use std::collections::HashMap; type Fp = fp::F1000000007; fn main() { let mut buf = ngtio::with_stdin(); let n = buf.usize(); let a = buf.vec::(n); 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 orig_cnt = map .iter() .map(|(&p, &(first, _))| Fp::new(p as i64).pow(first as u64)) .product::(); let mut cnt = vec![orig_cnt; n]; for (&p, &(first, ie)) in map.iter() { if let Some((i, e)) = ie { cnt[i] /= Fp::new(p as i64).pow((first - e) as u64); } } let mut b = std::iter::once(1) .chain(a.iter().copied()) .map(|x| Fp::new(x as i64)) .collect::>(); let mut c = std::iter::once(1) .chain(a.iter().rev().copied()) .map(|x| Fp::new(x as i64)) .collect::>(); accum::mul(&mut b); accum::mul(&mut c); for i in 0..n { let ans = b[i] * c[n - 1 - i] - cnt[i]; println!("{}", ans); } } // dbg {{{ #[allow(dead_code)] mod dbg { #[macro_export] macro_rules! lg { () => { $crate::eprintln!("[{}:{}]", $crate::file!(), $crate::line!()); }; ($val:expr) => { match $val { tmp => { eprintln!("[{}:{}] {} = {:?}", file!(), line!(), stringify!($val), &tmp); tmp } } }; ($val:expr,) => { $crate::lg!($val) }; ($($val:expr),+ $(,)?) => { ($($crate::lg!($val)),+,) }; } #[macro_export] macro_rules! lg_nl { () => { eprintln!("[{}:{}]", $crate::file!(), $crate::line!()); }; ($val:expr) => { match $val { tmp => { eprintln!("[{}:{}] {}:\n{:?}", file!(), line!(), stringify!($val), tmp); tmp } }; }; } #[macro_export] macro_rules! msg { () => { compile_error!(); }; ($msg:expr) => { $crate::eprintln!("[{}:{}][{}]", $crate::file!(), $crate::line!(), $msg); }; ($msg:expr, $val:expr) => { match $val { tmp => { eprintln!("[{}:{}][{}] {} = {:?}", file!(), line!(), $msg, stringify!($val), &tmp); tmp } } }; ($msg:expr, $val:expr,) => { msg!($msg, $val) }; ($msg:expr, $($val:expr),+ $(,)?) => { ($(msg!($msg, $val)),+,) }; } #[macro_export] macro_rules! tabular { ($val:expr) => { $crate::lg_nl!($crate::Tabular($val)) }; } #[macro_export] macro_rules! boolean_table { ($val:expr) => { $crate::lg_nl!($crate::BooleanTable($val)); }; } #[macro_export] macro_rules! boolean_slice { ($val:expr) => { $crate::lg!($crate::BooleanSlice($val)); }; } use std::fmt::{Debug, Formatter}; #[derive(Clone)] pub struct Tabular<'a, T: Debug>(pub &'a [T]); impl<'a, T: Debug> Debug for Tabular<'a, T> { fn fmt(&self, f: &mut Formatter) -> std::fmt::Result { for i in 0..self.0.len() { writeln!(f, "{:2} | {:?}", i, &self.0[i])?; } Ok(()) } } #[derive(Clone)] pub struct BooleanTable<'a>(pub &'a [Vec]); impl<'a> Debug for BooleanTable<'a> { fn fmt(&self, f: &mut Formatter) -> std::fmt::Result { for i in 0..self.0.len() { writeln!(f, "{:2} | {:?}", i, BooleanSlice(&self.0[i]))?; } Ok(()) } } #[derive(Clone)] pub struct BooleanSlice<'a>(pub &'a [bool]); impl<'a> Debug for BooleanSlice<'a> { fn fmt(&self, f: &mut Formatter) -> std::fmt::Result { write!( f, "{}", self.0 .iter() .map(|&b| if b { "1 " } else { "0 " }) .collect::() )?; Ok(()) } } } // }}} // small_fp {{{ #[allow(dead_code)] mod small_fp { use crate::fp::{Fp, Mod}; pub struct SmallInversions(Vec>); 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: i64) -> Fp { if 0 <= n && n < self.0.len() as i64 { self.inv_small(n as u32) } else { let n = Fp::::new(n).into_inner(); let m = Fp::::r#mod(); let q = m / n; let r = m % n; -Fp::new(q) * self.inv_large(r) } } } pub struct SmallestPrimeFactors(Vec); impl SmallestPrimeFactors { pub fn new(n: u32) -> Self { let mut vec = (0..n).collect::>(); 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(a: &mut [T]) { for_each_mut(a, |&mut x, y| *y += x); } pub fn add_inv(a: &mut [T]) { rfor_each_mut(a, |&mut x, y| *y -= x); } pub fn mul(a: &mut [T]) { for_each_mut(a, |&mut x, y| *y *= x); } pub fn mul_inv(a: &mut [T]) { rfor_each_mut(a, |&mut x, y| *y /= x); } // -- ord pub fn min(a: &mut [T]) { for_each_mut(a, |&mut x, y| *y = x.min(*y)); } pub fn max(a: &mut [T]) { for_each_mut(a, |&mut x, y| *y = x.max(*y)); } // -- bit pub fn xor(a: &mut [T]) { for_each_mut(a, |&mut x, y| *y ^= x); } pub fn xor_inv(a: &mut [T]) { rfor_each_mut(a, |&mut x, y| *y ^= x); } pub fn or(a: &mut [T]) { for_each_mut(a, |&mut x, y| *y |= x); } pub fn and(a: &mut [T]) { for_each_mut(a, |&mut x, y| *y &= x); } // -- for_each pub fn