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.Linq;
using System.IO;
using System.Threading;
using System.Runtime.CompilerServices;
using System.Text;
using System.Diagnostics;
using System.Numerics;
using static System.Console;
using static System.Convert;
using static System.Math;
using static Template;
using SC = FastScanner;

public partial class Solver
{
    public void Solve()
    {
        int N = sc.Int, Q = sc.Int;
        var seg = new LazySegmentTree<P, (ModInt a, ModInt b)>(N, new P(0, 0), (1, 0), (a, b) => new P(a.val + b.val, a.size + b.size), (a, b) => new P(a.val * b.a + a.size * b.b, a.size), (l, r) => (l.a * r.a, l.b * r.a + r.b));
        for (int i = 0; i < N; i++)
        {
            seg[i] = new P(sc.Int, 1);
        }
        seg.Build();
        while (Q-- > 0)
        {
            int t = sc.Int;
            if (t == 0)
            {
                int l = sc.Int, r = sc.Int, b = sc.Int, c = sc.Int;

                seg.Update(l, r, (b, c));
            }
            else
            {
                int l = sc.Int, r = sc.Int;
                Console.WriteLine(seg.Query(l, r).val);
            }
        }
    }
    struct P
    {
        public ModInt val; public int size;
        public P(ModInt v, int s) { val = v; size = s; }
    }
}

public class LazySegmentTree<T, E>
{
    protected readonly int size, _N, log;
    protected readonly T idT;
    protected readonly T[] dat;
    protected readonly E idE;
    protected readonly E[] lazy;
    protected readonly Func<T, T, T> mergeT;
    protected readonly Func<T, E, T> update;
    protected readonly Func<E, E, E> mergeE;

    public T this[int i]
    {
        get { return dat[i + size]; }
        set { dat[i + size] = value; }
    }

    public LazySegmentTree(int N, T idT, E idE, Func<T, T, T> mergeT, Func<T, E, T> update = null, Func<E, E, E> mergeE = null)
    {
        _N = N;
        this.idT = idT;
        this.idE = idE;
        this.mergeT = mergeT;
        this.update = update ?? ((a, b) => a);
        this.mergeE = mergeE ?? ((a, b) => b);
        while ((1 << log) < N) log++;
        size = 1 << log;
        dat = new T[2 * size];
        lazy = new E[size];
        for (var i = 0; i < dat.Length; i++) dat[i] = idT;
        for (int i = 0; i < lazy.Length; i++) lazy[i] = idE;
    }
    public void Build()
    {
        for (int i = size - 1; i >= 1; i--) Update(i);
    }
    public void Set(int p, T t)
    {
        p += size;
        for (int i = log; i >= 1; i--) Push(p >> i);
        dat[p] = t;
        for (int i = 1; i <= log; i++) Update(p >> i);
    }
    public T Get(int p)
    {
        p += size;
        for (int i = log; i >= 1; i--) Push(p >> i);
        return dat[p];
    }
    public T Query(int l, int r)
    {
        if (r <= l) return idT;
        l += size; r += size;
        for (int i = log; i >= 1; i--)
        {
            if (((l >> i) << i) != l) Push(l >> i);
            if (((r >> i) << i) != r) Push(r >> i);
        }
        var sml = idT; var smr = idT;
        while (l < r)
        {
            if ((l & 1) == 1) sml = mergeT(sml, dat[l++]);
            if ((r & 1) == 1) smr = mergeT(dat[--r], smr);
            l >>= 1; r >>= 1;
        }
        return mergeT(sml, smr);
    }
    public void Update(int l, int r, E e)
    {
        if (l == r) return;
        l += size; r += size;

