Problem:
Score : 100 points

Problem Statement

You are given two integer arrays a_0, a_1, ..., a_{N - 1} and b_0, b_1, ..., b_{M - 1}. Calculate the array c_0, c_1, ..., c_{(N - 1) + (M - 1)}, defined by c_i = \sum_{j = 0}^i a_j b_{i - j} \bmod 998244353.

Constraints

1 \leq N, M \leq 524288

0 \leq a_i, b_i < 998244353

All values in Input are integer.

Input

Input is given from Standard Input in the following format:

N M
a_0 a_1 ... a_{N-1}
b_0 b_1 ... b_{M-1}

Output

Print the answer in the following format:

c_0 c_1 ... c_{(N - 1) + (M - 1)}

Sample Input 1

4 5
1 2 3 4
5 6 7 8 9

Sample Output 1

5 16 34 60 70 70 59 36

Sample Input 2

1 1
10000000
10000000

Sample Output 2

871938225

Solution in Rust (1.42.0) (judge verdict: Accepted)

// ---------- begin ModInt ----------
mod modint {

    #[allow(dead_code)]
    pub struct Mod;
    impl ConstantModulo for Mod {
        const MOD: u32 = 1_000_000_007;
    }

    #[allow(dead_code)]
    pub struct StaticMod;
    static mut STATIC_MOD: u32 = 0;
    impl Modulo for StaticMod {
        fn modulo() -> u32 {
            unsafe { STATIC_MOD }
        }
    }

    #[allow(dead_code)]
    impl StaticMod {
        pub fn set_modulo(p: u32) {
            unsafe {
                STATIC_MOD = p;
            }
        }
    }

    use std::marker::*;
    use std::ops::*;

    pub trait Modulo {
        fn modulo() -> u32;
    }

    pub trait ConstantModulo {
        const MOD: u32;
    }

    impl<T> Modulo for T
    where
        T: ConstantModulo,
    {
        fn modulo() -> u32 {
            T::MOD
        }
    }

    pub struct ModInt<T>(pub u32, PhantomData<T>);

    impl<T> Clone for ModInt<T> {
        fn clone(&self) -> Self {
            ModInt::new_unchecked(self.0)
        }
    }

    impl<T> Copy for ModInt<T> {}

    impl<T: Modulo> Add for ModInt<T> {
        type Output = ModInt<T>;
        fn add(self, rhs: Self) -> Self::Output {
            let mut d = self.0 + rhs.0;
            if d >= T::modulo() {
                d -= T::modulo();
            }
            ModInt::new_unchecked(d)
        }
    }

    impl<T: Modulo> AddAssign for ModInt<T> {
        fn add_assign(&mut self, rhs: Self) {
            *self = *self + rhs;
        }
    }

    impl<T: Modulo> Sub for ModInt<T> {
        type Output = ModInt<T>;
        fn sub(self, rhs: Self) -> Self::Output {
            let mut d = T::modulo() + self.0 - rhs.0;
            if d >= T::modulo() {
                d -= T::modulo();
            }
            ModInt::new_unchecked(d)
        }
    }

    impl<T: Modulo> SubAssign for ModInt<T> {
        fn sub_assign(&mut self, rhs: Self) {
            *self = *self - rhs;
        }
    }

    impl<T: Modulo> Mul for ModInt<T> {
        type Output = ModInt<T>;
        fn mul(self, rhs: Self) -> Self::Output {
            let v = self.0 as u64 * rhs.0 as u64 % T::modulo() as u64;
            ModInt::new_unchecked(v as u32)
        }
    }

    impl<T: Modulo> MulAssign for ModInt<T> {
        fn mul_assign(&mut self, rhs: Self) {
            *self = *self * rhs;
        }
    }

    impl<T: Modulo> Neg for ModInt<T> {
        type Output = ModInt<T>;
        fn neg(self) -> Self::Output {
            if self.0 == 0 {
                Self::zero()
            } else {
                Self::new_unchecked(T::modulo() - self.0)
            }
        }
    }

    impl<T> std::fmt::Display for ModInt<T> {
        fn fmt<'a>(&self, f: &mut std::fmt::Formatter<'a>) -> std::fmt::Result {
            write!(f, "{}", self.0)
        }
    }

    impl<T: Modulo> std::str::FromStr for ModInt<T> {
        type Err = std::num::ParseIntError;
        fn from_str(s: &str) -> Result<Self, Self::Err> {
            let val = s.parse::<u32>()?;
            Ok(ModInt::new(val))
        }
    }

    impl<T: Modulo> From<usize> for ModInt<T> {
        fn from(val: usize) -> ModInt<T> {
            ModInt::new_unchecked((val % T::modulo() as usize) as u32)
        }
    }

    impl<T: Modulo> From<u64> for ModInt<T> {
        fn from(val: u64) -> ModInt<T> {
            ModInt::new_unchecked((val % T::modulo() as u64) as u32)
        }
    }

    impl<T: Modulo> From<i64> for ModInt<T> {
        fn from(val: i64) -> ModInt<T> {
            let m = T::modulo() as i64;
            ModInt::new((val % m + m) as u32)
        }
    }

