pub fn main() {
    crate::prepare!();
    sc!(n, a: [M; n], q);
    let to_val4 = |a| {
        let p0 = M::one();
        let p1 = p0 * a;
        let p2 = p1 * a;
        let p3 = p2 * a;
        let p4 = p3 * a;
        (p1, p2, p3, p4)
    };
    let to_val5 = |a| {
        let p0 = M::one();
        let p1 = p0 * a;
        let p2 = p1 * a;
        let p3 = p2 * a;
        let p4 = p3 * a;
        (p0, p1, p2, p3, p4)
    };
    let mut seg = LazySegmentTree::<X>::from_vec(a.iter().map(to_val5).collect());
    for _ in 0..q {
        sc!(ty, mut u: Usize1, mut v: Usize1, w: Usize1);
        if u > v {
            swap(&mut u, &mut v);
        }
        if ty == 0 {
            sc!(b: M);
            if u < w && w < v {
                seg.update(u, v + 1, Some(to_val4(b)));
            } else {
                seg.update(0, u + 1, Some(to_val4(b)));
                seg.update(v, n, Some(to_val4(b)));
            }
        } else {
            let (a, b, c, d, e) = if u < w && w < v {
                seg.fold(u, v + 1)
            } else {
                A5::operate(&seg.fold(0, u + 1), &seg.fold(v, n))
            };
            let (a, b, c, d, e) = (a / a, b / a, c / a, d / a, e / a);
            let ans = match ty {
                2 => a * b * b - M::new_unchecked(2) * b * b + c,
                3 => {
                    -a * b * b * b + M::new_unchecked(3) * b * b * b - M::new_unchecked(3) * b * c
                        + d
                }
                4 => {
                    a * b * b * b * b - M::new_unchecked(4) * b * b * b * b
                        + M::new_unchecked(6) * b * b * c
                        - M::new_unchecked(4) * b * d
                        + e
                }
                _ => M::zero(),
            };
            pp!(ans);
        }
    }
}
pub struct X;
impl MonoidAction for X {
    type MT = (M, M, M, M, M);
    type AT = Option<(M, M, M, M)>;
    type M = A5;
    type A = LastOperation<(M, M, M, M)>;
    fn act(&(a, b, c, d, e): &Self::MT, at: &Self::AT) -> Self::MT {
        if let Some((p, q, r, s)) = at {
            // (a.unwrap_or(x) * y, y)
            (a, p * a, q * a, r * a, s * a)
        } else {
            (a, b * a, c * a, d * a, e * a)
        }
    }
}
type A = AdditiveOperation<M>;
type A5 = (A, A, A, A, A);
pub type M = mint_basic::MInt998244353;
mod main_macros{#[doc=" Prepare useful macros."]#[doc=" - `prepare!();`: default (all scanner + buf print)"]#[doc=" - `prepare!(?);`: interactive (line scanner + buf print)"]#[macro_export]macro_rules!prepare{(@buf_print($dol:tt))=>{#[allow(unused_imports)]use std::io::Write as _;let __out=std::io::stdout();#[allow(unused_mut,unused_variables)]let mut __out=std::io::BufWriter::new(__out.lock());#[allow(unused_macros)]macro_rules!pp{($dol($dol t:tt)*)=>{$dol crate::iter_print!(__out,$dol($dol t)*)}}};(@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)*)}}$crate::prepare!