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:
// includes
#include <bits/stdc++.h>
using namespace std;

// macros
#define pb emplace_back
#define mk make_pair
#define FOR(i, a, b) for(int i=(a);i<(b);++i)
#define rep(i, n) FOR(i, 0, n)
#define rrep(i, n) for(int i=((int)(n)-1);i>=0;i--)
#define irep(itr, st) for(auto itr = (st).begin(); itr != (st).end(); ++itr)
#define irrep(itr, st) for(auto itr = (st).rbegin(); itr != (st).rend(); ++itr)
#define whole(x) (x).begin(),(x).end()
#define sz(x) ((int)(x).size())
#define bit(n) (1LL<<(n))
#define F first
#define S second
// functions
template <typename T> void unique(T& c){c.erase(std::unique(c.begin(), c.end()), c.end());}
template <class T>bool chmax(T &a, const T &b){if(a < b){a = b; return 1;} return 0;}
template <class T>bool chmin(T &a, const T &b){if(a > b){a = b; return 1;} return 0;}
template <typename T> istream &operator>>(istream &is, vector<T> &vec){for(auto &v: vec)is >> v; return is;}
template <typename T> ostream &operator<<(ostream &os, const vector<T>& vec){for(int i = 0; i < vec.size(); i++){ os << vec[i]; if(i + 1 != vec.size())os << " ";} return os;}
template <typename T> ostream &operator<<(ostream &os, const set<T>& st){for(auto itr = st.begin(); itr != st.end(); ++itr){ os << *itr; auto titr = itr; if(++titr != st.end())os << " ";} return os;}
template <typename T> ostream &operator<<(ostream &os, const unordered_set<T>& st){for(auto itr = st.begin(); itr != st.end(); ++itr){ os << *itr; auto titr = itr; if(++titr != st.end())os << " ";} return os;}
template <typename T> ostream &operator<<(ostream &os, const multiset<T>& st){for(auto itr = st.begin(); itr != st.end(); ++itr){ os << *itr; auto titr = itr; if(++titr != st.end())os << " ";} return os;}
template <typename T> ostream &operator<<(ostream &os, const unordered_multiset<T>& st){for(auto itr = st.begin(); itr != st.end(); ++itr){ os << *itr; auto titr = itr; if(++titr != st.end())os << " ";} return os;}
template <typename T1, typename T2> ostream &operator<<(ostream &os, const pair<T1, T2> &p){os << "(" << p.first << ", " << p.second << ")"; return os;}
template <typename T1, typename T2> ostream &operator<<(ostream &os, const map<T1, T2> &mp){for(auto itr = mp.begin(); itr != mp.end(); ++itr){ os << "(" << itr->first << ", " << itr->second << ")"; auto titr = itr; if(++titr != mp.end())os << " "; } return os;}
template <typename T1, typename T2> ostream &operator<<(ostream &os, const unordered_map<T1, T2> &mp){for(auto itr = mp.begin(); itr != mp.end(); ++itr){ os << "(" << itr->first << ", " << itr->second << ")"; auto titr = itr; if(++titr != mp.end())os << " "; } return os;}
//  types
using ll = long long int;
using P = pair<int, int>;
// constants
const int inf = 1e9;
const ll linf = 1LL << 60;
const double EPS = 1e-10;
const int mod = 998244353;
const int dx[4] = {-1, 0, 1, 0};
const int dy[4] = {0, -1, 0, 1};
// io
struct fast_io{
  fast_io(){ios_base::sync_with_stdio(false); cin.tie(nullptr); cout << fixed << setprecision(20);}
} fast_io_;

template <typename Monoid>
class LazySegmentTree{
  public:
    using T = typename Monoid::value_type;
    using E = typename Monoid::lazy_type;
    int n;
    T identity;
    E lazy_def;
    vector<T> val;
    vector<E> lazy;

