結果
| 問題 | No.2846 Birthday Cake |
| ユーザー |
 to-omer
|
| 提出日時 | 2024-08-24 00:57:39 |
| 言語 | Rust (1.77.0 + proconio) |
| 結果 |
AC
|
| 実行時間 | 12 ms / 2,000 ms |
| コード長 | 47,600 bytes |
| コンパイル時間 | 14,171 ms |
| コンパイル使用メモリ | 390,376 KB |
| 実行使用メモリ | 6,944 KB |
| 最終ジャッジ日時 | 2024-08-24 00:57:56 |
| 合計ジャッジ時間 | 15,889 ms |
|
ジャッジサーバーID （参考情報） |
judge3 / judge1 |
（要ログイン）
テストケース
テストケース表示| 入力 | 結果 | 実行時間 実行使用メモリ |
|---|---|---|
| testcase_00 | AC | 0 ms
6,812 KB |
| testcase_01 | AC | 1 ms
6,812 KB |
| testcase_02 | AC | 9 ms
6,940 KB |
| testcase_03 | AC | 1 ms
6,940 KB |
| testcase_04 | AC | 1 ms
6,940 KB |
| testcase_05 | AC | 9 ms
6,940 KB |
| testcase_06 | AC | 9 ms
6,940 KB |
| testcase_07 | AC | 9 ms
6,940 KB |
| testcase_08 | AC | 10 ms
6,940 KB |
| testcase_09 | AC | 10 ms
6,940 KB |
| testcase_10 | AC | 12 ms
6,944 KB |
| testcase_11 | AC | 12 ms
6,940 KB |
| testcase_12 | AC | 6 ms
6,940 KB |
| testcase_13 | AC | 6 ms
6,944 KB |
| testcase_14 | AC | 1 ms
6,944 KB |
| testcase_15 | AC | 1 ms
6,940 KB |
| testcase_16 | AC | 1 ms
6,944 KB |
| testcase_17 | AC | 8 ms
6,944 KB |
| testcase_18 | AC | 12 ms
6,940 KB |
| testcase_19 | AC | 1 ms
6,944 KB |
| testcase_20 | AC | 1 ms
6,944 KB |
| testcase_21 | AC | 1 ms
6,940 KB |
| testcase_22 | AC | 2 ms
6,944 KB |
| testcase_23 | AC | 2 ms
6,940 KB |
| testcase_24 | AC | 6 ms
6,944 KB |
| testcase_25 | AC | 1 ms
6,944 KB |
| testcase_26 | AC | 1 ms
6,940 KB |
| testcase_27 | AC | 2 ms
6,940 KB |
| testcase_28 | AC | 1 ms
6,940 KB |
| testcase_29 | AC | 1 ms
6,944 KB |
| testcase_30 | AC | 0 ms
6,944 KB |
| testcase_31 | AC | 1 ms
6,944 KB |
| testcase_32 | AC | 2 ms
6,940 KB |
| testcase_33 | AC | 7 ms
6,940 KB |
| testcase_34 | AC | 1 ms
6,940 KB |
| testcase_35 | AC | 2 ms
6,944 KB |
| testcase_36 | AC | 5 ms
6,944 KB |
ソースコード
pub fn solve() {
crate::prepare!();
sc!(k, n);
let mut fact = vec![1u128; n + 1];
for i in 1..=n {
fact[i] = fact[i - 1] * i as u128;
}
let mut lcm = 1usize;
for i in 1..=n {
lcm = lcm.lcm(i);
}
let mut c = vec![vec![]; 3];
let mut lcm2 = (1, 1);
let pl = PrimeList::new(200);
for i in 1..=n {
if i * 2 > n && pl.is_prime(i as _) {
c[2].push(i);
} else if lcm2.0.max(lcm2.1.lcm(i)) < lcm2.0.lcm(i).max(lcm2.1) {
lcm2 = (lcm2.0, lcm2.1.lcm(i));
c[1].push(i);
} else {
lcm2 = (lcm2.0.lcm(i), lcm2.1);
c[0].push(i);
}
}
let solve = |c: &[usize]| {
let mut dp: Vec<_> = (0..=k).map(|_| HashMap::<usize, u128>::new()).collect();
dp[0].insert(0, fact[k]);
for &x in c {
for i in (0..k).rev() {
let p = take(&mut dp[i]);
for (&a, &b) in &p {
for y in 1..=x {
let ni = i + y;
let na = a + y * lcm / x;
if ni > k || na > lcm {
break;
}
*dp[ni].entry(na).or_default() += b / fact[y];
}
}
dp[i] = p;
}
}
dp
};
let dp0 = solve(&c[0]);
let dp1 = solve(&c[1]);
let mut ans = 0;
for i in 0..=k {
for (&a, &b) in &dp0[i] {
if let Some(&c) = dp1[k - i].get(&(lcm - a)) {
ans += b * c / fact[k];
}
}
}
for &p in &c[2] {
ans += (p == k) as u128;
}
pp!(ans);
}
use std::mem::take;
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($))};}#[macro_export]macro_rules!main{()=>{fn main(){solve();}};(avx2)=>{fn main(){#[target_feature(enable="avx2")]unsafe fn solve_avx2(){solve();}unsafe{solve_avx2()}}};(large_stack)=>{fn main(){const STACK_SIZE:usize=512*1024*1024;::std::thread::Builder::new().stack_size(STACK_SIZE).spawn(solve).unwrap().join().unwrap();}};}}
