pub use __cargo_equip::prelude::*; use combination::Combination; use modint::ModInt998244353 as Mint; #[allow(unused_imports)] use proconio::{ input, marker::{Bytes, Chars, Usize1}, }; fn main() { input! { n: usize, m: usize, } let comb = Combination::::new(); let mut dp = vec![vec![Mint::new(0); n + 1]; n + 1]; dp[0][0] += 1; for i in 0..n { for j in 0..=i { let c = dp[i][j]; dp[i + 1][j] += c * j; dp[i + 1][j + 1] += c; } } let mut res = Mint::new(0); for i in 0..=n.min(m + 1) { for j in i..=n { let x = dp[j][i] * comb.fact(i); let y = comb.nck(n, j); let z = Mint::new(m + 1 + m.saturating_sub(i)).pow(n - j); res += x * y * z * i; } } println!("{}", res); } // The following code was expanded by `cargo-equip`. /// # Bundled libraries /// /// - `combination 0.1.0 (path+██████████████████████████████████████████████████████████████)` published in **missing** licensed under `CC0-1.0` as `crate::__cargo_equip::crates::combination` /// - `lazy_static 1.4.0 (registry+https://github.com/rust-lang/crates.io-index)` licensed under `MIT/Apache-2.0` as `crate::__cargo_equip::crates::__lazy_static_1_4_0` /// - `modint 0.1.0 (path+█████████████████████████████████████████████████████████)` published in **missing** licensed under `CC0-1.0` as `crate::__cargo_equip::crates::modint` /// - `proconio 0.4.3 (registry+https://github.com/rust-lang/crates.io-index)` licensed under `MIT OR Apache-2.0` as `crate::__cargo_equip::crates::proconio` /// /// # License and Copyright Notices /// /// - `lazy_static 1.4.0 (registry+https://github.com/rust-lang/crates.io-index)` /// /// ```text /// Copyright (c) 2010 The Rust Project Developers /// /// Permission is hereby granted, free of charge, to any /// person obtaining a copy of this software and associated /// documentation files (the "Software"), to deal in the /// Software without restriction, including without /// limitation the rights to use, copy, modify, merge, /// publish, distribute, sublicense, and/or sell copies of /// the Software, and to permit persons to whom the Software /// is furnished to do so, subject to the following /// conditions: /// /// The above copyright notice and this permission notice /// shall be included in all copies or substantial portions /// of the Software. /// /// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF /// ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED /// TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A /// PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT /// SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY /// CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION /// OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR /// IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER /// DEALINGS IN THE SOFTWARE. /// ``` /// /// - `proconio 0.4.3 (registry+https://github.com/rust-lang/crates.io-index)` /// /// ```text /// The MIT License /// Copyright 2019 (C) statiolake /// /// Permission is hereby granted, free of charge, to any person obtaining a copy of /// this software and associated documentation files (the "Software"), to deal in /// the Software without restriction, including without limitation the rights to /// use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of /// the Software, and to permit persons to whom the Software is furnished to do so, /// subject to the following conditions: /// /// The above copyright notice and this permission notice shall be included in all /// copies or substantial portions of the Software. /// /// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR /// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS /// FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR /// COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER /// IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN /// CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. /// /// Copyright for original `input!