結果
| 問題 | No.2231 Surprising Flash! |
| ユーザー |
 akakimidori
|
| 提出日時 | 2023-02-16 01:59:24 |
| 言語 | Rust (1.77.0) |
| 結果 |
WA
|
| 実行時間 | - |
| コード長 | 32,142 bytes |
| コンパイル時間 | 7,311 ms |
| コンパイル使用メモリ | 183,764 KB |
| 実行使用メモリ | 48,720 KB |
| 最終ジャッジ日時 | 2023-10-11 08:20:08 |
| 合計ジャッジ時間 | 19,390 ms |
|
ジャッジサーバーID （参考情報） |
judge12 / judge14 |
（要ログイン）
テストケース
テストケース表示| 入力 | 結果 | 実行時間 実行使用メモリ |
|---|---|---|
| testcase_00 | AC | 1 ms
4,368 KB |
| testcase_01 | AC | 3 ms
4,368 KB |
| testcase_02 | AC | 21 ms
4,372 KB |
| testcase_03 | AC | 351 ms
15,344 KB |
| testcase_04 | AC | 13 ms
4,372 KB |
| testcase_05 | AC | 25 ms
4,372 KB |
| testcase_06 | WA | - |
| testcase_07 | AC | 1 ms
4,372 KB |
| testcase_08 | AC | 3 ms
4,372 KB |
| testcase_09 | AC | 1 ms
4,372 KB |
| testcase_10 | AC | 4 ms
4,372 KB |
| testcase_11 | AC | 257 ms
39,264 KB |
| testcase_12 | AC | 293 ms
48,632 KB |
| testcase_13 | AC | 645 ms
48,720 KB |
| testcase_14 | AC | 327 ms
31,556 KB |
| testcase_15 | AC | 262 ms
39,248 KB |
| testcase_16 | AC | 197 ms
5,756 KB |
| testcase_17 | AC | 203 ms
7,872 KB |
| testcase_18 | AC | 539 ms
31,612 KB |
| testcase_19 | AC | 529 ms
31,500 KB |
| testcase_20 | AC | 532 ms
31,568 KB |
| testcase_21 | AC | 540 ms
31,632 KB |
| testcase_22 | AC | 542 ms
31,620 KB |
| testcase_23 | AC | 542 ms
31,676 KB |
| testcase_24 | AC | 558 ms
31,620 KB |
| testcase_25 | AC | 554 ms
31,616 KB |
| testcase_26 | AC | 552 ms
31,620 KB |
| testcase_27 | AC | 536 ms
31,596 KB |
| testcase_28 | AC | 520 ms
31,628 KB |
| testcase_29 | AC | 647 ms
37,204 KB |
| testcase_30 | AC | 650 ms
37,280 KB |
| testcase_31 | AC | 643 ms
37,272 KB |
| testcase_32 | AC | 660 ms
37,344 KB |
| testcase_33 | AC | 683 ms
37,296 KB |
| testcase_34 | AC | 286 ms
37,336 KB |
| testcase_35 | AC | 293 ms
37,272 KB |
| testcase_36 | AC | 296 ms
37,344 KB |
| testcase_37 | AC | 290 ms
37,288 KB |
| testcase_38 | AC | 287 ms
37,244 KB |
| testcase_39 | AC | 47 ms
4,368 KB |
| testcase_40 | AC | 35 ms
4,368 KB |
| testcase_41 | AC | 1 ms
4,368 KB |
| testcase_42 | WA | - |
| testcase_43 | WA | - |
| testcase_44 | WA | - |
コンパイルメッセージ
warning: function `shuffle` is never used
--> Main.rs:962:4
|
962 | fn shuffle<T>(a: &mut [T]) {
| ^^^^^^^
|
= note: `#[warn(dead_code)]` on by default
warning: fields `sa` and `lcp` are never read
--> Main.rs:972:5
|
970 | pub struct SAString<T> {
| -------- fields in this struct
971 | s: Vec<T>,
972 | sa: Vec<usize>,
| ^^
973 | isa: Vec<usize>,
974 | lcp: Vec<usize>,
| ^^^
warning: 2 warnings emitted
ソースコード
use std::io::Write;
fn main() {
input! {
t: usize,
ask: [(usize, usize, bytes, bytes); t],
}
let out = std::io::stdout();
let mut out = std::io::BufWriter::new(out.lock());
for (n, m, a, b) in ask {
let mut pos = wildcard_matching(&a, &b);
if pos.is_empty() {
writeln!(out, "-1").ok();
continue;
}
let s = a.iter().map(|a| if *a == b'?' {b'a'} else {*a}).chain(b.iter().cloned()).collect::<Vec<_>>();
let sa = SAString::new(s.clone());
let x = pos.pop().unwrap();
let mut ans = vec![(0, x), (n, n + m), (x + m, n)];
for x in pos {
let b = vec![(0, x), (n, n + m), (x + m, n)];
if sa.compare(b.clone(), ans.clone()) == std::cmp::Ordering::Less {
ans = b;
}
}
let ans = ans.into_iter().flat_map(|(l, r)| s[l..r].iter().cloned()).map(|c| c as char).collect::<String>();
writeln!(out, "{}", ans).ok();
