// ---------- begin input macro ---------- // reference: https://qiita.com/tanakh/items/0ba42c7ca36cd29d0ac8 macro_rules! input { (source = $s:expr, $($r:tt)*) => { let mut iter = $s.split_whitespace(); input_inner!{iter, $($r)*} }; ($($r:tt)*) => { let s = { use std::io::Read; let mut s = String::new(); std::io::stdin().read_to_string(&mut s).unwrap(); s }; let mut iter = s.split_whitespace(); input_inner!{iter, $($r)*} }; } macro_rules! input_inner { ($iter:expr) => {}; ($iter:expr, ) => {}; ($iter:expr, $var:ident : $t:tt $($r:tt)*) => { let $var = read_value!($iter, $t); input_inner!{$iter $($r)*} }; } macro_rules! read_value { ($iter:expr, ( $($t:tt),* )) => { ( $(read_value!($iter, $t)),* ) }; ($iter:expr, [ $t:tt ; $len:expr ]) => { (0..$len).map(|_| read_value!($iter, $t)).collect::>() }; ($iter:expr, chars) => { read_value!($iter, String).chars().collect::>() }; ($iter:expr, bytes) => { read_value!($iter, String).bytes().collect::>() }; ($iter:expr, usize1) => { read_value!($iter, usize) - 1 }; ($iter:expr, $t:ty) => { $iter.next().unwrap().parse::<$t>().expect("Parse error") }; } // ---------- end input macro ---------- fn run() { input!(a: usize, b: usize, c: usize, n: usize); let mut dp = vec![vec![vec![0f64; c + 1]; b + 1]; a + 1]; dp[a][b][c] = 1f64; for _ in 0..n { let mut next = vec![vec![vec![0f64; c + 1]; b + 1]; a + 1]; for (i, dp) in dp.iter().enumerate().skip(1) { for (j, dp) in dp.iter().enumerate().skip(1) { for (k, &dp) in dp.iter().enumerate().skip(1) { let s = i + j + k; let mut rem = 1f64; let p = (i * (i - 1) / 2) as f64 / (s * (s - 1) / 2) as f64; next[i - 1][j][k] += p * dp; rem -= p; let p = (j * (j - 1) / 2) as f64 / (s * (s - 1) / 2) as f64; next[i][j - 1][k] += p * dp; rem -= p; let p = (k * (k - 1) / 2) as f64 / (s * (s - 1) / 2) as f64; next[i][j][k - 1] += p * dp; rem -= p; next[i][j][k] += rem * dp; } } } dp = next; } let mut ans = (0f64, 0f64, 0f64); for (i, dp) in dp.iter().enumerate() { for (j, dp) in dp.iter().enumerate() { for (k, dp) in dp.iter().enumerate() { ans.0 += (a - i) as f64 * *dp; ans.1 += (b - j) as f64 * *dp; ans.2 += (c - k) as f64 * *dp; } } } println!("{:.7} {:.7} {:.7}", ans.0, ans.1, ans.2); } fn main() { run(); }