pub use self::iter_print::IterPrint;
mod iter_print{use std::{fmt::Display,io::{Error,Write}};pub trait IterPrint{fn iter_print<W,S>(self,writer:&mut W,sep:S,is_head:bool)->Result<(),Error>where W:Write,S:Display;}macro_rules!impl_iter_print_tuple{(@impl$($A:ident$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$d:ident)*)=>{impl_iter_print_tuple!(@impl,);impl_iter_print_tuple!(@inc$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::{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!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)*$U,$($Rest)*);};($($T:ident)*)=>{impl_iter_scan_tuple!(@inner,$($T)*);};}impl_iter_scan_tuple!(A B C D E F G H I J K);pub struct ScannerIter<'a,'b,T>{inner:&'b mut Scanner<'a>,_marker:std::marker::PhantomData<fn()->T>}impl<'a,'b,T>Iterator for ScannerIter<'a,'b,T>where T:IterScan{type Item=<T as IterScan>::Output;#[inline]fn next(&mut self)->Option<Self::Item>{<T as IterScan>::scan(&mut self.inner.iter)}}#[doc=" scan a value with Scanner"]#[doc=""]#[doc=" - `scan_value!(scanner, ELEMENT)`"]#[doc=""]#[doc=" ELEMENT :="]#[doc=" - `$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$scanner:expr,[$($args:tt)*])=>{::std::compile_error!(::std::stringify!($($args)*))};(src=$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 use self::integer::{BinaryRepr,ExtendedGcd,IntBase,Saturating,Signed,Unsigned,Wrapping};
mod integer{use super::{Bounded,IterScan,One,Zero};use std::{convert::TryFrom,fmt::{self,Display},ops::{Add,AddAssign,BitAnd,BitAndAssign,BitOr,BitOrAssign,BitXor,BitXorAssign,Div,DivAssign,Mul,MulAssign,Neg,Not,Rem,RemAssign,Shl,ShlAssign,Shr,ShrAssign,Sub,SubAssign},str::FromStr};#[doc=" Trait for basic primitive integer operations."]pub trait IntBase:Copy+Bounded+Zero+One+Eq+Ord+Default+FromStr+Display+Add<Output=Self>+Sub<Output=Self>+Mul<Output=Self>+Div<Output=Self>+Rem<Output=Self>+AddAssign+SubAssign+MulAssign+DivAssign+RemAssign{type Error;fn div_euclid(self,rhs:Self)->Self;fn rem_euclid(self,rhs:Self)->Self;fn pow(self,exp:u32)->Self;fn from_str_radix(src:&str,radix:u32)->Result<Self,Self::Error>;fn ilog(self,base:Self)->u32;fn ilog2(self)->u32;fn ilog10(self)->u32;}macro_rules!impl_int_base{($($t:ty)*)=>{$(impl IntBase for$t{type Error=std::num::ParseIntError;fn div_euclid(self,rhs:Self)->Self{self.div_euclid(rhs)}fn rem_euclid(self,rhs:Self)->Self{self.rem_euclid(rhs)}fn pow(self,exp:u32)->Self{self.pow(exp)}fn from_str_radix(src:&str,radix:u32)->Result<Self,Self::Error>{Self::from_str_radix(src,radix)}fn ilog(self,base:Self)->u32{self.ilog(base)}fn ilog2(self)->u32{self.ilog2()}fn ilog10(self)->u32{self.ilog10()}})*};}impl_int_base!(u8 i8 u16 i16 u32 i32 u64 i64 u128 i128 usize isize);#[doc=" extended_gcd(a,b): ax + by = g = gcd(a,b)"]pub struct ExtendedGcd<T:Unsigned>{#[doc=" gcd"]pub g:T,pub x:T::Signed,pub y:T::Signed}#[doc=" Trait for unsigned integer operations."]pub trait Unsigned:IntBase{type Signed:Signed<Unsigned=Self>;fn signed(self)->Self::Signed;fn abs_diff(self,other:Self)->Self;fn next_power_of_two(self)->Self;fn gcd(self,other:Self)->Self;fn lcm(self,other:Self)->Self{if self.is_zero()&&other.is_zero(){Self::zero()}else{self/self.gcd(other)*other}}fn extgcd(self,other:Self)->ExtendedGcd<Self>{let(mut a,mut b)=(self.signed(),other.signed());let(mut u,mut v,mut x,mut y)=(Self::Signed::one(),Self::Signed::zero(),Self::Signed::zero(),Self::Signed::one());while!a.is_zero(){let k=b/a;x-=k*u;y-=k*v;b-=k*a;std::mem::swap(&mut x,&mut u);std::mem::swap(&mut y,&mut v);std::mem::swap(&mut b,&mut a);}ExtendedGcd{g:b.unsigned(),x,y}}fn modinv(self,modulo:Self)->Self{assert!