pub use __cargo_equip::prelude::*;

use std::{cmp::Reverse, collections::BinaryHeap};

use algebraic::{algebra, monoid};
use chminmax::chmin;
use graph::Graph;
#[allow(unused_imports)]
use proconio::{
    input,
    marker::{Bytes, Chars, Usize1},
};
use tree_query::TreeQueryEdge;

algebra!(M, i64);
monoid!(M, 0, |a, b| a + b);

const INF: i64 = 1 << 60;

fn main() {
    input! {
        n: usize,
        k: usize,
    }
    let mut g = Graph::<(), i64>::new(n);
    for _ in 0..n - 1 {
        input! {
            a: Usize1,
            b: Usize1,
            c: i64,
        }
        g.add_undirected_edge(a, b, c);
    }
    let tq = TreeQueryEdge::<M>::build(&g);
    let mut p = vec![];
    let mut x = vec![vec![]; k];
    for i in 0..k {
        input! {
            m: usize,
            pi: i64,
        }
        p.push(pi);
        for _ in 0..m {
            input! {
                xi: Usize1,
            }
            x[i].push(xi);
        }
    }
    let mut d = vec![vec![INF; n]; k];
    for i in 0..k {
        let mut pq = BinaryHeap::new();
        for &xi in &x[i] {
            d[i][xi] = 0;
            pq.push(Reverse((0, xi)));
        }
        while let Some(Reverse((c, v))) = pq.pop() {
            if d[i][v] < c {
                continue;
            }
            for &(u, w) in g.out_edges(v) {
                if d[i][u] > c + w {
                    d[i][u] = c + w;
                    pq.push(Reverse((c + w, u)));
                }
            }
        }
    }
    let mut e = vec![vec![INF; k]; k];
    for i in 0..k {
        e[i][i] = 0;
    }
    for i in 0..k {
        for &x in &x[i] {
            for j in 0..k {
                chmin!(e[i][j], d[j][x] + p[j]);
            }
        }
    }
    for l in 0..k {
        for i in 0..k {
            for j in 0..k {
                chmin!(e[i][j], e[i][l] + e[l][j]);
            }
        }
    }
    for i in 0..k {
        for j in 0..k {
            e[i][j] += p[i];
        }
    }
    input! {
        q: usize,
    }
    for _ in 0..q {
        input! {
            u: Usize1,
            v: Usize1,
        }
        let mut res = tq.prod_path(u, v);
        for i in 0..k {
            for j in 0..k {
                chmin!(res, e[i][j] + d[i][u] + d[j][v]);
            }
        }
        println!("{res}");
    }
}

// The following code was expanded by `cargo-equip`.

///  # Bundled libraries
/// 
///  - `algebraic 0.1.0 (path+████████████████████████████████████████████████████████)`                                      published in **missing** licensed under `CC0-1.0`           as `crate::__cargo_equip::crates::algebraic`
///  - `chminmax 0.1.0 (path+████████████████████████████████████████████████████)`                                           published in **missing** licensed under `CC0-1.0`           as `crate::__cargo_equip::crates::chminmax`
///  - `graph 0.1.0 (path+████████████████████████████████████████████████)`                                                  published in **missing** licensed under `CC0-1.0`           as `crate::__cargo_equip::crates::graph`
///  - `heavy-light-decomposition 0.1.0 (path+█████████████████████████████████████████████████████████████████████████████)` published in **missing** licensed under `CC0-1.0`           as `crate::__cargo_equip::crates::heavy_light_decomposition`
///  - `lazy_static 1.4.0 (registry+https://github.com/rust-lang/crates.io-index)`                                                                     licensed under `MIT/Apache-2.0`    as `crate::__cargo_equip::crates::__lazy_static_1_4_0`
///  - `proconio 0.4.3 (registry+https://github.com/rust-lang/crates.io-index)`                                                                        licensed under `MIT OR Apache-2.0` as `crate::__cargo_equip::crates::proconio`
///  - `segment-tree 0.1.0 (path+████████████████████████████████████████████████████████████████)`                           published in **missing** licensed under `CC0-1.0`           as `crate::__cargo_equip::crates::segment_tree`
///  - `tree-query 0.1.0 (path+██████████████████████████████████████████████████████████████)`                               published in **missing** licensed under `CC0-1.0`           as `crate::__cargo_equip::crates::tree_query`
/// 
///  # Procedural macros
/// 
///  - `proconio-derive 0.2.1 (registry+https://github.com/rust-lang/crates.io-index)` licensed under `MIT OR Apache-2.0`
/// 
///  # License and Copyright Notices
/// 
///  - `lazy_static 1.4.0 (registry+https://github.com/rust-lang/crates.io-index)`
/// 
///      ```text
///      Copyright (c) 2010 The Rust Project Developers
/// 
///      Permission is hereby granted, free of charge, to any
///      person obtaining a copy of this software and associated
///      documentation files (the "Software"), to deal in the
///      Software without restriction, including without
///      limitation the rights to use, copy, modify, merge,
///      publish, distribute, sublicense, and/or sell copies of
///      the Software, and to permit persons to whom the Software
///      is furnished to do so, subject to the following
///      conditions:
/// 
///      The above copyright notice and this permission notice
///      shall be included in all copies or substantial portions
///      of the Software.
/// 
///      THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF
///      ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED
///      TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A
///      PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT
///      SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY
///      CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION
///      OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR
///      IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
///      DEALINGS IN THE SOFTWARE.
