#1139841 (Rust) No.3404 形式群法則

提出ソース
結果

問題	No.3404 形式群法則
コンテスト
ユーザー	to-omer
提出日時	2025-12-11 01:01:02
言語	Rust (1.83.0 + proconio)
結果	AC
実行時間	520 ms / 2,000 ms
コード長	47,948 bytes
記録記録タグの例: 初AC ショートコード純ショートコード純主流ショートコード最速実行時間
コンパイル時間	13,555 ms
コンパイル使用メモリ	400,276 KB
実行使用メモリ	7,848 KB
最終ジャッジ日時	2025-12-11 01:01:32
合計ジャッジ時間	17,460 ms
ジャッジサーバーID （参考情報）	judge5 / judge2
このコードへのチャレンジ
（要ログイン）
ファイルパターン	結果
other	AC * 25
権限があれば一括ダウンロードができます
ソースコード

raw source code
pub fn solve() {
    crate::prepare!();
    sc!(n, m, p: u32, a: [u64; n]);
    M::set_mod(p);
    let a: Vec<_> = [0].into_iter().chain(a).map(M::from).collect();
    let add = |a: &[M], b: &[M]| {
        let mut c = vec![M::zero(); a.len().max(b.len())];
        for i in 0..a.len() {
            c[i] += a[i];
        }
        for i in 0..b.len() {
            c[i] += b[i];
        }
        c
    };
    let mul = |a: &[M], b: &[M]| {
        let mut c = vec![M::zero(); a.len() + b.len() - 1];
        for i in 0..a.len() {
            for j in 0..b.len() {
                c[i + j] += a[i] * b[j];
            }
        }
        c
    };
    let inv = |a: &[M], deg: usize| {
        let mut c = vec![M::zero(); deg];
        c[0] = M::one() / a[0];
        for i in 1..deg {
            c[i] = M::zero();
            for j in 1..=i.min(a.len() - 1) {
                let x = c[i - j] * a[j];
                c[i] -= x;
            }
            c[i] /= a[0];
        }
        c
    };
    let star = |a: &[M], b: &[M]| {
        let mut c = mul(a, b);
        for c in &mut c {
            *c = -*c;
        }
        c[0] += M::one();
        c = mul(&add(a, b), &inv(&c, n + 1));
        c.truncate(n + 1);
        c
    };
    let pow = |a: &[M], mut m: usize| {
        let mut a = a.to_vec();
        let mut res = a.to_vec();
        m -= 1;
        while m > 0 {
            if m % 2 == 1 {
                res = star(&res, &a);
            }
            a = star(&a, &a);
            m /= 2;
        }
        res
    };
    let b = pow(&a, m);
    pp!(@it &b[1..]);
}
pub type M = mint_basic::DynMIntU32;
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]#[allow(clippy::crate_in_macro_def)]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)*)}}#[allow(unused_macros)]#[doc=" Scan a line, and previous line will be truncated in the next call."]macro_rules!svln{($dol($dol t:tt)*)=>{{let __in_buf=read_stdin_line();#[allow(unused_mut,unused_variables)]let mut __scanner=Scanner::new(&__in_buf);$dol crate::scan_value!(__scanner,$dol($dol t)*)}}}};()=>{$crate::prepare!(@output($));$crate::prepare!(@normal($))};(?)=>{$crate::prepare!(@output($));$crate::prepare!(@interactive($))};}#[macro_export]macro_rules!main{()=>{fn main(){solve();}};(avx2)=>{fn main(){#[target_feature(enable="avx2")]unsafe fn solve_avx2(){solve();}unsafe{solve_avx2()}}};(large_stack)=>{fn main(){const STACK_SIZE:usize=512*1024*1024;::std::thread::Builder::new().stack_size(STACK_SIZE).spawn(solve).unwrap().join().unwrap();}};}}
pub use self::iter_print::IterPrint;