(!self.is_zero(),"attempt to inverse zero with modulo {}",modulo);let extgcd=self.extgcd(modulo);assert!(extgcd.g.is_one(),"there is no inverse {} modulo {}",self,modulo);extgcd.x.rem_euclid(modulo.signed()).unsigned()}}#[doc=" Trait for signed integer operations."]pub trait Signed:IntBase+Neg<Output=Self>{type Unsigned:Unsigned<Signed=Self>;fn unsigned(self)->Self::Unsigned;fn abs(self)->Self;fn abs_diff(self,other:Self)->Self::Unsigned;fn is_negative(self)->bool;fn is_positive(self)->bool;fn signum(self)->Self;}macro_rules!impl_unsigned_signed{($($unsigned:ident$signed:ident)*)=>{$(impl Unsigned for$unsigned{type Signed=$signed;fn signed(self)->Self::Signed{self as Self::Signed}fn abs_diff(self,other:Self)->Self{self.abs_diff(other)}fn next_power_of_two(self)->Self{self.next_power_of_two()}fn gcd(self,other:Self)->Self{let(mut a,mut b)=(self,other);if a.is_zero()||b.is_zero(){return a|b;}let u=a.trailing_zeros();let v=b.trailing_zeros();a>>=u;b>>=v;let k=u.min(v);while a!=b{if a<b{std::mem::swap(&mut a,&mut b);}a-=b;a>>=a.trailing_zeros();}a<<k}}impl Signed for$signed{type Unsigned=$unsigned;fn unsigned(self)->Self::Unsigned{self as Self::Unsigned}fn abs_diff(self,other:Self)->Self::Unsigned{self.abs_diff(other)}fn abs(self)->Self{self.abs()}fn is_negative(self)->bool{self.is_negative()}fn is_positive(self)->bool{self.is_positive()}fn signum(self)->Self{self.signum()}})*};}impl_unsigned_signed!(u8 i8 u16 i16 u32 i32 u64 i64 u128 i128 usize isize);#[doc=" Trait for operations of integer in binary representation."]pub trait BinaryRepr<Size=u32>:Sized+Not<Output=Self>+BitAnd<Output=Self>+BitOr<Output=Self>+BitXor<Output=Self>+Shl<Size,Output=Self>+Shr<Size,Output=Self>+BitAndAssign+BitOrAssign+BitXorAssign+ShlAssign<Size>+ShrAssign<Size>{fn count_ones(self)->Size;fn count_zeros(self)->Size;fn leading_ones(self)->Size;fn leading_zeros(self)->Size;fn reverse_bits(self)->Self;fn rotate_left(self,n:Size)->Self;fn rotate_right(self,n:Size)->Self;fn swap_bytes(self)->Self;fn trailing_ones(self)->Size;fn trailing_zeros(self)->Size;}macro_rules!impl_binary_repr{($($t:ty)*)=>{$(impl BinaryRepr for$t{fn count_ones(self)->u32{self.count_ones()}fn count_zeros(self)->u32{self.count_zeros()}fn leading_ones(self)->u32{self.leading_ones()}fn leading_zeros(self)->u32{self.leading_zeros()}fn reverse_bits(self)->Self{self.reverse_bits()}fn rotate_left(self,n:u32)->Self{self.rotate_left(n)}fn rotate_right(self,n:u32)->Self{self.rotate_right(n)}fn swap_bytes(self)->Self{self.swap_bytes()}fn trailing_ones(self)->u32{self.trailing_ones()}fn trailing_zeros(self)->u32{self.trailing_zeros()}})*};}impl_binary_repr!