pub fn solve() {
    crate::prepare!();
    sc!(n, q, (mut g, _): @TreeGraphScanner::<Usize1>::new(n), st: [(Usize1, Usize1); q]);
    let hld = HeavyLightDecomposition::new(0, &mut g);
    let r = ReRooting::<AdditiveOperation<usize>, _>::new(&g, |x, _, _| x + 1);
    let mut eid = HashMap::new();
    for u in g.vertices() {
        for a in g.adjacencies(u) {
            eid.insert((u, a.to), a.id);
        }
    }
    let dep = g.tree_depth(0);
    let mut up = vec![hld.par.to_vec()];
    for _ in 0..20 {
        let pp = up.last().unwrap();
        let mut np = vec![0; n];
        for i in 0..n {
            np[i] = if pp[i] < n { pp[pp[i]] } else { pp[i] };
        }
        up.push(np);
    }
    let dist = |u: usize, v: usize| {
        let p = hld.lca(u, v);
        (dep[u] + dep[v] - dep[p] * 2) as usize
    };
    let jup = |u: usize, d: usize| {
        let mut x = u;
        for i in 0..20 {
            if d & 1 << i != 0 {
                x = up[i][x];
            }
        }
        x
    };
    let jump = |from: usize, to: usize, d: usize| {
        let lca = hld.lca(from, to);
        let e = (dep[from] - dep[lca]) as usize;
        if e >= d {
            jup(from, d)
        } else {
            jup(to, (dep[from] + dep[to] - dep[lca] * 2) as usize - d)
        }
    };
    for (s, t) in st {
        let d = dist(s, t);
        let ans = if d % 2 == 0 {
            let mid = jump(s, t, d / 2);
            let ss = jump(mid, s, 1);
            let tt = jump(mid, t, 1);
            let mut ans = n;
            for &ss in &[ss, tt] {
                let e = eid[&(mid, ss)];
                ans -= if hld.par[ss] == mid {
                    r.ep[e]
                } else {
                    r.ep[e + n - 1]
                };
            }
            ans
        } else {
            0
        };
        pp!(ans);
    }
}
crate::main!();
#[allow(unused_imports)]use std::{cmp::{Ordering,Reverse},collections::{BTreeMap,BTreeSet,BinaryHeap,HashMap,HashSet,VecDeque}};
mod main_macros{#[doc=" Prepare useful macros."]#[doc=" - `prepare!();`: default (all input scanner (`sc!`, `sv!`) + buf print (`pp!`, `dg!`))"]#[doc=" - `prepare!(?);`: interactive (line scanner (`scln!`) + buf print (`pp!`, `dg!`))"]#[macro_export]macro_rules!prepare{(@output($dol:tt))=>{#[allow(unused_imports)]use std::io::Write as _;let __out=std::io::stdout();#[allow(unused_mut,unused_variables)]let mut __out=std::io::BufWriter::new(__out.lock());#[allow(unused_macros)]#[doc=" [`iter_print!`] for buffered stdout."]macro_rules!pp{($dol($dol t:tt)*)=>{$dol crate::iter_print!(__out,$dol($dol t)*)}}#[cfg(debug_assertions)]#[allow(unused_macros)]#[doc=" [`iter_print!`] for buffered stderr. Do nothing in release mode."]macro_rules!dg{($dol($dol t:tt)*)=>{{#[allow(unused_imports)]use std::io::Write as _;let __err=std::io::stderr();#[allow(unused_mut,unused_variables)]let mut __err=std::io::BufWriter::new(__err.lock());$dol crate::iter_print!(__err,$dol($dol t)*);let _=__err.flush();}}}#[cfg(not(debug_assertions))]#[allow(unused_macros)]#[doc=" [`iter_print!`] for buffered stderr. Do nothing in release mode."]macro_rules!dg{($dol($dol t:tt)*)=>{}}};(@normal($dol:tt))=>{let __in_buf=read_stdin_all_unchecked();#[allow(unused_mut,unused_variables)]let mut __scanner=Scanner::new(&__in_buf);#[allow(unused_macros)]macro_rules!sc{($dol($dol t:tt)*)=>{$dol crate::scan!(__scanner,$dol($dol t)*)}}#[allow(unused_macros)]macro_rules!sv{($dol($dol t:tt)*)=>{$dol crate::scan_value!(__scanner,$dol($dol t)*)}}};(@interactive($dol:tt))=>{#[allow(unused_macros)]#[doc=" Scan a line, and previous line will be truncated in the next call."]macro_rules!scln{($dol($dol t:tt)*)=>{let __in_buf=read_stdin_line();#[allow(unused_mut,unused_variables)]let mut __scanner=Scanner::new(&__in_buf);$dol crate::scan!(__scanner,$dol($dol t)*)}}};()=>{$crate::prepare!(@output($));$crate::prepare!(@normal($))};(?)=>{$crate::prepare!(@output($));$crate::prepare!(@interactive($))};}#[macro_export]macro_rules!main{()=>{fn main(){solve();}};(avx2)=>{fn main(){#[target_feature(enable="avx2")]unsafe fn solve_avx2(){solve();}unsafe{solve_avx2()}}};(large_stack)=>{fn main(){const STACK_SIZE:usize=512*1024*1024;::std::thread::Builder::new().stack_size(STACK_SIZE).spawn(solve).unwrap().join().unwrap();}};}}
pub use self::iter_print::IterPrint;
mod iter_print{use std::{fmt::Display,io::{Error,Write}};pub trait IterPrint{fn iter_print<W,S>(self,writer:&mut W,sep:S,is_head:bool)->Result<(),Error>where W:Write,S:Display;}macro_rules!iter_print_tuple_impl{(@impl$($A:ident$a:ident)?,$($B:ident$b:ident)*)=>{impl<$($A,)?$($B),*>IterPrint for($($A,)?$($B),*)where$($A:Display,)?$($B:Display),*{#[allow(unused_variables)]fn iter_print<W,S>(self,writer:&mut W,sep:S,is_head:bool)->Result<(),Error>where W:Write,S:Display{let($($a,)?$($b,)*)=self;$(if is_head{::std::write!(writer,"{}",$a)?;}else{::std::write!(writer,"{}{}",sep,$a)?;})?$(::std::write!(writer,"{}{}",sep,$b)?;)*Ok(())}}};(@inc,,$C:ident$c:ident$($D:ident$d:ident)*)=>{iter_print_tuple_impl!(@impl,);iter_print_tuple_impl!(@inc$C$c,,$($D$d)*);};(@inc$A:ident$a:ident,$($B:ident$b:ident)*,$C:ident$c:ident$($D:ident$d:ident)*)=>{iter_print_tuple_impl!(@impl$A$a,$($B$b)*);iter_print_tuple_impl!(@inc$A$a,$($B$b)*$C$c,$($D$d)*);};(@inc$A:ident$a:ident,$($B:ident$b:ident)*,)=>{iter_print_tuple_impl!(@impl$A$a,$($B$b)*);};($($t:tt)*)=>{iter_print_tuple_impl!(@inc,,$($t)*);};}iter_print_tuple_impl!(A a B b C c D d E e F f G g H h I i J j K k);#[doc=" Print expressions with a separator."]#[doc=" - `iter_print!(writer, args...)`"]#[doc=" - `@sep $expr`: set separator (default: `' '`)"]#[doc=" - `@ns`: alias for `@sep \"\"`"]#[doc=" - `@lf`: alias for `@sep '\\n'`"]#[doc=" - `@sp`: alias for `@sep ' '`"]#[doc=" - `@fmt ($lit, $($expr),*)`: print `format!($lit, $($expr),*)`"]#[doc=" - `@flush`: flush writer (auto insert `!`)"]#[doc=" - `@it $expr`: print iterator"]#[doc=" - `@it1 $expr`: print iterator as 1-indexed"]#[doc=" - `@cw ($char $expr)`: print iterator as `(elem as u8 + $char as u8) as char`"]#[doc=" - `@bw ($byte $expr)`: print iterator as `(elem as u8 + $byte) as char`"]#[doc=" - `@it2d $expr`: print 2d-iterator"]#[doc=" - `@tup $expr`: print tuple (need to import [`IterPrint`])"]#[doc=" - `@ittup $expr`: print iterative tuple (need to import [`IterPrint`])"]#[doc=" - `$expr`: print expr"]#[doc=" - `{ args... }`: scoped"]#[doc=" - `;`: print `'\\n'`"]#[doc=" - `!