結果

問題 No.2305 [Cherry 5th Tune N] Until That Day...
ユーザー akakimidoriakakimidori
提出日時 2023-05-20 00:34:31
言語 Rust
(1.83.0 + proconio)
結果
TLE  
実行時間 -
コード長 25,258 bytes
コンパイル時間 20,497 ms
コンパイル使用メモリ 382,636 KB
実行使用メモリ 13,644 KB
最終ジャッジ日時 2024-12-21 02:17:39
合計ジャッジ時間 142,774 ms
ジャッジサーバーID
(参考情報)
judge1 / judge5
このコードへのチャレンジ
(要ログイン)
ファイルパターン 結果
other AC * 10 TLE * 11
権限があれば一括ダウンロードができます

ソースコード

diff #
プレゼンテーションモードにする

fn main() {
input! {
n: usize,
p: [usize; n],
w: [usize; n],
q: usize,
ask: [(usize, usize); q],
}
let mut w = w;
w.insert(0, 0);
let n = n + 1;
let mut child = vec![vec![]; n];
for (i, p) in p.iter().enumerate() {
child[*p].push(i + 1);
}
let mut dp = vec![vec![vec![]; 2]; n];
let mut mat = vec![vec![]; n];
for (i, c) in child.iter().enumerate().rev() {
if c.is_empty() {
dp[i][0] = vec![M::zero(), M::one()];
dp[i][1] = vec![-M::one()];
mat[i].push((0, M::one()));
continue;
}
let s = c.iter().fold(0, |s, c| s + w[*c]);
let mut a = vec![M::zero(), M::one()];
let mut b = vec![];
let mut d = vec![M::one()];
for &u in c.iter() {
let p = M::from(w[u]) * M::from(s).inv();
let x = std::mem::take(&mut dp[u]);
b = b.mul(&x[0]).sub(&d.mul(&x[1].mul(&[-p])));
a = a.mul(&x[0]);
d = d.mul(&x[0]);
mat[i].push((u, p));
}
dp[i] = vec![a, b];
}
let mut poly = dp[0][0].add(&dp[0][1]);
poly.pop();
for (pos, k) in ask {
let normalize = |dp: &mut Vec<M>| {
for i in (poly.len()..dp.len()).rev() {
let v = dp.pop().unwrap();
for (dp, poly) in dp[(i - poly.len())..].iter_mut().zip(poly.iter()) {
*dp -= *poly * v;
}
}
};
let mut k = k + 1;
let mut ans = vec![];
let mut mul = vec![M::one()];
let mut r = vec![M::zero(), M::one()];
while k > 0 {
if k & 1 == 1 {
ans.add_assign(&mul);
mul = mul.mul(&r);
normalize(&mut mul);
}
mul = mul.mul(&r.add(&[M::one()]));
r = r.mul(&r);
normalize(&mut mul);
normalize(&mut r);
k >>= 1;
}
let one = |dp: &[M]| -> Vec<M> {
let mut next = vec![M::zero(); n];
for (mat, dp) in mat.iter().zip(dp.iter()) {
for &(u, p) in mat.iter() {
next[u] += p * *dp;
}
}
next
};
let mut state = vec![M::zero(); n];
for a in ans.iter().rev() {
state = one(&state);
state[0] += *a;
}
let mut ans = state[pos];
if pos == 0 {
ans -= M::one();
}
println!("{}", ans);
// println!("{:?}, {:?}", a, state);
}
}
// ---------- begin input macro ----------
// reference: https://qiita.com/tanakh/items/0ba42c7ca36cd29d0ac8
#[macro_export]
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_export]
