <= distance[vertex][other] &&
                        distance[vertex][other] < right) {
                        expected += value[other];
                    }
                }
                assert(contour.sum(vertex, left, right) == expected);
            }
        }
    }

    m1une::graph::Graph<> empty_graph;
    m1une::tree::VertexAddRangeContourSum<long long> empty(empty_graph);
    assert(empty.empty());
}

void xor_group_test() {
    std::uint64_t state = 733;
    auto random = [&state]() {
        state ^= state << 7;
        state ^= state >> 9;
        return state;
    };

    using Group = m1une::monoid::Xor<std::uint64_t>;
    for (int trial = 0; trial < 120; trial++) {
        int n = int(random() % 20) + 1;
        m1une::graph::Graph<> graph(n);
        for (int vertex = 1; vertex < n; vertex++) {
            graph.add_edge(vertex, int(random() % std::uint64_t(vertex)));
        }
        auto distance = distances(graph);
        std::vector<std::uint64_t> value(n);
        for (auto& element : value) element = random();

        m1une::tree::VertexApplyRangeContourProduct<Group> contour(
            graph,
            value
        );
        for (int query = 0; query < 150; query++) {
            int vertex = int(random() % std::uint64_t(n));
            if (random() & 1) {
                std::uint64_t update = random();
                contour.apply(vertex, update);
                value[vertex] ^= update;
            } else {
                int left = int(random() % std::uint64_t(n + 3));
                int right = int(random() % std::uint64_t(n + 3));
                if (right < left) std::swap(left, right);
                std::uint64_t expected = 0;
                for (int other = 0; other < n; other++) {
                    if (left <= distance[vertex][other] &&
                        distance[vertex][other] < right) {
                        expected ^= value[other];
                    }
                }
                assert(contour.prod(vertex, left, right) == expected);
            }
        }
    }
}

}  // namespace

int main() {
    m1une::utilities::FastInput fast_input;
    m1une::utilities::FastOutput fast_output;

    randomized_test();
    xor_group_test();
    int n, query_count;
    fast_input >> n >> query_count;
    std::vector<long long> initial(n);
    for (long long& value : initial) fast_input >> value;

    m1une::graph::Graph<> graph(n);
    for (int index = 0; index + 1 < n; index++) {
        int first, second;
        fast_input >> first >> second;
        graph.add_edge(first, second);
    }
    m1une::tree::VertexAddRangeContourSum<long long> contour(graph, initial);

    while (query_count--) {
        int type, vertex;
        fast_input >> type >> vertex;
        if (type == 0) {
            long long delta;
            fast_input >> delta;
            contour.add(vertex, delta);
        } else {
            int left, right;
            fast_input >> left >> right;
            fast_output << contour.sum(vertex, left, right) << '\n';
        }
    }
}
#line 1 "verify/graph/tree/vertex_add_range_contour_sum_on_tree.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/vertex_add_range_contour_sum_on_tree"

#line 1 "graph/tree/range_contour_query.hpp"



#include <algorithm>
#include <cassert>
#include <vector>

#line 1 "monoid/add.hpp"



namespace m1une {
namespace monoid {

// Monoid for addition (Range Sum).
template <typename T>
struct Add {
    using value_type = T;
    static constexpr bool commutative = true;

    // Returns the identity element for addition, which is 0.
    static constexpr T id() {
        return T(0);
    }

    // Returns the sum of a and b.
    static constexpr T op(const T& a, const T& b) {
        return a + b;
    }

    static constexpr T inv(const T& x) {
        return -x;
    }
};

}  // namespace monoid
}  // namespace m1une


#line 1 "monoid/concept.hpp"



#include <concepts>

namespace m1une {
namespace monoid {

// Concept to check if a type satisfies the requirements of a Monoid.
// A Monoid must have a `value_type`, an identity element `id()`, and an associative binary operation `op()`.
template <typename M>
concept IsMonoid = requires(typename M::value_type a, typename M::value_type b) {
    // 1. Must define `value_type`
    typename M::value_type;

    // 2. Must have a static method `id()` returning `value_type`
    { M::id() } -> std::same_as<typename M::value_type>;

    // 3. Must have a static method `op(a, b)` returning `value_type`
    { M::op(a, b) } -> std::same_as<typename M::value_type>;
};

// Concept for groups. A type satisfying this concept must also obey the group
// laws; concepts can check the interface but not the algebraic properties.
template <typename M>
concept IsGroup = IsMonoid<M> && requires(typename M::value_type a) {
    { M::inv(a) } -> std::same_as<typename M::value_type>;
};

// Concept for commutative groups. Commutativity is a semantic requirement and
// cannot be checked by a C++ concept.
template <typename M>
concept IsCommutativeGroup = IsGroup<M>;

}  // namespace monoid
}  // namespace m1une


#line 1 "graph/graph.hpp"



#include <array>
#line 6 "graph/graph.hpp"
#include <utility>
#line 8 "graph/graph.hpp"

namespace m1une {
namespace graph {

template <class T = int>
struct Edge {
    using cost_type = T;

    int from;
    int to;
    T cost;
    int id;
    bool alive;

    Edge() : from(-1), to(-1), cost(T()), id(-1), alive(true) {}
    Edge(int from_, int to_, T cost_ = T(1), int id_ = -1, bool alive_ = true)
        : from(from_), to(to_), cost(cost_), id(id_), alive(alive_) {}

    int other(int v) const {
        assert(v == from || v == to);
        return from ^ to ^ v;
    }
};

template <class T = int>
struct Graph {
    using edge_type = Edge<T>;
    using cost_type = T;

   private:
    struct EdgePositions {
        std::array<std::pair<int, int>, 2> value{};
        int size = 0;

        void push_back(std::pair<int, int> position) {
            assert(size < 2);
            value[size++] = position;
        }
    };

    int _n;
    int _edge_count;
    std::vector<std::vector<edge_type>> _g;
    std::vector<EdgePositions> _edge_positions;

   public:
    Graph() : _n(0), _edge_count(0) {}
    explicit Graph(int n) : _n(n), _edge_count(0), _g(n) {
        assert(0 <= n);
    }

    int size() const {
        return _n;
    }

    bool empty() const {
        return _n == 0;
    }

    int edge_count() const {
        return _edge_count;
    }

    int add_vertex() {
        _g.emplace_back();
        return _n++;
    }

    int add_directed_edge(int from, int to, T cost = T(1)) {
        assert(0 <= from && from < _n);
        assert(0 <= to && to < _n);
        int id = _edge_count++;
        int idx = int(_g[from].size());
        _g[from].push_back(edge_type(from, to, cost, id));
        _edge_positions.emplace_back();
        _edge_positions.back().push_back({from, idx});
        return id;
    }