///      ```
/// 
///  - `proconio 0.4.3 (registry+https://github.com/rust-lang/crates.io-index)`
/// 
///      ```text
///      The MIT License
///      Copyright 2019 (C) statiolake <statiolake@gmail.com>
/// 
///      Permission is hereby granted, free of charge, to any person obtaining a copy of
///      this software and associated documentation files (the "Software"), to deal in
///      the Software without restriction, including without limitation the rights to
///      use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of
///      the Software, and to permit persons to whom the Software is furnished to do so,
///      subject to the following conditions:
/// 
///      The above copyright notice and this permission notice shall be included in all
///      copies or substantial portions of the Software.
/// 
///      THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
///      IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS
///      FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR
///      COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER
///      IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
///      CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
/// 
///      Copyright for original `input!` macro is held by Hideyuki Tanaka, 2019.  The
///      original macro is licensed under BSD 3-clause license.
/// 
///      Redistribution and use in source and binary forms, with or without
///      modification, are permitted provided that the following conditions are met:
/// 
///      1. Redistributions of source code must retain the above copyright notice, this
///         list of conditions and the following disclaimer.
/// 
///      2. Redistributions in binary form must reproduce the above copyright notice,
///         this list of conditions and the following disclaimer in the documentation
///         and/or other materials provided with the distribution.
/// 
///      3. Neither the name of the copyright holder nor the names of its contributors
///         may be used to endorse or promote products derived from this software
///         without specific prior written permission.
/// 
///      THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
///      ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
///      WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
///      DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE
///      FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
///      DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
///      SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
///      CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
///      OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
///      OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
///      ```
#[cfg_attr(any(), rustfmt::skip)]
#[allow(unused)]
mod __cargo_equip {
    pub(crate) mod crates {
        pub mod algebraic {pub use crate::__cargo_equip::macros::algebraic::*;pub trait Algebra{type S;}pub trait Act:Algebra{type X;fn act(f:&Self::S,x:&Self::X)->Self::X;}pub trait Monoid:Algebra{fn e()->Self::S;fn op(x:&Self::S,y:&Self::S)->Self::S;}pub trait Group:Monoid{fn inv(x:&Self::S)->Self::S;}#[macro_export]macro_rules!__cargo_equip_macro_def_algebraic_algebra{($ident:ident,$ty:ty)=>{#[derive(Clone)]enum$ident{}impl$crate::__cargo_equip::crates::algebraic::Algebra for$ident{type S=$ty;}};}macro_rules!algebra{($($tt:tt)*)=>(crate::__cargo_equip_macro_def_algebraic_algebra!{$($tt)*})}#[macro_export]macro_rules!__cargo_equip_macro_def_algebraic_act{($ident:ident,$tar:ty,$act:expr)=>{impl$crate::__cargo_equip::crates::algebraic::Act for$ident{type X=$tar;#[inline]fn act(f:&Self::S,x:&Self::X)->Self::X{$act(f,x)}}};}macro_rules!act{($($tt:tt)*)=>(crate::__cargo_equip_macro_def_algebraic_act!{$($tt)*})}#[macro_export]macro_rules!__cargo_equip_macro_def_algebraic_monoid{($ident:ident,$e:expr,$op:expr)=>{impl$crate::__cargo_equip::crates::algebraic::Monoid for$ident{#[inline]fn e()->Self::S{$e}#[inline]fn op(x:&Self::S,y:&Self::S)->Self::S{$op(x,y)}}};}macro_rules!monoid{($($tt:tt)*)=>(crate::__cargo_equip_macro_def_algebraic_monoid!{$($tt)*})}#[macro_export]macro_rules!__cargo_equip_macro_def_algebraic_group{($ident:ident,$e:expr,$op:expr,$inv:expr)=>{impl$crate::__cargo_equip::crates::algebraic::Monoid for$ident{#[inline]fn e()->Self::S{$e}#[inline]fn op(x:&Self::S,y:&Self::S)->Self::S{$op(x,y)}}impl$crate::__cargo_equip::crates::algebraic::Group for$ident{#[inline]fn inv(x:&Self::S)->Self::S{$inv(x)}}};}macro_rules!group{($($tt:tt)*)=>(crate::__cargo_equip_macro_def_algebraic_group!{$($tt)*})}}
