fn main() { let mut io = IO::new(); input!{ from io, n: usize, ed: [(usize, usize); n-1], q: usize } let mut hld = HeavyLightDecomposition::new(n); for &(u, v) in &ed { hld.add_edge(u, v); } hld.build(0); let mut seg = SegmentTree::::new(n); for _ in 0..q { let c = io.scan::(); if c == 'x' { let (i, (a0, a1, a2, a3)) = io.scan::<(usize, (i64, i64, i64, i64))>(); seg.set(hld.id(ed[i].0).max(hld.id(ed[i].1)), Mat(a0, a1, a2, a3)); } else { let (u, v) = io.scan::<(usize, usize)>(); let (rng1, rng2) = hld.for_each_edge(u, v); assert!(rng1.is_empty()); let mut res = Mat::zero(); for x in rng2 { res = res + seg.fold(x); } io.println(((res.0, res.1), (res.2, res.3))); } } } const MOD: i64 = 1_000_000_007; #[derive(Clone, PartialEq, Debug)] struct Mat(i64, i64, i64, i64); impl Associative for Mat {} impl Add for Mat { type Output = Self; fn add(self, rhs: Self) -> Self { Self( (self.0 * rhs.0 + self.1 * rhs.2) % MOD, (self.0 * rhs.1 + self.1 * rhs.3) % MOD, (self.2 * rhs.0 + self.3 * rhs.2) % MOD, (self.2 * rhs.1 + self.3 * rhs.3) % MOD ) } } impl Zero for Mat { fn zero() -> Self { Self(1, 0, 0, 1) } } use std::ops::Bound::{Excluded, Included, Unbounded}; use std::ops::RangeBounds; /// 区間を配列サイズに収まるように丸める。 /// /// 与えられた区間 `r` と `0..len` の共通部分を、有界な半開区間として返す。 /// /// # Examples /// ``` /// use bibliotheca::utils::bounds::bounds_within; /// /// assert_eq!(bounds_within(.., 7), 0..7); /// assert_eq!(bounds_within(..=4, 7), 0..5); /// ``` pub fn bounds_within>(r: R, len: usize) -> Range { let e_ex = match r.end_bound() { Included(&e) => e + 1, Excluded(&e) => e, Unbounded => len, } .min(len); let s_in = match r.start_bound() { Included(&s) => s, Excluded(&s) => s + 1, Unbounded => 0, } .min(e_ex); s_in..e_ex } // ------------ Segment Tree start ------------ pub struct SegmentTree { n: usize, size: usize, node: Vec } impl SegmentTree { pub fn new(n: usize) -> Self { let size = n.next_power_of_two(); let node = vec![T::zero(); size * 2]; SegmentTree { n, size, node } } pub fn set(&mut self, mut i: usize, x: T) { i += self.size; self.node[i] = x; self.fix(i); } fn fix(&mut self, mut i: usize) { while i > 0 { i >>= 1; self.node[i] = self.node[i << 1].clone() + self.node[(i << 1) + 1].clone(); } } pub fn fold>(&self, rng: R) -> T { let Range { start, end } = bounds_within(rng, self.size); let mut vl = T::zero(); let mut vr = T::zero(); let mut l = start + self.size; let mut r = end + self.size; while l < r { if l & 1 == 1 { vl = vl + self.node[l].clone(); l += 1; } if r & 1 == 1 { r -= 1; vr = self.node[r].clone() + vr; } l >>= 1; r >>= 1; } vl + vr } /// (j, t) => pred(j-1) = true, pred(j) = false pub fn partition(&self, pred: impl Fn(usize, &T) -> bool) -> (usize, T) { assert!