use std::io::*; fn main() { input! { n: usize, q: usize, edge: [(usize, usize); n - 1], query: [(usize, usize, usize); q], } let n = n + 1; let mut hld = HLD::new(n); hld.add_edge(0, 1); for &(a, b) in edge.iter() { hld.add_edge(a, b); } hld.build(0); let mut cnt = SegmentTreePURQ::new(n, 0, |a, b| *a + *b); let mut fix_root = LazySegmentTree::new(n, FixRoot); let mut move_root = LazySegmentTree::new(n, MoveRoot); for i in 1..n { let x = hld.vertex(i); let parent = hld.parent(x).unwrap(); move_root.get_mut(i, |p| p.3 = x as i64 - parent as i64); } let mut state = vec![0i64; n]; let mut range = vec![]; let out = std::io::stdout(); let mut out = std::io::BufWriter::new(out.lock()); for &(u, r, v) in query.iter() { let sign = (state[u] ^ 1) - state[u]; move_root.update(0, n, (sign, 0)); let mut sub = state[u]; hld.path_root(u, &mut range); for &(l, r) in range.iter().rev() { move_root.update(l, r, (-sign, sign)); let v = hld.vertex(r - 1); let p = hld.sub_tree(v); let c = cnt.find(p.0, p.1) - sub; fix_root.get_mut(r - 1, |p| { let v = v as i64; p.0 += sign * c * v; p.1 += sign * v; }); fix_root.update(l, r - 1, sign); let p = hld.sub_tree(hld.vertex(l)); sub = cnt.find(p.0, p.1); } state[u] ^= 1; cnt.update(hld.sub_tree(u).0, state[u]); let a = hld.sub_tree(r); let b = hld.sub_tree(v); let ans = if b.0 <= a.0 && a.1 <= b.1 { let mut all = fix_root.find(0, n).0; hld.path_root(v, &mut range); for &(l, r) in range.iter() { all += move_root.find(l, r).0; } if r != v { let x = hld.next(v, r); let p = hld.sub_tree(x); let c = cnt.find(0, n); let d = cnt.find(p.0, p.1); all -= v as i64 * (c - d) * d; all -= fix_root.find(p.0, p.1).0; } all } else { fix_root.find(b.0, b.1).0 }; writeln!(out, "{}", ans).ok(); } } struct FixRoot; impl TE for FixRoot { type T = (i64, i64); type E = i64; fn fold(&self, l: &Self::T, r: &Self::T) -> Self::T { (l.0 + r.0, l.1 + r.1) } fn eval(&self, x: &Self::T, f: &Self::E) -> Self::T { (x.0 + x.1 * *f, x.1) } fn merge(&self, g: &Self::E, h: &Self::E) -> Self::E { *g + *h } fn e(&self) -> Self::T { (0, 0) } fn id(&self) -> Self::E { 0 } } struct MoveRoot; impl TE for MoveRoot { // sum cab, sum ca, sum cb, sum c type T = (i64, i64, i64, i64); // a, b type E = (i64, i64); fn fold(&self, l: &Self::T, r: &Self::T) -> Self::T { (l.0 + r.0, l.1 + r.1, l.2 + r.2, l.3 + r.3) } fn eval(&self, x: &Self::T, f: &Self::E) -> Self::T { ( x.0 + f.0 * x.2 + f.1 * x.1 + f.0 * f.1 * x.3, x.1 + f.0 * x.3, x.2 + f.1 * x.3, x.3, ) } fn merge(&self, g: &Self::E, h: &Self::E) -> Self::E { (g.0 + h.0, g.1 + h.1) } fn e(&self) -> Self::T { (0, 0, 0, 0) } fn id(&self) -> Self::E { (0, 0) } } // ---------- begin segment tree Point Update Range Query ---------- pub struct SegmentTreePURQ { n: usize, size: usize, data: Vec, e: T, op: F, } impl SegmentTreePURQ where T: Clone, F: Fn(&T, &T) -> T, { pub fn new(n: usize, e: T, op: F) -> Self { assert!(n > 0); let size = n.next_power_of_two(); let data = vec![e.clone(); 2 * size]; SegmentTreePURQ { n, size, data, e, op, } } pub fn update_tmp(&mut self, x: usize, v: T) { assert!(x < self.n); self.data[x + self.size] = v; } pub fn update_all(&mut self) { for i in (1..self.size).rev() { self.data[i] = (self.op)(&self.data[2 * i], &self.data[2 * i + 1]); } } pub fn update(&mut self, x: usize, v: T) { assert!