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;
using ll = long long;

int main() {
  int K; cin >> K;
  cout << 1 << endl;
  auto S = [](ll x) {
    ll res = 0;
    while (x) res += x % 10, x /= 10;
    return res;
  };
  ll x = 1, sx = 1;
  while (--K) {
    ll n = x + sx;
    ll m = x + sx * 10;
    if (S(m) * (n) > S(n) * (m)) sx *= 10;
    x += sx;
    cout << x << endl;
  }
  return 0;
}