(pred(0, &T::zero()), "need to be pred(0, T::zero())"); if pred(self.n - 1, &self.node[1]) { return (self.n - 1, self.node[1].clone()) } let mut j = 1; let mut current = T::zero(); let mut idx = 0; let mut f = self.size; while j < self.size { j <<= 1; f >>= 1; let next = current.clone() + self.node[j].clone(); if pred(idx + f - 1, &next) { current = next; j |= 1; idx += f; } } (idx, current) } } impl From> for SegmentTree { fn from(vec: Vec) -> Self { let n = vec.len(); let size = n.next_power_of_two(); let mut node = vec![T::zero(); size << 1]; for (i, e) in vec.iter().cloned().enumerate() { node[i + size] = e; } for i in (1..size).rev() { node[i] = node[i << 1].clone() + node[(i << 1) + 1].clone(); } SegmentTree { n, size, node } } } impl Index for SegmentTree { type Output = T; fn index(&self, i: usize) -> &Self::Output { assert!(i < self.size, "index out of range: length is {}, but given {}.", self.size, i); &self.node[i + self.size] } } // ------------ Segment Tree end ------------ // ------------ algebraic traits start ------------ use std::marker::Sized; use std::ops::*; /// 元 pub trait Element: Sized + Clone + PartialEq {} impl Element for T {} /// 結合性 pub trait Associative: Magma {} /// マグマ pub trait Magma: Element + Add {} impl> Magma for T {} /// 半群 pub trait SemiGroup: Magma + Associative {} impl SemiGroup for T {} /// モノイド pub trait Monoid: SemiGroup + Zero {} impl Monoid for T {} pub trait ComMonoid: Monoid + AddAssign {} impl ComMonoid for T {} /// 群 pub trait Group: Monoid + Neg {} impl> Group for T {} pub trait ComGroup: Group + ComMonoid {} impl ComGroup for T {} /// 半環 pub trait SemiRing: ComMonoid + Mul + One {} impl + One> SemiRing for T {} /// 環 pub trait Ring: ComGroup + SemiRing {} impl Ring for T {} pub trait ComRing: Ring + MulAssign {} impl ComRing for T {} /// 体 pub trait Field: ComRing + Div + DivAssign {} impl + DivAssign> Field for T {} /// 加法単元 pub trait Zero: Element { fn zero() -> Self; fn is_zero(&self) -> bool { *self == Self::zero() } } /// 乗法単元 pub trait One: Element { fn one() -> Self; fn is_one(&self) -> bool { *self == Self::one() } } macro_rules! impl_integer { ($($T:ty,)*) => { $( impl Associative for $T {} impl Zero for $T { fn zero() -> Self { 0 } fn is_zero(&self) -> bool { *self == 0 } } impl<'a> Zero for &'a $T { fn zero() -> Self { &0 } fn is_zero(&self) -> bool { *self == &0 } } impl One for $T { fn one() -> Self { 1 } fn is_one(&self) -> bool { *self == 1 } } impl<'a> One for &'a $T { fn one() -> Self { &1 } fn is_one(&self) -> bool { *self == &1 } } )* }; } impl_integer! { i8, i16, i32, i64, i128, isize, u8, u16, u32, u64, u128, usize, } // ------------ algebraic traits end ------------ // ------------ Heavy Light Decomposition start ------------ use std::ops::Range; pub struct HeavyLightDecomposition { graph: Vec>, index: Vec, // 新しい頂点番号 parent: Vec, // 親 head: Vec, // 属するHeavy Pathの根 range: Vec, // 部分木の開区間右端 } impl HeavyLightDecomposition { pub fn new(n: usize) -> Self { Self { graph: vec![Vec::new(); n], index: Vec::new(), parent: Vec::new(), head: Vec::new(), range: Vec::new(), } } pub fn add_edge(&mut self, u: usize, v: usize) { self.graph[u].push(v); self.graph[v].push(u); } pub fn build(&mut self, root: usize) { let graph = &mut self.graph; let n = graph.len(); let mut index = vec![0; n]; let mut parent = vec![n; n]; let mut head = vec![root; n]; let mut range = vec![0; n]; let mut siz = vec![1; n]; let mut st = Vec::new(); st.push(root); while let Some(v) = st.pop() { if v < n { st.push(!v); if let