` macro is held by Hideyuki Tanaka, 2019. The /// original macro is licensed under BSD 3-clause license. /// /// Redistribution and use in source and binary forms, with or without /// modification, are permitted provided that the following conditions are met: /// /// 1. Redistributions of source code must retain the above copyright notice, this /// list of conditions and the following disclaimer. /// /// 2. Redistributions in binary form must reproduce the above copyright notice, /// this list of conditions and the following disclaimer in the documentation /// and/or other materials provided with the distribution. /// /// 3. Neither the name of the copyright holder nor the names of its contributors /// may be used to endorse or promote products derived from this software /// without specific prior written permission. /// /// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND /// ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED /// WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE /// DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE /// FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL /// DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR /// SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER /// CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, /// OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE /// OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. /// ``` #[cfg_attr(any(), rustfmt::skip)] #[allow(unused)] mod __cargo_equip { pub(crate) mod crates { pub mod combination {use crate::__cargo_equip::preludes::combination::*;use std::cell::RefCell;use modint::ModInt;pub struct Combination{inv:RefCell>,fact:RefCell>,fact_inv:RefCell>,}implCombination{pub fn new()->Self{Self{inv:RefCell::new(vec![M::from(0),M::from(1)]),fact:RefCell::new(vec![M::from(1);2]),fact_inv:RefCell::new(vec![M::from(1);2]),}}fn expand(&self,n:usize){let mut inv=self.inv.borrow_mut();let mut fact=self.fact.borrow_mut();let mut fact_inv=self.fact_inv.borrow_mut();let m=inv.len();let mut nn=m;while nn<=n{nn*=2;}inv.resize(nn,M::default());fact.resize(nn,M::default());fact_inv.resize(nn,M::default());let p=M::modulus()as usize;for i in m..nn{inv[i]=-inv[p%i]*M::from((p/i)as u32);fact[i]=fact[i-1]*M::from(i);fact_inv[i]=fact_inv[i-1]*inv[i];}}pub fn inv(&self,n:usize)->M{self.expand(n);self.inv.borrow()[n]}pub fn fact(&self,n:usize)->M{self.expand(n);self.fact.borrow()[n]}pub fn fact_inv(&self,n:usize)->M{self.expand(n);self.fact_inv.borrow()[n]}pub fn nck(&self,n:usize,k:usize)->M{if nM{if nM{if n==0&&k==0{M::from(1)}else{self.nck(n+k-1,k)}}pub fn catalan(&self,n:usize)->M{self.expand(n*2);self.fact.borrow()[n*2]*self.fact_inv.borrow()[n+1]*self.fact_inv.borrow()[n]}}} pub mod __lazy_static_1_4_0 {#![no_std]use crate::__cargo_equip::preludes::__lazy_static_1_4_0::*;pub use crate::__cargo_equip::macros::__lazy_static_1_4_0::*;#[path="inline_lazy.rs"]pub mod lazy{use crate::__cargo_equip::preludes::__lazy_static_1_4_0::*;extern crate core;extern crate std;use self::std::prelude::v1::*;use self::std::cell::Cell;use self::std::hint::unreachable_unchecked;use self::std::sync::Once;#[allow(deprecated)]pub use self::std::sync::ONCE_INIT;pub struct Lazy(Cell>,Once);implLazy{#[allow(deprecated)]pub const INIT:Self=Lazy(Cell::new(None),ONCE_INIT);#[inline(always)]pub fn get(&'static self,f:F)->&T where F:FnOnce()->T,{self.1.call_once(||{self.0.set(Some(f()));});unsafe{match*self.0.as_ptr(){Some(ref x)=>x,None=>{debug_assert!