Problem:
Score : 100 points

Problem Statement

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.

Sample Input 1

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

Sample Output 1

15
404
41511
4317767

Solution in C++ (GCC 9.2.1 with AC Library v1.1) (judge verdict: Accepted)

/* #region header */
#ifdef LOCAL
#include "cxx-prettyprint-master/prettyprint.hpp"
#define debug(x) cout << x << endl
#else
#define debug(...) 42
#endif

#pragma GCC optimize("Ofast")
#include <bits/stdc++.h>
using namespace std;
#include <atcoder/all>
// types
using ll = long long;
using ull = unsigned long long;
using ld = long double;
typedef pair<ll, ll> Pl;
typedef pair<int, int> Pi;
typedef vector<ll> vl;
typedef vector<int> vi;
typedef vector<char> vc;
template <typename T>
using mat = vector<vector<T>>;
typedef vector<vector<int>> vvi;
typedef vector<vector<long long>> vvl;
typedef vector<vector<char>> vvc;
template <int mod>
struct modint {
    int x;

    modint() : x(0) {}

    modint(int64_t y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {}

    modint& operator+=(const modint& p) {
        if ((x += p.x) >= mod) x -= mod;
        return *this;
    }

    modint& operator-=(const modint& p) {
        if ((x += mod - p.x) >= mod) x -= mod;
        return *this;
    }

    modint& operator*=(const modint& p) {
        x = (int)(1LL * x * p.x % mod);
        return *this;
    }

    modint& operator/=(const modint& p) {
        *this *= p.inverse();
        return *this;
    }

    modint operator-() const { return modint(-x); }

    modint operator+(const modint& p) const { return modint(*this) += p; }

    modint operator-(const modint& p) const { return modint(*this) -= p; }

    modint operator*(const modint& p) const { return modint(*this) *= p; }

    modint operator/(const modint& p) const { return modint(*this) /= p; }

    bool operator==(const modint& p) const { return x == p.x; }

    bool operator!=(const modint& p) const { return x != p.x; }

    modint inverse() const {
        int a = x, b = mod, u = 1, v = 0, t;
        while (b > 0) {
            t = a / b;
            swap(a -= t * b, b);
            swap(u -= t * v, v);
        }
        return modint(u);
    }

    modint pow(int64_t n) const {
        modint ret(1), mul(x);
        while (n > 0) {
            if (n & 1) ret *= mul;
            mul *= mul;
            n >>= 1;
        }
        return ret;
    }

    friend ostream& operator<<(ostream& os, const modint& p) {
        return os << p.x;
    }

    friend istream& operator>>(istream& is, modint& a) {
        int64_t t;
        is >> t;
        a = modint<mod>(t);
        return (is);
    }