(u8 i8 u16 i16 u32 i32 u64 i64 u128 i128 usize isize);macro_rules!impl_binop{(impl<$T:ident>$Trait:ident$impl:ident for$t:ty)=>{impl<$T>$Trait for$t where$T:$Trait<Output=$T>,{type Output=Self;fn$impl(self,rhs:Self)->Self::Output{Self($Trait::$impl(self.0,rhs.0))}}};}macro_rules!impl_opassign{(impl<$T:ident>$Trait:ident$impl:ident for$t:ty)=>{impl<$T>$Trait for$t where$T:$Trait,{fn$impl(&mut self,rhs:Self){$Trait::$impl(&mut self.0,rhs.0)}}};}#[derive(Default,PartialEq,Eq,PartialOrd,Ord,Hash,Clone,Copy)]#[repr(transparent)]#[doc=" Wrapper type of arithmetic `saturating_*` operations."]pub struct Saturating<T>(pub T);impl<T>fmt::Debug for Saturating<T>where T:fmt::Debug{fn fmt(&self,f:&mut fmt::Formatter<'_>)->fmt::Result{T::fmt(&self.0,f)}}impl<T>Bounded for Saturating<T>where T:Bounded{fn maximum()->Self{Self(T::maximum())}fn minimum()->Self{Self(T::minimum())}}impl<T>Zero for Saturating<T>where T:Zero{fn zero()->Self{Self(T::zero())}}impl<T>One for Saturating<T>where T:One{fn one()->Self{Self(T::one())}}impl<T>FromStr for Saturating<T>where T:FromStr{type Err=T::Err;fn from_str(s:&str)->Result<Self,Self::Err>{T::from_str(s).map(Self)}}impl<T>Display for Saturating<T>where T:Display{fn fmt(&self,f:&mut fmt::Formatter<'_>)->fmt::Result{T::fmt(&self.0,f)}}impl<T>IterScan for Saturating<T>where T:IterScan<Output=T>{type Output=Self;fn scan<'a,I:Iterator<Item=&'a str>>(iter:&mut I)->Option<Self::Output>{T::scan(iter).map(Self)}}impl_binop!(impl<T>Div div for Saturating<T>);impl_binop!(impl<T>Rem rem for Saturating<T>);impl_binop!(impl<T>BitAnd bitand for Saturating<T>);impl_binop!(impl<T>BitOr bitor for Saturating<T>);impl_binop!(impl<T>BitXor bitxor for Saturating<T>);impl_opassign!(impl<T>DivAssign div_assign for Saturating<T>);impl_opassign!(impl<T>RemAssign rem_assign for Saturating<T>);impl_opassign!(impl<T>BitAndAssign bitand_assign for Saturating<T>);impl_opassign!(impl<T>BitOrAssign bitor_assign for Saturating<T>);impl_opassign!(impl<T>BitXorAssign bitxor_assign for Saturating<T>);impl<T>Not for Saturating<T>where T:Not<Output=T>{type Output=Self;fn not(self)->Self::Output{Self(Not::not(self.0))}}macro_rules!impl_int_base_for_saturating{($($t:ty)*)=>{$(impl Add for Saturating<$t>{type Output=Self;fn add(self,rhs:Self)->Self::Output{Self(self.0 .saturating_add(rhs.0))}}impl Sub for Saturating<$t>{type Output=Self;fn sub(self,rhs:Self)->Self::Output{Self(self.0 .saturating_sub(rhs.0))}}impl Mul for Saturating<$t>{type Output=Self;fn mul(self,rhs:Self)->Self::Output{Self(self.0 .saturating_mul(rhs.0))}}impl AddAssign for Saturating<$t>{fn add_assign(&mut self,rhs:Self){*self=Add::add(*self,rhs);}}impl SubAssign for Saturating<$t>{fn sub_assign(&mut self,rhs:Self){*self=Sub::sub(*self,rhs);}}impl MulAssign for Saturating<$t>{fn mul_assign(&mut self,rhs:Self){*self=Mul::mul(*self,rhs);}}impl IntBase for Saturating<$t>{type Error=<$t as IntBase>::Error;fn div_euclid(self,rhs:Self)->Self{Self(self.0 .div_euclid(rhs.0))}fn rem_euclid(self,rhs:Self)->Self{Self(self.0 .rem_euclid(rhs.0))}fn pow(self,exp:u32)->Self{Self(self.0 .saturating_pow(exp))}fn from_str_radix(src:&str,radix:u32)->Result<Self,Self::Error>{<$t as IntBase>::from_str_radix(src,radix).map(Self)}fn ilog(self,base:Self)->u32{self.0 .ilog(base.0)}fn ilog2(self)->u32{self.0 .ilog2()}fn ilog10(self)->u32{self.0 .ilog10()}}impl From<$t>for Saturating<$t>{fn from(t:$t)->Self{Self(t)}})*};}impl_int_base_for_saturating!