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 PyPy3 (7.3.0) (judge verdict: Wrong Answer)

K = int(input())
if K < 10:
    print(*list(range(1, K + 1)), sep='\n')
    exit()
prev = list(range(1, 10))
ans = prev[:]
while len(ans) < K:
    cur = []
    for n in prev:
        cur.append(10 * n + 9)
    ans += cur
    prev = cur
print(*ans[:K], sep='\n')