#[allow(unused_imports)] use std::cmp::*; #[allow(unused_imports)] use std::collections::*; // 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:tt),* )) => { ($(read_value!($next, $t)),*) }; ($next:expr, [ $t:tt ; $len:expr ]) => { (0..$len).map(|_| read_value!($next, $t)).collect::>() }; ($next:expr, chars) => { read_value!($next, String).chars().collect::>() }; ($next:expr, usize1) => (read_value!($next, usize) - 1); ($next:expr, [ $t:tt ]) => {{ let len = read_value!($next, usize); read_value!($next, [$t; len]) }}; ($next:expr, $t:ty) => ($next().parse::<$t>().expect("Parse error")); } trait Change { fn chmax(&mut self, x: Self); fn chmin(&mut self, x: Self); } impl Change for T { fn chmax(&mut self, x: T) { if *self < x { *self = x; } } fn chmin(&mut self, x: T) { if *self > x { *self = x; } } } // Finds sum_{1 <= l < b^x} |l|. None if the result is >= b^n. fn calc(b: i32, x: usize, n: usize) -> Option> { if x >= n + 1 { return None; } let mut ans = vec![0; n]; for i in (0..x).rev() { let mut c = (i + 1) as i32 * (b - 1); let mut pos = n - i; while pos > 0 && c > 0 { ans[pos - 1] += c; c = ans[pos - 1] / b; ans[pos - 1] %= b; pos -= 1; } if pos == 0 && c != 0 { return None; } } Some(ans) } fn main() { input! { b: i32, d: chars, } let n = d.len(); let d: Vec = d.into_iter().map(|x| (x as u8 - b'0') as _).collect(); let mut pass = 0; let mut fail = n + 1; while fail - pass > 1 { let mid = (pass + fail) / 2; let res = calc(b, mid, n); if res.is_some() && res.unwrap() < d { pass = mid; } else { fail = mid; } } eprintln!("{}", fail); for i in 0..3 { eprintln!("{} => {:?}", i, calc(b, i, n)); } let lt = calc(b, pass, n).unwrap(); let mut rem = d.clone(); let mut c = 0; for i in (0..n).rev() { c = c + rem[i] - lt[i]; let mut nc = 0; if c < 0 { c += b; nc -= 1; } rem[i] = c; c = nc; } eprintln!("rem = {:?}", rem); // q = (rem - 1) / fail, r = (rem - 1) % fail // the (r+1)-st digit of (b^pass + q) is the answer. c = -1; for i in (0..n).rev() { c = rem[i] + c; let mut nc = 0; if c < 0 { c += b; nc -= 1; } rem[i] = c; c = nc; } c = 0; let mut quo = vec![0; n]; for i in 0..n { c = b * c + rem[i]; quo[i] = c / fail as i32; c %= fail as i32; } eprintln!("quo = {:?}, rem = {}", quo, c); quo[n - fail] += 1; println!("{}", quo[n - fail + c as usize]); }