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_export]
macro_rules! read_value {
($iter:expr, ( $($t:tt),* )) => {
( $(read_value!($iter, $t)),* )
};
($iter:expr, [ $t:tt ; $len:expr ]) => {
(0..$len).map(|_| read_value!($iter, $t)).collect::<Vec<_>>()
};
($iter:expr, chars) => {
read_value!($iter, String).chars().collect::<Vec<char>>()
};
($iter:expr, bytes) => {
read_value!($iter, String).bytes().collect::<Vec<u8>>()
};
($iter:expr, usize1) => {
read_value!($iter, usize) - 1
};
($iter:expr, $t:ty) => {
$iter.next().unwrap().parse::<$t>().expect("Parse error")
};
}
// ---------- end input macro ----------
// ---------- begin ModInt ----------
//
// Codeforces
//
// new_unchecked x 0 <= x < modulo
// ModInt
//
mod modint {
use std::marker::*;
use std::ops::*;
pub trait Modulo {
fn modulo() -> u32;
fn rem() -> u32;
fn ini() -> u64;
fn reduce(x: u64) -> u32 {
debug_assert!(x < (Self::modulo() as u64) << 32);
let b = (x as u32 * Self::rem()) as u64;
let t = x + b * Self::modulo() as u64;
let mut c = (t >> 32) as u32;
if c >= Self::modulo() {
c -= Self::modulo();
}
c as u32
}
}
#[allow(dead_code)]
pub enum Mod1_000_000_007 {}
impl Modulo for Mod1_000_000_007 {
fn modulo() -> u32 {
1_000_000_007
}
fn rem() -> u32 {
2226617417
}
fn ini() -> u64 {
582344008
}
}
#[allow(dead_code)]
pub enum Mod998_244_353 {}
impl Modulo for Mod998_244_353 {
fn modulo() -> u32 {
998_244_353
}
fn rem() -> u32 {
998244351
}
fn ini() -> u64 {
932051910
}
}
#[allow(dead_code)]
pub fn generate_umekomi_modulo(p: u32) {
assert!(
p < (1 << 31)
&& p > 2
&& p & 1 == 1
&& (2u32..).take_while(|v| v * v <= p).all(|k| p % k != 0)
);
let mut t = 1u32;
let mut s = !p + 1;
let mut n = !0u32 >> 2;
while n > 0 {
if n & 1 == 1 {
t *= s;
}
s *= s;
n >>= 1;
}
let mut ini = (1u64 << 32) % p as u64;
ini = (ini << 32) % p as u64;
assert!(t * p == !0);
println!("pub enum Mod{} {{}}", p);
println!("impl Modulo for Mod{} {{", p);
println!(" fn modulo() -> u32 {{");
println!(" {}", p);
println!(" }}");
println!(" fn rem() -> u32 {{");
println!(" {}", t);
println!(" }}");
println!(" fn ini() -> u64 {{");
println!(" {}", ini);
println!(" }}");
println!("}}");
let mut f = vec![];
let mut n = p - 1;
for i in 2.. {
if i * i > n {
break;
}
if n % i == 0 {
f.push(i);
while n % i == 0 {
n /= i;
}
}
}
if n > 1 {
f.push(n);
}
let mut order = 1;
let mut n = p - 1;
while n % 2 == 0 {
n /= 2;
order <<= 1;
}
let z = (2u64..)