`: not print `'\\n'` at the end"]#[macro_export]macro_rules!iter_print{(@@fmt$writer:expr,$sep:expr,$is_head:expr,($lit:literal$(,$e:expr)*$(,)?))=>{if!$is_head{::std::write!($writer,"{}",$sep).expect("io error");}::std::write!($writer,$lit,$($e),*).expect("io error");};(@@item$writer:expr,$sep:expr,$is_head:expr,$e:expr)=>{$crate::iter_print!(@@fmt$writer,$sep,$is_head,("{}",$e));};(@@line_feed$writer:expr$(,)?)=>{::std::writeln!($writer).expect("io error");};(@@it$writer:expr,$sep:expr,$is_head:expr,$iter:expr)=>{{let mut iter=$iter.into_iter();if let Some(item)=iter.next(){$crate::iter_print!(@@item$writer,$sep,$is_head,item);}for item in iter{$crate::iter_print!(@@item$writer,$sep,false,item);}}};(@@it1$writer:expr,$sep:expr,$is_head:expr,$iter:expr)=>{{let mut iter=$iter.into_iter();if let Some(item)=iter.next(){$crate::iter_print!(@@item$writer,$sep,$is_head,item+1);}for item in iter{$crate::iter_print!(@@item$writer,$sep,false,item+1);}}};(@@cw$writer:expr,$sep:expr,$is_head:expr,($ch:literal$iter:expr))=>{{let mut iter=$iter.into_iter();let b=$ch as u8;if let Some(item)=iter.next(){$crate::iter_print!(@@item$writer,$sep,$is_head,(item as u8+b)as char);}for item in iter{$crate::iter_print!(@@item$writer,$sep,false,(item as u8+b)as char);}}};(@@bw$writer:expr,$sep:expr,$is_head:expr,($b:literal$iter:expr))=>{{let mut iter=$iter.into_iter();let b:u8=$b;if let Some(item)=iter.next(){$crate::iter_print!(@@item$writer,$sep,$is_head,(item as u8+b)as char);}for item in iter{$crate::iter_print!(@@item$writer,$sep,false,(item as u8+b)as char);}}};(@@it2d$writer:expr,$sep:expr,$is_head:expr,$iter:expr)=>{let mut iter=$iter.into_iter();if let Some(item)=iter.next(){$crate::iter_print!(@@it$writer,$sep,$is_head,item);}for item in iter{$crate::iter_print!(@@line_feed$writer);$crate::iter_print!(@@it$writer,$sep,true,item);}};(@@tup$writer:expr,$sep:expr,$is_head:expr,$tuple:expr)=>{IterPrint::iter_print($tuple,&mut$writer,$sep,$is_head).expect("io error");};(@@ittup$writer:expr,$sep:expr,$is_head:expr,$iter:expr)=>{let mut iter=$iter.into_iter();if let Some(item)=iter.next(){$crate::iter_print!(@@tup$writer,$sep,$is_head,item);}for item in iter{$crate::iter_print!(@@line_feed$writer);$crate::iter_print!(@@tup$writer,$sep,true,item);}};(@@assert_tag item)=>{};(@@assert_tag it)=>{};(@@assert_tag it1)=>{};(@@assert_tag it2d)=>{};(@@assert_tag tup)=>{};(@@assert_tag ittup)=>{};(@@assert_tag$tag:ident)=>{::std::compile_error!(::std::concat!("invalid tag in `iter_print!`: `",std::stringify!($tag),"`"));};(@@inner$writer:expr,$sep:expr,$is_head:expr,@sep$e:expr,$($t:tt)*)=>{$crate::iter_print!(@@inner$writer,$e,$is_head,$($t)*);};(@@inner$writer:expr,$sep:expr,$is_head:expr,@ns$($t:tt)*)=>{$crate::iter_print!(@@inner$writer,"",$is_head,$($t)*);};(@@inner$writer:expr,$sep:expr,$is_head:expr,@lf$($t:tt)*)=>{$crate::iter_print!(@@inner$writer,'\n',$is_head,$($t)*);};(@@inner$writer:expr,$sep:expr,$is_head:expr,@sp$($t:tt)*)=>{$crate::iter_print!(@@inner$writer,' ',$is_head,$($t)*);};(@@inner$writer:expr,$sep:expr,$is_head:expr,@flush$($t:tt)*)=>{$writer.flush().expect("io error");$crate::iter_print!(@@inner$writer,$sep,$is_head,!$($t)*);};(@@inner$writer:expr,$sep:expr,$is_head:expr,@fmt$arg:tt$($t:tt)*)=>{$crate::iter_print!(@@fmt$writer,$sep,$is_head,$arg);$crate::iter_print!(@@inner$writer,$sep,$is_head,$($t)*);};(@@inner$writer:expr,$sep:expr,$is_head:expr,@cw$arg:tt$($t:tt)*)=>{$crate::iter_print!(@@cw$writer,$sep,$is_head,$arg);$crate::iter_print!(@@inner$writer,$sep,$is_head,$($t)*);};(@@inner$writer:expr,$sep:expr,$is_head:expr,@bw$arg:tt$($t:tt)*)=>{$crate::iter_print!(@@bw$writer,$sep,$is_head,$arg);$crate::iter_print!(@@inner$writer,$sep,$is_head,$($t)*);};(@@inner$writer:expr,$sep:expr,$is_head:expr,@$tag:ident$e:expr,$($t:tt)*)=>{$crate::iter_print!(@@assert_tag$tag);$crate::iter_print!(@@$tag$writer,$sep,$is_head,$e);$crate::iter_print!(@@inner$writer,$sep,false,$($t)*);};(@@inner$writer:expr,$sep:expr,$is_head:expr,@$tag:ident$e:expr;$($t:tt)*)=>{$crate::iter_print!(@@assert_tag$tag);$crate::iter_print!(@@$tag$writer,$sep,$is_head,$e);$crate::iter_print!(@@line_feed$writer);$crate::iter_print!(@@inner$writer,$sep,true,$($t)*);};(@@inner$writer:expr,$sep:expr,$is_head:expr,@$tag:ident$e:expr)=>{$crate::iter_print!(@@assert_tag$tag);$crate::iter_print!(@@$tag$writer,$sep,$is_head,$e);$crate::iter_print!(@@inner$writer,$sep,false,);};(@@inner$writer:expr,$sep:expr,$is_head:expr,@$tag:ident$($t:tt)*)=>{::std::compile_error!(::std::concat!("invalid expr in `iter_print!`: `",std::stringify!($($t)*),"`"));};(@@inner$writer:expr,$sep:expr,$is_head:expr,,$($t:tt)*)=>{$crate::iter_print!(@@inner$writer,$sep,$is_head,$($t)*);};(@@inner$writer:expr,$sep:expr,$is_head:expr,;$($t:tt)*)=>{$crate::iter_print!(@@line_feed$writer);$crate::iter_print!(@@inner$writer,$sep,$is_head,$($t)*);};(@@inner$writer:expr,$sep:expr,$is_head:expr,!$(,)?)=>{};(@@inner$writer:expr,$sep:expr,$is_head:expr,!$($t:tt)*)=>{$crate::iter_print!(@@inner$writer,$sep,$is_head,$($t)*);};(@@inner$writer:expr,$sep:expr,$is_head:expr,)=>{$crate::iter_print!(@@line_feed$writer);};(@@inner$writer:expr,$sep:expr,$is_head:expr,{$($t:tt)*}$($rest:tt)*)=>{$crate::iter_print!(@@inner$writer,$sep,$is_head,$($t)*,!);$crate::iter_print!(@@inner$writer,$sep,$is_head,$($rest)*);};(@@inner$writer:expr,$sep:expr,$is_head:expr,$($t:tt)*)=>{$crate::iter_print!(@@inner$writer,$sep,$is_head,@item$($t)*);};($writer:expr,$($t:tt)*)=>{{$crate::iter_print!(@@inner$writer,' ',true,$($t)*);}};}}
mod array{#[macro_export]macro_rules!array{[@inner$data:ident=[$init:expr;$len:expr]]=>{{use::std::mem::{ManuallyDrop,MaybeUninit};const LEN:usize=$len;let mut$data:[MaybeUninit<_>;LEN]=unsafe{MaybeUninit::uninit().assume_init()};$init;#[repr(C)]union __Transmuter<T:Copy>{src:ManuallyDrop<[MaybeUninit<T>;LEN]>,dst:ManuallyDrop<[T;LEN]>,}ManuallyDrop::into_inner(unsafe{__Transmuter{src:ManuallyDrop::new($data)}.dst})}};[||$e:expr;$len:expr]=>{$crate::array![@inner data=[data.iter_mut().for_each(|item|*item=MaybeUninit::new($e));$len]]};[|$i:pat_param|$e:expr;$len:expr]=>{$crate::array![@inner data=[data.iter_mut().enumerate().for_each(|($i,item)|*item=MaybeUninit::new($e));$len]]};[$e:expr;$len:expr]=>{{let e=$e;$crate::array![||Clone::clone(&e);$len]}};}}
pub use self::scanner::*;