{@buf_print($)}};(@interactive($dol:tt))=>{#[allow(unused_imports)]use std::io::Write as _;let __out=std::io::stdout();#[allow(unused_mut,unused_variables)]let mut __out=std::io::BufWriter::new(__out.lock());#[allow(unused_macros)]macro_rules!pp{($dol($dol t:tt)*)=>{$dol crate::iter_print!(__out,$dol($dol t)*)}}#[allow(unused_macros)]macro_rules!scln{($dol($dol t:tt)*)=>{{pp!(@flush);let __in_buf=read_stdin_line();#[allow(unused_mut,unused_variables)]let mut __scanner=Scanner::new(&__in_buf);$dol crate::scan!(__scanner,$dol($dol t)*)}}}};()=>{$crate::prepare!(@normal($))};(?)=>{$crate::prepare!(@interactive($))};}}
mod iter_print{use std::{fmt::Display,io::{Error,Write}};pub trait IterPrint{fn iter_print<W,S>(self,writer:&mut W,sep:S,is_head:bool)->Result<(),Error>where W:Write,S:Display;}macro_rules!iter_print_tuple_impl{(@impl$($A:ident$a:ident)?,$($B:ident$b:ident)*)=>{impl<$($A,)?$($B),*>IterPrint for($($A,)?$($B),*)where$($A:Display,)?$($B:Display),*{#[allow(unused_variables)]fn iter_print<W,S>(self,writer:&mut W,sep:S,is_head:bool)->Result<(),Error>where W:Write,S:Display{let($($a,)?$($b,)*)=self;$(if is_head{::std::write!(writer,"{}",$a)?;}else{::std::write!(writer,"{}{}",sep,$a)?;})?$(::std::write!(writer,"{}{}",sep,$b)?;)*Ok(())}}};(@inc,,$C:ident$c:ident$($D:ident$d:ident)*)=>{iter_print_tuple_impl!(@impl,);iter_print_tuple_impl!(@inc$C$c,,$($D$d)*);};(@inc$A:ident$a:ident,$($B:ident$b:ident)*,$C:ident$c:ident$($D:ident$d:ident)*)=>{iter_print_tuple_impl!(@impl$A$a,$($B$b)*);iter_print_tuple_impl!(@inc$A$a,$($B$b)*$C$c,$($D$d)*);};(@inc$A:ident$a:ident,$($B:ident$b:ident)*,)=>{iter_print_tuple_impl!(@impl$A$a,$($B$b)*);};($($t:tt)*)=>{iter_print_tuple_impl!(@inc,,$($t)*);};}iter_print_tuple_impl!(A a B b C c D d E e F f G g H h I i J j K k);#[doc=" Print expressions with a separator."]#[doc=" - `iter_print!(writer, args...)`"]#[doc=" - `@sep $expr,`: set separator (default: `' '`)"]#[doc=" - `@fmt $lit => {$($expr),*}`: print `format!($lit, $($expr),*)`"]#[doc=" - `@iter $expr`: print iterator"]#[doc=" - `@tuple $expr`: print tuple (need to import [`IterPrint`])"]#[doc=" - `$expr`: print expr"]#[doc=" - `;`: println"]#[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!($writer).expect("io error");};(@@iter$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,$sep,false,item);}}};(@@tuple$writer:expr,$sep:expr,$is_head:expr,$tuple:expr)=>{IterPrint::iter_print($tuple,&mut$writer,$sep,$is_head).expect("io error");};(@@assert_tag item)=>{};(@@assert_tag iter)=>{};(@@assert_tag tuple)=>{};(@@assert_tag$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,@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$lit:literal=>{$($e:expr),*$(,)?}$($t:tt)*)=>{$crate::iter_print!(@@fmt$writer,$sep,$is_head,$lit,$($e),*);$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,)=>{$crate::iter_print!(@@line_feed$writer);};(@@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)*);}};}}
