#line 1 "verify/yosupo/data-structure/link-cut-tree/lazy-reversible-splay-tree/dynamic_sequence_range_affine_range_sum.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/dynamic_sequence_range_affine_range_sum"
#line 2 "template.hpp"
#include<bits/stdc++.h>
using namespace std;
using ll = long long;
using db = long double;
using i128 = __int128_t;
using u32 = uint32_t;
using u64 = uint64_t;
template<class T>
using PQ = priority_queue<T,vector<T>,greater<T>>;
const int INF=INT_MAX/2;
const ll LINF=LLONG_MAX/4;
const db DINF=numeric_limits<db>::infinity();
const db EPS=1e-9;
const db PI=acos(db(-1));
#define ALL(a) a.begin(),a.end()
#define RALL(a) a.rbegin(),a.rend()
#define SZ(a) (int)(a.size())
#define SORT(a) sort(ALL(a))
#define RSORT(a) sort(RALL(a))
#define REV(a) reverse(ALL(a))
#define UNI(a) a.erase(unique(ALL(a)),a.end())
#define LB(a,x) (int)(lower_bound(ALL(a),x)-a.begin())
#define UB(a,x) (int)(upper_bound(ALL(a),x)-a.begin())
#define FIND(a,x) (int)(find(ALL(a),x)-a.begin())
#define COUNT(a,x) (int)count(ALL(a),x)
#define MIN(a) *min_element(ALL(a))
#define MAX(a) *max_element(ALL(a))
template<class T,class U>
bool chmin(T &a,U b){return b<a?a=b,1:0;}
template<class T,class U>
bool chmax(T &a,U b){return a<b?a=b,1:0;}
template<class T>
T floor(T a,T b){return a/b-((a^b)<0&&a%b);}
template<class T>
T ceil(T a,T b){return a/b+((a^b)>=0&&a%b);}
int popcnt(ll x){return __builtin_popcountll(x);}
int topbit(ll x){return x==0?-1:63-__builtin_clzll(x);}
int lowbit(ll x){return x==0?-1:__builtin_ctzll(x);}
template<class T,class U>
T SUM(const U &a){return accumulate(ALL(a),T{});}
template<class T>
vector<int> argsort(const vector<T> &a){
vector<int> p(SZ(a));
iota(ALL(p),0);
stable_sort(ALL(p),[&](int i,int j){return a[i]<a[j];});
return p;
}
template<class T,size_t D=0>
struct VecBuilder{
array<size_t,D> d;
VecBuilder<T,D+1> operator[](size_t n)const{
VecBuilder<T,D+1> res{};
for(size_t i=0;i<D;i++)res.d[i]=d[i];
res.d[D]=n;
return res;
}
template<size_t I=0>
auto build(const T &x)const{
if constexpr(I+1==D)return vector<T>(d[I],x);
else return vector<decltype(build<I+1>(x))>(d[I],build<I+1>(x));
}
auto operator()(const T &x=T())const{
static_assert(D>0);
return build(x);
}
};
template<class T>
inline constexpr VecBuilder<T> VEC{};
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
mt19937_64 rng64(chrono::steady_clock::now().time_since_epoch().count());
#line 2 "modular-arithmetic/modint.hpp"
/**
* Author: Teetat T.