Some(k) = graph[v].iter().position(|&u| u == parent[v]) { graph[v].swap_remove(k); } graph[v].iter().for_each(|&u| { parent[u] = v; st.push(u); }); } else { let v = !v; for i in 0..graph[v].len() { let u = graph[v][i]; siz[v] += siz[u]; if siz[graph[v][0]] < siz[u] { graph[v].swap(0, i); } } } } st.push(root); let mut c = 0; while let Some(v) = st.pop() { if v < n { st.push(!v); index[v] = c; c += 1; for &u in graph[v].iter().skip(1) { head[u] = u; st.push(u); } if let Some(&u) = graph[v].get(0) { head[u] = head[v]; st.push(u); } } else { range[!v] = c; } } self.index = index; self.parent = parent; self.head = head; self.range = range; } pub fn lca(&self, mut u: usize, mut v: usize) -> usize { let parent = &self.parent; let head = &self.head; let index = &self.index; while head[u] != head[v] { if index[u] < index[v] { v = parent[head[v]]; } else { u = parent[head[u]]; } } if index[u] < index[v] { u } else { v } } fn for_each(&self, mut u: usize, mut v: usize, b: usize) -> (Vec>, Vec>) { let parent = &self.parent; let head = &self.head; let index = &self.index; let mut up = Vec::new(); let mut down = Vec::new(); while head[u] != head[v] { if index[u] < index[v] { let h = head[v]; down.push(index[h]..index[v] + 1); v = parent[h]; } else { let h = head[u]; up.push(index[h]..index[u] + 1); u = parent[h]; } } if index[u] < index[v] { down.push(index[u] + b .. index[v] + 1); } else if index[v] + b < index[u] + 1 { up.push(index[v] + b .. index[u] + 1); } down.reverse(); (up, down) } pub fn id(&self, v: usize) -> usize { self.index[v] } pub fn for_each_vertex(&self, u: usize, v: usize) -> (Vec>, Vec>) { self.for_each(u, v, 0) } pub fn for_each_edge(&self, u: usize, v: usize) -> (Vec>, Vec>) { self.for_each(u, v, 1) } pub fn subtree_range(&self, v: usize) -> Range { self.index[v]..self.range[v] } } // ------------ Heavy Light Decomposition end ------------ // ------------ io module start ------------ use std::io::{stdout, BufWriter, Read, StdoutLock, Write}; pub struct IO { iter: std::str::SplitAsciiWhitespace<'static>, buf: BufWriter>, } impl IO { pub fn new() -> Self { let mut input = String::new(); std::io::stdin().read_to_string(&mut input).unwrap(); let input = Box::leak(input.into_boxed_str()); let out = Box::new(stdout()); IO { iter: input.split_ascii_whitespace(), buf: BufWriter::new(Box::leak(out).lock()), } } fn scan_str(&mut self) -> &'static str { self.iter.next().unwrap() } pub fn scan(&mut self) -> ::Output { ::scan(self) } pub fn scan_vec(&mut self, n: usize) -> Vec<::Output> { (0..n).map(|_| self.scan::()).collect() } pub fn print(&mut self, x: T) { ::print(self, x); } pub fn println(&mut self, x: T) { self.print(x); self.print("\n"); } pub fn iterln>(&mut self, mut iter: I, delim: &str) { if let Some(v) = iter.next() { self.print(v); for v in iter { self.print(delim); self.print(v); } } self.print("\n"); } pub fn flush(&mut self) { self.buf.flush().unwrap(); } } impl Default for IO { fn default() -> Self { Self::new() } } pub trait Scan { type Output; fn scan(io: &mut IO) -> Self::Output; } macro_rules! impl_scan { ($($t:tt),*) => { $( impl Scan for $t { type Output = Self; fn scan(s: &mut IO) -> Self::Output { s.scan_str().parse().unwrap() } } )* }; } impl_scan!