    #[allow(dead_code)]
    impl<T> ModInt<T> {
        pub fn new_unchecked(d: u32) -> Self {
            ModInt(d, PhantomData)
        }
        pub fn zero() -> Self {
            ModInt::new_unchecked(0)
        }
        pub fn one() -> Self {
            ModInt::new_unchecked(1)
        }
        pub fn is_zero(&self) -> bool {
            self.0 == 0
        }
    }

    #[allow(dead_code)]
    impl<T: Modulo> ModInt<T> {
        pub fn new(d: u32) -> Self {
            ModInt::new_unchecked(d % T::modulo())
        }
        pub fn pow(&self, mut n: u64) -> Self {
            let mut t = Self::one();
            let mut s = *self;
            while n > 0 {
                if n & 1 == 1 {
                    t *= s;
                }
                s *= s;
                n >>= 1;
            }
            t
        }
        pub fn inv(&self) -> Self {
            assert!(self.0 != 0);
            self.pow(T::modulo() as u64 - 2)
        }
    }

    #[allow(dead_code)]
    pub fn mod_pow(r: u64, mut n: u64, m: u64) -> u64 {
        let mut t = 1 % m;
        let mut s = r % m;
        while n > 0 {
            if n & 1 == 1 {
                t = t * s % m;
            }
            s = s * s % m;
            n >>= 1;
        }
        t
    }
}
// ---------- end ModInt ----------
// ---------- begin NTT ----------
#[allow(dead_code)]
mod transform {
    use super::modint::*;
    pub trait NTTFriendly: ConstantModulo {
        fn order() -> usize;
        fn zeta() -> u32;
    }
    pub fn ntt<T: NTTFriendly>(f: &mut [ModInt<T>]) {
        let n = f.len();
        assert!(n.count_ones() == 1);
        assert!(n <= T::order());
        let len = n.trailing_zeros() as usize;
        let mut zeta = Vec::with_capacity(len);
        let mut r = ModInt::new_unchecked(T::zeta()).pow((T::order() >> len) as u64);
        for _ in 0..len {
            zeta.push(r);
            r = r * r;
        }
        for (k, &z) in zeta.iter().rev().enumerate().rev() {
            let m = 1 << k;
            for f in f.chunks_exact_mut(2 * m) {
                let mut q = ModInt::one();
                let (x, y) = f.split_at_mut(m);
                for (x, y) in x.iter_mut().zip(y.iter_mut()) {
                    let a = *x;
                    let b = *y;
                    *x = a + b;
                    *y = (a - b) * q;
                    q *= z;
                }
            }
        }
    }
    pub fn intt<T: NTTFriendly>(f: &mut [ModInt<T>]) {
        let n = f.len();
        assert!(n.count_ones() == 1);
        assert!(n <= T::order());
        let len = n.trailing_zeros() as usize;
        let mut zeta = Vec::with_capacity(len);
        let mut r = ModInt::new_unchecked(T::zeta()).inv().pow((T::order() >> len) as u64);
        for _ in 0..len {
            zeta.push(r);
            r = r * r;
        }
        for (k, &z) in zeta.iter().rev().enumerate() {
            let m = 1 << k;
            for f in f.chunks_exact_mut(2 * m) {
                let mut q = ModInt::one();
                let (x, y) = f.split_at_mut(m);
                for (x, y) in x.iter_mut().zip(y.iter_mut()) {
                    let a = *x;
                    let b = *y * q;
                    *x = a + b;
                    *y = a - b;
                    q *= z;
                }
            }
        }
        let ik = ModInt::new_unchecked((T::MOD + 1) >> 1).pow(len as u64);
        for f in f.iter_mut() {
            *f *= ik;
        }
    }
    pub fn multiply<T: NTTFriendly>(a: &[ModInt<T>], b: &[ModInt<T>]) -> Vec<ModInt<T>> {
        if a.is_empty() || b.is_empty() {
            return vec![];
        }
        let n = a.len() + b.len() - 1;
        let k = n.next_power_of_two();
        assert!(k <= T::order());
        let mut f = Vec::with_capacity(k);
        let mut g = Vec::with_capacity(k);
        f.extend_from_slice(a);
        f.resize(k, ModInt::zero());
        ntt(&mut f);
        g.extend_from_slice(b);
        g.resize(k, ModInt::zero());
        ntt(&mut g);
        for (f, g) in f.iter_mut().zip(g.iter()) {
            *f *= *g;
        }
        intt(&mut f);
        f.truncate(n);
        f
    }
}
// ---------- end NTT ----------

use modint::*;
use proconio::*;

struct P;
impl ConstantModulo for P {
    const MOD: u32 = 998_244_353;
}

impl transform::NTTFriendly for P {
    fn order() -> usize {
        1 << 23
    }
    fn zeta() -> u32 {
        let p = Self::MOD as u64;
        mod_pow(3, (p - 1) >> 23, p) as u32
    }
}

type M = ModInt<P>;

#[fastout]
fn run() {
    input! {
        n: usize,
        m: usize,
        x: [M; n],
        y: [M; m],
    }
    let ans = transform::multiply(&x, &y);
    for (i, ans) in ans.into_iter().enumerate() {
        if i > 0 {
            print!(" ");
        }
        print!("{}", ans);
    }
    println!();
}

fn main() {
    run();
}