        for (int i = log; i >= 1; i--)
        {
            if (((l >> i) << i) != l) Push(l >> i);
            if (((r >> i) << i) != r) Push((r - 1) >> i);
        }
        int l2 = l, r2 = r;
        while (l < r)
        {
            if ((l & 1) == 1) Apply(l++, e);
            if ((r & 1) == 1) Apply(--r, e);
            l >>= 1;
            r >>= 1;
        }
        l = l2;
        r = r2;
        for (int 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> f)
    {
        if (l == _N) return _N;
        l += size;
        for (int i = log; i >= 1; i--) Push(l >> i);
        var sm = idT;
        do
        {
            while (l % 2 == 0) l >>= 1;
            if (!f(mergeT(sm, dat[l])))
            {
                while (l < size)
                {
                    Push(l);
                    l <<= 1;
                    if (f(mergeT(sm, dat[l])))
                    {
                        sm = mergeT(sm, dat[l]);
                        l++;
                    }
                }
                return l - size;
            }
            sm = mergeT(sm, dat[l]);
            l++;
        } while ((l & -l) != l);
        return _N;
    }
    public int MinLeft(int r, Func<T, bool> f)
    {
        if (r == 0) return 0;
        r += size;
        for (int i = log; i >= 1; i--) Push((r - 1) >> i);
        var sm = idT;
        do
        {
            r--;
            while (r > 1 && (r & 1) == 1) r >>= 1;
            if (!f(mergeT(dat[r], sm)))
            {
                while (r < size)
                {
                    Push(r);
                    r = (r << 1) | 1;
                    if (f(mergeT(dat[r], sm)))
                    {
                        sm = mergeT(dat[r], sm);
                        r--;
                    }
                }
                return r + 1 - size;
            }
            sm = mergeT(dat[r], sm);
        } while ((r & -r) != r);
        return 0;
    }
    void Apply(int k, E e)
    {
        dat[k] = update(dat[k], e);
        if (k < size) lazy[k] = mergeE(lazy[k], e);
    }
    void Push(int k)
    {
        Apply(k << 1, lazy[k]);
        Apply((k << 1) | 1, lazy[k]);
        lazy[k] = idE;
    }
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    void Update(int k) => dat[k] = mergeT(dat[k << 1], dat[(k << 1) | 1]);
}

public struct ModInt
{
    //public const long MOD = (int)1e9 + 7;
    public const long MOD = 998244353;
    public long Value { get; set; }
    public ModInt(long n = 0) { Value = n; }
    private static ModInt[] fac, inv, facinv;
    public override string ToString() => Value.ToString();
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static ModInt operator +(ModInt l, ModInt r)
    {
        l.Value += r.Value;
        if (l.Value >= MOD) l.Value -= MOD;
        return l;
    }
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static ModInt operator -(ModInt l, ModInt r)
    {
        l.Value -= r.Value;
        if (l.Value < 0) l.Value += MOD;
        return l;
    }
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static ModInt operator *(ModInt l, ModInt r) => new ModInt(l.Value * r.Value % MOD);
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static ModInt operator /(ModInt l, ModInt r) => l * Pow(r, MOD - 2);
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static implicit operator long(ModInt l) => l.Value;
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static implicit operator ModInt(long n)
    {
        n %= MOD; if (n < 0) n += MOD;
        return new ModInt(n);
    }

    public static ModInt Pow(ModInt m, long n)
    {
        if (n == 0) return 1;
        if (n % 2 == 0) return Pow(m * m, n >> 1);
        else return Pow(m * m, n >> 1) * m;
    }

    public static void Build(int n)
    {
        fac = new ModInt[n + 1];
        facinv = new ModInt[n + 1];
        inv = new ModInt[n + 1];
        inv[1] = fac[0] = fac[1] = facinv[0] = facinv[1] = 1;
        for (var i = 2; i <= n; i++)
        {
            fac[i] = fac[i - 1] * i;
            inv[i] = MOD - inv[MOD % i] * (MOD / i);
            facinv[i] = facinv[i - 1] * inv[i];
        }
    }
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static ModInt Fac(int n) => fac[n];
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static ModInt Inv(int n) => inv[n];
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static ModInt FacInv(int n) => facinv[n];
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static ModInt Comb(int n, int r)
    {
        if (n < r) return 0;
        if (n == r) return 1;
        return fac[n] * facinv[r] * facinv[n - r];
    }
    public static ModInt Perm(int n, int r)
    {
        if (n < r) return 0;
        return fac[n] * facinv[n - r];
    }