(x < self.n); let mut x = x + self.size; self.data[x] = v; x >>= 1; while x > 0 { self.data[x] = (self.op)(&self.data[2 * x], &self.data[2 * x + 1]); x >>= 1; } } pub fn find(&self, l: usize, r: usize) -> T { assert!(l <= r && r <= self.n); if l == r { return self.e.clone(); } let mut l = self.size + l; let mut r = self.size + r; let mut x = self.e.clone(); let mut y = self.e.clone(); while l < r { if l & 1 == 1 { x = (self.op)(&x, &self.data[l]); l += 1; } if r & 1 == 1 { r -= 1; y = (self.op)(&self.data[r], &y); } l >>= 1; r >>= 1; } (self.op)(&x, &y) } pub fn max_right

(&self, l: usize, f: P) -> usize where P: Fn(&T) -> bool, { assert!(l <= self.n); assert!(f(&self.e)); if l == self.n { return self.n; } let mut l = l + self.size; let mut sum = self.e.clone(); while { l >>= l.trailing_zeros(); let v = (self.op)(&sum, &self.data[l]); if !f(&v) { while l < self.size { l <<= 1; let v = (self.op)(&sum, &self.data[l]); if f(&v) { sum = v; l += 1; } } return l - self.size; } sum = v; l += 1; l.count_ones() > 1 } {} self.n } pub fn min_left

(&self, r: usize, f: P) -> usize where P: Fn(&T) -> bool, { assert!(r <= self.n); assert!(f(&self.e)); if r == 0 { return 0; } let mut r = r + self.size; let mut sum = self.e.clone(); while { r -= 1; while r > 1 && r & 1 == 1 { r >>= 1; } let v = (self.op)(&self.data[r], &sum); if !f(&v) { while r < self.size { r = 2 * r + 1; let v = (self.op)(&self.data[r], &sum); if f(&v) { sum = v; r -= 1; } } return r + 1 - self.size; } sum = v; (r & (!r + 1)) != r } {} 0 } } // ---------- end segment tree Point Update Range Query ---------- // ---------- begin Heavy-Light decomposition ---------- pub struct HLD { size: usize, edge: Vec<(usize, usize)>, child: Vec>, path_root: Vec, parent: Vec, left: Vec, right: Vec, inverse: Vec, } impl HLD { pub fn new(size: usize) -> Self { assert!(size <= 10usize.pow(8)); HLD { size: size, edge: Vec::with_capacity(size - 1), child: Vec::new(), path_root: Vec::new(), parent: Vec::new(), left: Vec::new(), right: Vec::new(), inverse: Vec::new(), } } pub fn add_edge(&mut self, a: usize, b: usize) { assert!(a != b && a < self.size && b < self.size); self.edge.push((a, b)); } pub fn build(&mut self, root: usize) { assert!(self.edge.len() + 1 == self.size); let size = self.size; let mut cnt = vec![0; size]; for &(a, b) in self.edge.iter() { cnt[a] += 1; cnt[b] += 1; } let mut child = cnt .into_iter() .map(|c| Vec::with_capacity(c)) .collect::>(); for &(a, b) in self.edge.iter() { child[a].push(b); child[b].push(a); } let mut parent = vec![size; size]; let mut q = Vec::with_capacity(size); q.push(root); parent[root] = root; for i in 0..size { let v = q[i]; for u in child[v].clone() { assert!(parent[u] == size); parent[u] = v; child[u].retain(|e| *e != v); q.push(u); } } let mut sum = vec![1; size]; for &v in q.iter().rev() { let child = &mut child[v]; if !child.is_empty() { let (pos, _) = child.iter().enumerate().max_by_key(|p| sum[*p.1]).unwrap(); child.swap(0, pos); sum[v] = 1 + child.iter().fold(0, |s, a| s + sum[*a]); } } let mut path_root = (0..size).collect::>(); let mut left = vec![0; size]; let mut right = vec![0; size]; let mut dfs = vec![(root, false)]; let mut id = 0; while let Some((v, end)) = dfs.pop() { if end { right[v] = id; continue; } left[v] = id; id += 1; dfs.push((v, true)); let child = &child[v]; if !child.is_empty() { for &u in child[1..].iter().rev() { path_root[u] = u; dfs.push((u, false)); } let u = child[0]; path_root[u] = path_root[v]; dfs.push((u, false)); } } let mut inverse = vec![size; size]; for (i, l) in left.iter().enumerate() { inverse[*l] = i; } self.child = child; self.parent = parent; self.left = left; self.right = right; self.path_root = path_root; self.inverse = inverse; } pub fn lca(&self, mut a: usize, mut b: usize) -> usize { assert!