        pub mod chminmax {pub use crate::__cargo_equip::macros::chminmax::*;#[macro_export]macro_rules!__cargo_equip_macro_def_chminmax_min{($a:expr$(,)*)=>{{$a}};($a:expr,$b:expr$(,)*)=>{{std::cmp::min($a,$b)}};($a:expr,$($rest:expr),+$(,)*)=>{{std::cmp::min($a,$crate::__cargo_equip::crates::chminmax::min!($($rest),+))}};}macro_rules!min{($($tt:tt)*)=>(crate::__cargo_equip_macro_def_chminmax_min!{$($tt)*})}#[macro_export]macro_rules!__cargo_equip_macro_def_chminmax_max{($a:expr$(,)*)=>{{$a}};($a:expr,$b:expr$(,)*)=>{{std::cmp::max($a,$b)}};($a:expr,$($rest:expr),+$(,)*)=>{{std::cmp::max($a,$crate::__cargo_equip::crates::chminmax::max!($($rest),+))}};}macro_rules!max{($($tt:tt)*)=>(crate::__cargo_equip_macro_def_chminmax_max!{$($tt)*})}#[macro_export]macro_rules!__cargo_equip_macro_def_chminmax_chmin{($base:expr,$($cmps:expr),+$(,)*)=>{{let cmp_min=$crate::__cargo_equip::crates::chminmax::min!($($cmps),+);if$base>cmp_min{$base=cmp_min;true}else{false}}};}macro_rules!chmin{($($tt:tt)*)=>(crate::__cargo_equip_macro_def_chminmax_chmin!{$($tt)*})}#[macro_export]macro_rules!__cargo_equip_macro_def_chminmax_chmax{($base:expr,$($cmps:expr),+$(,)*)=>{{let cmp_max=$crate::__cargo_equip::crates::chminmax::max!($($cmps),+);if$base<cmp_max{$base=cmp_max;true}else{false}}};}macro_rules!chmax{($($tt:tt)*)=>(crate::__cargo_equip_macro_def_chminmax_chmax!{$($tt)*})}}
        pub mod graph {#[derive(Clone)]pub struct Graph<V,E>where V:Clone,E:Clone,{vertices:Vec<V>,head:Vec<usize>,next:Vec<usize>,edges:Vec<(usize,E)>,}pub const GRID_NEIGHBOURS_4:&[(usize,usize)]=&[(!0,0),(0,!0),(1,0),(0,1)];pub const GRID_NEIGHBOURS_8:&[(usize,usize)]=&[(!0,0),(0,!0),(1,0),(0,1),(!0,!0),(!0,1),(1,!0),(1,1),];impl<V,E>Graph<V,E>where V:Clone+Default,E:Clone,{pub fn new(n:usize)->Self{Self{vertices:vec![Default::default();n],head:vec![!0;n],next:vec![],edges:vec![],}}}impl<V,E>From<Vec<V>>for Graph<V,E>where V:Clone,E:Clone,{fn from(vertices:Vec<V>)->Self{Self{head:vec![!0;vertices.len()],vertices,next:vec![],edges:vec![],}}}impl<V,E>Graph<V,E>where V:Clone,E:Clone,{pub fn size(&self)->usize{self.vertices.len()}pub fn set_vertex(&mut self,v:usize,w:V){self.vertices[v]=w;}pub fn add_vertex(&mut self,w:V)->usize{self.vertices.push(w);self.head.push(!0);self.vertices.len()-1}pub fn add_edge(&mut self,u:usize,v:usize,w:E){self.next.push(self.head[u]);self.head[u]=self.edges.len();self.edges.push((v,w));}pub fn add_undirected_edge(&mut self,u:usize,v:usize,w:E){self.add_edge(u,v,w.clone());self.add_edge(v,u,w);}pub fn vertices(&self)->&[V]{&self.vertices}pub fn out_edges(&self,v:usize)->impl Iterator<Item=&(usize,E)>{let mut e=self.head[v];std::iter::from_fn(move||{if e!=!0{let res=&self.edges[e];e=self.next[e];Some(res)}else{None}})}pub fn from_grid(grid:&Vec<Vec<V>>,neighbours:&[(usize,usize)],cost:impl Fn(&V,&V)->Option<E>,)->Self{let h=grid.len();let w=grid[0].len();let mut g=Self::from(grid.into_iter().flatten().cloned().collect::<Vec<_>>());for i in 0..h{for j in 0..w{for&(di,dj)in neighbours{let ni=i.wrapping_add(di);let nj=j.wrapping_add(dj);if ni>=h||nj>=w{continue;}if let Some(c)=cost(&grid[i][j],&grid[ni][nj]){g.add_edge(i*w+j,ni*w+nj,c);}}}}g}}}
        pub mod heavy_light_decomposition {use crate::__cargo_equip::preludes::heavy_light_decomposition::*;use graph::Graph;use std::mem::swap;pub struct HeavyLightDecomposition{t_in:Vec<usize>,t_out:Vec<usize>,ord:Vec<usize>,size:Vec<usize>,heavy:Vec<usize>,head:Vec<usize>,par:Vec<usize>,depth:Vec<usize>,}impl HeavyLightDecomposition{pub fn new<V,E>(g:&Graph<V,E>)->Self where V:Clone,E:Clone,{let n=g.size();let mut hld=HeavyLightDecomposition{t_in:vec![0;n],t_out:vec![0;n],ord:vec![],size:vec![0;n],heavy:vec![!0;n],head:vec![0;n],par:vec![!0;n],depth:vec![0;n],};hld.dfs_sz(g,0);hld.dfs_hld(g,0,&mut 0);hld}fn dfs_sz<V,E>(&mut self,g:&Graph<V,E>,v:usize)where V:Clone,E:Clone,{self.size[v]=1;for&(u,_)in g.out_edges(v){if u==self.par[v]{continue;}self.par[u]=v;self.depth[u]=self.depth[v]+1;self.dfs_sz(g,u);self.size[v]+=self.size[u];if self.heavy[v]==!0||self.size[u]>self.size[self.heavy[v]]{self.heavy[v]=u;}}}fn dfs_hld<V,E>(&mut self,g:&Graph<V,E>,v:usize,t:&mut usize)where V:Clone,E:Clone,{self.t_in[v]=*t;self.ord.push(v);*t+=1;if self.heavy[v]!