#[allow(unused_imports)] use std::cmp::*; #[allow(unused_imports)] use std::collections::*; use std::io::{Write, BufWriter}; // https://qiita.com/tanakh/items/0ba42c7ca36cd29d0ac8 macro_rules! input { ($($r:tt)*) => { let stdin = std::io::stdin(); let mut bytes = std::io::Read::bytes(std::io::BufReader::new(stdin.lock())); let mut next = move || -> String{ bytes .by_ref() .map(|r|r.unwrap() as char) .skip_while(|c|c.is_whitespace()) .take_while(|c|!c.is_whitespace()) .collect() }; input_inner!{next, $($r)*} }; } macro_rules! input_inner { ($next:expr) => {}; ($next:expr, ) => {}; ($next:expr, $var:ident : $t:tt $($r:tt)*) => { let $var = read_value!($next, $t); input_inner!{$next $($r)*} }; } macro_rules! read_value { ($next:expr, ( $($t:tt),* )) => { ( $(read_value!($next, $t)),* ) }; ($next:expr, [ $t:tt ; $len:expr ]) => { (0..$len).map(|_| read_value!($next, $t)).collect::>() }; ($next:expr, chars) => { read_value!($next, String).chars().collect::>() }; ($next:expr, usize1) => { read_value!($next, usize) - 1 }; ($next:expr, [ $t:tt ]) => {{ let len = read_value!($next, usize); (0..len).map(|_| read_value!($next, $t)).collect::>() }}; ($next:expr, $t:ty) => { $next().parse::<$t>().expect("Parse error") }; } #[allow(unused)] macro_rules! debug { ($($format:tt)*) => (write!(std::io::stderr(), $($format)*).unwrap()); } #[allow(unused)] macro_rules! debugln { ($($format:tt)*) => (writeln!(std::io::stderr(), $($format)*).unwrap()); } /** * Segment Tree. This data structure is useful for fast folding on intervals of an array * whose elements are elements of monoid I. Note that constructing this tree requires the identity * element of I and the operation of I. * Verified by: yukicoder No. 259 (http://yukicoder.me/submissions/100581) * AGC015-E (http://agc015.contest.atcoder.jp/submissions/1461001) */ struct SegTree { n: usize, dat: Vec, op: BiOp, e: I, } impl SegTree where BiOp: Fn(I, I) -> I, I: Copy { pub fn new(n_: usize, op: BiOp, e: I) -> Self { let mut n = 1; while n < n_ { n *= 2; } // n is a power of 2 SegTree {n: n, dat: vec![e; 2 * n - 1], op: op, e: e} } /* ary[k] <- v */ pub fn update(&mut self, idx: usize, v: I) { let mut k = idx + self.n - 1; self.dat[k] = v; while k > 0 { k = (k - 1) / 2; self.dat[k] = (self.op)(self.dat[2 * k + 1], self.dat[2 * k + 2]); } } /* [a, b) (note: half-inclusive) * http://proc-cpuinfo.fixstars.com/2017/07/optimize-segment-tree/ */ pub fn query(&self, mut a: usize, mut b: usize) -> I { let mut left = self.e; let mut right = self.e; a += self.n - 1; b += self.n - 1; while a < b { if (a & 1) == 0 { left = (self.op)(left, self.dat[a]); } if (b & 1) == 0 { right = (self.op)(self.dat[b - 1], right); } a = a / 2; b = (b - 1) / 2; } (self.op)(left, right) } } struct LCA { st: Vec, par: Vec, jmp: Vec, dep: Vec, } // Constant-factor speedup used in https://codeforces.com/contest/1083/submission/46874242. // Based on HL-decomposition. // par[root] = root should hold. // Verified by https://codeforces.com/contest/1083/submission/51934575. impl LCA { // For each node, make the most heavy child the first child. fn dfs_left(ch: &mut [Vec], v: usize, sz: &mut [usize], dep: &mut [usize], d: usize) { dep[v] = d; let mut s = 1; for i in 0..ch[v].len() { let w = ch[v][i]; Self::dfs_left(ch, w, sz, dep, d + 1); s += sz[w]; if sz[w] > sz[ch[v][0]] { ch[v].swap(i, 0); } } sz[v] = s; } fn dfs(ch: &[Vec], st: &mut [usize], v: usize, cnt: &mut usize, jmp: &mut [usize]) { st[v] = *cnt; *cnt += 1; if ch[v].len() >= 1 { jmp[ch[v][0]] = jmp[v]; } for &w in &ch[v] { Self::dfs(ch, st, w, cnt, jmp); } } fn new(ch: &mut [Vec], par: &[usize], root: usize) -> Self { let n = ch.len(); let mut st = vec![0; n]; let mut cnt = 0; let mut sz = vec![0; n]; let mut jmp = vec![0; n]; let mut dep = vec![0; n]; Self::dfs_left(ch, root, &mut sz, &mut dep, 0); for i in 0..n { jmp[i] = i; } Self::dfs(ch, &mut st, root, &mut cnt, &mut jmp); LCA { st: st, par: par.to_vec(), jmp: jmp, dep: dep, } } fn lca(&self, mut x: usize, mut y: usize) -> usize { let jmp = &self.jmp; let st = &self.st; while jmp[x] != jmp[y] { if st[x] < st[y] { std::mem::swap(&mut x, &mut y); } x = self.par[jmp[x]]; } if st[x] < st[y] { x } else { y } } } fn dfs(ch: &[Vec], ans: &mut [i64], c: &[i64], v: usize, x: i64) { let x = max(x, c[v]); ans[v] = x; for &w in &ch[v] { dfs(ch, ans, c, w, x); } } fn solve() { let out = std::io::stdout(); let mut out = BufWriter::new(out.lock()); macro_rules! puts { ($($format:tt)*) => (let _ = write!(out,$($format)*);); } input! { n: usize, k: usize, q: usize, c: [i64; n], a: [usize1; k], ef: [(usize1, usize1); n - 1], t: [(i32, usize1, usize1); q], } let mut ch = vec![vec![]; n]; let mut par = vec![0; n]; for &(e, f) in &ef { ch[f].push(e); par[e] = f; } let lca = LCA::new(&mut ch, &par, 0); // precomp let mut ans = vec![0; n]; dfs(&ch, &mut ans, &c, 0, 0); let mut st = SegTree::new(k, |x, y| { match (x, y) { (None, _) => y, (_, None) => x, (Some(x), Some(y)) => Some(lca.lca(x, y)) } }, None); for i in 0..k { st.update(i, Some(a[i])); } for (kind, x, y) in t { if kind == 1 { st.update(x, Some(y)); } else { let l = x; let r = y + 1; let v = st.query(l, r).unwrap(); puts!("{}\n", ans[v]); } } } fn main() { // In order to avoid potential stack overflow, spawn a new thread. let stack_size = 104_857_600; // 100 MB let thd = std::thread::Builder::new().stack_size(stack_size); thd.spawn(|| solve()).unwrap().join().unwrap(); }