(a < self.size && b < self.size); let path = &self.path_root; let parent = &self.parent; let index = &self.left; while path[a] != path[b] { if index[a] > index[b] { std::mem::swap(&mut a, &mut b); } b = parent[path[b]]; } std::cmp::min((index[a], a), (index[b], b)).1 } pub fn path_root(&self, mut v: usize, res: &mut Vec<(usize, usize)>) { assert!(v < self.size); res.clear(); let parent = &self.parent; let path_root = &self.path_root; let index = &self.left; while index[path_root[v]] != 0 { let p = path_root[v]; res.push((index[p], index[v] + 1)); v = parent[p]; } res.push((0, index[v] + 1)); res.reverse(); } pub fn path( &self, src: usize, dst: usize, up: &mut Vec<(usize, usize)>, down: &mut Vec<(usize, usize)>, ) { assert!(src < self.size && dst < self.size); up.clear(); down.clear(); let path = &self.path_root; let parent = &self.parent; let index = &self.left; let mut x = src; let mut y = dst; while path[x] != path[y] { if index[x] > index[y] { let p = path[x]; assert!(p == path[p]); up.push((index[p], index[x] + 1)); x = parent[p]; } else { let p = path[y]; assert!(p == path[p]); down.push((index[p], index[y] + 1)); y = parent[p]; } } if index[x] >= index[y] { up.push((index[y], index[x] + 1)); } else { down.push((index[x], index[y] + 1)); } down.reverse(); } pub fn sub_tree(&self, v: usize) -> (usize, usize) { assert!(v < self.size); (self.left[v], self.right[v]) } pub fn parent(&self, v: usize) -> Option { assert!(v < self.size); let p = self.parent[v]; if p == v { None } else { Some(p) } } // s -> t へのパスの2番目の頂点を返す pub fn next(&self, s: usize, t: usize) -> usize { assert!(s < self.size && t < self.size && s != t); let (a, b) = self.sub_tree(s); let (c, d) = self.sub_tree(t); if !(a <= c && d <= b) { return self.parent[s]; } let mut pos = t; let mut pre = t; while self.path_root[s] != self.path_root[pos] { pre = self.path_root[pos]; pos = self.parent[pre]; } if s == pos { pre } else { self.child[s][0] } } pub fn vertex(&self, x: usize) -> usize { assert!(x < self.size); self.inverse[x] } } // ---------- end Heavy-Light decomposition ---------- // ---------- begin Lazy Segment Tree ---------- pub trait TE { type T: Clone; type E: Clone; fn fold(&self, l: &Self::T, r: &Self::T) -> Self::T; fn eval(&self, x: &Self::T, f: &Self::E) -> Self::T; fn merge(&self, g: &Self::E, h: &Self::E) -> Self::E; fn e(&self) -> Self::T; fn id(&self) -> Self::E; } pub struct LazySegmentTree { n: usize, size: usize, bit: u32, op: R, data: Vec<(R::T, R::E)>, } impl LazySegmentTree { pub fn new(n: usize, op: R) -> Self { assert!(n > 0); let size = n.next_power_of_two(); let bit = size.trailing_zeros(); let data = vec![(op.e(), op.id()); 2 * size]; Self { n, size, bit, op, data, } } pub fn build(init: I, n: usize, op: R) -> Self where I: Iterator, { let mut seg = Self::new(n, op); for (data, ini) in seg.data[seg.size..].iter_mut().zip(init) { data.0 = ini; } for i in (1..seg.size).rev() { seg.pull(i); } seg } pub fn update(&mut self, l: usize, r: usize, f: R::E) { assert!