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: Runtime Error)

k = int(input())
i = 0
n = 1
while True:
    if n == k:
        break
    sn = 0
    sm = 0
    m = n+1
    for a in list(str(n)):
        sn += int(a)
    for b in list(str(m)):
        sm += int(b)
    left = n/sn
    
    if left <= m/sm and m(sm+1) > sm(m+1):
        print(n)
    
    n += 1