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# (.NET Core 3.1.201) (judge verdict: Accepted)

using System;
using System.Collections;
using System.Collections.Generic;
using System.IO;
using System.Linq;

namespace Tasks
{
    public class K
    {
        static void Main(string[] args)
        {
            var sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
            Console.SetOut(sw);
            Solve();
            Console.Out.Flush();
        }

        public static void Solve()
        {
            var (N, Q) = Scanner.Scan<int, int>();
            var A = Scanner.ScanEnumerable<int>().Select(x => new S(x, 1)).ToArray();
            Func<S, S, S> operation = (l, r) => new S(l.A + r.A, l.Size + r.Size);
            var identityS = new S(0, 0);
            Func<F, S, S> mapping = (l, r) => new S(r.A * l.A + r.Size * l.B, r.Size);
            Func<F, F, F> composition = (l, r) => new F(r.A * l.A, r.B * l.A + l.B);
            var identityF = new F(1, 0);

            var lseg = new LazySegTree<S, F>(A, operation, identityS, mapping, composition, identityF);

            for (var i = 0; i < Q; i++)
            {
                var q = Scanner.ScanEnumerable<int>().ToArray();
                if (q[0] == 0)
                {
                    var (l, r, c, d) = (q[1], q[2], q[3], q[4]);
                    lseg.Apply(l, r, new F(c, d));
                }
                else
                {
                    var (l, r) = (q[1], q[2]);
                    Console.WriteLine(lseg.Prod(l, r).A);
                }
            }
        }

        public struct S
        {
            public MInt A;
            public int Size;
            public S(MInt a, int size)
            {
                A = a;
                Size = size;
            }
        }

        public struct F
        {
            public MInt A;
            public MInt B;
            public F(MInt a, MInt b)
            {
                A = a;
                B = b;
            }
        }

        public readonly struct MInt
        {
            public long Value => _data;
            private const int Mod = 998244353;
            private readonly long _data;
            public MInt(long data) => _data = (0 <= data ? data : data + Mod) % Mod;
            public static implicit operator long(MInt mint) => mint._data;
            public static implicit operator MInt(long val) => new MInt(val);
            public static MInt operator +(MInt a, MInt b) => new MInt(a._data + b._data);
            public static MInt operator +(MInt a, long b) => a._data + b;
            public static MInt operator -(MInt a, MInt b) => new MInt(a._data - b._data);
            public static MInt operator -(MInt a, long b) => a._data - b;
            public static MInt operator *(MInt a, MInt b) => new MInt(a._data * b._data);
            public static MInt operator *(MInt a, long b) => a._data * (b % Mod);
            public static MInt operator /(MInt a, MInt b) => new MInt(a._data * GetInv(b));
            public static bool operator ==(MInt a, MInt b) => a._data == b._data;
            public static bool operator !=(MInt a, MInt b) => a._data != b._data;
            public override bool Equals(object obj) => _data.Equals(obj);
            public override int GetHashCode() => _data.GetHashCode();
            public override string ToString() => _data.ToString();

            private static long GetInv(long a)
            {
                a %= Mod;
                if (a < 0) a += Mod;
                if (a == 0) return 0;
                var (s, t, m0, m1) = ((long)Mod, a, 0L, 1L);
                while (t > 1)
                {
                    var u = s / t;
                    s -= t * u;
                    m0 -= m1 * u;
                    (s, t) = (t, s);
                    (m0, m1) = (m1, m0);
                }

                if (m0 < 0) m0 += Mod / s;
                return m0;
            }
        }

        public class LazySegTree<T, U>
        {
            private readonly int _n;
            private readonly int _size;
            private readonly int _log;
            private readonly T[] _data;
            private readonly U[] _lazy;
            private readonly Func<T, T, T> _operation;
            private readonly Func<U, T, T> _mapping;
            private readonly Func<U, U, U> _composition;
            private readonly T _identityT;
            private readonly U _identityU;

            public LazySegTree(int n, Func<T, T, T> operation, T identityT, Func<U, T, T> mapping,
                Func<U, U, U> composition, U identityU) :
                this(new T[n], operation, identityT, mapping, composition, identityU)
            {
            }

            public LazySegTree(IEnumerable<T> data, Func<T, T, T> operation, T identityT, Func<U, T, T> mapping,
                Func<U, U, U> composition, U identityU)
            {
                var d = data.ToArray();
                _n = d.Length;
                _operation = operation;
                _identityT = identityT;
                _mapping = mapping;
                _composition = composition;
                _identityU = identityU;
                _log = CeilPow2(_n);
                _size = 1 << _log;
                _data = Enumerable.Repeat(identityT, _size * 2).ToArray();
                _lazy = Enumerable.Repeat(identityU, _size).ToArray();
                for (var i = 0; i < _n; i++) _data[_size + i] = d[i];
                for (var i = _size - 1; i >= 1; i--) Update(i);
            }

            public void Set(int p, T x)
            {
                if (p < 0 || _n <= p) throw new ArgumentException(nameof(p));
                p += _size;
                for (var i = _log; i >= 1; i--) Push(p >> i);
                _data[p] = x;
                for (var i = 1; i <= _log; i++) Update(p >> i);
            }

            public T Get(int p)
            {
                if (p < 0 || _n <= p) throw new ArgumentException(nameof(p));
                p += _size;
                for (var i = _log; i >= 1; i--) Push(p >> i);
                return _data[p];
            }