(u8 i8 u16 i16 u32 i32 u64 i64 u128 i128 usize isize);macro_rules!impl_unsigned_signed_for_saturating{($($unsigned:ident$signed:ident)*)=>{$(impl Unsigned for Saturating<$unsigned>{type Signed=Saturating<$signed>;fn signed(self)->Self::Signed{Saturating(TryFrom::try_from(self.0).ok().unwrap_or_else($signed::maximum))}fn abs_diff(self,other:Self)->Self{Self(self.0 .abs_diff(other.0))}fn next_power_of_two(self)->Self{Self(self.0 .next_power_of_two())}fn gcd(self,other:Self)->Self{Self(self.0 .gcd(other.0))}}impl Signed for Saturating<$signed>{type Unsigned=Saturating<$unsigned>;fn unsigned(self)->Self::Unsigned{Saturating(TryFrom::try_from(self.0).ok().unwrap_or_else($unsigned::minimum))}fn abs(self)->Self{Self(self.0 .saturating_abs())}fn abs_diff(self,other:Self)->Self::Unsigned{Saturating(self.0 .abs_diff(other.0))}fn is_negative(self)->bool{self.0 .is_negative()}fn is_positive(self)->bool{self.0 .is_positive()}fn signum(self)->Self{Self(self.0 .signum())}}impl Neg for Saturating<$signed>{type Output=Self;fn neg(self)->Self::Output{Self(self.0 .saturating_neg())}})*};}impl_unsigned_signed_for_saturating!(u8 i8 u16 i16 u32 i32 u64 i64 u128 i128 usize isize);macro_rules!impl_binary_repr_for_saturating{($($t:ty)*)=>{$(impl Shl<u32>for Saturating<$t>{type Output=Self;fn shl(self,rhs:u32)->Self::Output{Self(self.0 .checked_shl(rhs).unwrap_or(0))}}impl Shr<u32>for Saturating<$t>{type Output=Self;fn shr(self,rhs:u32)->Self::Output{Self(self.0 .checked_shr(rhs).unwrap_or(0))}}impl ShlAssign<u32>for Saturating<$t>{fn shl_assign(&mut self,rhs:u32){*self=Shl::shl(*self,rhs);}}impl ShrAssign<u32>for Saturating<$t>{fn shr_assign(&mut self,rhs:u32){*self=Shr::shr(*self,rhs);}}impl BinaryRepr for Saturating<$t>{fn count_ones(self)->u32{self.0 .count_ones()}fn count_zeros(self)->u32{self.0 .count_zeros()}fn leading_ones(self)->u32{self.0 .leading_ones()}fn leading_zeros(self)->u32{self.0 .leading_zeros()}fn reverse_bits(self)->Self{Self(self.0 .reverse_bits())}fn rotate_left(self,n:u32)->Self{Self(self.0 .rotate_left(n))}fn rotate_right(self,n:u32)->Self{Self(self.0 .rotate_right(n))}fn swap_bytes(self)->Self{Self(self.0 .swap_bytes())}fn trailing_ones(self)->u32{self.0 .trailing_ones()}fn trailing_zeros(self)->u32{self.0 .trailing_zeros()}})*};}impl_binary_repr_for_saturating!(u8 i8 u16 i16 u32 i32 u64 i64 u128 i128 usize isize);#[derive(Default,PartialEq,Eq,PartialOrd,Ord,Hash,Clone,Copy)]#[repr(transparent)]#[doc=" Wrapper type of arithmetic `wrapping_*` operations."]pub struct Wrapping<T>(pub T);impl<T>fmt::Debug for Wrapping<T>where T:fmt::Debug{fn fmt(&self,f:&mut fmt::Formatter<'_>)->fmt::Result{T::fmt(&self.0,f)}}impl<T>Bounded for Wrapping<T>where T:Bounded{fn maximum()->Self{Self(T::maximum())}fn minimum()->Self{Self(T::minimum())}}impl<T>Zero for Wrapping<T>where T:Zero{fn zero()->Self{Self(T::zero())}}impl<T>One for Wrapping<T>where T:One{fn one()->Self{Self(T::one())}}impl<T>FromStr for Wrapping<T>where T:FromStr{type Err=T::Err;fn from_str(s:&str)->Result<Self,Self::Err>{T::from_str(s).map(Self)}}impl<T>Display for Wrapping<T>where T:Display{fn fmt(&self,f:&mut fmt::Formatter<'_>)->fmt::Result{T::fmt(&self.0,f)}}impl<T>IterScan for Wrapping<T>where T:IterScan<Output=T>{type Output=Self;fn scan<'a,I:Iterator<Item=&'a str>>(iter:&mut I)->Option<Self::Output>{T::scan(iter).map(Self)}}impl_binop!(impl<T>BitAnd bitand for Wrapping<T>);impl_binop!(impl<T>BitOr bitor for Wrapping<T>);impl_binop!(impl<T>BitXor bitxor for Wrapping<T>);impl_opassign!