結果
| 問題 | No.1411 Hundreds of Conditions Sequences |
| ユーザー |
 ngtkana
|
| 提出日時 | 2020-12-02 01:47:53 |
| 言語 | Rust (1.77.0 + proconio) |
| 結果 |
AC
|
| 実行時間 | 251 ms / 2,000 ms |
| コード長 | 37,178 bytes |
| コンパイル時間 | 13,735 ms |
| コンパイル使用メモリ | 401,764 KB |
| 実行使用メモリ | 18,928 KB |
| 最終ジャッジ日時 | 2024-09-22 11:02:04 |
| 合計ジャッジ時間 | 28,252 ms |
|
ジャッジサーバーID （参考情報） |
judge4 / judge2 |
（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
6,812 KB |
| testcase_01 | AC | 1 ms
6,816 KB |
| testcase_02 | AC | 1 ms
6,812 KB |
| testcase_03 | AC | 1 ms
6,944 KB |
| testcase_04 | AC | 1 ms
6,944 KB |
| testcase_05 | AC | 1 ms
6,944 KB |
| testcase_06 | AC | 1 ms
6,940 KB |
| testcase_07 | AC | 1 ms
6,944 KB |
| testcase_08 | AC | 1 ms
6,944 KB |
| testcase_09 | AC | 1 ms
6,940 KB |
| testcase_10 | AC | 1 ms
6,940 KB |
| testcase_11 | AC | 1 ms
6,940 KB |
| testcase_12 | AC | 212 ms
15,048 KB |
| testcase_13 | AC | 165 ms
13,020 KB |
| testcase_14 | AC | 95 ms
9,416 KB |
| testcase_15 | AC | 162 ms
12,904 KB |
| testcase_16 | AC | 28 ms
6,944 KB |
| testcase_17 | AC | 156 ms
12,504 KB |
| testcase_18 | AC | 210 ms
15,020 KB |
| testcase_19 | AC | 231 ms
15,792 KB |
| testcase_20 | AC | 92 ms
9,392 KB |
| testcase_21 | AC | 243 ms
16,556 KB |
| testcase_22 | AC | 100 ms
9,832 KB |
| testcase_23 | AC | 214 ms
15,192 KB |
| testcase_24 | AC | 19 ms
6,940 KB |
| testcase_25 | AC | 213 ms
14,996 KB |
| testcase_26 | AC | 155 ms
12,548 KB |
| testcase_27 | AC | 95 ms
9,600 KB |
| testcase_28 | AC | 177 ms
13,596 KB |
| testcase_29 | AC | 37 ms
6,940 KB |
| testcase_30 | AC | 134 ms
11,440 KB |
| testcase_31 | AC | 128 ms
10,960 KB |
| testcase_32 | AC | 246 ms
16,584 KB |
| testcase_33 | AC | 243 ms
16,480 KB |
| testcase_34 | AC | 248 ms
16,484 KB |
| testcase_35 | AC | 242 ms
16,508 KB |
| testcase_36 | AC | 247 ms
16,488 KB |
| testcase_37 | AC | 245 ms
16,560 KB |
| testcase_38 | AC | 248 ms
16,452 KB |
| testcase_39 | AC | 246 ms
16,480 KB |
| testcase_40 | AC | 247 ms
16,560 KB |
| testcase_41 | AC | 248 ms
16,644 KB |
| testcase_42 | AC | 249 ms
16,500 KB |
| testcase_43 | AC | 246 ms
16,528 KB |
| testcase_44 | AC | 246 ms
16,508 KB |
| testcase_45 | AC | 244 ms
16,508 KB |
| testcase_46 | AC | 247 ms
16,480 KB |
| testcase_47 | AC | 245 ms
16,488 KB |
| testcase_48 | AC | 249 ms
16,500 KB |
| testcase_49 | AC | 246 ms
16,460 KB |
| testcase_50 | AC | 247 ms
16,500 KB |
| testcase_51 | AC | 243 ms
16,492 KB |
| testcase_52 | AC | 251 ms
16,488 KB |
| testcase_53 | AC | 250 ms
16,488 KB |
| testcase_54 | AC | 247 ms
16,556 KB |
| testcase_55 | AC | 251 ms
16,512 KB |
| testcase_56 | AC | 249 ms
16,552 KB |
| testcase_57 | AC | 246 ms
16,616 KB |
| testcase_58 | AC | 245 ms
16,552 KB |
| testcase_59 | AC | 248 ms
16,560 KB |
| testcase_60 | AC | 248 ms
16,648 KB |
| testcase_61 | AC | 246 ms
16,556 KB |
| testcase_62 | AC | 198 ms
15,588 KB |
| testcase_63 | AC | 218 ms
18,928 KB |
コンパイルメッセージ
warning: unused import: `accumulate`
--> src/main.rs:118:32
|
118 | pub use self::accumulate::{accumulate, Accumulate};
| ^^^^^^^^^^
|
= note: `#[warn(unused_imports)]` on by default
warning: unused import: `cartesian_product`
--> src/main.rs:120:39
|
120 | pub use self::cartesian_product::{cartesian_product, CartesianProduct};
| ^^^^^^^^^^^^^^^^^
warning: unused import: `self::format_intersparse::format_intersparse`
--> src/main.rs:121:13
|
121 | pub use self::format_intersparse::format_intersparse;
| ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
warning: unused import: `intersperse`
--> src/main.rs:123:33
|
123 | pub use self::intersperse::{intersperse, Intersperse};
| ^^^^^^^^^^^
warning: unused imports: `MulStep`, `mul_step`
--> src/main.rs:124:30
|
124 | pub use self::mul_step::{mul_step, MulStep};
| ^^^^^^^^ ^^^^^^^
warning: unused imports: `RepeatWith`, `repeat_with`
--> src/main.rs:125:33
|
125 | pub use self::repeat_with::{repeat_with, RepeatWith};
| ^^^^^^^^^^^ ^^^^^^^^^^
warning: unused import: `Step`
--> src/main.rs:126:32
|
126 | pub use self::step::{step, Step};
| ^^^^
warning: unused imports: `Leaf`, `Tuple`, `VecLen`
--> src/main.rs:973:37
|
973 | pub use self::multi_token::{Leaf, Parser, ParserTuple, RawTuple, Tuple, VecLen};
| ^^^^ ^^^^^ ^^^^^^
warning: unused import: `with_str`
--> src/main.rs:1228:35
|
1228 | pub use self::i::{with_stdin, with_str};
| ^^^^^^^^
warning: unused imports: `ParserTuple`, `Parser`, `RawTuple`, `Token`, `Usize1`
--> src/main.rs:1231:28
|
1231 |
ソースコード
/*
SmallestPrimeFactors を使って素因数分解を高速化です。
さらに、ウェイトの減少を高速化です。
約数の個数テーブルを Vec から HashMap に変更です。
逆元前計算で高速化です。
逆元前計算を 10 ^ 5 で止めます。
約数の個数テーブルを顕に持たないように変更です。
逆元前計算をやめます。
*/
type Fp = fp::F1000000007;
use std::collections::HashMap;
fn main() {
let mut buf = ngtio::with_stdin();
let n = buf.usize();
let a = buf.vec::<u32>(n);
let a_max = *a.iter().max().unwrap();
let sp = SmallestPrimeFactors::new(a_max + 1);
let div = a.iter().map(|&x| sp.factorize(x)).collect::<Vec<_>>();
let (ratio, top) = {
let mut top = HashMap::new();
let mut ratio = Fp::new(1);
for &(p, m) in div.iter().flatten() {
let entry = top.entry(p).or_insert((0, 0));
if entry.0 <= m {
entry.1 = entry.0;
entry.0 = m;
} else if entry.1 <= m {
entry.1 = m;
}
ratio *= Fp::new(p as i64).inv().pow(m as u64);
}
ratio *= top
.iter()
.map(|(&p, &(first, _))| Fp::new(p as i64).pow(first as u64))
.product::<Fp>();
(ratio, top)
};
let prod = a.iter().map(|&x| Fp::new(x as i64)).product::<Fp>();
for (div, &x) in div.iter().zip(a.iter()) {
let ratio = ratio
* div
.iter()
.copied()
.map(|(p, m)| {
Fp::new(p as i64).pow({
let &(first, second) = top.get(&p).unwrap();
if m == first {
second
} else {
m
}
} as u64)
})
.product::<Fp>();
let ans = prod * Fp::new(x as i64).inv() * (Fp::new(1) - ratio);
println!("{}", ans);
}
}
pub struct SmallInversions(Vec<Fp>);
impl SmallInversions {
pub fn new(n: u32) -> Self {
let mut vec = vec![Fp::new(1); n as usize];
for x in (2..n).map(|x| x as i64) {
let q = Fp::r#mod() / x;
let r = Fp::r#mod() % x;
vec[x as usize] = -Fp::new(q) * vec[r as usize];
}
Self(vec)
}
pub fn inv_small(&self, n: u32) -> Fp {
self.0[n as usize]
}
pub fn inv_large(&self, n: u32) -> Fp {
if n < self.0.len() as u32 {
self.inv_small(n)
} else {
let q = Fp::r#mod() / n as i64;
let r = Fp::r#mod() % n as i64;
-Fp::new(q) * self.inv_large(r as u32)
}
}
}
pub struct SmallestPrimeFactors(Vec<u32>);
impl SmallestPrimeFactors {
pub fn new(n: u32) -> Self {
let mut vec = (0..n).collect::<Vec<_>>();
for p in (2..).take_while(|&p| p * p < n) {
for i in seq::step(2 * p, p).take_while(|&i| i < n) {
if vec[i as usize] == i {
vec[i as usize] = p
}
}
}
Self(vec)
}
pub fn factorize(&self, mut n: u32) -> Vec<(u32, u32)> {
let mut ans = Vec::new();
while n != 1 {
let p = self.0[n as usize];
if ans.last().map_or(true, |&(p1, _)| p1 != p) {
ans.push((p, 0));
}
ans.last_mut().unwrap().1 += 1;
n /= p;
}
ans
}
}
// seq {{{
#[allow(dead_code)]
mod seq {
#![warn(missing_docs, missing_doc_code_examples)]