    int add_edge(int u, int v, T cost = T(1)) {
        assert(0 <= u && u < _n);
        assert(0 <= v && v < _n);
        int id = _edge_count++;
        int u_idx = int(_g[u].size());
        _g[u].push_back(edge_type(u, v, cost, id));
        int v_idx = int(_g[v].size());
        _g[v].push_back(edge_type(v, u, cost, id));
        _edge_positions.emplace_back();
        _edge_positions.back().push_back({u, u_idx});
        _edge_positions.back().push_back({v, v_idx});
        return id;
    }

    void set_edge_alive(int id, bool alive) {
        assert(0 <= id && id < _edge_count);
        for (int i = 0; i < _edge_positions[id].size; ++i) {
            auto [v, idx] = _edge_positions[id].value[i];
            _g[v][idx].alive = alive;
        }
    }

    void erase_edge(int id) {
        set_edge_alive(id, false);
    }

    void revive_edge(int id) {
        set_edge_alive(id, true);
    }

    bool is_edge_alive(int id) const {
        assert(0 <= id && id < _edge_count);
        assert(_edge_positions[id].size != 0);
        auto [v, idx] = _edge_positions[id].value[0];
        return _g[v][idx].alive;
    }

    const std::vector<edge_type>& operator[](int v) const {
        assert(0 <= v && v < _n);
        return _g[v];
    }

    std::vector<edge_type>& operator[](int v) {
        assert(0 <= v && v < _n);
        return _g[v];
    }

    const std::vector<std::vector<edge_type>>& adjacency() const {
        return _g;
    }

    std::vector<std::vector<edge_type>>& adjacency() {
        return _g;
    }

    std::vector<edge_type> edges(bool include_inactive = false) const {
        std::vector<edge_type> result;
        result.reserve(_edge_count);
        std::vector<char> used(_edge_count, false);
        for (int v = 0; v < _n; v++) {
            for (const auto& e : _g[v]) {
                if (!include_inactive && !e.alive) continue;
                if (0 <= e.id && e.id < _edge_count) {
                    if (used[e.id]) continue;
                    used[e.id] = true;
                }
                result.push_back(e);
            }
        }
        return result;
    }

    Graph reversed() const {
        Graph result(_n);
        result._edge_count = _edge_count;
        result._edge_positions.assign(_edge_count, {});
        for (int v = 0; v < _n; v++) {
            for (const auto& e : _g[v]) {
                int idx = int(result._g[e.to].size());
                result._g[e.to].push_back(edge_type(e.to, e.from, e.cost, e.id, e.alive));
                if (0 <= e.id && e.id < _edge_count) result._edge_positions[e.id].push_back({e.to, idx});
            }
        }
        return result;
    }
};

}  // namespace graph
}  // namespace m1une


#line 1 "graph/tree/centroid_decomposition.hpp"



#line 6 "graph/tree/centroid_decomposition.hpp"

#line 8 "graph/tree/centroid_decomposition.hpp"

namespace m1une {
namespace tree {

template <class T = int>
struct CentroidDecomposition {
    int n;
    std::vector<int> parent;
    std::vector<int> depth;
    std::vector<int> order;
    std::vector<int> roots;
    std::vector<std::vector<int>> children;

   private:
    std::vector<int> _subtree_size;
    std::vector<int> _work_parent;
    std::vector<char> _removed;

    void build_component(const m1une::graph::Graph<T>& g, int start, int p, int d) {
        std::vector<int> nodes;
        std::vector<int> stack = {start};
        _work_parent[start] = -2;
        while (!stack.empty()) {
            int v = stack.back();
            stack.pop_back();
            nodes.push_back(v);
            for (const auto& e : g[v]) {
                if (!e.alive || _removed[e.to]) continue;
                if (_work_parent[e.to] != -1) continue;
                _work_parent[e.to] = v;
                stack.push_back(e.to);
            }
        }

        for (int v : nodes) _subtree_size[v] = 1;
        for (int i = int(nodes.size()) - 1; i >= 0; i--) {
            int v = nodes[i];
            if (_work_parent[v] >= 0) _subtree_size[_work_parent[v]] += _subtree_size[v];
        }

        int total = int(nodes.size());
        int centroid = start;
        int best = total + 1;
        for (int v : nodes) {
            int largest = total - _subtree_size[v];
            for (const auto& e : g[v]) {
                if (!e.alive || _removed[e.to]) continue;
                if (_work_parent[e.to] == v) largest = std::max(largest, _subtree_size[e.to]);
            }
            if (largest < best) {
                best = largest;
                centroid = v;
            }
        }

        for (int v : nodes) _work_parent[v] = -1;

        parent[centroid] = p;
        depth[centroid] = d;
        order.push_back(centroid);
        if (p == -1) {
            roots.push_back(centroid);
        } else {
            children[p].push_back(centroid);
        }
        _removed[centroid] = true;

        for (const auto& e : g[centroid]) {
            if (!e.alive || _removed[e.to]) continue;
            build_component(g, e.to, centroid, d + 1);
        }
    }

   public:
    CentroidDecomposition() : n(0) {}
    explicit CentroidDecomposition(const m1une::graph::Graph<T>& g) {
        build(g);
    }

    void build(const m1une::graph::Graph<T>& g) {
        n = g.size();
        parent.assign(n, -1);
        depth.assign(n, -1);
        order.clear();
        order.reserve(n);
        roots.clear();
        children.assign(n, {});
        _subtree_size.assign(n, 0);
        _work_parent.assign(n, -1);
        _removed.assign(n, false);

        for (int v = 0; v < n; v++) {
            if (depth[v] == -1) build_component(g, v, -1, 0);
        }
    }

    int size() const {
        return n;
    }

    bool empty() const {
        return n == 0;
    }

    int root() const {
        return roots.empty() ? -1 : roots[0];
    }
};

}  // namespace tree
}  // namespace m1une


#line 1 "graph/tree/rooted_tree.hpp"



#line 7 "graph/tree/rooted_tree.hpp"