    static int get_mod() { return mod; }
};
// abreviations
#define all(x) (x).begin(), (x).end()
#define rall(x) (x).rbegin(), (x).rend()
#define rep_(i, a_, b_, a, b, ...) for (ll i = (a), max_i = (b); i < max_i; i++)
#define rep(i, ...) rep_(i, __VA_ARGS__, __VA_ARGS__, 0, __VA_ARGS__)
#define rrep_(i, a_, b_, a, b, ...) \
    for (ll i = (b - 1), min_i = (a); i >= min_i; i--)
#define rrep(i, ...) rrep_(i, __VA_ARGS__, __VA_ARGS__, 0, __VA_ARGS__)
#define srep(i, a, b, c) for (ll i = (a), max_i = (b); i < max_i; i += c)
#define SZ(x) ((int)(x).size())
#define pb(x) push_back(x)
#define eb(x) emplace_back(x)
#define mp make_pair
//入出力
#define print(x) cout << x << endl
template <class T>
ostream& operator<<(ostream& os, const vector<T>& v) {
    for (auto& e : v) cout << e << " ";
    cout << endl;
    return os;
}
void scan(int& a) { cin >> a; }
void scan(long long& a) { cin >> a; }
void scan(char& a) { cin >> a; }
void scan(double& a) { cin >> a; }
void scan(string& a) { cin >> a; }
template <class T>
void scan(vector<T>& a) {
    for (auto& i : a) scan(i);
}
#define vsum(x) accumulate(all(x), 0LL)
#define vmax(a) *max_element(all(a))
#define vmin(a) *min_element(all(a))
#define lb(c, x) distance((c).begin(), lower_bound(all(c), (x)))
#define ub(c, x) distance((c).begin(), upper_bound(all(c), (x)))
// functions
// gcd(0, x) fails.
ll gcd(ll a, ll b) { return b ? gcd(b, a % b) : a; }
ll lcm(ll a, ll b) { return a / gcd(a, b) * b; }
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 (b < a) {
        a = b;
        return 1;
    }
    return 0;
}
template <typename T>
T mypow(T x, ll n) {
    T ret = 1;
    while (n > 0) {
        if (n & 1) (ret *= x);
        (x *= x);
        n >>= 1;
    }
    return ret;
}
ll modpow(ll x, ll n, const ll mod) {
    ll ret = 1;
    while (n > 0) {
        if (n & 1) (ret *= x);
        (x *= x);
        n >>= 1;
        x %= mod;
        ret %= mod;
    }
    return ret;
}
template <typename T>
uint64_t my_rand(void) {
    static uint64_t x = 88172645463325252ULL;
    x = x ^ (x << 13);
    x = x ^ (x >> 7);
    return x = x ^ (x << 17);
}
int popcnt(ull x) { return __builtin_popcountll(x); }
// graph template
template <typename T>
struct edge {
    int src, to;
    T cost;

    edge(int to, T cost) : src(-1), to(to), cost(cost) {}

    edge(int src, int to, T cost) : src(src), to(to), cost(cost) {}

    edge& operator=(const int& x) {
        to = x;
        return *this;
    }

    bool operator<(const edge<T>& r) const { return cost < r.cost; }

    operator int() const { return to; }
};
template <typename T>
using Edges = vector<edge<T>>;
template <typename T>
using WeightedGraph = vector<Edges<T>>;
using UnWeightedGraph = vector<vector<int>>;
struct Timer {
    clock_t start_time;
    void start() { start_time = clock(); }
    int lap() {
        // return x ms.
        return (clock() - start_time) * 1000 / CLOCKS_PER_SEC;
    }
};
/* #endregion*/
// constant
#define inf 4000000000ll
#define INF 4000000004000000000LL
#define mod 998244353ll
using mint = modint<mod>;
typedef vector<mint> vmint;
typedef vector<vector<mint>> vvmint;
#define endl '\n'
const long double eps = 0.000000000000001;
const long double PI = 3.141592653589793;
// library
/**
 * @brief Lazy-Segment-Tree(遅延伝搬セグメント木)
 * @docs docs/lazy-segment-tree.md
 */
template <typename Monoid, typename OperatorMonoid>
struct LazySegmentTree {
    int n, sz, height;
    vector<Monoid> data;
    vector<OperatorMonoid> lazy;
    using F = function<Monoid(Monoid, Monoid)>;
    using G = function<Monoid(Monoid, OperatorMonoid)>;
    using H = function<OperatorMonoid(OperatorMonoid, OperatorMonoid)>;
    const F f;
    const G g;
    const H h;
    const Monoid M1;
    const OperatorMonoid OM0;

