#![allow(unused_imports)] use input::*; use std::{ collections::*, io::{self, BufWriter, Read, Write}, }; fn run(mut ss: I, mut out: O) { let t: u32 = 1; for _ in 0..t { case(&mut ss, &mut out); } } fn case(mut ss: I, mut out: O) { let (r, k): (i32, i32) = ss.parse(); let r = r as f64; let sc = r * r * std::f64::consts::PI; for i in 1..=k { let mut ylo = -r; let mut yhi = r; while yhi - ylo >= 1e-6 { let y = (ylo + yhi) / 2.0; let x = (r * r - y * y).sqrt(); let t = x.atan2(y); let s = r * r * t - x * y; if s > sc * (i as f64 / (k + 1) as f64) { ylo = y; } else { yhi = y; } } wln!(out, "{}", -(ylo + yhi) / 2.0); } } fn main() { let stdin = io::stdin(); let ss = SplitWs::new(stdin.lock()); let stdout = io::stdout(); let out = BufWriter::new(stdout.lock()); run(ss, out); } pub mod input { use std::{ io::{self, prelude::*}, marker::PhantomData, }; #[macro_export] macro_rules ! input { ($ src : expr , $ ($ var : ident $ (($ count : expr $ (, $ map : expr) ?)) ? $ (: $ ty : ty) ?) ,* $ (,) ?) => { $ (input ! (@ $ src , $ var $ (($ count $ (, $ map) ?)) ? $ (: $ ty) ?) ;) * } ; (@ $ src : expr , $ var : ident $ (: $ ty : ty) ?) => { let $ var $ (: $ ty) ? = $ src . parse () ; } ; (@ $ src : expr , $ var : ident ($ count : expr) : $ ($ ty : ty) ?) => { let $ var $ (: $ ty) ? = $ src . seq () . take ($ count) . collect () ; } ; (@ $ src : expr , $ var : ident ($ count : expr , $ map : expr) : $ ($ ty : ty) ?) => { let $ var $ (: $ ty) ? = $ src . seq () . take ($ count) . map ($ map) . collect () ; } ; } pub trait Input { fn bytes(&mut self) -> &[u8]; fn bytes_vec(&mut self) -> Vec { self.bytes().to_vec() } fn str(&mut self) -> &str { std::str::from_utf8(self.bytes()).unwrap() } fn parse(&mut self) -> T { self.parse_with(DefaultParser) } fn parse_with(&mut self, mut parser: impl Parser) -> T { parser.parse(self) } fn seq(&mut self) -> Seq { self.seq_with(DefaultParser) } fn seq_with>(&mut self, parser: P) -> Seq { Seq { input: self, parser, marker: PhantomData, } } fn collect>(&mut self, n: usize) -> C { self.seq().take(n).collect() } } impl Input for &mut T { fn bytes(&mut self) -> &[u8] { (**self).bytes() } } pub trait Parser { fn parse(&mut self, s: &mut I) -> T; } impl> Parser for &mut P { fn parse(&mut self, s: &mut I) -> T { (**self).parse(s) } } pub trait Parse { fn parse(s: &mut I) -> Self; } pub struct DefaultParser; impl Parser for DefaultParser { fn parse(&mut self, s: &mut I) -> T { T::parse(s) } } pub struct Seq<'a, T, I: ?Sized, P> { input: &'a mut I, parser: P, marker: PhantomData<*const T>, } impl<'a, T, I: Input + ?Sized, P: Parser> Iterator for Seq<'a, T, I, P> { type Item = T; #[inline] fn next(&mut self) -> Option { Some(self.input.parse_with(&mut self.parser)) } fn size_hint(&self) -> (usize, Option) { (!0, None) } } impl Parse for char { #[inline] fn parse(s: &mut I) -> Self { let s = s.bytes(); debug_assert_eq!