結果
問題 | No.1411 Hundreds of Conditions Sequences |
ユーザー |
![]() |
提出日時 | 2020-12-02 14:45:08 |
言語 | Rust (1.83.0 + proconio) |
結果 |
AC
|
実行時間 | 209 ms / 2,000 ms |
コード長 | 39,692 bytes |
コンパイル時間 | 13,359 ms |
コンパイル使用メモリ | 401,876 KB |
実行使用メモリ | 19,584 KB |
最終ジャッジ日時 | 2024-09-22 11:15:25 |
合計ジャッジ時間 | 26,058 ms |
ジャッジサーバーID (参考情報) |
judge5 / judge1 |
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ファイルパターン | 結果 |
---|---|
sample | AC * 2 |
other | AC * 62 |
コンパイルメッセージ
warning: unused import: `accumulate` --> src/main.rs:198:32 | 198 | pub use self::accumulate::{accumulate, Accumulate}; | ^^^^^^^^^^ | = note: `#[warn(unused_imports)]` on by default warning: unused import: `cartesian_product` --> src/main.rs:200:39 | 200 | pub use self::cartesian_product::{cartesian_product, CartesianProduct}; | ^^^^^^^^^^^^^^^^^ warning: unused import: `self::format_intersparse::format_intersparse` --> src/main.rs:201:13 | 201 | pub use self::format_intersparse::format_intersparse; | ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ warning: unused import: `intersperse` --> src/main.rs:203:33 | 203 | pub use self::intersperse::{intersperse, Intersperse}; | ^^^^^^^^^^^ warning: unused imports: `MulStep`, `mul_step` --> src/main.rs:204:30 | 204 | pub use self::mul_step::{mul_step, MulStep}; | ^^^^^^^^ ^^^^^^^ warning: unused imports: `RepeatWith`, `repeat_with` --> src/main.rs:205:33 | 205 | pub use self::repeat_with::{repeat_with, RepeatWith}; | ^^^^^^^^^^^ ^^^^^^^^^^ warning: unused imports: `Step`, `step` --> src/main.rs:206:26 | 206 | pub use self::step::{step, Step}; | ^^^^ ^^^^ warning: unused imports: `Leaf`, `Tuple`, `VecLen` --> src/main.rs:1053:37 | 1053 | pub use self::multi_token::{Leaf, Parser, ParserTuple, RawTuple, Tuple, VecLen}; | ^^^^ ^^^^^ ^^^^^^ warning: unused import: `with_str` --> src/main.rs:1308:35 | 1308 | pub use self::i::{with_stdin, with_str}; | ^^^^^^^^ warning: unused imports: `ParserTuple`, `Parser`, `RawTuple`, `Token`, `Usize1` --> src/main.rs:1311:28 |
ソースコード
use std::collections::HashMap;type Fp = fp::F1000000007;fn main() {let mut buf = ngtio::with_stdin();let n = buf.usize();let a = buf.vec::<u32>(n);// 制約チェックassert!((3..=100_000).contains(&n));a.iter().for_each(|&x| assert!((1..=10_000_000).contains(&x)));let sp = small_fp::SmallestPrimeFactors::new(a.iter().max().unwrap() + 1);let mut map = HashMap::new();a.iter().map(|&x| sp.factorize(x)).enumerate().map(|(i, div)| div.into_iter().map(move |(p, e)| (i, p, e))).flatten().for_each(|(i, p, e)| {let (first, ie) = map.entry(p).or_insert((0, None));if *first < e {*ie = Some((i, *first));*first = e;} else if *first == e {*ie = None;} else if let Some((_, second)) = ie {if *second < e {*second = e;}}});let lcm = map.iter().map(|(&p, &(first, _))| Fp::new(p as i64).pow(first as u64)).product::<Fp>();let mut lcm = vec![lcm; n];for (&p, &(first, ie)) in map.iter() {if let Some((i, second)) = ie {lcm[i] /= Fp::new(p as i64).pow((first - second) as u64);}}let prod = a.iter().map(|&x| Fp::new(x as i64)).product::<Fp>();for (&x, &lcm) in a.iter().zip(lcm.iter()) {let ans = prod / Fp::new(x as i64) - lcm;println!("{}", ans);}}// small_fp {{{#[allow(dead_code)]mod small_fp {use crate::fp::{Fp, Mod};pub struct SmallInversions<T>(Vec<Fp<T>>);impl<T: Mod> SmallInversions<T> {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::<T>::r#mod() / x;let r = Fp::<T>::r#mod() % x;vec[x as usize] = -Fp::new(q) * vec[r as usize];}Self(vec)}pub fn inv_small(&self, n: u32) -> Fp<T> {self.0[n as usize]}pub fn inv_large(&self, n: i64) -> Fp<T> {if 0 <= n && n < self.0.len() as i64 {self.inv_small(n as u32)} else {let n = Fp::<T>::new(n).into_inner();let m = Fp::<T>::r#mod();let q = m / n;let r = m % n;-Fp::new(q) * self.inv_large(r)}}}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) {let mut i = 2 * p;while i < n {if vec[i as usize] == i {vec[i as usize] = p}i += p;}}Self(vec)}pub fn get(&self, n: u32) -> u32 {assert!