mod scanner{use std::{iter::{from_fn,repeat_with,FromIterator},marker::PhantomData};pub fn read_stdin_all()->String{use std::io::Read as _;let mut s=String::new();std::io::stdin().read_to_string(&mut s).expect("io error");s}pub fn read_stdin_all_unchecked()->String{use std::io::Read as _;let mut buf=Vec::new();std::io::stdin().read_to_end(&mut buf).expect("io error");unsafe{String::from_utf8_unchecked(buf)}}pub fn read_all(mut reader:impl std::io::Read)->String{let mut s=String::new();reader.read_to_string(&mut s).expect("io error");s}pub fn read_all_unchecked(mut reader:impl std::io::Read)->String{let mut buf=Vec::new();reader.read_to_end(&mut buf).expect("io error");unsafe{String::from_utf8_unchecked(buf)}}pub fn read_stdin_line()->String{let mut s=String::new();std::io::stdin().read_line(&mut s).expect("io error");s}pub trait IterScan:Sized{type Output;fn scan<'a,I:Iterator<Item=&'a str>>(iter:&mut I)->Option<Self::Output>;}pub trait MarkedIterScan:Sized{type Output;fn mscan<'a,I:Iterator<Item=&'a str>>(self,iter:&mut I)->Option<Self::Output>;}#[derive(Clone,Debug)]pub struct Scanner<'a>{iter:std::str::SplitAsciiWhitespace<'a>}impl<'a>Scanner<'a>{#[inline]pub fn new(s:&'a str)->Self{let iter=s.split_ascii_whitespace();Self{iter}}#[inline]pub fn scan<T>(&mut self)-><T as IterScan>::Output where T:IterScan{<T as IterScan>::scan(&mut self.iter).expect("scan error")}#[inline]pub fn mscan<T>(&mut self,marker:T)-><T as MarkedIterScan>::Output where T:MarkedIterScan{marker.mscan(&mut self.iter).expect("scan error")}#[inline]pub fn scan_vec<T>(&mut self,size:usize)->Vec<<T as IterScan>::Output>where T:IterScan{(0..size).map(|_|<T as IterScan>::scan(&mut self.iter).expect("scan error")).collect()}#[inline]pub fn iter<'b,T>(&'b mut self)->ScannerIter<'a,'b,T>where T:IterScan{ScannerIter{inner:self,_marker:std::marker::PhantomData}}}macro_rules!iter_scan_impls{($($t:ty)*)=>{$(impl IterScan for$t{type Output=Self;#[inline]fn scan<'a,I:Iterator<Item=&'a str>>(iter:&mut I)->Option<Self>{iter.next()?.parse::<$t>().ok()}})*};}iter_scan_impls!(char u8 u16 u32 u64 usize i8 i16 i32 i64 isize f32 f64 u128 i128 String);macro_rules!iter_scan_tuple_impl{(@impl$($T:ident)*)=>{impl<$($T:IterScan),*>IterScan for($($T,)*){type Output=($(<$T as IterScan>::Output,)*);#[inline]fn scan<'a,It:Iterator<Item=&'a str>>(_iter:&mut It)->Option<Self::Output>{Some(($(<$T as IterScan>::scan(_iter)?,)*))}}};(@inner$($T:ident)*,)=>{iter_scan_tuple_impl!(@impl$($T)*);};(@inner$($T:ident)*,$U:ident$($Rest:ident)*)=>{iter_scan_tuple_impl!(@impl$($T)*);iter_scan_tuple_impl!(@inner$($T)*$U,$($Rest)*);};($($T:ident)*)=>{iter_scan_tuple_impl!(@inner,$($T)*);};}iter_scan_tuple_impl!(A B C D E F G H I J K);pub struct ScannerIter<'a,'b,T>{inner:&'b mut Scanner<'a>,_marker:std::marker::PhantomData<fn()->T>}impl<'a,'b,T>Iterator for ScannerIter<'a,'b,T>where T:IterScan{type Item=<T as IterScan>::Output;#[inline]fn next(&mut self)->Option<Self::Item>{<T as IterScan>::scan(&mut self.inner.iter)}}#[doc=" scan a value with Scanner"]#[doc=""]#[doc=" - `scan_value!(scanner, ELEMENT)`"]#[doc=""]#[doc=" ELEMENT :="]#[doc=" - `$ty`: IterScan"]#[doc=" - `@$expr`: MarkedIterScan"]#[doc=" - `[ELEMENT; $expr]`: vector"]#[doc=" - `[ELEMENT; const $expr]`: array"]#[doc=" - `[ELEMENT]`: iterator"]#[doc=" - `($(ELEMENT)*,)`: tuple"]#[macro_export]macro_rules!scan_value{(@repeat$scanner:expr,[$($t:tt)*]$($len:expr)?)=>{::std::iter::repeat_with(||$crate::scan_value!(@inner$scanner,[]$($t)*))$(.take($len).collect::<Vec<_>>())?};(@array$scanner:expr,[$($t:tt)*]$len:expr)=>{$crate::array![||$crate::scan_value!(@inner$scanner,[]$($t)*);$len]};(@tuple$scanner:expr,[$([$($args:tt)*])*])=>{($($($args)*,)*)};(@$tag:ident$scanner:expr,[[$($args:tt)*]])=>{$($args)*};(@$tag:ident$scanner:expr,[$($args:tt)*]@$e:expr)=>{$crate::scan_value!(@$tag$scanner,[$($args)*[$scanner.mscan($e)]])};(@$tag:ident$scanner:expr,[$($args:tt)*]@$e:expr,$($t:tt)*)=>{$crate::scan_value!(@$tag$scanner,[$($args)*[$scanner.mscan($e)]]$($t)*)};(@$tag:ident$scanner:expr,[$($args:tt)*]($($tuple:tt)*)$($t:tt)*)=>{$crate::scan_value!(@$tag$scanner,[$($args)*[$crate::scan_value!(@tuple$scanner,[]$($tuple)*)]]$($t)*)};(@$tag:ident$scanner:expr,[$($args:tt)*][@$e:expr;const$len:expr]$($t:tt)*)=>{$crate::scan_value!(@$tag$scanner,[$($args)*[$crate::scan_value!(@array$scanner,[@$e]$len)]]$($t)*)};(@$tag:ident$scanner:expr,[$($args:tt)*][@$e:expr;$len:expr]$($t:tt)*)=>{$crate::scan_value!(@$tag$scanner,[$($args)*[$crate::scan_value!(@repeat$scanner,[@$e]$len)]]$($t)*)};(@$tag:ident$scanner:expr,[$($args:tt)*][[$($tt:tt)*];const$len:expr]$($t:tt)*)=>{$crate::scan_value!(@$tag$scanner,[$($args)*[$crate::scan_value!(@array$scanner,[[$($tt)*]]$len)]]$($t)*)};(@$tag:ident$scanner:expr,[$($args:tt)*][[$($tt:tt)*];$len:expr]$($t:tt)*)=>{$crate::scan_value!(@$tag$scanner,[$($args)*[$crate::scan_value!(@repeat$scanner,[[$($tt)*]]$len)]]$($t)*)};(@$tag:ident$scanner:expr,[$($args:tt)*][($($tt:tt)*);const$len:expr]$($t:tt)*)=>{$crate::scan_value!(@$tag$scanner,[$($args)*[$crate::scan_value!(@array$scanner,[($($tt)*)]$len)]]$($t)*)};(@$tag:ident$scanner:expr,[$($args:tt)*][($($tt:tt)*);$len:expr]$($t:tt)*)=>{$crate::scan_value!(@$tag$scanner,[$($args)*[$crate::scan_value!(@repeat$scanner,[($($tt)*)]$len)]]$($t)*)};(@$tag:ident$scanner:expr,[$($args:tt)*][$ty:ty;const$len:expr]$($t:tt)*)=>{$crate::scan_value!(@$tag$scanner,[$($args)*[$crate::scan_value!(@array$scanner,[$ty]$len)]]$($t)*)};(@$tag:ident$scanner:expr,[$($args:tt)*][$ty:ty;$len:expr]$($t:tt)*)=>{$crate::scan_value!(@$tag$scanner,[$($args)*[$crate::scan_value!(@repeat$scanner,[$ty]$len)]]$($t)*)};(@$tag:ident$scanner:expr,[$($args:tt)*][$($tt:tt)*]$($t:tt)*)=>{$crate::scan_value!(@$tag$scanner,[$($args)*[$crate::scan_value!(@repeat$scanner,[$($tt)*])]]$($t)*)};(@$tag:ident$scanner:expr,[$($args:tt)*]$ty:ty)=>{$crate::scan_value!(@$tag$scanner,[$($args)*[$scanner.scan::<$ty>()]])};(@$tag:ident$scanner:expr,[$($args:tt)*]$ty:ty,$($t:tt)*)=>{$crate::scan_value!(@$tag$scanner,[$($args)*[$scanner.scan::<$ty>()]]$($t)*)};(@$tag:ident$scanner:expr,[$($args:tt)*],$($t:tt)*)=>{$crate::scan_value!(@$tag$scanner,[$($args)*]$($t)*)};(@$tag:ident$scanner:expr,[$($args:tt)*])=>{::std::compile_error!(::std::stringify!($($args)*))};($scanner:expr,$($t:tt)*)=>{$crate::scan_value!(@inner$scanner,[]$($t)*)}}#[doc=" scan and bind values with Scanner"]#[doc=""]#[doc=" - `scan!