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,
    19,29,39,49,59,69,79,89,99,
    199,299,399,499,599,699,799,899,999
]

n9 = 2
while ans.length < K
    nn9 = [n9, 9].min
    (1...nn9).each do |i|
        (0..9).each do |j|
            num = (i.to_s + j.to_s + ('9' * n9)).to_i
            ans.push(num)
            break if num >= 10**16
        end
    end
    (nn9..9).each do |i|
        num = (i.to_s + ('9'*(n9+1))).to_i
        ans.push(num)
    end
    n9 += 1
end
puts ans[0, K]