for_each(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(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(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(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 Seq for I {} pub trait Seq: Iterator + Sized { fn adjacent(self) -> Adjacent where Self::Item: Clone, { adjacent(self) } fn grid_next(self, ij: (usize, usize), h: usize, w: usize) -> GridNext where Self: Iterator, { grid_next(self, ij, h, w) } fn cartesian_product(self, other: J) -> CartesianProduct where Self: Sized, Self::Item: Clone, J: IntoIterator, J::IntoIter: Clone, { cartesian_product::cartesian_product(self, other.into_iter()) } fn accumulate(self, init: T) -> Accumulate where T: Clone + ops::AddAssign, { accumulate::accumulate(self, init) } fn intersperse(self, elt: Self::Item) -> Intersperse { intersperse::intersperse(self, elt) } fn format_intersparse(self, separator: T) -> String where Self::Item: fmt::Display, T: fmt::Display, { self.map(|x| format!("{}", x)) .intersperse(format!("{}", separator)) .collect::() } } mod adjacent { #[allow(missing_docs)] pub fn adjacent(mut iter: I) -> Adjacent where I: Iterator, T: Clone, { if let Some(first) = iter.next() { Adjacent { iter, prv: Some(first), } } else { Adjacent { iter, prv: None } } } #[allow(missing_docs)] pub struct Adjacent where I: Iterator, { iter: I, prv: Option, } impl Iterator for Adjacent where I: Iterator, 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(difference: T, ij: (usize, usize), h: usize, w: usize) -> GridNext where T: Iterator, { 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 { i: i64, j: i64, h: i64, w: i64, difference: T, } impl Iterator for GridNext where T: Iterator, { 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(init: T, step: U) -> Step where T: Copy, U: Copy, T: ::std::ops::Add, { Step { now: init, step } } #[allow(missing_docs)] #[derive(Debug, Clone)] pub struct Step { now: T, step: U, } #[allow(missing_docs)] impl Iterator for Step where T: Copy, U: Copy, T: ::std::ops::Add, { type Item = T; fn next(&mut self) -> Option { let next = self.now + self.step; Some(::std::mem::replace(&mut self.now, next)) } } } mod mul_step { #[allow(missing_docs)] pub fn mul_step(init: T, step: U) -> MulStep where T: Copy, U: Copy, T: ::std::ops::Mul, { MulStep { now: init, step } } #[allow(missing_docs)] #[derive(Debug, Clone)] pub struct MulStep { now: T, step: U, } #[allow(missing_docs)] impl Iterator for MulStep where T: Copy, U: Copy, T: ::std::ops::Mul, { type Item = T; fn next(&mut self) -> Option { 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>(repeater: F) -> RepeatWith { RepeatWith { repeater } } #[allow(missing_docs)] #[derive(Debug, Clone)] pub struct RepeatWith { repeater: F, } impl A> Iterator for RepeatWith { type Item = A; #[inline] fn next(&mut self) -> Option { Some((self.repeater)()) } #[inline] fn size_hint(&self) -> (usize, Option) { (::std::usize::MAX, None) } } } mod accumulate { use super::*; #[allow(missing_docs)] #[derive(Debug, Clone)] pub struct Accumulate { prev: Option, iter: I, } #[allow(missing_docs)] pub fn accumulate(iter: I, init: T) -> Accumulate where I: Iterator, T: Clone + ops::AddAssign, { Accumulate { prev: Some(init), iter, } } impl Iterator for Accumulate where I: Iterator, T: Clone + ops::AddAssign, { type Item = T; fn next(&mut self) -> Option { 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) { size_hint::add_scalar(self.iter.size_hint(), 1) } } } mod cartesian_product { #[allow(missing_docs)] #[derive(Debug, Clone)] pub struct CartesianProduct where I: Iterator, { a: I, a_cur: Option, b: J, b_orig: J, } #[allow(missing_docs)] pub fn cartesian_product(mut i: I, j: J) -> CartesianProduct where I: Iterator, J: Clone + Iterator, I::Item: Clone, { CartesianProduct { a_cur: i.next(), a: i, b_orig: j.clone(), b: j, } } impl Iterator for CartesianProduct 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) { 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(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 where I: Iterator, { element: I::Item, iter: iter::Fuse, peek: Option, } pub fn intersperse(iter: I, elt: I::Item) -> Intersperse where I: Iterator, { let mut iter = iter.fuse(); Intersperse { peek: iter.next(), iter, element: elt, } } impl Iterator for Intersperse where I: Iterator, I::Item: Clone, { type Item = I::Item; #[inline] fn next(&mut self) -> Option { 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) { // 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(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(iter: I, separator: T) -> String where I: Iterator, I::Item: fmt::Display, T: fmt::Display, { iter.map(|x| format!