(scanner, $($pat $(: ELEMENT)?),*)`"]#[macro_export]macro_rules!scan{(@assert$p:pat)=>{};(@assert$($p:tt)*)=>{::std::compile_error!(::std::concat!("expected pattern, found `",::std::stringify!($($p)*),"`"));};(@pat$scanner:expr,[][])=>{};(@pat$scanner:expr,[][],$($t:tt)*)=>{$crate::scan!(@pat$scanner,[][]$($t)*)};(@pat$scanner:expr,[$($p:tt)*][]$x:ident$($t:tt)*)=>{$crate::scan!(@pat$scanner,[$($p)*$x][]$($t)*)};(@pat$scanner:expr,[$($p:tt)*][]::$($t:tt)*)=>{$crate::scan!(@pat$scanner,[$($p)*::][]$($t)*)};(@pat$scanner:expr,[$($p:tt)*][]&$($t:tt)*)=>{$crate::scan!(@pat$scanner,[$($p)*&][]$($t)*)};(@pat$scanner:expr,[$($p:tt)*][]($($x:tt)*)$($t:tt)*)=>{$crate::scan!(@pat$scanner,[$($p)*($($x)*)][]$($t)*)};(@pat$scanner:expr,[$($p:tt)*][][$($x:tt)*]$($t:tt)*)=>{$crate::scan!(@pat$scanner,[$($p)*[$($x)*]][]$($t)*)};(@pat$scanner:expr,[$($p:tt)*][]{$($x:tt)*}$($t:tt)*)=>{$crate::scan!(@pat$scanner,[$($p)*{$($x)*}][]$($t)*)};(@pat$scanner:expr,[$($p:tt)*][]:$($t:tt)*)=>{$crate::scan!(@ty$scanner,[$($p)*][]$($t)*)};(@pat$scanner:expr,[$($p:tt)*][]$($t:tt)*)=>{$crate::scan!(@let$scanner,[$($p)*][usize]$($t)*)};(@ty$scanner:expr,[$($p:tt)*][$($tt:tt)*]@$e:expr)=>{$crate::scan!(@let$scanner,[$($p)*][$($tt)*@$e])};(@ty$scanner:expr,[$($p:tt)*][$($tt:tt)*]@$e:expr,$($t:tt)*)=>{$crate::scan!(@let$scanner,[$($p)*][$($tt)*@$e],$($t)*)};(@ty$scanner:expr,[$($p:tt)*][$($tt:tt)*]($($x:tt)*)$($t:tt)*)=>{$crate::scan!(@let$scanner,[$($p)*][$($tt)*($($x)*)]$($t)*)};(@ty$scanner:expr,[$($p:tt)*][$($tt:tt)*][$($x:tt)*]$($t:tt)*)=>{$crate::scan!(@let$scanner,[$($p)*][$($tt)*[$($x)*]]$($t)*)};(@ty$scanner:expr,[$($p:tt)*][$($tt:tt)*]$ty:ty)=>{$crate::scan!(@let$scanner,[$($p)*][$($tt)*$ty])};(@ty$scanner:expr,[$($p:tt)*][$($tt:tt)*]$ty:ty,$($t:tt)*)=>{$crate::scan!(@let$scanner,[$($p)*][$($tt)*$ty],$($t)*)};(@let$scanner:expr,[$($p:tt)*][$($tt:tt)*]$($t:tt)*)=>{$crate::scan!{@assert$($p)*}let$($p)* =$crate::scan_value!($scanner,$($tt)*);$crate::scan!(@pat$scanner,[][]$($t)*)};($scanner:expr,$($t:tt)*)=>{$crate::scan!(@pat$scanner,[][]$($t)*)}}#[derive(Debug,Copy,Clone)]pub enum Usize1{}impl IterScan for Usize1{type Output=usize;#[inline]fn scan<'a,I:Iterator<Item=&'a str>>(iter:&mut I)->Option<Self::Output>{<usize as IterScan>::scan(iter)?.checked_sub(1)}}#[derive(Debug,Copy,Clone)]pub struct CharWithBase(pub char);impl MarkedIterScan for CharWithBase{type Output=usize;#[inline]fn mscan<'a,I:Iterator<Item=&'a str>>(self,iter:&mut I)->Option<Self::Output>{Some((<char as IterScan>::scan(iter)?as u8-self.0 as u8)as usize)}}#[derive(Debug,Copy,Clone)]pub enum Chars{}impl IterScan for Chars{type Output=Vec<char>;#[inline]fn scan<'a,I:Iterator<Item=&'a str>>(iter:&mut I)->Option<Self::Output>{Some(iter.next()?.chars().collect())}}#[derive(Debug,Copy,Clone)]pub struct CharsWithBase(pub char);impl MarkedIterScan for CharsWithBase{type Output=Vec<usize>;#[inline]fn mscan<'a,I:Iterator<Item=&'a str>>(self,iter:&mut I)->Option<Self::Output>{Some(iter.next()?.chars().map(|c|(c as u8-self.0 as u8)as usize).collect())}}#[derive(Debug,Copy,Clone)]pub enum Byte1{}impl IterScan for Byte1{type Output=u8;#[inline]fn scan<'a,I:Iterator<Item=&'a str>>(iter:&mut I)->Option<Self::Output>{let bytes=iter.next()?.as_bytes();assert_eq!(bytes.len(),1);Some(bytes[0])}}#[derive(Debug,Copy,Clone)]pub struct ByteWithBase(pub u8);impl MarkedIterScan for ByteWithBase{type Output=usize;#[inline]fn mscan<'a,I:Iterator<Item=&'a str>>(self,iter:&mut I)->Option<Self::Output>{Some((<char as IterScan>::scan(iter)?as u8-self.0)as usize)}}#[derive(Debug,Copy,Clone)]pub enum Bytes{}impl IterScan for Bytes{type Output=Vec<u8>;#[inline]fn scan<'a,I:Iterator<Item=&'a str>>(iter:&mut I)->Option<Self::Output>{Some(iter.next()?.bytes().collect())}}#[derive(Debug,Copy,Clone)]pub struct BytesWithBase(pub u8);impl MarkedIterScan for BytesWithBase{type Output=Vec<usize>;#[inline]fn mscan<'a,I:Iterator<Item=&'a str>>(self,iter:&mut I)->Option<Self::Output>{Some(iter.next()?.bytes().map(|c|(c-self.0)as usize).collect())}}#[derive(Debug,Copy,Clone)]pub struct Collect<T,B=Vec<<T as IterScan>::Output>>where T:IterScan,B:FromIterator<<T as IterScan>::Output>{size:usize,_marker:PhantomData<fn()->(T,B)>}impl<T,B>Collect<T,B>where T:IterScan,B:FromIterator<<T as IterScan>::Output>{pub fn new(size:usize)->Self{Self{size,_marker:PhantomData}}}impl<T,B>MarkedIterScan for Collect<T,B>where T:IterScan,B:FromIterator<<T as IterScan>::Output>{type Output=B;#[inline]fn mscan<'a,I:Iterator<Item=&'a str>>(self,iter:&mut I)->Option<Self::Output>{repeat_with(||<T as IterScan>::scan(iter)).take(self.size).collect()}}#[derive(Debug,Copy,Clone)]pub struct SizedCollect<T,B=Vec<<T as IterScan>::Output>>where T:IterScan,B:FromIterator<<T as IterScan>::Output>{_marker:PhantomData<fn()->(T,B)>}impl<T,B>IterScan for SizedCollect<T,B>where T:IterScan,B:FromIterator<<T as IterScan>::Output>{type Output=B;#[inline]fn scan<'a,I:Iterator<Item=&'a str>>(iter:&mut I)->Option<Self::Output>{let size=usize::scan(iter)?;repeat_with(||<T as IterScan>::scan(iter)).take(size).collect()}}#[derive(Debug,Copy,Clone)]pub struct Splitted<T,P>where T:IterScan{pat:P,_marker:PhantomData<fn()->T>}impl<T,P>Splitted<T,P>where T:IterScan{pub fn new(pat:P)->Self{Self{pat,_marker:PhantomData}}}impl<T>MarkedIterScan for Splitted<T,char>where T:IterScan{type Output=Vec<<T as IterScan>::Output>;fn mscan<'a,I:Iterator<Item=&'a str>>(self,iter:&mut I)->Option<Self::Output>{let mut iter=iter.next()?.split(self.pat);Some(from_fn(||<T as IterScan>::scan(&mut iter)).collect())}}impl<T>MarkedIterScan for Splitted<T,&str>where T:IterScan{type Output=Vec<<T as IterScan>::Output>;fn mscan<'a,I:Iterator<Item=&'a str>>(self,iter:&mut I)->Option<Self::Output>{let mut iter=iter.next()?.split(self.pat);Some(from_fn(||<T as IterScan>::scan(&mut iter)).collect())}}impl<T,F>MarkedIterScan for F where F:Fn(&str)->Option<T>{type Output=T;fn mscan<'a,I:Iterator<Item=&'a str>>(self,iter:&mut I)->Option<Self::Output>{self(iter.next()?)}}}
pub use self::sparse_graph::*;