=!0{let u=self.heavy[v];self.head[u]=self.head[v];self.dfs_hld(g,u,t);}for&(u,_)in g.out_edges(v){if u==self.par[v]{continue;}if u==self.heavy[v]{continue;}self.head[u]=u;self.dfs_hld(g,u,t);}self.t_out[v]=*t;}}impl HeavyLightDecomposition{pub fn kth_ancestor(&self,mut v:usize,mut k:usize)->usize{if self.depth[v]<k{return!0;}loop{let u=self.head[v];if self.t_in[v]-k>=self.t_in[u]{return self.ord[self.t_in[v]-k];}k-=1+self.t_in[v]-self.t_in[u];v=self.par[u];}}pub fn lca(&self,mut u:usize,mut v:usize)->usize{loop{if self.t_in[u]>self.t_in[v]{swap(&mut u,&mut v);}if self.head[u]==self.head[v]{return u;}v=self.par[self.head[v]];}}pub fn dist(&self,u:usize,v:usize)->usize{let l=self.lca(u,v);self.depth[u]+self.depth[v]-self.depth[l]*2}pub fn jump(&self,u:usize,v:usize,k:usize)->usize{if k==0{return u;}let l=self.lca(u,v);let d_lu=self.depth[u]-self.depth[l];let d_lv=self.depth[v]-self.depth[l];if k>d_lu+d_lv{!0}else if k<=d_lu{self.kth_ancestor(u,k)}else{self.kth_ancestor(v,d_lu+d_lv-k)}}pub fn vertex(&self,v:usize)->usize{self.t_in[v]}pub fn edge(&self,u:usize,v:usize)->usize{if self.depth[u]<self.depth[v]{self.t_in[v]}else{self.t_in[u]}}pub fn path(&self,mut u:usize,mut v:usize,edge:bool,)->(Vec<(usize,usize)>,Vec<(usize,usize)>){let mut up=vec![];let mut down=vec![];let e=if edge{1}else{0};while self.head[u]!=self.head[v]{if self.t_in[u]<self.t_in[v]{down.push((self.t_in[self.head[v]],self.t_in[v]+1));v=self.par[self.head[v]];}else{up.push((self.t_in[self.head[u]],self.t_in[u]+1));u=self.par[self.head[u]];}}if self.t_in[u]<self.t_in[v]{down.push((self.t_in[u]+e,self.t_in[v]+1));}else if self.t_in[u]>=self.t_in[v]+e{up.push((self.t_in[v]+e,self.t_in[u]+1));}down.reverse();(up,down)}pub fn subtree(&self,v:usize,edge:bool)->(usize,usize){let e=if edge{1}else{0};(self.t_in[v]+e,self.t_out[v])}}}
        pub mod __lazy_static_1_4_0 {#![no_std]use crate::__cargo_equip::preludes::__lazy_static_1_4_0::*;pub use crate::__cargo_equip::macros::__lazy_static_1_4_0::*;#[path="inline_lazy.rs"]pub mod lazy{use crate::__cargo_equip::preludes::__lazy_static_1_4_0::*;extern crate core;extern crate std;use self::std::prelude::v1::*;use self::std::cell::Cell;use self::std::hint::unreachable_unchecked;use self::std::sync::Once;#[allow(deprecated)]pub use self::std::sync::ONCE_INIT;pub struct Lazy<T:Sync>(Cell<Option<T>>,Once);impl<T:Sync>Lazy<T>{#[allow(deprecated)]pub const INIT:Self=Lazy(Cell::new(None),ONCE_INIT);#[inline(always)]pub fn get<F>(&'static self,f:F)->&T where F:FnOnce()->T,{self.1.call_once(||{self.0.set(Some(f()));});unsafe{match*self.0.as_ptr(){Some(ref x)=>x,None=>{debug_assert!(false,"attempted to derefence an uninitialized lazy static. This is a bug");unreachable_unchecked()},}}}}unsafe impl<T:Sync>Sync for Lazy<T>{}#[macro_export]macro_rules!__cargo_equip_macro_def___lazy_static_1_4_0___lazy_static_create{($NAME:ident,$T:ty)=>{static$NAME:$crate::__cargo_equip::crates::__lazy_static_1_4_0::lazy::Lazy<$T> =$crate::__cargo_equip::crates::__lazy_static_1_4_0::lazy::Lazy::INIT;};}macro_rules!__lazy_static_create{($($tt:tt)*)=>(crate::__cargo_equip_macro_def___lazy_static_1_4_0___lazy_static_create!{$($tt)*})}}pub use core::ops::Deref as __Deref;#[macro_export(local_inner_macros)]macro_rules!__cargo_equip_macro_def___lazy_static_1_4_0___lazy_static_internal{($(#[$attr:meta])*($($vis:tt)*)static ref$N:ident:$T:ty=$e:expr;$($t:tt)*)=>{__lazy_static_internal!(@MAKE TY,$(#[$attr])*,($($vis)*),$N);__lazy_static_internal!(@TAIL,$N:$T=$e);lazy_static!($($t)*);};(@TAIL,$N:ident:$T:ty=$e:expr)=>{impl$crate::__cargo_equip::crates::__lazy_static_1_4_0::__Deref for$N{type Target=$T;fn deref(&self)->&$T{#[inline(always)]fn __static_ref_initialize()->$T{$e}#[inline(always)]fn __stability()->&'static$T{__lazy_static_create!(LAZY,$T);LAZY.get(__static_ref_initialize)}__stability()}}impl$crate::__cargo_equip::crates::__lazy_static_1_4_0::LazyStatic for$N{fn initialize(lazy:&Self){let _=&**lazy;}}};(@MAKE TY,$(#[$attr:meta])*,($($vis:tt)*),$N:ident)=>{#[allow(missing_copy_implementations)]#[allow(non_camel_case_types)]#[allow(dead_code)]$(#[$attr])*$($vis)*struct$N{__private_field:()}#[doc(hidden)]$($vis)*static$N:$N=$N{__private_field:()};};()=>()}macro_rules!__lazy_static_internal{($($tt:tt)*)=>(crate::__cargo_equip_macro_def___lazy_static_1_4_0___lazy_static_internal!{$($tt)*})}#[macro_export(local_inner_macros)]macro_rules!__cargo_equip_macro_def___lazy_static_1_4_0_lazy_static{($(#[$attr:meta])*static ref$N:ident:$T:ty=$e:expr;$($t:tt)*)=>{__lazy_static_internal!($(#[$attr])*()static ref$N:$T=$e;$($t)*);};($(#[$attr:meta])*pub static ref$N:ident:$T:ty=$e:expr;$($t:tt)*)=>{__lazy_static_internal!($(#[$attr])*(pub)static ref$N:$T=$e;$($t)*);};($(#[$attr:meta])*pub($($vis:tt)+)static ref$N:ident:$T:ty=$e:expr;$($t:tt)*)=>{__lazy_static_internal!($(#[$attr])*(pub($($vis)+))static ref$N:$T=$e;$($t)*);};()=>()}macro_rules!lazy_static{($($tt:tt)*)=>(crate::__cargo_equip_macro_def___lazy_static_1_4_0_lazy_static!{$($tt)*})}pub trait LazyStatic{fn initialize(lazy:&Self);}pub fn initialize<T:LazyStatic>(lazy:&T){LazyStatic::initialize(lazy);}}