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_stdin_line()->String{let mut s=String::new();std::io::stdin().read_line(&mut s).expect("io error");s}
use std::mem::swap;

pub use scanner_impls::{IterScan,MarkedIterScan,Scanner};
mod scanner_impls{pub trait IterScan:Sized{type Output;fn scan<'a,I:Iterator<Item=&'a str>>(iter:&mut I)->Option<Self::Output>;}pub trait MarkedIterScan:Sized{type Output;fn mscan<'a,I:Iterator<Item=&'a str>>(self,iter:&mut I)->Option<Self::Output>;}#[derive(Clone,Debug)]pub struct Scanner<'a>{iter:std::str::SplitAsciiWhitespace<'a>}impl<'a>Scanner<'a>{#[inline]pub fn new(s:&'a str)->Self{let iter=s.split_ascii_whitespace();Self{iter}}#[inline]pub fn scan<T>(&mut self)-><T as IterScan>::Output where T:IterScan{<T as IterScan>::scan(&mut self.iter).expect("scan error")}#[inline]pub fn mscan<T>(&mut self,marker:T)-><T as MarkedIterScan>::Output where T:MarkedIterScan{marker.mscan(&mut self.iter).expect("scan error")}#[inline]pub fn scan_vec<T>(&mut self,size:usize)->Vec<<T as IterScan>::Output>where T:IterScan{(0..size).map(|_|<T as IterScan>::scan(&mut self.iter).expect("scan error")).collect()}#[inline]pub fn iter<'b,T>(&'b mut self)->ScannerIter<'a,'b,T>where T:IterScan{ScannerIter{inner:self,_marker:std::marker::PhantomData}}}macro_rules!iter_scan_impls{($($t:ty)*)=>{$(impl IterScan for$t{type Output=Self;#[inline]fn scan<'a,I:Iterator<Item=&'a str>>(iter:&mut I)->Option<Self>{iter.next()?.parse::<$t>().ok()}})*};}iter_scan_impls!(char u8 u16 u32 u64 usize i8 i16 i32 i64 isize f32 f64 u128 i128 String);macro_rules!iter_scan_tuple_impl{($($T:ident)*)=>{impl<$($T:IterScan),*>IterScan for($($T,)*){type Output=($(<$T as IterScan>::Output,)*);#[inline]fn scan<'a,It:Iterator<Item=&'a str>>(_iter:&mut It)->Option<Self::Output>{Some(($(<$T as IterScan>::scan(_iter)?,)*))}}};}iter_scan_tuple_impl!();iter_scan_tuple_impl!(A);iter_scan_tuple_impl!(A B);iter_scan_tuple_impl!(A B C);iter_scan_tuple_impl!(A B C D);iter_scan_tuple_impl!(A B C D E);iter_scan_tuple_impl!(A B C D E F);iter_scan_tuple_impl!(A B C D E F G);iter_scan_tuple_impl!(A B C D E F G H);iter_scan_tuple_impl!(A B C D E F G H I);iter_scan_tuple_impl!(A B C D E F G H I J);iter_scan_tuple_impl!(A B C D E F G H I J K);pub struct ScannerIter<'a,'b,T>{inner:&'b mut Scanner<'a>,_marker:std::marker::PhantomData<fn()->T>}impl<'a,'b,T>Iterator for ScannerIter<'a,'b,T>where T:IterScan{type Item=<T as IterScan>::Output;#[inline]fn next(&mut self)->Option<Self::Item>{<T as IterScan>::scan(&mut self.inner.iter)}}#[macro_export]macro_rules!scan_value{($scanner:expr,($($t:tt),*))=>{($($crate::scan_value!($scanner,$t)),*)};($scanner:expr,[$t:tt;$len:expr])=>{(0..$len).map(|_|$crate::scan_value!($scanner,$t)).collect::<Vec<_>>()};($scanner:expr,[$t:ty;$len:expr])=>{$scanner.scan_vec::<$t>($len)};($scanner:expr,[$t:ty])=>{$scanner.iter::<$t>()};($scanner:expr,{$e:expr})=>{$scanner.mscan($e)};($scanner:expr,$t:ty)=>{$scanner.scan::<$t>()};}#[macro_export]macro_rules!scan{($scanner:expr)=>{};($scanner:expr,)=>{};($scanner:expr,mut$var:tt:$t:tt)=>{let mut$var=$crate::scan_value!