(n != 0 && n < self.0.len() as u32);self.0[n as usize]}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}}}// }}}// accum {{{#[allow(dead_code)]mod accum {use std::{cmp::Ord,ops::{AddAssign, BitAndAssign, BitOrAssign, BitXorAssign, DivAssign, MulAssign, SubAssign,},};pub fn add<T: Copy + AddAssign>(a: &mut [T]) {for_each_mut(a, |&mut x, y| *y += x);}pub fn add_inv<T: Copy + SubAssign>(a: &mut [T]) {rfor_each_mut(a, |&mut x, y| *y -= x);}pub fn mul<T: Copy + MulAssign>(a: &mut [T]) {for_each_mut(a, |&mut x, y| *y *= x);}pub fn mul_inv<T: Copy + DivAssign>(a: &mut [T]) {rfor_each_mut(a, |&mut x, y| *y /= x);}// -- ordpub fn min<T: Copy + Ord>(a: &mut [T]) {for_each_mut(a, |&mut x, y| *y = x.min(*y));}pub fn max<T: Copy + Ord>(a: &mut [T]) {for_each_mut(a, |&mut x, y| *y = x.max(*y));}// -- bitpub fn xor<T: Copy + BitXorAssign>(a: &mut [T]) {for_each_mut(a, |&mut x, y| *y ^= x);}pub fn xor_inv<T: Copy + BitXorAssign>(a: &mut [T]) {rfor_each_mut(a, |&mut x, y| *y ^= x);}pub fn or<T: Copy + BitOrAssign>(a: &mut [T]) {for_each_mut(a, |&mut x, y| *y |= x);}pub fn and<T: Copy + BitAndAssign>(a: &mut [T]) {for_each_mut(a, |&mut x, y| *y &= x);}// -- for_eachpub fn for_each<T>(a: &[T], mut f: impl FnMut(&T, &T)) {if !a.is_empty() {for i in 1..a.len() {let (left, right) = a.split_at(i);f(left.last().unwrap(), right.first().unwrap());}}}pub fn rfor_each<T>(a: &[T], mut f: impl FnMut(&T, &T)) {if !a.is_empty() {for i in (1..a.len()).rev() {let (left, right) = a.split_at(i);f(left.last().unwrap(), right.first().unwrap());}}}pub fn for_each_mut<T>(a: &mut [T], mut f: impl FnMut(&mut T, &mut T)) {if !a.is_empty() {for i in 1..a.len() {let (left, right) = a.split_at_mut(i);f(left.last_mut().unwrap(), right.first_mut().unwrap());}}}pub fn rfor_each_mut<T>(a: &mut [T], mut f: impl FnMut(&mut T, &mut T)) {if !a.is_empty() {for i in (1..a.len()).rev() {let (left, right) = a.split_at_mut(i);f(left.last_mut().unwrap(), right.first_mut().unwrap());}}}}// }}}// 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>whereSelf::Item: Clone,{adjacent(self)}fn grid_next(self, ij: (usize, usize), h: usize, w: usize) -> GridNext<Self>whereSelf: Iterator<Item = (i64, i64)>,{grid_next(self, ij, h, w)}fn cartesian_product<J>(self, other: J) -> CartesianProduct<Self, J::IntoIter>whereSelf: 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>whereT: 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) -> StringwhereSelf::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>whereI: 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>whereI: Iterator<Item = T>,{iter: I,prv: Option<T>,}impl<I, T> Iterator for Adjacent<I, T>whereI: 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>whereT: 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>whereT: 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>whereT: 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>whereT: 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>whereT: 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>whereT: 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>whereI: Iterator,T: Clone + ops::AddAssign<I::Item>,{Accumulate {prev: Some(init),iter,}}impl<I, T> Iterator for Accumulate<I, T>whereI: 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>whereI: 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>whereI: 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>whereI: 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 usizelet (b_min, b_max) = self.b.size_hint();// Compute a * b_orig + b for both lower and upper boundsuper::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) -> AccwhereG: 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>whereI: Iterator,{element: I::Item,iter: iter::Fuse<I>,peek: Option<I::Item>,}pub fn intersperse<I>(iter: I, elt: I::Item) -> Intersperse<I>whereI: Iterator,{let mut iter = iter.fuse();Intersperse {peek: iter.next(),iter,element: elt,}}impl<I> Iterator for Intersperse<I>whereI: 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) -> BwhereSelf: 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) -> StringwhereI: 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, addimpl SubAssign, sub_assign, subimpl MulAssign, mul_assign, mulimpl 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, addimpl Sub, subimpl Mul, mulimpl 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) -> SelfwhereI: 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) -> SelfwhereI: 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) -> SelfwhereI: 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) -> SelfwhereI: 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) -> BwhereB: 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>>whereT: 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 TwhereT: 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};}}// }}}