.find(|z| {
f.iter()
.all(|f| mod_pow(*z, ((p - 1) / *f) as u64, p as u64) != 1)
})
.unwrap();
let zeta = mod_pow(z, ((p - 1) / order) as u64, p as u64);
println!("impl transform::NTTFriendly for Mod{} {{", p);
println!(" fn order() -> usize {{");
println!(" {}", order);
println!(" }}");
println!(" fn zeta() -> u32 {{");
println!(" {}", zeta);
println!(" }}");
println!("}}");
}
pub struct ModInt<T>(u32, PhantomData<T>);
impl<T> Clone for ModInt<T> {
fn clone(&self) -> Self {
ModInt::build(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();
}
Self::build(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 = self.0 - rhs.0;
if self.0 < rhs.0 {
d += T::modulo();
}
Self::build(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 {
Self::build(T::reduce(self.0 as u64 * rhs.0 as u64))
}
}
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::build(T::modulo() - self.0)
}
}
}
impl<T: Modulo> std::fmt::Display for ModInt<T> {
fn fmt<'a>(&self, f: &mut std::fmt::Formatter<'a>) -> std::fmt::Result {
write!(f, "{}", self.get())
}
}
impl<T: Modulo> std::fmt::Debug for ModInt<T> {
fn fmt<'a>(&self, f: &mut std::fmt::Formatter<'a>) -> std::fmt::Result {
write!(f, "{}", self.get())
}
}
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> {
fn build(d: u32) -> Self {
ModInt(d, PhantomData)
}
pub fn zero() -> Self {
Self::build(0)
}
pub fn is_zero(&self) -> bool {
self.0 == 0
}
}
#[allow(dead_code)]
impl<T: Modulo> ModInt<T> {
pub fn new_unchecked(d: u32) -> Self {
Self::build(T::reduce(d as u64 * T::ini()))
}
pub fn new(d: u32) -> Self {
Self::new_unchecked(d % T::modulo())
}
pub fn one() -> Self {
Self::new_unchecked(1)
}
pub fn get(&self) -> u32 {
T::reduce(self.0 as u64)
}
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.is_zero());
self.pow((T::modulo() - 2) as u64)
}
}
pub fn mod_pow(mut r: u64, mut n: u64, m: u64) -> u64 {
let mut t = 1 % m;
while n > 0 {
if n & 1 == 1 {
t = t * r % m;
}
r = r * r % m;
n >>= 1;
}
t
}
}
// ---------- end ModInt ----------
// ---------- begin Precalc ----------
mod precalc {
use super::modint::*;
#[allow(dead_code)]
pub struct Precalc<T> {
inv: Vec<ModInt<T>>,
fact: Vec<ModInt<T>>,
ifact: Vec<ModInt<T>>,
}
#[allow(dead_code)]
impl<T: Modulo> Precalc<T> {
pub fn new(n: usize) -> Precalc<T> {
let mut inv = vec![ModInt::one(); n + 1];
let mut fact = vec![ModInt::one(); n + 1];
let mut ifact = vec![ModInt::one(); n + 1];
for i in 2..(n + 1) {
fact[i] = fact[i - 1] * ModInt::new_unchecked(i as u32);
}
ifact[n] = fact[n].inv();
if n > 0 {
inv[n] = ifact[n] * fact[n - 1];
}
for i in (1..n).rev() {
ifact[i] = ifact[i + 1] * ModInt::new_unchecked((i + 1) as u32);
inv[i] = ifact[i] * fact[i - 1];
}
Precalc {
inv: inv,
fact: fact,
ifact: ifact,
}
}
pub fn inv(&self, n: usize) -> ModInt<T> {
assert!(n > 0);
self.inv[n]
}
pub fn fact(&self, n: usize) -> ModInt<T> {
self.fact[n]
}
pub fn ifact(&self, n: usize) -> ModInt<T> {
self.ifact[n]
}
pub fn perm(&self, n: usize, k: usize) -> ModInt<T> {
if k > n {
return ModInt::zero();
}
self.fact[n] * self.ifact[n - k]
}
pub fn comb(&self, n: usize, k: usize) -> ModInt<T> {
if k > n {
return ModInt::zero();
}
self.fact[n] * self.ifact[k] * self.ifact[n - k]
}
}
}
// ---------- end Precalc ----------
use modint::*;
pub trait NTTFriendly: modint::Modulo {
fn order() -> usize;
fn zeta() -> u32;
}
type M = ModInt<Mod998_244_353>;
impl NTTFriendly for Mod998_244_353 {
fn order() -> usize {
8388608
}
fn zeta() -> u32 {
15311432
}
}
//
// modint, primitive type 使
// +, -, *
// zero
//
//
//
// dotok
//
// 0
// dot
// dot?
