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 Kotlin (1.3.71) (judge verdict: Accepted)

@file:Suppress("NOTHING_TO_INLINE", "EXPERIMENTAL_FEATURE_WARNING", "OVERRIDE_BY_INLINE")
//@file:OptIn(ExperimentalStdlibApi::class)

import java.io.PrintWriter
import java.util.PriorityQueue
import kotlin.math.*
import kotlin.random.Random
import kotlin.collections.sort as _sort
import kotlin.collections.sortDescending as _sortDescending
import kotlin.io.println as iprintln


/** @author Spheniscine */
fun main() { _writer.solve(); _writer.flush() }
fun PrintWriter.solve() {
//    val startTime = System.nanoTime()

    val numCases = 1//readInt()
    case@ for(case in 1..numCases) {
//        print("Case #$case: ")

        val n = readInt()
        val q = readInt()

        val A = PropagatingSegmentTree(n)
        A.build { ModInt(readInt()) }

        repeat(q) {
            val op = readInt()
            val l = readInt()
            val r = readInt()

            if(op == 0) {
                val a = readInt()
                val b = readInt()

                A.update(l, r, Affine(a, b))
            } else {
                val ans = A.query(l, r)
                println(ans)
            }
        }
    }

//    iprintln("Time: ${(System.nanoTime() - startTime) / 1000000} ms")
}

data class Affine(val a: ModInt, val b: ModInt) {
    fun compose(other: Affine) = Affine(a * other.a, b * other.a + other.b)
}
fun Affine(a: Int, b: Int) = Affine(ModInt(a), ModInt(b))

class PropagatingSegmentTree(
    val size: Int //,
//    val identityValue: T,
//    val combiner: (T, T) -> T,
//    val updateIdentity: U,
//    val updateCombiner: (U, U) -> U,
//    val updater: (T, U) -> T
) {
    /* degenericization helpers */
    inline val identityValue: ModInt get() = ModInt(0)
    inline fun combiner(a: ModInt, b: ModInt): ModInt = a + b
    inline val updateIdentity: Affine get() = Affine(1, 0)
    inline fun updateCombiner(a: Affine, b: Affine): Affine = a.compose(b)
    inline fun updater(t: ModInt, u: Affine, a: Int, b: Int): ModInt {
        val sz = b-a+1
        return t * u.a + u.b * sz
    }

    private inline fun treeSize() = if(size == 0) 0 else Integer.highestOneBit(size.shl(2) - 1)

    @Suppress("UNCHECKED_CAST")
    private val tree = ModIntArray(treeSize())// { identityValue } as Array<ModInt>
    @Suppress("UNCHECKED_CAST")
    private val lazy = Array<Affine>(tree.size) { updateIdentity }

    fun build(list: ModIntArray) {
        if(size == 0) return
        build(list, 1, 0, size-1)
    }

    inline fun build(generator: (Int) -> ModInt) { build(ModIntArray(size) { generator(it) }) }

    private inline fun mid(low: Int, high: Int) = (low + high) shr 1
    private fun build(list: ModIntArray, node: Int, a: Int, b: Int) {
        if(a == b) {
            tree[node] = list[a]
            return
        }

        build(list, node shl 1, a, mid(a, b))
        build(list, node shl 1 or 1, 1 + mid(a, b), b)
        updateNode(node)
    }

    private inline fun updateNode(i: Int) {
        tree[i] = combiner(tree[i shl 1], tree[i shl 1 or 1])
    }

    fun update(start: Int, endx: Int, value: Affine) {
        update(1, 0, size-1, start, endx-1, value)
    }
    fun update(range: IntRange, value: Affine) {
        update(range.first, range.last + 1, value)
    }

    private inline fun updateLazy(i: Int, u: Affine) {
        lazy[i] = updateCombiner(lazy[i], u)
    }

    private fun propagate(node: Int, a: Int, b: Int) {
        tree[node] = updater(tree[node], lazy[node], a, b)
        if(a != b) {
            updateLazy(node shl 1, lazy[node])
            updateLazy(node shl 1 or 1, lazy[node])
        }
        lazy[node] = updateIdentity
    }

    private fun update(node: Int, a: Int, b: Int, i: Int, j: Int, u: Affine) {
        if(lazy[node] != updateIdentity) {
            propagate(node, a, b)
        }

