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.Generic;
using System.IO;
using System.Linq;
using static System.Math;
using System.Text;
using System.Threading;
using System.Globalization;
using System.Runtime.CompilerServices;
using Library;

namespace Program
{
    public static class ProblemD
    {
        static bool SAIKI = false;
        static public int numberOfRandomCases = 0;
        static public void MakeTestCase(List<string> _input, List<string> _output, ref Func<string[], bool> _outputChecker)
        {
        }
        readonly struct E : IEquatable<E>
        {
            public readonly int b;
            public readonly int c;
            public bool Equals(E other) => b == other.b && c == other.c;
            public E(int b, int c) { this.b = b; this.c = c; }
        }
        static public void Solve()
        {
            var N = NN;
            var Q = NN;
            var aList = NNList(N);
            var seg = new LIB_LazySegTree<int, E>(N, 0, new E(1, 0),
                (in int x, in int y) =>
                {
                    var t = x + y;
                    if (t >= 998244353) return t - 998244353;
                    return t;
                },
                (in int x, in E y, in int c) => (int)(((long)x * y.b + (long)y.c * c) % 998244353),
                (in E x, in E y) => new E((int)(((long)x.b * y.b) % 998244353), (int)(((long)x.c * y.b + y.c) % 998244353))
            );
            for (var i = 0; i < N; i++) seg[i] = (int)aList[i];
            for (var i = 0; i < Q; i++)
            {
                if (NN == 0)
                {
                    var l = NN;
                    var r = NN;
                    var b = NN;
                    var c = NN;
                    seg.Update(l, r, new E((int)b, (int)c));
                }
                else
                {
                    var l = NN;
                    var r = NN;
                    Console.WriteLine(seg.Query(l, r));
                }
            }
        }
        class Printer : StreamWriter
        {
            public override IFormatProvider FormatProvider { get { return CultureInfo.InvariantCulture; } }
            public Printer(Stream stream) : base(stream, new UTF8Encoding(false, true)) { base.AutoFlush = false; }
            public Printer(Stream stream, Encoding encoding) : base(stream, encoding) { base.AutoFlush = false; }
        }
        static LIB_FastIO fastio = new LIB_FastIODebug();
        static public void Main(string[] args) { if (args.Length == 0) { fastio = new LIB_FastIO(); Console.SetOut(new Printer(Console.OpenStandardOutput())); } if (SAIKI) { var t = new Thread(Solve, 134217728); t.Start(); t.Join(); } else Solve(); Console.Out.Flush(); }
        static long NN => fastio.Long();
        static double ND => fastio.Double();
        static string NS => fastio.Scan();
        static long[] NNList(long N) => Repeat(0, N).Select(_ => NN).ToArray();
        static double[] NDList(long N) => Repeat(0, N).Select(_ => ND).ToArray();
        static string[] NSList(long N) => Repeat(0, N).Select(_ => NS).ToArray();
        static long Count<T>(this IEnumerable<T> x, Func<T, bool> pred) => Enumerable.Count(x, pred);
        static IEnumerable<T> Repeat<T>(T v, long n) => Enumerable.Repeat<T>(v, (int)n);
        static IEnumerable<int> Range(long s, long c) => Enumerable.Range((int)s, (int)c);
        static IOrderedEnumerable<T> OrderByRand<T>(this IEnumerable<T> x) => Enumerable.OrderBy(x, _ => xorshift);
        static IOrderedEnumerable<T> OrderBy<T>(this IEnumerable<T> x) => Enumerable.OrderBy(x.OrderByRand(), e => e);
        static IOrderedEnumerable<T1> OrderBy<T1, T2>(this IEnumerable<T1> x, Func<T1, T2> selector) => Enumerable.OrderBy(x.OrderByRand(), selector);
        static IOrderedEnumerable<T> OrderByDescending<T>(this IEnumerable<T> x) => Enumerable.OrderByDescending(x.OrderByRand(), e => e);
        static IOrderedEnumerable<T1> OrderByDescending<T1, T2>(this IEnumerable<T1> x, Func<T1, T2> selector) => Enumerable.OrderByDescending(x.OrderByRand(), selector);
        static IOrderedEnumerable<string> OrderBy(this IEnumerable<string> x) => x.OrderByRand().OrderBy(e => e, StringComparer.OrdinalIgnoreCase);
        static IOrderedEnumerable<T> OrderBy<T>(this IEnumerable<T> x, Func<T, string> selector) => x.OrderByRand().OrderBy(selector, StringComparer.OrdinalIgnoreCase);
        static IOrderedEnumerable<string> OrderByDescending(this IEnumerable<string> x) => x.OrderByRand().OrderByDescending(e => e, StringComparer.OrdinalIgnoreCase);
        static IOrderedEnumerable<T> OrderByDescending<T>(this IEnumerable<T> x, Func<T, string> selector) => x.OrderByRand().OrderByDescending(selector, StringComparer.OrdinalIgnoreCase);