mod iter_print{use std::{fmt::Display,io::{Error,Write}};pub trait IterPrint{fn iter_print<W,S>(self,writer:&mut W,sep:S,is_head:bool)->Result<(),Error>where W:Write,S:Display;}macro_rules!impl_iter_print_tuple{(@impl,)=>{impl IterPrint for(){fn iter_print<W,S>(self,_writer:&mut W,_sep:S,_is_head:bool)->Result<(),Error>where W:Write,S:Display{Ok(())}}};(@impl$($A:ident$a:ident)?,$($B:ident$b:ident)*)=>{impl<$($A,)?$($B),*>IterPrint for($($A,)?$($B),*)where$($A:Display,)?$($B:Display),*{fn iter_print<W,S>(self,writer:&mut W,sep:S,is_head:bool)->Result<(),Error>where W:Write,S:Display{let($($a,)?$($b,)*)=self;$(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$d:ident)*)=>{impl_iter_print_tuple!(@impl,);impl_iter_print_tuple!(@inc$C$c,,$($D$d)*);};(@inc$A:ident$a:ident,$($B:ident$b:ident)*,$C:ident$c:ident$($D:ident$d:ident)*)=>{impl_iter_print_tuple!(@impl$A$a,$($B$b)*);impl_iter_print_tuple!(@inc$A$a,$($B$b)*$C$c,$($D$d)*);};(@inc$A:ident$a:ident,$($B:ident$b:ident)*,)=>{impl_iter_print_tuple!(@impl$A$a,$($B$b)*);};($($t:tt)*)=>{impl_iter_print_tuple!(@inc,,$($t)*);};}impl_iter_print_tuple!(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;$len:expr]]=>{{use::std::mem::{ManuallyDrop,MaybeUninit};let mut$data:[MaybeUninit<_>;$len]=unsafe{MaybeUninit::uninit().assume_init()};$init;#[repr(C)]union __Transmuter<const N:usize,T:Clone>{src:ManuallyDrop<[MaybeUninit<T>;N]>,dst:ManuallyDrop<[T;N]>,}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::{FromIterator,from_fn,repeat_with},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!impl_iter_scan{($($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::<$t>().ok()}})*};}impl_iter_scan!(char u8 u16 u32 u64 usize i8 i16 i32 i64 isize f32 f64 u128 i128 String);macro_rules!impl_iter_scan_tuple{(@impl$($T:ident)*)=>{impl<$($T:IterScan),*>IterScan for($($T,)*){type Output=($(<$T as IterScan>::Output,)*);#[inline]fn scan<'a,It:Iterator<Item=&'a str>>(_iter:&mut It)->Option<Self::Output>{Some(($(<$T as IterScan>::scan(_iter)?,)*))}}};(@inner$($T:ident)*,)=>{impl_iter_scan_tuple!(@impl$($T)*);};(@inner$($T:ident)*,$U:ident$($Rest:ident)*)=>{impl_iter_scan_tuple!(@impl$($T)*);impl_iter_scan_tuple!(@inner$($T)*$U,$($Rest)*);};($($T:ident)*)=>{impl_iter_scan_tuple!(@inner,$($T)*);};}impl_iter_scan_tuple!(A B C D E F G H I J K);pub struct ScannerIter<'a,'b,T>{inner:&'b mut Scanner<'a>,_marker:std::marker::PhantomData<fn()->T>}impl<T>Iterator for ScannerIter<'_,'_,T>where T:IterScan{type Item=<T as IterScan>::Output;#[inline]fn next(&mut self)->Option<Self::Item>{<T as IterScan>::scan(&mut self.inner.iter)}}#[doc=" scan a value with Scanner"]#[doc=""]#[doc=" - `scan_value!(scanner, ELEMENT)`"]#[doc=""]#[doc=" ELEMENT :="]#[doc=" - `$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$scanner:expr,[$($args:tt)*])=>{::std::compile_error!(::std::stringify!($($args)*))};(src=$src:expr,$($t:tt)*)=>{{let mut __scanner=Scanner::new($src);$crate::scan_value!(@inner __scanner,[]$($t)*)}};($scanner:expr,$($t:tt)*)=>{$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)*)};(src=$src:expr,$($t:tt)*)=>{let mut __scanner=Scanner::new($src);$crate::scan!(@pat __scanner,[][]$($t)*)};($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 mod mint_basic{use super::*;use std::{cell::UnsafeCell,mem::swap};#[macro_export]macro_rules!define_basic_mintbase{($name:ident,$m:expr,$basety:ty,$signedty:ty,$upperty:ty,[$($unsigned:ty),*],[$($signed:ty),*])=>{pub enum$name{}impl MIntBase for$name{type Inner=$basety;#[inline]fn get_mod()->Self::Inner{$m}#[inline]fn mod_zero()->Self::Inner{0}#[inline]fn mod_one()->Self::Inner{1}#[inline]fn mod_add(x:Self::Inner,y:Self::Inner)->Self::Inner{let z=x+y;let m=Self::get_mod();if z>=m{z-m}else{z}}#[inline]fn mod_sub(x:Self::Inner,y:Self::Inner)->Self::Inner{if x<y{x+Self::get_mod()-y}else{x-y}}#[inline]fn mod_mul(x:Self::Inner,y:Self::Inner)->Self::Inner{$name::rem(x as$upperty*y as$upperty)as$basety}#[inline]fn mod_div(x:Self::Inner,y:Self::Inner)->Self::Inner{Self::mod_mul(x,Self::mod_inv(y))}#[inline]fn mod_neg(x:Self::Inner)->Self::Inner{if x==0{0}else{Self::get_mod()-x}}fn mod_inv(x:Self::Inner)->Self::Inner{let p=Self::get_mod()as$signedty;let(mut a,mut b)=(x as$signedty,p);let(mut u,mut x)=(1,0);while a!