(false,"attempted to derefence an uninitialized lazy static. This is a bug");unreachable_unchecked()},}}}}unsafe implSync for Lazy{}#[macro_export]macro_rules!__cargo_equip_macro_def___lazy_static_1_4_0___lazy_static_create{($NAME:ident,$T:ty)=>{static$NAME:$crate::__cargo_equip::crates::__lazy_static_1_4_0::lazy::Lazy<$T> =$crate::__cargo_equip::crates::__lazy_static_1_4_0::lazy::Lazy::INIT;};}macro_rules!__lazy_static_create{($($tt:tt)*)=>(crate::__cargo_equip_macro_def___lazy_static_1_4_0___lazy_static_create!{$($tt)*})}}pub use core::ops::Deref as __Deref;#[macro_export(local_inner_macros)]macro_rules!__cargo_equip_macro_def___lazy_static_1_4_0___lazy_static_internal{($(#[$attr:meta])*($($vis:tt)*)static ref$N:ident:$T:ty=$e:expr;$($t:tt)*)=>{__lazy_static_internal!(@MAKE TY,$(#[$attr])*,($($vis)*),$N);__lazy_static_internal!(@TAIL,$N:$T=$e);lazy_static!($($t)*);};(@TAIL,$N:ident:$T:ty=$e:expr)=>{impl$crate::__cargo_equip::crates::__lazy_static_1_4_0::__Deref for$N{type Target=$T;fn deref(&self)->&$T{#[inline(always)]fn __static_ref_initialize()->$T{$e}#[inline(always)]fn __stability()->&'static$T{__lazy_static_create!(LAZY,$T);LAZY.get(__static_ref_initialize)}__stability()}}impl$crate::__cargo_equip::crates::__lazy_static_1_4_0::LazyStatic for$N{fn initialize(lazy:&Self){let _=&**lazy;}}};(@MAKE TY,$(#[$attr:meta])*,($($vis:tt)*),$N:ident)=>{#[allow(missing_copy_implementations)]#[allow(non_camel_case_types)]#[allow(dead_code)]$(#[$attr])*$($vis)*struct$N{__private_field:()}#[doc(hidden)]$($vis)*static$N:$N=$N{__private_field:()};};()=>()}macro_rules!__lazy_static_internal{($($tt:tt)*)=>(crate::__cargo_equip_macro_def___lazy_static_1_4_0___lazy_static_internal!{$($tt)*})}#[macro_export(local_inner_macros)]macro_rules!__cargo_equip_macro_def___lazy_static_1_4_0_lazy_static{($(#[$attr:meta])*static ref$N:ident:$T:ty=$e:expr;$($t:tt)*)=>{__lazy_static_internal!($(#[$attr])*()static ref$N:$T=$e;$($t)*);};($(#[$attr:meta])*pub static ref$N:ident:$T:ty=$e:expr;$($t:tt)*)=>{__lazy_static_internal!($(#[$attr])*(pub)static ref$N:$T=$e;$($t)*);};($(#[$attr:meta])*pub($($vis:tt)+)static ref$N:ident:$T:ty=$e:expr;$($t:tt)*)=>{__lazy_static_internal!($(#[$attr])*(pub($($vis)+))static ref$N:$T=$e;$($t)*);};()=>()}macro_rules!lazy_static{($($tt:tt)*)=>(crate::__cargo_equip_macro_def___lazy_static_1_4_0_lazy_static!{$($tt)*})}pub trait LazyStatic{fn initialize(lazy:&Self);}pub fn initialize(lazy:&T){LazyStatic::initialize(lazy);}} pub mod 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},};#[derive(Clone,Copy,Default,PartialEq,Eq,Hash)]#[repr(transparent)]pub struct StaticModInt(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+FromStr+From+From+From+From+From+From+From+From+From+From+From+From+Copy+Eq+Hash+fmt::Display+fmt::Debug+Neg+Add+Sub+Mul+Div+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;}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 ix 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(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{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*xModInt for StaticModInt