mod sparse_graph{use super::{Adjacencies,AdjacenciesWithEindex,AdjacencyIndex,AdjacencyIndexWithEindex,AdjacencyView,AdjacencyViewIterFromEindex,EIndexedGraph,EdgeMap,EdgeSize,EdgeView,GraphBase,IterScan,MarkedIterScan,VertexMap,VertexSize,VertexView,Vertices};use std::{iter::Cloned,marker::PhantomData,ops,slice};type Marker<T>=PhantomData<fn()->T>;#[derive(Clone,Copy,Debug,Eq,PartialEq,Ord,PartialOrd,Hash)]pub enum DirectedEdge{}#[derive(Clone,Copy,Debug,Eq,PartialEq,Ord,PartialOrd,Hash)]pub enum UndirectedEdge{}#[derive(Clone,Copy,Debug,Eq,PartialEq,Ord,PartialOrd,Hash)]pub enum BidirectionalEdge{}#[derive(Clone,Copy,Debug,Default,Eq,PartialEq,Ord,PartialOrd,Hash)]pub struct Adjacency{pub id:usize,pub to:usize}impl Adjacency{pub fn new(id:usize,to:usize)->Adjacency{Adjacency{id,to}}}#[doc=" Static Sparse Graph represented as Compressed Sparse Row."]#[derive(Debug,Clone)]pub struct SparseGraph<D>{vsize:usize,pub start:Vec<usize>,pub elist:Vec<Adjacency>,pub edges:Vec<(usize,usize)>,_marker:Marker<D>}impl<D>SparseGraph<D>{#[doc=" Return the number of vertices."]pub fn vertices_size(&self)->usize{self.vsize}#[doc=" Return the number of edges."]pub fn edges_size(&self)->usize{self.edges.len()}#[doc=" Return an iterator over graph vertices."]pub fn vertices(&self)->ops::Range<usize>{0..self.vertices_size()}#[doc=" Return a slice of adjacency vertices."]pub fn adjacencies(&self,v:usize)->slice::Iter<'_,Adjacency>{self.elist[self.start[v]..self.start[v+1]].iter()}pub fn builder<T>(vsize:usize)->SparseGraphBuilder<T,D>{SparseGraphBuilder::new(vsize)}pub fn builder_with_esize<T>(vsize:usize,esize:usize)->SparseGraphBuilder<T,D>{SparseGraphBuilder::new_with_esize(vsize,esize)}}pub trait SparseGraphConstruction:Sized{fn construct_graph(vsize:usize,edges:Vec<(usize,usize)>)->SparseGraph<Self>;}impl<D>SparseGraph<D>where D:SparseGraphConstruction{#[doc=" Construct graph from edges."]pub fn from_edges(vsize:usize,edges:Vec<(usize,usize)>)->Self{D::construct_graph(vsize,edges)}}impl SparseGraphConstruction for DirectedEdge{fn construct_graph(vsize:usize,edges:Vec<(usize,usize)>)->SparseGraph<Self>{let mut start:Vec<_>=vec![0usize;vsize+1];for(from,_)in edges.iter().cloned(){start[from]+=1;}for i in 1..=vsize{start[i]+=start[i-1];}let mut elist=Vec::<Adjacency>::with_capacity(edges.len());let ptr=elist.as_mut_ptr();for(id,(from,to))in edges.iter().cloned().enumerate(){start[from]-=1;unsafe{ptr.add(start[from]).write(Adjacency::new(id,to))};}unsafe{elist.set_len(edges.len())};SparseGraph{vsize,start,elist,edges,_marker:PhantomData}}}impl SparseGraphConstruction for UndirectedEdge{fn construct_graph(vsize:usize,edges:Vec<(usize,usize)>)->SparseGraph<Self>{let mut start:Vec<_>=vec![0usize;vsize+1];for(from,to)in edges.iter().cloned(){start[to]+=1;start[from]+=1;}for i in 1..=vsize{start[i]+=start[i-1];}let mut elist=Vec::<Adjacency>::with_capacity(edges.len()*2);let ptr=elist.as_mut_ptr();for(id,(from,to))in edges.iter().cloned().enumerate(){start[from]-=1;unsafe{ptr.add(start[from]).write(Adjacency::new(id,to))};start[to]-=1;unsafe{ptr.add(start[to]).write(Adjacency::new(id,from))};}unsafe{elist.set_len(edges.len()*2)};SparseGraph{vsize,start,elist,edges,_marker:PhantomData}}}impl SparseGraphConstruction for BidirectionalEdge{fn construct_graph(vsize:usize,edges:Vec<(usize,usize)>)->SparseGraph<Self>{let mut start:Vec<_>=vec![0usize;vsize+1];for(from,to)in edges.iter().cloned(){start[to]+=1;start[from]+=1;}for i in 1..=vsize{start[i]+=start[i-1];}let mut elist=Vec::<Adjacency>::with_capacity(edges.len()*2);let ptr=elist.as_mut_ptr();for(id,(from,to))in edges.iter().cloned().enumerate(){start[from]-=1;unsafe{ptr.add(start[from]).write(Adjacency::new(id*2,to))};start[to]-=1;unsafe{ptr.add(start[to]).write(Adjacency::new(id*2+1,from))};}unsafe{elist.set_len(edges.len()*2)};SparseGraph{vsize,start,elist,edges,_marker:PhantomData}}}pub type DirectedSparseGraph=SparseGraph<DirectedEdge>;pub type UndirectedSparseGraph=SparseGraph<UndirectedEdge>;pub type BidirectionalSparseGraph=SparseGraph<BidirectionalEdge>;pub struct SparseGraphBuilder<T,D>{vsize:usize,edges:Vec<(usize,usize)>,rest:Vec<T>,_marker:Marker<D>}impl<T,D>SparseGraphBuilder<T,D>{pub fn new(vsize:usize)->Self{Self{vsize,edges:Default::default(),rest:Default::default(),_marker:PhantomData}}pub fn new_with_esize(vsize:usize,esize:usize)->Self{Self{vsize,edges:Vec::with_capacity(esize),rest:Vec::with_capacity(esize),_marker:PhantomData}}pub fn add_edge(&mut self,u:usize,v:usize,w:T){self.edges.push((u,v));self.rest.push(w);}}impl<T,D>SparseGraphBuilder<T,D>where D:SparseGraphConstruction{pub fn build(self)->(SparseGraph<D>,Vec<T>){let graph=SparseGraph::from_edges(self.vsize,self.edges);(graph,self.rest)}}pub struct SparseGraphScanner<U,T,D>where U:IterScan<Output=usize>,T:IterScan{vsize:usize,esize:usize,_marker:Marker<(U,T,D)>}impl<U,T,D>SparseGraphScanner<U,T,D>where U:IterScan<Output=usize>,T:IterScan{pub fn new(vsize:usize,esize:usize)->Self{Self{vsize,esize,_marker:PhantomData}}}impl<U,T,D>MarkedIterScan for SparseGraphScanner<U,T,D>where U:IterScan<Output=usize>,T:IterScan,D:SparseGraphConstruction{type Output=(SparseGraph<D>,Vec<<T as IterScan>::Output>);fn mscan<'a,I:Iterator<Item=&'a str>>(self,iter:&mut I)->Option<Self::Output>{let mut builder=SparseGraphBuilder::new_with_esize(self.vsize,self.esize);for _ in 0..self.esize{builder.add_edge(U::scan(iter)?,U::scan(iter)?,T::scan(iter)?);}Some(builder.build())}}pub type DirectedGraphScanner<U,T=()>=SparseGraphScanner<U,T,DirectedEdge>;pub type UndirectedGraphScanner<U,T=()>=SparseGraphScanner<U,T,UndirectedEdge>;pub type BidirectionalGraphScanner<U,T=()>=SparseGraphScanner<U,T,BidirectionalEdge>;pub struct TreeGraphScanner<U,T=()>where U:IterScan<Output=usize>,T:IterScan{vsize:usize,_marker:Marker<(U,T)>}impl<U,T>TreeGraphScanner<U,T>where U:IterScan<Output=usize>,T:IterScan{pub fn new(vsize:usize)->Self{Self{vsize,_marker:PhantomData}}}impl<U,T>MarkedIterScan for TreeGraphScanner<U,T>where U:IterScan<Output=usize>,T:IterScan{type Output=(UndirectedSparseGraph,Vec<<T as IterScan>::Output>);fn mscan<'a,I:Iterator<Item=&'a str>>(self,iter:&mut I)->Option<Self::Output>{UndirectedGraphScanner::<U,T>::new(self.vsize,self.vsize-1).mscan(iter)}}impl<D>GraphBase<'_>for SparseGraph<D>{type VIndex=usize;}impl<D>EIndexedGraph<'_>for SparseGraph<D>{type EIndex=usize;}impl<D>VertexSize<'_>for SparseGraph<D>{fn vsize(&self)->usize{self.vsize}}impl<D>EdgeSize<'_>for SparseGraph<D>{fn esize(&self)->usize{self.edges.len()}}impl<D>Vertices<'_>for SparseGraph<D>{type VIter=ops::Range<usize>;fn vertices(&self)->Self::VIter{0..self.vsize}}impl<'g,D>Adjacencies<'g>for SparseGraph<D>{type AIndex=Adjacency;type AIter=Cloned<slice::Iter<'g,Adjacency>>;fn adjacencies(&'g self,vid:Self::VIndex)->Self::AIter{self.elist[self.start[vid]..self.start[vid+1]].iter().cloned()}}impl<'g,D>AdjacenciesWithEindex<'g>for SparseGraph<D>{type AIndex=Adjacency;type AIter=Cloned<slice::Iter<'g,Adjacency>>;fn adjacencies_with_eindex(&'g self,vid:Self::VIndex)->Self::AIter{self.elist[self.start[vid]..self.start[vid+1]].iter().cloned()}}impl AdjacencyIndex for Adjacency{type VIndex=usize;fn vindex(&self)->Self::VIndex{self.to}}impl AdjacencyIndexWithEindex for Adjacency{type EIndex=usize;fn eindex(&self)->Self::EIndex{self.id}}impl<D,T>VertexMap<'_,T>for SparseGraph<D>{type Vmap=Vec<T>;fn construct_vmap<F>(&self,f:F)->Self::Vmap where F:FnMut()->T{let mut v=Vec::with_capacity(self.vsize);v.resize_with(self.vsize,f);v}fn vmap_get<'a>(&self,map:&'a Self::Vmap,vid:Self::VIndex)->&'a T{assert!