pub use __cargo_equip::prelude::*;

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

use chminmax::chmin;
use fast_factorize::factor_count;
use modint::ModInt998244353 as Mint;
#[allow(unused_imports)]
use proconio::{
    input,
    marker::{Bytes, Chars, Usize1},
};

const INF: usize = 1 << 60;

fn main() {
    input! {
        n: usize,
        m: usize,
        a: [usize; n],
    }
    let mut g = vec![vec![]; n];
    for _ in 0..m {
        input! {
            u: Usize1,
            v: Usize1,
        }
        g[u].push(v);
        g[v].push(u);
    }
    let mut ps = a
        .iter()
        .map(|&x| factor_count(x).into_iter().map(|(p, _)| p))
        .flatten()
        .collect::<Vec<_>>();
    ps.sort_unstable();
    ps.dedup();
    let mut res = vec![Mint::new(1); n];
    for &p in &ps {
        let mut b = vec![0; n];
        for i in 0..n {
            let mut x = a[i];
            while x % p == 0 {
                x /= p;
                b[i] += 1;
            }
        }
        let mut d = vec![INF; n];
        d[0] = b[0];
        let mut pq = BinaryHeap::new();
        pq.push(Reverse((d[0], 0)));
        while let Some(Reverse((s, v))) = pq.pop() {
            if d[v] < s {
                continue;
            }
            for &u in &g[v] {
                if chmin!(d[u], s.max(b[u])) {
                    pq.push(Reverse((d[u], u)));
                }
            }
        }
        for i in 0..n {
            res[i] *= Mint::new(p).pow(d[i]);
        }
    }
    for &x in &res {
        println!("{}", x);
    }
}

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

///  # Bundled libraries
/// 
///  - `algebraic 0.1.0 (path+███████████████████████████████████████████████)`            published in **missing** licensed under `CC0-1.0` as `crate::__cargo_equip::crates::algebraic`
///  - `chminmax 0.1.0 (path+███████████████████████████████████████████)`                 published in **missing** licensed under `CC0-1.0` as `crate::__cargo_equip::crates::chminmax`
///  - `fast-factorize 0.1.0 (path+███████████████████████████████████████████████)`       published in **missing** licensed under `CC0-1.0` as `crate::__cargo_equip::crates::fast_factorize`
///  - `modint 0.1.0 (path+████████████████████████████████████████████████)`              published in **missing** licensed under `CC0-1.0` as `crate::__cargo_equip::crates::modint`
///  - `montgomery-modint 0.1.0 (path+██████████████████████████████████████████████████)` published in **missing** licensed under `CC0-1.0` as `crate::__cargo_equip::crates::montgomery_modint`
#[cfg_attr(any(), rustfmt::skip)]
#[allow(unused)]
mod __cargo_equip {
    pub(crate) mod crates {
        pub mod algebraic {pub use crate::__cargo_equip::macros::algebraic::*;pub trait Algebra{type S;}pub trait Act:Algebra{type X;fn act(f:&Self::S,x:&Self::X)->Self::X;}pub trait Monoid:Algebra{fn e()->Self::S;fn op(x:&Self::S,y:&Self::S)->Self::S;}pub trait Group:Monoid{fn inv(x:&Self::S)->Self::S;}pub trait Zero{fn zero()->Self;fn is_zero(&self)->bool;}pub trait One{fn one()->Self;fn is_one(&self)->bool;}#[macro_export]macro_rules!