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: Time Limit Exceeded)

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

namespace AtCoderLibraryCSharp.Examples
{
    public static class Program
    {
        public static void Main()
        {
            var sw = new StreamWriter(Console.OpenStandardOutput()) {AutoFlush = false};
            Console.SetOut(sw);

            var NQ = Console.ReadLine().Split(" ").Select(int.Parse).ToArray();
            var (N, Q) = (NQ[0], NQ[1]);
            var A = Console.ReadLine().Split(" ").Select(x => new S(int.Parse(x), 1)).ToArray();

            var identityS = new S(0, 0);
            var identityF = new F(1, 0);

            Func<S, S, S> operation = (l, r) => new S(l.A + r.A, l.Size + r.Size);
            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 lst = new LazySegmentTree<S, F>(A, operation, identityS, mapping, composition, identityF);

            for (var i = 0; i < Q; i++)
            {
                var q = Console.ReadLine().Split(" ").Select(int.Parse).ToArray();
                if (q[0] == 0) lst.Apply(q[1], q[2], new F(q[3], q[4]));
                else Console.WriteLine(lst.Query(q[1], q[2]).A);
            }

            Console.Out.Flush();
        }

        public readonly struct S
        {
            public readonly ModuloInteger A;
            public readonly int Size;

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

        public readonly struct F
        {
            public readonly ModuloInteger A;
            public readonly ModuloInteger B;

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

    public class LazySegmentTree<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 LazySegmentTree(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 LazySegmentTree(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;
            while (1 << _log < _n) _log++;
            _size = 1 << _log;
            _data = Enumerable.Repeat(identityT, _size << 1).ToArray();
            _lazy = Enumerable.Repeat(identityU, _size).ToArray();
            d.CopyTo(_data, _size);
            for (var i = _size - 1; i >= 1; i--) Update(i);
        }

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

        public T Query(int l, int r)
        {
            if (l < 0 || r < l || _n < r) throw new IndexOutOfRangeException();
            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 QueryToAll() => _data[1];

        public void Apply(int p, U u)
        {
            if (p < 0 || _n <= p) throw new IndexOutOfRangeException(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 (l < 0 || r < l || _n < r) throw new IndexOutOfRangeException();
            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) ApplyToAll(l2++, u);
                if ((r2 & 1) == 1) ApplyToAll(--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 IndexOutOfRangeException(nameof(l));
            if (!func(_identityT)) throw new ArgumentException(nameof(func));
            if (l == _n) return _n;
            l += _size;
            var sm = _identityT;
            do
            {
                while ((l & 1) == 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 IndexOutOfRangeException(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 & 1) == 0) r >>= 1;
                if (!func(_operation(_data[r], sm)))
                {
                    while (r < _size)
                    {
                        r = (r << 1) + 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 << 1], _data[(k << 1) + 1]);

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

        private void Push(int k)
        {
            ApplyToAll(k << 1, _lazy[k]);
            ApplyToAll((k << 1) + 1, _lazy[k]);
            _lazy[k] = _identityU;
        }
    }

    public readonly struct ModuloInteger
    {
        public long Value { get; }
        public static long Modulo { get; private set; } = 998244353;

        public ModuloInteger(long data) => Value = (0 <= data ? data : data + Modulo) % Modulo;
        public static implicit operator long(ModuloInteger mint) => mint.Value;
        public static implicit operator int(ModuloInteger mint) => (int) mint.Value;
        public static implicit operator ModuloInteger(long val) => new ModuloInteger(val);
        public static implicit operator ModuloInteger(int val) => new ModuloInteger(val);
        public static ModuloInteger operator +(ModuloInteger a, ModuloInteger b) => a.Value + b.Value;
        public static ModuloInteger operator +(ModuloInteger a, long b) => a.Value + b;
        public static ModuloInteger operator +(ModuloInteger a, int b) => a.Value + b;
        public static ModuloInteger operator -(ModuloInteger a, ModuloInteger b) => a.Value - b.Value;
        public static ModuloInteger operator -(ModuloInteger a, long b) => a.Value - b;
        public static ModuloInteger operator -(ModuloInteger a, int b) => a.Value - b;
        public static ModuloInteger operator *(ModuloInteger a, ModuloInteger b) => a.Value * b.Value;
        public static ModuloInteger operator *(ModuloInteger a, long b) => a.Value * (b % Modulo);
        public static ModuloInteger operator *(ModuloInteger a, int b) => a.Value * (b % Modulo);
        public static ModuloInteger operator /(ModuloInteger a, ModuloInteger b) => a * b.Inverse();
        public static ModuloInteger operator /(ModuloInteger a, long b) => a.Value * Inverse(b);
        public static ModuloInteger operator /(ModuloInteger a, int b) => a.Value * Inverse(b);
        public static bool operator ==(ModuloInteger a, ModuloInteger b) => a.Value == b.Value;
        public static bool operator !=(ModuloInteger a, ModuloInteger b) => a.Value != b.Value;
        public bool Equals(ModuloInteger other) => Value == other.Value;
        public override bool Equals(object obj) => obj is ModuloInteger other && Equals(other);
        public override int GetHashCode() => Value.GetHashCode();
        public override string ToString() => Value.ToString();

        public ModuloInteger Inverse() => Inverse(Value);

        public static ModuloInteger Inverse(long a)
        {
            if (a == 0) return 0;
            var p = Modulo;
            var (x1, y1, x2, y2) = (1L, 0L, 0L, 1L);
            while (true)
            {
                if (p == 1) return (x2 % Modulo + Modulo) % Modulo;
                var div = a / p;
                x1 -= x2 * div;
                y1 -= y2 * div;
                a %= p;
                if (a == 1) return (x1 % Modulo + Modulo) % Modulo;
                div = p / a;
                x2 -= x1 * div;
                y2 -= y1 * div;
                p %= a;
            }
        }

        public ModuloInteger Power(long n) => Power(Value, n);

        public static ModuloInteger Power(ModuloInteger x, long n)
        {
            if (n < 0) throw new ArgumentException();
            var r = new ModuloInteger(1);
            while (n > 0)
            {
                if ((n & 1) > 0) r *= x;
                x *= x;
                n >>= 1;
            }

            return r;
        }

        public static void SetMod(long m) => Modulo = m;
        public static void SetMod998244353() => SetMod(998244353);
        public static void SetMod1000000007() => SetMod(1000000007);
    }
}