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| #include<cstdio> #include<cstring> #include<algorithm> #define RG register #define file(x) freopen(#x".in", "r", stdin);freopen(#x".out", "w", stdout); #define clear(x, y) memset(x, y, sizeof(x));
inline int read() { int data = 0, w = 1; char ch = getchar(); while(ch != '-' && (ch < '0' || ch > '9')) ch = getchar(); if(ch == '-') w = -1, ch = getchar(); while(ch >= '0' && ch <= '9') data = data * 10 + (ch ^ 48), ch = getchar(); return data*w; }
const int maxn(80010); struct edge { int next, to; } e[maxn << 1]; int head[maxn], e_num, n, q; inline void add_edge(int from, int to) { e[++e_num] = (edge) {head[from], to}; head[from] = e_num; } int pos[maxn], fa[maxn], size[maxn], heavy[maxn], belong[maxn], dep[maxn], cnt;
void dfs(int x) { size[x] = 1; for(RG int i = head[x]; i; i = e[i].next) { int to = e[i].to; if(to == fa[x]) continue; fa[to] = x; dep[to] = dep[x] + 1; dfs(to); size[x] += size[to]; if(size[heavy[x]] < size[to]) heavy[x] = to; } }
void dfs(int x, int chain) { pos[x] = ++cnt; belong[x] = chain; if(!heavy[x]) return; dfs(heavy[x], chain); for(RG int i = head[x]; i; i = e[i].next) { int to = e[i].to; if(to == fa[x] || to == heavy[x]) continue; dfs(to, to); } }
int sum, ans[maxn], c[maxn], T[maxn]; struct qry { int k, a, b, id, opt; } p[maxn << 1], pl[maxn << 1], pr[maxn << 1]; inline void add(int x, int v) { while(x <= n) c[x] += v, x += x & -x; } inline int query(int x) { int ans = 0; while(x) ans += c[x], x -= x & -x; return ans; } inline int LCA(int a, int b) { while(belong[a] ^ belong[b]) { if(pos[belong[a]] < pos[belong[b]]) std::swap(a, b); a = fa[belong[a]]; } return pos[a] < pos[b] ? a : b; }
inline int Query(int a, int b) { int ans = 0; while(belong[a] ^ belong[b]) { if(pos[belong[a]] < pos[belong[b]]) std::swap(a, b); ans += query(pos[a]) - query(pos[belong[a]] - 1); a = fa[belong[a]]; } if(pos[a] < pos[b]) std::swap(a, b); return ans + query(pos[a]) - query(pos[b] - 1); }
void Div(int l, int r, int ql, int qr) { if(ql > qr) return; if(l == r) { for(RG int i = ql; i <= qr; i++) if((!p[i].opt) && (~ans[p[i].id])) ans[p[i].id] = l; return; }
int mid = (l + r) >> 1, tl = 0, tr = 0; for(RG int i = ql; i <= qr; i++) { if(p[i].k == 0) if(p[i].b <= mid) pl[++tl] = p[i]; else pr[++tr] = p[i], add(pos[p[i].a], p[i].id); else { int sum = Query(p[i].a, p[i].b); if(sum >= p[i].k) pr[++tr] = p[i]; else p[i].k -= sum, pl[++tl] = p[i]; } }
for(RG int i = ql; i <= qr; i++) if(p[i].opt && p[i].b > mid) add(pos[p[i].a], -p[i].id); for(RG int i = 1; i <= tl; i++) p[ql + i - 1] = pl[i]; for(RG int i = 1; i <= tr; i++) p[ql + tl + i - 1] = pr[i]; Div(l, mid, ql, ql + tl - 1); Div(mid + 1, r, ql + tl, qr); }
int main() { #ifndef ONLINE_JUDGE file(cpp); #endif
n = read(); q = read(); int tot = 0; for(RG int i = 1; i <= n; i++) p[++tot] = (qry) {0, i, T[i] = read(), 1, 1}; for(RG int i = 1, a, b; i < n; i++) a = read(), b = read(), add_edge(a, b), add_edge(b, a); dfs(1); dfs(1, 1);
for(RG int i = 1, k, a, b; i <= q; i++) { k = read(); a = read(); b = read(); if(k) { p[++tot] = (qry) {k, a, b, ++sum, 0}; int dis = dep[a] + dep[b] - (dep[LCA(a, b)] << 1) + 1; if(p[tot].k > dis) ans[p[tot].id] = -1; } else p[++tot] = (qry) {0, a, T[a], -1, 1}, p[++tot] = (qry) {0, a, T[a] = b, 1, 1}; }
Div(1, 100000000, 1, tot); for(RG int i = 1; i <= sum; i++) (~ans[i]) ? printf("%d\n", ans[i]) : puts("invalid request!"); return 0; }
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