#include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #define endl codeforces #define ALL(v) std::begin(v), std::end(v) #define ALLR(v) std::rbegin(v), std::rend(v) using ll = std::int64_t; using ull = std::uint64_t; using pii = std::pair; using tii = std::tuple; using pll = std::pair; using tll = std::tuple; template using vec = std::vector; template using vvec = vec>; template const T& var_min(const T &t) { return t; } template const T& var_max(const T &t) { return t; } template const T& var_min(const T &t, const Tail&... tail) { return std::min(t, var_min(tail...)); } template const T& var_max(const T &t, const Tail&... tail) { return std::max(t, var_max(tail...)); } template void chmin(T &t, const Tail&... tail) { t = var_min(t, tail...); } template void chmax(T &t, const Tail&... tail) { t = var_max(t, tail...); } template const T& clamp(const T &t, const T &low, const T &high) { return std::max(low, std::min(high, t)); } template void chclamp(T &t, const T &low, const T &high) { return t = clamp(t, low, high); } template T make_v(T init) { return init; } template auto make_v(T init, std::size_t s, Tail... tail) { auto v = std::move(make_v(init, tail...)); return vec(s, v); } template struct multi_dem_array { using type = std::array::type, Head>; }; template struct multi_dem_array { using type = std::array; }; template using mdarray = typename multi_dem_array::type; namespace init__ { struct InitIO { InitIO() { std::cin.tie(nullptr); std::ios_base::sync_with_stdio(false); std::cout << std::fixed << std::setprecision(30); } } init_io; } namespace graph { using Node = ll; using Weight = ll; using Edge = std::pair; template struct Graph : public vvec { using vvec::vvec; void add_edge(Node f, Node t, Weight w = 1) { (*this)[f].emplace_back(t, w); if (!Directed) (*this)[t].emplace_back(f, w); } Graph build_inv() const { Graph ret(this->size()); for (Node i = 0; i < this->size(); i++) { for (const Edge &e : (*this)[i]) { Node j; Weight w; std::tie(j, w) = e; if (!Directed && j < i) continue; ret.add_edge(j, i, w); } } return ret; } }; template class dst_iterator { Iterator ite; public: dst_iterator(Iterator ite) : ite(ite) { } bool operator ==(const dst_iterator &oth) const { return ite == oth.ite; } bool operator !=(const dst_iterator &oth) const { return !(*this == oth); } bool operator <(const dst_iterator &oth) const { return ite < oth.ite; } bool operator >(const dst_iterator &oth) const { return ite > oth.ite; } bool operator <=(const dst_iterator &oth) const { return ite <= oth.ite; } bool operator >=(const dst_iterator &oth) const { return ite >= oth.ite; } const Node& operator *() { return ite->first; } const Node& operator *() const { return ite->first; } dst_iterator operator ++() { ++ite; return ite; } }; class dst_iteration { using ite_type = vec::const_iterator; const vec &edges; public: dst_iteration(const vec &edges) : edges(edges) { } auto begin() const { return dst_iterator(edges.cbegin()); } auto end() const { return dst_iterator(edges.cend()); } }; dst_iteration dst(const vec &edges) { return dst_iteration(edges); } } ssize_t ceil_pow2(ssize_t s) { ssize_t ret = 1; while (ret <= s) ret *= 2; return ret; } namespace segtree { template struct SegmentTree { using Merge = std::function; vec nodes; Merge merge_f; T id_ele; SegmentTree(const vec &init_v, Merge merge_f, T id_ele) : nodes(ceil_pow2(init_v.size()) * 2 - 1, id_ele), merge_f(merge_f), id_ele(id_ele) { build(init_v); } void build(const vec &v) { if (size() < v.size()) nodes.resize(ceil_pow2(v.size()) * 2 - 1); ssize_t s = size(); for (ssize_t i = 0; i < v.size(); i++) nodes[i + s - 1] = v[i]; for (ssize_t i = v.size(); i + s - 1 < nodes.size(); i++) nodes[i + s - 1] = id_ele; build_parents(); } void build_parents() { ssize_t s = size(); for (ssize_t i = s - 2; 0 <= i; i--) nodes[i] = get_merged(i); } size_t size() const { return (nodes.size() + 1) / 2; } const T& operator [](ll idx) const { return nodes[idx + size() - 1]; } T get_query(ll ql, ll qr, ll nl, ll nr, ll nidx) const { if (nr <= ql || qr <= nl) return id_ele; if (ql <= nl && nr <= qr) return nodes[nidx]; ll mid = (nl + nr) / 2; ll lidx, ridx; std::tie(lidx, ridx) = get_children_idx(nidx); auto lv = get_query(ql, qr, nl, mid, lidx); auto rv = get_query(ql, qr, mid, nr, ridx); return merge_f(lv, rv); } T get_query(ll ql, ll qr) const { return get_query(ql, qr, 0, size(), 0); } void update_query(ll idx, T val) { idx += size() - 1; nodes[idx] = val; while (idx) { ll pidx = (idx - 1) / 2; nodes[pidx] = get_merged(pidx); idx = pidx; } } // FIXME : test T lower_bound(ll idx, std::function check, T sum) const { if (size() - 1 <= idx) return idx - (size() - 1); ll lidx, ridx; std::tie(lidx, ridx) = get_children_idx(idx); auto lv = merge_f(sum, nodes[lidx]); if (check(lv)) return lower_bound(lidx, check, sum); else return lower_bound(ridx, check, lv); } T lower_bound(std::function check) const { return lower_bound(0, check, id_ele); } private: pll get_children_idx(ll idx) const { return pll(2 * idx + 1, 2 * idx + 2); } T get_merged(ll idx) const { ll a, b; std::tie(a, b) = get_children_idx(idx); return merge_f(nodes[a], nodes[b]); } }; } const ll inf = 5e15; struct LCA { const graph::Graph &g; ll n; const vec &cv; vec ord, path, depth, max_c; segtree::SegmentTree *segs; segtree::SegmentTree *min_ord, *max_ord; LCA(const graph::Graph &g, const vec &cv, const vec &city) : g(g), n(g.size()), cv(cv), ord(n), path(2 * n - 1), depth(2 * n - 1), max_c(n) { ll k = 0; dfs(0, -1, -1, k, 0); vec init_v(2 * n - 1); for (ll i = 0; i < 2 * n - 1; i++) init_v[i] = pll(depth[i], i); segs = new segtree::SegmentTree(init_v, [](pll a, pll b) { return std::min(a, b); }, pll(inf, inf)); min_ord = new segtree::SegmentTree(city, [&](ll a, ll b) { return get_ord(a) < get_ord(b) ? a : b; }, -1); max_ord = new segtree::SegmentTree(city, [&](ll a, ll b) { return get_ord(a) > get_ord(b) ? a : b; }, -2); } ll get_ord(ll idx) { if (idx == -1) return inf; if (idx == -2) return -inf; return ord[idx]; } ll get_lca(ll l, ll r) { ll u = ord[min_ord->get_query(l, r)]; ll v = ord[max_ord->get_query(l, r)]; return path[segs->get_query(u, v + 1).second]; } ll get_maxc(ll l, ll r) { return max_c[get_lca(l, r)]; } void dfs(ll cur, ll pre, ll mc, ll &k, ll d) { max_c[cur] = std::max(mc, cv[cur]); ord[cur] = k; path[k] = cur; depth[k++] = d; for (ll nxt : graph::dst(g[cur])) if (nxt != pre) { dfs(nxt, cur, max_c[cur], k, d + 1); path[k] = cur; depth[k++] = d; } } void moving(ll src, ll dst) { min_ord->update_query(src, dst); max_ord->update_query(src, dst); } }; int main() { ll n, k, q; std::cin >> n >> k >> q; graph::Graph g(n); vec cv(n), av(k); for (ll &e : cv) std::cin >> e; for (ll &e : av) { std::cin >> e; e--; } for (ll i = 1; i < n; i++) { ll e, f; std::cin >> e >> f; g.add_edge(e - 1, f - 1); } LCA lca(g, cv, av); while (q--) { ll t, x, y; std::cin >> t >> x >> y; x--; if (t == 1) lca.moving(x, y - 1); else std::cout << lca.get_maxc(x, y) << '\n'; } return 0; }