#include "circuit.h"
#ifndef LOCAL
#pragma GCC optimize ("Ofast")
#pragma GCC optimize ("unroll-loops")
#endif
#include <bits/stdc++.h>
using namespace std;
using ll=long long;
//#define int ll
#define rng(i,a,b) for(int i=int(a);i<int(b);i++)
#define rep(i,b) rng(i,0,b)
#define gnr(i,a,b) for(int i=int(b)-1;i>=int(a);i--)
#define per(i,b) gnr(i,0,b)
#define pb push_back
#define eb emplace_back
#define a first
#define b second
#define bg begin()
#define ed end()
#define all(x) x.bg,x.ed
#define si(x) int(x.size())
#ifdef LOCAL
#define dmp(x) cerr<<__LINE__<<" "<<#x<<" "<<x<<endl
#else
#define dmp(x) void(0)
#endif
template<class t,class u> bool chmax(t&a,u b){if(a<b){a=b;return true;}else return false;}
template<class t,class u> bool chmin(t&a,u b){if(b<a){a=b;return true;}else return false;}
template<class t> using vc=vector<t>;
template<class t> using vvc=vc<vc<t>>;
using pi=pair<int,int>;
using vi=vc<int>;
template<class t,class u>
ostream& operator<<(ostream& os,const pair<t,u>& p){
return os<<"{"<<p.a<<","<<p.b<<"}";
}
template<class t> ostream& operator<<(ostream& os,const vc<t>& v){
os<<"{";
for(auto e:v)os<<e<<",";
return os<<"}";
}
#define mp make_pair
#define mt make_tuple
#define one(x) memset(x,-1,sizeof(x))
#define zero(x) memset(x,0,sizeof(x))
#ifdef LOCAL
void dmpr(ostream&os){os<<endl;}
template<class T,class... Args>
void dmpr(ostream&os,const T&t,const Args&... args){
os<<t<<" ";
dmpr(os,args...);
}
#define dmp2(...) dmpr(cerr,__LINE__,##__VA_ARGS__)
#else
#define dmp2(...) void(0)
#endif
using uint=unsigned;
using ull=unsigned long long;
template<class t,size_t n>
ostream& operator<<(ostream&os,const array<t,n>&a){
return os<<vc<t>(all(a));
}
template<int i,class T>
void print_tuple(ostream&,const T&){
}
template<int i,class T,class H,class ...Args>
void print_tuple(ostream&os,const T&t){
if(i)os<<",";
os<<get<i>(t);
print_tuple<i+1,T,Args...>(os,t);
}
template<class ...Args>
ostream& operator<<(ostream&os,const tuple<Args...>&t){
os<<"{";
print_tuple<0,tuple<Args...>,Args...>(os,t);
return os<<"}";
}
ll read(){
ll i;
cin>>i;
return i;
}
vi readvi(int n,int off=0){
vi v(n);
rep(i,n)v[i]=read()+off;
return v;
}
pi readpi(int off=0){
int a,b;cin>>a>>b;
return pi(a+off,b+off);
}
template<class t>
void print_single(t x,int suc=1){
cout<<x;
if(suc==1)
cout<<"\n";
if(suc==2)
cout<<" ";
}
template<class t,class u>
void print_single(const pair<t,u>&p,int suc=1){
print_single(p.a,2);
print_single(p.b,suc);
}
template<class T>
void print_single(const vector<T>&v,int suc=1){
rep(i,v.size())
print_single(v[i],i==int(v.size())-1?suc:2);
}
template<class T>
void print_offset(const vector<T>&v,ll off,int suc=1){
rep(i,v.size())
print_single(v[i]+off,i==int(v.size())-1?suc:2);
}
template<class T,size_t N>
void print_single(const array<T,N>&v,int suc=1){