        pub mod proconio {#![allow(clippy::needless_doctest_main,clippy::print_literal)]use crate::__cargo_equip::preludes::proconio::*;pub use crate::__cargo_equip::macros::proconio::*;pub use proconio_derive::*;pub mod marker{use crate::__cargo_equip::preludes::proconio::*;use crate::__cargo_equip::crates::proconio::source::{Readable,Source};use std::io::BufRead;pub enum Chars{}impl Readable for Chars{type Output=Vec<char>;fn read<R:BufRead,S:Source<R>>(source:&mut S)->Vec<char>{source.next_token_unwrap().chars().collect()}}pub enum Bytes{}impl Readable for Bytes{type Output=Vec<u8>;fn read<R:BufRead,S:Source<R>>(source:&mut S)->Vec<u8>{source.next_token_unwrap().bytes().collect()}}pub enum Usize1{}impl Readable for Usize1{type Output=usize;fn read<R:BufRead,S:Source<R>>(source:&mut S)->usize{usize::read(source).checked_sub(1).expect("attempted to read the value 0 as a Usize1")}}pub enum Isize1{}impl Readable for Isize1{type Output=isize;fn read<R:BufRead,S:Source<R>>(source:&mut S)->isize{isize::read(source).checked_sub(1).unwrap_or_else(||{panic!(concat!("attempted to read the value {} as a Isize1:"," the value is isize::MIN and cannot be decremented"),std::isize::MIN,)})}}}pub mod source{use crate::__cargo_equip::preludes::proconio::*;use std::any::type_name;use std::fmt::Debug;use std::io::BufRead;use std::str::FromStr;pub mod line{use crate::__cargo_equip::preludes::proconio::*;use super::Source;use std::io::BufRead;use std::iter::Peekable;use std::str::SplitWhitespace;pub struct LineSource<R:BufRead>{tokens:Peekable<SplitWhitespace<'static>>,current_context:Box<str>,reader:R,}impl<R:BufRead>LineSource<R>{pub fn new(reader:R)->LineSource<R>{LineSource{current_context:"".to_string().into_boxed_str(),tokens:"".split_whitespace().peekable(),reader,}}fn prepare(&mut self){while self.tokens.peek().is_none(){let mut line=String::new();let num_bytes=self.reader.read_line(&mut line).expect("failed to get linel maybe an IO error.");if num_bytes==0{return;}self.current_context=line.into_boxed_str();self.tokens=unsafe{std::mem::transmute::<_,&'static str>(&*self.current_context)}.split_whitespace().peekable();}}}impl<R:BufRead>Source<R>for LineSource<R>{fn next_token(&mut self)->Option<&str>{self.prepare();self.tokens.next()}fn is_empty(&mut self)->bool{self.prepare();self.tokens.peek().is_none()}}use std::io::BufReader;impl<'a>From<&'a str>for LineSource<BufReader<&'a[u8]>>{fn from(s:&'a str)->LineSource<BufReader<&'a[u8]>>{LineSource::new(BufReader::new(s.as_bytes()))}}}pub mod once{use crate::__cargo_equip::preludes::proconio::*;use super::Source;use std::io::BufRead;use std::iter::Peekable;use std::marker::PhantomData;use std::str::SplitWhitespace;pub struct OnceSource<R:BufRead>{tokens:Peekable<SplitWhitespace<'static>>,context:Box<str>,_read:PhantomData<R>,}impl<R:BufRead>OnceSource<R>{pub fn new(mut source:R)->OnceSource<R>{let mut context=String::new();source.read_to_string(&mut context).expect("failed to read from source; maybe an IO error.");let context=context.into_boxed_str();let mut res=OnceSource{context,tokens:"".split_whitespace().peekable(),_read:PhantomData,};use std::mem;let context:&'static str=unsafe{mem::transmute(&*res.context)};res.tokens=context.split_whitespace().peekable();res}}impl<R:BufRead>Source<R>for OnceSource<R>{fn next_token(&mut self)->Option<&str>{self.tokens.next()}fn is_empty(&mut self)->bool{self.tokens.peek().is_none()}}use std::io::BufReader;impl<'a>From<&'a str>for OnceSource<BufReader<&'a[u8]>>{fn from(s:&'a str)->OnceSource<BufReader<&'a[u8]>>{OnceSource::new(BufReader::new(s.as_bytes()))}}}pub mod auto{use crate::__cargo_equip::preludes::proconio::*;#[cfg(debug_assertions)]pub use super::line::LineSource as AutoSource;#[cfg(not(debug_assertions))]pub use super::once::OnceSource as AutoSource;}pub trait Source<R:BufRead>{fn next_token(&mut self)->Option<&str>;fn is_empty(&mut self)->bool;fn next_token_unwrap(&mut self)->&str{self.next_token().expect(concat!