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 Rust (1.42.0) (judge verdict: Accepted)

#[allow(unused_imports)]
use std::cmp::*;
#[allow(unused_imports)]
use std::collections::*;
use std::io::Read;

#[allow(dead_code)]
fn getline() -> String {
    let mut ret = String::new();
    std::io::stdin().read_line(&mut ret).ok().unwrap();
    ret
}

fn get_word() -> String {
    let stdin = std::io::stdin();
    let mut stdin=stdin.lock();
    let mut u8b: [u8; 1] = [0];
    loop {
        let mut buf: Vec<u8> = Vec::with_capacity(16);
        loop {
            let res = stdin.read(&mut u8b);
            if res.unwrap_or(0) == 0 || u8b[0] <= b' ' {
                break;
            } else {
                buf.push(u8b[0]);
            }
        }
        if buf.len() >= 1 {
            let ret = String::from_utf8(buf).unwrap();
            return ret;
        }
    }
}

#[allow(dead_code)]
fn get<T: std::str::FromStr>() -> T { get_word().parse().ok().unwrap() }

/**
 * Lazy Segment Tree. This data structure is useful for fast folding and updating on intervals of an array
 * whose elements are elements of monoid T. Note that constructing this tree requires the identity
 * element of T and the operation of T. This is monomorphised, because of efficiency. T := i64, biop = max, upop = (+)
 * Reference: http://d.hatena.ne.jp/kyuridenamida/20121114/1352835261
 * Verified by https://codeforces.com/contest/1114/submission/49759034
 */
pub trait ActionRing {
    type T: Clone + Copy; // data
    type U: Clone + Copy + PartialEq + Eq; // action
    fn biop(x: Self::T, y: Self::T) -> Self::T;
    fn update(x: Self::T, a: Self::U, height: usize) -> Self::T;
    fn upop(fst: Self::U, snd: Self::U) -> Self::U;
    fn e() -> Self::T;
    fn upe() -> Self::U; // identity for upop
}
pub struct LazySegTree<R: ActionRing> {
    n: usize,
    dep: usize,
    dat: Vec<R::T>,
    lazy: Vec<R::U>,
}

impl<R: ActionRing> LazySegTree<R> {
    pub fn new(n_: usize) -> Self {
        let mut n = 1;
        let mut dep = 0;
        while n < n_ { n *= 2; dep += 1; } // n is a power of 2
        LazySegTree {
            n: n,
            dep: dep,
            dat: vec![R::e(); 2 * n - 1],
            lazy: vec![R::upe(); 2 * n - 1]
        }
    }
    #[inline]
    fn lazy_evaluate_node(&mut self, k: usize, height: usize) {
        if self.lazy[k] == R::upe() { return; }
        self.dat[k] = R::update(self.dat[k], self.lazy[k], height);
        if k < self.n - 1 {
            self.lazy[2 * k + 1] = R::upop(self.lazy[2 * k + 1], self.lazy[k]);
            self.lazy[2 * k + 2] = R::upop(self.lazy[2 * k + 2], self.lazy[k]);
        }
        self.lazy[k] = R::upe(); // identity for upop
    }
    #[inline]
    fn update_node(&mut self, k: usize) {
        self.dat[k] = R::biop(self.dat[2 * k + 1], self.dat[2 * k + 2]);
    }
    fn update_sub(&mut self, a: usize, b: usize, v: R::U, k: usize, height: usize, l: usize, r: usize) {
        self.lazy_evaluate_node(k, height);

        // [a,b) and  [l,r) intersects?
        if r <= a || b <= l {return;}
        if a <= l && r <= b {
            self.lazy[k] = R::upop(self.lazy[k], v);
            self.lazy_evaluate_node(k, height);
            return;
        }

        self.update_sub(a, b, v, 2 * k + 1, height - 1, l, (l + r) / 2);
        self.update_sub(a, b, v, 2 * k + 2, height - 1, (l + r) / 2, r);
        self.update_node(k);
    }
    /* ary[i] = upop(ary[i], v) for i in [a, b) (half-inclusive) */
    #[inline]
    pub fn update(&mut self, a: usize, b: usize, v: R::U) {
        let n = self.n;
        let dep = self.dep;
        self.update_sub(a, b, v, 0, dep, 0, n);
    }
    /* l,r are for simplicity */
    fn query_sub(&mut self, a: usize, b: usize, k: usize, height: usize, l: usize, r: usize) -> R::T {
        self.lazy_evaluate_node(k, height);

        // [a,b) and  [l,r) intersect?
        if r <= a || b <= l {return R::e();}
        if a <= l && r <= b {return self.dat[k];}
        let vl = self.query_sub(a, b, 2 * k + 1, height - 1, l, (l + r) / 2);
        let vr = self.query_sub(a, b, 2 * k + 2, height - 1, (l + r) / 2, r);
        self.update_node(k);
        R::biop(vl, vr)
    }
    /* [a, b) (note: half-inclusive) */
    #[inline]
    pub fn query(&mut self, a: usize, b: usize) -> R::T {
        let n = self.n;
        let dep = self.dep;
        self.query_sub(a, b, 0, dep, 0, n)
    }
}