rep(i,N)
print_single(v[i],i==int(N)-1?suc:2);
}
template<class T>
void print(const T&t){
print_single(t);
}
template<class T,class ...Args>
void print(const T&t,const Args&...args){
print_single(t,2);
print(args...);
}
string readString(){
string s;
cin>>s;
return s;
}
template<class T>
T sq(const T& t){
return t*t;
}
void YES(bool ex=true){
cout<<"YES\n";
if(ex)exit(0);
#ifdef LOCAL
cout.flush();
#endif
}
void NO(bool ex=true){
cout<<"NO\n";
if(ex)exit(0);
#ifdef LOCAL
cout.flush();
#endif
}
void Yes(bool ex=true){
cout<<"Yes\n";
if(ex)exit(0);
#ifdef LOCAL
cout.flush();
#endif
}
void No(bool ex=true){
cout<<"No\n";
if(ex)exit(0);
#ifdef LOCAL
cout.flush();
#endif
}
//#define CAPITAL
/*
void yes(bool ex=true){
#ifdef CAPITAL
cout<<"YES"<<"\n";
#else
cout<<"Yes"<<"\n";
#endif
if(ex)exit(0);
#ifdef LOCAL
cout.flush();
#endif
}
void no(bool ex=true){
#ifdef CAPITAL
cout<<"NO"<<"\n";
#else
cout<<"No"<<"\n";
#endif
if(ex)exit(0);
#ifdef LOCAL
cout.flush();
#endif
}*/
void possible(bool ex=true){
#ifdef CAPITAL
cout<<"POSSIBLE"<<"\n";
#else
cout<<"Possible"<<"\n";
#endif
if(ex)exit(0);
#ifdef LOCAL
cout.flush();
#endif
}
void impossible(bool ex=true){
#ifdef CAPITAL
cout<<"IMPOSSIBLE"<<"\n";
#else
cout<<"Impossible"<<"\n";
#endif
if(ex)exit(0);
#ifdef LOCAL
cout.flush();
#endif
}
constexpr ll ten(int n){
return n==0?1:ten(n-1)*10;
}
const ll infLL=LLONG_MAX/3;
#ifdef int
const int inf=infLL;
#else
const int inf=INT_MAX/2-100;
#endif
int topbit(signed t){
return t==0?-1:31-__builtin_clz(t);
}
int topbit(ll t){
return t==0?-1:63-__builtin_clzll(t);
}
int topbit(ull t){
return t==0?-1:63-__builtin_clzll(t);
}
int botbit(signed a){
return a==0?32:__builtin_ctz(a);
}
int botbit(ll a){
return a==0?64:__builtin_ctzll(a);
}
int botbit(ull a){
return a==0?64:__builtin_ctzll(a);
}
int popcount(signed t){
return __builtin_popcount(t);
}
int popcount(ll t){
return __builtin_popcountll(t);
}
int popcount(ull t){
return __builtin_popcountll(t);
}
int bitparity(ll t){
return __builtin_parityll(t);
}
bool ispow2(int i){
return i&&(i&-i)==i;
}
ll mask(int i){
return (ll(1)<<i)-1;
}
ull umask(int i){
return (ull(1)<<i)-1;
}
ll minp2(ll n){
if(n<=1)return 1;
else return ll(1)<<(topbit(n-1)+1);
}
bool inc(int a,int b,int c){
return a<=b&&b<=c;
}
template<class t> void mkuni(vc<t>&v){
sort(all(v));
v.erase(unique(all(v)),v.ed);
}
ll rand_int(ll l, ll r) { //[l, r]
//#ifdef LOCAL
static mt19937_64 gen;
/*#else
static mt19937_64 gen(chrono::steady_clock::now().time_since_epoch().count());
#endif*/
return uniform_int_distribution<ll>(l, r)(gen);
}
ll rand_int(ll k){ //[0,k)
return rand_int(0,k-1);
}
template<class t>
void myshuffle(vc<t>&a){
rep(i,si(a))swap(a[i],a[rand_int(0,i)]);
}
template<class t>
int lwb(const vc<t>&v,const t&a){
return lower_bound(all(v),a)-v.bg;