=0{let k=b/a;x-=k*u;b-=k*a;swap(&mut x,&mut u);swap(&mut b,&mut a);}(if x<0{x+p}else{x})as _}}$(impl MIntConvert<$unsigned>for$name{#[inline]fn from(x:$unsigned)->Self::Inner{(x%<Self as MIntBase>::get_mod()as$unsigned)as$basety}#[inline]fn into(x:Self::Inner)->$unsigned{x as$unsigned}#[inline]fn mod_into()->$unsigned{<Self as MIntBase>::get_mod()as$unsigned}})*$(impl MIntConvert<$signed>for$name{#[inline]fn from(x:$signed)->Self::Inner{let x=x%<Self as MIntBase>::get_mod()as$signed;if x<0{(x+<Self as MIntBase>::get_mod()as$signed)as$basety}else{x as$basety}}#[inline]fn into(x:Self::Inner)->$signed{x as$signed}#[inline]fn mod_into()->$signed{<Self as MIntBase>::get_mod()as$signed}})*};}#[macro_export]macro_rules!define_basic_mint32{($([$name:ident,$m:expr,$mint_name:ident]),*)=>{$(define_basic_mintbase!($name,$m,u32,i32,u64,[u32,u64,u128,usize],[i32,i64,i128,isize]);impl$name{fn rem(x:u64)->u64{x%$m}}pub type$mint_name=MInt<$name>;)*};}thread_local!(static DYN_MODULUS_U32:UnsafeCell<BarrettReduction<u64>> =const{UnsafeCell::new(BarrettReduction::<u64>::new_with_im(1_000_000_007,!0/1_000_000_007))});impl DynModuloU32{pub fn set_mod(m:u32){DYN_MODULUS_U32.with(|cell|unsafe{*cell.get()=BarrettReduction::<u64>::new(m as u64)});}fn rem(x:u64)->u64{DYN_MODULUS_U32.with(|cell|unsafe{(*cell.get()).rem(x)})}}impl DynMIntU32{pub fn set_mod(m:u32){DynModuloU32::set_mod(m)}}thread_local!(static DYN_MODULUS_U64:UnsafeCell<BarrettReduction<u128>> =const{UnsafeCell::new(BarrettReduction::<u128>::new_with_im(1_000_000_007,!0/1_000_000_007))});impl DynModuloU64{pub fn set_mod(m:u64){DYN_MODULUS_U64.with(|cell|unsafe{*cell.get()=BarrettReduction::<u128>::new(m as u128)})}fn rem(x:u128)->u128{DYN_MODULUS_U64.with(|cell|unsafe{(*cell.get()).rem(x)})}}impl DynMIntU64{pub fn set_mod(m:u64){DynModuloU64::set_mod(m)}}define_basic_mint32!([Modulo998244353,998_244_353,MInt998244353],[Modulo1000000007,1_000_000_007,MInt1000000007],[Modulo1000000009,1_000_000_009,MInt1000000009]);define_basic_mintbase!(DynModuloU32,DYN_MODULUS_U32.with(|cell|unsafe{(*cell.get()).get_mod()as u32}),u32,i32,u64,[u32,u64,u128,usize],[i32,i64,i128,isize]);pub type DynMIntU32=MInt<DynModuloU32>;define_basic_mintbase!(DynModuloU64,DYN_MODULUS_U64.with(|cell|unsafe{(*cell.get()).get_mod()as u64}),u64,i64,u128,[u64,u128,usize],[i64,i128,isize]);pub type DynMIntU64=MInt<DynModuloU64>;pub struct Modulo2;impl MIntBase for Modulo2{type Inner=u32;#[inline]fn get_mod()->Self::Inner{2}#[inline]fn mod_zero()->Self::Inner{0}#[inline]fn mod_one()->Self::Inner{1}#[inline]fn mod_add(x:Self::Inner,y:Self::Inner)->Self::Inner{x^y}#[inline]fn mod_sub(x:Self::Inner,y:Self::Inner)->Self::Inner{x^y}#[inline]fn mod_mul(x:Self::Inner,y:Self::Inner)->Self::Inner{x&y}#[inline]fn mod_div(x:Self::Inner,y:Self::Inner)->Self::Inner{assert_ne!(y,0);x}#[inline]fn mod_neg(x:Self::Inner)->Self::Inner{x}#[inline]fn mod_inv(x:Self::Inner)->Self::Inner{assert_ne!(x,0);x}#[inline]fn mod_pow(x:Self::Inner,y:usize)->Self::Inner{if y==0{1}else{x}}}macro_rules!impl_to_mint_base_for_modulo2{($name:ident,$basety:ty,[$($t:ty),*])=>{$(impl MIntConvert<$t>for$name{#[inline]fn from(x:$t)->Self::Inner{(x&1)as$basety}#[inline]fn into(x:Self::Inner)->$t{x as$t}#[inline]fn mod_into()->$t{1}})*};}impl_to_mint_base_for_modulo2!(Modulo2,u32,[u8,u16,u32,u64,u128,usize,i8,i16,i32,i64,i128,isize]);pub type MInt2=MInt<Modulo2>;}