            public T Prod(int l, int r)
            {
                if (0 > l || l > r || r > _n) throw new ArgumentException();
                if (l == r) return _identityT;
                l += _size;
                r += _size;
                for (var i = _log; i >= 1; i--)
                {
                    if ((l >> i) << i != l) Push(l >> i);
                    if ((r >> i) << i != r) Push(r >> i);
                }

                var (sml, smr) = (_identityT, _identityT);
                while (l < r)
                {
                    if ((l & 1) == 1) sml = _operation(sml, _data[l++]);
                    if ((r & 1) == 1) smr = _operation(_data[--r], smr);
                    l >>= 1;
                    r >>= 1;
                }

                return _operation(sml, smr);
            }

            public T AllProd() => _data[1];

            public void Apply(int p, U u)
            {
                if (p < 0 || _n <= p) throw new ArgumentException(nameof(p));
                p += _size;
                for (var i = _log; i >= 1; i--) Push(p >> i);
                _data[p] = _mapping(u, _data[p]);
                for (var i = 1; i <= _log; i++) Update(p >> i);
            }

            public void Apply(int l, int r, U u)
            {
                if (0 > l || l > r || r > _n) throw new ArgumentException();
                if (l == r) return;
                l += _size;
                r += _size;
                for (var i = _log; i >= 1; i--)
                {
                    if ((l >> i) << i != l) Push(l >> i);
                    if ((r >> i) << i != r) Push((r - 1) >> i);
                }

                var (l2, r2) = (l, r);
                while (l2 < r2)
                {
                    if ((l2 & 1) == 1) AllApply(l2++, u);
                    if ((r2 & 1) == 1) AllApply(--r2, u);
                    l2 >>= 1;
                    r2 >>= 1;
                }

                for (var i = 1; i <= _log; i++)
                {
                    if ((l >> i) << i != l) Update(l >> i);
                    if ((r >> i) << i != r) Update((r - 1) >> i);
                }
            }

            public int MaxRight(int l, Func<T, bool> func)
            {
                if (l < 0 || _n <= l) throw new ArgumentException(nameof(l));
                if (!func(_identityT)) throw new ArgumentException(nameof(func));
                if (l == _n) return _n;
                l += _size;
                var sm = _identityT;
                do
                {
                    while (l % 2 == 0) l >>= 1;
                    if (!func(_operation(sm, _data[l])))
                    {
                        while (l < _size)
                        {
                            l *= 2;
                            var tmp = _operation(sm, _data[l]);
                            if (!func(tmp)) continue;
                            sm = tmp;
                            l++;
                        }

                        return l - _size;
                    }

                    sm = _operation(sm, _data[l]);
                    l++;
                } while ((l & -l) != l);

                return _n;
            }

            public int MinLeft(int r, Func<T, bool> func)
            {
                if (r < 0 || _n <= r) throw new ArgumentException(nameof(r));
                if (!func(_identityT)) throw new ArgumentException(nameof(func));
                if (r == 0) return 0;
                r += _size;
                var sm = _identityT;
                do
                {
                    r--;
                    while (r > 1 && r % 2 == 0) r >>= 1;
                    if (!func(_operation(_data[r], sm)))
                    {
                        while (r < _size)
                        {
                            r = r * 2 + 1;
                            var tmp = _operation(_data[r], sm);
                            if (!func(tmp)) continue;
                            sm = tmp;
                            r--;
                        }

                        return r + 1 - _size;
                    }

                    sm = _operation(_data[r], sm);
                    r++;
                } while ((r & -r) != r);

                return 0;
            }

            private void Update(int k) => _data[k] = _operation(_data[k * 2], _data[k * 2 + 1]);

            private void AllApply(int k, U u)
            {
                _data[k] = _mapping(u, _data[k]);
                if (k < _size) _lazy[k] = _composition(u, _lazy[k]);
            }

            private void Push(int k)
            {
                AllApply(k * 2, _lazy[k]);
                AllApply(k * 2 + 1, _lazy[k]);
                _lazy[k] = _identityU;
            }

            private static int CeilPow2(int n)
            {
                var x = 0;
                while (1 << x < n) x++;
                return x;
            }
        }

        public static class Scanner
        {
            private static Queue<string> queue = new Queue<string>();
            public static T Next<T>()
            {
                if (!queue.Any()) foreach (var item in Console.ReadLine().Trim().Split(" ")) queue.Enqueue(item);
                return (T)Convert.ChangeType(queue.Dequeue(), typeof(T));
            }
            public static T Scan<T>() => Next<T>();
            public static (T1, T2) Scan<T1, T2>() => (Next<T1>(), Next<T2>());
            public static (T1, T2, T3) Scan<T1, T2, T3>() => (Next<T1>(), Next<T2>(), Next<T3>());
            public static (T1, T2, T3, T4) Scan<T1, T2, T3, T4>() => (Next<T1>(), Next<T2>(), Next<T3>(), Next<T4>());
            public static (T1, T2, T3, T4, T5) Scan<T1, T2, T3, T4, T5>() => (Next<T1>(), Next<T2>(), Next<T3>(), Next<T4>(), Next<T5>());
            public static IEnumerable<T> ScanEnumerable<T>() => Console.ReadLine().Trim().Split(" ").Select(x => (T)Convert.ChangeType(x, typeof(T)));
        }
    }
}