{#[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.sqrt()}}implStaticModInt

{#[inline]pub fn new>>(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{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<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.sqrt()}}impl DynamicModInt{#[inline]pub fn new>(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{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<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);implFromStr for StaticModInt

{type Err=ParseIntError;fn from_str(s:&str)->Result{s.parse::().map(Self::from)}}impl FromStr for DynamicModInt{type Err=ParseIntError;fn from_str(s:&str)->Result{s.parse::().map(Self::from)}}implfmt::Display for StaticModInt

{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)}}implfmt::Debug for StaticModInt

{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,$t2:ty)),*)=>{$(implFrom<$t1>for StaticModInt

{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>AddAssignfor StaticModInt

{fn add_assign(&mut self,rhs:T){self.0+=rhs.into().0;if self.0>=P{self.0-=P;}}}impl>AddAssignfor DynamicModInt{fn add_assign(&mut self,rhs:T){self.0+=rhs.into().0;if self.0>=Self::modulus(){self.0-=Self::modulus();}}}impl>SubAssignfor StaticModInt

{fn sub_assign(&mut self,rhs:T){let rhs=rhs.into().0;if self.0>SubAssignfor DynamicModInt{fn sub_assign(&mut self,rhs:T){let rhs=rhs.into().0;if self.0>MulAssignfor StaticModInt

{fn mul_assign(&mut self,rhs:T){*self=Self((self.0 as u64*rhs.into().0 as u64%P as u64)as u32);}}impl>MulAssignfor DynamicModInt{fn mul_assign(&mut self,rhs:T){*self=Self(BARRETT.mul(self.0,rhs.into().0));}}impl>DivAssignfor StaticModInt

{fn div_assign(&mut self,rhs:T){*self*=rhs.into().inv()}}impl>DivAssignfor DynamicModInt{fn div_assign(&mut self,rhs:T){*self=*self*rhs.into().inv()}}implNeg for StaticModInt

{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)}}}implNeg for&StaticModInt

{type Output=StaticModInt

;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$trait_assign<&StaticModInt

>for StaticModInt

{fn$fn_assign(&mut self,rhs:&StaticModInt

){self.$fn_assign(*rhs);}}impl>>$traitfor StaticModInt

{type Output=StaticModInt

;fn$fn(mut self,rhs:T)->Self::Output{self.$fn_assign(rhs.into());self}}impl$trait<&StaticModInt

>for StaticModInt

{type Output=StaticModInt

;fn$fn(self,rhs:&StaticModInt

)->Self::Output{self.$fn(*rhs)}}impl>>$traitfor&StaticModInt

{type Output=StaticModInt

;fn$fn(self,rhs:T)->Self::Output{(*self).$fn(rhs.into())}}impl$trait<&StaticModInt

>for&StaticModInt

{type Output=StaticModInt

;fn$fn(self,rhs:&StaticModInt

)->Self::Output{(*self).$fn(*rhs)}}impl$trait_assign<&DynamicModInt>for DynamicModInt{fn$fn_assign(&mut self,rhs:&DynamicModInt){self.$fn_assign(*rhs);}}impl>$traitfor DynamicModInt{type Output=DynamicModInt;fn$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>$traitfor&DynamicModInt{type Output=DynamicModInt;fn$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,}implSum for StaticModInt

{fn sum>(iter:I)->Self{iter.fold(Self::raw(0),|b,x|b+x)}}implProduct for StaticModInt

{fn product>(iter:I)->Self{iter.fold(Self::from(1),|b,x|b*x)}}impl<'a,const P:u32>Sum<&'a Self>for StaticModInt

{fn sum>(iter:I)->Self{iter.fold(Self::raw(0),|b,x|b+x)}}impl<'a,const P:u32>Product<&'a Self>for StaticModInt