($scanner,$t);};($scanner:expr,$var:tt:$t:tt)=>{let$var=$crate::scan_value!($scanner,$t);};($scanner:expr,mut$var:tt:$t:tt,$($rest:tt)*)=>{let mut$var=$crate::scan_value!($scanner,$t);scan!($scanner,$($rest)*)};($scanner:expr,$var:tt:$t:tt,$($rest:tt)*)=>{let$var=$crate::scan_value!($scanner,$t);scan!($scanner,$($rest)*)};($scanner:expr,mut$var:tt)=>{let mut$var=$crate::scan_value!($scanner,usize);};($scanner:expr,$var:tt)=>{let$var=$crate::scan_value!($scanner,usize);};($scanner:expr,mut$var:tt,$($rest:tt)*)=>{let mut$var=$crate::scan_value!($scanner,usize);scan!($scanner,$($rest)*)};($scanner:expr,$var:tt,$($rest:tt)*)=>{let$var=$crate::scan_value!($scanner,usize);scan!($scanner,$($rest)*)};}}
pub use marker_impls::{CharWithBase,Chars,CharsWithBase,Collect,SizedCollect,Usize1};
mod marker_impls{use super::*;use std::{iter::{repeat_with,FromIterator},marker::PhantomData};#[derive(Debug,Copy,Clone)]pub struct 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 struct 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 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()}}}
pub mod mint_basic{use super::*;#[macro_export]macro_rules!define_basic_mintbase{($name:ident,$m:expr,$basety:ty,$signedty:ty,$upperty:ty,[$($unsigned:ty),*],[$($signed:ty),*])=>{pub struct$name;impl MIntBase for$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{(x as$upperty*y as$upperty%Self::get_mod()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;std::mem::swap(&mut x,&mut u);std::mem::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]),*)=>{$(crate::define_basic_mintbase!($name,$m,u32,i32,u64,[u32,u64,u128,usize],[i32,i64,i128,isize]);pub type$mint_name=MInt<$name>;)*};}define_basic_mint32!([Modulo998244353,998_244_353,MInt998244353],[Modulo1000000007,1_000_000_007,MInt1000000007],[Modulo1000000009,1_000_000_009,MInt1000000009],[DynModuloU32,DYN_MODULUS_U32.with(|cell|unsafe{*cell.get()}),DynMIntU32]);thread_local!(static DYN_MODULUS_U32:std::cell::UnsafeCell<u32> =std::cell::UnsafeCell::new(1_000_000_007));impl DynModuloU32{pub fn set_mod(m:u32){DYN_MODULUS_U32.with(|cell|unsafe{*cell.get()=m})}}thread_local!(static DYN_MODULUS_U64:std::cell::UnsafeCell<u64> =std::cell::UnsafeCell::new(1_000_000_007));define_basic_mintbase!(DynModuloU64,DYN_MODULUS_U64.with(|cell|unsafe{*cell.get()}),u64,i64,u128,[u64,u128,usize],[i64,i128,isize]);impl DynModuloU64{pub fn set_mod(m:u64){DYN_MODULUS_U64.with(|cell|unsafe{*cell.get()=m})}}pub type DynMIntU64=MInt<DynModuloU64>;pub struct Modulo2;impl MIntBase for Modulo2{type Inner=u32;#[inline]fn get_mod()->Self::Inner{2}#[inline]fn mod_zero()->Self::Inner{0}#[inline]fn mod_one()->Self::Inner{1}#[inline]fn mod_add(x:Self::Inner,y:Self::Inner)->Self::Inner{x^y}#[inline]fn mod_sub(x:Self::Inner,y:Self::Inner)->Self::Inner{x^y}#[inline]fn mod_mul(x:Self::Inner,y:Self::Inner)->Self::Inner{x&y}#[inline]fn mod_div(x:Self::Inner,y:Self::Inner)->Self::Inner{assert_ne!