Problem:
Score : 500 points

Problem Statement

Let S(n) denote the sum of the digits in the decimal notation of n.
For example, S(123) = 1 + 2 + 3 = 6.

We will call an integer n a Snuke number when, for all positive integers m such that m > n, \frac{n}{S(n)} \leq \frac{m}{S(m)} holds.

Given an integer K, list the K smallest Snuke numbers.

Constraints

1 \leq K

The K-th smallest Snuke number is not greater than 10^{15}.

Input

Input is given from Standard Input in the following format:

K

Output

Print K lines. The i-th line should contain the i-th smallest Snuke number.

Sample Input 1

10

Sample Output 1

1
2
3
4
5
6
7
8
9
19

Solution in Rust (1.15.1) (judge verdict: Wrong Answer)

use std::io::stdin;
fn get_string() -> String {
    let mut s = String::new();
    stdin().read_line(&mut s).unwrap();
    s.trim().to_string()
}

macro_rules! input {
    ($single:ty) => ( get_string().parse::<$single>().unwrap() );
    ($plural:ty,) => ({
        let line = get_string();
        line.split_whitespace().map(|v| v.parse::<$plural>().unwrap()).collect::<Vec<$plural>>()
    });
    ($($plural:ty),+) => ({
        let line = get_string();
        let mut iter = line.split_whitespace();
        ($(iter.next().unwrap().parse::<$plural>().unwrap()),+)
    });
    ($single:ty; $times:expr) => ( (0..$times).map(|_| input!($single)).collect::<Vec<$single>>() );
    ($($plural:ty),+; $times:expr) => ( (0..$times).map(|_| input!($($plural),+)).collect::<Vec<($($plural),+)>>() );
}

#[allow(dead_code)]
fn get_value<T: std::str::FromStr>() -> T {
    get_string().parse().ok().unwrap()
}
#[allow(dead_code)]
fn get_values_for<T: std::str::FromStr>(times: u64) -> Vec<T> {
    (0..times).map(|_| get_value()).collect()
}
#[allow(dead_code)]
fn get_vector<T: std::str::FromStr>() -> Vec<T> {
    get_string()
        .split_whitespace()
        .map(|v| v.parse().ok().unwrap())
        .collect()
}
#[allow(dead_code)]
fn get_vectors_for<T: std::str::FromStr>(times: u64) -> Vec<Vec<T>> {
    (0..times).map(|_| get_vector()).collect()
}

fn main() {
    let k = input!(usize);
    let mut snuke = Vec::new();
    snuke.extend(1..10);
    snuke.extend((1..10).map(|v| 9 + 10 * v));
    snuke
        .into_iter()
        .chain((1..).map(|v| 99 + v * 100))
        .take(k)
        .inspect(|v| println!("{}", v))
        .last();
}