Path Queries II

                                #include "bits/stdc++.h"
using namespace std;

const int N = 2e5+5;
const int D = 19;
const int S = (1<<D);

int n, q, v[N];
vector<int> adj[N];

int sz[N], p[N], dep[N];
int st[S], id[N], tp[N];

void update(int idx, int val) {
	st[idx += n] = val;
	for (idx /= 2; idx; idx /= 2)
		st[idx] = max(st[2 * idx], st[2 * idx + 1]);
}

int query(int lo, int hi) {
	int ra = 0, rb = 0;
	for (lo += n, hi += n + 1; lo < hi; lo /= 2, hi /= 2) {
		if (lo & 1)
			ra = max(ra, st[lo++]);
		if (hi & 1)
			rb = max(rb, st[--hi]);
	}
	return max(ra, rb);
}

int dfs_sz(int cur, int par) {
	sz[cur] = 1;
	p[cur] = par;
	for(int chi : adj[cur]) {
		if(chi == par) continue;
		dep[chi] = dep[cur] + 1;
		p[chi] = cur;
		sz[cur] += dfs_sz(chi, cur);
	}
	return sz[cur];
}

int ct = 1;

void dfs_hld(int cur, int par, int top) {
	id[cur] = ct++;
	tp[cur] = top;
	update(id[cur], v[cur]);
	int h_chi = -1, h_sz = -1;
	for(int chi : adj[cur]) {
		if(chi == par) continue;
		if(sz[chi] > h_sz) {
			h_sz = sz[chi];
			h_chi = chi;
		}
	}
	if(h_chi == -1) return;
	dfs_hld(h_chi, cur, top);
	for(int chi : adj[cur]) {
		if(chi == par || chi == h_chi) continue;
		dfs_hld(chi, cur, chi);
	}
}

int path(int x, int y){
	int ret = 0;
	while(tp[x] != tp[y]){
		if(dep[tp[x]] < dep[tp[y]])swap(x,y);
		ret = max(ret, query(id[tp[x]],id[x]));
		x = p[tp[x]];
	}
	if(dep[x] > dep[y])swap(x,y);
	ret = max(ret, query(id[x],id[y]));
	return ret;
}

int main() {
	scanf("%d%d", &n, &q);
	for(int i=1; i<=n; i++) scanf("%d", &v[i]);
	for(int i=2; i<=n; i++) {
		int a, b;
		scanf("%d%d", &a, &b);
		adj[a].push_back(b);
		adj[b].push_back(a);
	}
	dfs_sz(1, 1);
	dfs_hld(1, 1, 1);
	while(q--) {
		int t;
		scanf("%d", &t);
		if(t == 1) {
			int s, x;
			scanf("%d%d", &s, &x);
			v[s] = x;
			update(id[s], v[s]);
		} else {
			int a, b;
			scanf("%d%d", &a, &b);
			int res = path(a,b);
			printf("%d\n ", res);
		}
	}
}