}

public class FastScanner
{
    //0x0a:LF 0x20:SPC 0x2d:- 0x30 ~ 0x39: 0 ~ 9
    static System.IO.Stream str = System.Console.OpenStandardInput();
    const int size = 1 << 10;
    static byte[] buffer = new byte[size];
    static int ptr;
    static int len;
    public int Int
    {
        get
        {
            var c = Read();
            while (c < 0x21)
            {
                c = Read();
            }
            var n = false;
            if (c == '-')
            {
                n = true;
                c = Read();
            }
            var ret = 0;
            while (c >= 0x30)
            {
                ret = ret * 10 + (c & 15);
                c = Read();
            }
            return n ? -ret : ret;
        }
    }
    public long Long
    {
        get
        {
            var c = Read();
            while (c < 0x21)
            {
                c = Read();
            }
            var n = false;
            if (c == '-')
            {
                n = true;
                c = Read();
            }
            var ret = 0L;
            while (c >= 0x30)
            {
                ret = ret * 10 + (c & 15);
                c = Read();
            }
            return n ? -ret : ret;
        }
    }
    byte Read()
    {
        if (ptr == len)
        {
            len = str.Read(buffer, 0, size);
            if (len == 0) return 0;
            ptr = 0;
        }
        return buffer[ptr++];
    }
}

