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.Diagnostics;
using System.Globalization;
using System.IO;
using System.Runtime.CompilerServices;
using System.Text;

internal partial class Solver {
    public void Run() {
        var n = ni();
        var q = ni();
        var a = nl(n);
        var seg = new LazySegmentTreeMulAndAddMonoidOperator(998244353).CreateLazySegmentTree();
        seg.Build(a);
        for (var _ = 0; _ < q; _++) {
            var t = ni();
            if (t == 0) {
                var l = ni();
                var r = ni();
                var b = ni();
                var c = ni();
                seg.LazyUpdate(l, r, new MulAndAddOperatorMonoid { Mul = b, Add = c });
            } else {
                var l = ni();
                var r = ni();
                cout.WriteLine(seg.Query(l, r));
            }
        }
    }
}

public interface ILazySegmentTreeDefinition<TMonoid, TOperatorMonoid> {
    TMonoid Merge(TMonoid left, TMonoid right);
    TMonoid Apply(TMonoid monoid, int begin, int @end, TOperatorMonoid operation);
    TOperatorMonoid MergeOperator(TOperatorMonoid current, TOperatorMonoid append);

    TMonoid Identity { get; }
    TOperatorMonoid OperatorIdentity { get; }
}
public static class LazySegmentTreeExtension {
    public static LazySegmentTree<TMonoid, TOperatorMonoid> CreateLazySegmentTree<TMonoid, TOperatorMonoid>
        (this ILazySegmentTreeDefinition<TMonoid, TOperatorMonoid> lazySegmentTreeMonoidOperator)
         where TOperatorMonoid : IEquatable<TOperatorMonoid> {
        return new LazySegmentTree<TMonoid, TOperatorMonoid>(
            lazySegmentTreeMonoidOperator.Merge,
            lazySegmentTreeMonoidOperator.Apply,
            lazySegmentTreeMonoidOperator.MergeOperator,
            lazySegmentTreeMonoidOperator.Identity,
            lazySegmentTreeMonoidOperator.OperatorIdentity
        );
    }

    public static bool Check<TMonoid, TOperatorMonoid>
        (this ILazySegmentTreeDefinition<TMonoid, TOperatorMonoid> lazySegmentTreeMonoidOperator, TMonoid m, TOperatorMonoid o1, TOperatorMonoid o2) {
        var r1 = lazySegmentTreeMonoidOperator.Apply(lazySegmentTreeMonoidOperator.Apply(m, 1, 2, o1), 1, 2, o2);
        var r2 = lazySegmentTreeMonoidOperator.Apply(m, 1, 2, lazySegmentTreeMonoidOperator.MergeOperator(o1, o2));
        return r1.Equals(r2);
    }
}

public sealed class LazySegmentTree<TMonoid, TOperatorMonoid> where TOperatorMonoid : IEquatable<TOperatorMonoid> {
    private int Count;

    private TMonoid[] _node;
    private TOperatorMonoid[] _operators;
    private int[] _height;
    private int[] _begin, _end;
    private readonly TMonoid _identity;
    private readonly TOperatorMonoid _operatorIdentity;
    private readonly Func<TMonoid, TMonoid, TMonoid> _merge;
    private readonly Func<TMonoid, int, int, TOperatorMonoid, TMonoid> _apply;
    private readonly Func<TOperatorMonoid, TOperatorMonoid, TOperatorMonoid> _mergeOperator;

    public LazySegmentTree(
        Func<TMonoid, TMonoid, TMonoid> merge,
        Func<TMonoid, int, int, TOperatorMonoid, TMonoid> apply,
        Func<TOperatorMonoid, TOperatorMonoid, TOperatorMonoid> mergeOperator,
        TMonoid identity,
        TOperatorMonoid operatorIdentity) {
        _merge = merge;
        _apply = apply;
        _mergeOperator = mergeOperator;
        _identity = identity;
        _operatorIdentity = operatorIdentity;
    }

    public void Build(IList<TMonoid> array) {
        Build(array.Count, i => array[i]);
    }

    public void Build(int n, Func<int, TMonoid> create) {
        Count = n;

