题目描述
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.
Example
Input
10
Output
1
2
3
4
5
6
7
8
9
19
输入格式
见题面
输出格式
见题面
样例输入
10
样例输出
1
2
3
4
5
6
7
8
9
19