__cargo_equip_macro_def_algebraic_algebra{($ident:ident,$ty:ty)=>{#[derive(Clone)]enum$ident{}impl$crate::__cargo_equip::crates::algebraic::Algebra for$ident{type S=$ty;}};}macro_rules!algebra{($($tt:tt)*)=>(crate::__cargo_equip_macro_def_algebraic_algebra!{$($tt)*})}#[macro_export]macro_rules!__cargo_equip_macro_def_algebraic_act{($ident:ident,$tar:ty,$act:expr)=>{impl$crate::__cargo_equip::crates::algebraic::Act for$ident{type X=$tar;#[inline]fn act(f:&Self::S,x:&Self::X)->Self::X{$act(f,x)}}};}macro_rules!act{($($tt:tt)*)=>(crate::__cargo_equip_macro_def_algebraic_act!{$($tt)*})}#[macro_export]macro_rules!__cargo_equip_macro_def_algebraic_monoid{($ident:ident,$e:expr,$op:expr)=>{impl$crate::__cargo_equip::crates::algebraic::Monoid for$ident{#[inline]fn e()->Self::S{$e}#[inline]fn op(x:&Self::S,y:&Self::S)->Self::S{$op(x,y)}}};}macro_rules!monoid{($($tt:tt)*)=>(crate::__cargo_equip_macro_def_algebraic_monoid!{$($tt)*})}#[macro_export]macro_rules!__cargo_equip_macro_def_algebraic_group{($ident:ident,$e:expr,$op:expr,$inv:expr)=>{impl$crate::__cargo_equip::crates::algebraic::Monoid for$ident{#[inline]fn e()->Self::S{$e}#[inline]fn op(x:&Self::S,y:&Self::S)->Self::S{$op(x,y)}}impl$crate::__cargo_equip::crates::algebraic::Group for$ident{#[inline]fn inv(x:&Self::S)->Self::S{$inv(x)}}};}macro_rules!group{($($tt:tt)*)=>(crate::__cargo_equip_macro_def_algebraic_group!{$($tt)*})}macro_rules!impl_zero_one{($($t:ty)*)=>{$(impl$crate::__cargo_equip::crates::algebraic::Zero for$t{fn zero()->Self{0}fn is_zero(&self)->bool{*self==0}}impl$crate::__cargo_equip::crates::algebraic::One for$t{fn one()->Self{1}fn is_one(&self)->bool{*self==1}})*};}impl_zero_one!(usize u8 u16 u32 u64 u128 isize i8 i16 i32 i64 i128);}
        pub mod chminmax {pub use crate::__cargo_equip::macros::chminmax::*;#[macro_export]macro_rules!__cargo_equip_macro_def_chminmax_min{($a:expr$(,)*)=>{{$a}};($a:expr,$b:expr$(,)*)=>{{std::cmp::min($a,$b)}};($a:expr,$($rest:expr),+$(,)*)=>{{std::cmp::min($a,$crate::__cargo_equip::crates::chminmax::min!($($rest),+))}};}macro_rules!min{($($tt:tt)*)=>(crate::__cargo_equip_macro_def_chminmax_min!{$($tt)*})}#[macro_export]macro_rules!__cargo_equip_macro_def_chminmax_max{($a:expr$(,)*)=>{{$a}};($a:expr,$b:expr$(,)*)=>{{std::cmp::max($a,$b)}};($a:expr,$($rest:expr),+$(,)*)=>{{std::cmp::max($a,$crate::__cargo_equip::crates::chminmax::max!($($rest),+))}};}macro_rules!max{($($tt:tt)*)=>(crate::__cargo_equip_macro_def_chminmax_max!{$($tt)*})}#[macro_export]macro_rules!__cargo_equip_macro_def_chminmax_chmin{($base:expr,$($cmps:expr),+$(,)*)=>{{let cmp_min=$crate::__cargo_equip::crates::chminmax::min!($($cmps),+);if$base>cmp_min{$base=cmp_min;true}else{false}}};}macro_rules!chmin{($($tt:tt)*)=>(crate::__cargo_equip_macro_def_chminmax_chmin!{$($tt)*})}#[macro_export]macro_rules!__cargo_equip_macro_def_chminmax_chmax{($base:expr,$($cmps:expr),+$(,)*)=>{{let cmp_max=$crate::__cargo_equip::crates::chminmax::max!($($cmps),+);if$base<cmp_max{$base=cmp_max;true}else{false}}};}macro_rules!chmax{($($tt:tt)*)=>(crate::__cargo_equip_macro_def_chminmax_chmax!{$($tt)*})}}
