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
#res  = []
#100000.times{|i|
##  res << (i+1)/digit_sum(i+1).to_f
#}
#puts res
res = [*1..9]
res = res.concat([*1..9].map{|i| i*10+9})
res = res.concat([*1..9].map{|i| i*100+99})
((K-27)/90+1).times{|n|
  base = 10**(n+2)
  [*1..9].each{|i|
    [*0..9].each{|j|
      res << j*base+i*base*10+base-1
    }
  }
}
if res.max > 10*14
  [*1..2].each{|j|
    [*0..9].each{|i|
      res << (10**14*j+10**12-1+i*10**12)
    }
  }
end
puts res.sort[0..(K-1)]