        static string Join<T>(this IEnumerable<T> x, string separator = "") => string.Join(separator, x);
        static uint xorshift { get { _xsi.MoveNext(); return _xsi.Current; } }
        static IEnumerator<uint> _xsi = _xsc();
        static IEnumerator<uint> _xsc() { uint x = 123456789, y = 362436069, z = 521288629, w = (uint)(DateTime.Now.Ticks & 0xffffffff); while (true) { var t = x ^ (x << 11); x = y; y = z; z = w; w = (w ^ (w >> 19)) ^ (t ^ (t >> 8)); yield return w; } }
    }
}
namespace Library {
    class LIB_FastIO
    {
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public LIB_FastIO() { str = Console.OpenStandardInput(); }
        readonly Stream str;
        readonly byte[] buf = new byte[1024];
        int len, ptr;
        public bool isEof = false;
        public bool IsEndOfStream
        {
            [MethodImpl(MethodImplOptions.AggressiveInlining)]
            get { return isEof; }
        }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        byte read()
        {
            if (isEof) throw new EndOfStreamException();
            if (ptr >= len)
            {
                ptr = 0;
                if ((len = str.Read(buf, 0, 1024)) <= 0)
                {
                    isEof = true;
                    return 0;
                }
            }
            return buf[ptr++];
        }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        char Char()
        {
            byte b = 0;
            do b = read();
            while (b < 33 || 126 < b);
            return (char)b;
        }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        virtual public string Scan()
        {
            var sb = new StringBuilder();
            for (var b = Char(); b >= 33 && b <= 126; b = (char)read())
                sb.Append(b);
            return sb.ToString();
        }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        virtual public long Long()
        {
            long ret = 0; byte b = 0; var ng = false;
            do b = read();
            while (b != '-' && (b < '0' || '9' < b));
            if (b == '-') { ng = true; b = read(); }
            for (; true; b = read())
            {
                if (b < '0' || '9' < b)
                    return ng ? -ret : ret;
                else ret = ret * 10 + b - '0';
            }
        }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        virtual public double Double() { return double.Parse(Scan(), CultureInfo.InvariantCulture); }
    }
    class LIB_FastIODebug : LIB_FastIO
    {
        Queue<string> param = new Queue<string>();
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        string NextString() { if (param.Count == 0) foreach (var item in Console.ReadLine().Split(' ')) param.Enqueue(item); return param.Dequeue(); }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public LIB_FastIODebug() { }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public override string Scan() => NextString();
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public override long Long() => long.Parse(NextString());
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public override double Double() => double.Parse(NextString());
    }
    class LIB_LazySegTree<T, E> where E : IEquatable<E>
    {
        public delegate T F(in T x, in T y);
        public delegate T G(in T x, in E y, in int c);
        public delegate E H(in E x, in E y);
        int n, height, sz;
        int[] rangeSz;
        T ti;
        E ei;
        F f;
        G g;
        H h;
        T[] dat;
        E[] laz;
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public LIB_LazySegTree(long _n, T _ti, E _ei, F _f, G _g, H _h)
        {
            n = 1; height = 0; sz = (int)_n;
            while (n < _n) { n <<= 1; ++height; }
            ti = _ti;
            ei = _ei;
            f = _f;
            g = _g;
            h = _h;
            dat = Enumerable.Repeat(ti, n << 1).ToArray();
            laz = Enumerable.Repeat(ei, n).ToArray();
            rangeSz = new int[n << 1];
            for (var i = 0; i < sz; i++) rangeSz[n + i] = 1;
            for (var i = n - 1; i > 0; i--)
            {
                rangeSz[i] = rangeSz[(i << 1) | 0] + rangeSz[(i << 1) | 1];
                dat[i] = f(dat[(i << 1) | 0], dat[(i << 1) | 1]);
            }
        }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public LIB_LazySegTree(IEnumerable<T> l, T _ti, E _ei, F _f, G _g, H _h) : this(l.Count(), _ti, _ei, _f, _g, _h)
        {
            var idx = 0;
            foreach (var item in l) dat[n + idx++] = item;