        pub mod fast_factorize {use crate::__cargo_equip::preludes::fast_factorize::*;use std::{convert::{TryFrom,TryInto},fmt::Debug,mem::swap,};use montgomery_modint::MontgomeryModInt;pub fn is_prime(n:impl TryInto<u64,Error=impl Debug>)->bool{let n:u64=n.try_into().unwrap();if n&1==0{n==2}else if n<=1{false}else if n<1<<30{miller_rabin(n,&[2,7,61])}else{miller_rabin(n,&[2,325,9375,28178,450775,9780504,1795265022])}}pub fn factorize<N,E,F>(n:N)->Vec<N>where N:TryInto<u64,Error=E>+TryFrom<u64,Error=F>+Ord+Copy,E:Debug,F:Debug,{let n=n.try_into().unwrap();let mut f=factorize_(n);f.sort();f.into_iter().map(|x|x.try_into().unwrap()).collect()}pub fn factor_count<N,E,F>(n:N)->Vec<(N,usize)>where N:TryInto<u64,Error=E>+TryFrom<u64,Error=F>+Ord+Copy,E:Debug,F:Debug,{let f=factorize(n);if f.len()==0{return vec![];}let mut r=vec![(f[0],0)];for p in f{if r.last().unwrap().0==p{r.last_mut().unwrap().1+=1;}else{r.push((p,1));}}r}pub fn divisors<N,E,F>(n:N)->Vec<N>where N:TryInto<u64,Error=E>+TryFrom<u64,Error=F>+Ord+Copy,E:Debug,F:Debug,{let n=n.try_into().unwrap();if n==0{return vec![];}let fc=factor_count(n);let mut r=vec![1];for(p,c)in fc{for i in 0..r.len(){let mut x=r[i];for _ in 0..c{x*=p;r.push(x);}}}r.sort();r.into_iter().map(|x|x.try_into().unwrap()).collect()}fn gcd(mut a:u64,mut b:u64)->u64{while b!=0{a%=b;swap(&mut a,&mut b);}a}fn miller_rabin(n:u64,a:&[u64])->bool{MontgomeryModInt::set_modulus(n);let d=(n-1)>>(n-1).trailing_zeros();let e=MontgomeryModInt::new(1);let r=MontgomeryModInt::new(n-1);for&a in a{if n<=a{break;}let mut t=d;let mut y=MontgomeryModInt::new(a).pow(t);while t!=n-1&&y!=e&&y!=r{y*=y;t*=2;}if y!=r&&t%2==0{return false;}}true}fn pollard_rho(n:u64)->u64{if n&1==0{return 2;}else if is_prime(n){return n;}let m=1<<(64-n.leading_zeros())/8;let o=MontgomeryModInt::new(1);let mut c=o;loop{let f=|x:MontgomeryModInt|x*x+c;let mut x=o;let mut y=MontgomeryModInt::new(2);let mut ys=o;let mut q=o;let mut r=1;let mut g=1;while g==1{x=y;for _ in 0..r{y=f(y);}for k in(0..r).step_by(m){if g!=1{break;}ys=y;for _ in 0..m.min(r-k){y=f(y);q*=x-y;}g=gcd(q.val(),n);}r<<=1;}if g==n{g=1;while g==1{ys=f(ys);g=gcd((x-ys).val(),n);}}if g<n{return if is_prime(g){g}else if is_prime(n/g){n/g}else{pollard_rho(g)};}c+=o;}}fn factorize_(n:u64)->Vec<u64>{if n<=1{return vec![];};let p=pollard_rho(n);if p==n{return vec![p];}let mut r=factorize_(p);r.extend(factorize_(n/p));r}}
        pub mod modint {use crate::__cargo_equip::preludes::modint::*;use std::{fmt,hash::Hash,iter::{Product,Sum},num::ParseIntError,ops::{Add,AddAssign,Div,DivAssign,Mul,MulAssign,Neg,Sub,SubAssign},str::FromStr,sync::atomic::{self,AtomicU32,AtomicU64},};use algebraic::{One,Zero};#[derive(Clone,Copy,Default,PartialEq,Eq,Hash)]#[repr(transparent)]pub struct StaticModInt<const P:u32>(u32);#[derive(Clone,Copy,Default,PartialEq,Eq,Hash)]#[repr(transparent)]pub struct DynamicModInt(u32);pub type ModInt998244353=StaticModInt<998_244_353>;pub type ModInt1000000007=StaticModInt<1_000_000_007>;pub trait ModInt:Default+Zero+One+FromStr+From<i8>+From<i16>+From<i32>+From<i64>+From<i128>+From<isize>+From<u8>+From<u16>+From<u32>+From<u64>+From<u128>+From<usize>+Copy+Eq+Hash+fmt::Display+fmt::Debug+Neg<Output=Self>+Add<Output=Self>+Sub<Output=Self>+Mul<Output=Self>+Div<Output=Self>+AddAssign+SubAssign+MulAssign+DivAssign{fn modulus()->u32;fn raw(val:u32)->Self;fn val(self)->u32;fn inv(self)->Self;fn pow(self,k:usize)->Self;fn sqrt(self)->Option<Self>;}const fn mul(x:u32,y:u32,m:u32)->u32{(x as u64*y as u64%m as u64)as u32}const fn pow(x:u32,mut n:u32,m:u32)->u32{if m==1{return 0;}let mut r=1u64;let mut y=(x%m)as u64;while n!