}
}
pub fn wildcard_matching(a: &[u8], b: &[u8]) -> Vec<usize> {
let n = a.len();
let m = b.len();
assert!(m > 0);
if n < m {
return vec![];
}
let mut map = std::collections::BTreeMap::new();
let a = a
.iter()
.map(|a| {
if *a == b'?' {
M::zero()
} else {
let po = map.entry(*a).or_insert_with(rand);
M::from(*po)
}
})
.collect::<Vec<_>>();
let b = b
.iter()
.map(|a| {
if *a == b'?' {
M::zero()
} else {
let po = map.entry(*a).or_insert_with(rand);
M::from(*po)
}
})
.rev()
.collect::<Vec<_>>();
let size = n.next_power_of_two();
let mut s = vec![M::zero(); size];
{
let mut a = a
.iter()
.cloned()
.chain(std::iter::repeat(M::zero()))
.take(size)
.map(|a| a * a)
.collect::<Vec<_>>();
let mut b = b
.iter()
.cloned()
.chain(std::iter::repeat(M::zero()))
.take(size)
.collect::<Vec<_>>();
a.ntt();
b.ntt();
for ((s, a), b) in s.iter_mut().zip(a).zip(b) {
*s += a * b;
}
}
{
let mut a = a
.iter()
.cloned()
.chain(std::iter::repeat(M::zero()))
.take(size)
.collect::<Vec<_>>();
let mut b = b
.iter()
.cloned()
.chain(std::iter::repeat(M::zero()))
.take(size)
.map(|a| a * a)
.collect::<Vec<_>>();
a.ntt();
b.ntt();
for ((s, a), b) in s.iter_mut().zip(a).zip(b) {
*s -= a * b;
}
}
s.intt();
((m - 1)..n)
.filter(|x| s[*x].is_zero())
.map(|x| x - (m - 1))
.collect()
}
// ---------- 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 ----------
// モンゴメリ乗算を用いる
// ほぼCodeforces用
// 注意
// new_unchecked は値xが 0 <= x < modulo であることを仮定
// ModInt の中身は正規化された値で持ってるので直接読んだり書いたりするとぶっ壊れる
// 奇素数のみ
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
}
}
// 列に対する命令をテキトーに詰めあわせ
// modint, primitive type の２つあたりで使うことを想定
// +, -, *
// zero を要求してないのに仮定してる場所がある
//
// 何も考えずに書き始めたらいろいろよくわからないことになった
// 整理
// 長さが等しいときの加算、減算、dot積はok
// 長さが異なるときはどうする？
// 0埋めされてるというイメージなので
// 加算、減算は素直だがdot積はイマイチ
// dot積だけ長さが等しいとしておく?
// あるいは0埋めのイメージを消すか
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
//
// ---------- begin rand ----------
fn rand_memory() -> usize {
Box::into_raw(Box::new("I hope this is a random number")) as usize
}
fn rand() -> usize {
static mut X: usize = 0;
unsafe {
if X == 0 {
X = rand_memory();
}
X ^= X << 13;
X ^= X >> 17;
X ^= X << 5;
X
}
}
fn shuffle<T>(a: &mut [T]) {
for i in 1..a.len() {
let p = rand() % (i + 1);
a.swap(i, p);
}
}
// ---------- end rand ----------
pub struct SAString<T> {
s: Vec<T>,
sa: Vec<usize>,
isa: Vec<usize>,
lcp: Vec<usize>,
rmq: RMQ<usize>,
}
impl<T: Ord> SAString<T> {
pub fn new(s: Vec<T>) -> Self {
let (sa, isa, lcp) = suffix_array(&s);
let rmq = RMQ::new(lcp.clone());
Self {
s,
sa,
isa,
lcp,
rmq,
}
}
pub fn find_lcp(&self, x: usize, y: usize) -> usize {
assert!(x.max(y) < self.s.len());
if x == y {
self.s.len() - x.max(y)
} else {
let a = self.isa[x.min(y)];
let b = self.isa[x.max(y)];
self.rmq.find(a.min(b) + 1, a.max(b) + 1)
}
}
pub fn compare(&self, mut a: Vec<(usize, usize)>, mut b: Vec<(usize, usize)>) -> std::cmp::Ordering {
assert!(a
.iter()
.chain(b.iter())
.all(|p| p.0 <= p.1 && p.1 <= self.s.len()));
a.retain(|p| p.0 < p.1);
b.retain(|p| p.0 < p.1);
let mut x = 0;
let mut y = 0;
while x < a.len() && y < b.len() {
let a = &mut a[x];
let b = &mut b[y];
let len = (a.1 - a.0).min(b.1 - b.0);
let lcp = self.find_lcp(a.0, b.0).min(len);
a.0 += lcp;
b.0 += lcp;
if a.0 < a.1 && b.0 < b.1 {
return self.s[a.0].cmp(&self.s[b.0]);
}
if a.0 == a.1 {
x += 1;
}