("{}", x)) .intersperse(format!("{}", separator)) .collect::() } } mod size_hint { use std::cmp; use std::usize; pub type SizeHint = (usize, Option); #[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 Add for Fp { 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 Sub for Fp { 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 Mul for Fp { type Output = Self; fn mul(self, rhs: Self) -> Self { Self::new(self.0 * rhs.0) } } #[allow(clippy::suspicious_arithmetic_impl)] impl Div for Fp { type Output = Self; fn div(self, rhs: Self) -> Self { self * rhs.inv() } } impl Neg for Fp { type Output = Self; fn neg(self) -> Self { if self.0 == 0 { Self::unchecked(0) } else { Self::unchecked(M::MOD - self.0) } } } impl Neg for &Fp { type Output = Fp; 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 $trait for Fp { 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> for &'a Fp { type Output = Fp; fn $method(self, other: Fp) -> Self::Output { $imp::$method(*self, other) } } impl<'a, T: Mod> $imp<&'a Fp> for Fp { type Output = Fp; fn $method(self, other: &Fp) -> Self::Output { $imp::$method(self, *other) } } impl<'a, T: Mod> $imp<&'a Fp> for &'a Fp { type Output = Fp; fn $method(self, other: &Fp) -> 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(i64, PhantomData); pub trait Mod: Debug + Clone + PartialEq + Copy + Eq + Hash { const MOD: i64; } impl Fp { 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 iter::Sum> for Fp { fn sum(iter: I) -> Self where I: iter::Iterator>, { iter.fold(Fp::new(0), ops::Add::add) } } impl<'a, T: 'a + Mod> iter::Sum<&'a Fp> for Fp { fn sum(iter: I) -> Self where I: iter::Iterator>, { iter.fold(Fp::new(0), ops::Add::add) } } impl iter::Product> for Fp { fn product(iter: I) -> Self where I: iter::Iterator>, { iter.fold(Self::new(1), ops::Mul::mul) } } impl<'a, T: 'a + Mod> iter::Product<&'a Fp> for Fp { fn product(iter: I) -> Self where I: iter::Iterator>, { iter.fold(Self::new(1), ops::Mul::mul) } } impl Debug for Fp { 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 Display for Fp { 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::new(io::stdin()).tokenizer() } pub fn with_str(src: &str) -> Tokenizer<&[u8]> { src.as_bytes().tokenizer() } pub struct Tokenizer { queue: Vec, // 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 Tokenizer { 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(&mut self) -> T::Output { T::parse(&self.token()) } pub fn parse_collect(&mut self, n: usize) -> B where B: iter::FromIterator, { iter::repeat_with(|| self.parse::()).take(n).collect() } pub fn tuple(&mut self) -> ::Output { T::leaf_tuple().parse(self) } pub fn vec(&mut self, len: usize) -> Vec { T::leaf().vec(len).parse(self) } pub fn vec_tuple( &mut self, len: usize, ) -> Vec<::Output> { T::leaf_tuple().vec(len).parse(self) } pub fn vec2(&mut self, height: usize, width: usize) -> Vec> { T::leaf().vec(width).vec(height).parse(self) } pub fn vec2_tuple( &mut self, height: usize, width: usize, ) -> Vec::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 { Leaf(marker::PhantomData) } } impl Token for T where T: 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::(),) }) } } 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(&self, server: &mut Tokenizer) -> Self::Output; fn vec(self, len: usize) -> VecLen { VecLen { len, elem: self } } } pub struct Leaf(pub(super) marker::PhantomData); impl Parser for Leaf { type Output = T::Output; fn parse(&self, server: &mut Tokenizer) -> T::Output { server.parse::() } } pub struct VecLen { pub len: usize, pub elem: T, } impl Parser for VecLen { type Output = Vec; fn parse(&self, server: &mut Tokenizer) -> 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(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(&self, server: &mut Tokenizer) -> 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 { Tokenizer::new(self) } } impl Scanner for R {} } pub use self::i::{with_stdin, with_str}; pub mod prelude { pub use super::i::{Parser, ParserTuple, RawTuple, Token, Usize1}; } } // }}}