=0{if n&1!=0{r=r*y%m as u64;}y=y*y%m as u64;n>>=1;}r as u32}const fn is_prime(n:u32)->bool{match n{_ if n<=1=>return false,2|7|61=>return true,_ if n&1==0=>return false,_=>{}}let mut d=n-1;while d&1==0{d>>=1;}let a=[2,7,61];let mut i=0;while i<3{let mut t=d;let mut y=pow(a[i],t,n);while t!=n-1&&y!=1&&y!=n-1{y=(y as u64*y as u64%n as u64)as u32;t<<=1;}if y!=n-1&&t&1==0{return false;}i+=1;}true}const fn extgcd(mut a:u32,b:u32)->(u32,u32){a=a%b;if a==0{return(b,0);}let mut s=b as i64;let mut t=a as i64;let mut m0=0;let mut m1=1;while t!=0{let u=s/t;s-=t*u;m0-=m1*u;let tmp=s;s=t;t=tmp;let tmp=m0;m0=m1;m1=tmp;}if m0<0{m0+=b as i64/s;}(s as u32,m0 as u32)}const fn primitive_root(m:u32)->u32{match m{2=>return 1,167_772_161=>return 3,469_762_049=>return 3,754_974_721=>return 11,998_244_353=>return 3,_=>{}}let mut divs=[0;20];divs[0]=2;let mut cnt=1;let mut x=(m-1)/2;while x%2==0{x/=2;}let mut i=3;while i<std::u32::MAX{if i as u64*i as u64>x as u64{break;}if x%i==0{divs[cnt]=i;cnt+=1;while x%i==0{x/=i;}}i+=2;}if x>1{divs[cnt]=x;cnt+=1;}let mut g=2;loop{let mut i=0;while i<cnt{if pow(g,(m-1)/divs[i],m)==1{break;}i+=1;}if i==cnt{break g;}g+=1;}}const fn ntt_info(m:u32,)->(u32,usize,[u32;30],[u32;30],[u32;30],[u32;30],[u32;30],[u32;30],){let g=primitive_root(m);let rank2=(m-1).trailing_zeros()as usize;let mut root=[0;30];let mut iroot=[0;30];let mut rate2=[0;30];let mut irate2=[0;30];let mut rate3=[0;30];let mut irate3=[0;30];root[rank2]=pow(g,(m-1)>>rank2,m);iroot[rank2]=extgcd(root[rank2],m).1;let mut i=rank2;while i>0{i-=1;root[i]=mul(root[i+1],root[i+1],m);iroot[i]=mul(iroot[i+1],iroot[i+1],m);}let mut prod=1;let mut iprod=1;let mut i=0;while i+2<=rank2{rate2[i]=mul(root[i+2],prod,m);irate2[i]=mul(iroot[i+2],iprod,m);prod=mul(prod,iroot[i+2],m);iprod=mul(iprod,root[i+2],m);i+=1;}let mut prod=1;let mut iprod=1;let mut i=0;while i+3<=rank2{rate3[i]=mul(root[i+3],prod,m);irate3[i]=mul(iroot[i+3],iprod,m);prod=mul(prod,iroot[i+3],m);iprod=mul(iprod,root[i+3],m);i+=1;}(g,rank2,root,iroot,rate2,irate2,rate3,irate3)}fn rat_convert(x:u64,m:u64,d:u64)->Option<(u64,u64)>{let n=m/(2*d);if x<n&&1<d{return Some((x,1));}let mut l=(0,1);let mut r=(1,0);loop{let num=l.0+r.0;let den=l.1+r.1;let(i,q)=match(num*m).cmp(&(den*x)){std::cmp::Ordering::Less=>{let k=(x*l.1-m*l.0-1)/(m*r.0-x*r.1);l.0+=k*r.0;l.1+=k*r.1;l}std::cmp::Ordering::Equal=>return None,std::cmp::Ordering::Greater=>{let k=(m*r.0-x*r.1-1)/(x*l.1-m*l.0);r.0+=k*l.0;r.1+=k*l.1;r}};if q*x<i*m{continue;}let p=q*x-i*m;if p<n&&q<d{return Some((p,q));}}}impl<const P:u32>ModInt for StaticModInt<P>{#[inline(always)]fn modulus()->u32{P}#[inline]fn raw(val:u32)->Self{Self(val)}#[inline]fn val(self)->u32{self.0}#[inline]fn inv(self)->Self{self.inv()}fn pow(self,k:usize)->Self{self.pow(k)}fn sqrt(self)->Option<Self>{self.sqrt()}}impl<const P:u32>StaticModInt<P>{#[inline]pub fn new<T:Into<StaticModInt<P>>>(x:T)->Self{x.into()}#[inline(always)]pub fn modulus()->u32{P}#[inline]pub fn raw(val:u32)->Self{Self(val)}#[inline]pub fn val(self)->u32{self.0}#[inline]pub fn inv(self)->Self{assert_ne!