/// Verified by https://atcoder.jp/contests/arc093/submissions/3968098
mod mod_int {
    use std::ops::*;
    pub trait Mod: Copy { fn m() -> i64; }
    #[derive(Copy, Clone, Hash, PartialEq, Eq, PartialOrd, Ord)]
    pub struct ModInt<M> { pub x: i64, phantom: ::std::marker::PhantomData<M> }
    impl<M: Mod> ModInt<M> {
        // x >= 0
        pub fn new(x: i64) -> Self { ModInt::new_internal(x % M::m()) }
        fn new_internal(x: i64) -> Self {
            ModInt { x: x, phantom: ::std::marker::PhantomData }
        }
        pub fn pow(self, mut e: i64) -> Self {
            debug_assert!(e >= 0);
            let mut sum = ModInt::new_internal(1);
            let mut cur = self;
            while e > 0 {
                if e % 2 != 0 { sum *= cur; }
                cur *= cur;
                e /= 2;
            }
            sum
        }
        #[allow(dead_code)]
        pub fn inv(self) -> Self { self.pow(M::m() - 2) }
    }
    impl<M: Mod, T: Into<ModInt<M>>> Add<T> for ModInt<M> {
        type Output = Self;
        fn add(self, other: T) -> Self {
            let other = other.into();
            let mut sum = self.x + other.x;
            if sum >= M::m() { sum -= M::m(); }
            ModInt::new_internal(sum)
        }
    }
    impl<M: Mod, T: Into<ModInt<M>>> Sub<T> for ModInt<M> {
        type Output = Self;
        fn sub(self, other: T) -> Self {
            let other = other.into();
            let mut sum = self.x - other.x;
            if sum < 0 { sum += M::m(); }
            ModInt::new_internal(sum)
        }
    }
    impl<M: Mod, T: Into<ModInt<M>>> Mul<T> for ModInt<M> {
        type Output = Self;
        fn mul(self, other: T) -> Self { ModInt::new(self.x * other.into().x % M::m()) }
    }
    impl<M: Mod, T: Into<ModInt<M>>> AddAssign<T> for ModInt<M> {
        fn add_assign(&mut self, other: T) { *self = *self + other; }
    }
    impl<M: Mod, T: Into<ModInt<M>>> SubAssign<T> for ModInt<M> {
        fn sub_assign(&mut self, other: T) { *self = *self - other; }
    }
    impl<M: Mod, T: Into<ModInt<M>>> MulAssign<T> for ModInt<M> {
        fn mul_assign(&mut self, other: T) { *self = *self * other; }
    }
    impl<M: Mod> Neg for ModInt<M> {
        type Output = Self;
        fn neg(self) -> Self { ModInt::new(0) - self }
    }
    impl<M> ::std::fmt::Display for ModInt<M> {
        fn fmt(&self, f: &mut ::std::fmt::Formatter) -> ::std::fmt::Result {
            self.x.fmt(f)
        }
    }
    impl<M: Mod> ::std::fmt::Debug for ModInt<M> {
        fn fmt(&self, f: &mut ::std::fmt::Formatter) -> ::std::fmt::Result {
            let (mut a, mut b, _) = red(self.x, M::m());
            if b < 0 {
                a = -a;
                b = -b;
            }
            write!(f, "{}/{}", a, b)
        }
    }
    impl<M: Mod> From<i64> for ModInt<M> {
        fn from(x: i64) -> Self { Self::new(x) }
    }
    // Finds the simplest fraction x/y congruent to r mod p.
    // The return value (x, y, z) satisfies x = y * r + z * p.
    fn red(r: i64, p: i64) -> (i64, i64, i64) {
        if r.abs() <= 10000 {
            return (r, 1, 0);
        }
        let mut nxt_r = p % r;
        let mut q = p / r;
        if 2 * nxt_r >= r {
            nxt_r -= r;
            q += 1;
        }
        if 2 * nxt_r <= -r {
            nxt_r += r;
            q -= 1;
        }
        let (x, z, y) = red(nxt_r, r);
        (x, y - q * z, z)
    }
} // mod mod_int

macro_rules! define_mod {
    ($struct_name: ident, $modulo: expr) => {
        #[derive(Copy, Clone, PartialEq, Eq, PartialOrd, Ord, Hash)]
        struct $struct_name {}
        impl mod_int::Mod for $struct_name { fn m() -> i64 { $modulo } }
    }
}
const MOD: i64 = 998_244_353;
define_mod!(P, MOD);
type ModInt = mod_int::ModInt<P>;

enum Affine {}

impl ActionRing for Affine {
    type T = ModInt; // data
    type U = (ModInt, ModInt); // action, (a, b) |-> x |-> ax + b
    fn biop(x: Self::T, y: Self::T) -> Self::T {
        x + y
    }
    fn update(x: Self::T, (a, b): Self::U, height: usize) -> Self::T {
        x * a + b * (1 << height)
    }
    fn upop(fst: Self::U, snd: Self::U) -> Self::U {
        let (a, b) = fst;
        let (c, d) = snd;
        (a * c, b * c + d)
    }
    fn e() -> Self::T {
        0.into()
    }
    fn upe() -> Self::U { // identity for upop
        (1.into(), 0.into())
    }
}

fn solve() {
    let n: usize = get();
    let q: usize = get();
    let a: Vec<i64> = (0..n).map(|_| get()).collect();
    let mut st = LazySegTree::<Affine>::new(n);
    for i in 0..n {
        st.update(i, i + 1, (0.into(), a[i].into()));
    }
    for _ in 0..q {
        let ty: i32 = get();
        let l: usize = get();
        let r: usize = get();
        if ty == 0 {
            let b: i64 = get();
            let c: i64 = get();
            st.update(l, r, (b.into(), c.into()));
        } else {
            println!("{}", st.query(l, r));
        }
    }
}

fn main() {
    // In order to avoid potential stack overflow, spawn a new thread.
    let stack_size = 104_857_600; // 100 MB
    let thd = std::thread::Builder::new().stack_size(stack_size);
    thd.spawn(|| solve()).unwrap().join().unwrap();
}