(s.len(), 1); *s.first().expect("zero length") as char } } macro_rules ! tuple { ($ ($ T : ident) ,*) => { impl <$ ($ T : Parse) ,*> Parse for ($ ($ T ,) *) { # [inline] # [allow (unused_variables)] # [allow (clippy :: unused_unit)] fn parse < I : Input + ? Sized > (s : & mut I) -> Self { ($ ($ T :: parse (s) ,) *) } } } ; } tuple!(); tuple!(A); tuple!(A, B); tuple!(A, B, C); tuple!(A, B, C, D); tuple!(A, B, C, D, E); tuple!(A, B, C, D, E, F); tuple!(A, B, C, D, E, F, G); #[cfg(feature = "newer")] impl Parse for [T; N] { fn parse(s: &mut I) -> Self { use std::{ mem::{self, MaybeUninit}, ptr, }; struct Guard { arr: [MaybeUninit; N], i: usize, } impl Drop for Guard { fn drop(&mut self) { unsafe { ptr::drop_in_place(&mut self.arr[..self.i] as *mut _ as *mut [T]); } } } let mut g = Guard:: { arr: unsafe { MaybeUninit::uninit().assume_init() }, i: 0, }; while g.i < N { g.arr[g.i] = MaybeUninit::new(s.parse()); g.i += 1; } unsafe { mem::transmute_copy(&g.arr) } } } macro_rules! uint { ($ ty : ty) => { impl Parse for $ty { #[inline] fn parse(s: &mut I) -> Self { let s = s.bytes(); s.iter().fold(0, |x, d| 10 * x + (0xf & d) as $ty) } } }; } macro_rules! int { ($ ty : ty) => { impl Parse for $ty { #[inline] fn parse(s: &mut I) -> Self { let f = |s: &[u8]| { s.iter() .fold(0 as $ty, |x, d| (10 * x).wrapping_add((0xf & d) as $ty)) }; let s = s.bytes(); if let Some((b'-', s)) = s.split_first() { f(s).wrapping_neg() } else { f(s) } } } }; } macro_rules! float { ($ ty : ty) => { impl Parse for $ty { fn parse(s: &mut I) -> Self { const POW: [$ty; 18] = [ 1e0, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9, 1e10, 1e11, 1e12, 1e13, 1e14, 1e15, 1e16, 1e17, ]; let s = s.bytes(); let (minus, s) = if let Some((b'-', s)) = s.split_first() { (true, s) } else { (false, s) }; let (int, fract) = if let Some(p) = s.iter().position(|c| *c == b'.') { (&s[..p], &s[p + 1..]) } else { (s, &[][..]) }; let x = int .iter() .chain(fract) .fold(0u64, |x, d| 10 * x + (0xf & *d) as u64); let x = x as $ty; let x = if minus { -x } else { x }; let exp = fract.len(); if exp == 0 { x } else if let Some(pow) = POW.get(exp) { x / pow } else { x / (10.0 as $ty).powi(exp as i32) } } } }; } macro_rules! from_bytes { ($ ty : ty) => { impl Parse for $ty { #[inline] fn parse(s: &mut I) -> Self { s.bytes().into() } } }; } macro_rules! from_str { ($ ty : ty) => { impl Parse for $ty { #[inline] fn parse(s: &mut I) -> Self { s.str().into() } } }; } macro_rules ! impls { ($ m : ident , $ ($ ty : ty) ,*) => { $ ($ m ! ($ ty) ;) * } ; } impls!(uint, usize, u8, u16, u32, u64, u128); impls!(int, isize, i8, i16, i32, i64, i128); impls!(float, f32, f64); impls!(from_bytes, Vec, Box<[u8]>); impls!