    LazySegmentTree(int n, const F f, const G g, const H h, const Monoid& M1,
                    const OperatorMonoid OM0)
        : n(n), f(f), g(g), h(h), M1(M1), OM0(OM0) {
        sz = 1;
        height = 0;
        while (sz < n) sz <<= 1, height++;
        data.assign(2 * sz, M1);
        lazy.assign(2 * sz, OM0);
    }

    void set(int k, const Monoid& x) { data[k + sz] = x; }

    void build() {
        for (int k = sz - 1; k > 0; k--) {
            data[k] = f(data[2 * k + 0], data[2 * k + 1]);
        }
    }

    inline void propagate(int k) {
        lazy[2 * k + 0] = h(lazy[2 * k + 0], lazy[k]);
        lazy[2 * k + 1] = h(lazy[2 * k + 1], lazy[k]);
        data[k] = apply(k);
        lazy[k] = OM0;
    }

    inline Monoid apply(int k) { return g(data[k], lazy[k]); }

    inline void recalc(int k) {
        while (k >>= 1) data[k] = f(apply(2 * k + 0), apply(2 * k + 1));
    }

    inline void thrust(int k) {
        for (int i = height; i > 0; i--) propagate(k >> i);
    }

    void update(int a, int b, const OperatorMonoid& x) {
        if (a >= b) return;
        thrust(a += sz);
        thrust(b += sz - 1);
        for (int l = a, r = b + 1; l < r; l >>= 1, r >>= 1) {
            if (l & 1) lazy[l] = h(lazy[l], x), ++l;
            if (r & 1) --r, lazy[r] = h(lazy[r], x);
        }
        recalc(a);
        recalc(b);
    }

    Monoid query(int a, int b) {
        if (a >= b) return M1;
        thrust(a += sz);
        thrust(b += sz - 1);
        Monoid L = M1, R = M1;
        for (int l = a, r = b + 1; l < r; l >>= 1, r >>= 1) {
            if (l & 1) L = f(L, apply(l++));
            if (r & 1) R = f(apply(--r), R);
        }
        return f(L, R);
    }

    Monoid operator[](const int& k) { return query(k, k + 1); }

    template <typename C>
    int find_subtree(int a, const C& check, Monoid& M, bool type) {
        while (a < sz) {
            propagate(a);
            Monoid nxt =
                type ? f(apply(2 * a + type), M) : f(M, apply(2 * a + type));
            if (check(nxt))
                a = 2 * a + type;
            else
                M = nxt, a = 2 * a + 1 - type;
        }
        return a - sz;
    }

    template <typename C>
    int find_first(int a, const C& check) {
        Monoid L = M1;
        if (a <= 0) {
            if (check(f(L, apply(1)))) return find_subtree(1, check, L, false);
            return -1;
        }
        thrust(a + sz);
        int b = sz;
        for (a += sz, b += sz; a < b; a >>= 1, b >>= 1) {
            if (a & 1) {
                Monoid nxt = f(L, apply(a));
                if (check(nxt)) return find_subtree(a, check, L, false);
                L = nxt;
                ++a;
            }
        }
        return -1;
    }

    template <typename C>
    int find_last(int b, const C& check) {
        Monoid R = M1;
        if (b >= sz) {
            if (check(f(apply(1), R))) return find_subtree(1, check, R, true);
            return -1;
        }
        thrust(b + sz - 1);
        int a = sz;
        for (b += sz; a < b; a >>= 1, b >>= 1) {
            if (b & 1) {
                Monoid nxt = f(apply(--b), R);
                if (check(nxt)) return find_subtree(b, check, R, true);
                R = nxt;
            }
        }
        return -1;
    }

    void show() {
        rep(i, n) cout << query(i, i + 1) << ' ';
        cout << endl;
    }
};