pub use self::barrett_reduction::{BarrettReduction,Barrettable};
mod barrett_reduction{use super::{One,Zero};use std::ops::{Add,Mul,Sub};#[derive(Debug,Clone,Copy)]pub struct BarrettReduction<T>{m:T,im:T}impl<T>BarrettReduction<T>where T:Barrettable{pub fn new(m:T)->Self{Self{m,im:T::inv_mod_approx(m)}}pub const fn new_with_im(m:T,im:T)->Self{Self{m,im}}pub const fn get_mod(&self)->T{self.m}pub fn div_rem(&self,a:T)->(T,T){T::barrett_reduce(a,self.m,self.im)}pub fn div(&self,a:T)->T{self.div_rem(a).0}pub fn rem(&self,a:T)->T{self.div_rem(a).1}}pub trait Barrettable:Sized+Copy+PartialOrd+Zero+One+Add<Output=Self>+Sub<Output=Self>+Mul<Output=Self>{fn inv_mod_approx(m:Self)->Self;fn div_approx(self,im:Self)->Self;fn barrett_reduce(self,m:Self,im:Self)->(Self,Self){if m==Self::one(){return(self,Self::zero());}let q=self.div_approx(im);let r=self-q*m;if m<=r{(q+Self::one(),r-m)}else{(q,r)}}}impl Barrettable for u32{fn inv_mod_approx(m:Self)->Self{!0/m}fn div_approx(self,im:Self)->Self{((self as u64*im as u64)>>32)as u32}}impl Barrettable for u64{fn inv_mod_approx(m:Self)->Self{!0/m}fn div_approx(self,im:Self)->Self{((self as u128*im as u128)>>64)as u64}}impl Barrettable for u128{fn inv_mod_approx(m:Self)->Self{!0/m}fn div_approx(self,im:Self)->Self{const MASK64:u128=0xffff_ffff_ffff_ffff;let au=self>>64;let ad=self&MASK64;let imu=im>>64;let imd=im&MASK64;let mut res=au*imu;let x=(ad*imd)>>64;let(x,c)=x.overflowing_add(au*imd);res+=c as u128;let(x,c)=x.overflowing_add(ad*imu);res+=c as u128;res+(x>>64)}}}
pub use mint_base::{MInt,MIntBase,MIntConvert};
mod mint_base{use super::*;use std::{fmt::{self,Debug,Display},hash::{Hash,Hasher},iter::{Product,Sum},marker::PhantomData,ops::{Add,AddAssign,Div,DivAssign,Mul,MulAssign,Neg,Sub,SubAssign},str::FromStr};#[repr(transparent)]pub struct MInt<M>where M:MIntBase{x:M::Inner,_marker:PhantomData<fn()->M>}pub trait MIntConvert<T=<Self as MIntBase>::Inner>:MIntBase{fn from(x:T)-><Self as MIntBase>::Inner;fn into(x:<Self as MIntBase>::Inner)->T;fn mod_into()->T;}pub trait MIntBase{type Inner:Sized+Copy+Eq+Debug+Hash;fn get_mod()->Self::Inner;fn mod_zero()->Self::Inner;fn mod_one()->Self::Inner;fn mod_add(x:Self::Inner,y:Self::Inner)->Self::Inner;fn mod_sub(x:Self::Inner,y:Self::Inner)->Self::Inner;fn mod_mul(x:Self::Inner,y:Self::Inner)->Self::Inner;fn mod_div(x:Self::Inner,y:Self::Inner)->Self::Inner;fn mod_neg(x:Self::Inner)->Self::Inner;fn mod_inv(x:Self::Inner)->Self::Inner;fn mod_pow(x:Self::Inner,y:usize)->Self::Inner{let(mut x,mut y,mut z)=(x,y,Self::mod_one());while y>0{if y&1==1{z=Self::mod_mul(z,x);}x=Self::mod_mul(x,x);y>>=1;}z}fn mod_inner(x:Self::Inner)->Self::Inner{x}}impl<M>MInt<M>where M:MIntConvert{#[inline]pub fn new(x:M::Inner)->Self{Self::new_unchecked(<M as MIntConvert<M::Inner>>::from(x))}}impl<M>MInt<M>where M:MIntBase{#[inline]pub const fn new_unchecked(x:M::Inner)->Self{Self{x,_marker:PhantomData}}#[inline]pub fn get_mod()->M::Inner{M::get_mod()}#[inline]pub fn pow(self,y:usize)->Self{Self::new_unchecked(M::mod_pow(self.x,y))}#[inline]pub fn inv(self)->Self{Self::new_unchecked(M::mod_inv(self.x))}#[inline]pub fn inner(self)->M::Inner{M::mod_inner(self.x)}}impl<M>Clone for MInt<M>where M:MIntBase{#[inline]fn clone(&self)->Self{*self}}impl<M>Copy for MInt<M>where M:MIntBase{}impl<M>Debug for MInt<M>where M:MIntBase{fn fmt(&self,f:&mut fmt::Formatter<'_>)->fmt::Result{Debug::fmt(&self.inner(),f)}}impl<M>Default for