        if(a > b || a > j || b < i) return

        if(a >= i && b <= j) {
            lazy[node] = u
            propagate(node, a, b)
            return
        }

        update(node shl 1, a, mid(a, b), i, j, u)
        update(node shl 1 or 1, 1 + mid(a, b), b, i, j, u)

        updateNode(node)
    }

    fun query(start: Int, endx: Int) =
        query(1, 0, size-1, start, endx-1)
    fun query(range: IntRange) =
        query(range.first, range.last+1)

    private fun query(node: Int, a: Int, b: Int, i: Int, j: Int): ModInt {
        if(a > b || a > j || b < i) return identityValue
        if(lazy[node] != updateIdentity) {
            propagate(node, a, b)
        }

        if(a >= i && b <= j) {
            return tree[node]
        }

        val l = query(node shl 1, a, mid(a, b), i, j)
        val r = query(node shl 1 or 1, 1 + mid(a, b), b, i, j)

        return combiner(l, r)
    }

    val root get() = tree[1]
}

const val MOD = 998244353
const val TOTIENT = MOD - 1 // assumes MOD is prime

infix fun Int.modulo(mod: Int): Int = (this % mod).let { (it shr Int.SIZE_BITS - 1 and mod) + it }
infix fun Long.modulo(mod: Long) = (this % mod).let { (it shr Long.SIZE_BITS - 1 and mod) + it }
infix fun Long.modulo(mod: Int) = modulo(mod.toLong()).toInt()

fun Int.mulMod(other: Int, mod: Int) = toLong() * other modulo mod

fun Int.powMod(exponent: Long, mod: Int): Int {
    if(exponent < 0) error("Inverse not implemented")
    var res = 1L
    var e = exponent
    var b = modulo(mod).toLong()

    while(e > 0) {
        if(e and 1 == 1L) {
            res = res * b % mod
        }
        e = e shr 1
        b = b * b % mod
    }
    return res.toInt()
}
fun Int.powMod(exponent: Int, mod: Int) = powMod(exponent.toLong(), mod)
fun Int.modPowArray(n: Int, mod: Int): IntArray {
    val res = IntArray(n+1)
    res[0] = 1
    for(i in 1..n) res[i] = mulMod(res[i-1], mod)
    return res
}

inline fun Int.toModInt() = ModInt(this modulo MOD)
inline fun Long.toModInt() = ModInt(this modulo MOD)

/** note: Only use constructor for int within modulo range, otherwise use toModInt **/
inline class ModInt(val int: Int) {
    companion object {
        /** can't seem to make these private or inlined without causing compiler issues */
        @JvmField val _invMemo = HashMap<ModInt, ModInt>()
        fun _invMemoized(m: ModInt) = _invMemo.getOrPut(m) { m.inv_unmemoized() }
    }

    // normalizes an integer that's within range [-MOD, MOD) without branching
    private inline fun normalize(int: Int) = ModInt((int shr Int.SIZE_BITS - 1 and MOD) + int)

    operator fun plus(other: ModInt) = normalize(int + other.int - MOD) // overflow-safe even if MOD >= 2^30
    inline operator fun plus(other: Int) = plus(other.toModInt())
    operator fun inc() = normalize(int + (1 - MOD))

    operator fun minus(other: ModInt) = normalize(int - other.int)
    inline operator fun minus(other: Int) = minus(other.toModInt())
    operator fun dec() = normalize(int - 1)
    operator fun unaryMinus() = normalize(-int)

    operator fun times(other: ModInt) = ModInt((int.toLong() * other.int % MOD).toInt())
    inline operator fun times(other: Int) = ModInt(int.mulMod(other, MOD))

    fun pow(exponent: Int): ModInt {
        val e = if(exponent < 0) {
            require(int != 0) { "Can't invert/divide by 0" }
            exponent modulo TOTIENT
        } else exponent
        return ModInt(int.powMod(e, MOD))
    }

    fun pow(exponent: Long) = if(int == 0) when {
        exponent > 0 -> this
        exponent == 0L -> ModInt(1)
        else -> error("Can't invert/divide by 0")
    } else pow(exponent modulo TOTIENT)

    inline fun inverse() = inv_memoized() /** NOTE: Change if necessary */

    fun inv_unmemoized(): ModInt {
        require(int != 0) { "Can't invert/divide by 0" }
        return pow(TOTIENT - 1)
    }
    inline fun inv_memoized() = _invMemoized(this)