(vid<self.vsize,"expected 0..{}, but {}",self.vsize,vid);unsafe{map.get_unchecked(vid)}}fn vmap_get_mut<'a>(&self,map:&'a mut Self::Vmap,vid:Self::VIndex)->&'a mut T{assert!(vid<self.vsize,"expected 0..{}, but {}",self.vsize,vid);unsafe{map.get_unchecked_mut(vid)}}}impl<D,T>VertexView<'_,Vec<T>,T>for SparseGraph<D>where T:Clone{fn vview(&self,map:&Vec<T>,vid:Self::VIndex)->T{self.vmap_get(map,vid).clone()}}impl<D,T>VertexView<'_,[T],T>for SparseGraph<D>where T:Clone{fn vview(&self,map:&[T],vid:Self::VIndex)->T{assert!(vid<self.vsize,"expected 0..{}, but {}",self.vsize,vid);unsafe{map.get_unchecked(vid)}.clone()}}impl<D,T>EdgeMap<'_,T>for SparseGraph<D>{type Emap=Vec<T>;fn construct_emap<F>(&self,f:F)->Self::Emap where F:FnMut()->T{let mut v=Vec::with_capacity(self.vsize);v.resize_with(self.vsize,f);v}fn emap_get<'a>(&self,map:&'a Self::Emap,eid:Self::EIndex)->&'a T{let esize=self.edges.len();assert!(eid<esize,"expected 0..{}, but {}",esize,eid);unsafe{map.get_unchecked(eid)}}fn emap_get_mut<'a>(&self,map:&'a mut Self::Emap,eid:Self::EIndex)->&'a mut T{let esize=self.edges.len();assert!(eid<esize,"expected 0..{}, but {}",esize,eid);unsafe{map.get_unchecked_mut(eid)}}}impl<D,T>EdgeView<'_,Vec<T>,T>for SparseGraph<D>where T:Clone{fn eview(&self,map:&Vec<T>,eid:Self::EIndex)->T{self.emap_get(map,eid).clone()}}impl<D,T>EdgeView<'_,[T],T>for SparseGraph<D>where T:Clone{fn eview(&self,map:&[T],eid:Self::EIndex)->T{let esize=self.edges.len();assert!(eid<esize,"expected 0..{}, but {}",esize,eid);unsafe{map.get_unchecked(eid)}.clone()}}impl<'g,'a,D:'g,M,T>AdjacencyView<'g,'a,M,T>for SparseGraph<D>where Self:AdjacenciesWithEindex<'g>+EdgeView<'g,M,T>,T:Clone,M:'a{type AViewIter=AdjacencyViewIterFromEindex<'g,'a,Self,M,T>;fn aviews(&'g self,map:&'a M,vid:Self::VIndex)->Self::AViewIter{AdjacencyViewIterFromEindex::new(self.adjacencies_with_eindex(vid),self,map)}}}
pub use self::graph_base::*;
mod graph_base{use std::marker::PhantomData;pub trait GraphBase<'g>{type VIndex:Copy+Eq;}pub trait EIndexedGraph<'g>:GraphBase<'g>{type EIndex:Copy+Eq;}pub trait VertexSize<'g>:GraphBase<'g>{fn vsize(&'g self)->usize;}pub trait EdgeSize<'g>:GraphBase<'g>{fn esize(&'g self)->usize;}pub trait Vertices<'g>:GraphBase<'g>{type VIter:'g+Iterator<Item=Self::VIndex>;fn vertices(&'g self)->Self::VIter;}pub trait Edges<'g>:EIndexedGraph<'g>{type EIter:'g+Iterator<Item=Self::EIndex>;fn edges(&'g self)->Self::EIter;}pub trait AdjacencyIndex{type VIndex:Copy+Eq;fn vindex(&self)->Self::VIndex;}pub trait Adjacencies<'g>:GraphBase<'g>{type AIndex:'g+AdjacencyIndex<VIndex=Self::VIndex>;type AIter:'g+Iterator<Item=Self::AIndex>;fn adjacencies(&'g self,vid:Self::VIndex)->Self::AIter;}pub trait AdjacenciesWithEindex<'g>:EIndexedGraph<'g>{type AIndex:'g+AdjacencyIndexWithEindex<VIndex=Self::VIndex,EIndex=Self::EIndex>;type AIter:'g+Iterator<Item=Self::AIndex>;fn adjacencies_with_eindex(&'g self,vid:Self::VIndex)->Self::AIter;}pub trait AdjacencyIndexWithEindex:AdjacencyIndex{type EIndex:Copy+Eq;fn eindex(&self)->Self::EIndex;}pub trait AdjacencyIndexWithValue:AdjacencyIndex{type AValue:Clone;fn avalue(&self)->Self::AValue;}pub trait AdjacenciesWithValue<'g,T>:GraphBase<'g>where T:Clone{type AIndex:'g+AdjacencyIndexWithValue<VIndex=Self::VIndex,AValue=T>;type AIter:'g+Iterator<Item=Self::AIndex>;fn adjacencies_with_value(&'g self,vid:Self::VIndex)->Self::AIter;}impl AdjacencyIndex for usize{type VIndex=usize;fn vindex(&self)->Self::VIndex{*self}}impl<V,E>AdjacencyIndex for(V,E)where V:Copy+Eq,E:Copy+Eq{type VIndex=V;fn vindex(&self)->Self::VIndex{self.0}}impl<V,E>AdjacencyIndexWithEindex for(V,E)where V:Copy+Eq,E:Copy+Eq{type EIndex=E;fn eindex(&self)->Self::EIndex{self.1}}#[derive(Debug,Clone,Copy,PartialEq,Eq,PartialOrd,Ord,Hash)]pub struct VIndex<V>(V);#[derive(Debug,Clone,Copy,PartialEq,Eq,PartialOrd,Ord,Hash)]pub struct VIndexWithEIndex<V,E>(V,E);#[derive(Debug,Clone,Copy,PartialEq,Eq,PartialOrd,Ord,Hash)]pub struct VIndexWithValue<V,T>(V,T);#[derive(Debug,Clone,Copy,PartialEq,Eq,PartialOrd,Ord,Hash)]pub struct VIndexWithEIndexValue<V,E,T>(V,E,T);impl<V>AdjacencyIndex for VIndex<V>where V:Eq+Copy{type VIndex=V;fn vindex(&self)->Self::VIndex{self.0}}impl<V,E>AdjacencyIndex for VIndexWithEIndex<V,E>where V:Eq+Copy{type VIndex=V;fn vindex(&self)->Self::VIndex{self.0}}impl<V,E>AdjacencyIndexWithEindex for VIndexWithEIndex<V,E>where V:Eq+Copy,E:Eq+Copy{type EIndex=E;fn eindex(&self)->Self::EIndex{self.1}}impl<V,T>AdjacencyIndex for VIndexWithValue<V,T>where V:Eq+Copy{type VIndex=V;fn vindex(&self)->Self::VIndex{self.0}}impl<V,T>AdjacencyIndexWithValue for VIndexWithValue<V,T>where V:Eq+Copy,T:Clone{type AValue=T;fn avalue(&self)->Self::AValue{self.1.clone()}}impl<V,E,T>AdjacencyIndex for VIndexWithEIndexValue<V,E,T>where V:Eq+Copy{type VIndex=V;fn vindex(&self)->Self::VIndex{self.0}}impl<V,E,T>AdjacencyIndexWithEindex for VIndexWithEIndexValue<V,E,T>where V:Eq+Copy,E:Eq+Copy{type EIndex=E;fn eindex(&self)->Self::EIndex{self.1}}impl<V,E,T>AdjacencyIndexWithValue for VIndexWithEIndexValue<V,E,T>where V:Eq+Copy,T:Clone{type AValue=T;fn avalue(&self)->Self::AValue{self.2.clone()}}impl<V>From<V>for VIndex<V>{fn from(vid:V)->Self{VIndex(vid)}}impl<V,E>From<(V,E)>for VIndexWithEIndex<V,E>{fn from((vid,eid):(V,E))->Self{VIndexWithEIndex(vid,eid)}}impl<V,T>From<(V,T)>for VIndexWithValue<V,T>{fn from((vid,value):(V,T))->Self{VIndexWithValue(vid,value)}}impl<V,E,T>From<(V,E,T)>for VIndexWithEIndexValue<V,E,T>{fn from((vid,eid,value):(V,E,T))->Self{VIndexWithEIndexValue(vid,eid,value)}}impl<V,T>VIndexWithValue<V,T>{pub