(impl<T>BitAndAssign bitand_assign for Wrapping<T>);impl_opassign!(impl<T>BitOrAssign bitor_assign for Wrapping<T>);impl_opassign!(impl<T>BitXorAssign bitxor_assign for Wrapping<T>);impl<T>Not for Wrapping<T>where T:Not<Output=T>{type Output=Self;fn not(self)->Self::Output{Self(Not::not(self.0))}}macro_rules!impl_int_base_for_wrapping{($($t:ty)*)=>{$(impl Add for Wrapping<$t>{type Output=Self;fn add(self,rhs:Self)->Self::Output{Self(self.0 .wrapping_add(rhs.0))}}impl Sub for Wrapping<$t>{type Output=Self;fn sub(self,rhs:Self)->Self::Output{Self(self.0 .wrapping_sub(rhs.0))}}impl Mul for Wrapping<$t>{type Output=Self;fn mul(self,rhs:Self)->Self::Output{Self(self.0 .wrapping_mul(rhs.0))}}impl Div for Wrapping<$t>{type Output=Self;fn div(self,rhs:Self)->Self::Output{Self(self.0 .wrapping_div(rhs.0))}}impl Rem for Wrapping<$t>{type Output=Self;fn rem(self,rhs:Self)->Self::Output{Self(self.0 .wrapping_rem(rhs.0))}}impl AddAssign for Wrapping<$t>{fn add_assign(&mut self,rhs:Self){*self=Add::add(*self,rhs);}}impl SubAssign for Wrapping<$t>{fn sub_assign(&mut self,rhs:Self){*self=Sub::sub(*self,rhs);}}impl MulAssign for Wrapping<$t>{fn mul_assign(&mut self,rhs:Self){*self=Mul::mul(*self,rhs);}}impl DivAssign for Wrapping<$t>{fn div_assign(&mut self,rhs:Self){*self=Div::div(*self,rhs);}}impl RemAssign for Wrapping<$t>{fn rem_assign(&mut self,rhs:Self){*self=Rem::rem(*self,rhs);}}impl IntBase for Wrapping<$t>{type Error=<$t as IntBase>::Error;fn div_euclid(self,rhs:Self)->Self{Self(self.0 .wrapping_div_euclid(rhs.0))}fn rem_euclid(self,rhs:Self)->Self{Self(self.0 .wrapping_rem_euclid(rhs.0))}fn pow(self,exp:u32)->Self{Self(self.0 .wrapping_pow(exp))}fn from_str_radix(src:&str,radix:u32)->Result<Self,Self::Error>{<$t as IntBase>::from_str_radix(src,radix).map(Self)}fn ilog(self,base:Self)->u32{self.0 .ilog(base.0)}fn ilog2(self)->u32{self.0 .ilog2()}fn ilog10(self)->u32{self.0 .ilog10()}}impl From<$t>for Wrapping<$t>{fn from(t:$t)->Self{Self(t)}})*};}impl_int_base_for_wrapping!(u8 i8 u16 i16 u32 i32 u64 i64 u128 i128 usize isize);macro_rules!impl_unsigned_signed_for_wrapping{($($unsigned:ident$signed:ident)*)=>{$(impl Unsigned for Wrapping<$unsigned>{type Signed=Wrapping<$signed>;fn signed(self)->Self::Signed{Wrapping(self.0 .signed())}fn abs_diff(self,other:Self)->Self{Self(self.0 .abs_diff(other.0))}fn next_power_of_two(self)->Self{Self(self.0 .next_power_of_two())}fn gcd(self,other:Self)->Self{Self(self.0 .gcd(other.0))}}impl Signed for Wrapping<$signed>{type Unsigned=Wrapping<$unsigned>;fn unsigned(self)->Self::Unsigned{Wrapping(self.0 .unsigned())}fn abs(self)->Self{Self(self.0 .wrapping_abs())}fn abs_diff(self,other:Self)->Self::Unsigned{Wrapping(self.0 .abs_diff(other.0))}fn is_negative(self)->bool{self.0 .is_negative()}fn is_positive(self)->bool{self.0 .is_positive()}fn signum(self)->Self{Self(self.0 .signum())}}impl Neg for Wrapping<$signed>{type Output=Self;fn neg(self)->Self::Output{Self(self.0 .wrapping_neg())}})*};}impl_unsigned_signed_for_wrapping!