#![allow(unused)] use kyoproio::*; use std::{ collections::*, io::{self, prelude::*}, iter, mem::{replace, swap}, }; fn main() -> io::Result<()> { std::thread::Builder::new() .stack_size(10 * 1024 * 1024) .spawn(solve)? .join() .unwrap(); Ok(()) } fn solve() { let stdin = io::stdin(); let mut kin = KInput::new(stdin.lock()); let stdout = io::stdout(); let mut out = io::BufWriter::new(stdout.lock()); macro_rules! output { ($($args:expr),+) => { write!(&mut out, $($args),+) }; } macro_rules! outputln { ($($args:expr),+) => { output!($($args),+); outputln!(); }; () => { output!("\n"); if cfg!(debug_assertions) { out.flush(); } } } let (n, p, q): (usize, f64, f64) = kin.input(); let mut pc = p; let mut qc = q; for _ in 1..n { let d = 1. - pc * p; pc = pc + qc * qc * p / d; qc = qc * q / d; } outputln!("{}", pc); } use std::cell::UnsafeCell; struct Lazy(UnsafeCell>); enum Inner { Thunk(F), Value(T), Empty, } use Inner::*; impl T> Lazy { fn thunk(f: F) -> Self { Self(UnsafeCell::new(Thunk(f))) } fn value(v: T) -> Self { Self(UnsafeCell::new(Value(v))) } fn get(&self) -> &T { unsafe { if let Thunk(_) = &*self.0.get() { if let Thunk(f) = self.0.get().replace(Empty) { self.0.get().replace(Value(f())); } } match &*self.0.get() { Value(v) => v, _ => unreachable!(), } } } fn into_inner(self) -> T { self.get(); match self.0.into_inner() { Value(v) => v, _ => unreachable!() } } } // ----------------------------------------------------------------------------- pub mod kyoproio { #![warn(unused)] use std::io::prelude::*; pub trait Input: Sized { fn str(&mut self) -> &str; fn bytes(&mut self) -> &[u8] { self.str().as_ref() } fn input(&mut self) -> T { self.input_fallible().expect("input error") } fn input_fallible(&mut self) -> Result { T::input(self) } fn iter(&mut self) -> Iter { Iter { input: self, _t: std::marker::PhantomData, } } fn seq>(&mut self, n: usize) -> B { self.iter().take(n).collect() } } pub struct KInput { src: R, buf: String, pos: usize, } impl KInput { pub fn new(src: R) -> Self { Self { src, buf: String::with_capacity(1024), pos: 0, } } } impl Input for KInput { fn str(&mut self) -> &str { loop { if self.pos >= self.buf.len() { self.pos = 0; self.buf.clear(); if self.src.read_line(&mut self.buf).expect("io error") == 0 { return &self.buf; } } let range = self.pos ..self.buf[self.pos..] .find(|c: char| c.is_ascii_whitespace()) .map(|i| i + self.pos) .unwrap_or_else(|| self.buf.len()); self.pos = range.end + 1; if range.end > range.start { return &self.buf[range]; } } } } pub struct Iter<'a, T, I> { input: &'a mut I, _t: std::marker::PhantomData<*const T>, } impl<'a, T: InputParse, I: Input> Iterator for Iter<'a, T, I> { type Item = T; fn next(&mut self) -> Option { Some(self.input.input()) } } pub trait InputParse: Sized { type Err: std::fmt::Debug; fn input(input: &mut I) -> Result; } macro_rules! from_str_impls { { $($T:ty)* } => { $(impl InputParse for $T { type Err = <$T as std::str::FromStr>::Err; fn input(input: &mut I) -> Result { input.str().parse::<$T>() } })* }; } from_str_impls! { String char bool f32 f64 isize i8 i16 i32 i64 i128 usize u8 u16 u32 u64 u128 } macro_rules! tuple_impls { ($H:ident $($T:ident)*) => { impl<$H: InputParse, $($T: InputParse),*> InputParse for ($H, $($T),*) { type Err = (); fn input(input: &mut I) -> Result { // ? Ok(($H::input(input).unwrap(), $($T::input(input).unwrap()),*)) } } tuple_impls!($($T)*); }; () => {}; } tuple_impls!(A B C D E F G); }