#line 9 "graph/tree/rooted_tree.hpp"

namespace m1une {
namespace tree {

template <class T = int>
struct RootedTree {
    using cost_type = T;
    using edge_type = m1une::graph::Edge<T>;

    int root;
    std::vector<int> parent;
    std::vector<int> parent_edge;
    std::vector<int> depth;
    std::vector<T> dist;
    std::vector<int> subtree_size;
    std::vector<int> tin;
    std::vector<int> tout;
    std::vector<int> order;
    std::vector<std::vector<int>> up;

   private:
    int _n;
    int _log;

    void check_vertex(int v) const {
        assert(0 <= v && v < _n);
        assert(tin[v] != -1);
    }

   public:
    RootedTree() : root(-1), _n(0), _log(0) {}
    explicit RootedTree(const m1une::graph::Graph<T>& g, int root_ = 0) {
        build(g, root_);
    }

    void build(const m1une::graph::Graph<T>& g, int root_ = 0) {
        _n = g.size();
        root = _n == 0 ? -1 : root_;
        _log = 1;
        while ((1U << _log) <= (unsigned int)(std::max(1, _n))) _log++;

        parent.assign(_n, -1);
        parent_edge.assign(_n, -1);
        depth.assign(_n, 0);
        dist.assign(_n, T(0));
        subtree_size.assign(_n, 0);
        tin.assign(_n, -1);
        tout.assign(_n, -1);
        order.clear();
        order.reserve(_n);
        up.assign(_log, std::vector<int>(_n, -1));

        if (_n == 0) return;
        assert(0 <= root && root < _n);

        struct Frame {
            int v;
            int state;
        };

        std::vector<char> visited(_n, false);
        std::vector<Frame> stack;
        stack.push_back({root, 0});
        visited[root] = true;
        int timer = 0;

        while (!stack.empty()) {
            Frame frame = stack.back();
            stack.pop_back();
            int v = frame.v;
            if (frame.state == 0) {
                tin[v] = timer++;
                order.push_back(v);
                up[0][v] = parent[v];
                for (int k = 1; k < _log; k++) {
                    int p = up[k - 1][v];
                    up[k][v] = p == -1 ? -1 : up[k - 1][p];
                }

                stack.push_back({v, 1});
                const auto& adj = g[v];
                for (int i = int(adj.size()) - 1; i >= 0; i--) {
                    const auto& e = adj[i];
                    if (!e.alive) continue;
                    if (visited[e.to]) continue;
                    visited[e.to] = true;
                    parent[e.to] = v;
                    parent_edge[e.to] = e.id;
                    depth[e.to] = depth[v] + 1;
                    dist[e.to] = dist[v] + e.cost;
                    stack.push_back({e.to, 0});
                }
            } else {
                subtree_size[v]++;
                if (parent[v] != -1) subtree_size[parent[v]] += subtree_size[v];
                tout[v] = timer;
            }
        }
    }

    int size() const {
        return _n;
    }

    bool empty() const {
        return _n == 0;
    }

    int log() const {
        return _log;
    }

    bool is_ancestor(int u, int v) const {
        check_vertex(u);
        check_vertex(v);
        return tin[u] <= tin[v] && tout[v] <= tout[u];
    }

    bool in_subtree(int v, int u) const {
        return is_ancestor(u, v);
    }

    int kth_ancestor(int v, int k) const {
        check_vertex(v);
        assert(0 <= k);
        int bit = 0;
        while (k > 0 && v != -1) {
            if (k & 1) {
                if (_log <= bit) return -1;
                v = up[bit][v];
            }
            k >>= 1;
            bit++;
        }
        return v;
    }

    int lca(int u, int v) const {
        check_vertex(u);
        check_vertex(v);
        if (depth[u] < depth[v]) std::swap(u, v);
        u = kth_ancestor(u, depth[u] - depth[v]);
        if (u == v) return u;
        for (int k = _log - 1; k >= 0; k--) {
            if (up[k][u] != up[k][v]) {
                u = up[k][u];
                v = up[k][v];
            }
        }
        return parent[u];
    }

    int dist_edges(int u, int v) const {
        int w = lca(u, v);
        return depth[u] + depth[v] - 2 * depth[w];
    }

    T dist_cost(int u, int v) const {
        int w = lca(u, v);
        return dist[u] + dist[v] - dist[w] - dist[w];
    }

    int jump(int from, int to, int k) const {
        check_vertex(from);
        check_vertex(to);
        assert(0 <= k);
        int w = lca(from, to);
        int up_len = depth[from] - depth[w];
        int down_len = depth[to] - depth[w];
        if (up_len + down_len < k) return -1;
        if (k <= up_len) return kth_ancestor(from, k);
        return kth_ancestor(to, down_len - (k - up_len));
    }

    std::vector<int> path(int u, int v) const {
        check_vertex(u);
        check_vertex(v);
        int w = lca(u, v);
        std::vector<int> a, b;
        for (int x = u; x != w; x = parent[x]) a.push_back(x);
        a.push_back(w);
        for (int x = v; x != w; x = parent[x]) b.push_back(x);
        std::reverse(b.begin(), b.end());
        a.insert(a.end(), b.begin(), b.end());
        return a;
    }

    std::vector<int> path_edges(int u, int v) const {
        check_vertex(u);
        check_vertex(v);
        int w = lca(u, v);
        std::vector<int> a, b;
        for (int x = u; x != w; x = parent[x]) a.push_back(parent_edge[x]);
        for (int x = v; x != w; x = parent[x]) b.push_back(parent_edge[x]);
        std::reverse(b.begin(), b.end());
        a.insert(a.end(), b.begin(), b.end());
        return a;
    }

    std::pair<int, int> subtree_range(int v) const {
        check_vertex(v);
        return {tin[v], tout[v]};
    }

    std::vector<int> subtree_vertices(int v) const {
        check_vertex(v);
        return std::vector<int>(order.begin() + tin[v], order.begin() + tout[v]);
    }
};

}  // namespace tree
}  // namespace m1une


#line 13 "graph/tree/range_contour_query.hpp"

namespace m1une {
namespace tree {

namespace internal {

struct RangeContourPathEntry {
    int centroid;
    int distance;
    int subtree;
};

struct RangeContourLayout {
    int n = 0;
    std::vector<std::vector<RangeContourPathEntry>> path;
    std::vector<int> all_size;
    std::vector<int> subtree_size;

    template <class EdgeCost>
    void build(const m1une::graph::Graph<EdgeCost>& graph) {
        n = graph.size();
        path.assign(n, {});
        all_size.assign(n, 0);
        subtree_size.assign(n, 0);
        if (n == 0) return;

#ifndef NDEBUG
        std::vector<int> incidence(graph.edge_count(), 0);
        for (int vertex = 0; vertex < n; vertex++) {
            for (const auto& edge : graph[vertex]) {
                if (!edge.alive) continue;
                assert(0 <= edge.id && edge.id < graph.edge_count());
                incidence[edge.id]++;
            }
        }
        int active_edges = 0;
        for (int count : incidence) {
            if (count == 0) continue;
            assert(count == 2);
            active_edges++;
        }
        assert(active_edges == n - 1);
#endif

        RootedTree<EdgeCost> rooted(graph, 0);
        assert(int(rooted.order.size()) == n);
        CentroidDecomposition<EdgeCost> decomposition(graph);

        for (int vertex = 0; vertex < n; vertex++) {
            int previous = -1;
            for (
                int centroid = vertex;
                centroid != -1;
                centroid = decomposition.parent[centroid]
            ) {
                int distance = rooted.dist_edges(vertex, centroid);
                path[vertex].push_back(
                    RangeContourPathEntry{centroid, distance, previous}
                );
                all_size[centroid] = std::max(
                    all_size[centroid],
                    distance + 1
                );
                if (previous != -1) {
                    subtree_size[previous] = std::max(
                        subtree_size[previous],
                        distance + 1
                    );
                }
                previous = centroid;
            }
        }
    }
};

template <m1une::monoid::IsCommutativeGroup Group>
class RangeContourFenwick {
   public:
    using T = typename Group::value_type;

   private:
    int _n = 0;
    std::vector<T> _data;