}
template<class t>
bool bis(const vc<t>&v,const t&a){
return binary_search(all(v),a);
}
vvc<int> readGraph(int n,int m){
vvc<int> g(n);
rep(i,m){
int a,b;
cin>>a>>b;
//sc.read(a,b);
a--;b--;
g[a].pb(b);
g[b].pb(a);
}
return g;
}
vvc<int> readTree(int n){
return readGraph(n,n-1);
}
template<class t>
vc<t> presum(const vc<t>&a){
vc<t> s(si(a)+1);
rep(i,si(a))s[i+1]=s[i]+a[i];
return s;
}
vc<ll> presum(const vi&a){
vc<ll> s(si(a)+1);
rep(i,si(a))s[i+1]=s[i]+a[i];
return s;
}
//BIT で数列を管理するときに使う (CF850C)
template<class t>
vc<t> predif(vc<t> a){
gnr(i,1,si(a))a[i]-=a[i-1];
return a;
}
template<class t>
vvc<ll> imos(const vvc<t>&a){
int n=si(a),m=si(a[0]);
vvc<ll> b(n+1,vc<ll>(m+1));
rep(i,n)rep(j,m)
b[i+1][j+1]=b[i+1][j]+b[i][j+1]-b[i][j]+a[i][j];
return b;
}
//verify してないや
void transvvc(int&n,int&m){
swap(n,m);
}
template<class t,class... Args>
void transvvc(int&n,int&m,vvc<t>&a,Args&...args){
assert(si(a)==n);
vvc<t> b(m,vi(n));
rep(i,n){
assert(si(a[i])==m);
rep(j,m)b[j][i]=a[i][j];
}
a.swap(b);
transvvc(n,m,args...);
}
//CF854E
void rotvvc(int&n,int&m){
swap(n,m);
}
template<class t,class... Args>
void rotvvc(int&n,int&m,vvc<t>&a,Args&...args){
assert(si(a)==n);
vvc<t> b(m,vi(n));
rep(i,n){
assert(si(a[i])==m);
rep(j,m)b[m-1-j][i]=a[i][j];
}
a.swap(b);
rotvvc(n,m,args...);
}
//ソートして i 番目が idx[i]
//CF850C
template<class t>
vi sortidx(const vc<t>&a){
int n=si(a);
vi idx(n);iota(all(idx),0);
sort(all(idx),[&](int i,int j){return a[i]<a[j];});
return idx;
}
//vs[i]=a[idx[i]]
//例えば sortidx で得た idx を使えば単にソート列になって返ってくる
//CF850C
template<class t>
vc<t> a_idx(const vc<t>&a,const vi&idx){
int n=si(a);
assert(si(idx)==n);
vc<t> vs(n);
rep(i,n)vs[i]=a[idx[i]];
return vs;
}
//CF850C
vi invperm(const vi&p){
int n=si(p);
vi q(n);
rep(i,n)q[p[i]]=i;
return q;
}
template<class t,class s=t>
s SUM(const vc<t>&a){
return accumulate(all(a),s(0));
}
template<class t>
t MAX(const vc<t>&a){
return *max_element(all(a));
}
template<class t>
pair<t,int> MAXi(const vc<t>&a){
auto itr=max_element(all(a));
return mp(*itr,itr-a.bg);
}
template<class t>
t MIN(const vc<t>&a){
return *min_element(all(a));
}
template<class t>
pair<t,int> MINi(const vc<t>&a){
auto itr=min_element(all(a));
return mp(*itr,itr-a.bg);
}
template<class t,class u>
pair<t,u> operator+(const pair<t,u>&a,const pair<t,u>&b){
return mp(a.a+b.a,a.b+b.b);
}
vi vid(int n){
vi res(n);iota(all(res),0);
return res;
}
template<class S>
S revv(S s){
reverse(all(s));
return s;
}
pi operator+(pi a,pi b){return pi(a.a+b.a,a.b+b.b);}
template<class t>
t gpp(vc<t>&vs){
assert(si(vs));
t res=move(vs.back());
vs.pop_back();
return res;
}
template<class t>
void pb(vc<t>&a,const vc<t>&b){
a.insert(a.ed,all(b));
}
template<class t>
vc<t> cat(vc<t> a,const vc<t>&b){
pb(a,b);
return a;
}
template<class t,class u>
