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)

from math import log10 as l
s=lambda f:sum(map(int,list(str(f))))
p=lambda a,j:(a//10**(j+1)+1)*10**(j+1)-1
n=int(input())
a=1
for i in range(n):
  print(a)
  if(a<10):
    a+=1
    continue
  a+=1
  k=[p(a,j) for j in range(int(l(a)))]
  o=[p(a,j)/s(p(a,j)) for j in range(int(l(a)))]
  a=k[o.index(min(o))]