(y,0);x}#[inline]fn mod_neg(x:Self::Inner)->Self::Inner{x}#[inline]fn mod_inv(x:Self::Inner)->Self::Inner{assert_ne!(x,0);x}#[inline]fn mod_pow(x:Self::Inner,y:usize)->Self::Inner{if y==0{1}else{x}}}macro_rules!impl_to_mint_base_for_modulo2{($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>;}
#[repr(transparent)]pub struct MInt<M>where M:MIntBase{x:M::Inner,_marker:std::marker::PhantomData<fn()->M>}
pub trait MIntBase{type Inner:Sized+Copy+Eq+std::fmt::Debug+std::hash::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}}
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;}
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};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))}#[inline]pub fn inner(self)->M::Inner{<M as MIntConvert<M::Inner>>::into(self.x)}}impl<M>MInt<M>where M:MIntBase{#[inline]pub 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))}}impl<M>Clone for MInt<M>where M:MIntBase{#[inline]fn clone(&self)->Self{Self{x:Clone::clone(&self.x),_marker:PhantomData}}}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.x,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:MIntConvert,M::Inner:Display{fn fmt<'a>(&self,f:&mut fmt::Formatter<'a>)->Result<(),fmt::Error>{write!(f,"{}",self.inner())}}impl<M>FromStr for MInt<M>where M:MIntConvert,M::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,M::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()}}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::$method(self,*other);}}};}impl_mint_ref_op_assign!(AddAssign,add_assign,MInt<M>,Add,add);impl_mint_ref_op_assign!(SubAssign,sub_assign,MInt<M>,Sub,sub);impl_mint_ref_op_assign!(MulAssign,mul_assign,MInt<M>,Mul,mul);impl_mint_ref_op_assign!(DivAssign,div_assign,MInt<M>,Div,div);}
pub trait Zero:Sized{fn zero()->Self;#[inline]fn is_zero(&self)->bool where Self:PartialEq{self==&Self::zero()}#[inline]fn set_zero(&mut self){*self=Self::zero();}}
pub trait One:Sized{fn one()->Self;#[inline]fn is_one(&self)->bool where Self:PartialEq{self==&Self::one()}#[inline]fn set_one(&mut self){*self=Self::one();}}
macro_rules!zero_one_impls{($({$Trait:ident$method:ident$($t:ty)*,$e:expr})*)=>{$($(impl$Trait for$t{fn$method()->Self{$e}})*)*};}
zero_one_impls!({Zero zero u8 u16 u32 u64 usize i8 i16 i32 i64 isize u128 i128,0}{Zero zero f32 f64,0.}{One one u8 u16 u32 u64 usize i8 i16 i32 i64 isize u128 i128,1}{One one f32 f64,1.});
#[derive(Clone,Debug)]pub struct LazySegmentTree<M>where M:MonoidAction,M::AT:PartialEq{n:usize,seg:Vec<(M::MT,M::AT)>}