vc<t>& operator+=(vc<t>&a,u x){
for(auto&v:a)v+=x;
return a;
}
template<class t,class u>
vc<t> operator+(vc<t> a,u x){
return a+=x;
}
template<class t,class u>
vc<t>& operator-=(vc<t>&a,u x){
for(auto&v:a)v-=x;
return a;
}
template<class t,class u>
vc<t>& operator-(vc<t> a,u x){
return a-=x;
}
//mint107 は verify してねえ
//#define DYNAMIC_MOD
struct modinfo{uint mod,root;
#ifdef DYNAMIC_MOD
constexpr modinfo(uint m,uint r):mod(m),root(r),im(0){set_mod(m);}
ull im;
constexpr void set_mod(uint m){
mod=m;
im=ull(-1)/m+1;
}
uint product(uint a,uint b)const{
ull z=ull(a)*b;
uint x=((unsigned __int128)z*im)>>64;
uint v=uint(z)-x*mod;
return v<mod?v:v+mod;
}
#endif
};
template<modinfo const&ref>
struct modular{
static constexpr uint const &mod=ref.mod;
static modular root(){return modular(ref.root);}
uint v;
//modular(initializer_list<uint>ls):v(*ls.bg){}
modular(ll vv=0){s(vv%mod+mod);}
modular& s(uint vv){
v=vv<mod?vv:vv-mod;
return *this;
}
modular operator-()const{return modular()-*this;}
modular& operator+=(const modular&rhs){return s(v+rhs.v);}
modular&operator-=(const modular&rhs){return s(v+mod-rhs.v);}
modular&operator*=(const modular&rhs){
#ifndef DYNAMIC_MOD
v=ull(v)*rhs.v%mod;
#else
v=ref.product(v,rhs.v);
#endif
return *this;
}
modular&operator/=(const modular&rhs){return *this*=rhs.inv();}
modular operator+(const modular&rhs)const{return modular(*this)+=rhs;}
modular operator-(const modular&rhs)const{return modular(*this)-=rhs;}
modular operator*(const modular&rhs)const{return modular(*this)*=rhs;}
modular operator/(const modular&rhs)const{return modular(*this)/=rhs;}
modular pow(ll n)const{
if(n<0)return inv().pow(-n);
modular res(1),x(*this);
while(n){
if(n&1)res*=x;
x*=x;
n>>=1;
}
return res;
}
modular inv()const{return pow(mod-2);}
/*modular inv()const{
int x,y;
int g=extgcd<ll>(v,mod,x,y);
assert(g==1);
if(x<0)x+=mod;
return modular(x);
}*/
friend modular operator+(ll x,const modular&y){
return modular(x)+y;
}
friend modular operator-(ll x,const modular&y){
return modular(x)-y;
}
friend modular operator*(ll x,const modular&y){
return modular(x)*y;
}
friend modular operator/(ll x,const modular&y){
return modular(x)/y;
}
friend ostream& operator<<(ostream&os,const modular&m){
return os<<m.v;
}
friend istream& operator>>(istream&is,modular&m){
ll x;is>>x;
m=modular(x);
return is;
}
bool operator<(const modular&r)const{return v<r.v;}
bool operator==(const modular&r)const{return v==r.v;}
bool operator!=(const modular&r)const{return v!=r.v;}
explicit operator bool()const{
return v;
}
};
#ifndef DYNAMIC_MOD
extern constexpr modinfo base{1000002022,3};
//extern constexpr modinfo base{1000000007,0};
//extern constexpr modinfo base{2147483579,0};//2^31 未満の最大の安全素数
//modinfo base{1,0};
#ifdef USE_GOOD_MOD
static_assert(base.mod==998244353);
#endif
#else
