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: Accepted)

K = int(input())

def S(n):
    return sum(int(c) for c in str(n))

n9 = 0  # the number of 9s

count = 0
upper = 1
while count < K:
    n = int(str(upper) + ('9' * n9))
    if n <= S(n) * (10 ** n9):
        print(n)
        count += 1
        upper += 1
    else:
        n9 += 1
        upper //= 10