(l <= r && r <= self.n); if l == r { return; } self.push_range(l, r); let mut s = l + self.size; let mut t = r + self.size; while s < t { if s & 1 == 1 { self.apply(s, &f); s += 1; } if t & 1 == 1 { t -= 1; self.apply(t, &f); } s >>= 1; t >>= 1; } let l = l + self.size; let r = r + self.size; for k in 1..=self.bit { if (l >> k) << k != l { self.pull(l >> k); } if (r >> k) << k != r { self.pull((r - 1) >> k); } } } pub fn find(&mut self, l: usize, r: usize) -> R::T { assert!(l <= r && r <= self.n); if l == r { return self.op.e(); } self.push_range(l, r); let mut l = l + self.size; let mut r = r + self.size; let mut p = self.op.e(); let mut q = self.op.e(); while l < r { if l & 1 == 1 { p = self.op.fold(&p, &self.data[l].0); l += 1; } if r & 1 == 1 { r -= 1; q = self.op.fold(&self.data[r].0, &q); } l >>= 1; r >>= 1; } self.op.fold(&p, &q) } pub fn get_mut(&mut self, x: usize, f: F) where F: FnOnce(&mut R::T), { assert!(x < self.n); let x = x + self.size; for k in (1..=self.bit).rev() { self.push(x >> k); } f(&mut self.data[x].0); for k in 1..=self.bit { self.pull(x >> k); } } pub fn set_at(&mut self, x: usize, v: R::T) { assert!(x < self.n); let x = x + self.size; for k in (1..=self.bit).rev() { self.push(x >> k); } self.data[x].0 = v; for k in 1..=self.bit { self.pull(x >> k); } } fn push_range(&mut self, l: usize, r: usize) { let l = l + self.size; let r = r + self.size; for k in (1..=self.bit).rev() { if (l >> k) << k != l { self.push(l >> k); } if (r >> k) << k != r { self.push((r - 1) >> k); } } } fn apply(&mut self, x: usize, f: &R::E) { self.data[x].0 = self.op.eval(&self.data[x].0, f); self.data[x].1 = self.op.merge(&self.data[x].1, f); } fn push(&mut self, x: usize) { let f = std::mem::replace(&mut self.data[x].1, self.op.id()); self.apply(2 * x, &f); self.apply(2 * x + 1, &f); } fn pull(&mut self, x: usize) { self.data[x].0 = self.op.fold(&self.data[2 * x].0, &self.data[2 * x + 1].0); } } // ---------- end Lazy Segment Tree ---------- // ---------- begin input macro ---------- // reference: https://qiita.com/tanakh/items/0ba42c7ca36cd29d0ac8 #[macro_export] macro_rules! input { (source = $s:expr, $($r:tt)*) => { let mut iter = $s.split_whitespace(); input_inner!{iter, $($r)*} }; ($($r:tt)*) => { let s = { use std::io::Read; let mut s = String::new(); std::io::stdin().read_to_string(&mut s).unwrap(); s }; let mut iter = s.split_whitespace(); input_inner!{iter, $($r)*} }; } #[macro_export] macro_rules! input_inner { ($iter:expr) => {}; ($iter:expr, ) => {}; ($iter:expr, $var:ident : $t:tt $($r:tt)*) => { let $var = read_value!($iter, $t); input_inner!{$iter $($r)*} }; } #[macro_export] macro_rules! read_value { ($iter:expr, ( $($t:tt),* )) => { ( $(read_value!($iter, $t)),* ) }; ($iter:expr, [ $t:tt ; $len:expr ]) => { (0..$len).map(|_| read_value!($iter, $t)).collect::>() }; ($iter:expr, chars) => { read_value!($iter, String).chars().collect::>() }; ($iter:expr, bytes) => { read_value!($iter, String).bytes().collect::>() }; ($iter:expr, usize1) => { read_value!($iter, usize) - 1 }; ($iter:expr, $t:ty) => { $iter.next().unwrap().parse::<$t>().expect("Parse error") }; } // ---------- end input macro ----------