// ---------- 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 Modulo for T where T: ConstantModulo, { fn modulo() -> u32 { T::MOD } } pub struct ModInt(pub u32, PhantomData); impl Clone for ModInt { fn clone(&self) -> Self { ModInt::new_unchecked(self.0) } } impl Copy for ModInt {} impl Add for ModInt { type Output = ModInt; 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 AddAssign for ModInt { fn add_assign(&mut self, rhs: Self) { *self = *self + rhs; } } impl Sub for ModInt { type Output = ModInt; 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 SubAssign for ModInt { fn sub_assign(&mut self, rhs: Self) { *self = *self - rhs; } } impl Mul for ModInt { type Output = ModInt; 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 MulAssign for ModInt { fn mul_assign(&mut self, rhs: Self) { *self = *self * rhs; } } impl Neg for ModInt { type Output = ModInt; fn neg(self) -> Self::Output { if self.0 == 0 { Self::zero() } else { Self::new_unchecked(T::modulo() - self.0) } } } impl std::fmt::Display for ModInt { fn fmt<'a>(&self, f: &mut std::fmt::Formatter<'a>) -> std::fmt::Result { write!(f, "{}", self.0) } } impl std::str::FromStr for ModInt { type Err = std::num::ParseIntError; fn from_str(s: &str) -> Result { let val = s.parse::()?; Ok(ModInt::new(val)) } } impl From for ModInt { fn from(val: usize) -> ModInt { ModInt::new_unchecked((val % T::modulo() as usize) as u32) } } impl From for ModInt { fn from(val: u64) -> ModInt { ModInt::new_unchecked((val % T::modulo() as u64) as u32) } } impl From for ModInt { fn from(val: i64) -> ModInt { let m = T::modulo() as i64; ModInt::new((val % m + m) as u32) } } #[allow(dead_code)] impl ModInt { 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 ModInt { 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(f: &mut [ModInt]) { 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(f: &mut [ModInt]) { 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(a: &[ModInt], b: &[ModInt]) -> Vec> { 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::*; 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

; // ---------- begin input macro ---------- // reference: https://qiita.com/tanakh/items/0ba42c7ca36cd29d0ac8 macro_rules! input { (source = $s:expr, $($r:tt)*) => { let mut iter = $s.split_whitespace(); input_inner!{iter, $($r)*} }; ($($r:tt)*) => { let s = { use std::io::Read; let mut s = String::new(); std::io::stdin().read_to_string(&mut s).unwrap(); s }; let mut iter = s.split_whitespace(); input_inner!{iter, $($r)*} }; } macro_rules! input_inner { ($iter:expr) => {}; ($iter:expr, ) => {}; ($iter:expr, $var:ident : $t:tt $($r:tt)*) => { let $var = read_value!($iter, $t); input_inner!{$iter $($r)*} }; } macro_rules! read_value { ($iter:expr, ( $($t:tt),* )) => { ( $(read_value!($iter, $t)),* ) }; ($iter:expr, [ $t:tt ; $len:expr ]) => { (0..$len).map(|_| read_value!($iter, $t)).collect::>() }; ($iter:expr, chars) => { read_value!($iter, String).chars().collect::>() }; ($iter:expr, bytes) => { read_value!($iter, String).bytes().collect::>() }; ($iter:expr, usize1) => { read_value!($iter, usize) - 1 }; ($iter:expr, $t:ty) => { $iter.next().unwrap().parse::<$t>().expect("Parse error") }; } // ---------- end input macro ---------- fn run() { input! { n: usize, q: usize, a: [M; n], r: [usize; q], } let mut c = vec![M::zero(); n]; for r in r { c[n - 1 - r] += M::one(); } let a = a.iter().cloned().cycle().take(2 * n).collect::>(); let b = transform::multiply(&a, &c); let mut s = String::new(); for b in b[(n - 1)..].iter().take(n) { s.push_str(&format!("{} ", *b)); } s.pop(); println!("{}", s); } fn main() { run(); }