    T prefix_product(int right) const {
        T result = Group::id();
        while (right > 0) {
            result = Group::op(result, _data[right]);
            right -= right & -right;
        }
        return result;
    }

   public:
    RangeContourFenwick() : _data(1, Group::id()) {}

    explicit RangeContourFenwick(int n)
        : _n(n), _data(n + 1, Group::id()) {
        assert(0 <= n);
    }

    int size() const {
        return _n;
    }

    void apply(int index, const T& value) {
        assert(0 <= index && index < _n);
        for (index++; index <= _n; index += index & -index) {
            _data[index] = Group::op(_data[index], value);
        }
    }

    T product(int left, int right) const {
        left = std::max(left, 0);
        right = std::min(right, _n);
        if (right <= left) return Group::id();
        return Group::op(
            Group::inv(prefix_product(left)),
            prefix_product(right)
        );
    }

    void range_apply(int left, int right, const T& value) {
        left = std::max(left, 0);
        right = std::min(right, _n);
        if (right <= left) return;
        apply(left, value);
        if (right < _n) apply(right, Group::inv(value));
    }

    T get(int index) const {
        assert(0 <= index && index < _n);
        return prefix_product(index + 1);
    }
};

}  // namespace internal

template <m1une::monoid::IsCommutativeGroup Group>
class VertexApplyRangeContourProduct {
   public:
    using T = typename Group::value_type;

   private:
    internal::RangeContourLayout _layout;
    std::vector<T> _value;
    std::vector<internal::RangeContourFenwick<Group>> _all;
    std::vector<internal::RangeContourFenwick<Group>> _subtree;

    void check_vertex(int vertex) const {
        assert(0 <= vertex && vertex < size());
    }

   public:
    VertexApplyRangeContourProduct() = default;

    template <class EdgeCost>
    explicit VertexApplyRangeContourProduct(
        const m1une::graph::Graph<EdgeCost>& graph,
        const std::vector<T>& initial = {}
    ) {
        build(graph, initial);
    }

    template <class EdgeCost>
    void build(
        const m1une::graph::Graph<EdgeCost>& graph,
        const std::vector<T>& initial = {}
    ) {
        assert(initial.empty() || int(initial.size()) == graph.size());
        _layout.build(graph);
        const int n = _layout.n;
        _value.assign(n, Group::id());
        _all.assign(n, internal::RangeContourFenwick<Group>());
        _subtree.assign(n, internal::RangeContourFenwick<Group>());
        for (int index = 0; index < n; index++) {
            _all[index] =
                internal::RangeContourFenwick<Group>(_layout.all_size[index]);
            _subtree[index] =
                internal::RangeContourFenwick<Group>(
                    _layout.subtree_size[index]
                );
        }
        if (!initial.empty()) {
            for (int vertex = 0; vertex < n; vertex++) {
                apply(vertex, initial[vertex]);
            }
        }
    }

    int size() const {
        return _layout.n;
    }

    bool empty() const {
        return size() == 0;
    }

    T get(int vertex) const {
        check_vertex(vertex);
        return _value[vertex];
    }

    void apply(int vertex, const T& value) {
        check_vertex(vertex);
        _value[vertex] = Group::op(_value[vertex], value);
        for (const auto& entry : _layout.path[vertex]) {
            _all[entry.centroid].apply(entry.distance, value);
            if (entry.subtree != -1) {
                _subtree[entry.subtree].apply(entry.distance, value);
            }
        }
    }

    void set(int vertex, const T& value) {
        check_vertex(vertex);
        apply(vertex, Group::op(Group::inv(_value[vertex]), value));
    }

    T prod(int vertex, int left_distance, int right_distance) const {
        check_vertex(vertex);
        assert(0 <= left_distance && left_distance <= right_distance);
        T result = Group::id();
        for (const auto& entry : _layout.path[vertex]) {
            int left = left_distance - entry.distance;
            int right = right_distance - entry.distance;
            result = Group::op(
                result,
                _all[entry.centroid].product(left, right)
            );
            if (entry.subtree != -1) {
                result = Group::op(
                    result,
                    Group::inv(
                        _subtree[entry.subtree].product(left, right)
                    )
                );
            }
        }
        return result;
    }
};

template <m1une::monoid::IsCommutativeGroup Group>
class VertexGetRangeContourApply {
   public:
    using T = typename Group::value_type;

   private:
    internal::RangeContourLayout _layout;
    std::vector<T> _base;
    std::vector<internal::RangeContourFenwick<Group>> _all;
    std::vector<internal::RangeContourFenwick<Group>> _subtree;

    void check_vertex(int vertex) const {
        assert(0 <= vertex && vertex < size());
    }

   public:
    VertexGetRangeContourApply() = default;

    template <class EdgeCost>
    explicit VertexGetRangeContourApply(
        const m1une::graph::Graph<EdgeCost>& graph,
        const std::vector<T>& initial = {}
    ) {
        build(graph, initial);
    }

    template <class EdgeCost>
    void build(
        const m1une::graph::Graph<EdgeCost>& graph,
        const std::vector<T>& initial = {}
    ) {
        assert(initial.empty() || int(initial.size()) == graph.size());
        _layout.build(graph);
        const int n = _layout.n;
        _base = initial.empty() ? std::vector<T>(n, Group::id()) : initial;
        _all.assign(n, internal::RangeContourFenwick<Group>());
        _subtree.assign(n, internal::RangeContourFenwick<Group>());
        for (int index = 0; index < n; index++) {
            _all[index] =
                internal::RangeContourFenwick<Group>(_layout.all_size[index]);
            _subtree[index] =
                internal::RangeContourFenwick<Group>(
                    _layout.subtree_size[index]
                );
        }
    }

    int size() const {
        return _layout.n;
    }

    bool empty() const {
        return size() == 0;
    }

    T get(int vertex) const {
        check_vertex(vertex);
        T result = _base[vertex];
        for (const auto& entry : _layout.path[vertex]) {
            result = Group::op(
                result,
                _all[entry.centroid].get(entry.distance)
            );
            if (entry.subtree != -1) {
                result = Group::op(
                    result,
                    Group::inv(
                        _subtree[entry.subtree].get(entry.distance)
                    )
                );
            }
        }
        return result;
    }

    void point_apply(int vertex, const T& value) {
        check_vertex(vertex);
        _base[vertex] = Group::op(_base[vertex], value);
    }

    void set(int vertex, const T& value) {
        check_vertex(vertex);
        _base[vertex] = Group::op(
            _base[vertex],
            Group::op(Group::inv(get(vertex)), value)
        );
    }