    operator fun div(other: ModInt) = times(other.inverse())
    inline operator fun div(other: Int) = div(other.toModInt())

    override inline fun toString() = int.toString()
}

inline operator fun Int.plus(modInt: ModInt) = modInt + this
inline operator fun Int.minus(modInt: ModInt) = toModInt() - modInt
inline operator fun Int.times(modInt: ModInt) = modInt * this
inline operator fun Int.div(modInt: ModInt) = modInt.inverse() * this

inline class ModIntArray(val intArray: IntArray): Collection<ModInt> {
    inline operator fun get(i: Int) = ModInt(intArray[i])
    inline operator fun set(i: Int, v: ModInt) { intArray[i] = v.int }

    override inline val size: Int get() = intArray.size
    inline val lastIndex get() = intArray.lastIndex
    inline val indices get() = intArray.indices

    override inline fun contains(element: ModInt): Boolean = element.int in intArray

    override fun containsAll(elements: Collection<ModInt>): Boolean = elements.all(::contains)

    override inline fun isEmpty(): Boolean = intArray.isEmpty()

    override fun iterator(): Iterator<ModInt> = object: Iterator<ModInt> {
        var index = 0
        override fun hasNext(): Boolean = index < size
        override fun next(): ModInt = get(index++)
    }

    fun copyOf(newSize: Int) = ModIntArray(intArray.copyOf(newSize))
    fun copyOf() = copyOf(size)
}
fun ModIntArray.copyInto(destination: ModIntArray, destinationOffset: Int = 0, startIndex: Int = 0, endIndex: Int = size) =
    ModIntArray(intArray.copyInto(destination.intArray, destinationOffset, startIndex, endIndex))
inline fun ModIntArray(size: Int) = ModIntArray(IntArray(size))
inline fun ModIntArray(size: Int, init: (Int) -> ModInt) = ModIntArray(IntArray(size) { init(it).int })

fun ModInt.powArray(n: Int) = ModIntArray(int.modPowArray(n, MOD))

inline fun ModIntArray.first() = get(0)
inline fun ModIntArray.last() = get(lastIndex)
inline fun ModIntArray.joinToString(separator: CharSequence) = intArray.joinToString(separator)
inline fun <R> ModIntArray.fold(init: R, op: (acc: R, ModInt) -> R) = intArray.fold(init) { acc, i -> op(acc, ModInt(i)) }
inline fun <R> ModIntArray.foldRight(init: R, op: (ModInt, acc: R) -> R) = intArray.foldRight(init) { i, acc -> op(ModInt(i), acc) }
fun ModIntArray.sum() = fold(ModInt(0), ModInt::plus)
fun ModIntArray.product() = fold(ModInt(1), ModInt::times)

inline fun <T> Iterable<T>.sumByModInt(func: (T) -> ModInt) = fold(ModInt(0)) { acc, t -> acc + func(t) }
inline fun <T> Iterable<T>.productByModInt(func: (T) -> ModInt) = fold(ModInt(1)) { acc, t -> acc * func(t) }
inline fun <T> Sequence<T>.sumByModInt(func: (T) -> ModInt) = fold(ModInt(0)) { acc, t -> acc + func(t) }
inline fun <T> Sequence<T>.productByModInt(func: (T) -> ModInt) = fold(ModInt(1)) { acc, t -> acc * func(t) }
inline fun <T> Array<T>.sumByModInt(func: (T) -> ModInt) = fold(ModInt(0)) { acc, t -> acc + func(t) }
inline fun <T> Array<T>.productByModInt(func: (T) -> ModInt) = fold(ModInt(1)) { acc, t -> acc * func(t) }
fun Iterable<ModInt>.sum() = sumByModInt { it }
fun Sequence<ModInt>.sum() = sumByModInt { it }
fun Iterable<ModInt>.product() = productByModInt { it }
fun Sequence<ModInt>.product() = productByModInt { it }
fun Collection<ModInt>.toModIntArray() = ModIntArray(size).also { var i = 0; for(e in this) { it[i++] = e } }


