Problem: You are given an array a_0, a_1, ..., a_{N-1} of length N. Process Q queries of the following types.

* `0 l r b c`: For each i = l, l+1, \dots, {r - 1}, set a_i \gets b \times a_i + c.
* `1 l r`: Print \sum_{i = l}^{r - 1} a_i \bmod 998244353.

Constraints

* 1 \leq N, Q \leq 500000
* 0 \leq a_i, c < 998244353
* 1 \leq b < 998244353
* 0 \leq l < r \leq N
* All values in Input are integer.

Input

Input is given from Standard Input in the following format:


N Q
a_0 a_1 ... a_{N - 1}
\textrm{Query}_0
\textrm{Query}_1
:
\textrm{Query}_{Q - 1}


Output

For each query of the latter type, print the answer.

Example

Input

5 7
1 2 3 4 5
1 0 5
0 2 4 100 101
1 0 3
0 1 3 102 103
1 2 5
0 2 5 104 105
1 0 5


Output

15
404
41511
4317767

Solution (in CPP):

Solution:
#include<iostream>
using namespace std;
#include<vector>
#include<functional>
template<typename T>
struct lazysegtree{
	using F=function<T(T,T)>;
	using G=function<T(T,T,int,int)>;
	const F calcfn,lazycalcfn;
	const G updatefn;
	int n;
	T defvalue,lazydefvalue;
	vector<T>dat,lazy;
	vector<bool>lazyflag;
	lazysegtree(int n_=0,T defvalue_=0,
		const F calcfn_=[](T a,T b){return a+b;},
		const F lazycalcfn_=[](T a,T b){return a+b;},
		const G updatefn_=[](T a,T b,int l,int r){return a+b*(r-l);},
		T lazydefvalue_=0
	):defvalue(defvalue_),lazydefvalue(lazydefvalue_),
		calcfn(calcfn_),lazycalcfn(lazycalcfn_),updatefn(updatefn_)
	{
		n=1;
		while(n<n_)n<<=1;
		dat.assign(2*n-1,defvalue);
		lazy.assign(2*n-1,lazydefvalue);
		lazyflag.assign(2*n-1,false);
	}
	void copy(const vector<T>&v)
	{
		for(int i=0;i<v.size();i++)dat[i+n-1]=v[i];
		for(int i=n-2;i>=0;i--)dat[i]=calcfn(dat[2*i+1],dat[2*i+2]);
	}
	void eval(int i,int l,int r)
	{
		if(lazyflag[i])
		{
			dat[i]=updatefn(dat[i],lazy[i],l,r);
			if(r-l>1)
			{
				lazy[2*i+1]=lazycalcfn(lazy[2*i+1],lazy[i]);
				lazy[2*i+2]=lazycalcfn(lazy[2*i+2],lazy[i]);
				lazyflag[2*i+1]=lazyflag[2*i+2]=true;
			}
			lazy[i]=lazydefvalue;
			lazyflag[i]=false;
		}
	}
	void update(int a,int b,T x,int k=0,int l=0,int r=-1)//[a,b)
	{
		if(r<0)r=n;
		eval(k,l,r);
		if(b<=l||r<=a)return;
		else if(a<=l&&r<=b)
		{
			lazy[k]=lazycalcfn(lazy[k],x);
			lazyflag[k]=true;
			eval(k,l,r);
		}
		else
		{
			update(a,b,x,2*k+1,l,(l+r)/2);
			update(a,b,x,2*k+2,(l+r)/2,r);
			dat[k]=calcfn(dat[2*k+1],dat[2*k+2]);
		}
	}
	T query(int a,int b,int k=0,int l=0,int r=-1)//[a,b)
	{
		if(r<0)r=n;
		eval(k,l,r);
		if(b<=l||r<=a)return defvalue;
		else if(a<=l&&r<=b)return dat[k];
		else return calcfn(
			query(a,b,2*k+1,l,(l+r)/2),
			query(a,b,2*k+2,(l+r)/2,r)
		);
	}
};
const long mod=998244353;
int main()
{
	int N,Q;
	cin>>N>>Q;
	lazysegtree<pair<long,long> >P(N,make_pair(0,0),
		[](pair<long,long>a,pair<long,long>b){return make_pair((a.first+b.first)%mod,0);},
		[](pair<long,long>a,pair<long,long>b){return make_pair(a.first*b.first%mod,(a.second*b.first+b.second)%mod);},
		[](pair<long,long>a,pair<long,long>b,int l,int r){return make_pair((a.first*b.first%mod+b.second*(r-l)%mod)%mod,0);},
	make_pair(1,0));
	vector<pair<long,long> >A(N);
	for(int i=0;i<N;i++)cin>>A[i].first;
	P.copy(A);
	for(int i=0;i<Q;i++)
	{
		int t,l,r;cin>>t>>l>>r;
		if(t==0)
		{
			pair<long,long>q;cin>>q.first>>q.second;
			P.update(l,r,q);
		}
		else
		{
			cout<<P.query(l,r).first<<endl;
		}
	}
}