            for (var i = n - 1; i > 0; i--) dat[i] = f(dat[(i << 1) | 0], dat[(i << 1) | 1]);
        }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        void Apply(long i, in E v)
        {
            if (v.Equals(ei)) return;
            dat[i] = g(dat[i], v, rangeSz[i]);
            if (i < n) laz[i] = h(laz[i], v);
        }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        void Up(long i) => dat[i] = f(dat[i << 1], dat[(i << 1) | 1]);
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        void Down(long i)
        {
            if (laz[i].Equals(ei)) return;
            var cl = i << 1;
            var cr = cl + 1;
            Apply(cl, laz[i]);
            Apply(cr, laz[i]);
            laz[i] = ei;
        }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        void Thrust(long i)
        {
            for (var j = height; j > 0; j--) Down(i >> j);
        }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        void Recalc(long i)
        {
            while ((i >>= 1) > 0) Up(i);
        }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public void Update(long l, long r, E v)
        {
            if (l == r) return;
            l += n;
            r += n;
            for (var i = height; i >= 1; --i)
            {
                if (((l >> i) << i) != l) Down(l >> i);
                if (((r >> i) << i) != r) Down((r - 1) >> i);
            }
            for (long li = l, ri = r; li < ri; li >>= 1, ri >>= 1)
            {
                if ((li & 1) == 1) { Apply(li, v); ++li; }
                if ((ri & 1) == 1) { --ri; Apply(ri, v); }
            }
            for (var i = 1; i <= height; ++i)
            {
                if (((l >> i) << i) != l) Up(l >> i);
                if (((r >> i) << i) != r) Up((r - 1) >> i);
            }
        }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public T Query(long l, long r)
        {
            if (l == r) return ti;
            l += n;
            r += n;
            for (var i = height; i >= 1; --i)
            {
                if (((l >> i) << i) != l) Down(l >> i);
                if (((r >> i) << i) != r) Down((r - 1) >> i);
            }
            var vl = ti; var vr = ti;
            for (long li = l, ri = r; li < ri; li >>= 1, ri >>= 1)
            {
                if ((li & 1) == 1) vl = f(vl, dat[li++]);
                if ((ri & 1) == 1) vr = f(dat[--ri], vr);
            }
            return f(vl, vr);
        }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        int FindToRight(int st, Func<T, bool> check, ref T acc, int k, int l, int r)
        {
            if (l + 1 == r)
            {
                acc = f(acc, dat[k]);
                return check(acc) ? k - n : sz;
            }
            Down(k);
            int m = (l + r) >> 1;
            if (m <= st) return FindToRight(st, check, ref acc, (k << 1) | 1, m, r);
            if (st <= l && !check(f(acc, dat[k])))
            {
                acc = f(acc, dat[k]);
                return sz;
            }
            int vl = FindToRight(st, check, ref acc, (k << 1) | 0, l, m);
            if (vl != sz) return vl;
            return FindToRight(st, check, ref acc, (k << 1) | 1, m, r);
        }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public int FindToRight(int st, Func<T, bool> check)
        {
            T acc = ti;
            return FindToRight(st, check, ref acc, 1, 0, n);
        }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        int FindToLeft(int st, Func<T, bool> check, ref T acc, int k, int l, int r)
        {
            if (l + 1 == r)
            {
                acc = f(dat[k], acc);
                return check(acc) ? k - n : -1;
            }
            Down(k);
            int m = (l + r) >> 1;
            if (m > st) return FindToLeft(st, check, ref acc, (k << 1) | 0, l, m);
            if (st >= r - 1 && !check(f(dat[k], acc)))
            {
                acc = f(dat[k], acc);
                return -1;
            }
            int vr = FindToLeft(st, check, ref acc, (k << 1) | 1, m, r);
            if (vr != -1) return vr;
            return FindToLeft(st, check, ref acc, (k << 1) | 0, l, m);
        }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public int FindToLeft(int st, Func<T, bool> check)
        {
            T acc = ti;
            return FindToLeft(st, check, ref acc, 1, 0, n);
        }
        public T this[long idx]
        {
            [MethodImpl(MethodImplOptions.AggressiveInlining)]
            get { Thrust(idx += n); return dat[idx]; }
            [MethodImpl(MethodImplOptions.AggressiveInlining)]
            set { Thrust(idx += n); dat[idx] = value; Recalc(idx); }
        }
    }
}