("failed to get the next token; ","maybe reader reached an end of input. ","ensure that arguments for `input!` macro is correctly ","specified to match the problem input."))}}impl<R:BufRead,S:Source<R>>Source<R>for&'_ mut S{fn next_token(&mut self)->Option<&str>{(*self).next_token()}fn is_empty(&mut self)->bool{(*self).is_empty()}}pub trait Readable{type Output;fn read<R:BufRead,S:Source<R>>(source:&mut S)->Self::Output;}impl<T:FromStr>Readable for T where T::Err:Debug,{type Output=T;fn read<R:BufRead,S:Source<R>>(source:&mut S)->T{let token=source.next_token_unwrap();match token.parse(){Ok(v)=>v,Err(e)=>panic!(concat!("failed to parse the input `{input}` ","to the value of type `{ty}`: {err:?}; ","ensure that the input format is collectly specified ","and that the input value must handle specified type.",),input=token,ty=type_name::<T>(),err=e,),}}}}use crate::__cargo_equip::crates::proconio::source::auto::AutoSource;use lazy_static::lazy_static;use std::io;use std::io::{BufReader,Stdin};use std::sync::Mutex;pub use crate::__cargo_equip::crates::proconio::source::Readable as __Readable;lazy_static!{#[doc(hidden)]pub static ref STDIN_SOURCE:Mutex<AutoSource<BufReader<Stdin>>>=Mutex::new(AutoSource::new(BufReader::new(io::stdin())));}#[macro_export]macro_rules!__cargo_equip_macro_def_proconio_input{(@from[$source:expr]@rest)=>{};(@from[$source:expr]@rest mut$($rest:tt)*)=>{$crate::__cargo_equip::crates::proconio::input!{@from[$source]@mut[mut]@rest$($rest)*}};(@from[$source:expr]@rest$($rest:tt)*)=>{$crate::__cargo_equip::crates::proconio::input!{@from[$source]@mut[]@rest$($rest)*}};(@from[$source:expr]@mut[$($mut:tt)?]@rest$var:tt:$($rest:tt)*)=>{$crate::__cargo_equip::crates::proconio::input!{@from[$source]@mut[$($mut)*]@var$var@kind[]@rest$($rest)*}};(@from[$source:expr]@mut[$($mut:tt)?]@var$var:tt@kind[$($kind:tt)*]@rest)=>{let$($mut)*$var=$crate::__cargo_equip::crates::proconio::read_value!(@source[$source]@kind[$($kind)*]);};(@from[$source:expr]@mut[$($mut:tt)?]@var$var:tt@kind[$($kind:tt)*]@rest,$($rest:tt)*)=>{$crate::__cargo_equip::crates::proconio::input!(@from[$source]@mut[$($mut)*]@var$var@kind[$($kind)*]@rest);$crate::__cargo_equip::crates::proconio::input!(@from[$source]@rest$($rest)*);};(@from[$source:expr]@mut[$($mut:tt)?]@var$var:tt@kind[$($kind:tt)*]@rest$tt:tt$($rest:tt)*)=>{$crate::__cargo_equip::crates::proconio::input!(@from[$source]@mut[$($mut)*]@var$var@kind[$($kind)*$tt]@rest$($rest)*);};(from$source:expr,$($rest:tt)*)=>{#[allow(unused_variables,unused_mut)]let mut s=$source;$crate::__cargo_equip::crates::proconio::input!{@from[&mut s]@rest$($rest)*}};($($rest:tt)*)=>{let mut locked_stdin=$crate::__cargo_equip::crates::proconio::STDIN_SOURCE.lock().expect(concat!("failed to lock the stdin; please re-run this program.  ","If this issue repeatedly occur, this is a bug in `proconio`.  ","Please report this issue from ","<https://github.com/statiolake/proconio-rs/issues>."));$crate::__cargo_equip::crates::proconio::input!{@from[&mut*locked_stdin]@rest$($rest)*}drop(locked_stdin);};}macro_rules!input{($($tt:tt)*)=>(crate::__cargo_equip_macro_def_proconio_input!{$($tt)*})}#[macro_export]macro_rules!__cargo_equip_macro_def_proconio_read_value{(@source[$source:expr]@kind[[$($kind:tt)*]])=>{$crate::__cargo_equip::crates::proconio::read_value!(@array@source[$source]@kind[]@rest$($kind)*)};(@array@source[$source:expr]@kind[$($kind:tt)*]@rest)=>{{let len=<usize as$crate::__cargo_equip::crates::proconio::__Readable>::read($source);$crate::__cargo_equip::crates::proconio::read_value!(@source[$source]@kind[[$($kind)*;len]])}};(@array@source[$source:expr]@kind[$($kind:tt)*]@rest;$($rest:tt)*)=>{$crate::__cargo_equip::crates::proconio::read_value!(@array@source[$source]@kind[$($kind)*]@len[$($rest)*])};(@array@source[$source:expr]@kind[$($kind:tt)*]@rest$tt:tt$($rest:tt)*)=>{$crate::__cargo_equip::crates::proconio::read_value!(@array@source[$source]@kind[$($kind)*$tt]@rest$($rest)*)};(@array@source[$source:expr]@kind[$($kind:tt)*]@len[$($len:tt)*])=>{{let len=$($len)*;(0..len).map(|_|$crate::__cargo_equip::crates::proconio::read_value!(@source[$source]@kind[$($kind)*])).collect::<Vec<_>>()}};(@source[$source:expr]@kind[($($kinds:tt)*)])=>{$crate::__cargo_equip::crates::proconio::read_value!(@tuple@source[$source]@kinds[]@current[]@rest$($kinds)*)};(@tuple@source[$source:expr]@kinds[$([$($kind:tt)*])*]@current[]@rest)=>{($($crate::__cargo_equip::crates::proconio::read_value!