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)

def get_sum(n):
    str_n = str(n)
    ans = 0
    for d in str_n:
        d = int(d)
        ans += d
    return ans


def get_until(n):
    str_n = str(n)
    keta = len(str_n) - 2
    if keta < 0:
        return 0
    return 10 ** keta


def solve():
    k = int(input())
    n = 1
    while k != 0:
        nsum = get_sum(n)
        next_n = n + get_until(n)
        next_nsum = get_sum(next_n)
        if (n / nsum) <= (next_n / next_nsum):
            print(n)
            k -= 1
        n += 1

if __name__ == '__main__':
  solve()