// 0
use std::ops::*;
pub trait Zero: Sized + Add<Output = Self> {
fn zero() -> Self;
}
pub fn zero<T: Zero>() -> T {
T::zero()
}
impl<T: Modulo> Zero for ModInt<T> {
fn zero() -> Self {
Self::zero()
}
}
impl Zero for usize {
fn zero() -> Self {
0
}
}
pub trait ArrayAdd {
type Item;
fn add(&self, rhs: &[Self::Item]) -> Vec<Self::Item>;
}
impl<T> ArrayAdd for [T]
where
T: Zero + Copy,
{
type Item = T;
fn add(&self, rhs: &[Self::Item]) -> Vec<Self::Item> {
let mut c = vec![T::zero(); self.len().max(rhs.len())];
c[..self.len()].copy_from_slice(self);
c.add_assign(rhs);
c
}
}
pub trait ArrayAddAssign {
type Item;
fn add_assign(&mut self, rhs: &[Self::Item]);
}
impl<T> ArrayAddAssign for [T]
where
T: Add<Output = T> + Copy,
{
type Item = T;
fn add_assign(&mut self, rhs: &[Self::Item]) {
assert!(self.len() >= rhs.len());
self.iter_mut().zip(rhs).for_each(|(x, a)| *x = *x + *a);
}
}
impl<T> ArrayAddAssign for Vec<T>
where
T: Zero + Add<Output = T> + Copy,
{
type Item = T;
fn add_assign(&mut self, rhs: &[Self::Item]) {
if self.len() < rhs.len() {
self.resize(rhs.len(), T::zero());
}
self.as_mut_slice().add_assign(rhs);
}
}
pub trait ArraySub {
type Item;
fn sub(&self, rhs: &[Self::Item]) -> Vec<Self::Item>;
}
impl<T> ArraySub for [T]
where
T: Zero + Sub<Output = T> + Copy,
{
type Item = T;
fn sub(&self, rhs: &[Self::Item]) -> Vec<Self::Item> {
let mut c = vec![T::zero(); self.len().max(rhs.len())];
c[..self.len()].copy_from_slice(self);
c.sub_assign(rhs);
c
}
}
pub trait ArraySubAssign {
type Item;
fn sub_assign(&mut self, rhs: &[Self::Item]);
}
impl<T> ArraySubAssign for [T]
where
T: Sub<Output = T> + Copy,
{
type Item = T;
fn sub_assign(&mut self, rhs: &[Self::Item]) {
assert!(self.len() >= rhs.len());
self.iter_mut().zip(rhs).for_each(|(x, a)| *x = *x - *a);
}
}
impl<T> ArraySubAssign for Vec<T>
where
T: Zero + Sub<Output = T> + Copy,
{
type Item = T;
fn sub_assign(&mut self, rhs: &[Self::Item]) {
if self.len() < rhs.len() {
self.resize(rhs.len(), T::zero());
}
self.as_mut_slice().sub_assign(rhs);
}
}
pub trait ArrayDot {
type Item;
fn dot(&self, rhs: &[Self::Item]) -> Vec<Self::Item>;
}
impl<T> ArrayDot for [T]
where
T: Mul<Output = T> + Copy,
{
type Item = T;
fn dot(&self, rhs: &[Self::Item]) -> Vec<Self::Item> {
assert!(self.len() == rhs.len());
self.iter().zip(rhs).map(|p| *p.0 * *p.1).collect()
}
}
pub trait ArrayDotAssign {
type Item;
fn dot_assign(&mut self, rhs: &[Self::Item]);
}
impl<T> ArrayDotAssign for [T]
where
T: MulAssign + Copy,
{
type Item = T;
fn dot_assign(&mut self, rhs: &[Self::Item]) {
assert!(self.len() == rhs.len());
self.iter_mut().zip(rhs).for_each(|(x, a)| *x *= *a);
}
}
pub trait ArrayMul {
type Item;
fn mul(&self, rhs: &[Self::Item]) -> Vec<Self::Item>;
}
impl<T> ArrayMul for [T]
where
T: Zero + Mul<Output = T> + Copy,
{
type Item = T;
fn mul(&self, rhs: &[Self::Item]) -> Vec<Self::Item> {
if self.is_empty() || rhs.is_empty() {
return vec![];
}
let mut res = vec![zero(); self.len() + rhs.len() - 1];
for (i, a) in self.iter().enumerate() {