(from_str, String); #[derive(Clone)] pub struct SplitWs { src: T, buf: Vec, pos: usize, len: usize, } const BUF_SIZE: usize = 1 << 26; impl SplitWs { pub fn new(src: T) -> Self { Self { src, buf: vec![0; BUF_SIZE], pos: 0, len: 0, } } #[inline(always)] fn peek(&self) -> &[u8] { unsafe { self.buf.get_unchecked(self.pos..self.len) } } #[inline(always)] fn consume(&mut self, n: usize) -> &[u8] { let pos = self.pos; self.pos += n; unsafe { self.buf.get_unchecked(pos..self.pos) } } fn read(&mut self) -> usize { self.buf.copy_within(self.pos..self.len, 0); self.len -= self.pos; self.pos = 0; if self.len == self.buf.len() { self.buf.resize(2 * self.buf.len(), 0); } loop { match self.src.read(&mut self.buf[self.len..]) { Ok(n) => { self.len += n; return n; } Err(e) if e.kind() == io::ErrorKind::WouldBlock => {} Err(e) => panic!("io error: {:?}", e), } } } } impl Input for SplitWs { #[inline] fn bytes(&mut self) -> &[u8] { loop { if let Some(del) = self.peek().iter().position(|c| c.is_ascii_whitespace()) { if del > 0 { let s = self.consume(del + 1); return s.split_last().unwrap().1; } else { self.consume(1); } } else if self.read() == 0 { return self.consume(self.len - self.pos); } } } } } pub mod macros { extern "C" { pub fn isatty(fd: i32) -> i32; } #[macro_export] macro_rules ! w { ($ dst : expr , $ ($ arg : tt) *) => { if cfg ! (debug_assertions) && unsafe { $ crate :: macros :: isatty (1) } != 0 { write ! ($ dst , "\x1B[1;33m") . unwrap () ; write ! ($ dst , $ ($ arg) *) . unwrap () ; write ! ($ dst , "\x1B[0m") . unwrap () ; } else { write ! ($ dst , $ ($ arg) *) . unwrap () ; } } } #[macro_export] macro_rules ! wln { ($ dst : expr $ (, $ ($ arg : tt) *) ?) => { { if cfg ! (debug_assertions) && unsafe { $ crate :: macros :: isatty (1) } != 0 { write ! ($ dst , "\x1B[1;33m") . unwrap () ; writeln ! ($ dst $ (, $ ($ arg) *) ?) . unwrap () ; write ! ($ dst , "\x1B[0m") . unwrap () ; } else { writeln ! ($ dst $ (, $ ($ arg) *) ?) . unwrap () ; } # [cfg (debug_assertions)] $ dst . flush () . unwrap () ; } } } #[macro_export] macro_rules! w_iter { ($ dst : expr , $ fmt : expr , $ iter : expr , $ delim : expr) => {{ let mut first = true; for elem in $iter { if first { w!($dst, $fmt, elem); first = false; } else { w!($dst, concat!($delim, $fmt), elem); } } }}; ($ dst : expr , $ fmt : expr , $ iter : expr) => { w_iter!($dst, $fmt, $iter, " ") }; } #[macro_export] macro_rules ! w_iter_ln { ($ dst : expr , $ ($ t : tt) *) => { { w_iter ! ($ dst , $ ($ t) *) ; wln ! ($ dst) ; } } } #[macro_export] macro_rules ! e { ($ ($ t : tt) *) => { # [cfg (debug_assertions)] eprint ! ($ ($ t) *) } } #[macro_export] macro_rules ! eln { ($ ($ t : tt) *) => { # [cfg (debug_assertions)] eprintln ! ($ ($ t) *) } } #[macro_export] #[doc(hidden)] macro_rules ! __tstr { ($ h : expr $ (, $ t : expr) +) => { concat ! (__tstr ! ($ ($ t) ,+) , ", " , __tstr ! (@)) } ; ($ h : expr) => { concat ! (__tstr ! () , " " , __tstr ! (@)) } ; () => { "\x1B[94m[{}:{}]\x1B[0m" } ; (@) => { "\x1B[1;92m{}\x1B[0m = {:?}" } } #[macro_export] macro_rules ! d { ($ ($ a : expr) ,*) => { if std :: env :: var ("ND") . map (| v | & v == "0") . unwrap_or (true) { eln ! (__tstr ! ($ ($ a) ,*) , file ! () , line ! () , $ (stringify ! ($ a) , $ a) ,*) ; } } ; } }