    void apply(
        int vertex,
        int left_distance,
        int right_distance,
        const T& value
    ) {
        check_vertex(vertex);
        assert(0 <= left_distance && left_distance <= right_distance);
        for (const auto& entry : _layout.path[vertex]) {
            int left = left_distance - entry.distance;
            int right = right_distance - entry.distance;
            _all[entry.centroid].range_apply(left, right, value);
            if (entry.subtree != -1) {
                _subtree[entry.subtree].range_apply(left, right, value);
            }
        }
    }
};

template <class T>
class VertexAddRangeContourSum
    : public VertexApplyRangeContourProduct<m1une::monoid::Add<T>> {
   private:
    using Base = VertexApplyRangeContourProduct<m1une::monoid::Add<T>>;

   public:
    using Base::Base;

    void add(int vertex, const T& delta) {
        Base::apply(vertex, delta);
    }

    T sum(int vertex, int left_distance, int right_distance) const {
        return Base::prod(vertex, left_distance, right_distance);
    }
};

template <class T>
class VertexGetRangeContourAdd
    : public VertexGetRangeContourApply<m1une::monoid::Add<T>> {
   private:
    using Base = VertexGetRangeContourApply<m1une::monoid::Add<T>>;

   public:
    using Base::Base;

    void add(int vertex, const T& delta) {
        Base::point_apply(vertex, delta);
    }
};

}  // namespace tree
}  // namespace m1une


#line 1 "monoid/xor.hpp"



namespace m1une {
namespace monoid {

// Monoid for bitwise XOR (Range XOR).
template <typename T>
struct Xor {
    using value_type = T;
    static constexpr bool commutative = true;

    // Returns the identity element for bitwise XOR, which is 0.
    static constexpr T id() {
        return T(0);
    }

    // Returns the bitwise XOR of a and b.
    static constexpr T op(const T& a, const T& b) {
        return a ^ b;
    }

    static constexpr T inv(const T& x) {
        return x;
    }
};

}  // namespace monoid
}  // namespace m1une


#line 5 "verify/graph/tree/vertex_add_range_contour_sum_on_tree.test.cpp"

#line 7 "verify/graph/tree/vertex_add_range_contour_sum_on_tree.test.cpp"
#include <cstdint>
#line 1 "utilities/fast_io.hpp"



#line 6 "utilities/fast_io.hpp"
#include <cerrno>
#include <charconv>
#include <cstddef>
#include <cstdio>
#include <cstdlib>
#line 12 "utilities/fast_io.hpp"
#include <cstring>
#include <iterator>
#include <string>
#include <sys/stat.h>
#include <type_traits>
#line 18 "utilities/fast_io.hpp"
#include <unistd.h>
#line 20 "utilities/fast_io.hpp"

namespace m1une {
namespace utilities {

struct FastOutput;

namespace internal {

// Shared with the convenience helpers in template.hpp.
inline FastOutput* standard_output_instance = nullptr;

// Detect std::begin(x), std::end(x).
template <class T, class = void>
struct is_range : std::false_type {};

template <class T>
struct is_range<T, std::void_t<
    decltype(std::begin(std::declval<T&>())),
    decltype(std::end(std::declval<T&>()))
>> : std::true_type {};

template <class T>
inline constexpr bool is_range_v = is_range<T>::value;

template <class T>
using range_reference_t = decltype(*std::begin(std::declval<T&>()));

template <class T>
using range_value_t = std::remove_cv_t<std::remove_reference_t<range_reference_t<T>>>;

template <class T, class = void>
struct range_stored_value {
    using type = range_value_t<T>;
};

template <class T>
struct range_stored_value<T, std::void_t<typename std::remove_cv_t<std::remove_reference_t<T>>::value_type>> {
    using type = typename std::remove_cv_t<std::remove_reference_t<T>>::value_type;
};

template <class T>
using range_stored_value_t = typename range_stored_value<T>::type;

// Treat strings and C strings as scalar output objects, not as ranges.
template <class T>
struct is_char_array : std::false_type {};

template <class T, std::size_t N>
struct is_char_array<T[N]>
    : std::bool_constant<std::is_same_v<std::remove_cv_t<T>, char>> {};

template <class T>
struct is_string_like
    : std::bool_constant<
          std::is_same_v<std::decay_t<T>, std::string>
          || std::is_same_v<std::decay_t<T>, const char*>
          || std::is_same_v<std::decay_t<T>, char*>
          || is_char_array<std::remove_reference_t<T>>::value
      > {};

template <class T>
inline constexpr bool is_string_like_v = is_string_like<T>::value;

// ModInt-like type: x.val() is printable, and x can be assigned from long long.
template <class T, class = void>
struct has_val_method : std::false_type {};

template <class T>
struct has_val_method<T, std::void_t<decltype(std::declval<const T&>().val())>>
    : std::true_type {};

template <class T>
inline constexpr bool has_val_method_v = has_val_method<T>::value;

template <class T, class = void>
struct has_static_mod_raw : std::false_type {};

template <class T>
struct has_static_mod_raw<
    T, std::void_t<decltype(T::mod()), decltype(T::raw(std::declval<uint32_t>()))>>
    : std::true_type {};

template <class T>
inline constexpr bool has_static_mod_raw_v = has_static_mod_raw<T>::value;

// libstdc++ before GCC 16 does not classify __int128 as an integral type in
// strict ISO modes such as -std=c++23. Keep the fast-I/O interface independent
// of that implementation detail.
template <class T>
inline constexpr bool is_integral_v =
    std::is_integral_v<T>
    || std::is_same_v<std::remove_cv_t<T>, __int128_t>
    || std::is_same_v<std::remove_cv_t<T>, __uint128_t>;

template <class T>
inline constexpr bool is_signed_v =
    std::is_signed_v<T>
    || std::is_same_v<std::remove_cv_t<T>, __int128_t>;

template <class T>
struct make_unsigned {
    using type = std::make_unsigned_t<T>;
};

template <>
struct make_unsigned<__int128_t> {
    using type = __uint128_t;
};

template <>
struct make_unsigned<__uint128_t> {
    using type = __uint128_t;
};

template <class T>
using make_unsigned_t = typename make_unsigned<std::remove_cv_t<T>>::type;

