#[allow(unused_imports)] use std::cmp::*; #[allow(unused_imports)] use std::collections::*; use std::io::{Write, BufWriter}; // https://qiita.com/tanakh/items/0ba42c7ca36cd29d0ac8 macro_rules! input { ($($r:tt)*) => { let stdin = std::io::stdin(); let mut bytes = std::io::Read::bytes(std::io::BufReader::new(stdin.lock())); let mut next = move || -> String{ bytes.by_ref().map(|r|r.unwrap() as char) .skip_while(|c|c.is_whitespace()) .take_while(|c|!c.is_whitespace()) .collect() }; input_inner!{next, $($r)*} }; } macro_rules! input_inner { ($next:expr) => {}; ($next:expr, ) => {}; ($next:expr, $var:ident : $t:tt $($r:tt)*) => { let $var = read_value!($next, $t); input_inner!{$next $($r)*} }; } macro_rules! read_value { ($next:expr, [graph1; $len:expr]) => {{ let mut g = vec![vec![]; $len]; let ab = read_value!($next, [(usize1, usize1)]); for (a, b) in ab { g[a].push(b); g[b].push(a); } g }}; ($next:expr, ( $($t:tt),* )) => { ( $(read_value!($next, $t)),* ) }; ($next:expr, [ $t:tt ; $len:expr ]) => { (0..$len).map(|_| read_value!($next, $t)).collect::>() }; ($next:expr, chars) => { read_value!($next, String).chars().collect::>() }; ($next:expr, usize1) => (read_value!($next, usize) - 1); ($next:expr, [ $t:tt ]) => {{ let len = read_value!($next, usize); read_value!($next, [$t; len]) }}; ($next:expr, $t:ty) => ($next().parse::<$t>().expect("Parse error")); } #[allow(unused)] macro_rules! debug { ($($format:tt)*) => (write!(std::io::stderr(), $($format)*).unwrap()); } #[allow(unused)] macro_rules! debugln { ($($format:tt)*) => (writeln!(std::io::stderr(), $($format)*).unwrap()); } /// 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 { pub x: i64, phantom: ::std::marker::PhantomData } impl ModInt { // 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>> Add for ModInt { 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>> Sub for ModInt { 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>> Mul for ModInt { type Output = Self; fn mul(self, other: T) -> Self { ModInt::new(self.x * other.into().x % M::m()) } } impl>> AddAssign for ModInt { fn add_assign(&mut self, other: T) { *self = *self + other; } } impl>> SubAssign for ModInt { fn sub_assign(&mut self, other: T) { *self = *self - other; } } impl>> MulAssign for ModInt { fn mul_assign(&mut self, other: T) { *self = *self * other; } } impl Neg for ModInt { type Output = Self; fn neg(self) -> Self { ModInt::new(0) - self } } impl ::std::fmt::Display for ModInt { fn fmt(&self, f: &mut ::std::fmt::Formatter) -> ::std::fmt::Result { self.x.fmt(f) } } impl ::std::fmt::Debug for ModInt { 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 From for ModInt { 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 MInt = mod_int::ModInt

; // https://atcoder.jp/contests/joisc2007/submissions/18675713 fn karatsuba_convolution_sub(a: &[MInt], b: &[MInt], out: &mut [MInt]) { let n = a.len(); let m = b.len(); if n == 0 || m == 0 { return; } if min(n, m) <= 64 { for i in 0..n { for j in 0..m { if i + j < out.len() { out[i + j] += a[i] * b[j]; } } } return; } let l = max(n, m); let al = &a[..min(a.len(), l / 2)]; let bl = &b[..min(b.len(), l / 2)]; let ah = &a[min(a.len(), l / 2)..]; let bh = &b[min(b.len(), l / 2)..]; if ah.is_empty() || bh.is_empty() { karatsuba_convolution_sub(&al, &bl, out); if out.len() >= l / 2 { karatsuba_convolution_sub(&al, &bh, &mut out[l / 2..]); karatsuba_convolution_sub(&ah, &bl, &mut out[l / 2..]); if out.len() >= l / 2 * 2 { karatsuba_convolution_sub(&ah, &bh, &mut out[l / 2 * 2..]); } } return; } let mut lo = vec![MInt::new(0); al.len() + bl.len()]; karatsuba_convolution_sub(&al, &bl, &mut lo); let mut hi = vec![MInt::new(0); ah.len() + bh.len()]; karatsuba_convolution_sub(&ah, &bh, &mut hi); // al * bh + ah * bl = al * bl + ah * bh - (al - ah) * (bl - bh) let mut dif_a = vec![MInt::new(0); l - l / 2]; // ah - al let mut dif_b = vec![MInt::new(0); l - l / 2]; // bl - bh for i in 0..l / 2 { if i < al.len() { dif_a[i] = -al[i]; } if i < bl.len() { dif_b[i] = bl[i]; } } for i in 0..l - l / 2 { if i < ah.len() { dif_a[i] += ah[i]; } if i < bh.len() { dif_b[i] -= bh[i]; } } if out.len() > l / 2 { karatsuba_convolution_sub(&dif_a, &dif_b, &mut out[l / 2..]); } for i in 0..min(lo.len(), out.len()) { out[i] += lo[i]; if i + l / 2 < out.len() { out[i + l / 2] += lo[i]; } } for i in 0..min(hi.len(), out.len()) { if i + l / 2 * 2 < out.len() { out[i + l / 2 * 2] += hi[i]; } if i + l / 2 < out.len() { out[i + l / 2] += hi[i]; } } } fn karatsuba_convolution(a: &[MInt], b: &[MInt]) -> Vec { let n = a.len(); let m = b.len(); let mut ret = vec![MInt::new(0); n + m - 1]; karatsuba_convolution_sub(a, b, &mut ret); ret } // Tags: fft, convolution, karatsuba fn main() { let out = std::io::stdout(); let mut out = BufWriter::new(out.lock()); macro_rules! puts { ($($format:tt)*) => (let _ = write!(out,$($format)*);); } input! { n: usize, q: usize, a: [i64; n], r: [usize; q], } let mut f = vec![MInt::new(0); n]; let mut g = vec![MInt::new(0); n + 1]; for i in 0..n { f[i] += a[i]; } for r in r { g[n - r] += 1; } let res = karatsuba_convolution(&f, &g); let mut ans = vec![MInt::new(0); n]; for i in 0..res.len() { ans[i % n] += res[i]; } for i in 0..n { puts!("{}{}", ans[i], if i + 1 == n { "\n" } else { " " }); } }