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 Ruby (2.3.3) (judge verdict: Accepted)

k = gets.chomp.to_i

def s(n)
    nn = n
    ret = 0
    while(nn>0) do
        ret += nn % 10
        nn /= 10
    end
    return ret
end

def f(n)
    nn = n
    i = 0
    ret = 0
    val = 10 ** 16
    while(nn>0) do
        nn /= 10
        i += 1
        m = (nn+1) * 10 ** i - 1
        if val > m.to_f / s(m)
            val = m.to_f / s(m)
            ret = m
        end
    end
    return ret
end

(1..9).each do |i|
    puts i
    k -= 1
    exit if k == 0
end

n = 10
while(k>0)
    n = f(n+1)
    puts n
    k -= 1
end