MInt<M>where M:MIntBase{#[inline]fn default()->Self{<Self as Zero>::zero()}}impl<M>PartialEq for MInt<M>where M:MIntBase{#[inline]fn eq(&self,other:&Self)->bool{PartialEq::eq(&self.x,&other.x)}}impl<M>Eq for MInt<M>where M:MIntBase{}impl<M>Hash for MInt<M>where M:MIntBase{#[inline]fn hash<H:Hasher>(&self,state:&mut H){Hash::hash(&self.x,state)}}macro_rules!impl_mint_from{($($t:ty),*)=>{$(impl<M>From<$t>for MInt<M>where M:MIntConvert<$t>,{#[inline]fn from(x:$t)->Self{Self::new_unchecked(<M as MIntConvert<$t>>::from(x))}}impl<M>From<MInt<M>>for$t where M:MIntConvert<$t>,{#[inline]fn from(x:MInt<M>)->$t{<M as MIntConvert<$t>>::into(x.x)}})*};}impl_mint_from!(u8,u16,u32,u64,u128,usize,i8,i16,i32,i64,i128,isize);impl<M>Zero for MInt<M>where M:MIntBase{#[inline]fn zero()->Self{Self::new_unchecked(M::mod_zero())}}impl<M>One for MInt<M>where M:MIntBase{#[inline]fn one()->Self{Self::new_unchecked(M::mod_one())}}impl<M>Add for MInt<M>where M:MIntBase{type Output=Self;#[inline]fn add(self,rhs:Self)->Self::Output{Self::new_unchecked(M::mod_add(self.x,rhs.x))}}impl<M>Sub for MInt<M>where M:MIntBase{type Output=Self;#[inline]fn sub(self,rhs:Self)->Self::Output{Self::new_unchecked(M::mod_sub(self.x,rhs.x))}}impl<M>Mul for MInt<M>where M:MIntBase{type Output=Self;#[inline]fn mul(self,rhs:Self)->Self::Output{Self::new_unchecked(M::mod_mul(self.x,rhs.x))}}impl<M>Div for MInt<M>where M:MIntBase{type Output=Self;#[inline]fn div(self,rhs:Self)->Self::Output{Self::new_unchecked(M::mod_div(self.x,rhs.x))}}impl<M>Neg for MInt<M>where M:MIntBase{type Output=Self;#[inline]fn neg(self)->Self::Output{Self::new_unchecked(M::mod_neg(self.x))}}impl<M>Sum for MInt<M>where M:MIntBase{#[inline]fn sum<I:Iterator<Item=Self>>(iter:I)->Self{iter.fold(<Self as Zero>::zero(),Add::add)}}impl<M>Product for MInt<M>where M:MIntBase{#[inline]fn product<I:Iterator<Item=Self>>(iter:I)->Self{iter.fold(<Self as One>::one(),Mul::mul)}}impl<'a,M:'a>Sum<&'a MInt<M>>for MInt<M>where M:MIntBase{#[inline]fn sum<I:Iterator<Item=&'a Self>>(iter:I)->Self{iter.fold(<Self as Zero>::zero(),Add::add)}}impl<'a,M:'a>Product<&'a MInt<M>>for MInt<M>where M:MIntBase{#[inline]fn product<I:Iterator<Item=&'a Self>>(iter:I)->Self{iter.fold(<Self as One>::one(),Mul::mul)}}impl<M>Display for MInt<M>where M:MIntBase<Inner:Display>{fn fmt(&self,f:&mut fmt::Formatter<'_>)->Result<(),fmt::Error>{write!(f,"{}",self.inner())}}impl<M>FromStr for MInt<M>where M:MIntConvert+MIntBase<Inner:FromStr>{type Err=<M::Inner as FromStr>::Err;#[inline]fn from_str(s:&str)->Result<Self,Self::Err>{s.parse::<M::Inner>().map(Self::new)}}impl<M>IterScan for MInt<M>where M:MIntConvert+MIntBase<Inner:FromStr>{type Output=Self;#[inline]fn scan<'a,I:Iterator<Item=&'a str>>(iter:&mut I)->Option<Self::Output>{iter.next()?.parse::<MInt<M>>().ok()}}impl<M>SerdeByteStr for MInt<M>where M:MIntBase<Inner:SerdeByteStr>{fn serialize(&self,buf:&mut Vec<u8>){self.inner().serialize(buf)}fn deserialize<I>(iter:&mut I)->Self where I:Iterator<Item=u8>{Self::new_unchecked(M::Inner::deserialize(iter))}}macro_rules!impl_mint_ref_binop{($imp:ident,$method:ident,$t:ty)=>{impl<M>$imp<$t>for&$t where M:MIntBase,{type Output=<$t as$imp<$t>>::Output;#[inline]fn$method(self,other:$t)-><$t as$imp<$t>>::Output{$imp::$method(*self,other)}}impl<M>$imp<&$t>for$t where M:MIntBase,{type Output=<$t as$imp<$t>>::Output;#[inline]fn$method(self,other:&$t)-><$t as$imp<$t>>::Output{$imp::$method(self,*other)}}impl<M>$imp<&$t>for&$t where M:MIntBase,{type Output=<$t as$imp<$t>>::Output;#[inline]fn$method(self,other:&$t)-><$t as$imp<$t>>::Output{$imp::$method(*self,*other)}}};}impl_mint_ref_binop!