pub use self::accumulate::{accumulate, Accumulate};
pub use self::adjacent::{adjacent, Adjacent};
pub use self::cartesian_product::{cartesian_product, CartesianProduct};
pub use self::format_intersparse::format_intersparse;
pub use self::grid_next::{grid_next, GridNext};
pub use self::intersperse::{intersperse, Intersperse};
pub use self::mul_step::{mul_step, MulStep};
pub use self::repeat_with::{repeat_with, RepeatWith};
pub use self::step::{step, Step};
use std::{fmt, ops};
impl<I: Iterator> Seq for I {}
pub trait Seq: Iterator + Sized {
fn adjacent(self) -> Adjacent<Self, Self::Item>
where
Self::Item: Clone,
{
adjacent(self)
}
fn grid_next(self, ij: (usize, usize), h: usize, w: usize) -> GridNext<Self>
where
Self: Iterator<Item = (i64, i64)>,
{
grid_next(self, ij, h, w)
}
fn cartesian_product<J>(self, other: J) -> CartesianProduct<Self, J::IntoIter>
where
Self: Sized,
Self::Item: Clone,
J: IntoIterator,
J::IntoIter: Clone,
{
cartesian_product::cartesian_product(self, other.into_iter())
}
fn accumulate<T>(self, init: T) -> Accumulate<Self, T>
where
T: Clone + ops::AddAssign<Self::Item>,
{
accumulate::accumulate(self, init)
}
fn intersperse(self, elt: Self::Item) -> Intersperse<Self> {
intersperse::intersperse(self, elt)
}
fn format_intersparse<T>(self, separator: T) -> String
where
Self::Item: fmt::Display,
T: fmt::Display,
{
self.map(|x| format!("{}", x))
.intersperse(format!("{}", separator))
.collect::<String>()
}
}
mod adjacent {
#[allow(missing_docs)]
pub fn adjacent<I, T>(mut iter: I) -> Adjacent<I, T>
where
I: Iterator<Item = T>,
T: Clone,
{
if let Some(first) = iter.next() {
Adjacent {
iter,
prv: Some(first),
}
} else {
Adjacent { iter, prv: None }
}
}
#[allow(missing_docs)]
pub struct Adjacent<I, T>
where
I: Iterator<Item = T>,
{
iter: I,
prv: Option<T>,
}
impl<I, T> Iterator for Adjacent<I, T>
where
I: Iterator<Item = T>,
T: Clone,
{
type Item = (T, T);
fn next(&mut self) -> Option<(T, T)> {
self.prv.as_ref().cloned().and_then(|first| {
self.iter.next().map(|second| {
self.prv = Some(second.clone());
(first, second)
})
})
}
}
}
mod grid_next {
#[allow(missing_docs)]
pub fn grid_next<T>(difference: T, ij: (usize, usize), h: usize, w: usize) -> GridNext<T>
where
T: Iterator<Item = (i64, i64)>,
{
GridNext {
i: ij.0 as i64,
j: ij.1 as i64,
h: h as i64,
w: w as i64,
difference,
}
}
#[allow(missing_docs)]
#[derive(Debug, Clone)]
pub struct GridNext<T> {
i: i64,
j: i64,
h: i64,
w: i64,
difference: T,
}
impl<T> Iterator for GridNext<T>
where
T: Iterator<Item = (i64, i64)>,
{
type Item = (usize, usize);
fn next(&mut self) -> Option<(usize, usize)> {
while let Some((di, dj)) = self.difference.next() {
let ni = self.i + di;
let nj = self.j + dj;
if 0 <= ni && ni < self.h && 0 <= nj && nj < self.w {
return Some((ni as usize, nj as usize));
}
}
None
}
}
}
mod step {
#[allow(missing_docs)]
pub fn step<T, U>(init: T, step: U) -> Step<T, U>
where
T: Copy,
U: Copy,
T: ::std::ops::Add<U, Output = T>,
{
Step { now: init, step }
}
#[allow(missing_docs)]
#[derive(Debug, Clone)]
pub struct Step<T, U> {
now: T,
step: U,
}
#[allow(missing_docs)]
impl<T, U> Iterator for Step<T, U>
where
T: Copy,
U: Copy,
T: ::std::ops::Add<U, Output = T>,
{
type Item = T;
fn next(&mut self) -> Option<T> {
let next = self.now + self.step;
Some(::std::mem::replace(&mut self.now, next))
}
}
}
mod mul_step {
#[allow(missing_docs)]
pub fn mul_step<T, U>(init: T, step: U) -> MulStep<T, U>
where
T: Copy,
U: Copy,