        _node = new TMonoid[2 * Count];
        _operators = new TOperatorMonoid[2 * Count];
        _begin = new int[2 * Count];
        _end = new int[2 * Count];
        _height = new int[2 * Count];
        for (var i = 0; i < _node.Length; i++) {
            _node[i] = _identity;
            _operators[i] = _operatorIdentity;
        }

        for (var i = 0; i < n; i++) {
            _node[i + Count] = create(i);
            _begin[i + Count] = i;
            _end[i + Count] = i + 1;
        }

        for (var i = 2; i < _height.Length; i++) {
            _height[i] = _height[i >> 1] + 1;
        }

        for (var i = Count - 1; i > 0; i--) {
            _node[i] = _merge(_node[i << 1], _node[i << 1 | 1]);
            _begin[i] = _begin[i << 1];
            _end[i] = _end[i << 1 | 1];
        }
    }

    private void Propagate(int k) {
        if (_operators[k].Equals(_operatorIdentity)) return;
        int childL = k << 1, childR = childL | 1;
        _operators[childL] = _mergeOperator(_operators[childL], _operators[k]);
        _operators[childR] = _mergeOperator(_operators[childR], _operators[k]);
        _node[k] = Apply(k);
        _operators[k] = _operatorIdentity;
    }

    public TMonoid Query(int begin, int end) {
        TMonoid lv = _identity, rv = _identity;
        begin += Count;
        end += Count;
        TopDownOperators(begin);
        TopDownOperators(end - 1);
        for (int l = begin, r = end - 1; l <= r; l >>= 1, r >>= 1) {
            if ((l & 1) == 1) { lv = _merge(lv, Apply(l++)); }
            if ((r & 1) == 0) { rv = _merge(Apply(r--), rv); }
        }
        return _merge(lv, rv);
    }

    public void LazyUpdate(int begin, int end, TOperatorMonoid @operator) {
        begin += Count;
        end += Count;
        TopDownOperators(begin);
        TopDownOperators(end - 1);
        for (int l = begin, r = end - 1; l <= r; l >>= 1, r >>= 1) {
            if ((l & 1) == 1) { _operators[l] = _mergeOperator(_operators[l], @operator); l++; }
            if ((r & 1) == 0) { _operators[r] = _mergeOperator(_operators[r], @operator); r--; }
        }
        BottomUpMonoids(begin);
        BottomUpMonoids(end - 1);
    }

    private void TopDownOperators(int k) {
        for (var i = _height[k]; i > 0; i--) {
            Propagate(k >> i);
        }
    }

    private TMonoid Apply(int k) {
        if (_operators[k].Equals(_operatorIdentity)) return _node[k];
        return _apply(_node[k], _begin[k], _end[k], _operators[k]);
    }

    private void BottomUpMonoids(int k) {
        while ((k >>= 1) > 0) {
            _node[k] = _merge(Apply(k << 1), Apply(k << 1 | 1));
        }
    }

    public TMonoid this[int index] {
        get {
            index += Count;
            TopDownOperators(index);
            return Apply(index);
        }
        set {
            index += Count;
            TopDownOperators(index);
            _node[index] = value;
            _operators[index] = _operatorIdentity;
            BottomUpMonoids(index);
        }
    }

    public void Diagonsis() {
        for (var i = 1; i < Count; i++) {
            Propagate(i);
            var ex = _merge(Apply(i << 1), Apply(i << 1 | 1));
            var ex2 = Apply(i);
            if (!ex2.Equals(ex)) throw new Exception();
        }
    }

}



// example

public struct MulAndAddOperatorMonoid : IEquatable<MulAndAddOperatorMonoid> {
    public long Mul;
    public long Add;

    public bool Equals(MulAndAddOperatorMonoid other) {
        return Mul == other.Mul && Add == other.Add;
    }
}

/// <summary>
/// query       : a1 + a2 + ... + an
/// range-update: a <- a * Mul + Add
/// </summary>
public class LazySegmentTreeMulAndAddMonoidOperator : ILazySegmentTreeDefinition<long, MulAndAddOperatorMonoid> {
    private readonly int _mod;

    public long Identity { get { return 0; } }
    public MulAndAddOperatorMonoid OperatorIdentity { get { return new MulAndAddOperatorMonoid { Mul = 1 }; } }

    public LazySegmentTreeMulAndAddMonoidOperator(int mod) {
        _mod = mod;
    }

    public long Merge(long left, long right) {
        return (left + right) % _mod;
    }

    public long Apply(long monoid, int begin, int end, MulAndAddOperatorMonoid operation) {
        if (operation.Mul == 1 && operation.Add == 0) return monoid;
        // (a1 * mul + add) + (a2 * mul + add) + ... (a_n * mul + add)
        // (a1 + .. a_n) * mul + add * n
        return (1L * monoid * operation.Mul + 1L * operation.Add * (end - begin)) % _mod;
    }

