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: Accepted)

def s(n)
  ret=0
  while n>0
    ret+=n%10
    n/=10
  end
  ret
end
k=[*1..9]
1.upto(9){|i|k<<10*i+9}
2.upto(9){|i|
  d=10**i
  nnn=d-1
  100.times{|j|
    k<<j*d+nnn
  }
}
10.upto(16){|i|
  d=10**i
  nnn=d-1 
  1000.times{|j|
    k<<j*d+nnn
  } 
}
k.sort!
k.uniq!
min=10**18
ans=[]
k.reverse.each{|a|
  f=a.to_f/s(a)
  if f<=min
    min=f
    ans<<a
  end
}

n=gets.to_i
puts ans.reverse.take(n)