}  // namespace internal

struct FastInput {
    static constexpr int buffer_size = 1 << 20;

   private:
    std::FILE* _stream;
    char _buffer[buffer_size];
    int _position;
    int _length;
    int _file_descriptor;
    bool _streaming;

    bool refill() {
        _position = 0;
        if (_streaming) {
            ssize_t length;
            do {
                length = ::read(_file_descriptor, _buffer, buffer_size);
            } while (length < 0 && errno == EINTR);
            if (length <= 0) {
                _length = 0;
                return false;
            }
            _length = int(length);
        } else {
            _length = int(std::fread(_buffer, 1, buffer_size, _stream));
        }
        return _length != 0;
    }

    template <class T>
    bool read_integer_from_stream(T& value) {
        if (!skip_spaces()) return false;
        int c = read_char_raw();

        bool negative = false;
        if (c == '-') {
            negative = true;
            c = read_char_raw();
        }

        if constexpr (internal::is_signed_v<T>) {
            T result = 0;
            while ('0' <= c && c <= '9') {
                result = negative ? result * 10 - (c - '0')
                                  : result * 10 + (c - '0');
                c = read_char_raw();
            }
            value = result;
        } else {
            T result = 0;
            while ('0' <= c && c <= '9') {
                result = result * 10 + T(c - '0');
                c = read_char_raw();
            }
            value = negative ? T(0) - result : result;
        }
        return true;
    }

    bool prepare_number() {
        if (_length - _position >= 64) return true;
        const int remaining = _length - _position;
        if (remaining > 0) std::memmove(_buffer, _buffer + _position, remaining);
        const int added = int(std::fread(_buffer + remaining, 1, buffer_size - remaining, _stream));
        _position = 0;
        _length = remaining + added;
        if (_length < buffer_size) _buffer[_length] = '\0';
        return _length != 0;
    }

   public:
    explicit FastInput(std::FILE* stream = stdin)
        : _stream(stream),
          _position(0),
          _length(0),
          _file_descriptor(::fileno(stream)),
          _streaming([&] {
              struct stat status;
              return _file_descriptor >= 0
                     && ::fstat(_file_descriptor, &status) == 0
                     && !S_ISREG(status.st_mode);
          }()) {}

    FastInput(const FastInput&) = delete;
    FastInput& operator=(const FastInput&) = delete;

    int read_char_raw() {
        if (_position == _length && !refill()) return EOF;
        return _buffer[_position++];
    }

    bool skip_spaces() {
        int c = read_char_raw();
        while (c != EOF && c <= ' ') c = read_char_raw();
        if (c == EOF) return false;
        --_position;
        return true;
    }

    bool read(char& value) {
        if (!skip_spaces()) return false;
        value = char(read_char_raw());
        return true;
    }

    bool read(std::string& value) {
        if (!skip_spaces()) return false;
        value.clear();
        while (true) {
            const int begin = _position;
            while (_position < _length &&
                   static_cast<unsigned char>(_buffer[_position]) > ' ') {
                ++_position;
            }
            value.append(_buffer + begin, _position - begin);
            if (_position < _length) {
                ++_position;
                return true;
            }
            if (!refill()) return true;
        }
    }

    bool read(bool& value) {
        int x;
        if (!read(x)) return false;
        value = x != 0;
        return true;
    }

    template <class T>
    std::enable_if_t<
        internal::is_integral_v<T>
            && !std::is_same_v<std::remove_cv_t<T>, bool>
            && !std::is_same_v<std::remove_cv_t<T>, char>,
        bool
    >
    read(T& value) {
        if (_streaming) return read_integer_from_stream(value);
        if (!prepare_number()) return false;
        int c = static_cast<unsigned char>(_buffer[_position++]);
        while (c <= ' ') c = static_cast<unsigned char>(_buffer[_position++]);

        bool negative = false;
        if (c == '-') {
            negative = true;
            c = static_cast<unsigned char>(_buffer[_position++]);
        }

        if constexpr (internal::is_signed_v<T>) {
            T result = 0;
            while ('0' <= c && c <= '9') {
                const int first = c - '0';
                const int second = static_cast<unsigned char>(_buffer[_position]) - '0';
                if (0 <= second && second <= 9) {
                    result = negative ? result * 100 - (first * 10 + second)
                                      : result * 100 + (first * 10 + second);
                    ++_position;
                } else {
                    result = negative ? result * 10 - first : result * 10 + first;
                }
                c = static_cast<unsigned char>(_buffer[_position++]);
            }
            value = result;
        } else {
            T result = 0;
            while ('0' <= c && c <= '9') {
                const unsigned first = unsigned(c - '0');
                const int second = static_cast<unsigned char>(_buffer[_position]) - '0';
                if (0 <= second && second <= 9) {
                    result = result * 100 + T(first * 10 + unsigned(second));
                    ++_position;
                } else {
                    result = result * 10 + T(first);
                }
                c = static_cast<unsigned char>(_buffer[_position++]);
            }
            value = negative ? T(0) - result : result;
        }
        if (_position > _length) _position = _length;
        return true;
    }

    template <class T>
    std::enable_if_t<std::is_floating_point_v<T>, bool>
    read(T& value) {
        if (!skip_spaces()) return false;
        int c = read_char_raw();
        bool negative = false;
        if (c == '-' || c == '+') {
            negative = c == '-';
            c = read_char_raw();
        }

        long double result = 0;
        while ('0' <= c && c <= '9') {
            result = result * 10 + (c - '0');
            c = read_char_raw();
        }
        if (c == '.') {
            long double place = 0.1L;
            c = read_char_raw();
            while ('0' <= c && c <= '9') {
                result += (c - '0') * place;
                place *= 0.1L;
                c = read_char_raw();
            }
        }
        if (c == 'e' || c == 'E') {
            c = read_char_raw();
            bool exponent_negative = false;
            if (c == '-' || c == '+') {
                exponent_negative = c == '-';
                c = read_char_raw();
            }
            int exponent = 0;
            while ('0' <= c && c <= '9') {
                exponent = exponent * 10 + (c - '0');
                c = read_char_raw();
            }
            long double scale = 1;
            long double power = 10;
            while (exponent > 0) {
                if (exponent & 1) scale *= power;
                power *= power;
                exponent >>= 1;
            }
            result = exponent_negative ? result / scale : result * scale;
        }
        value = static_cast<T>(negative ? -result : result);
        return true;
    }

    template <class T>
    std::enable_if_t<
        internal::has_val_method_v<T>
            && !internal::is_integral_v<T>
            && !internal::is_range_v<T>,
        bool
    >
    read(T& value) {
        long long x;
        if (!read(x)) return false;
        if constexpr (internal::has_static_mod_raw_v<T>) {
            if (x >= 0 && uint64_t(x) < uint64_t(T::mod())) {
                value = T::raw(uint32_t(x));
            } else {
                value = T(x);
            }
        } else {
            value = T(x);
        }
        return true;
    }

    template <class First, class Second>
    bool read(std::pair<First, Second>& value) {
        if (!read(value.first)) return false;
        return read(value.second);
    }

    template <class Range>
    std::enable_if_t<
        internal::is_range_v<Range>
            && !internal::is_string_like_v<Range>,
        bool
    >
    read(Range& range) {
        using StoredValue = internal::range_stored_value_t<Range>;
        constexpr bool nested = internal::is_range_v<StoredValue>
                                && !internal::is_string_like_v<StoredValue>;