T: ::std::ops::Mul<U, Output = T>,
{
MulStep { now: init, step }
}
#[allow(missing_docs)]
#[derive(Debug, Clone)]
pub struct MulStep<T, U> {
now: T,
step: U,
}
#[allow(missing_docs)]
impl<T, U> Iterator for MulStep<T, U>
where
T: Copy,
U: Copy,
T: ::std::ops::Mul<U, Output = T>,
{
type Item = T;
fn next(&mut self) -> Option<T> {
let next = self.now * self.step;
Some(::std::mem::replace(&mut self.now, next))
}
}
}
mod repeat_with {
#[allow(missing_docs)]
pub fn repeat_with<A, F: FnMut() -> A>(repeater: F) -> RepeatWith<F> {
RepeatWith { repeater }
}
#[allow(missing_docs)]
#[derive(Debug, Clone)]
pub struct RepeatWith<F> {
repeater: F,
}
impl<A, F: FnMut() -> A> Iterator for RepeatWith<F> {
type Item = A;
#[inline]
fn next(&mut self) -> Option<A> {
Some((self.repeater)())
}
#[inline]
fn size_hint(&self) -> (usize, Option<usize>) {
(::std::usize::MAX, None)
}
}
}
mod accumulate {
use super::*;
#[allow(missing_docs)]
#[derive(Debug, Clone)]
pub struct Accumulate<I, T> {
prev: Option<T>,
iter: I,
}
#[allow(missing_docs)]
pub fn accumulate<I, T>(iter: I, init: T) -> Accumulate<I, T>
where
I: Iterator,
T: Clone + ops::AddAssign<I::Item>,
{
Accumulate {
prev: Some(init),
iter,
}
}
impl<I, T> Iterator for Accumulate<I, T>
where
I: Iterator,
T: Clone + ops::AddAssign<I::Item>,
{
type Item = T;
fn next(&mut self) -> Option<T> {
let res = self.prev.clone();
if let Some(prev) = self.prev.as_mut() {
if let Some(next) = self.iter.next() {
*prev += next;
} else {
self.prev = None;
}
}
res
}
fn size_hint(&self) -> (usize, Option<usize>) {
size_hint::add_scalar(self.iter.size_hint(), 1)
}
}
}
mod cartesian_product {
#[allow(missing_docs)]
#[derive(Debug, Clone)]
pub struct CartesianProduct<I, J>
where
I: Iterator,
{
a: I,
a_cur: Option<I::Item>,
b: J,
b_orig: J,
}
#[allow(missing_docs)]
pub fn cartesian_product<I, J>(mut i: I, j: J) -> CartesianProduct<I, J>
where
I: Iterator,
J: Clone + Iterator,
I::Item: Clone,
{
CartesianProduct {
a_cur: i.next(),
a: i,
b_orig: j.clone(),
b: j,
}
}
impl<I, J> Iterator for CartesianProduct<I, J>
where
I: Iterator,
J: Clone + Iterator,
I::Item: Clone,
{
type Item = (I::Item, J::Item);
fn next(&mut self) -> Option<(I::Item, J::Item)> {
let elt_b = match self.b.next() {
None => {
self.b = self.b_orig.clone();
match self.b.next() {
None => return None,
Some(x) => {
self.a_cur = self.a.next();
x
}
}
}
Some(x) => x,
};
match self.a_cur {
None => None,
Some(ref a) => Some((a.clone(), elt_b)),
}
}
fn size_hint(&self) -> (usize, Option<usize>) {
let has_cur = self.a_cur.is_some() as usize;
// Not ExactSizeIterator because size may be larger than usize
let (b_min, b_max) = self.b.size_hint();
// Compute a * b_orig + b for both lower and upper bound
super::size_hint::add(
super::size_hint::mul(self.a.size_hint(), self.b_orig.size_hint()),
(b_min * has_cur, b_max.map(move |x| x * has_cur)),
)
}
fn fold<Acc, G>(mut self, mut accum: Acc, mut f: G) -> Acc
where
G: FnMut(Acc, Self::Item) -> Acc,
{
if let Some(mut a) = self.a_cur.take() {
let mut b = self.b;
loop {
accum = b.fold(accum, |acc, elt| f(acc, (a.clone(), elt)));
// we can only continue iterating a if we had a first element;
if let Some(next_a) = self.a.next() {
b = self.b_orig.clone();
a = next_a;
} else {
break;
}
}
}
accum
}
}
}
#[allow(missing_docs)]
mod intersperse {
use super::size_hint;
use std::iter;
#[derive(Debug, Clone)]
#[must_use = "iterator adaptors are lazy and do nothing unless consumed"]
pub struct Intersperse<I>
