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: Time Limit Exceeded)

# coding: utf-8
# Your code here!
k = int(input())

count = 0
ans = []
minN = 10**15

for i in reversed(range(10)):
    for j in reversed(range(1,10**5)):
        num = str(j)+"9"*i
        n = sum([int(k) for k in num])
        n = int(num)/n
        if(minN > n or n==1):
            minN = n
            ans.append(num)

print(len(ans[0]))
for i in list(reversed(ans))[:k]:
    print(i)