10472: ABC101 —— D - Snuke Numbers
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Description
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.
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.
Input
Input is given from Standard Input in the following format:
```
$K$
```
```
$K$
```
Output
Print $K$ lines. The $i$-th line should contain the $i$-th smallest Snuke number.
Constraints
- $1 \leq K$
- The $K$\-th smallest Snuke number is not greater than $10^{15}$.
- The $K$\-th smallest Snuke number is not greater than $10^{15}$.
Sample 1 Input
10
Sample 1 Output
1
2
3
4
5
6
7
8
9
19