// ---------- begin binary_gcd ---------- pub fn binary_gcd(a: u128, b: u128) -> u128 { if a == 0 || b == 0 { return a + b; } let x = a.trailing_zeros(); let y = b.trailing_zeros(); let mut a = a >> x; let mut b = b >> y; while a != b { let x = (a ^ b).trailing_zeros(); if a < b { std::mem::swap(&mut a, &mut b); } a = (a - b) >> x; } a << x.min(y) } // ---------- end binary_gcd ---------- // ---------- 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! { n: usize, k: usize, a: [u128; n], } if n == 1 { println!("1/1"); return; } if k == 1 { println!("0"); return; } let mut dp = vec![(0, 1); n]; for i in 1..(n - 1) { let l = a[i - 1]; let r = a[i + 1]; let g = binary_gcd(l, r); let l = l / g; let r = r / g; let (y, x) = dp[i - 1]; let nu = r * x; let de = (l + r) * x - l * y; assert!(nu <= de); let g = binary_gcd(nu, de); dp[i] = (nu / g, de / g); } dp[n - 1] = (1, 1); for i in (1..(n - 1)).rev() { let (a, b) = dp[i]; let (c, d) = dp[i + 1]; let x = binary_gcd(a, d); let y = binary_gcd(c, b); dp[i] = (a / x * (c / y), (b / y) * (d / x)); } let (x, y) = dp[k - 1]; println!("{}/{}", x, y); } fn main() { run(); }