where
I: Iterator,
{
element: I::Item,
iter: iter::Fuse<I>,
peek: Option<I::Item>,
}
pub fn intersperse<I>(iter: I, elt: I::Item) -> Intersperse<I>
where
I: Iterator,
{
let mut iter = iter.fuse();
Intersperse {
peek: iter.next(),
iter,
element: elt,
}
}
impl<I> Iterator for Intersperse<I>
where
I: Iterator,
I::Item: Clone,
{
type Item = I::Item;
#[inline]
fn next(&mut self) -> Option<I::Item> {
if self.peek.is_some() {
self.peek.take()
} else {
self.peek = self.iter.next();
if self.peek.is_some() {
Some(self.element.clone())
} else {
None
}
}
}
fn size_hint(&self) -> (usize, Option<usize>) {
// 2 * SH + { 1 or 0 }
let has_peek = self.peek.is_some() as usize;
let sh = self.iter.size_hint();
size_hint::add_scalar(size_hint::add(sh, sh), has_peek)
}
fn fold<B, F>(mut self, init: B, mut f: F) -> B
where
Self: Sized,
F: FnMut(B, Self::Item) -> B,
{
let mut accum = init;
if let Some(x) = self.peek.take() {
accum = f(accum, x);
}
let element = &self.element;
self.iter.fold(accum, |accum, x| {
let accum = f(accum, element.clone());
f(accum, x)
})
}
}
}
#[allow(missing_docs)]
mod format_intersparse {
use super::Seq;
use std::fmt;
pub fn format_intersparse<I, T>(iter: I, separator: T) -> String
where
I: Iterator,
I::Item: fmt::Display,
T: fmt::Display,
{
iter.map(|x| format!("{}", x))
.intersperse(format!("{}", separator))
.collect::<String>()
}
}
mod size_hint {
use std::cmp;
use std::usize;
pub type SizeHint = (usize, Option<usize>);
#[inline]
pub fn add(a: SizeHint, b: SizeHint) -> SizeHint {
let min = a.0.saturating_add(b.0);
let max = match (a.1, b.1) {
(Some(x), Some(y)) => x.checked_add(y),
_ => None,
};
(min, max)
}
#[inline]
#[allow(dead_code)]
pub fn add_scalar(sh: SizeHint, x: usize) -> SizeHint {
let (mut low, mut hi) = sh;
low = low.saturating_add(x);
hi = hi.and_then(|elt| elt.checked_add(x));
(low, hi)
}
#[inline]
#[allow(dead_code)]
pub fn sub_scalar(sh: SizeHint, x: usize) -> SizeHint {
let (mut low, mut hi) = sh;
low = low.saturating_sub(x);
hi = hi.map(|elt| elt.saturating_sub(x));
(low, hi)
}
#[inline]
#[allow(dead_code)]
pub fn mul(a: SizeHint, b: SizeHint) -> SizeHint {
let low = a.0.saturating_mul(b.0);
let hi = match (a.1, b.1) {
(Some(x), Some(y)) => x.checked_mul(y),
(Some(0), None) | (None, Some(0)) => Some(0),
_ => None,
};
(low, hi)
}
#[inline]
#[allow(dead_code)]
pub fn mul_scalar(sh: SizeHint, x: usize) -> SizeHint {
let (mut low, mut hi) = sh;
low = low.saturating_mul(x);
hi = hi.and_then(|elt| elt.checked_mul(x));
(low, hi)
}
#[inline]
#[allow(dead_code)]
pub fn max(a: SizeHint, b: SizeHint) -> SizeHint {
let (a_lower, a_upper) = a;
let (b_lower, b_upper) = b;
let lower = cmp::max(a_lower, b_lower);
let upper = match (a_upper, b_upper) {
(Some(x), Some(y)) => Some(cmp::max(x, y)),
_ => None,
};
(lower, upper)
}
#[inline]
#[allow(dead_code)]
pub fn min(a: SizeHint, b: SizeHint) -> SizeHint {
let (a_lower, a_upper) = a;
let (b_lower, b_upper) = b;
let lower = cmp::min(a_lower, b_lower);
let upper = match (a_upper, b_upper) {
(Some(u1), Some(u2)) => Some(cmp::min(u1, u2)),
_ => a_upper.or(b_upper),
};
(lower, upper)
}
}
}
// }}}
// fp {{{
#[allow(dead_code)]
mod fp {
mod arith {
use super::{Fp, Mod};
use std::ops::*;
impl<T: Mod> Add for Fp<T> {
type Output = Self;
fn add(self, rhs: Self) -> Self {
let res = self.0 + rhs.0;
Self::unchecked(if T::MOD <= res { res - T::MOD } else { res })
}
}
impl<T: Mod> Sub for Fp<T> {
type Output = Self;
fn sub(self, rhs: Self) -> Self {