* Date: 2026-04-15
* Description: modular arithmetic operations
*/
template<int mod,int root=0>
struct ModInt{
using mint = ModInt;
static_assert(mod>0,"mod must be positive");
int x;
constexpr ModInt():x(0){}
constexpr ModInt(ll x):x((x%=mod)<0?x+mod:x){}
constexpr explicit operator int()const{return x;}
constexpr int val()const{return x;}
constexpr static int get_mod(){return mod;}
constexpr static mint get_root(){return mint(root);}
constexpr mint operator-()const{
mint res;
res.x=x?mod-x:0;
return res;
}
constexpr mint operator+()const{return *this;}
constexpr mint inv()const{
int a=x,b=mod,u=1,v=0,q=0;
while(b>0){
q=a/b;
swap(a-=q*b,b);
swap(u-=q*v,v);
}
return mint(u);
}
constexpr mint pow(ll n)const{
mint res=1,a=*this;
for(;n>0;a*=a,n>>=1)if(n&1)res*=a;
return res;
}
constexpr mint &operator+=(const mint &o){
if((x+=o.x)>=mod)x-=mod;
return *this;
}
constexpr mint &operator-=(const mint &o){
if((x-=o.x)<0)x+=mod;
return *this;
}
constexpr mint &operator*=(const mint &o){
x=(ll(x)*o.x)%mod;
return *this;
}
constexpr mint &operator/=(const mint &o){
return *this*=o.inv();
}
constexpr mint operator+(const mint &o)const{return mint(*this)+=o;}
constexpr mint operator-(const mint &o)const{return mint(*this)-=o;}
constexpr mint operator*(const mint &o)const{return mint(*this)*=o;}
constexpr mint operator/(const mint &o)const{return mint(*this)/=o;}
constexpr mint &operator++(){return *this+=mint(1);}
constexpr mint &operator--(){return *this-=mint(1);}
constexpr mint operator++(int){mint res=*this;*this+=mint(1);return res;}
constexpr mint operator--(int){mint res=*this;*this-=mint(1);return res;}
constexpr bool operator==(const mint &o)const{return x==o.x;}
constexpr bool operator!=(const mint &o)const{return x!=o.x;}
constexpr bool operator<(const mint &o)const{return x<o.x;}
friend istream &operator>>(istream &is,mint &o){ll x{};is>>x;o=mint(x);return is;}
friend ostream &operator<<(ostream &os,const mint &o){return os<<o.x;}
};
using mint998 = ModInt<998244353,3>;
using mint107 = ModInt<1000000007>;
#line 2 "data-structure/link-cut-tree/splay-tree-base.hpp"
/**
* Author: Teetat T.
* Date: 2024-04-13
* Description: Splay Tree. splay(u) will make node u be the root of the tree in amortized O(log n) time.
*/
template<class Node>
struct SplayTreeBase{
using Ptr = Node*;
bool is_root(Ptr t){
return !(t->p)||(t->p->l!=t&&t->p->r!=t);
} // The parent of the root stores the path parant in link cut tree.
int size(Ptr t){
return t?t->size:0;
}
virtual void push(Ptr t){};
virtual void pull(Ptr t){};
int pos(Ptr t){
if(t->p){
if(t->p->l==t)return -1;
if(t->p->r==t)return 1;
}
return 0;
}
void rotate(Ptr t){
Ptr x=t->p,y=x->p;
if(pos(t)==-1){
if((x->l=t->r))t->r->p=x;
t->r=x,x->p=t;
}else{
if((x->r=t->l))t->l->p=x;
t->l=x,x->p=t;
}
pull(x),pull(t);
if((t->p=y)){
if(y->l==x)y->l=t;
if(y->r==x)y->r=t;
}
}
void splay(Ptr t){
if(!t)return;
push(t);
while(!is_root(t)){
Ptr x=t->p;
if(is_root(x)){
push(x),push(t);
rotate(t);
}else{
Ptr y=x->p;
push(y),push(x),push(t);
if(pos(x)==pos(t))rotate(x),rotate(t);
else rotate(t),rotate(t);
}
}
}
void splay_kth(Ptr &t,int k){
assert(0<=k&&k<size(t));
while(true){
push(t);
if(k<size(t->l))t=t->l;
else if(size(t->l)==k)break;
else{
k-=size(t->l)+1;
t=t->r;
}
}
splay(t);
}
Ptr get_first(Ptr t){
while(t->l)push(t),t=t->l;
splay(t);
return t;
}
Ptr get_last(Ptr t){
while(t->r)push(t),t=t->r;
splay(t);
return t;
}
Ptr merge(Ptr l,Ptr r){
splay(l),splay(r);
if(!l)return r;
if(!r)return l;
l=get_last(l);
l->r=r;
r->p=l;
pull(l);
return l;
}
pair<Ptr,Ptr> split(Ptr t,int k){
if(!t)return {nullptr,nullptr};
if(k==0)return {nullptr,t};
if(k==size(t))return {t,nullptr};
splay_kth(t,k-1);
Ptr x=t->r;
t->r=x->p=nullptr;
pull(t);
return {t,x};
}
void insert(Ptr &t,int k,Ptr v){
splay(t);
auto x=split(t,k);
t=merge(merge(x.first,v),x.second);
}
void erase(Ptr &t,int k){
splay(t);
auto x=split(t,k);
auto y=split(x.second,1);
// delete y.first;
t=merge(x.first,y.second);
}
template<class T>
Ptr build(const vector<T> &v){
if(v.empty())return nullptr;
function<Ptr(int,int)> build=[&](int l,int r){
if(l==r)return new Node(v[l]);
int m=(l+r)/2;
return merge(build(l,m),build(m+1,r));
};
return build(0,v.size()-1);
}
};
#line 2 "data-structure/link-cut-tree/lazy-reversible-bbst.hpp"
/**
* Author: Teetat Info.