(Add,add,MInt<M>);impl_mint_ref_binop!(Sub,sub,MInt<M>);impl_mint_ref_binop!(Mul,mul,MInt<M>);impl_mint_ref_binop!(Div,div,MInt<M>);macro_rules!impl_mint_ref_unop{($imp:ident,$method:ident,$t:ty)=>{impl<M>$imp for&$t where M:MIntBase,{type Output=<$t as$imp>::Output;#[inline]fn$method(self)-><$t as$imp>::Output{$imp::$method(*self)}}};}impl_mint_ref_unop!(Neg,neg,MInt<M>);macro_rules!impl_mint_ref_op_assign{($imp:ident,$method:ident,$t:ty,$fromimp:ident,$frommethod:ident)=>{impl<M>$imp<$t>for$t where M:MIntBase,{#[inline]fn$method(&mut self,rhs:$t){*self=$fromimp::$frommethod(*self,rhs);}}impl<M>$imp<&$t>for$t where M:MIntBase,{#[inline]fn$method(&mut self,other:&$t){$imp::$method(self,*other);}}};}impl_mint_ref_op_assign!(AddAssign,add_assign,MInt<M>,Add,add);impl_mint_ref_op_assign!(SubAssign,sub_assign,MInt<M>,Sub,sub);impl_mint_ref_op_assign!(MulAssign,mul_assign,MInt<M>,Mul,mul);impl_mint_ref_op_assign!(DivAssign,div_assign,MInt<M>,Div,div);}
pub use self::coding::{SerdeByteStr,unescape};
mod coding{use std::{char::from_u32_unchecked,cmp::Reverse,collections::{BTreeMap,BTreeSet,BinaryHeap,HashMap,HashSet,VecDeque},hash::Hash,iter::repeat_with,mem::size_of};pub fn unescape(bytes:&[u8])->Vec<u8>{let mut buf=Vec::with_capacity(bytes.len());let mut escape=false;for b in bytes{match(escape,*b){(true,b'n')=>{buf.push(b'\n');escape=false;}(true,b'r')=>{buf.push(b'\r');escape=false;}(true,b't')=>{buf.push(b'\t');escape=false;}(true,b'\\')=>{buf.push(b'\\');escape=false;}(true,b'0')=>{buf.push(b'\0');escape=false;}(true,b'"')=>{buf.push(b'"');escape=false;}(false,b'\\')=>{escape=true;}(_,b)=>{buf.push(b);escape=false;}}}buf}fn to_bytestring(bytes:&[u8])->String{let mut count=[0usize;128];let mut c=0u8;let mut w=0u32;for&b in bytes{w+=1;count[(c|(b>>w))as usize]+=1;if w==7{count[(b&0b1111111u8)as usize]+=1;c=0;w=0;}else{c=(b<<(7-w))&0b1111111u8;}}if w>0{count[c as usize]+=1;c=0;w=0;}let mut salt=0u8;let mut extra_min=!0usize;for s in 0u8..128{let mut extra=0usize;for&b in b"\n\r\t\\\0\""{extra+=count[(b^s)as usize];extra+=(b==s)as usize;}if extra<extra_min{extra_min=extra;salt=s;}}let cap=extra_min+count.iter().sum::<usize>()+1;let mut buf=String::with_capacity(cap);macro_rules!escape_branch{($e:literal)=>{{buf.push('\\');buf.push($e);}};}macro_rules!escape{($b:expr)=>{match($b)^salt{b'\n'=>escape_branch!('n'),b'\r'=>escape_branch!('r'),b'\t'=>escape_branch!('t'),b'\\'=>escape_branch!('\\'),b'\0'=>escape_branch!('0'),b'"'=>escape_branch!('"'),b=>buf.push(b as char),}};}escape!(0);for&b in bytes{w+=1;escape!(c|(b>>w));if w==7{escape!(b&0b1111111u8);c=0;w=0;}else{c=(b<<(7-w))&0b1111111u8;}}if w>0{escape!(c);}assert_eq!(cap,buf.len());buf}fn from_bytestring(bytes:&[u8])->Vec<u8>{assert!(!bytes.is_empty());let cap=(bytes.len()-1)*7/8;let mut buf=Vec::with_capacity(cap);let salt=bytes[0];let bytes=&bytes[1..];let mut c=0u8;let mut w=0u32;for&b in bytes{let b=b^salt;if w==0{c=b<<1;w=7;}else{w-=1;buf.push(c|(b>>w));c=if w>0{b<<(8-w)}else{0};}}assert_eq!