template <class T, class F = T>
T myreplace(T x, F y) {
    if (y != numeric_limits<F>::max()) x = y;
    return x;
}
template <class T>
T mymax(T x, T y) {
    return max(x, y);
}
template <class T>
T mymin(T x, T y) {
    return min(x, y);
}
template <class T, class F = T>
T myadd(T x, F y) {
    return x + y;
}
template <class T>
struct segobj {
    T val;
    int size;
    segobj(T x, int y) : val(x), size(y) {}
    segobj() : val(0), size(0) {}
    segobj& operator+=(const segobj& p) {
        val += p.val;
        size += p.size;
        return *this;
    }
    segobj& operator+=(const T& p) {
        val += p * size;
        return *this;
    }
    segobj& operator=(const T& p) {
        val = p * size;
        return *this;
    }
    friend ostream& operator<<(ostream& os, const segobj& p) {
        return os << p.val;
    }
    segobj operator+(const segobj& p) const { return segobj(*this) += p; }
    segobj operator+(const T& p) const { return segobj(*this) += p; }
};
template <class T>
struct RMRRQ : LazySegmentTree<T, T> {
    using Seg = LazySegmentTree<T, T>;
    RMRRQ(int n)
        : Seg(n, mymax<T>, myreplace<T>, myreplace<T>, numeric_limits<T>::min(),
              numeric_limits<T>::max()) {}
};
template <class T>
struct RmRRQ : LazySegmentTree<T, T> {
    using Seg = LazySegmentTree<T, T>;
    RmRRQ(int n)
        : Seg(n, mymin<T>, myreplace<T>, myreplace<T>, numeric_limits<T>::max(),
              numeric_limits<T>::max()) {}
};
template <class T>
struct RMRAQ : LazySegmentTree<T, T> {
    using Seg = LazySegmentTree<T, T>;
    RMRAQ(int n)
        : Seg(n, mymax<T>, plus<T>(), plus<T>(), numeric_limits<T>::min() / 2,
              T()) {}
};
template <class T>
struct RmRAQ : LazySegmentTree<T, T> {
    using Seg = LazySegmentTree<T, T>;
    RmRAQ(int n)
        : Seg(n, mymin<T>, plus<T>(), plus<T>(), numeric_limits<T>::max() / 2,
              T()) {}
};
template <class T>
struct RSRAQ : LazySegmentTree<segobj<T>, T> {
    using Seg = LazySegmentTree<segobj<T>, T>;
    RSRAQ(int n)
        : Seg(n, plus<segobj<T>>(), myadd<segobj<T>, T>, plus<T>(), segobj<T>(),
              T()) {
        rep(i, n) this->set(i, segobj<T>(0, 1));
        this->build();
    }
    T sum(int l, int r) { return this->query(l, r).val; }
};
template <class T>
struct RSRRQ : LazySegmentTree<segobj<T>, T> {
    using Seg = LazySegmentTree<segobj<T>, T>;
    using obj = segobj<T>;
    RSRRQ(int n)
        : Seg(n, plus<obj>(), myreplace<obj, T>, myreplace<T>, segobj<T>(),
              numeric_limits<T>::max()) {
        rep(i, n) this->set(i, segobj<T>(0, 1));
        this->build();
    }
    T sum(int l, int r) { return this->query(l, r).val; }
};

struct X {
    mint val, size;
};
struct F {
    mint b, c;
};
X f(X x, X y) { return X{x.val + y.val, x.size + y.size}; };
X g(X x, F ff) { return X{x.size * ff.c + x.val * ff.b, x.size}; };
F h(F ff, F gg) { return F{ff.b * gg.b, ff.c * gg.b + gg.c}; };

int main() {
    cin.tie(0);
    ios::sync_with_stdio(0);
    cout << setprecision(30);
    int n, q;
    cin >> n >> q;
    LazySegmentTree<X, F> seg(n, f, g, h, X{0, 0}, F{1, 0});
    rep(i, n) {
        ll a;
        cin >> a;
        seg.set(i, X{a, 1});
    }
    seg.build();
    cout << endl;
    while (q--) {
        int t;
        cin >> t;
        if (t == 0) {
            ll l, r, b, c;
            cin >> l >> r >> b >> c;
            seg.update(l, r, F{b, c});
        } else {
            ll l, r;
            cin >> l >> r;
            print(seg.query(l, r).val);
        }
    }
}