/** IO */
//@JvmField val INPUT = File("input.txt").inputStream()
//@JvmField val OUTPUT = File("output.txt").outputStream()
@JvmField val INPUT = System.`in`
@JvmField val OUTPUT = System.out

const val _BUFFER_SIZE = 1 shl 16
@JvmField val _buffer = ByteArray(_BUFFER_SIZE)
@JvmField var _bufferPt = 0
@JvmField var _bytesRead = 0

tailrec fun readChar(): Char {
    if(_bufferPt == _bytesRead) {
        _bufferPt = 0
        _bytesRead = INPUT.read(_buffer, 0, _BUFFER_SIZE)
    }
    return if(_bytesRead < 0) Char.MIN_VALUE
    else {
        val c = _buffer[_bufferPt++].toChar()
        if (c == '\r') readChar()
        else c
    }
}

fun readLine(): String? {
    var c = readChar()
    return if(c == Char.MIN_VALUE) null
    else buildString {
        while(c != '\n' && c != Char.MIN_VALUE) {
            append(c)
            c = readChar()
        }
    }
}
fun readLn() = readLine()!!

fun read() = buildString {
    var c = readChar()
    while(c <= ' ') {
        if(c == Char.MIN_VALUE) return@buildString
        c = readChar()
    }
    do {
        append(c)
        c = readChar()
    } while(c > ' ')
}
fun readInt() = read().toInt()
fun readDouble() = read().toDouble()
fun readLong() = read().toLong()
fun readStrings(n: Int) = List(n) { read() }
fun readLines(n: Int) = List(n) { readLn() }
fun readInts(n: Int) = List(n) { read().toInt() }
fun readIntArray(n: Int) = IntArray(n) { read().toInt() }
fun readDoubles(n: Int) = List(n) { read().toDouble() }
fun readDoubleArray(n: Int) = DoubleArray(n) { read().toDouble() }
fun readLongs(n: Int) = List(n) { read().toLong() }
fun readLongArray(n: Int) = LongArray(n) { read().toLong() }

@JvmField val _writer = PrintWriter(OUTPUT, false)

/** shuffles and sort overrides to avoid quicksort attacks */
private inline fun <T> _shuffle(rnd: Random, get: (Int) -> T, set: (Int, T) -> Unit, size: Int) {
    // Fisher-Yates shuffle algorithm
    for (i in size - 1 downTo 1) {
        val j = rnd.nextInt(i + 1)
        val temp = get(i)
        set(i, get(j))
        set(j, temp)
    }
}

@JvmField var _random: Random? = null
val random get() = _random ?: Random(0x594E215C123 * System.nanoTime()).also { _random = it }

fun IntArray.shuffle(rnd: Random = random) = _shuffle(rnd, ::get, ::set, size)
fun IntArray.sort() { shuffle(); _sort() }
fun IntArray.sortDescending() { shuffle(); _sortDescending() }

fun LongArray.shuffle(rnd: Random = random) = _shuffle(rnd, ::get, ::set, size)
fun LongArray.sort() { shuffle(); _sort() }
fun LongArray.sortDescending() { shuffle(); _sortDescending() }

fun DoubleArray.shuffle(rnd: Random = random) = _shuffle(rnd, ::get, ::set, size)
fun DoubleArray.sort() { shuffle(); _sort() }
fun DoubleArray.sortDescending() { shuffle(); _sortDescending() }

fun CharArray.shuffle(rnd: Random = random) = _shuffle(rnd, ::get, ::set, size)
inline fun CharArray.sort() { _sort() }
inline fun CharArray.sortDescending() { _sortDescending() }

inline fun <T: Comparable<T>> Array<out T>.sort() = _sort()
inline fun <T: Comparable<T>> Array<out T>.sortDescending() = _sortDescending()
inline fun <T: Comparable<T>> MutableList<out T>.sort() = _sort()
inline fun <T: Comparable<T>> MutableList<out T>.sortDescending() = _sortDescending()

fun `please stop removing these imports IntelliJ`() { iprintln(max(1, 2)) }

/** additional commons */
inline fun <T> Iterable<T>.sumByLong(func: (T) -> Long) = fold(0L) { acc, t -> acc + func(t) }
inline fun <T> Sequence<T>.sumByLong(func: (T) -> Long) = fold(0L) { acc, t -> acc + func(t) }
inline fun <T> Array<T>.sumByLong(func: (T) -> Long) = fold(0L) { acc, t -> acc + func(t) }
fun IntArray.sumLong() = fold(0L, Long::plus)