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
for w in 1..9
break if k==0
p w
k-=1
end
c=1
loop{break if k==0
for w in 1..9
break if k==0

if  w==1  && c==3
break if  k==0
p 1099
break if  k==0
p 1199
break if  k==0
p 1299
break if  k==0
p 1399
break if  k==0
p 1499
break if  k==0
p 1599
break if  k==0
p 1699
break if  k==0
p 1799
break if  k==0
p 1899
break if  k==0
p 1999
end

p w*(10**c)+10**c-1
k-=1
end
c+=1
}