for (c, b) in res[i..].iter_mut().zip(rhs) {
*c = *c + *a * *b;
}
}
res
}
}
pub trait ArrayNTT {
type Item;
fn ntt(&mut self);
fn intt(&mut self);
fn multiply(&self, rhs: &[Self::Item]) -> Vec<Self::Item>;
}
impl<T> ArrayNTT for [ModInt<T>]
where
T: NTTFriendly,
{
type Item = ModInt<T>;
fn ntt(&mut self) {
let f = self;
let n = f.len();
assert!(n.count_ones() == 1);
assert!(n <= T::order());
let len = n.trailing_zeros() as usize;
let mut es = [ModInt::zero(); 30];
let mut ies = [ModInt::zero(); 30];
let mut sum_e = [ModInt::zero(); 30];
let cnt2 = T::order().trailing_zeros() as usize;
let mut e = ModInt::new_unchecked(T::zeta());
let mut ie = e.inv();
for i in (2..=cnt2).rev() {
es[i - 2] = e;
ies[i - 2] = ie;
e = e * e;
ie = ie * ie;
}
let mut now = ModInt::one();
for i in 0..(cnt2 - 1) {
sum_e[i] = es[i] * now;
now *= ies[i];
}
for ph in 1..=len {
let p = 1 << (len - ph);
let mut now = ModInt::one();
for (i, f) in f.chunks_exact_mut(2 * p).enumerate() {
let (x, y) = f.split_at_mut(p);
for (x, y) in x.iter_mut().zip(y.iter_mut()) {
let l = *x;
let r = *y * now;
*x = l + r;
*y = l - r;
}
now *= sum_e[(!i).trailing_zeros() as usize];
}
}
}
fn intt(&mut self) {
let f = self;
let n = f.len();
assert!(n.count_ones() == 1);
assert!(n <= T::order());
let len = n.trailing_zeros() as usize;
let mut es = [ModInt::zero(); 30];
let mut ies = [ModInt::zero(); 30];
let mut sum_ie = [ModInt::zero(); 30];
let cnt2 = T::order().trailing_zeros() as usize;
let mut e = ModInt::new_unchecked(T::zeta());
let mut ie = e.inv();
for i in (2..=cnt2).rev() {
es[i - 2] = e;
ies[i - 2] = ie;
e = e * e;
ie = ie * ie;
}
let mut now = ModInt::one();
for i in 0..(cnt2 - 1) {
sum_ie[i] = ies[i] * now;
now *= es[i];
}
for ph in (1..=len).rev() {
let p = 1 << (len - ph);
let mut inow = ModInt::one();
for (i, f) in f.chunks_exact_mut(2 * p).enumerate() {
let (x, y) = f.split_at_mut(p);
for (x, y) in x.iter_mut().zip(y.iter_mut()) {
let l = *x;
let r = *y;
*x = l + r;
*y = (l - r) * inow;
}
inow *= sum_ie[(!i).trailing_zeros() as usize];
}
}
let ik = ModInt::new_unchecked((T::modulo() + 1) >> 1).pow(len as u64);
for f in f.iter_mut() {
*f *= ik;
}
}
fn multiply(&self, rhs: &[Self::Item]) -> Vec<Self::Item> {
if self.len().min(rhs.len()) <= 32 {
return self.mul(rhs);
}
let size = (self.len() + rhs.len() - 1).next_power_of_two();
let mut f = vec![ModInt::zero(); size];
let mut g = vec![ModInt::zero(); size];
f[..self.len()].copy_from_slice(self);
g[..rhs.len()].copy_from_slice(rhs);
f.ntt();
g.ntt();
f.dot_assign(&g);
f.intt();
f.truncate(self.len() + rhs.len() - 1);
f
}
}
pub trait PolynomialOperation {
type Item;
fn eval(&self, x: Self::Item) -> Self::Item;
fn derivative(&self) -> Vec<Self::Item>;
fn integral(&self) -> Vec<Self::Item>;
}
impl<T: Modulo> PolynomialOperation for [ModInt<T>] {
type Item = ModInt<T>;
fn eval(&self, x: Self::Item) -> Self::Item {
self.iter().rev().fold(ModInt::zero(), |s, a| s * x + *a)
}
fn derivative(&self) -> Vec<Self::Item> {
if self.len() <= 1 {
return vec![];
}
self[1..]