let res = self.0 - rhs.0;
Self::unchecked(if res < 0 { res + T::MOD } else { res })
}
}
impl<T: Mod> Mul for Fp<T> {
type Output = Self;
fn mul(self, rhs: Self) -> Self {
Self::new(self.0 * rhs.0)
}
}
#[allow(clippy::suspicious_arithmetic_impl)]
impl<T: Mod> Div for Fp<T> {
type Output = Self;
fn div(self, rhs: Self) -> Self {
self * rhs.inv()
}
}
impl<M: Mod> Neg for Fp<M> {
type Output = Self;
fn neg(self) -> Self {
if self.0 == 0 {
Self::unchecked(0)
} else {
Self::unchecked(M::MOD - self.0)
}
}
}
impl<M: Mod> Neg for &Fp<M> {
type Output = Fp<M>;
fn neg(self) -> Self::Output {
if self.0 == 0 {
Fp::unchecked(0)
} else {
Fp::unchecked(M::MOD - self.0)
}
}
}
macro_rules! forward_assign_biop {
($(impl $trait:ident, $fn_assign:ident, $fn:ident)*) => {
$(
impl<M: Mod> $trait for Fp<M> {
fn $fn_assign(&mut self, rhs: Self) {
*self = self.$fn(rhs);
}
}
)*
};
}
forward_assign_biop! {
impl AddAssign, add_assign, add
impl SubAssign, sub_assign, sub
impl MulAssign, mul_assign, mul
impl DivAssign, div_assign, div
}
macro_rules! forward_ref_binop {
($(impl $imp:ident, $method:ident)*) => {
$(
impl<'a, T: Mod> $imp<Fp<T>> for &'a Fp<T> {
type Output = Fp<T>;
fn $method(self, other: Fp<T>) -> Self::Output {
$imp::$method(*self, other)
}
}
impl<'a, T: Mod> $imp<&'a Fp<T>> for Fp<T> {
type Output = Fp<T>;
fn $method(self, other: &Fp<T>) -> Self::Output {
$imp::$method(self, *other)
}
}
impl<'a, T: Mod> $imp<&'a Fp<T>> for &'a Fp<T> {
type Output = Fp<T>;
fn $method(self, other: &Fp<T>) -> Self::Output {
$imp::$method(*self, *other)
}
}
)*
};
}
forward_ref_binop! {
impl Add, add
impl Sub, sub
impl Mul, mul
impl Div, div
}
}
use std::{
fmt::{Debug, Display},
hash::Hash,
iter,
marker::PhantomData,
ops,
};
// NOTE: `crate::` がないとうまく展開できません。
crate::define_fp!(pub F998244353, Mod998244353, 998244353);
crate::define_fp!(pub F1000000007, Mod1000000007, 1000000007);
#[derive(Clone, PartialEq, Copy, Eq, Hash)]
pub struct Fp<T>(i64, PhantomData<T>);
pub trait Mod: Debug + Clone + PartialEq + Copy + Eq + Hash {
const MOD: i64;
}
impl<T: Mod> Fp<T> {
pub fn new(mut x: i64) -> Self {
x %= T::MOD;
Self::unchecked(if x < 0 { x + T::MOD } else { x })
}
pub fn into_inner(self) -> i64 {
self.0
}
pub fn r#mod() -> i64 {
T::MOD
}
pub fn inv(self) -> Self {
assert_ne!(self.0, 0, "Zero division");
let (sign, x) = if self.0 * 2 < T::MOD {
(1, self.0)
} else {
(-1, T::MOD - self.0)
};
let (g, _a, b) = ext_gcd(T::MOD, x);
let ans = sign * b;
assert_eq!(g, 1);
Self::unchecked(if ans < 0 { ans + T::MOD } else { ans })
}
pub fn frac(x: i64, y: i64) -> Self {
Fp::new(x) / Fp::new(y)
}
pub fn pow(mut self, mut p: u64) -> Self {
let mut ans = Fp::new(1);
while p != 0 {
if p % 2 == 1 {
ans *= self;
}
self *= self;
p /= 2;
}
ans
}
fn unchecked(x: i64) -> Self {
Self(x, PhantomData)
}
}
impl<T: Mod> iter::Sum<Fp<T>> for Fp<T> {
fn sum<I>(iter: I) -> Self
where
I: iter::Iterator<Item = Fp<T>>,
{
iter.fold(Fp::new(0), ops::Add::add)
}
}
impl<'a, T: 'a + Mod> iter::Sum<&'a Fp<T>> for Fp<T> {
fn sum<I>(iter: I) -> Self
where
I: iter::Iterator<Item = &'a Fp<T>>,
{
iter.fold(Fp::new(0), ops::Add::add)
}
}
impl<T: Mod> iter::Product<Fp<T>> for Fp<T> {
fn product<I>(iter: I) -> Self
where
I: iter::Iterator<Item = Fp<T>>,
{
iter.fold(Self::new(1), ops::Mul::mul)
}
}
impl<'a, T: 'a + Mod> iter::Product<&'a Fp<T>> for Fp<T> {
fn product<I>(iter: I) -> Self
where
I: iter::Iterator<Item = &'a Fp<T>>,
{
iter.fold(Self::new(1), ops::Mul::mul)
}
}