modinfo base(1,0);
extern constexpr modinfo base107(1000000007,0);
using mint107=modular<base107>;
#endif
using mint=modular<base>;
mint parity(int i){
return i%2==0?1:-1;
}
//atcoder-library をまあまあコピーして使っている
//N() が単位元
//merge で片方が inactive のときはもう片方をそのまま返す，
//といったときに，lazy の情報までコピーして渡さないようにする
//クエリできる点が[0,s)だったのを[0,n)に変えた (UCUP1-21D)
//ch,max_rightは動くと思う
//ちゃんと test してないから assert とかが壊れたらごめん
//VERIFY:
//https://atcoder.jp/contests/practice2/tasks/practice2_k
template<class N,bool Beats=false>
struct seglazy{
vc<N> x;
int n,L,s;
seglazy(){}
template<class T>
seglazy(const vc<T>& a){
n=a.size();
L=0;
while((1<<L)<n)L++;
s=1<<L;
x.resize(s*2);
rep(i,n)x[s+i]=N(a[i]);
gnr(i,1,s)upd(i);
}
seglazy(int nn){
n=nn;
L=0;
while((1<<L)<n)L++;
s=1<<L;
x.assign(s*2,N());
gnr(i,1,s)upd(i);
}
void upd(int i){
x[i]=N::merge(x[i*2],x[i*2+1]);
}
void push(int i){
x[i].push(x[i*2],x[i*2+1]);
}
N composite(int l,int r){
assert(0<=l&&l<=r&&r<=n);
if(l==r)return N();
l+=s;
r+=s;
for (int i = L; i >= 1; i--) {
if (((l >> i) << i) != l) push(l >> i);
if (((r >> i) << i) != r) push((r - 1) >> i);
}
N sml,smr;
while (l < r) {
if (l & 1) sml = N::merge(sml, x[l++]);
if (r & 1) smr = N::merge(x[--r], smr);
l >>= 1;
r >>= 1;
}
return N::merge(sml, smr);
}
//UCUP1-21 D
template<class F,class... Args>
void ch_beats(int i,F f,Args&&... args){
if((x[i].*f)(forward<Args>(args)...))return;
push(i);
ch_beats(i*2,f,forward<Args>(args)...);
ch_beats(i*2+1,f,forward<Args>(args)...);
upd(i);
}
template<class F,class... Args>
void ch(int l, int r, F f,Args&&... args) {
assert(0<=l&&l<=r&&r<=n);
if (l == r) return;
l+=s;
r+=s;
for (int i = L; i >= 1; i--) {
if (((l >> i) << i) != l) push(l >> i);
if (((r >> i) << i) != r) push((r - 1) >> i);
}
static int buf[2][30];
int cnt[2]{};
{
int l2 = l, r2 = r;
while (l < r) {
if (l & 1){
//(x[l++].*f)(forward<Args>(args)...);
buf[0][cnt[0]++]=l++;
}
if (r & 1){
//(x[--r].*f)(forward<Args>(args)...);
buf[1][cnt[1]++]=--r;
}
l >>= 1;
r >>= 1;
}
l = l2;
r = r2;
}
if constexpr(Beats){
rep(i,cnt[0])ch_beats(buf[0][i],f,forward<Args>(args)...);
per(i,cnt[1])ch_beats(buf[1][i],f,forward<Args>(args)...);
}else{
rep(i,cnt[0])(x[buf[0][i]].*f)(forward<Args>(args)...);
per(i,cnt[1])(x[buf[1][i]].*f)(forward<Args>(args)...);
}
for (int i = 1; i <= L; i++) {
if (((l >> i) << i) != l) upd(l >> i);
if (((r >> i) << i) != r) upd((r - 1) >> i);
}
}
template<class F,class... Args>
void chall(F f,Args&&... args){
if constexpr(Beats){
ch_beats(1,f,forward<Args>(args)...);
}else{
(x[1].*f)(forward<Args>(args)...);
}
}
N getall(){return x[1];}
template <class F,class... Args>
pair<int,N> max_right(int l,F f,Args&&... args){
assert(0<=l&&l<=n);
if(l==n)return mp(n,N());
l+=s;
for (int i = L; i >= 1; i--) push(l >> i);
N sm;
assert((sm.*f)(forward<Args>(args)...));
do {