.iter()
.enumerate()
.map(|(k, a)| ModInt::new_unchecked(k as u32 + 1) * *a)
.collect()
}
fn integral(&self) -> Vec<Self::Item> {
if self.is_empty() {
return vec![];
}
let mut inv = vec![ModInt::one(); self.len() + 1];
let mut mul = ModInt::zero();
for i in 1..=self.len() {
mul += ModInt::one();
inv[i] = inv[i - 1] * mul;
}
let mut prod = inv[self.len()].inv();
for i in (1..=self.len()).rev() {
inv[i] = self[i - 1] * inv[i - 1] * prod;
prod *= mul;
mul -= ModInt::one();
}
inv[0] = ModInt::zero();
inv
}
}
pub trait FPSOperation {
type Item;
fn inverse(&self, n: usize) -> Vec<Self::Item>;
fn log(&self, n: usize) -> Vec<Self::Item>;
fn exp(&self, n: usize) -> Vec<Self::Item>;
}
impl<T: NTTFriendly> FPSOperation for [ModInt<T>] {
type Item = ModInt<T>;
fn inverse(&self, n: usize) -> Vec<Self::Item> {
assert!(self.len() > 0 && !self[0].is_zero());
let len = n.next_power_of_two();
assert!(2 * len <= T::order());
let mut b = vec![ModInt::zero(); n];
b[0] = self[0].inv();
let mut f = Vec::with_capacity(2 * len);
let mut g = Vec::with_capacity(2 * len);
let mut size = 1;
while size < n {
g.clear();
g.extend(b.iter().take(size));
g.resize(2 * size, ModInt::zero());
f.clear();
f.extend(self.iter().take(2 * size));
f.resize(2 * size, ModInt::zero());
f.ntt();
g.ntt();
f.dot_assign(&g);
f.intt();
f[..size].iter_mut().for_each(|f| *f = ModInt::zero());
f.ntt();
f.dot_assign(&g);
f.intt();
for (b, g) in b[size..].iter_mut().zip(&f[size..]) {
*b = *b - *g;
}
size *= 2;
}
b
}
fn log(&self, n: usize) -> Vec<Self::Item> {
assert!(self.get(0).map_or(false, |p| p.get() == 1));
let mut b = self.derivative().multiply(&self.inverse(n));
b.truncate(n - 1);
let mut b = b.integral();
b.resize(n, ModInt::zero());
b
}
fn exp(&self, n: usize) -> Vec<Self::Item> {
assert!(self.get(0).map_or(true, |a| a.is_zero()));
assert!(n <= T::order());
let mut b = vec![ModInt::one()];
let mut size = 1;
while size < n {
size <<= 1;
let f = b.log(size);
let g = self[..self.len().min(size)].sub(&f);
b = b.multiply(&g).add(&b);
b.truncate(size);
}
b.truncate(n);
b.resize(n, ModInt::zero());
b
}
}
// test
// yuki907: https://yukicoder.me/submissions/712523
// hhkb2020: https://atcoder.jp/contests/hhkb2020/submissions/26997806
//
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