fn map<U,F>(self,mut f:F)->VIndexWithValue<V,U>where F:FnMut(T)->U{VIndexWithValue(self.0,f(self.1))}}impl<V,E,T>VIndexWithEIndexValue<V,E,T>{pub fn map<U,F>(self,mut f:F)->VIndexWithEIndexValue<V,E,U>where F:FnMut(T)->U{VIndexWithEIndexValue(self.0,self.1,f(self.2))}}pub trait VertexMap<'g,T>:GraphBase<'g>{type Vmap;fn construct_vmap<F>(&self,f:F)->Self::Vmap where F:FnMut()->T;fn vmap_get<'a>(&self,map:&'a Self::Vmap,vid:Self::VIndex)->&'a T;fn vmap_get_mut<'a>(&self,map:&'a mut Self::Vmap,vid:Self::VIndex)->&'a mut T;fn vmap_set(&self,map:&mut Self::Vmap,vid:Self::VIndex,x:T){*self.vmap_get_mut(map,vid)=x;}}pub trait VertexView<'g,M,T>:GraphBase<'g>where M:?Sized{fn vview(&self,map:&M,vid:Self::VIndex)->T;}pub trait EdgeMap<'g,T>:EIndexedGraph<'g>{type Emap;fn construct_emap<F>(&self,f:F)->Self::Emap where F:FnMut()->T;fn emap_get<'a>(&self,map:&'a Self::Emap,eid:Self::EIndex)->&'a T;fn emap_get_mut<'a>(&self,map:&'a mut Self::Emap,eid:Self::EIndex)->&'a mut T;fn emap_set(&self,map:&mut Self::Emap,eid:Self::EIndex,x:T){*self.emap_get_mut(map,eid)=x;}}pub trait EdgeView<'g,M,T>:EIndexedGraph<'g>where M:?Sized{fn eview(&self,map:&M,eid:Self::EIndex)->T;}impl<'g,G,F,T>VertexView<'g,F,T>for G where G:GraphBase<'g>,F:Fn(Self::VIndex)->T{fn vview(&self,map:&F,vid:Self::VIndex)->T{(map)(vid)}}impl<'g,G,F,T>EdgeView<'g,F,T>for G where G:EIndexedGraph<'g>,F:Fn(Self::EIndex)->T{fn eview(&self,map:&F,eid:Self::EIndex)->T{(map)(eid)}}pub trait AdjacencyView<'g,'a,M,T>:GraphBase<'g>where M:?Sized{type AViewIter:Iterator<Item=VIndexWithValue<Self::VIndex,T>>;fn aviews(&'g self,map:&'a M,vid:Self::VIndex)->Self::AViewIter;}pub struct AdjacencyViewIterFromEindex<'g,'a,G,M,T>where G:AdjacenciesWithEindex<'g>{iter:G::AIter,g:&'g G,map:&'a M,_marker:PhantomData<fn()->T>}impl<'g,'a,G,M,T>AdjacencyViewIterFromEindex<'g,'a,G,M,T>where G:AdjacenciesWithEindex<'g>{pub fn new(iter:G::AIter,g:&'g G,map:&'a M)->Self{Self{iter,g,map,_marker:PhantomData}}}impl<'g,'a,G,M,T>Iterator for AdjacencyViewIterFromEindex<'g,'a,G,M,T>where G:'g+AdjacenciesWithEindex<'g>+EdgeView<'g,M,T>,M:'a{type Item=VIndexWithValue<G::VIndex,T>;fn next(&mut self)->Option<Self::Item>{self.iter.next().map(|adj|(adj.vindex(),self.g.eview(self.map,adj.eindex())).into())}}pub struct AdjacencyViewIterFromValue<'g,'a,G,M,T,U>where G:AdjacenciesWithValue<'g,T>,T:Clone{iter:G::AIter,map:&'a M,_marker:PhantomData<fn()->U>}impl<'g,'a,G,M,T,U>AdjacencyViewIterFromValue<'g,'a,G,M,T,U>where G:AdjacenciesWithValue<'g,T>,T:Clone{pub fn new(iter:G::AIter,map:&'a M)->Self{Self{iter,map,_marker:PhantomData}}}impl<'g,'a,G,M,T,U>Iterator for AdjacencyViewIterFromValue<'g,'a,G,M,T,U>where G:'g+AdjacenciesWithValue<'g,T>,T:Clone,M:'a+Fn(T)->U{type Item=VIndexWithValue<G::VIndex,U>;fn next(&mut self)->Option<Self::Item>{self.iter.next().map(|adj|(adj.vindex(),(self.map)(adj.avalue())).into())}}}
pub struct HeavyLightDecomposition{pub par:Vec<usize>,size:Vec<usize>,head:Vec<usize>,pub vidx:Vec<usize>}
impl HeavyLightDecomposition{pub fn new(root:usize,graph:&mut UndirectedSparseGraph)->Self{let mut self_=Self{par:vec![0;graph.vertices_size()],size:vec![0;graph.vertices_size()],head:vec![0;graph.vertices_size()],vidx:vec![0;graph.vertices_size()]};self_.build(root,graph);self_}fn dfs_size(&mut self,u:usize,p:usize,graph:&mut UndirectedSparseGraph){self.par[u]=p;self.size[u]=1;let base=graph.start[u];if graph.adjacencies(u).len()>1&&graph.adjacencies(u).next().unwrap().to==p{graph.elist.swap(base,base+1);}for i in base..graph.start[u+1]{let a=graph.elist[i];if a.to!=p{self.dfs_size(a.to,u,graph);self.size[u]+=self.size[a.to];if self.size[graph.elist[base].to]<self.size[a.to]{graph.elist.swap(base,i);}}}}fn dfs_hld(&mut self,u:usize,p:usize,t:&mut usize,graph:&UndirectedSparseGraph){self.vidx[u]=*t;*t+=1;let mut adjacencies=graph.adjacencies(u).filter(|a|a.to!=p);if let Some(a)=adjacencies.next(){self.head[a.to]=self.head[u];self.dfs_hld(a.to,u,t,graph);}for a in adjacencies{self.head[a.to]=a.to;self.dfs_hld(a.to,u,t,graph);}}fn build(&mut self,root:usize,graph:&mut UndirectedSparseGraph){self.head[root]=root;self.dfs_size(root,graph.vertices_size(),graph);let mut t=0;self.dfs_hld(root,graph.vertices_size(),&mut t,graph);}pub fn lca(&self,mut u:usize,mut v:usize)->usize{loop{if self.vidx[u]>self.vidx[v]{std::mem::swap(&mut u,&mut v);}if self.head[u]==self.head[v]{return u;}v=self.par[self.head[v]];}}pub fn update<F:FnMut(usize,usize)>(&self,mut u:usize,mut v:usize,is_edge:bool,mut f:F){loop{if self.vidx[u]>self.vidx[v]{std::mem::swap(&mut u,&mut v);}if self.head[u]==self.head[v]{break;}f(self.vidx[self.head[v]],self.vidx[v]+1);v=self.par[self.head[v]];}f(self.vidx[u]+is_edge as usize,self.vidx[v]+1);}pub fn query<M:Monoid,F:FnMut(usize,usize)->M::T>(&self,mut u:usize,mut v:usize,is_edge:bool,mut f:F)->M::T{let(mut l,mut r)=(M::unit(),M::unit());loop{if self.vidx[u]>self.vidx[v]{std::mem::swap(&mut u,&mut v);std::mem::swap(&mut l,&mut r);}if self.head[u]==self.head[v]{break;}l=M::operate(&f(self.vidx[self.head[v]],self.vidx[v]+1),&l);v=self.par[self.head[v]];}M::operate(&M::operate(&f(self.vidx[u]+is_edge as usize,self.vidx[v]+1),&l),&r)}pub fn query_noncom<M:Monoid,F1:FnMut(usize,usize)->M::T,F2:FnMut(usize,usize)->M::T>(&self,mut u:usize,mut v:usize,is_edge:bool,mut f1:F1,mut f2:F2)->M::T{let(mut l,mut r)=(M::unit(),M::unit());while self.head[u]!=self.head[v]{if self.vidx[u]>self.vidx[v]{l=M::operate(&l,&f2(self.vidx[self.head[u]],self.vidx[u]+1));u=self.par[self.head[u]];}else{r=M::operate(&f1(self.vidx[self.head[v]],self.vidx[v]+1),&r);v=self.par[self.head[v]];}}M::operate(&M::operate(&l,&if self.vidx[u]>self.vidx[v]{f2(self.vidx[v]+is_edge as usize,self.vidx[u]+1)}else{f1(self.vidx[u]+is_edge as usize,self.vidx[v]+1)}),&r)}}
pub use self::magma::*;
