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: Accepted)

#include <bits/stdc++.h>

using namespace std;


namespace XDYIMCMI0LY {
  inline int s(long long x) {
    int res = 0;
    while (x) {
      res += x % 10;
      x /= 10;
    }
    return res;
  }

  inline double calc(long long x) {
    return (double) x / s(x);
  }

  inline long long merge(long long x, int k) {
    while (k--) {
      x = x * 10 + 9;
    }
    return x;
  }
  
  void main() {
    vector<long long> ans;
    for (int i = 1; i <= 9; ++i) {
      ans.push_back(i);
    }
    long long x = 1;
    int k = 1;
    while (merge(x, k) <= 1e15) {
      long long nw = merge(x, k);
      long long nxt = merge(x + 1, k);
      if (calc(nw) <= calc(nxt)) {
        ans.push_back(nw);
        ++x;
      } else {
        x /= 10;
        ++k;
      }
    }
    int c;
    cin >> c;
    for (int i = 0; i < c; ++i) {
      cout << ans[i] << endl;
    }
    return ;
  }
}

int main() {
  cin.tie(0);
  ios::sync_with_stdio(false);
  XDYIMCMI0LY::main();
  return 0;
}