(self.0,0);self.pow(P as usize-2)}pub fn pow(mut self,mut k:usize)->Self{let mut res=Self::from(1);while k!=0{if k&1!=0{res*=self;}k>>=1;self*=self;}res}pub fn sqrt(self)->Option<Self>{let p=Self::modulus()as usize;if self.val()<2{return Some(self);}else if self.pow(p-1>>1).val()!=1{return None;}let mut b=Self::from(1);while b.pow((p-1>>1)as usize).val()==1{b+=1;}let mut e=(p-1).trailing_zeros()as usize;let m=(p-1)>>e;let mut x=self.pow(m-1>>1);let mut y=self*x*x;x*=self;let mut z=b.pow(m);while y.val()!=1{let mut j=0;let mut t=y;while t.val()!=1{j+=1;t*=t;}z=z.pow(1<<e-j-1);x*=z;z*=z;y*=z;e=j;}Some(x)}}impl ModInt for DynamicModInt{#[inline(always)]fn modulus()->u32{BARRETT.modulus()}#[inline]fn raw(val:u32)->Self{Self(val)}#[inline]fn val(self)->u32{self.0}#[inline]fn inv(self)->Self{self.inv()}fn pow(self,k:usize)->Self{self.pow(k)}fn sqrt(self)->Option<Self>{self.sqrt()}}impl DynamicModInt{#[inline]pub fn new<T:Into<DynamicModInt>>(x:T)->Self{x.into()}#[inline(always)]pub fn modulus()->u32{BARRETT.modulus()}#[inline]pub fn raw(val:u32)->Self{Self(val)}#[inline]pub fn val(self)->u32{self.0}#[inline]pub fn inv(self)->Self{let(g,x)=extgcd(self.0,Self::modulus());assert_eq!(g,1);Self(x)}pub fn pow(mut self,mut k:usize)->Self{let mut res=Self::from(1);while k!=0{if k&1!=0{res*=self;}k>>=1;self*=self;}res}pub fn sqrt(self)->Option<Self>{let p=Self::modulus()as usize;if self.val()<2{return Some(self);}else if self.pow(p-1>>1).val()!=1{return None;}let mut b=Self::from(1);while b.pow((p-1>>1)as usize).val()==1{b+=1;}let mut e=(p-1).trailing_zeros()as usize;let m=(p-1)>>e;let mut x=self.pow(m-1>>1);let mut y=self*x*x;x*=self;let mut z=b.pow(m);while y.val()!=1{let mut j=0;let mut t=y;while t.val()!=1{j+=1;t*=t;}z=z.pow(1<<e-j-1);x*=z;z*=z;y*=z;e=j;}Some(x)}pub fn set_modulus(modulus:u32){BARRETT.set(modulus)}}struct Barrett{m:AtomicU32,im:AtomicU64,}impl Barrett{const fn new(m:u32)->Self{Self{m:AtomicU32::new(m),im:AtomicU64::new((!0/m as u64).wrapping_add(1)),}}#[inline]fn set(&self,m:u32){let im=(!0/m as u64).wrapping_add(1);self.m.store(m,atomic::Ordering::SeqCst);self.im.store(im,atomic::Ordering::SeqCst);}#[inline]fn modulus(&self)->u32{self.m.load(atomic::Ordering::SeqCst)}#[inline]fn mul(&self,a:u32,b:u32)->u32{let m=self.m.load(atomic::Ordering::SeqCst);let im=self.im.load(atomic::Ordering::SeqCst);let mut z=a as u64;z*=b as u64;let x=(((z as u128)*(im as u128))>>64)as u64;let mut v=z.wrapping_sub(x.wrapping_mul(m as u64))as u32;if m<=v{v=v.wrapping_add(m);}v}}static BARRETT:Barrett=Barrett::new(998_244_353);impl<const P:u32>FromStr for StaticModInt<P>{type Err=ParseIntError;fn from_str(s:&str)->Result<Self,Self::Err>{s.parse::<i64>().map(Self::from)}}impl FromStr for DynamicModInt{type Err=ParseIntError;fn from_str(s:&str)->Result<Self,Self::Err>{s.parse::<i64>().map(Self::from)}}impl<const P:u32>fmt::Display for StaticModInt<P>{fn fmt(&self,f:&mut fmt::Formatter<'_>)->fmt::Result{write!(f,"{}",self.0)}}impl fmt::Display for DynamicModInt{fn fmt(&self,f:&mut fmt::Formatter<'_>)->fmt::Result{write!