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 Python (3.4.3) (judge verdict: Wrong Answer)

K = int(input())
S = "1"
for i in range(K):
  print(S)
  if len(str(S)) <= 3:
    if int(S[0]) != 9:
      n = int(S[0]) + 1
      S = str(n) + S[1:]
    else:
      S = "1" + S[:]
  else:
    m = len(str(S))
    n = int(S[:2]) + 1
    S = str(n) + (m - 2) * "9"
print(2099/21, 2199/22, 2999/29)