#![allow(unused_imports, unused_macros)] use kyoproio::*; use std::{ collections::*, io::{self, prelude::*}, iter, mem::{replace, swap}, }; fn main() -> io::Result<()> { std::thread::Builder::new() .stack_size(64 * 1024 * 1024) .spawn(solve)? .join() .unwrap(); Ok(()) } fn solve() { let stdin = io::stdin(); let mut kin = KInput::new(stdin.lock()); let stdout = io::stdout(); let mut out = io::BufWriter::new(stdout.lock()); macro_rules! output { ($($args:expr),+) => { write!(&mut out, $($args),+).unwrap(); }; } macro_rules! outputln { ($($args:expr),+) => { output!($($args),+); outputln!(); }; () => { output!("\n"); if cfg!(debug_assertions) { out.flush().unwrap(); } } } let (n, q): (usize, usize) = kin.input(); let dft = Dft::new(n + 1); let mut ps = vec![Vec::new(); n]; for i in 0..n { let a: i64 = kin.input(); ps[i] = vec![a - 1, 1]; } while ps.len() > 1 { let mut ps_new = Vec::new(); for i in (0..ps.len() / 2 * 2).step_by(2) { ps_new.push(dft.convolution(&ps[i], &ps[i + 1])); } if ps.len() % 2 == 1 { ps_new.push(ps.last().unwrap().clone()); } ps = ps_new; } for b in kin.iter::().take(q) { outputln!("{}", ps[0][b]); } } const MOD: i64 = 998244353; // 2^23 * 7 * 17 + 1 pub fn mod_pow(mut a: i64, mut b: i64, m: i64) -> i64 { let mut y = 1; while b > 0 { if b & 1 == 1 { y = y * a % m; } a = a * a % m; b >>= 1; } y } pub struct Dft { n: usize, w: Vec, iw: Vec, } impl Dft { pub fn new(n: usize) -> Self { let n = n.next_power_of_two(); let b = mod_pow(3, (MOD - 1) / n as i64, MOD); Self { n, iw: Self::basis(b), w: Self::basis(mod_pow(b, MOD - 2, MOD)) } } pub fn size(&self) -> usize { self.w.len() - 1 } fn basis(z: i64) -> Vec { let mut w: Vec<_> = std::iter::successors(Some(z), |x| Some(x * x % MOD)) .take_while(|&x| x != 1) .collect(); w.reverse(); w } pub fn dft(&self, a: &mut [i64]) { self.dft_impl(a, &self.w); } pub fn idft(&self, a: &mut [i64]) { self.dft_impl(a, &self.iw); for x in a { *x = *x * mod_pow(self.n as i64, MOD - 2, MOD) % MOD; } } fn dft_impl(&self, a: &mut [i64], ws: &[i64]) { let n = self.n; for i in 0..n { let j = i.reverse_bits() >> (n.leading_zeros() + 1); if i < j { a.swap(i, j); } } for (k, m) in (0..).map(|k| (k, 1 << k)).take_while(|&(_, m)| 2 * m <= n) { for chunk in a.chunks_mut(2 * m) { let mut w = 1; for i in 0..m { let j = i + m; let x = chunk[j] * w % MOD; chunk[j] = chunk[i] - x; if chunk[j] < 0 { chunk[j] += MOD; } chunk[i] += x; if chunk[i] > MOD { chunk[i] -= MOD; } w = w * ws[k] % MOD; } } } } pub fn convolution(&self, a: &[i64], b: &[i64]) -> Vec { let mut fa = a.to_owned(); let mut fb = b.to_owned(); fa.resize(self.n, 0); fb.resize(self.n, 0); self.dft(&mut fa); self.dft(&mut fb); for (x, &y) in fa.iter_mut().zip(fb.iter()) { *x = *x * y % MOD; } self.idft(&mut fa); fa } } // ----------------------------------------------------------------------------- pub mod kyoproio { use std::io::prelude::*; pub trait Input { fn str(&mut self) -> &str; fn input(&mut self) -> T { T::input(self) } fn iter(&mut self) -> Iter { Iter(self, std::marker::PhantomData) } fn seq>(&mut self, n: usize) -> B { self.iter().take(n).collect() } } pub struct KInput { src: R, buf: String, pos: usize, } impl KInput { pub fn new(src: R) -> Self { Self { src, buf: String::with_capacity(1024), pos: 0, } } pub fn src(&mut self) -> &mut R { &mut self.src } } impl Input for KInput { fn str(&mut self) -> &str { loop { if self.pos >= self.buf.len() { self.pos = 0; self.buf.clear(); if self.src.read_line(&mut self.buf).expect("io error") == 0 { return &self.buf; } } let range = self.pos ..self.buf[self.pos..] .find(|c: char| c.is_ascii_whitespace()) .map(|i| i + self.pos) .unwrap_or_else(|| self.buf.len()); self.pos = range.end + 1; if range.end > range.start { return &self.buf[range]; } } } } pub struct Iter<'a, T, I: ?Sized>(&'a mut I, std::marker::PhantomData<*const T>); impl<'a, T: InputParse, I: Input + ?Sized> Iterator for Iter<'a, T, I> { type Item = T; fn next(&mut self) -> Option { Some(self.0.input()) } } pub trait InputParse: Sized { fn input(src: &mut I) -> Self; } impl InputParse for Vec { fn input(src: &mut I) -> Self { src.str().as_bytes().to_owned() } } macro_rules! from_str_impl { { $($T:ty)* } => { $(impl InputParse for $T { fn input(src: &mut I) -> Self { src.str().parse::<$T>().expect("parse error") } })* } } from_str_impl! { String char bool f32 f64 isize i8 i16 i32 i64 i128 usize u8 u16 u32 u64 u128 } macro_rules! tuple_impl { ($H:ident $($T:ident)*) => { impl<$H: InputParse, $($T: InputParse),*> InputParse for ($H, $($T),*) { fn input(src: &mut I) -> Self { ($H::input(src), $($T::input(src)),*) } } tuple_impl!($($T)*); }; () => {} } tuple_impl!(A B C D E F G); #[macro_export] macro_rules! kdbg { ($($v:expr),*) => { if cfg!(debug_assertions) { dbg!($($v),*) } else { ($($v),*) } } } }