    LazySegmentTree(){}
    LazySegmentTree(int n_, vector<T> v=vector<T>()){
      identity = Monoid::identity;
      lazy_def = Monoid::lazy_def;
      n = 1;
      while(n < n_)n *= 2;
      val.assign(2*n-1, identity);
      lazy.assign(2*n-1, lazy_def);

      for(size_t i = 0; i < v.size(); i++){
        val[i+n-1] = v[i];
      }
      for(int i = n - 2; i >= 0; i--){
        val[i] = Monoid::operation(val[2*i+1], val[2*i+2]);
      }
    }
    void eval(int k, int len){
      if(lazy[k] == lazy_def)return;
      if(k < n - 1){
        lazy[2*k+1] = Monoid::lazy_accumulate(lazy[2*k+1], lazy[k]);
        lazy[2*k+2] = Monoid::lazy_accumulate(lazy[2*k+2], lazy[k]);
      }
      val[k] = Monoid::lazy_update(val[k], lazy[k], len);
      lazy[k] = lazy_def;
    }
    T update(int a,int b, E &e, int k, int l, int r){
      eval(k, r - l);
      if(r <= a || b <= l)return val[k];
      else if(a <= l && r <= b){
        lazy[k] = Monoid::lazy_accumulate(lazy[k], e);
        eval(k, r - l);
        return val[k];
      }else{
        T lv = update(a, b, e, 2*k+1, l, (l+r)/2);
        T rv = update(a, b, e, 2*k+2, (l+r)/2, r);
        return val[k] = Monoid::operation(lv, rv);
      }
    }
    T update(int a, int b, E e){
      return update(a, b, e, 0, 0, n);
    }
    T query(int a, int b, int k, int l, int r){
      eval(k, r - l);
      if(r <= a || b <= l)return identity;
      if(a <= l && r <= b)return val[k];
      T lv = query(a, b, 2*k+1, l, (l+r)/2);
      T rv = query(a, b, 2*k+2, (l+r)/2, r);
      return Monoid::operation(lv, rv);
    }
    T query(int a, int b){
      return query(a, b, 0, 0, n);
    }
    T get(int i){
      return query(i, i + 1);
    }
};

template <typename T, typename E>
class RSQRUQ{
  public:
    using value_type = T;
    using lazy_type = E;
    const static T identity;
    const static E lazy_def;
    RSQRUQ(){}
    static T operation(T &l, T &r){
      return (l + r) % mod;
    }
    static E lazy_accumulate(E &l, E &r){
      if(l == lazy_def)return r;
      return mk(r.first * l.first % mod, (r.first * l.second % mod + r.second) % mod);
    }
    static T lazy_update(T &t, E &e, int len){
      return (t * e.first % mod + e.second * len % mod) % mod;
    }
};
// b(dx + e) + c = bd x + be + c

template <typename T, typename E>
const T RSQRUQ<T, E>::identity = 0;
//template <typename T, typename E>
//const E RSQRUQ<T, E>::lazy_def = numeric_limits<E>::min();
template<>
const pair<ll, ll> RSQRUQ<ll, pair<ll, ll>>::lazy_def = mk(-1, -1);


int main(int argc, char const* argv[])
{
  int n, q; cin >> n >> q;
  vector<ll> a(n); cin >> a;
  LazySegmentTree<RSQRUQ<ll, pair<ll, ll>>> seg(n, a);
  rep(i, q){
    /*
    cout << "-------------" << endl;
    rep(j, sz(seg.val)){
      if(j == 1 || j == 3 || j == 7 || j == 15)cout << endl;
      cout << seg.val[j] << " ";
    }
    cout << endl;
    rep(j, sz(seg.lazy)){
      if(j == 1 || j == 3 || j == 7 || j == 15)cout << endl;
      cout << seg.lazy[j] << " ";
    }
    cout << endl;
    cout << "-------------" << endl;
    */
    int t; cin >> t;
    if(t == 0){
      int l, r; cin >> l >> r;
      ll b, c; cin >> b >> c;
      seg.update(l, r, mk(b, c));
    }else{
      int l, r; cin >> l >> r;
      //cout << seg.query(l, r) << "\n";
      cout << seg.query(l, r) << "\n";
    }
  }
  cout << flush;
  return 0;
}