impl<M>LazySegmentTree<M>where M:MonoidAction,M::AT:PartialEq{pub fn new(n:usize)->Self{let seg=vec![(M::munit(),M::aunit());2*n];Self{n,seg}}pub fn from_vec(v:Vec<M::MT>)->Self{let n=v.len();let mut seg=vec![(M::munit(),M::aunit());2*n];for(i,x)in v.into_iter().enumerate(){seg[i+n].0=x;}for i in(1..n).rev(){seg[i].0=M::moperate(&seg[2*i].0,&seg[2*i+1].0);}Self{n,seg}}#[inline]fn propagate(&mut self,k:usize){debug_assert!(k<self.n);let x=std::mem::replace(&mut self.seg[k].1,M::aunit());if!<M::A as Unital>::is_unit(&x){self.seg[2*k].1=M::aoperate(&self.seg[2*k].1,&x);self.seg[2*k+1].1=M::aoperate(&self.seg[2*k+1].1,&x);M::act_assign(&mut self.seg[k].0,&x);}}#[inline]fn thrust(&mut self,k:usize){for i in(1..(k+1).next_power_of_two().trailing_zeros()).rev(){self.propagate(k>>i);}}#[inline]fn reflect(&self,k:usize)->M::MT{if!<M::A as Unital>::is_unit(&self.seg[k].1){M::act(&self.seg[k].0,&self.seg[k].1)}else{self.seg[k].0.clone()}}#[inline]fn recalc(&mut self,mut k:usize){k/=2;while k>0{self.seg[k].0=M::moperate(&self.reflect(2*k),&self.reflect(2*k+1));k/=2;}}pub fn update(&mut self,l:usize,r:usize,x:M::AT){debug_assert!(l<=r);debug_assert!(r<=self.n);let mut a=l+self.n;let mut b=r+self.n;self.thrust(a);self.thrust(b-1);while a<b{if a&1!=0{self.seg[a].1=M::aoperate(&self.seg[a].1,&x);a+=1;}if b&1!=0{b-=1;self.seg[b].1=M::aoperate(&self.seg[b].1,&x);}a/=2;b/=2;}self.recalc(l+self.n);self.recalc(r+self.n-1);}pub fn fold(&mut self,l:usize,r:usize)->M::MT{debug_assert!(l<=r);debug_assert!(r<=self.n);let mut l=l+self.n;let mut r=r+self.n;self.thrust(l);self.thrust(r-1);let mut vl=M::munit();let mut vr=M::munit();while l<r{if l&1!=0{vl=M::moperate(&vl,&self.reflect(l));l+=1;}if r&1!=0{r-=1;vr=M::moperate(&self.reflect(r),&vr);}l/=2;r/=2;}M::moperate(&vl,&vr)}pub fn set(&mut self,k:usize,x:M::MT){let k=k+self.n;self.thrust(k);self.seg[k].0=x;self.seg[k].1=M::aunit();self.recalc(k);}pub fn get(&mut self,k:usize)->M::MT{self.fold(k,k+1)}pub fn fold_all(&mut self)->M::MT{self.fold(0,self.n)}fn bisect_perfect<P>(&mut self,mut pos:usize,mut acc:M::MT,p:P)->(usize,M::MT)where P:Fn(&M::MT)->bool{while pos<self.n{self.propagate(pos);pos<<=1;let nacc=M::moperate(&acc,&self.reflect(pos));if!p(&nacc){acc=nacc;pos+=1;}}(pos-self.n,acc)}fn rbisect_perfect<P>(&mut self,mut pos:usize,mut acc:M::MT,p:P)->(usize,M::MT)where P:Fn(&M::MT)->bool{while pos<self.n{self.propagate(pos);pos=pos*2+1;let nacc=M::moperate(&self.reflect(pos),&acc);if!p(&nacc){acc=nacc;pos-=1;}}(pos-self.n,acc)}#[doc=" Returns the first index that satisfies a accumlative predicate."]pub fn position_acc<P>(&mut self,l:usize,r:usize,p:P)->Option<usize>where P:Fn(&M::MT)->bool{let mut l=l+self.n;let r=r+self.n;self.thrust(l);self.thrust(r-1);let mut k=0usize;let mut acc=M::munit();while l<r>>k{if l&1!=0{let nacc=M::moperate(&acc,&self.reflect(l));if p(&nacc){return Some(self.bisect_perfect(l,acc,p).0);}acc=nacc;l+=1;}l>>=1;k+=1;}for k in(0..k).rev(){let r=r>>k;if r&1!=0{let nacc=M::moperate(&acc,&self.reflect(r-1));if p(&nacc){return Some(self.bisect_perfect(r-1,acc,p).0);}acc=nacc;}}None}#[doc=" Returns the last index that satisfies a accumlative predicate."]pub fn rposition_acc<P>(&mut self,l:usize,r:usize,p:P)->Option<usize>where P:Fn(&M::MT)->bool{let mut l=l+self.n;let mut r=r+self.n;self.thrust(l);self.thrust(r-1);let mut c=0usize;let mut k=0usize;let mut acc=M::munit();while l>>k<r{c<<=1;if l&1<<k!