    public MulAndAddOperatorMonoid MergeOperator(MulAndAddOperatorMonoid current, MulAndAddOperatorMonoid append) {
        if (current.Mul == 1 && current.Add == 0) return append;
        // (x * mul1 + add1) * mul2 + add2
        // x * mul1 * mul2 + add1 * mul2 + add2
        return new MulAndAddOperatorMonoid {
            Mul = current.Mul * append.Mul % _mod,
            Add = (current.Add * append.Mul + append.Add) % _mod,
        };
    }
}
// PREWRITEN CODE BEGINS FROM HERE
internal partial class Solver : Scanner {
    public static void Main(string[] args) {
#if LOCAL
        var inputBuffer = new byte[1000000];
        var inputStream = Console.OpenStandardInput(inputBuffer.Length);
        using (var reader = new StreamReader(inputStream, Console.InputEncoding, false, inputBuffer.Length)) {
            Console.SetIn(reader);
            new Solver(Console.In, Console.Out).Run();
        }
#else
        Console.SetOut(new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false });
        new Solver(Console.In, Console.Out).Run();
        Console.Out.Flush();
#endif
    }

#pragma warning disable IDE0052
    private readonly TextReader cin;
    private readonly TextWriter cout;
#pragma warning restore IDE0052

    public Solver(TextReader reader, TextWriter writer)
        : base(reader) {
        cin = reader;
        cout = writer;
    }
    public Solver(string input, TextWriter writer)
        : this(new StringReader(input), writer) {
    }

#pragma warning disable IDE1006
#pragma warning disable IDE0051
    private int ni() { return NextInt(); }
    private int[] ni(int n) { return NextIntArray(n); }
    private long nl() { return NextLong(); }
    private long[] nl(int n) { return NextLongArray(n); }
    private double nd() { return NextDouble(); }
    private double[] nd(int n) { return NextDoubleArray(n); }
    private string ns() { return Next(); }
    private string[] ns(int n) { return NextArray(n); }
#pragma warning restore IDE1006
#pragma warning restore IDE0051
}

internal static class LinqPadExtension {
    [Conditional("DEBUG")]
    public static void Dump<T>(this T obj) {
#if DEBUG
        LINQPad.Extensions.Dump(obj);
#endif
    }
}

public class Scanner {
    private readonly TextReader Reader;
    private readonly CultureInfo ci = CultureInfo.InvariantCulture;

    private readonly char[] buffer = new char[2 * 1024];
    private int cursor = 0, length = 0;
    private string Token;
    private readonly StringBuilder sb = new StringBuilder(1024);

    public Scanner()
        : this(Console.In) {
    }

    public Scanner(TextReader reader) {
        Reader = reader;
    }

    public int NextInt() { return checked((int)NextLong()); }
    public long NextLong() {
        var s = Next();
        long r = 0;
        var i = 0;
        var negative = false;
        if (s[i] == '-') {
            negative = true;
            i++;
        }
        for (; i < s.Length; i++) {
            r = r * 10 + (s[i] - '0');
#if DEBUG
            if (!char.IsDigit(s[i])) {
                throw new FormatException();
            }
#endif
        }
        return negative ? -r : r;
    }
    public double NextDouble() { return double.Parse(Next(), ci); }
    public string[] NextArray(int size) {
        var array = new string[size];
        for (var i = 0; i < size; i++) {
            array[i] = Next();
        }

        return array;
    }
    public int[] NextIntArray(int size) {
        var array = new int[size];
        for (var i = 0; i < size; i++) {
            array[i] = NextInt();
        }

        return array;
    }

    public long[] NextLongArray(int size) {
        var array = new long[size];
        for (var i = 0; i < size; i++) {
            array[i] = NextLong();
        }

        return array;
    }

    public double[] NextDoubleArray(int size) {
        var array = new double[size];
        for (var i = 0; i < size; i++) {
            array[i] = NextDouble();
        }

        return array;
    }

    public string Next() {
        if (Token == null) {
            if (!StockToken()) {
                throw new InvalidOperationException();
            }
        }
        var token = Token;
        Token = null;
        return token;
    }

    public bool HasNext() {
        if (Token != null) {
            return true;
        }

        return StockToken();
    }

    private bool StockToken() {
        while (true) {
            sb.Clear();
            while (true) {
                if (cursor >= length) {
                    cursor = 0;
                    if ((length = Reader.Read(buffer, 0, buffer.Length)) <= 0) {
                        break;
                    }
                }
                var c = buffer[cursor++];
                if (33 <= c && c <= 126) {
                    sb.Append(c);
                } else {
                    if (sb.Length > 0) {
                        break;
                    }
                }
            }

            if (sb.Length > 0) {
                Token = sb.ToString();
                return true;
            }

            return false;
        }
    }
}