        for (auto&& value : range) {
            if constexpr (std::is_same_v<StoredValue, bool> && !nested) {
                bool x;
                if (!read(x)) return false;
                value = x;
            } else {
                if (!read(value)) return false;
            }
        }
        return true;
    }

    template <class First, class Second, class... Rest>
    bool read(First& first, Second& second, Rest&... rest) {
        if (!read(first)) return false;
        return read(second, rest...);
    }

    template <class T>
    FastInput& operator>>(T& value) {
        if (!read(value)) std::abort();
        return *this;
    }
};

struct FastOutput {
    static constexpr int buffer_size = 1 << 20;

   private:
    inline static const auto digit_quads = [] {
        std::array<char, 40000> result{};
        for (int i = 0; i < 10000; i++) {
            int value = i;
            for (int j = 3; j >= 0; j--) {
                result[4 * i + j] = char('0' + value % 10);
                value /= 10;
            }
        }
        return result;
    }();

    std::FILE* _stream;
    char _buffer[buffer_size];
    int _position;
    int _precision;
    std::chars_format _float_format;
    char _range_separator;
    std::string* _capture = nullptr;

    template <class T>
    std::string format_cell(const T& value) {
        std::string result;
        struct CaptureGuard {
            std::string*& target;
            std::string* previous;
            ~CaptureGuard() { target = previous; }
        } guard{_capture, _capture};
        _capture = &result;
        write(value);
        return result;
    }

    template <class Matrix>
    void write_aligned_matrix(const Matrix& matrix) {
        std::vector<std::vector<std::string>> rows;
        std::vector<std::size_t> widths;
        for (const auto& row : matrix) {
            auto& cells = rows.emplace_back();
            std::size_t column = 0;
            for (const auto& value : row) {
                cells.push_back(format_cell(value));
                if (column == widths.size()) widths.push_back(0);
                widths[column] = std::max(widths[column], cells.back().size());
                ++column;
            }
        }
        bool first = true;
        for (const auto& row : rows) {
            if (!first) write_char('\n');
            first = false;
            for (std::size_t column = 0; column < row.size(); ++column) {
                if (column != 0) write_char(_range_separator);
                for (std::size_t padding = row[column].size();
                     padding < widths[column]; ++padding) {
                    write_char(' ');
                }
                write(row[column]);
            }
        }
    }

   public:
    explicit FastOutput(std::FILE* stream = stdout)
        : _stream(stream),
          _position(0),
          _precision(6),
          _float_format(std::chars_format::general),
          _range_separator(' ') {
        if (_stream == stdout
            && internal::standard_output_instance == nullptr) {
            internal::standard_output_instance = this;
        }
    }

    FastOutput(const FastOutput&) = delete;
    FastOutput& operator=(const FastOutput&) = delete;

    ~FastOutput() {
        flush();
        if (internal::standard_output_instance == this) {
            internal::standard_output_instance = nullptr;
        }
    }

    void flush() {
        if (_position != 0) {
            std::fwrite(_buffer, 1, _position, _stream);
            _position = 0;
        }
        std::fflush(_stream);
    }

    void write_char(char c) {
        if (_capture != nullptr) {
            _capture->push_back(c);
            return;
        }
        if (_position == buffer_size) flush();
        _buffer[_position++] = c;
    }

    void write(const char* s) {
        while (*s != '\0') write_char(*s++);
    }

    void write(const std::string& s) {
        if (_capture != nullptr) {
            _capture->append(s);
            return;
        }
        std::size_t position = 0;
        while (position < s.size()) {
            if (_position == buffer_size) flush();
            const std::size_t copied =
                std::min<std::size_t>(buffer_size - _position, s.size() - position);
            std::memcpy(_buffer + _position, s.data() + position, copied);
            _position += int(copied);
            position += copied;
        }
    }

    void write(char c) {
        write_char(c);
    }

    void write(bool value) {
        write_char(value ? '1' : '0');
    }

    template <class T>
    std::enable_if_t<std::is_floating_point_v<T>>
    write(T value) {
        char digits[128];
        auto [end, error] = std::to_chars(
            digits,
            digits + sizeof(digits),
            value,
            _float_format,
            _precision
        );
        if (error != std::errc()) std::abort();
        for (const char* pointer = digits; pointer != end; pointer++) {
            write_char(*pointer);
        }
    }

    template <class T>
    std::enable_if_t<
        internal::is_integral_v<T>
            && !std::is_same_v<std::remove_cv_t<T>, bool>
            && !std::is_same_v<std::remove_cv_t<T>, char>
    >
    write(T value) {
        using Raw = std::remove_cv_t<T>;
        using Unsigned = internal::make_unsigned_t<Raw>;

        Unsigned magnitude;
        if constexpr (internal::is_signed_v<Raw>) {
            if (value < 0) {
                write_char('-');
                magnitude = Unsigned(0) - Unsigned(value);
            } else {
                magnitude = Unsigned(value);
            }
        } else {
            magnitude = value;
        }

        if (magnitude == 0) {
            write_char('0');
            return;
        }

        unsigned chunks[16];
        int count = 0;
        while (magnitude >= 10000) {
            const Unsigned quotient = magnitude / 10000;
            chunks[count++] = unsigned(magnitude - quotient * 10000);
            magnitude = quotient;
        }
        if (_capture == nullptr && _position > buffer_size - 64) flush();
        char captured[64];
        char* const begin = _capture != nullptr ? captured : _buffer + _position;
        char* destination = begin;
        const unsigned leading = unsigned(magnitude);
        const char* first = digit_quads.data() + 4 * leading;
        int skip = leading < 10 ? 3 : leading < 100 ? 2 : leading < 1000 ? 1 : 0;
        for (; skip < 4; skip++) *destination++ = first[skip];
        while (count--) {
            const char* digits = digit_quads.data() + 4 * chunks[count];
            std::memcpy(destination, digits, 4);
            destination += 4;
        }
        if (_capture != nullptr) {
            _capture->append(begin, destination - begin);
        } else {
            _position += int(destination - begin);
        }
    }

    template <class T>
    std::enable_if_t<
        internal::has_val_method_v<T>
            && !internal::is_integral_v<T>
            && !internal::is_range_v<T>
    >
    write(const T& value) {
        write(value.val());
    }

    template <class First, class Second>
    void write(const std::pair<First, Second>& value) {
        write(value.first);
        write_char(' ');
        write(value.second);
    }

    template <class Range>
    std::enable_if_t<
        internal::is_range_v<Range>
            && !internal::is_string_like_v<Range>
    >
    write(const Range& range) {
        using StoredValue = internal::range_stored_value_t<const Range>;
        constexpr bool nested = internal::is_range_v<StoredValue>
                                && !internal::is_string_like_v<StoredValue>;

