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
]

base = 100
while ans.length < K
    ((base/10)...base).each do |i|
        num = i * base + base - 1
        if i % 10000 == 9999
            add = 10000
        elsif i % 1000 == 999
            add = 1000
        elsif i % 100 == 99
            add = 100
        elsif i % 99 == 9
            add = 10
        else
            add = 1
        end
        rival = num + add
        if num * digitsum(rival) <= rival * digitsum(num)
            ans.push(num)
        end
    end
    ((base/10)...base).each do |i|
        num = i * base * 10 + base * 10 - 1
        if i % 10000 == 9999
            add = 10000
        elsif i % 1000 == 999
            add = 1000
        elsif i % 100 == 99
            add = 100
        elsif i % 99 == 9
            add = 10
        else
            add = 1
        end
        rival = num + add
        if num * digitsum(rival) <= rival * digitsum(num)
            ans.push(num)
        end
    end
    base *= 10
end
puts ans[0, K]