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)

fn main() {
    let k: i64 = read();

    let mut s: Vec<i64> = Vec::new();

    for i in 1..10 {
        s.push(i);
    }
    for i in 1..10 {
        s.push(i * 10 + 9);
    }
    for i in 1..14 {
        for i1 in i..(i * 10 + 9) {
            let a = i1 * i64::pow(10, (i + 1) as u32) + make9(i + 1);
            s.push(a);
        }
    }

    for i in 0..k {
        println!("{}", s[i as usize]);
    }
}

fn make9(n: i64) -> i64 {
    let mut r = 0;
    for i in 0..n {
        r += 9 * i64::pow(10, (i) as u32);
    }
    r
}

fn read<T: std::str::FromStr>() -> T {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    s.trim().parse().ok().unwrap()
}