#include #include using namespace std; // 解説の計算を、次数で平方分割する template struct sparse_table { public: sparse_table() {} sparse_table(const std::vector& v) : _n(int(v.size())) { int max_log = 0; log_table.resize(_n + 1); log_table[1] = 0; for (int i = 2; i < _n + 1; i++) { log_table[i] = log_table[i >> 1] + 1; max_log = log_table[i]; } table.resize(max_log + 1); for (int i = 0; i <= max_log; i++) { table[i].resize(_n); } for (int j = 0; j < _n; j++) { table[0][j] = v[j]; } for (int i = 1; i <= max_log; i++) { for (int j = 0; j < _n; j++) { if (j + (1 << (i - 1)) >= _n) continue; table[i][j] = op(table[i - 1][j], table[i - 1][j + (1 << (i - 1))]); } } } S query(int l, int r) { assert(0 <= l && l < _n); assert(0 < r && r <= _n); assert(l < r); int i = log_table[r - l]; return op(table[i][l], table[i][r - (1 << i)]); } private: int _n; std::vector log_table; std::vector> table; }; // returns a list of (vertex, depth) pairs inline std::vector> euler_tour(const int n, const std::vector>& edges, const int root = 0) { std::vector adj[n]; for (auto&& [u, v] : edges) { adj[u].push_back(v); adj[v].push_back(u); } std::vector> ret; std::function dfs = [&](int v, int p = -1, int d = 0) -> void { for (auto&& u : adj[v]) { if (u != p) { ret.push_back({v, d}); dfs(u, v, d + 1); } } ret.push_back({v, d}); }; dfs(root, -1, 0); return ret; } namespace nu50218 { inline std::pair lca_st_op(std::pair x, std::pair y) { return min(x, y); } }; // namespace nu50218 struct LCA { int lca(int u, int v) { if (idx[u] > idx[v]) std::swap(u, v); return st.query(idx[u], idx[v] + 1).second; } int depth(int v) { return dep[v]; } int dist(int u, int v) { return dep[u] + dep[v] - 2 * dep[lca(u, v)]; } LCA(const int n, const std::vector>& edges, const int root = 0) { dep.resize(n); idx.resize(n); auto tour = euler_tour(n, edges, root); std::vector> a(tour.size()); for (int i = 0; i < (int)tour.size(); i++) { auto [v, d] = tour[i]; dep[v] = d; idx[v] = i; a[i] = {d, v}; } st = sparse_table, nu50218::lca_st_op>(a); } private: std::vector dep; std::vector idx; inline std::pair op(std::pair x, std::pair y) { return min(x, y); } sparse_table, nu50218::lca_st_op> st; }; template struct vertex_add_path_sum { vertex_add_path_sum(const int n, const std::vector>& edges) : n(n), index(n), fwt(2 * n + 1), lca(n, edges, 0) { std::vector> adj(n); for (auto&& [u, v] : edges) { adj[u].push_back(v); adj[v].push_back(u); } int i = 1; std::function dfs = [&](int v, int p = -1) -> void { index[v].first = i++; for (auto&& u : adj[v]) { if (u != p) { dfs(u, v); } } index[v].second = i++; }; dfs(0, -1); } void add(int p, T x) { fwt.add(index[p].first, x); fwt.add(index[p].second, -x); } T sum(int u, int v) { auto sub = index[lca.lca(u, v)].first; return fwt.sum(0, index[u].first + 1) + fwt.sum(0, index[v].first + 1) - fwt.sum(0, sub) - fwt.sum(0, sub + 1); } private: int n; std::vector> index; atcoder::fenwick_tree fwt; LCA lca; }; using ll = long long; // sqrt(200000) const int border = 447; int main() { ios::sync_with_stdio(false); cin.tie(nullptr); int N, Q; cin >> N >> Q; vector a(N); for (auto&& x : a) { cin >> x; } vector> edges; for (int i = 0; i < N - 1; i++) { int u, v; cin >> u >> v; u--; v--; edges.emplace_back(u, v); } vector> adj(N); for (auto&& [u, v] : edges) { adj[u].push_back(v); adj[v].push_back(u); } vector heavy_vertices; for (int i = 0; i < N; i++) { if ((int)adj[i].size() > border) { heavy_vertices.push_back(i); } } LCA lca(N, edges); // a の path sum を計算する vertex_add_path_sum a_sum(N, edges); for (int i = 0; i < N; i++) { a_sum.add(i, a[i]); } // 各頂点の重み := 隣接する「次数が border 以下」頂点の a の合計 // に対して path sum を計算する vertex_add_path_sum low_deg_neighbor_sum(N, edges); for (int i = 0; i < N; i++) { if ((int)adj[i].size() <= border) { for (auto&& v : adj[i]) { low_deg_neighbor_sum.add(v, a[i]); } } } for (int q = 0; q < Q; q++) { int t; cin >> t; if (t == 0) { int u; ll x; cin >> u >> x; u--; a[u] += x; a_sum.add(u, x); // 次数が小さい頂点は愚直に反映する if ((int)adj[u].size() <= border) { for (auto&& v : adj[u]) { low_deg_neighbor_sum.add(v, x); } } continue; } if (t == 1) { int u, v; cin >> u >> v; u--; v--; ll ans = low_deg_neighbor_sum.sum(u, v); ans -= a_sum.sum(u, v); ans += a[u] + a[v]; // 次数が大きい頂点が u-v パスの近くにあったら調整する for (auto&& h : heavy_vertices) { int dist_uv = lca.dist(u, v); int dist_uh = lca.dist(u, h); int dist_hv = lca.dist(h, v); // h がパスの頂点に隣接している if (dist_uv + 2 >= dist_uh + dist_hv) { ans += a[h]; } // h がパスの2頂点に隣接している if (dist_uv == dist_uh + dist_hv && h != u && h != v) { ans += a[h]; } } cout << ans << "\n"; continue; } } }