mod magma{#![doc=" algebraic traits"]#[doc=" binary operaion: $T \\circ T \\to T$"]pub trait Magma{#[doc=" type of operands: $T$"]type T:Clone;#[doc=" binary operaion: $\\circ$"]fn operate(x:&Self::T,y:&Self::T)->Self::T;#[inline]fn reverse_operate(x:&Self::T,y:&Self::T)->Self::T{Self::operate(y,x)}#[inline]fn operate_assign(x:&mut Self::T,y:&Self::T){*x=Self::operate(x,y);}}#[doc=" $\\forall a,\\forall b,\\forall c \\in T, (a \\circ b) \\circ c = a \\circ (b \\circ c)$"]pub trait Associative{}#[doc=" associative binary operation"]pub trait SemiGroup:Magma+Associative{}impl<S>SemiGroup for S where S:Magma+Associative{}#[doc=" $\\exists e \\in T, \\forall a \\in T, e \\circ a = a \\circ e = e$"]pub trait Unital:Magma{#[doc=" identity element: $e$"]fn unit()->Self::T;#[inline]fn is_unit(x:&Self::T)->bool where<Self as Magma>::T:PartialEq{x==&Self::unit()}#[inline]fn set_unit(x:&mut Self::T){*x=Self::unit();}}#[doc=" associative binary operation and an identity element"]pub trait Monoid:SemiGroup+Unital{#[doc=" binary exponentiation: $x^n = x\\circ\\ddots\\circ x$"]fn pow(mut x:Self::T,mut n:usize)->Self::T{let mut res=Self::unit();while n>0{if n&1==1{res=Self::operate(&res,&x);}x=Self::operate(&x,&x);n>>=1;}res}}impl<M>Monoid for M where M:SemiGroup+Unital{}#[doc=" $\\exists e \\in T, \\forall a \\in T, \\exists b,c \\in T, b \\circ a = a \\circ c = e$"]pub trait Invertible:Magma{#[doc=" $a$ where $a \\circ x = e$"]fn inverse(x:&Self::T)->Self::T;#[inline]fn rinv_operate(x:&Self::T,y:&Self::T)->Self::T{Self::operate(x,&Self::inverse(y))}}#[doc=" associative binary operation and an identity element and inverse elements"]pub trait Group:Monoid+Invertible{}impl<G>Group for G where G:Monoid+Invertible{}#[doc=" $\\forall a,\\forall b \\in T, a \\circ b = b \\circ a$"]pub trait Commutative{}#[doc=" commutative monoid"]pub trait AbelianMonoid:Monoid+Commutative{}impl<M>AbelianMonoid for M where M:Monoid+Commutative{}#[doc=" commutative group"]pub trait AbelianGroup:Group+Commutative{}impl<G>AbelianGroup for G where G:Group+Commutative{}#[doc=" $\\forall a \\in T, a \\circ a = a$"]pub trait Idempotent{}#[doc=" idempotent monoid"]pub trait IdempotentMonoid:Monoid+Idempotent{}impl<M>IdempotentMonoid for M where M:Monoid+Idempotent{}#[macro_export]macro_rules!monoid_fold{($m:ty)=>{<$m as Unital>::unit()};($m:ty,)=>{<$m as Unital>::unit()};($m:ty,$f:expr)=>{$f};($m:ty,$f:expr,$($ff:expr),*)=>{<$m as Magma>::operate(&($f),&monoid_fold!($m,$($ff),*))};}#[macro_export]macro_rules!define_monoid{($Name:ident,$t:ty,|$x:ident,$y:ident|$op:expr,$unit:expr)=>{struct$Name;impl Magma for$Name{type T=$t;fn operate($x:&Self::T,$y:&Self::T)->Self::T{$op}}impl Unital for$Name{fn unit()->Self::T{$unit}}impl Associative for$Name{}};}}
impl UndirectedSparseGraph{fn depth_dfs(&self,u:usize,p:usize,d:u64,depth:&mut Vec<u64>){depth[u]=d;for a in self.adjacencies(u).filter(|a|a.to!=p){self.depth_dfs(a.to,u,d+1,depth);}}pub fn tree_depth(&self,root:usize)->Vec<u64>{let mut depth=vec![0;self.vertices_size()];self.depth_dfs(root,self.vertices_size(),0,&mut depth);depth}}
#[doc=" dynamic programming on all-rooted trees"]#[doc=""]#[doc=" caluculate all subtrees (hanging on the edge) in specific ordering,"]#[doc=" each subtree calculated in the order of merge and rooting"]#[derive(Clone,Debug)]pub struct ReRooting<'a,M:Monoid,F:Fn(&M::T,usize,Option<usize>)->M::T>{graph:&'a UndirectedSparseGraph,#[doc=" dp\\[v\\]: result of v-rooted tree"]pub dp:Vec<M::T>,#[doc=" ep\\[e\\]: result of e-subtree, if e >= n then reversed-e-subtree"]pub ep:Vec<M::T>,#[doc=" rooting(data, vid, (Optional)eid): add root node(vid), result subtree is edge(eid)"]rooting:F}
impl<'a,M,F>ReRooting<'a,M,F>where M:Monoid,F:Fn(&M::T,usize,Option<usize>)->M::T{pub fn new(graph:&'a UndirectedSparseGraph,rooting:F)->Self{let dp=vec![M::unit();graph.vertices_size()];let ep=vec![M::unit();graph.vertices_size()*2];let mut self_=Self{graph,dp,ep,rooting};self_.rerooting();self_}#[inline]fn eidx(&self,u:usize,a:&Adjacency)->usize{a.id+self.graph.edges_size()*(u>a.to)as usize}#[inline]fn reidx(&self,u:usize,a:&Adjacency)->usize{a.id+self.graph.edges_size()*(u<a.to)as usize}#[inline]fn merge(&self,x:&M::T,y:&M::T)->M::T{M::operate(x,y)}#[inline]fn add_subroot(&self,x:&M::T,vid:usize,eid:usize)->M::T{(self.rooting)(x,vid,Some(eid))}#[inline]fn add_root(&self,x:&M::T,vid:usize)->M::T{(self.rooting)(x,vid,None)}fn dfs(&mut self,pa:&Adjacency,p:usize){let u=pa.to;let pi=self.eidx(p,pa);for a in self.graph.adjacencies(u).filter(|a|a.to!=p){let i=self.eidx(u,a);self.dfs(a,u);self.ep[pi]=self.merge(&self.ep[pi],&self.ep[i]);}self.ep[pi]=self.add_subroot(&self.ep[pi],u,pa.id);}fn efs(&mut self,u:usize,p:usize){let m=self.graph.adjacencies(u).len();let mut left=vec![M::unit();m+1];let mut right=vec![M::unit();m+1];for(k,a)in self.graph.adjacencies(u).enumerate(){let i=self.eidx(u,a);left[k+1]=self.merge(&left[k],&self.ep[i]);}for(k,a)in self.graph.adjacencies(u).enumerate().rev(){let i=self.eidx(u,a);right[k]=self.merge(&right[k+1],&self.ep[i]);}self.dp[u]=self.add_root(&left[m],u);for(k,a)in self.graph.adjacencies(u).enumerate(){if a.to!=p{let i=self.reidx(u,a);self.ep[i]=self.merge(&left[k],&right[k+1]);self.ep[i]=self.add_subroot(&self.ep[i],u,a.id);self.efs(a.to,u);}}}fn rerooting(&mut self){for a in self.graph.adjacencies(0){self.dfs(a,0);}self.efs(0,std::usize::MAX);}}
pub use self::additive_operation_impl::AdditiveOperation;
mod additive_operation_impl{use super::*;use std::{marker::PhantomData,ops::{Add,Neg,Sub}};#[doc=" $+$"]pub struct AdditiveOperation<T:Clone+Zero+Add<Output=T>>{_marker:PhantomData<fn()->T>}impl<T:Clone+Zero+Add<Output=T>>Magma for AdditiveOperation<T>{type T=T;#[inline]fn operate(x:&Self::T,y:&Self::T)->Self::T{x.clone()+y.clone()}}impl<T:Clone+Zero+Add<Output=T>>Unital for AdditiveOperation<T>{#[inline]fn unit()->Self::T{Zero::zero()}}impl<T:Clone+Zero+Add<Output=T>>Associative for AdditiveOperation<T>{}impl<T:Clone+Zero+Add<Output=T>>Commutative for AdditiveOperation<T>{}impl<T:Clone+Zero+Add<Output=T>+Sub<Output=T>+Neg<Output=T>>Invertible for AdditiveOperation<T>{#[inline]fn inverse(x:&Self::T)->Self::T{-x.clone()}#[inline]fn rinv_operate(x:&Self::T,y:&Self::T)->Self::T{x.clone()-y.clone()}}}
pub use self::zero_one::{One,Zero};
mod zero_one{pub trait Zero:Sized{fn zero()->Self;#[inline]fn is_zero(&self)->bool where Self:PartialEq{self==&Self::zero()}#[inline]fn set_zero(&mut self){*self=Self::zero();}}pub trait One:Sized{fn one()->Self;#[inline]fn is_one(&self)->bool where Self:PartialEq{self==&Self::one()}#[inline]fn set_one(&mut self){*self=Self::one();}}macro_rules!zero_one_impls{($({$Trait:ident$method:ident$($t:ty)*,$e:expr})*)=>{$($(impl$Trait for$t{fn$method()->Self{$e}})*)*};}zero_one_impls!({Zero zero u8 u16 u32 u64 usize i8 i16 i32 i64 isize u128 i128,0}{Zero zero f32 f64,0.}{One one u8 u16 u32 u64 usize i8 i16 i32 i64 isize u128 i128,1}{One one f32 f64,1.});}