* Date: 2024-04-13
* Description: Lazy Reversible BBST Base.
*/
template<class Tree,class Node,class MonoidAction>
struct LazyReversibleBBST:Tree{
using Tree::merge;
using Tree::split;
using typename Tree::Ptr;
using InfoMonoid = typename MonoidAction::InfoMonoid;
using TagMonoid = typename MonoidAction::TagMonoid;
using Info = typename MonoidAction::Info;
using Tag = typename MonoidAction::Tag;
LazyReversibleBBST()=default;
Info sum(Ptr t){
return t?t->sum:InfoMonoid::unit();
}
void pull(Ptr t){
if(!t)return;
push(t);
t->size=1;
t->sum=t->val;
t->revsum=t->val;
if(t->l){
t->size+=t->l->size;
t->sum=InfoMonoid::op(t->l->sum,t->sum);
t->revsum=InfoMonoid::op(t->revsum,t->l->revsum);
}
if(t->r){
t->size+=t->r->size;
t->sum=InfoMonoid::op(t->sum,t->r->sum);
t->revsum=InfoMonoid::op(t->r->revsum,t->revsum);
}
}
void push(Ptr t){
if(!t)return;
if(t->rev){
toggle(t->l);
toggle(t->r);
t->rev=false;
}
if(t->lz!=TagMonoid::unit()){
propagate(t->l,t->lz);
propagate(t->r,t->lz);
t->lz=TagMonoid::unit();
}
}
void toggle(Ptr t){
if(!t)return;
swap(t->l,t->r);
swap(t->sum,t->revsum);
t->rev^=true;
}
void propagate(Ptr t,const Tag &v){
if(!t)return;
t->val=MonoidAction::op(t->val,v);
t->sum=MonoidAction::op(t->sum,v);
t->revsum=MonoidAction::op(t->revsum,v);
t->lz=TagMonoid::op(t->lz,v);
}
void apply(Ptr &t,int l,int r,const Tag &v){
if(l>r)return;
auto x=split(t,l);
auto y=split(x.second,r-l+1);
propagate(y.first,v);
t=merge(x.first,merge(y.first,y.second));
}
Info query(Ptr &t,int l,int r){
if(l>r)return InfoMonoid::unit();
auto x=split(t,l);
auto y=split(x.second,r-l+1);
Info res=sum(y.first);
t=merge(x.first,merge(y.first,y.second));
return res;
}
void reverse(Ptr &t,int l,int r){
if(l>r)return;
auto x=split(t,l);
auto y=split(x.second,r-l+1);
toggle(y.first);
t=merge(x.first,merge(y.first,y.second));
}
};
#line 4 "data-structure/link-cut-tree/lazy-reversible-splay-tree.hpp"
/**
* Author: Teetat T.
* Date: 2024-04-13
* Description: Lazy Reversible Splay Tree.