(cap,buf.len());buf}#[derive(Debug,PartialEq,Eq,PartialOrd,Ord)]enum HuffmanTree{Leaf(u8),Node(Box<HuffmanTree>,Box<HuffmanTree>)}#[derive(Debug)]struct BitWriter{bytes:Vec<u8>,last:u8,w:u32}impl Default for BitWriter{fn default()->Self{Self{bytes:Default::default(),last:Default::default(),w:8}}}impl BitWriter{fn push_bit(&mut self,b:bool){self.w-=1;self.last|=(b as u8)<<self.w;if self.w==0{self.bytes.push(self.last);self.w=8;self.last=0;}}fn push_u8(&mut self,b:u8){self.bytes.push(self.last|(b>>(8-self.w)));if self.w<8{self.last=b<<self.w;}}fn push_u64(&mut self,b:u64,mut c:u32){let k=self.w.min(c);self.w-=k;c-=k;self.last|=(b>>c<<self.w)as u8;if self.w==0{self.bytes.push(self.last);let(s,t)=(c/8,c%8);for _ in 0..s{c-=8;self.bytes.push((b>>c)as u8);}self.last=0;self.w=8-t;if t>0{self.last=(b as u8)<<self.w;}}}fn into_inner(mut self)->Vec<u8>{if self.w<8{self.bytes.push(self.last);}self.bytes}}#[derive(Debug)]struct BitReader<'a>{bytes:&'a[u8],pos:u32}impl<'a>BitReader<'a>{fn new(bytes:&'a[u8])->Self{Self{bytes,pos:0}}fn read_bit(&mut self)->bool{let b=(self.bytes[0]>>(7-self.pos))&1==1;self.pos+=1;if self.pos==8{self.pos=0;self.bytes=&self.bytes[1..];}b}fn read_u8(&mut self)->u8{let b=self.bytes[0]<<self.pos;self.bytes=&self.bytes[1..];if self.pos==0{b}else{b|(self.bytes[0]>>(8-self.pos))}}}fn huffman_coding(bytes:&[u8])->Vec<u8>{fn make_table(t:&HuffmanTree,code:u64,len:u32,table:&mut[(u64,u32)]){match t{HuffmanTree::Leaf(i)=>{table[*i as usize]=(code,len.max(1));}HuffmanTree::Node(l,r)=>{make_table(l,code<<1,len+1,table);make_table(r,(code<<1)|1,len+1,table);}}}fn output_tree(t:&HuffmanTree,buf:&mut BitWriter){match t{HuffmanTree::Leaf(i)=>{buf.push_bit(false);buf.push_u8(*i);}HuffmanTree::Node(l,r)=>{buf.push_bit(true);output_tree(l,buf);output_tree(r,buf);}}}let mut freq=[0usize;256];for&b in&bytes.len().to_le_bytes(){freq[b as usize]+=1;}for&b in bytes{freq[b as usize]+=1;}let mut heap=BinaryHeap::new();for(i,&f)in freq.iter().enumerate(){if f>0{heap.push(Reverse((f,0usize,HuffmanTree::Leaf(i as _))));}}let t=if heap.is_empty(){HuffmanTree::Node(Box::new(HuffmanTree::Leaf(0)),Box::new(HuffmanTree::Leaf(0)))}else{loop{let Reverse((f,c,t))=heap.pop().unwrap();if let Some(Reverse((ff,cc,tt)))=heap.pop(){heap.push(Reverse((f+ff,c.max(cc)+1,HuffmanTree::Node(Box::new(t),Box::new(tt)))));}else{break t;}}};let mut table=vec![(0u64,0u32);256];make_table(&t,0,0,&mut table);let mut buf=BitWriter::default();output_tree(&t,&mut buf);for&b in&bytes.len().to_le_bytes(){let(x,y)=table[b as usize];buf.push_u64(x,y);}for&b in bytes{let(x,y)=table[b as usize];buf.push_u64(x,y);}buf.into_inner()}fn huffman_decoding(bytes:&[u8])->Vec<u8>{fn read_tree(reader:&mut BitReader)->HuffmanTree{if reader.read_bit(){HuffmanTree::Node(Box::new(read_tree(reader)),Box::new(read_tree(reader)))}else{HuffmanTree::Leaf(reader.read_u8())}}fn decode(mut t:&HuffmanTree,reader:&mut BitReader)->u8{loop{match t{HuffmanTree::Leaf(i)=>break*i,HuffmanTree::Node(l,r)=>t=if reader.read_bit(){r}else{l},}}}let mut reader=BitReader::new(bytes);let t=read_tree(&mut reader);const C:usize=size_of::<usize>();let mut size:[u8;C]=[0u8;C];for b in&mut size{*b=decode(&t,&mut reader);}let size=usize::from_le_bytes(size);let mut buf=vec![];for i in 0..size{buf.push(decode(&t,&mut reader));if i<10{}}buf}pub trait SerdeByteStr{fn serialize(&self,buf:&mut Vec<u8>);fn deserialize<I>(iter:&mut I)->Self where I:Iterator<Item=u8>;fn serialize_bytestr(&self)->String{let mut bytes=vec![];self.serialize(&mut bytes);let bytes=huffman_coding(&bytes);to_bytestring(&bytes)}fn deserialize_from_bytes(bytes:&[u8])->Self where Self:Sized{let bytes=from_bytestring(bytes);let bytes=huffman_decoding(&bytes);Self::deserialize(&mut bytes.as_slice().iter().cloned())}}impl SerdeByteStr for bool{fn serialize(&self,buf:&mut Vec<u8>){(*self as u8).serialize(buf)}fn deserialize<I>(iter:&mut I)->Self where I:Iterator<Item=u8>{iter.next().unwrap()!