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
ans = []
for i in 0..2
  temp = "9"*i
  for j in 1..9
    ans << j.to_s+temp
  end
end
for i in 2..10
  temp = "9"*i
  for j in 1..i-1
    for k in 0..9
      ans << j.to_s+k.to_s+temp
    end
  end
  temp += "9"
  for j in i..9
    ans << j.to_s+temp
  end
end
for i in 11..13
  temp = "9"*(i-1)
  for j in 1..i-10
    for k in 0..9
      for l in 0..9
        ans << j.to_s+k.to_s+l.to_s+temp
      end
    end
  end
  temp += "9"
  for j in i-10+1..9
    for k in 0..9
      ans << j.to_s+k.to_s+temp
    end
  end
end
puts ans[0..K-1]