if b.0 == b.1 {
y += 1;
}
}
(x < a.len()).cmp(&(y < b.len()))
}
}
// O(N (log N)^2)
// 文字種によらない
// O(N log N) の実装が悪く、log2つの方が早かったので一時的にこちらに更新
// ---------- begin suffix array ----------
fn suffix_array<T: Ord>(s: &[T]) -> (Vec<usize>, Vec<usize>, Vec<usize>) {
let n = s.len();
let mut z = s.iter().collect::<Vec<_>>();
z.sort();
z.dedup();
let mut ord = Vec::with_capacity(n);
for s in s.iter() {
ord.push(z.binary_search(&s).unwrap() as u32 + 1);
}
let mut z = (0..n).map(|p| ((ord[p], 0), p)).collect::<Vec<_>>();
z.sort_by_key(|p| p.0);
let mut len = 1;
while len < n {
for z in z.iter_mut() {
z.0 = (ord[z.1], ord.get(z.1 + len).map_or(0, |p| *p));
}
z.sort_by_key(|p| p.0);
let mut id = 1;
let mut prev = z[0].0;
for z in z.iter_mut() {
if z.0 != prev {
id += 1;
prev = z.0;
}
ord[z.1] = id;
}
len <<= 1;
}
let sa = z.into_iter().map(|p| p.1).collect::<Vec<_>>();
let mut isa = vec![0; s.len()];
for (i, sa) in sa.iter().enumerate() {
isa[*sa] = i;
}
let mut lcp = vec![0; s.len()];
let mut h = 0;
for i in 0..sa.len() {
if isa[i] + 1 < sa.len() {
let j = sa[isa[i] + 1];
while i.max(j) + h < sa.len() && s[i + h] == s[j + h] {
h += 1;
}
lcp[isa[i] + 1] = h;
if h > 0 {
h -= 1;
}
}
}
(sa, isa, lcp)
}
// ---------- end suffix array ----------
pub struct RMQ<T> {
data: Vec<T>,
table: SparseTable<T>,
bit: Vec<usize>,
}
impl<T> RMQ<T>
where
T: Ord + Copy,
{
pub fn new(data: Vec<T>) -> Self {
assert!(!data.is_empty());
let mut bit = vec![0; data.len()];
let w = 8 * std::mem::size_of_val(&bit[0]);
let mut stack: Vec<usize> = vec![];
let mut table_ini = Vec::with_capacity((data.len() + w - 1) / w);
for (bit, data) in bit.chunks_mut(w).zip(data.chunks(w)) {
stack.clear();
let mut b = 0;
for (i, (bit, d)) in bit.iter_mut().zip(data.iter()).enumerate() {
while stack.last().map_or(false, |x| data[*x] > *d) {
b ^= 1 << stack.pop().unwrap();
}
b |= 1 << i;
*bit = b;
stack.push(i);
}
table_ini.push(data[stack[0]]);
}
let table = SparseTable::new(table_ini);
RMQ { data, table, bit }
}
pub fn find(&self, l: usize, r: usize) -> T {
assert!(l < r && r <= self.data.len());
let w = 8 * std::mem::size_of_val(&self.bit[0]);
let r = r - 1;
let p = l / w;
let q = r / w;
if p == q {
let pos = l + (self.bit[r] >> (l % w)).trailing_zeros() as usize;
self.data[pos]
} else {
let lw = l + (self.bit[p * w + w - 1] >> (l % w)).trailing_zeros() as usize;
let rw = q * w + self.bit[r].trailing_zeros() as usize;
let mut res = std::cmp::min(self.data[lw], self.data[rw]);
if p + 1 < q {
res = std::cmp::min(res, self.table.find(p + 1, q));
}
res
}
}
}
// ---------- begin sparse table (min) ----------
pub struct SparseTable<T> {
table: Vec<Vec<T>>,
size: usize,
}
impl<T> SparseTable<T>
where
T: Ord + Copy,
{
pub fn new(mut a: Vec<T>) -> Self {
assert!(a.len() > 0);
let size = a.len();
let mut table = vec![];
let mut w = 1;
while w + 1 <= a.len() {
let next = a
.iter()
.zip(a[w..].iter())
.map(|p| std::cmp::min(*p.0, *p.1))
.collect::<Vec<_>>();
table.push(a);
a = next;
w <<= 1;
}
table.push(a);
SparseTable {
table: table,
size: size,
}
}
pub fn find(&self, l: usize, r: usize) -> T {
assert!(l < r && r <= self.size);
let k = 8 * std::mem::size_of::<usize>() - 1 - (r - l).leading_zeros() as usize;
let table = &self.table[k];
std::cmp::min(table[l], table[r - (1 << k)])
}
}
// ---------- end sparse table (min) ----------