*/
template<class MonoidAction>
struct LazyReversibleSplayTreeNode{
using Ptr = LazyReversibleSplayTreeNode*;
using InfoMonoid = typename MonoidAction::InfoMonoid;
using TagMonoid = typename MonoidAction::TagMonoid;
using Info = typename MonoidAction::Info;
using Tag = typename MonoidAction::Tag;
using value_type = Info;
Ptr l,r,p;
Info val,sum,revsum;
Tag lz;
int size;
bool rev;
LazyReversibleSplayTreeNode(const Info &_val=InfoMonoid::unit(),const Tag &_lz=TagMonoid::unit())
:l(),r(),p(),val(_val),sum(_val),revsum(_val),lz(_lz),size(1),rev(false){}
};
template<class MonoidAction>
struct LazyReversibleSplayTree
: LazyReversibleBBST<SplayTreeBase<LazyReversibleSplayTreeNode<MonoidAction>>,
LazyReversibleSplayTreeNode<MonoidAction>,MonoidAction>{
using Node = LazyReversibleSplayTreeNode<MonoidAction>;
};
#line 2 "group/monoid/affine.hpp"
/**
* Author: Teetat T.
* Date: 2024-04-14
* Description: Affine Transformation Monoid class.
*/
template<class T>
struct AffineMonoid{
using P = pair<T,T>;
using value_type = P;
static constexpr P op(const P &x,const P &y){
return P(x.first*y.first,x.second*y.first+y.second);
}
static constexpr P unit(){return P(T(1),T(0));}
static constexpr T eval(const P &f,const T &x){
return f.first*x+f.second;
}
};
#line 2 "group/monoid/add-count.hpp"
/**
* Author: Teetat T.
* Date: 2024-04-14
* Description: Add & Count Monoid class.
*/
template<class T>
struct AddCountMonoid{
using P = pair<T,ll>;
using value_type = P;
static constexpr P op(const P &x,const P &y){
return P(x.first+y.first,x.second+y.second);
}
static constexpr P inverse(const P &x){return P(-x.first,-x.second);}
static constexpr P unit(){return P(T(0),0LL);}
static constexpr P make(const T &x){return P(x,1LL);}
};
#line 4 "group/monoid-action/add-count-affine.hpp"
/**
* Author: Teetat T.
* Date: 2024-04-14
* Description: Affine to Add & Count Action class.
*/
template<class T>
struct AddCountAffineAction{
using InfoMonoid = AddCountMonoid<T>;
using TagMonoid = AffineMonoid<T>;
using Info = typename InfoMonoid::value_type;
using Tag = typename TagMonoid::value_type;
static constexpr Info op(const Info &a,const Tag &b){
return Info(a.first*b.first+T(a.second)*b.second,a.second);
}
};
#line 6 "verify/yosupo/data-structure/link-cut-tree/lazy-reversible-splay-tree/dynamic_sequence_range_affine_range_sum.test.cpp"
using mint = mint998;
using Action = AddCountAffineAction<mint>;
using Info = Action::Info;
using Tag = Action::Tag;
int main(){
cin.tie(nullptr)->sync_with_stdio(false);
int n,q;
cin >> n >> q;
vector<Info> a(n);
for(auto &[x,y]:a)cin >> x,y=1;
using Tree = LazyReversibleSplayTree<Action>;
using Node = Tree::Node;
using Ptr = Node*;
Tree s;
Ptr root=s.build(a);
while(q--){
int op;
cin >> op;
if(op==0){
int i;
mint x;
cin >> i >> x;
s.insert(root,i,new Node(Info(x,1)));
}else if(op==1){
int i;
cin >> i;
s.erase(root,i);
}else if(op==2){
int l,r;
cin >> l >> r;
s.reverse(root,l,r-1);
}else if(op==3){
int l,r;
mint b,c;
cin >> l >> r >> b >> c;
s.apply(root,l,r-1,Tag(b,c));
}else{
int l,r;
cin >> l >> r;
cout << s.query(root,l,r-1).first << "\n";
}
}
}
verify/yosupo/data-structure/link-cut-tree/lazy-reversible-splay-tree/dynamic_sequence_range_affine_range_sum.test.cpp