(f,"{}",self.0)}}impl<const P:u32>fmt::Debug for StaticModInt<P>{fn fmt(&self,f:&mut fmt::Formatter<'_>)->fmt::Result{if let Some((num,den))=rat_convert(self.0 as u64,P as u64,1025){write!(f,"{}",num)?;if den!=1{write!(f,"/{}",den)?;}}else if let Some((num,den))=rat_convert((P-self.0)as u64,P as u64,1025){write!(f,"-{}",num)?;if den!=1{write!(f,"/{}",den)?;}}else{write!(f,"{}",self.0)?;}Ok(())}}impl fmt::Debug for DynamicModInt{fn fmt(&self,f:&mut fmt::Formatter<'_>)->fmt::Result{write!(f,"{}",self.0)}}macro_rules!impl_from_integer{($(($t1:ty,$t2:ty)),*)=>{$(impl<const P:u32>From<$t1>for StaticModInt<P>{fn from(x:$t1)->Self{Self((x as$t2).rem_euclid(P as$t2)as u32)}}impl From<$t1>for DynamicModInt{fn from(x:$t1)->Self{Self((x as$t2).rem_euclid(Self::modulus()as$t2)as u32)}})*};}impl_from_integer!((i8,i32),(i16,i32),(i32,i32),(i64,i64),(isize,i64),(i128,i128),(u8,u32),(u16,u32),(u32,u32),(u64,u64),(usize,u64),(u128,u128));impl<const P:u32,T:Into<Self>>AddAssign<T>for StaticModInt<P>{fn add_assign(&mut self,rhs:T){self.0+=rhs.into().0;if self.0>=P{self.0-=P;}}}impl<T:Into<Self>>AddAssign<T>for DynamicModInt{fn add_assign(&mut self,rhs:T){self.0+=rhs.into().0;if self.0>=Self::modulus(){self.0-=Self::modulus();}}}impl<const P:u32,T:Into<Self>>SubAssign<T>for StaticModInt<P>{fn sub_assign(&mut self,rhs:T){let rhs=rhs.into().0;if self.0<rhs{self.0+=P;}self.0-=rhs;}}impl<T:Into<Self>>SubAssign<T>for DynamicModInt{fn sub_assign(&mut self,rhs:T){let rhs=rhs.into().0;if self.0<rhs{self.0+=Self::modulus();}self.0-=rhs;}}impl<const P:u32,T:Into<Self>>MulAssign<T>for StaticModInt<P>{fn mul_assign(&mut self,rhs:T){*self=Self((self.0 as u64*rhs.into().0 as u64%P as u64)as u32);}}impl<T:Into<Self>>MulAssign<T>for DynamicModInt{fn mul_assign(&mut self,rhs:T){*self=Self(BARRETT.mul(self.0,rhs.into().0));}}impl<const P:u32,T:Into<Self>>DivAssign<T>for StaticModInt<P>{fn div_assign(&mut self,rhs:T){*self*=rhs.into().inv()}}impl<T:Into<Self>>DivAssign<T>for DynamicModInt{fn div_assign(&mut self,rhs:T){*self=*self*rhs.into().inv()}}impl<const P:u32>Neg for StaticModInt<P>{type Output=Self;fn neg(self)->Self::Output{if self.0==0{Self(0)}else{Self(P-self.0)}}}impl Neg for DynamicModInt{type Output=Self;fn neg(self)->Self::Output{if self.0==0{Self(0)}else{Self(Self::modulus()-self.0)}}}impl<const P:u32>Neg for&StaticModInt<P>{type Output=StaticModInt<P>;fn neg(self)->Self::Output{if self.0==0{StaticModInt(0)}else{StaticModInt(P-self.0)}}}impl Neg for&DynamicModInt{type Output=DynamicModInt;fn neg(self)->Self::Output{if self.0==0{DynamicModInt(0)}else{DynamicModInt(DynamicModInt::modulus()-self.0)}}}macro_rules!impl_ops{($($trait:ident,$trait_assign:ident,$fn:ident,$fn_assign:ident,)*)=>{$(impl<const P:u32>$trait_assign<&StaticModInt<P>>for StaticModInt<P>{fn$fn_assign(&mut self,rhs:&StaticModInt<P>){self.$fn_assign(*rhs);}}impl<const P:u32,T:Into<StaticModInt<P>>>$trait<T>for StaticModInt<P>{type Output=StaticModInt<P>;fn$fn(mut self,rhs:T)->Self::Output{self.$fn_assign(rhs.into());self}}impl<const P:u32>$trait<&StaticModInt<P>>for StaticModInt<P>{type Output=StaticModInt<P>;fn$fn(self,rhs:&StaticModInt<P>)->Self::Output{self.