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)

import math
K = int(input())
if K < 10:
  for i in range(1, K + 1):
    print(i)
else:
  count = 0
  for i in range(1, 10):
    print(i)
  count += 9
  now = 9
  while(True):
    keta = int(math.log10(now)) + 1
    if now == 10**keta - 1:
      now = (10**keta) * 2 - 1
    else:
      now += 10**(keta - 1)
    count += 1
    print(now)
    if count >= K:
      break