(@source[$source]@kind[$($kind)*]),)*)};(@tuple@source[$source:expr]@kinds[$($kinds:tt)*]@current[$($curr:tt)*]@rest)=>{$crate::__cargo_equip::crates::proconio::read_value!(@tuple@source[$source]@kinds[$($kinds)*[$($curr)*]]@current[]@rest)};(@tuple@source[$source:expr]@kinds[$($kinds:tt)*]@current[$($curr:tt)*]@rest,$($rest:tt)*)=>{$crate::__cargo_equip::crates::proconio::read_value!(@tuple@source[$source]@kinds[$($kinds)*[$($curr)*]]@current[]@rest$($rest)*)};(@tuple@source[$source:expr]@kinds[$($kinds:tt)*]@current[$($curr:tt)*]@rest$tt:tt$($rest:tt)*)=>{$crate::__cargo_equip::crates::proconio::read_value!(@tuple@source[$source]@kinds[$($kinds)*]@current[$($curr)*$tt]@rest$($rest)*)};(@source[$source:expr]@kind[])=>{compile_error!(concat!("Reached unreachable statement while parsing macro input.  ","This is a bug in `proconio`.  ","Please report this issue from ","<https://github.com/statiolake/proconio-rs/issues>."));};(@source[$source:expr]@kind[$kind:ty])=>{<$kind as$crate::__cargo_equip::crates::proconio::__Readable>::read($source)}}macro_rules!read_value{($($tt:tt)*)=>(crate::__cargo_equip_macro_def_proconio_read_value!{$($tt)*})}pub fn is_stdin_empty()->bool{use crate::__cargo_equip::crates::proconio::source::Source;let mut lock=STDIN_SOURCE.lock().expect(concat!("failed to lock the stdin; please re-run this program.  ","If this issue repeatedly occur, this is a bug in `proconio`.  ","Please report this issue from ","<https://github.com/statiolake/proconio-rs/issues>."));lock.is_empty()}}
        pub mod __proconio_derive_0_2_1 {pub use crate::__cargo_equip::macros::__proconio_derive_0_2_1::*;#[macro_export]macro_rules!__cargo_equip_macro_def___proconio_derive_0_2_1_derive_readable{($(_:tt)*)=>(::std::compile_error!("`derive_readable` from `proconio-derive 0.2.1` should have been expanded");)}#[macro_export]macro_rules!__cargo_equip_macro_def___proconio_derive_0_2_1_fastout{($(_:tt)*)=>(::std::compile_error!("`fastout` from `proconio-derive 0.2.1` should have been expanded");)}}
        pub mod segment_tree {use crate::__cargo_equip::preludes::segment_tree::*;use std::ops::{Bound,RangeBounds};use algebraic::Monoid;#[derive(Clone)]pub struct SegmentTree<M>where M:Monoid,M::S:Clone,{n:usize,v:Vec<M::S>,}impl<M>SegmentTree<M>where M:Monoid,M::S:Clone,{pub fn new(n:usize)->Self{Self{n,v:vec![M::e();n*2],}}pub fn set(&mut self,mut k:usize,x:M::S){k+=self.n;self.v[k]=x;while k>1{k>>=1;self.v[k]=M::op(&self.v[k*2],&self.v[k*2+1]);}}pub fn get(&self,k:usize)->M::S{assert!(k<self.n);self.v[k+self.n].clone()}pub fn prod<R>(&self,range:R)->M::S where R:RangeBounds<usize>,{let mut l=match range.start_bound(){Bound::Excluded(&l)=>l+1,Bound::Included(&l)=>l,Bound::Unbounded=>0,};let mut r=match range.end_bound(){Bound::Excluded(&r)=>r,Bound::Included(&r)=>r+1,Bound::Unbounded=>self.n,};assert!(l<=r);assert!(r<=self.n);l+=self.n;r+=self.n;let mut sl=M::e();let mut sr=M::e();while l<r{if l&1!=0{sl=M::op(&sl,&self.v[l]);l+=1;}if r&1!=0{r-=1;sr=M::op(&self.v[r],&sr);}l>>=1;r>>=1;}M::op(&sl,&sr)}pub fn max_right<P>(&self,mut l:usize,pred:P)->usize where P:Fn(&M::S)->bool,{assert!(l<=self.n);assert!(pred(&M::e()));if pred(&self.prod(l..)){return self.n;}l+=self.n;let mut s=M::e();loop{while l&1==0&&self.is_good_node(l>>1){l>>=1;}if!pred(&M::op(&s,&self.v[l])){while l<self.n{l<<=1;let t=M::op(&s,&self.v[l]);if pred(&t){s=t;l+=1;}}return l-self.n;}s=M::op(&s,&self.v[l]);l+=1;}}pub fn min_left<P>(&self,mut r:usize,pred:P)->usize where P:Fn(&M::S)->bool,{assert!(r<=self.n);assert!(pred(&M::e()));if pred(&self.prod(..r)){return 0;}r+=self.n;let mut s=M::e();loop{r-=1;while!self.is_good_node(r){r=r*2+1;}while r&1!=0&&self.is_good_node(r>>1){r>>=1;}if!pred(&M::op(&self.v[r],&s)){while r<self.n{r=r*2+1;let t=M::op(&self.v[r],&s);if pred(&t){s=t;r-=1;}}return r+1-self.n;}s=M::op(&self.v[r],&s);}}#[inline]fn is_good_node(&self,k:usize)->bool{if k>=self.n{true}else{let d=k.leading_zeros()-self.n.leading_zeros();self.n>>d!=k||self.n>>d<<d==self.n}}}impl<M>From<Vec<M::S>>for SegmentTree<M>where M:Monoid,M::S:Clone,{fn from(mut a:Vec<M::S>)->Self{let n=a.len();let mut v=vec![M::e();n];v.append(&mut a);for i in(1..n).rev(){v[i]=M::op(&v[i*2],&v[i*2+1]);}Self{n,v}}}}