while (l % 2 == 0) l >>= 1;
if (!(N::merge(sm,x[l]).*f)(forward<Args>(args)...)){
while (l < s) {
push(l);
l = (2 * l);
N tmp=N::merge(sm,x[l]);
if ((tmp.*f)(forward<Args>(args)...)) {
sm = tmp;
l++;
}
}
return mp(l - s,sm);
}
sm = N::merge(sm, x[l]);
l++;
} while ((l & -l) != l);
return mp(n,sm);
}
//XXI Opencup Krakow M
template <class F,class... Args>
pair<int,N> min_left(int r,F f,Args&&... args){
assert(0<=r&&r<=n);
if(r==0)return mp(0,N());
r+=s;
for (int i = L; i >= 1; i--) push((r - 1) >> i);
N sm;
do {
r--;
while (r > 1 && (r % 2)) r >>= 1;
if (!(N::merge(x[r],sm).*f)(forward<Args>(args)...)) {
while (r < s) {
push(r);
r = (2 * r + 1);
N tmp=N::merge(x[r],sm);
if ((tmp.*f)(forward<Args>(args)...)) {
sm = tmp;
r--;
}
}
return mp(r + 1 - s,sm);
}
sm = N::merge(x[r], sm);
} while ((r & -r) != r);
return mp(0,sm);
}
template<class F,class...Args>
void point_change(int p,F f,Args&&...args){
assert(0 <= p && p < n);
p += s;
for (int i = L; i >= 1; i--) push(p >> i);
(x[p].*f)(forward<Args>(args)...);
for (int i = 1; i <= L; i++) upd(p >> i);
}
void point_merge(int p,const N&t){
assert(0 <= p && p < n);
p += s;
for (int i = L; i >= 1; i--) push(p >> i);
x[p]=N::merge(x[p],t);
for (int i = 1; i <= L; i++) upd(p >> i);
}
N point_get(int p){
assert(0 <= p && p < n);
p += s;
for (int i = L; i >= 1; i--) push(p >> i);
return x[p];
}
void point_set(int p,N val){
assert(0 <= p && p < n);
p += s;
for (int i = L; i >= 1; i--) push(p >> i);
x[p]=val;
for (int i = 1; i <= L; i++) upd(p >> i);
}
void enumerater(int l,int r,int i,int b,int e,vc<N>&dst){
if(e<=l||r<=b)
return;
if(l+1==r){
dst.pb(x[i]);
return;
}
push(i);
int m=(l+r)/2;
enumerater(l,m,i*2,b,e,dst);
enumerater(m,r,i*2+1,b,e,dst);
}
void enumerate(int b,int e,vc<N>&dst){
assert(0<=b&&b<=e&&e<=n);
return enumerater(0,s,1,b,e,dst);
}
};
struct N{
mint v[2];
bool lz;
N():v{},lz(false){}
N(pair<mint,mint> ab):v{ab.a,ab.b},lz(false){}
void flip(){
swap(v[0],v[1]);
lz^=true;
}
void push(N&x,N&y){
if(lz){
x.flip();
y.flip();
}
lz=false;
}
static N merge(const N&x,const N&y){
N res;
rep(k,2)res.v[k]=x.v[k]+y.v[k];
return res;
}
};
bool dbg=false;
int off;
seglazy<N> seg;
void init(int n,int m,vi p,vi a){
off=n;
vvc<int> t(n+m);
rng(i,1,n+m)t[p[i]].pb(i);
vc<mint> prod(n+m);
per(i,n+m){
if(t[i].empty()){
prod[i]=1;
}else{
prod[i]=si(t[i]);
for(auto j:t[i])prod[i]*=prod[j];
}
}
vc<mint> dp(n+m);
dp[0]=1;
rep(i,n+m){
int s=si(t[i]);
vc<mint> pre(s+1,1);
vc<mint> suf(s+1,1);
rep(j,s)pre[j+1]=pre[j]*prod[t[i][j]];
per(j,s)suf[j]=suf[j+1]*prod[t[i][j]];
rep(j,s)dp[t[i][j]]=dp[i]*pre[j]*suf[j+1];
}
vc<pair<mint,mint>> ini(m);
rep(i,m){
if(a[i]==0)ini[i].a=dp[n+i];
if(a[i]==1)ini[i].b=dp[n+i];
}
seg=seglazy<N>(ini);
}
int count_ways(int l,int r){
l-=off;
r-=off;
r++;
seg.ch(l,r,&N::flip);
return seg.getall().v[1].v;
}