(u8 i8 u16 i16 u32 i32 u64 i64 u128 i128 usize isize);macro_rules!impl_binary_repr_for_wrapping{($($t:ty)*)=>{$(impl Shl<u32>for Wrapping<$t>{type Output=Self;fn shl(self,rhs:u32)->Self::Output{Self(self.0 .wrapping_shl(rhs))}}impl Shr<u32>for Wrapping<$t>{type Output=Self;fn shr(self,rhs:u32)->Self::Output{Self(self.0 .wrapping_shr(rhs))}}impl ShlAssign<u32>for Wrapping<$t>{fn shl_assign(&mut self,rhs:u32){*self=Shl::shl(*self,rhs);}}impl ShrAssign<u32>for Wrapping<$t>{fn shr_assign(&mut self,rhs:u32){*self=Shr::shr(*self,rhs);}}impl BinaryRepr for Wrapping<$t>{fn count_ones(self)->u32{self.0 .count_ones()}fn count_zeros(self)->u32{self.0 .count_zeros()}fn leading_ones(self)->u32{self.0 .leading_ones()}fn leading_zeros(self)->u32{self.0 .leading_zeros()}fn reverse_bits(self)->Self{Self(self.0 .reverse_bits())}fn rotate_left(self,n:u32)->Self{Self(self.0 .rotate_left(n))}fn rotate_right(self,n:u32)->Self{Self(self.0 .rotate_right(n))}fn swap_bytes(self)->Self{Self(self.0 .swap_bytes())}fn trailing_ones(self)->u32{self.0 .trailing_ones()}fn trailing_zeros(self)->u32{self.0 .trailing_zeros()}})*};}impl_binary_repr_for_wrapping!(u8 i8 u16 i16 u32 i32 u64 i64 u128 i128 usize isize);}
pub use self::bounded::Bounded;
mod bounded{#[doc=" Trait for max/min bounds"]pub trait Bounded:Sized+PartialOrd{fn maximum()->Self;fn minimum()->Self;fn is_maximum(&self)->bool{self==&Self::maximum()}fn is_minimum(&self)->bool{self==&Self::minimum()}fn set_maximum(&mut self){*self=Self::maximum()}fn set_minimum(&mut self){*self=Self::minimum()}}macro_rules!impl_bounded_num{($($t:ident)*)=>{$(impl Bounded for$t{fn maximum()->Self{std::$t::MAX}fn minimum()->Self{std::$t::MIN}})*};}impl_bounded_num!(u8 u16 u32 u64 u128 usize i8 i16 i32 i64 i128 isize f32 f64);macro_rules!impl_bounded_tuple{(@impl$($T:ident)*)=>{impl<$($T:Bounded),*>Bounded for($($T,)*){fn maximum()->Self{($(<$T as Bounded>::maximum(),)*)}fn minimum()->Self{($(<$T as Bounded>::minimum(),)*)}}};(@inner$($T:ident)*,)=>{impl_bounded_tuple!(@impl$($T)*);};(@inner$($T:ident)*,$U:ident$($Rest:ident)*)=>{impl_bounded_tuple!(@impl$($T)*);impl_bounded_tuple!(@inner$($T)*$U,$($Rest)*);};($T:ident$($Rest:ident)*)=>{impl_bounded_tuple!(@inner$T,$($Rest)*);};}impl_bounded_tuple!(A B C D E F G H I J);impl Bounded for(){fn maximum()->Self{}fn minimum()->Self{}}impl Bounded for bool{fn maximum()->Self{true}fn minimum()->Self{false}}impl<T>Bounded for Option<T>where T:Bounded{fn maximum()->Self{Some(<T as Bounded>::maximum())}fn minimum()->Self{None}}impl<T>Bounded for std::cmp::Reverse<T>where T:Bounded{fn maximum()->Self{std::cmp::Reverse(<T as Bounded>::minimum())}fn minimum()->Self{std::cmp::Reverse(<T as Bounded>::maximum())}}}
pub use self::zero_one::{One,Zero};
mod zero_one{pub trait Zero:Sized{fn zero()->Self;#[inline]fn is_zero(&self)->bool where Self:PartialEq{self==&Self::zero()}#[inline]fn set_zero(&mut self){*self=Self::zero();}}pub trait One:Sized{fn one()->Self;#[inline]fn is_one(&self)->bool where Self:PartialEq{self==&Self::one()}#[inline]fn set_one(&mut self){*self=Self::one();}}macro_rules!impl_zero_one{($({$Trait:ident$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.});}
pub use self::prime_list::{with_prime_list,PrimeList};