{fn product>(iter:I)->Self{iter.fold(Self::from(1),|b,x|b*x)}}implStaticModInt

{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;}} pub mod proconio {#![allow(clippy::needless_doctest_main,clippy::print_literal)]use crate::__cargo_equip::preludes::proconio::*;pub use crate::__cargo_equip::macros::proconio::*;pub mod marker{use crate::__cargo_equip::preludes::proconio::*;use crate::__cargo_equip::crates::proconio::source::{Readable,Source};use std::io::BufRead;pub enum Chars{}impl Readable for Chars{type Output=Vec;fn read>(source:&mut S)->Vec{source.next_token_unwrap().chars().collect()}}pub enum Bytes{}impl Readable for Bytes{type Output=Vec;fn read>(source:&mut S)->Vec{source.next_token_unwrap().bytes().collect()}}pub enum Usize1{}impl Readable for Usize1{type Output=usize;fn read>(source:&mut S)->usize{usize::read(source).checked_sub(1).expect("attempted to read the value 0 as a Usize1")}}pub enum Isize1{}impl Readable for Isize1{type Output=isize;fn read>(source:&mut S)->isize{isize::read(source).checked_sub(1).unwrap_or_else(||{panic!(concat!("attempted to read the value {} as a Isize1:"," the value is isize::MIN and cannot be decremented"),std::isize::MIN,)})}}}pub mod source{use crate::__cargo_equip::preludes::proconio::*;use std::any::type_name;use std::fmt::Debug;use std::io::BufRead;use std::str::FromStr;pub mod line{use crate::__cargo_equip::preludes::proconio::*;use super::Source;use std::io::BufRead;use std::iter::Peekable;use std::str::SplitWhitespace;pub struct LineSource{tokens:Peekable>,current_context:Box,reader:R,}implLineSource{pub fn new(reader:R)->LineSource{LineSource{current_context:"".to_string().into_boxed_str(),tokens:"".split_whitespace().peekable(),reader,}}fn prepare(&mut self){while self.tokens.peek().is_none(){let mut line=String::new();let num_bytes=self.reader.read_line(&mut line).expect("failed to get linel maybe an IO error.");if num_bytes==0{return;}self.current_context=line.into_boxed_str();self.tokens=unsafe{std::mem::transmute::<_,&'static str>(&*self.current_context)}.split_whitespace().peekable();}}}implSourcefor LineSource{fn next_token(&mut self)->Option<&str>{self.prepare();self.tokens.next()}fn is_empty(&mut self)->bool{self.prepare();self.tokens.peek().is_none()}}use std::io::BufReader;impl<'a>From<&'a str>for LineSource>{fn from(s:&'a str)->LineSource>{LineSource::new(BufReader::new(s.as_bytes()))}}}pub mod once{use crate::__cargo_equip::preludes::proconio::*;use super::Source;use std::io::BufRead;use std::iter::Peekable;use std::marker::PhantomData;use std::str::SplitWhitespace;pub struct OnceSource{tokens:Peekable>,context:Box,_read:PhantomData,}implOnceSource{pub fn new(mut source:R)->OnceSource{let mut context=String::new();source.read_to_string(&mut context).expect("failed to read from source; maybe an IO error.");let context=context.into_boxed_str();let mut res=OnceSource{context,tokens:"".split_whitespace().peekable(),_read:PhantomData,};use std::mem;let context:&'static str=unsafe{mem::transmute(&*res.context)};res.tokens=context.split_whitespace().peekable();res}}implSourcefor OnceSource{fn next_token(&mut self)->Option<&str>{self.tokens.next()}fn is_empty(&mut self)->bool{self.tokens.peek().is_none()}}use std::io::BufReader;impl<'a>From<&'a str>for OnceSource>{fn from(s:&'a str)->OnceSource>{OnceSource::new(BufReader::new(s.as_bytes()))}}}pub mod auto{use crate::__cargo_equip::preludes::proconio::*;#[cfg(debug_assertions)]pub use super::line::LineSource as AutoSource;#[cfg(not(debug_assertions))]pub use super::once::OnceSource as AutoSource;}pub trait Source{fn next_token(&mut self)->Option<&str>;fn is_empty(&mut self)->bool;fn next_token_unwrap(&mut self)->&str{self.next_token().expect(concat!