impl<T: Mod> Debug for Fp<T> {
fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> Result<(), std::fmt::Error> {
let (x, y, _z) = reduce(self.0, T::MOD);
let (x, y) = match y.signum() {
1 => (x, y),
-1 => (-x, -y),
_ => unreachable!(),
};
if y == 1 {
write!(f, "{}", x)
} else {
write!(f, "{}/{}", x, y)
}
}
}
impl<T: Mod> Display for Fp<T> {
fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> Result<(), std::fmt::Error> {
write!(f, "{}", self.0)
}
}
// ax + by = gcd(x, y) なる、互いに素な (a, b) を一組探して、(g, a, b) を返します。
//
// | 0 -x | | y -x | | x 0 |
// | 1 b | = | a b | | y 1 |
fn ext_gcd(x: i64, y: i64) -> (i64, i64, i64) {
let (b, g) = {
let mut x = x;
let mut y = y;
let mut u = 0;
let mut v = 1;
while x != 0 {
let q = y / x;
y -= q * x;
v -= q * u;
std::mem::swap(&mut x, &mut y);
std::mem::swap(&mut u, &mut v);
}
(v, y)
};
assert_eq!((g - b * y) % x, 0);
let a = (g - b * y) / x;
(g, a, b)
}
fn reduce(a: i64, m: i64) -> (i64, i64, i64) {
if a.abs() < 10_000 {
(a, 1, 0)
} else {
let mut q = m.div_euclid(a);
let mut r = m.rem_euclid(a);
if a <= 2 * r {
q += 1;
r -= a;
}
let (x, z, y) = reduce(r, a);
(x, y - q * z, z)
}
}
#[macro_export]
macro_rules! define_fp {
($vis:vis $fp:ident, $t:ident, $mod:expr) => {
#[derive(Debug, Clone, PartialEq, Copy, Eq, Hash)]
$vis struct $t;
// NOTE: `$crate::` があるとうまく展開できません。
impl Mod for $t {
const MOD: i64 = $mod;
}
// NOTE: `$crate::` があるとうまく展開できません。
$vis type $fp = Fp<$t>;
}
}
}
// }}}
// ngtio {{{
#[allow(dead_code)]
mod ngtio {
#![warn(missing_docs)]
mod i {
use std::{
io::{self, BufRead},
iter,
};
pub use self::multi_token::{Leaf, Parser, ParserTuple, RawTuple, Tuple, VecLen};
pub use self::token::{Token, Usize1};
pub fn with_stdin() -> Tokenizer<io::BufReader<io::Stdin>> {
io::BufReader::new(io::stdin()).tokenizer()
}
pub fn with_str(src: &str) -> Tokenizer<&[u8]> {
src.as_bytes().tokenizer()
}
pub struct Tokenizer<S: BufRead> {
queue: Vec<String>, // FIXME: String のみにすると速そうです。
scanner: S,
}
macro_rules! prim_method {
($name:ident: $T:ty) => {
#[allow(missing_docs)]
pub fn $name(&mut self) -> $T {
<$T>::leaf().parse(self)
}
};
($name:ident) => {
prim_method!($name: $name);
};
}
macro_rules! prim_methods {
($name:ident: $T:ty; $($rest:tt)*) => {
prim_method!($name:$T);
prim_methods!($($rest)*);
};
($name:ident; $($rest:tt)*) => {
prim_method!($name);
prim_methods!($($rest)*);
};
() => ()
}
impl<S: BufRead> Tokenizer<S> {
pub fn token(&mut self) -> String {
self.load();
self.queue.pop().expect("入力が終了したのですが。")
}
pub fn new(scanner: S) -> Self {
Self {
queue: Vec::new(),
scanner,
}
}
fn load(&mut self) {
while self.queue.is_empty() {
let mut s = String::new();
let length = self.scanner.read_line(&mut s).unwrap(); // 入力が UTF-8 でないときにエラーだそうです。
if length == 0 {
break;
}
self.queue = s.split_whitespace().rev().map(str::to_owned).collect();
}
}
pub fn skip_line(&mut self) {
assert!(
self.queue.is_empty(),
"行の途中で呼ばないでいただきたいです。現在のトークンキュー: {:?}",
&self.queue
);
self.load();
}
pub fn end(&mut self) {
self.load();
assert!(self.queue.is_empty(), "入力はまだあります！");
}
pub fn parse<T: Token>(&mut self) -> T::Output {
T::parse(&self.token())
}
pub fn parse_collect<T: Token, B>(&mut self, n: usize) -> B
where
B: iter::FromIterator<T::Output>,
{
iter::repeat_with(|| self.parse::<T>()).take(n).collect()
}
pub fn tuple<T: RawTuple>(&mut self) -> <T::LeafTuple as Parser>::Output {
T::leaf_tuple().parse(self)
}
pub fn vec<T: Token>(&mut self, len: usize) -> Vec<T::Output> {