=0}}macro_rules!impl_serdebytestr_num{($($t:ty)*)=>{$(impl SerdeByteStr for$t{fn serialize(&self,buf:&mut Vec<u8>){buf.extend(self.to_le_bytes().iter());}fn deserialize<I>(iter:&mut I)->Self where I:Iterator<Item=u8>,{const C:usize=size_of::<$t>();let mut bytes:[u8;C]=[0u8;C];for(b,i)in bytes.iter_mut().zip(iter){*b=i;}<$t>::from_le_bytes(bytes)}})*};}impl_serdebytestr_num!(u8 u16 u32 u64 u128 usize i8 i16 i32 i64 i128 isize f32 f64);impl SerdeByteStr for char{fn serialize(&self,buf:&mut Vec<u8>){(*self as u32).serialize(buf)}fn deserialize<I>(iter:&mut I)->Self where I:Iterator<Item=u8>{unsafe{from_u32_unchecked(u32::deserialize(iter))}}}impl SerdeByteStr for(){fn serialize(&self,_buf:&mut Vec<u8>){}fn deserialize<I>(_iter:&mut I)->Self where I:Iterator<Item=u8>{}}macro_rules!impl_serdebytestr_tuple{(@impl$($A:ident$a:ident)*)=>{impl<$($A,)*>SerdeByteStr for($($A,)*)where$($A:SerdeByteStr),*{fn serialize(&self,buf:&mut Vec<u8>){let($($a,)*)=self;$(SerdeByteStr::serialize($a,buf));*}fn deserialize<Iter>(iter:&mut Iter)->Self where Iter:Iterator<Item=u8>,{($(<$A as SerdeByteStr>::deserialize(iter),)*)}}};(@inc,$B:ident$b:ident$($C:ident$c:ident)*)=>{impl_serdebytestr_tuple!(@inc$B$b,$($C$c)*);};(@inc$($A:ident$a:ident)*,$B:ident$b:ident$($C:ident$c:ident)*)=>{impl_serdebytestr_tuple!(@impl$($A$a)*);impl_serdebytestr_tuple!(@inc$($A$a)*$B$b,$($C$c)*);};(@inc$($A:ident$a:ident)*,)=>{impl_serdebytestr_tuple!(@impl$($A$a)*);};($($t:tt)*)=>{impl_serdebytestr_tuple!(@inc,$($t)*);};}impl_serdebytestr_tuple!(A a B b C c D d E e F f G g H h I i J j K k);impl<T>SerdeByteStr for Option<T>where T:SerdeByteStr{fn serialize(&self,buf:&mut Vec<u8>){self.is_some().serialize(buf);if let Some(x)=self{x.serialize(buf);}}fn deserialize<I>(iter:&mut I)->Self where I:Iterator<Item=u8>{if bool::deserialize(iter){Some(T::deserialize(iter))}else{None}}}impl SerdeByteStr for String{fn serialize(&self,buf:&mut Vec<u8>){let bytes=self.bytes();bytes.len().serialize(buf);for x in bytes{x.serialize(buf);}}fn deserialize<I>(iter:&mut I)->Self where I:Iterator<Item=u8>{let n=usize::deserialize(iter);unsafe{String::from_utf8_unchecked(repeat_with(| |u8::deserialize(iter)).take(n).collect::<Vec<u8>>())}}}macro_rules!impl_serdebytestr_seq{($([$($g:ident)*]$t:ty$(where[$($tt:tt)*])?),*$(,)?)=>{$(impl<$($g),*>SerdeByteStr for$t where$($g:SerdeByteStr,)*$($($tt)*)?{fn serialize(&self,buf:&mut Vec<u8>){self.len().serialize(buf);for x in self{x.serialize(buf);}}fn deserialize<I>(iter:&mut I)->Self where I:Iterator<Item=u8>,{let n=usize::deserialize(iter);repeat_with(||SerdeByteStr::deserialize(iter)).take(n).collect()}})*};(@kv$([$($g:ident)*]$t:ty$(where[$($tt:tt)*])?),*$(,)?)=>{$(impl<$($g),*>SerdeByteStr for$t where$($g:SerdeByteStr,)*$($($tt)*)?{fn serialize(&self,buf:&mut Vec<u8>){self.len().serialize(buf);for(k,v)in self{k.serialize(buf);v.serialize(buf);}}fn deserialize<I>(iter:&mut I)->Self where I:Iterator<Item=u8>,{let n=usize::deserialize(iter);repeat_with(||SerdeByteStr::deserialize(iter)).take(n).collect()}})*};}impl_serdebytestr_seq!([T]Vec<T>,[T]VecDeque<T>,[T]BinaryHeap<T>where[T:Ord],[T]BTreeSet<T>where[T:Ord],[T]HashSet<T>where[T:Eq+Hash],);impl_serdebytestr_seq!(@kv[K V]BTreeMap<K,V>where[K:Ord],[K V]HashMap<K,V>where[K:Eq+Hash],);}
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!impl_zero_one{($({$Trait:ident$method:ident$($t:ty)*,$e:expr})*)=>{$($(impl$Trait for$t{fn$method()->Self{$e}})*)*};}impl_zero_one!({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.});}
yukicoder

結果

ソースコード