$fn(*rhs)}}impl<const P:u32,T:Into<StaticModInt<P>>>$trait<T>for&StaticModInt<P>{type Output=StaticModInt<P>;fn$fn(self,rhs:T)->Self::Output{(*self).$fn(rhs.into())}}impl<const P:u32>$trait<&StaticModInt<P>>for&StaticModInt<P>{type Output=StaticModInt<P>;fn$fn(self,rhs:&StaticModInt<P>)->Self::Output{(*self).$fn(*rhs)}}impl$trait_assign<&DynamicModInt>for DynamicModInt{fn$fn_assign(&mut self,rhs:&DynamicModInt){self.$fn_assign(*rhs);}}impl<T:Into<DynamicModInt>>$trait<T>for DynamicModInt{type Output=DynamicModInt;fn$fn(mut self,rhs:T)->Self::Output{self.$fn_assign(rhs.into());self}}impl$trait<&DynamicModInt>for DynamicModInt{type Output=DynamicModInt;fn$fn(self,rhs:&DynamicModInt)->Self::Output{self.$fn(*rhs)}}impl<T:Into<DynamicModInt>>$trait<T>for&DynamicModInt{type Output=DynamicModInt;fn$fn(self,rhs:T)->Self::Output{(*self).$fn(rhs.into())}}impl$trait<&DynamicModInt>for&DynamicModInt{type Output=DynamicModInt;fn$fn(self,rhs:&DynamicModInt)->Self::Output{(*self).$fn(*rhs)}})*};}impl_ops!{Add,AddAssign,add,add_assign,Sub,SubAssign,sub,sub_assign,Mul,MulAssign,mul,mul_assign,Div,DivAssign,div,div_assign,}impl<const P:u32>Sum for StaticModInt<P>{fn sum<I:Iterator<Item=Self>>(iter:I)->Self{iter.fold(Self::raw(0),|b,x|b+x)}}impl<const P:u32>Product for StaticModInt<P>{fn product<I:Iterator<Item=Self>>(iter:I)->Self{iter.fold(Self::from(1),|b,x|b*x)}}impl<'a,const P:u32>Sum<&'a Self>for StaticModInt<P>{fn sum<I:Iterator<Item=&'a Self>>(iter:I)->Self{iter.fold(Self::raw(0),|b,x|b+x)}}impl<'a,const P:u32>Product<&'a Self>for StaticModInt<P>{fn product<I:Iterator<Item=&'a Self>>(iter:I)->Self{iter.fold(Self::from(1),|b,x|b*x)}}impl<const P:u32>StaticModInt<P>{pub const G:u32=ntt_info(P).0;pub const RANK2:usize=ntt_info(P).1;pub const ROOT:[u32;30]=ntt_info(P).2;pub const IROOT:[u32;30]=ntt_info(P).3;pub const RATE2:[u32;30]=ntt_info(P).4;pub const IRATE2:[u32;30]=ntt_info(P).5;pub const RATE3:[u32;30]=ntt_info(P).6;pub const IRATE3:[u32;30]=ntt_info(P).7;pub const IS_NTT_FRIENDLY:bool=is_prime(P)&&Self::RANK2>=21;}impl<const P:u32>Zero for StaticModInt<P>{fn zero()->Self{Self(0)}fn is_zero(&self)->bool{self.0==0}}impl<const P:u32>One for StaticModInt<P>{fn one()->Self{Self::new(1)}fn is_one(&self)->bool{self==&Self::one()}}impl Zero for DynamicModInt{fn zero()->Self{Self(0)}fn is_zero(&self)->bool{self.0==0}}impl One for DynamicModInt{fn one()->Self{Self::new(1)}fn is_one(&self)->bool{self==&Self::one()}}}
        pub mod montgomery_modint {use crate::__cargo_equip::preludes::montgomery_modint::*;use std::{convert::TryInto,fmt::Debug,ops::{Add,AddAssign,Mul,MulAssign,Neg,Sub,SubAssign},sync::atomic::{AtomicU64,Ordering::SeqCst},};use algebraic::{One,Zero};struct Montgomery{m:AtomicU64,r:AtomicU64,n2:AtomicU64,}impl Montgomery{const fn new()->Self{Self{m:AtomicU64::new(0),r:AtomicU64::new(0),n2:AtomicU64::new(0),}}fn set(&self,m:u64){assert!(m<1<<62);assert!(m&1!=0);if self.m.load(SeqCst)==m{return;}let n2=((m as u128).wrapping_neg()%m as u128)as u64;let mut r=m;for _ in 0..5{r=r.wrapping_mul(2u64.wrapping_sub(m.wrapping_mul(r)));}assert!