// https://qiita.com/tanakh/items/0ba42c7ca36cd29d0ac8 macro_rules! input { ($($r:tt)*) => { let stdin = std::io::stdin(); let mut bytes = std::io::Read::bytes(std::io::BufReader::new(stdin.lock())); let mut next = move || -> String{ bytes.by_ref().map(|r|r.unwrap() as char) .skip_while(|c|c.is_whitespace()) .take_while(|c|!c.is_whitespace()) .collect() }; input_inner!{next, $($r)*} }; } macro_rules! input_inner { ($next:expr) => {}; ($next:expr, ) => {}; ($next:expr, $var:ident : $t:tt $($r:tt)*) => { let $var = read_value!($next, $t); input_inner!{$next $($r)*} }; } macro_rules! read_value { ($next:expr, $t:ty) => ($next().parse::<$t>().expect("Parse error")); } const PI: f64 = 3.1415926535897932; fn zeta(k: usize) -> f64 { if k == 2 { return PI * PI / 6.0; } if k == 3 { return 1.20205690315959428539973816151144999076498629; } if k == 4 { return PI.powf(4.0) / 90.0; } if k >= 50 { return 1.0; } let mut ans = 0.0; for i in (1..100).rev() { let mut v = 1.0; for _ in 0..k { v /= i as f64; } ans += v; } ans } // Tags: multiple-zeta-function fn solve() { input!(x: i32, k: usize); if x == 1 { let mut prod = 1.0; for _ in 0..k + 1 { prod /= 2.0; } println!("{}", 1.0 - prod); return; } if k == 1 { println!("0.5"); return; } let mut dp = vec![0.0; k + 1]; let mut acc = vec![0.0; k + 1]; acc[1] = 1.0; dp[1] = 1.0; for i in 2..k + 1 { dp[i] = zeta(i) * (i - 1) as f64 - acc[i - 1]; acc[i] = acc[i - 1] + dp[i]; } println!("{}", dp[k]); } fn main() { // In order to avoid potential stack overflow, spawn a new thread. let stack_size = 104_857_600; // 100 MB let thd = std::thread::Builder::new().stack_size(stack_size); thd.spawn(|| solve()).unwrap().join().unwrap(); }