("failed to get the next token; ","maybe reader reached an end of input. ","ensure that arguments for `input!` macro is correctly ","specified to match the problem input."))}}impl>Sourcefor&'_ mut S{fn next_token(&mut self)->Option<&str>{(*self).next_token()}fn is_empty(&mut self)->bool{(*self).is_empty()}}pub trait Readable{type Output;fn read>(source:&mut S)->Self::Output;}implReadable for T where T::Err:Debug,{type Output=T;fn read>(source:&mut S)->T{let token=source.next_token_unwrap();match token.parse(){Ok(v)=>v,Err(e)=>panic!(concat!("failed to parse the input `{input}` ","to the value of type `{ty}`: {err:?}; ","ensure that the input format is collectly specified ","and that the input value must handle specified type.",),input=token,ty=type_name::(),err=e,),}}}}use crate::__cargo_equip::crates::proconio::source::auto::AutoSource;use lazy_static::lazy_static;use std::io;use std::io::{BufReader,Stdin};use std::sync::Mutex;pub use crate::__cargo_equip::crates::proconio::source::Readable as __Readable;lazy_static!{#[doc(hidden)]pub static ref STDIN_SOURCE:Mutex>>=Mutex::new(AutoSource::new(BufReader::new(io::stdin())));}#[macro_export]macro_rules!__cargo_equip_macro_def_proconio_input{(@from[$source:expr]@rest)=>{};(@from[$source:expr]@rest mut$($rest:tt)*)=>{$crate::__cargo_equip::crates::proconio::input!{@from[$source]@mut[mut]@rest$($rest)*}};(@from[$source:expr]@rest$($rest:tt)*)=>{$crate::__cargo_equip::crates::proconio::input!{@from[$source]@mut[]@rest$($rest)*}};(@from[$source:expr]@mut[$($mut:tt)?]@rest$var:tt:$($rest:tt)*)=>{$crate::__cargo_equip::crates::proconio::input!{@from[$source]@mut[$($mut)*]@var$var@kind[]@rest$($rest)*}};(@from[$source:expr]@mut[$($mut:tt)?]@var$var:tt@kind[$($kind:tt)*]@rest)=>{let$($mut)*$var=$crate::__cargo_equip::crates::proconio::read_value!(@source[$source]@kind[$($kind)*]);};(@from[$source:expr]@mut[$($mut:tt)?]@var$var:tt@kind[$($kind:tt)*]@rest,$($rest:tt)*)=>{$crate::__cargo_equip::crates::proconio::input!(@from[$source]@mut[$($mut)*]@var$var@kind[$($kind)*]@rest);$crate::__cargo_equip::crates::proconio::input!(@from[$source]@rest$($rest)*);};(@from[$source:expr]@mut[$($mut:tt)?]@var$var:tt@kind[$($kind:tt)*]@rest$tt:tt$($rest:tt)*)=>{$crate::__cargo_equip::crates::proconio::input!(@from[$source]@mut[$($mut)*]@var$var@kind[$($kind)*$tt]@rest$($rest)*);};(from$source:expr,$($rest:tt)*)=>{#[allow(unused_variables,unused_mut)]let mut s=$source;$crate::__cargo_equip::crates::proconio::input!{@from[&mut s]@rest$($rest)*}};($($rest:tt)*)=>{let mut locked_stdin=$crate::__cargo_equip::crates::proconio::STDIN_SOURCE.lock().expect(concat!("failed to lock the stdin; please re-run this program. ","If this issue repeatedly occur, this is a bug in `proconio`. ","Please report this issue from ","."));$crate::__cargo_equip::crates::proconio::input!{@from[&mut*locked_stdin]@rest$($rest)*}drop(locked_stdin);};}macro_rules!input{($($tt:tt)*)=>(crate::__cargo_equip_macro_def_proconio_input!{$($tt)*})}#[macro_export]macro_rules!__cargo_equip_macro_def_proconio_read_value{(@source[$source:expr]@kind[[$($kind:tt)*]])=>{$crate::__cargo_equip::crates::proconio::read_value!