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 Pascal (FPC 2.6.2) (judge verdict: Accepted)

var
    ans,k,tot1,tot2:int64;
    n:longint;
function s(x:int64):int64;
begin
    if x=0 then exit(0)
    else exit(x mod 10+s(x div 10));
end;
begin
    readln(n);
    ans:=1;k:=1;
    while n>0 do
        begin
            writeln(ans);
            tot1:=ans+k;
            tot2:=ans+k*10;
            if tot1*s(tot2)<=tot2*s(tot1) then ans:=tot1
            else
                begin
                    ans:=tot2;
                    k:=k*10;
                end;
            dec(n);
        end;
end.