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 C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <iostream>
#include <algorithm>
using namespace std; typedef long long ll; const int INF=1e9;
typedef pair<int,int> P;
int main() {
  int k; cin>>k;
  if (k>2e6) return 0;
  for(int i=0,j=1;i<min(9,k);i++,j++) {
    cout<<j<<endl;
  }
  for(int i=9,j=1;i<min(18,k);i++,j++) {
    cout<<j<<9<<endl;
  }
  for(int i=18,j=1;i<k;i++,j++) {
    cout<<j<<99<<endl;
  }
}