(@array@source[$source]@kind[]@rest$($kind)*)};(@array@source[$source:expr]@kind[$($kind:tt)*]@rest)=>{{let len=::read($source);$crate::__cargo_equip::crates::proconio::read_value!(@source[$source]@kind[[$($kind)*;len]])}};(@array@source[$source:expr]@kind[$($kind:tt)*]@rest;$($rest:tt)*)=>{$crate::__cargo_equip::crates::proconio::read_value!(@array@source[$source]@kind[$($kind)*]@len[$($rest)*])};(@array@source[$source:expr]@kind[$($kind:tt)*]@rest$tt:tt$($rest:tt)*)=>{$crate::__cargo_equip::crates::proconio::read_value!(@array@source[$source]@kind[$($kind)*$tt]@rest$($rest)*)};(@array@source[$source:expr]@kind[$($kind:tt)*]@len[$($len:tt)*])=>{{let len=$($len)*;(0..len).map(|_|$crate::__cargo_equip::crates::proconio::read_value!(@source[$source]@kind[$($kind)*])).collect::>()}};(@source[$source:expr]@kind[($($kinds:tt)*)])=>{$crate::__cargo_equip::crates::proconio::read_value!(@tuple@source[$source]@kinds[]@current[]@rest$($kinds)*)};(@tuple@source[$source:expr]@kinds[$([$($kind:tt)*])*]@current[]@rest)=>{($($crate::__cargo_equip::crates::proconio::read_value!(@source[$source]@kind[$($kind)*]),)*)};(@tuple@source[$source:expr]@kinds[$($kinds:tt)*]@current[$($curr:tt)*]@rest)=>{$crate::__cargo_equip::crates::proconio::read_value!(@tuple@source[$source]@kinds[$($kinds)*[$($curr)*]]@current[]@rest)};(@tuple@source[$source:expr]@kinds[$($kinds:tt)*]@current[$($curr:tt)*]@rest,$($rest:tt)*)=>{$crate::__cargo_equip::crates::proconio::read_value!(@tuple@source[$source]@kinds[$($kinds)*[$($curr)*]]@current[]@rest$($rest)*)};(@tuple@source[$source:expr]@kinds[$($kinds:tt)*]@current[$($curr:tt)*]@rest$tt:tt$($rest:tt)*)=>{$crate::__cargo_equip::crates::proconio::read_value!(@tuple@source[$source]@kinds[$($kinds)*]@current[$($curr)*$tt]@rest$($rest)*)};(@source[$source:expr]@kind[])=>{compile_error!(concat!("Reached unreachable statement while parsing macro input. ","This is a bug in `proconio`. ","Please report this issue from ","."));};(@source[$source:expr]@kind[$kind:ty])=>{<$kind as$crate::__cargo_equip::crates::proconio::__Readable>::read($source)}}macro_rules!read_value{($($tt:tt)*)=>(crate::__cargo_equip_macro_def_proconio_read_value!{$($tt)*})}pub fn is_stdin_empty()->bool{use crate::__cargo_equip::crates::proconio::source::Source;let mut lock=STDIN_SOURCE.lock().expect(concat!("failed to lock the stdin; please re-run this program. ","If this issue repeatedly occur, this is a bug in `proconio`. ","Please report this issue from ","."));lock.is_empty()}} } pub(crate) mod macros { pub mod combination {} pub mod __lazy_static_1_4_0 {pub use crate::{__cargo_equip_macro_def___lazy_static_1_4_0___lazy_static_create as __lazy_static_create,__cargo_equip_macro_def___lazy_static_1_4_0___lazy_static_internal as __lazy_static_internal,__cargo_equip_macro_def___lazy_static_1_4_0_lazy_static as lazy_static};} pub mod modint {} pub mod proconio {pub use crate::{__cargo_equip_macro_def_proconio_input as input,__cargo_equip_macro_def_proconio_read_value as read_value};} } pub(crate) mod prelude {pub use crate::__cargo_equip::{crates::*,macros::__lazy_static_1_4_0::*};} mod preludes { pub mod combination {pub(in crate::__cargo_equip)use crate::__cargo_equip::crates::modint;} pub mod __lazy_static_1_4_0 {pub(in crate::__cargo_equip)use crate::__cargo_equip::macros::__lazy_static_1_4_0::*;} pub mod modint {} pub mod proconio {pub(in crate::__cargo_equip)use crate::__cargo_equip::macros::__lazy_static_1_4_0::*;pub(in crate::__cargo_equip)use crate::__cargo_equip::crates::__lazy_static_1_4_0 as lazy_static;} } }