fn main() { let mut abcn = String::new(); std::io::stdin().read_line(&mut abcn).ok(); let abcn: Vec = abcn.trim().split_whitespace().map(|s| s.parse().unwrap()).collect(); let a = abcn[0]; let b = abcn[1]; let c = abcn[2]; let n = abcn[3]; let mut dp = vec![vec![vec![vec![0.; c+1]; b+1]; a+1]; n+1]; dp[0][a][b][c] = 1.; for i in 0..n { for red in 0..=a { for black in 0..=b { for brown in 0..=c { if dp[i][red][black][brown] == 0. { continue; } let summary = red + black + brown; let denom = (summary * (summary-1) / 2) as f64; let mut others = 1.; if red > 1 { dp[i+1][red-1][black][brown] += dp[i][red][black][brown] * (red * (red-1) / 2) as f64 / denom; others -= (red * (red-1) / 2) as f64 / denom; } if black > 1 { dp[i+1][red][black-1][brown] += dp[i][red][black][brown] * (black * (black-1) / 2) as f64 / denom; others -= (black * (black-1) / 2) as f64 / denom; } if brown > 1 { dp[i+1][red][black][brown-1] += dp[i][red][black][brown] * (brown * (brown-1) / 2) as f64 / denom; others -= (brown * (brown-1) / 2) as f64 / denom; } dp[i+1][red][black][brown] += dp[i][red][black][brown] * others; } } } } let mut red_exp = 0.; let mut black_exp = 0.; let mut brown_exp = 0.; for red in 0..=a { for black in 0..=b { for brown in 0..=c { let base = dp[n][red][black][brown]; red_exp += (a - red) as f64 * base; black_exp += (b - black) as f64 * base; brown_exp += (c - brown) as f64 * base; } } } println!("{:.09} {:.09} {:.09}", red_exp, black_exp, brown_exp); }