(r.wrapping_mul(m)==1);self.m.store(m,SeqCst);self.r.store(r,SeqCst);self.n2.store(n2,SeqCst);}fn reduce(&self,x:u128)->u64{let r=self.r.load(SeqCst);let m=self.m.load(SeqCst);(x.wrapping_add(((x as u64).wrapping_mul(r.wrapping_neg())as u128).wrapping_mul(m as u128),)>>64)as u64}}static MONTGOMERY:Montgomery=Montgomery::new();#[derive(Default,Clone,Copy)]pub struct MontgomeryModInt(u64);impl MontgomeryModInt{pub fn set_modulus(m:u64){MONTGOMERY.set(m);}pub fn modulus()->u64{MONTGOMERY.m.load(SeqCst)}pub fn new(x:u64)->Self{Self(MONTGOMERY.reduce((x as u128).wrapping_add(Self::modulus()as u128).wrapping_mul(MONTGOMERY.n2.load(SeqCst)as u128),),)}pub fn pow(mut self,k:impl TryInto<u128,Error=impl Debug>)->Self{let mut k:u128=k.try_into().unwrap();let mut r=Self::new(1);while k>0{if k&1!=0{r*=self;}self*=self;k>>=1;}r}pub fn val(self)->u64{let x=MONTGOMERY.reduce(self.0 as u128);let m=Self::modulus();if x>=m{x-m}else{x}}}impl Neg for MontgomeryModInt{type Output=Self;fn neg(self)->Self::Output{Self::new(0)-self}}impl AddAssign<Self>for MontgomeryModInt{fn add_assign(&mut self,rhs:Self){let m=Self::modulus();self.0=self.0.wrapping_add(rhs.0.wrapping_sub(m*2));if(self.0 as i64)<0{self.0=self.0.wrapping_add(m*2);}}}impl SubAssign<Self>for MontgomeryModInt{fn sub_assign(&mut self,rhs:Self){let m=Self::modulus();self.0=self.0.wrapping_sub(rhs.0);if(self.0 as i64)<0{self.0=self.0.wrapping_add(m*2);}}}impl MulAssign<Self>for MontgomeryModInt{fn mul_assign(&mut self,rhs:Self){self.0=MONTGOMERY.reduce(self.0 as u128*rhs.0 as u128);}}impl Add<Self>for MontgomeryModInt{type Output=Self;fn add(mut self,rhs:Self)->Self::Output{self+=rhs;self}}impl Sub<Self>for MontgomeryModInt{type Output=Self;fn sub(mut self,rhs:Self)->Self::Output{self-=rhs;self}}impl Mul<Self>for MontgomeryModInt{type Output=Self;fn mul(mut self,rhs:Self)->Self::Output{self*=rhs;self}}impl PartialEq for MontgomeryModInt{fn eq(&self,other:&Self)->bool{let m=Self::modulus();(if self.0>=m{self.0-m}else{self.0})==(if other.0>=m{other.0-m}else{other.0})}}impl Eq for MontgomeryModInt{}impl Zero for MontgomeryModInt{fn zero()->Self{Self(0)}fn is_zero(&self)->bool{self.0==0}}impl One for MontgomeryModInt{fn one()->Self{Self(1)}fn is_one(&self)->bool{self==&Self::new(1)}}}
    }

    pub(crate) mod macros {
        pub mod algebraic {pub use crate::{__cargo_equip_macro_def_algebraic_act as act,__cargo_equip_macro_def_algebraic_algebra as algebra,__cargo_equip_macro_def_algebraic_group as group,__cargo_equip_macro_def_algebraic_monoid as monoid};}
        pub mod chminmax {pub use crate::{__cargo_equip_macro_def_chminmax_chmax as chmax,__cargo_equip_macro_def_chminmax_chmin as chmin,__cargo_equip_macro_def_chminmax_max as max,__cargo_equip_macro_def_chminmax_min as min};}
        pub mod fast_factorize {}
        pub mod modint {}
        pub mod montgomery_modint {}
    }

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

    mod preludes {
        pub mod algebraic {}
        pub mod chminmax {}
        pub mod fast_factorize {pub(in crate::__cargo_equip)use crate::__cargo_equip::crates::montgomery_modint;}
        pub mod modint {pub(in crate::__cargo_equip)use crate::__cargo_equip::crates::algebraic;}
        pub mod montgomery_modint {pub(in crate::__cargo_equip)use crate::__cargo_equip::crates::algebraic;}
    }
}