mod prime_list{use std::{cell::UnsafeCell,mem::replace,slice::Iter};#[derive(Debug,Clone)]pub struct PrimeList{primes:Vec<u64>,max_n:u64}impl Default for PrimeList{fn default()->Self{Self{primes:Default::default(),max_n:1}}}impl PrimeList{pub fn new(max_n:u64)->Self{let mut self_:Self=Default::default();self_.reserve(max_n);self_}pub fn primes(&self)->&[u64]{self.primes.as_slice()}pub fn primes_lte(&self,n:u64)->&[u64]{assert!(n<=self.max_n,"expected `n={} <= {}`",n,self.max_n);let i=self.primes.partition_point(|&p|p<=n);&self.primes[..i]}pub fn is_prime(&self,n:u64)->bool{assert!(n<=self.max_n,"expected `n={} <= {}`",n,self.max_n);self.primes.binary_search(&n).is_ok()}pub fn trial_division(&self,n:u64)->PrimeListTrialDivision<'_>{let bound=self.max_n.saturating_mul(self.max_n);assert!(n<=bound,"expected `n={} <= {}`",n,bound);PrimeListTrialDivision{primes:self.primes.iter(),n}}pub fn prime_factors(&self,n:u64)->Vec<(u64,u32)>{self.trial_division(n).collect()}pub fn count_divisors(&self,n:u64)->u64{let mut divisor_cnt=1u64;for(_,cnt)in self.trial_division(n){divisor_cnt*=cnt as u64+1;}divisor_cnt}pub fn divisors(&self,n:u64)->Vec<u64>{let mut d=vec![1u64];for(p,c)in self.trial_division(n){let k=d.len();let mut acc=p;for _ in 0..c{for i in 0..k{d.push(d[i]*acc);}acc*=p;}}d.sort_unstable();d}#[doc=" list primes less than or equal to `max_n` by segmented sieve"]pub fn reserve(&mut self,max_n:u64){if max_n<=self.max_n||max_n<2{return;}if self.primes.is_empty(){self.primes.push(2);self.max_n=2;}if max_n==2{return;}let max_n=(max_n+1)/2*2;let sqrt_n=((max_n as f64).sqrt()as usize+1)/2*2;let mut table=Vec::with_capacity(sqrt_n>>1);if self.max_n<sqrt_n as u64{let start=(self.max_n as usize+1)|1;let end=sqrt_n+1;let sqrt_end=(sqrt_n as f64).sqrt()as usize;let plen=self.primes[1..].binary_search(&(sqrt_end as u64+1)).unwrap_or_else(|x|x);table.resize(end/2-start/2,false);for&p in self.primes.iter().skip(1).take(plen){let y=p.max((start as u64+p-1)/(2*p)*2+1)*p/2;(y as usize-start/2..end/2-start/2).step_by(p as usize).for_each(|i|table[i]=true);}for i in 0..=(sqrt_end/2).saturating_sub(start/2){if!table[i]{let p=(i+start/2)*2+1;for j in(p*p/2-start/2..sqrt_n/2-start/2).step_by(p){table[j]=true;}}}self.primes.extend(table.iter().cloned().enumerate().filter_map(|(i,b)|{if!b{Some((i+start/2)as u64*2+1)}else{None}}));self.max_n=sqrt_n as u64;}let sqrt_n=sqrt_n as u64;for start in(self.max_n+1..=max_n).step_by(sqrt_n as usize){let end=(start+sqrt_n).min(max_n+1);let sqrt_end=(end as f64).sqrt()as u64;let length=end-start;let plen=self.primes[1..].binary_search(&(sqrt_end+1)).unwrap_or_else(|x|x);table.clear();table.resize(length as usize/2,false);for&p in self.primes.iter().skip(1).take(plen){let y=p.max((start+p-1)/(2*p)*2+1)*p/2;((y-start/2)as usize..length as usize/2).step_by(p as usize).for_each(|i|table[i]=true);}self.primes.extend(table.iter().cloned().enumerate().filter_map(|(i,b)|{if!b{Some((i as u64+start/2)*2+1)}else{None}}));}self.max_n=max_n;}}#[derive(Debug,Clone)]pub struct PrimeListTrialDivision<'p>{primes:Iter<'p,u64>,n:u64}impl Iterator for PrimeListTrialDivision<'_>{type Item=(u64,u32);fn next(&mut self)->Option<Self::Item>{if self.n<=1{return None;}loop{match self.primes.next(){Some(&p)if p*p<=self.n=>{if self.n%p==0{let mut cnt=1u32;self.n/=p;while self.n%p==0{cnt+=1;self.n/=p;}return Some((p,cnt));}}_=>break,}}if self.n>1{return Some((replace(&mut self.n,1),1));}None}}pub fn with_prime_list<F>(max_n:u64,f:F)where F:FnOnce(&PrimeList){thread_local!(static PRIME_LIST:UnsafeCell<PrimeList> =Default::default());PRIME_LIST.with(|cell|{unsafe{let pl=&mut*cell.get();pl.reserve(max_n);f(pl);};});}}