(i16, i32, i64, isize, u16, u32, u64, usize, String, f32, f64); pub enum Bytes {} impl Scan for Bytes { type Output = &'static [u8]; fn scan(s: &mut IO) -> Self::Output { s.scan_str().as_bytes() } } impl Scan for char { type Output = char; fn scan(s: &mut IO) -> Self::Output { s.scan_str().chars().next().unwrap() } } pub enum Chars {} impl Scan for Chars { type Output = Vec; fn scan(s: &mut IO) -> Self::Output { s.scan_str().chars().collect() } } pub enum Usize1 {} impl Scan for Usize1 { type Output = usize; fn scan(s: &mut IO) -> Self::Output { s.scan::().wrapping_sub(1) } } impl Scan for (T, U) { type Output = (T::Output, U::Output); fn scan(s: &mut IO) -> Self::Output { (T::scan(s), U::scan(s)) } } impl Scan for (T, U, V) { type Output = (T::Output, U::Output, V::Output); fn scan(s: &mut IO) -> Self::Output { (T::scan(s), U::scan(s), V::scan(s)) } } impl Scan for (T, U, V, W) { type Output = (T::Output, U::Output, V::Output, W::Output); fn scan(s: &mut IO) -> Self::Output { (T::scan(s), U::scan(s), V::scan(s), W::scan(s)) } } pub trait Print { fn print(w: &mut IO, x: Self); } macro_rules! impl_print_int { ($($t:ty),*) => { $( impl Print for $t { fn print(w: &mut IO, x: Self) { w.buf.write_all(x.to_string().as_bytes()).unwrap(); } } )* }; } impl_print_int!(i16, i32, i64, isize, u16, u32, u64, usize, f32, f64); impl Print for u8 { fn print(w: &mut IO, x: Self) { w.buf.write_all(&[x]).unwrap(); } } impl Print for &[u8] { fn print(w: &mut IO, x: Self) { w.buf.write_all(x).unwrap(); } } impl Print for &str { fn print(w: &mut IO, x: Self) { w.print(x.as_bytes()); } } impl Print for String { fn print(w: &mut IO, x: Self) { w.print(x.as_bytes()); } } impl Print for (T, U) { fn print(w: &mut IO, (x, y): Self) { w.print(x); w.print(" "); w.print(y); } } impl Print for (T, U, V) { fn print(w: &mut IO, (x, y, z): Self) { w.print(x); w.print(" "); w.print(y); w.print(" "); w.print(z); } } mod neboccoio_macro { #[macro_export] macro_rules! input { (@start $io:tt @read @rest) => {}; (@start $io:tt @read @rest, $($rest: tt)*) => { input!(@start $io @read @rest $($rest)*) }; (@start $io:tt @read @rest mut $($rest:tt)*) => { input!(@start $io @read @mut [mut] @rest $($rest)*) }; (@start $io:tt @read @rest $($rest:tt)*) => { input!(@start $io @read @mut [] @rest $($rest)*) }; (@start $io:tt @read @mut [$($mut:tt)?] @rest $var:tt: [[$kind:tt; $len1:expr]; $len2:expr] $($rest:tt)*) => { let $($mut)* $var = (0..$len2).map(|_| $io.scan_vec::<$kind>($len1)).collect::>>(); input!(@start $io @read @rest $($rest)*) }; (@start $io:tt @read @mut [$($mut:tt)?] @rest $var:tt: [$kind:tt; $len:expr] $($rest:tt)*) => { let $($mut)* $var = $io.scan_vec::<$kind>($len); input!(@start $io @read @rest $($rest)*) }; (@start $io:tt @read @mut [$($mut:tt)?] @rest $var:tt: $kind:tt $($rest:tt)*) => { let $($mut)* $var = $io.scan::<$kind>(); input!(@start $io @read @rest $($rest)*) }; (from $io:tt $($rest:tt)*) => { input!(@start $io @read @rest $($rest)*) }; } } // ------------ io module end ------------