=0{l+=1<<k;c+=1;}if r&1!=0{r-=1;let nacc=M::moperate(&self.reflect(r),&acc);if p(&nacc){return Some(self.rbisect_perfect(r,acc,p).0);}acc=nacc;}r>>=1;k+=1;}for k in(0..k).rev(){if c&1!=0{l-=1<<k;let l=l>>k;let nacc=M::moperate(&self.reflect(l),&acc);if p(&nacc){return Some(self.rbisect_perfect(l,acc,p).0);}acc=nacc;}c>>=1;}None}}
pub trait MonoidAction{type MT:Clone;type AT:Clone;type M:Monoid<T=Self::MT>;type A:Monoid<T=Self::AT>;fn act(x:&Self::MT,a:&Self::AT)->Self::MT;#[inline]fn act_assign(x:&mut Self::MT,a:&Self::AT){*x=Self::act(x,a);}#[inline]fn munit()->Self::MT{<Self::M as Unital>::unit()}#[inline]fn aunit()->Self::AT{<Self::A as Unital>::unit()}#[inline]fn moperate(x:&Self::MT,y:&Self::MT)->Self::MT{<Self::M as Magma>::operate(x,y)}#[inline]fn aoperate(x:&Self::AT,y:&Self::AT)->Self::AT{<Self::A as Magma>::operate(x,y)}}
#[doc=" binary operaion: $T \\circ T \\to T$"]pub trait Magma{#[doc=" type of operands: $T$"]type T:Clone;#[doc=" binary operaion: $\\circ$"]fn operate(x:&Self::T,y:&Self::T)->Self::T;#[inline]fn reverse_operate(x:&Self::T,y:&Self::T)->Self::T{Self::operate(y,x)}#[inline]fn operate_assign(x:&mut Self::T,y:&Self::T){*x=Self::operate(x,y);}}
#[doc=" $\\forall a,\\forall b,\\forall c \\in T, (a \\circ b) \\circ c = a \\circ (b \\circ c)$"]pub trait Associative{}
#[doc=" associative binary operation"]pub trait SemiGroup:Magma+Associative{}
impl<S:Magma+Associative>SemiGroup for S{}
#[doc=" $\\exists e \\in T, \\forall a \\in T, e \\circ a = a \\circ e = e$"]pub trait Unital:Magma{#[doc=" identity element: $e$"]fn unit()->Self::T;#[inline]fn is_unit(x:&Self::T)->bool where<Self as Magma>::T:PartialEq{x==&Self::unit()}#[inline]fn set_unit(x:&mut Self::T){*x=Self::unit();}}
#[doc=" associative binary operation and an identity element"]pub trait Monoid:SemiGroup+Unital{#[doc=" binary exponentiation: $x^n = x\\circ\\ddots\\circ x$"]fn pow(mut x:Self::T,mut n:usize)->Self::T{let mut res=Self::unit();while n>0{if n&1==1{res=Self::operate(&res,&x);}x=Self::operate(&x,&x);n>>=1;}res}}
impl<M:SemiGroup+Unital>Monoid for M{}
#[doc=" $\\exists e \\in T, \\forall a \\in T, \\exists b,c \\in T, b \\circ a = a \\circ c = e$"]pub trait Invertible:Magma{#[doc=" $a$ where $a \\circ x = e$"]fn inverse(x:&Self::T)->Self::T;#[inline]fn rinv_operate(x:&Self::T,y:&Self::T)->Self::T{Self::operate(x,&Self::inverse(y))}}
#[doc=" associative binary operation and an identity element and inverse elements"]pub trait Group:Monoid+Invertible{}
impl<G:Monoid+Invertible>Group for G{}
#[doc=" $\\forall a,\\forall b \\in T, a \\circ b = b \\circ a$"]pub trait Commutative{}
#[doc=" commutative monoid"]pub trait AbelianMonoid:Monoid+Commutative{}
impl<M:Monoid+Commutative>AbelianMonoid for M{}
#[doc=" commutative group"]pub trait AbelianGroup:Group+Commutative{}