        bool first = true;
        for (const auto& value : range) {
            if (!first) write_char(nested ? '\n' : _range_separator);
            first = false;
            if constexpr (std::is_same_v<StoredValue, bool> && !nested) {
                write(static_cast<bool>(value));
            } else {
                write(value);
            }
        }
    }

    template <class First, class... Rest>
    void print(const First& first, const Rest&... rest) {
        write(first);
        ((write_char(' '), write(rest)), ...);
    }

    void println() {
        write_char('\n');
    }

    void set_precision(int precision) {
        _precision = precision;
    }

    void set_fixed(int precision = 6) {
        _float_format = std::chars_format::fixed;
        _precision = precision;
    }

    void set_general(int precision = 6) {
        _float_format = std::chars_format::general;
        _precision = precision;
    }

    void set_range_separator(char separator) {
        _range_separator = separator;
    }

    template <class Matrix>
    void write_aligned(const Matrix& matrix) {
        using Row = internal::range_stored_value_t<const Matrix>;
        using Cell = internal::range_stored_value_t<const Row>;
        static_assert(internal::is_range_v<Row> && !internal::is_string_like_v<Row>,
                      "write_aligned requires a two-dimensional range");
        static_assert(!internal::is_range_v<Cell> || internal::is_string_like_v<Cell>,
                      "write_aligned requires scalar cells");
        write_aligned_matrix(matrix);
    }

    template <class Matrix>
    void println_aligned(const Matrix& matrix) {
        write_aligned(matrix);
        write_char('\n');
    }

    template <class... Args>
    void println(const Args&... args) {
        print(args...);
        write_char('\n');
    }

    template <class T>
    FastOutput& operator<<(const T& value) {
        write(value);
        return *this;
    }
};

}  // namespace utilities
}  // namespace m1une


#line 9 "verify/graph/tree/vertex_add_range_contour_sum_on_tree.test.cpp"
#include <queue>
#line 11 "verify/graph/tree/vertex_add_range_contour_sum_on_tree.test.cpp"

namespace {

std::vector<std::vector<int>> distances(
    const m1une::graph::Graph<>& graph
) {
    const int n = graph.size();
    std::vector<std::vector<int>> result(n, std::vector<int>(n, -1));
    for (int start = 0; start < n; start++) {
        std::queue<int> queue;
        result[start][start] = 0;
        queue.push(start);
        while (!queue.empty()) {
            int vertex = queue.front();
            queue.pop();
            for (const auto& edge : graph[vertex]) {
                if (result[start][edge.to] != -1) continue;
                result[start][edge.to] = result[start][vertex] + 1;
                queue.push(edge.to);
            }
        }
    }
    return result;
}

void randomized_test() {
    std::uint64_t state = 311;
    auto random = [&state]() {
        state ^= state << 7;
        state ^= state >> 9;
        return state;
    };

    for (int trial = 0; trial < 250; trial++) {
        int n = int(random() % 20) + 1;
        m1une::graph::Graph<> graph(n);
        for (int vertex = 1; vertex < n; vertex++) {
            graph.add_edge(vertex, int(random() % std::uint64_t(vertex)));
        }
        auto distance = distances(graph);
        std::vector<long long> value(n);
        for (long long& element : value) {
            element = static_cast<long long>(random() % 21) - 10;
        }

        m1une::tree::VertexAddRangeContourSum<long long> contour(graph, value);
        assert(contour.size() == n);
        assert(!contour.empty());
        for (int query = 0; query < 250; query++) {
            int vertex = int(random() % std::uint64_t(n));
            int type = int(random() % 4);
            if (type == 0) {
                long long delta = static_cast<long long>(random() % 21) - 10;
                contour.add(vertex, delta);
                value[vertex] += delta;
            } else if (type == 1) {
                long long replacement =
                    static_cast<long long>(random() % 21) - 10;
                contour.set(vertex, replacement);
                value[vertex] = replacement;
            } else if (type == 2) {
                assert(contour.get(vertex) == value[vertex]);
            } else {
                int left = int(random() % std::uint64_t(n + 3));
                int right = int(random() % std::uint64_t(n + 3));
                if (right < left) std::swap(left, right);
                long long expected = 0;
                for (int other = 0; other < n; other++) {
                    if (left <= distance[vertex][other] &&
                        distance[vertex][other] < right) {
                        expected += value[other];
                    }
                }
                assert(contour.sum(vertex, left, right) == expected);
            }
        }
    }

    m1une::graph::Graph<> empty_graph;
    m1une::tree::VertexAddRangeContourSum<long long> empty(empty_graph);
    assert(empty.empty());
}

void xor_group_test() {
    std::uint64_t state = 733;
    auto random = [&state]() {
        state ^= state << 7;
        state ^= state >> 9;
        return state;
    };

    using Group = m1une::monoid::Xor<std::uint64_t>;
    for (int trial = 0; trial < 120; trial++) {
        int n = int(random() % 20) + 1;
        m1une::graph::Graph<> graph(n);
        for (int vertex = 1; vertex < n; vertex++) {
            graph.add_edge(vertex, int(random() % std::uint64_t(vertex)));
        }
        auto distance = distances(graph);
        std::vector<std::uint64_t> value(n);
        for (auto& element : value) element = random();

        m1une::tree::VertexApplyRangeContourProduct<Group> contour(
            graph,
            value
        );
        for (int query = 0; query < 150; query++) {
            int vertex = int(random() % std::uint64_t(n));
            if (random() & 1) {
                std::uint64_t update = random();
                contour.apply(vertex, update);
                value[vertex] ^= update;
            } else {
                int left = int(random() % std::uint64_t(n + 3));
                int right = int(random() % std::uint64_t(n + 3));
                if (right < left) std::swap(left, right);
                std::uint64_t expected = 0;
                for (int other = 0; other < n; other++) {
                    if (left <= distance[vertex][other] &&
                        distance[vertex][other] < right) {
                        expected ^= value[other];
                    }
                }
                assert(contour.prod(vertex, left, right) == expected);
            }
        }
    }
}

}  // namespace

int main() {
    m1une::utilities::FastInput fast_input;
    m1une::utilities::FastOutput fast_output;

    randomized_test();
    xor_group_test();
    int n, query_count;
    fast_input >> n >> query_count;
    std::vector<long long> initial(n);
    for (long long& value : initial) fast_input >> value;

    m1une::graph::Graph<> graph(n);
    for (int index = 0; index + 1 < n; index++) {
        int first, second;
        fast_input >> first >> second;
        graph.add_edge(first, second);
    }
    m1une::tree::VertexAddRangeContourSum<long long> contour(graph, initial);

    while (query_count--) {
        int type, vertex;
        fast_input >> type >> vertex;
        if (type == 0) {
            long long delta;
            fast_input >> delta;
            contour.add(vertex, delta);
        } else {
            int left, right;
            fast_input >> left >> right;
            fast_output << contour.sum(vertex, left, right) << '\n';
        }
    }
}
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