        pub mod tree_query {use crate::__cargo_equip::preludes::tree_query::*;use std::marker::PhantomData;use algebraic::Monoid;use graph::Graph;use heavy_light_decomposition::HeavyLightDecomposition;use segment_tree::SegmentTree;pub type TreeQueryVertex<M> =TreeQuery<M,Vertex>;pub type TreeQueryEdge<M> =TreeQuery<M,Edge>;pub trait QueryType{fn vertex()->bool;fn edge()->bool;}pub enum Vertex{}pub enum Edge{}impl QueryType for Vertex{fn vertex()->bool{true}fn edge()->bool{false}}impl QueryType for Edge{fn vertex()->bool{false}fn edge()->bool{true}}pub struct TreeQuery<M,Q>where M:Monoid,M::S:Clone,Q:QueryType,{n:usize,hld:HeavyLightDecomposition,seg_up:SegmentTree<M>,seg_down:SegmentTree<M>,_marker:PhantomData<fn()->Q>,}impl<M,Q>TreeQuery<M,Q>where M:Monoid,M::S:Clone,Q:QueryType,{pub fn prod_path(&self,u:usize,v:usize)->M::S{let(up,down)=self.hld.path(u,v,Q::edge());let mut res=M::e();for&(l,r)in&up{let t=self.seg_up.prod(self.n-r..self.n-l);res=M::op(&res,&t);}for&(l,r)in&down{let t=self.seg_down.prod(l..r);res=M::op(&res,&t);}res}pub fn prod_subtree(&self,v:usize)->M::S{let(l,r)=self.hld.subtree(v,Q::edge());self.seg_down.prod(l..r)}}impl<V,M>TreeQuery<M,Vertex>where V:Clone,M:Monoid<S=V>,{pub fn build<E>(g:&Graph<V,E>)->Self where E:Clone,{let n=g.size();let hld=HeavyLightDecomposition::new(g);let mut a=vec![M::e();n];for v in 0..n{let k=hld.vertex(v);a[k]=g.vertices()[v].clone();}let seg_down=SegmentTree::from(a.clone());a.reverse();let seg_up=SegmentTree::from(a);Self{n,hld,seg_up,seg_down,_marker:PhantomData::default(),}}pub fn set(&mut self,v:usize,x:M::S){let k=self.hld.vertex(v);self.seg_up.set(self.n-1-k,x.clone());self.seg_down.set(k,x);}pub fn get(&self,v:usize)->M::S{let k=self.hld.vertex(v);self.seg_down.get(k)}}impl<E,M>TreeQuery<M,Edge>where E:Clone,M:Monoid<S=E>,{pub fn build<V>(g:&Graph<V,E>)->Self where V:Clone,{let n=g.size();let hld=HeavyLightDecomposition::new(g);let mut a=vec![M::e();n];for v in 0..n{for(u,w)in g.out_edges(v){let k=hld.edge(*u,v);a[k]=w.clone();}}let seg_down=SegmentTree::from(a.clone());a.reverse();let seg_up=SegmentTree::from(a);Self{n,hld,seg_up,seg_down,_marker:PhantomData::default(),}}pub fn set(&mut self,u:usize,v:usize,x:M::S){let k=self.hld.edge(u,v);self.seg_up.set(self.n-1-k,x.clone());self.seg_down.set(k,x);}pub fn get(&self,u:usize,v:usize)->M::S{let k=self.hld.edge(u,v);self.seg_down.get(k)}}}
    }

    pub(crate) mod macros {
        pub mod algebraic {pub use crate::{__cargo_equip_macro_def_algebraic_act as act,__cargo_equip_macro_def_algebraic_algebra as algebra,__cargo_equip_macro_def_algebraic_group as group,__cargo_equip_macro_def_algebraic_monoid as monoid};}
        pub mod chminmax {pub use crate::{__cargo_equip_macro_def_chminmax_chmax as chmax,__cargo_equip_macro_def_chminmax_chmin as chmin,__cargo_equip_macro_def_chminmax_max as max,__cargo_equip_macro_def_chminmax_min as min};}
        pub mod graph {}
        pub mod heavy_light_decomposition {}
        pub mod __lazy_static_1_4_0 {pub use crate::{__cargo_equip_macro_def___lazy_static_1_4_0___lazy_static_create as __lazy_static_create,__cargo_equip_macro_def___lazy_static_1_4_0___lazy_static_internal as __lazy_static_internal,__cargo_equip_macro_def___lazy_static_1_4_0_lazy_static as lazy_static};}
        pub mod proconio {pub use crate::{__cargo_equip_macro_def_proconio_input as input,__cargo_equip_macro_def_proconio_read_value as read_value};}
        pub mod __proconio_derive_0_2_1 {pub use crate::{__cargo_equip_macro_def___proconio_derive_0_2_1_derive_readable as derive_readable,__cargo_equip_macro_def___proconio_derive_0_2_1_fastout as fastout};}
        pub mod segment_tree {}
        pub mod tree_query {}
    }

    pub(crate) mod prelude {pub use crate::__cargo_equip::{crates::*,macros::__lazy_static_1_4_0::*};}

    mod preludes {
        pub mod algebraic {}
        pub mod chminmax {}
        pub mod graph {}
        pub mod heavy_light_decomposition {pub(in crate::__cargo_equip)use crate::__cargo_equip::crates::graph;}
        pub mod __lazy_static_1_4_0 {pub(in crate::__cargo_equip)use crate::__cargo_equip::macros::__lazy_static_1_4_0::*;}
        pub mod proconio {pub(in crate::__cargo_equip)use crate::__cargo_equip::macros::__lazy_static_1_4_0::*;pub(in crate::__cargo_equip)use crate::__cargo_equip::crates::{__lazy_static_1_4_0 as lazy_static,__proconio_derive_0_2_1 as proconio_derive};}
        pub mod __proconio_derive_0_2_1 {}
        pub mod segment_tree {pub(in crate::__cargo_equip)use crate::__cargo_equip::crates::algebraic;}
        pub mod tree_query {pub(in crate::__cargo_equip)use crate::__cargo_equip::crates::{algebraic,graph,heavy_light_decomposition,segment_tree};}
    }
}