#region Template
public partial class Solver
{
    public SC sc = new SC();
    static void Main(string[] args)
    {
        Console.SetOut(new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false });
        var sol = new Solver();
        int testcase = 1;
        //testcase = sol.sc.Int;
        //var th = new Thread(sol.Solve, 1 << 26);th.Start();th.Join();
        while (testcase-- > 0)
            sol.Solve();
        Console.Out.Flush();
    }
}
public static class Template
{
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static bool chmin<T>(ref T a, T b) where T : IComparable<T> { if (a.CompareTo(b) > 0) { a = b; return true; } return false; }
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static bool chmax<T>(ref T a, T b) where T : IComparable<T> { if (a.CompareTo(b) < 0) { a = b; return true; } return false; }
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static void swap<T>(ref T a, ref T b) { var t = b; b = a; a = t; }
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static void swap<T>(this IList<T> A, int i, int j) { var t = A[i]; A[i] = A[j]; A[j] = t; }
    public static T[] Create<T>(int n, Func<T> f) { var rt = new T[n]; for (var i = 0; i < rt.Length; ++i) rt[i] = f(); return rt; }
    public static T[] Create<T>(int n, Func<int, T> f) { var rt = new T[n]; for (var i = 0; i < rt.Length; ++i) rt[i] = f(i); return rt; }
    public static void Out<T>(this IList<T> A, out T a) => a = A[0];
    public static void Out<T>(this IList<T> A, out T a, out T b) { a = A[0]; b = A[1]; }
    public static void Out<T>(this IList<T> A, out T a, out T b, out T c) { A.Out(out a, out b); c = A[2]; }
    public static void Out<T>(this IList<T> A, out T a, out T b, out T c, out T d) { A.Out(out a, out b, out c); d = A[3]; }
    public static string Concat<T>(this IEnumerable<T> A, string sp) => string.Join(sp, A);
    public static char ToChar(this int s, char begin = '0') => (char)(s + begin);
    public static IEnumerable<T> Shuffle<T>(this IEnumerable<T> A) => A.OrderBy(v => Guid.NewGuid());
    public static int CompareTo<T>(this T[] A, T[] B, Comparison<T> cmp = null) { cmp = cmp ?? Comparer<T>.Default.Compare; for (var i = 0; i < Min(A.Length, B.Length); i++) { int c = cmp(A[i], B[i]); if (c > 0) return 1; else if (c < 0) return -1; } if (A.Length == B.Length) return 0; if (A.Length > B.Length) return 1; else return -1; }
    public static string ToStr<T>(this T[][] A) => A.Select(a => a.Concat(" ")).Concat("\n");
    public static int ArgMax<T>(this IList<T> A, Comparison<T> cmp = null) { cmp = cmp ?? Comparer<T>.Default.Compare; T max = A[0]; int rt = 0; for (int i = 1; i < A.Count; i++) if (cmp(max, A[i]) < 0) { max = A[i]; rt = i; } return rt; }
    public static T PopBack<T>(this List<T> A) { var v = A[A.Count - 1]; A.RemoveAt(A.Count - 1); return v; }
    public static void Fail<T>(T s) { Console.WriteLine(s); Console.Out.Close(); Environment.Exit(0); }
}
public class Scanner
{
    public string Str => Console.ReadLine().Trim();
    public int Int => int.Parse(Str);
    public long Long => long.Parse(Str);
    public double Double => double.Parse(Str);
    public int[] ArrInt => Str.Split(' ').Select(int.Parse).ToArray();
    public long[] ArrLong => Str.Split(' ').Select(long.Parse).ToArray();
    public char[][] Grid(int n) => Create(n, () => Str.ToCharArray());
    public int[] ArrInt1D(int n) => Create(n, () => Int);
    public long[] ArrLong1D(int n) => Create(n, () => Long);
    public int[][] ArrInt2D(int n) => Create(n, () => ArrInt);
    public long[][] ArrLong2D(int n) => Create(n, () => ArrLong);
    private Queue<string> q = new Queue<string>();
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public T Next<T>() { if (q.Count == 0) foreach (var item in Str.Split(' ')) q.Enqueue(item); return (T)Convert.ChangeType(q.Dequeue(), typeof(T)); }
    public void Make<T1>(out T1 v1) => v1 = Next<T1>();
    public void Make<T1, T2>(out T1 v1, out T2 v2) { v1 = Next<T1>(); v2 = Next<T2>(); }
    public void Make<T1, T2, T3>(out T1 v1, out T2 v2, out T3 v3) { Make(out v1, out v2); v3 = Next<T3>(); }
    public void Make<T1, T2, T3, T4>(out T1 v1, out T2 v2, out T3 v3, out T4 v4) { Make(out v1, out v2, out v3); v4 = Next<T4>(); }
    public void Make<T1, T2, T3, T4, T5>(out T1 v1, out T2 v2, out T3 v3, out T4 v4, out T5 v5) { Make(out v1, out v2, out v3, out v4); v5 = Next<T5>(); }
    public void Make<T1, T2, T3, T4, T5, T6>(out T1 v1, out T2 v2, out T3 v3, out T4 v4, out T5 v5, out T6 v6) { Make(out v1, out v2, out v3, out v4, out v5); v6 = Next<T6>(); }
    public void Make<T1, T2, T3, T4, T5, T6, T7>(out T1 v1, out T2 v2, out T3 v3, out T4 v4, out T5 v5, out T6 v6, out T7 v7) { Make(out v1, out v2, out v3, out v4, out v5, out v6); v7 = Next<T7>(); }
    public (T1, T2) Make<T1, T2>() { Make(out T1 v1, out T2 v2); return (v1, v2); }
    public (T1, T2, T3) Make<T1, T2, T3>() { Make(out T1 v1, out T2 v2, out T3 v3); return (v1, v2, v3); }
    public (T1, T2, T3, T4) Make<T1, T2, T3, T4>() { Make(out T1 v1, out T2 v2, out T3 v3, out T4 v4); return (v1, v2, v3, v4); }
}

#endregion