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: Wrong Answer)

K = gets.to_i

def digitsum(num)
    ret = 0
    while num > 0
        ret += num % 10
        num /= 10
    end
    ret
end

ans = [1,2,3,4,5,6,7,8,9]
pool = [1,2,3,4,5,6,7,8,9]

while ans.length < K
    np = []
    pool.each do |i|
        num = i * 10 + 9
        rival = num + 10
        if num * digitsum(rival) <= rival * digitsum(num)
            ans.push(num)
            np.push(num)
        end
    end
    #p ans
    pool = np
end
puts ans[0, K]