#![allow(unused_macros, unused_imports)] macro_rules! dbg { ($($xs:expr),+) => { if cfg!(debug_assertions) { std::dbg!($($xs),+) } else { ($($xs),+) } } } fn main() { input!{ a: usize, b: usize, c: usize, n: usize, } let m = 51; let mut dp = vec![vec![vec![vec![[0.0; 3]; 51]; 51]; 51]; 51]; for i in 1..=n { for j in 0..=a { for k in 0..=b { for l in 0..=c { if j+k+l <= 1 { continue; } let t = ((j+k+l) * (j+k+l-1) / 2) as f64; let p = if j > 0 { (j*(j-1)/2) as f64 / t } else { 0.0 }; let q = if k > 0 { (k*(k-1)/2) as f64 / t } else { 0.0 }; let r = if l > 0 { (l*(l-1)/2) as f64 / t } else { 0.0 }; // eprintln!("{} {} {} {} {} {} {}", i, j, k, l, p, q, r); for h in 0..3 { dp[i][j][k][l][h] += (1.0-p-q-r) * dp[i-1][j][k][l][h]; } if j > 0 { dp[i][j][k][l][0] += p * (dp[i-1][j-1][k][l][0] + 1.0); dp[i][j][k][l][1] += p * dp[i-1][j-1][k][l][1]; dp[i][j][k][l][2] += p * dp[i-1][j-1][k][l][2]; } if k > 0 { dp[i][j][k][l][0] += q * dp[i-1][j][k-1][l][0]; dp[i][j][k][l][1] += q * (dp[i-1][j][k-1][l][1] + 1.0); dp[i][j][k][l][2] += q * dp[i-1][j][k-1][l][2]; } if l > 0 { dp[i][j][k][l][0] += r * dp[i-1][j][k][l-1][0]; dp[i][j][k][l][1] += r * dp[i-1][j][k][l-1][1]; dp[i][j][k][l][2] += r * (dp[i-1][j][k][l-1][2] + 1.0); } } } } } println!("{} {} {}", dp[n][a][b][c][0], dp[n][a][b][c][1], dp[n][a][b][c][2]); } pub mod proconio { #[macro_export] macro_rules! input{ (sc=$sc:expr,$($r:tt)*)=>{ input_inner!{$sc,$($r)*} }; ($($r:tt)*)=>{ let mut sc=proconio::Scanner::new(std::io::stdin().lock()); input_inner!{sc,$($r)*} }; } #[macro_export] macro_rules! input_inner{ ($sc:expr)=>{}; ($sc:expr,)=>{}; ($sc:expr,$var:ident:$t:tt$($r:tt)*)=>{ let $var=read_value!($sc,$t); input_inner!{$sc $($r)*} }; } #[macro_export] macro_rules! read_value{ ($sc:expr,($($t:tt),*))=>{ ($(read_value!($sc,$t)),*) }; ($sc:expr,[$t:tt;$len:expr])=>{ (0..$len).map(|_|read_value!($sc,$t)).collect::>() }; ($sc:expr,Chars)=>{read_value!($sc,String).chars().collect::>()}; ($sc:expr,Usize1)=>{read_value!($sc,usize)-1}; ($sc:expr,$t:ty)=>{$sc.next::<$t>()}; } pub struct Scanner { s: Box, input: std::iter::Peekable>, } impl Scanner { pub fn new(mut reader: R) -> Self { let s = { let mut s = String::new(); reader.read_to_string(&mut s).unwrap(); s.into_boxed_str() }; let mut sc = Scanner { s, input: "".split_ascii_whitespace().peekable(), }; use std::mem; let s: &'static str = unsafe { mem::transmute(&*sc.s) }; sc.input = s.split_ascii_whitespace().peekable(); sc } #[inline] pub fn next(&mut self) -> T where T::Err: std::fmt::Debug, { self.input .next() .unwrap() .parse::() .expect("Parse error") } } }