impl<G:Group+Commutative>AbelianGroup for G{}
#[doc=" $\\forall a \\in T, a \\circ a = a$"]pub trait Idempotent{}
#[doc=" idempotent monoid"]pub trait IdempotentMonoid:Monoid+Idempotent{}
impl<M:Monoid+Idempotent>IdempotentMonoid for M{}
mod monoid_macros{#[macro_export]macro_rules!monoid_fold{($m:ty)=>{<$m as Unital>::unit()};($m:ty,)=>{<$m as Unital>::unit()};($m:ty,$f:expr)=>{$f};($m:ty,$f:expr,$($ff:expr),*)=>{<$m as Magma>::operate(&($f),&monoid_fold!($m,$($ff),*))};}}
#[doc=" $+$"]pub struct AdditiveOperation<T:Clone+Zero+std::ops::Add<Output=T>>{_marker:std::marker::PhantomData<fn()->T>}
mod additive_operation_impl{use super::*;use std::ops::{Add,Neg,Sub};impl<T:Clone+Zero+Add<Output=T>>Magma for AdditiveOperation<T>{type T=T;#[inline]fn operate(x:&Self::T,y:&Self::T)->Self::T{x.clone()+y.clone()}}impl<T:Clone+Zero+Add<Output=T>>Unital for AdditiveOperation<T>{#[inline]fn unit()->Self::T{Zero::zero()}}impl<T:Clone+Zero+Add<Output=T>>Associative for AdditiveOperation<T>{}impl<T:Clone+Zero+Add<Output=T>>Commutative for AdditiveOperation<T>{}impl<T:Clone+Zero+Add<Output=T>+Sub<Output=T>+Neg<Output=T>>Invertible for AdditiveOperation<T>{#[inline]fn inverse(x:&Self::T)->Self::T{-x.clone()}#[inline]fn rinv_operate(x:&Self::T,y:&Self::T)->Self::T{x.clone()-y.clone()}}}
mod tuple_operation_impl{#![allow(unused_variables)]use super::*;macro_rules!impl_tuple_operation{($($M:ident)*,$($i:tt)*)=>{impl<$($M:Magma),*>Magma for($($M,)*){type T=($(<$M as Magma>::T,)*);#[inline]fn operate(x:&Self::T,y:&Self::T)->Self::T{($(<$M as Magma>::operate(&x.$i,&y.$i),)*)}}impl<$($M:Unital),*>Unital for($($M,)*){#[inline]fn unit()->Self::T{($(<$M as Unital>::unit(),)*)}}impl<$($M:Associative),*>Associative for($($M,)*){}impl<$($M:Commutative),*>Commutative for($($M,)*){}impl<$($M:Idempotent),*>Idempotent for($($M,)*){}impl<$($M:Invertible),*>Invertible for($($M,)*){#[inline]fn inverse(x:&Self::T)->Self::T{($(<$M as Invertible>::inverse(&x.$i),)*)}}};}impl_tuple_operation!(,);impl_tuple_operation!(A,0);impl_tuple_operation!(A B,0 1);impl_tuple_operation!(A B C,0 1 2);impl_tuple_operation!(A B C D,0 1 2 3);impl_tuple_operation!(A B C D E,0 1 2 3 4);impl_tuple_operation!(A B C D E F,0 1 2 3 4 5);impl_tuple_operation!(A B C D E F G,0 1 2 3 4 5 6);impl_tuple_operation!(A B C D E F G H,0 1 2 3 4 5 6 7);impl_tuple_operation!(A B C D E F G H I,0 1 2 3 4 5 6 7 8);impl_tuple_operation!(A B C D E F G H I J,0 1 2 3 4 5 6 7 8 9);}

#[doc=" retain the last element"]pub struct LastOperation<T:Clone>{_marker:std::marker::PhantomData<fn()->T>}
mod last_operation_impl{use super::*;impl<T:Clone>Magma for LastOperation<T>{type T=Option<T>;#[inline]fn operate(x:&Self::T,y:&Self::T)->Self::T{y.as_ref().or_else(||x.as_ref()).cloned()}}impl<T:Clone>Unital for LastOperation<T>{#[inline]fn unit()->Self::T{None}}impl<T:Clone>Associative for LastOperation<T>{}impl<T:Clone>Idempotent for LastOperation<T>{}}