T::leaf().vec(len).parse(self)
}
pub fn vec_tuple<T: RawTuple>(
&mut self,
len: usize,
) -> Vec<<T::LeafTuple as Parser>::Output> {
T::leaf_tuple().vec(len).parse(self)
}
pub fn vec2<T: Token>(&mut self, height: usize, width: usize) -> Vec<Vec<T::Output>> {
T::leaf().vec(width).vec(height).parse(self)
}
pub fn vec2_tuple<T>(
&mut self,
height: usize,
width: usize,
) -> Vec<Vec<<T::LeafTuple as Parser>::Output>>
where
T: RawTuple,
{
T::leaf_tuple().vec(width).vec(height).parse(self)
}
prim_methods! {
u8; u16; u32; u64; u128; usize;
i8; i16; i32; i64; i128; isize;
char; string: String;
}
}
mod token {
use super::multi_token::Leaf;
use std::{any, fmt, marker, str};
pub trait Token: Sized {
type Output;
fn parse(s: &str) -> Self::Output;
fn leaf() -> Leaf<Self> {
Leaf(marker::PhantomData)
}
}
impl<T> Token for T
where
T: str::FromStr,
<T as str::FromStr>::Err: fmt::Debug,
{
type Output = T;
fn parse(s: &str) -> Self::Output {
s.parse().unwrap_or_else(|_| {
panic!("Parse error!: ({}: {})", s, any::type_name::<T>(),)
})
}
}
pub struct Usize1 {}
impl Token for Usize1 {
type Output = usize;
fn parse(s: &str) -> Self::Output {
usize::parse(s)
.checked_sub(1)
.expect("Parse error! (Zero substruction error of Usize1)")
}
}
}
mod multi_token {
use super::{Token, Tokenizer};
use std::{io::BufRead, iter, marker};
pub trait Parser: Sized {
type Output;
fn parse<S: BufRead>(&self, server: &mut Tokenizer<S>) -> Self::Output;
fn vec(self, len: usize) -> VecLen<Self> {
VecLen { len, elem: self }
}
}
pub struct Leaf<T>(pub(super) marker::PhantomData<T>);
impl<T: Token> Parser for Leaf<T> {
type Output = T::Output;
fn parse<S: BufRead>(&self, server: &mut Tokenizer<S>) -> T::Output {
server.parse::<T>()
}
}
pub struct VecLen<T> {
pub len: usize,
pub elem: T,
}
impl<T: Parser> Parser for VecLen<T> {
type Output = Vec<T::Output>;
fn parse<S: BufRead>(&self, server: &mut Tokenizer<S>) -> Self::Output {
iter::repeat_with(|| self.elem.parse(server))
.take(self.len)
.collect()
}
}
pub trait RawTuple {
type LeafTuple: Parser;
fn leaf_tuple() -> Self::LeafTuple;
}
pub trait ParserTuple {
type Tuple: Parser;
fn tuple(self) -> Self::Tuple;
}
pub struct Tuple<T>(pub T);
macro_rules! impl_tuple {
($($t:ident: $T:ident),*) => {
impl<$($T),*> Parser for Tuple<($($T,)*)>
where
$($T: Parser,)*
{
type Output = ($($T::Output,)*);
#[allow(unused_variables)]
fn parse<S: BufRead >(&self, server: &mut Tokenizer<S>) -> Self::Output {
match self {
Tuple(($($t,)*)) => {
($($t.parse(server),)*)
}
}
}
}
impl<$($T: Token),*> RawTuple for ($($T,)*) {
type LeafTuple = Tuple<($(Leaf<$T>,)*)>;
fn leaf_tuple() -> Self::LeafTuple {
Tuple(($($T::leaf(),)*))
}
}
impl<$($T: Parser),*> ParserTuple for ($($T,)*) {
type Tuple = Tuple<($($T,)*)>;
fn tuple(self) -> Self::Tuple {
Tuple(self)
}
}
};
}
impl_tuple!();
impl_tuple!(t1: T1);
impl_tuple!(t1: T1, t2: T2);
impl_tuple!(t1: T1, t2: T2, t3: T3);
impl_tuple!(t1: T1, t2: T2, t3: T3, t4: T4);
impl_tuple!(t1: T1, t2: T2, t3: T3, t4: T4, t5: T5);
impl_tuple!(t1: T1, t2: T2, t3: T3, t4: T4, t5: T5, t6: T6);
impl_tuple!(t1: T1, t2: T2, t3: T3, t4: T4, t5: T5, t6: T6, t7: T7);
impl_tuple!(
t1: T1,
t2: T2,
t3: T3,
t4: T4,
t5: T5,
t6: T6,
t7: T7,
t8: T8
);
}
trait Scanner: BufRead + Sized {
fn tokenizer(self) -> Tokenizer<Self> {
Tokenizer::new(self)
}
}
impl<R: BufRead> Scanner for R {}
}
pub use self::i::{with_stdin, with_str};
pub mod prelude {
pub use super::i::{Parser, ParserTuple, RawTuple, Token, Usize1};
}
}
// }}}