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 <bits/stdc++.h>
#define pb push_back
#define REP(i, n) for (signed long long i = 0; i < (n); i++)
#define MOD 1000000007
#define bitcnt(a) (ll) __builtin_popcount((a))
using namespace std;
typedef long long ll;
typedef pair<ll, ll> P;

int main() {
  ll k;
  cin >> k;
  REP(i, k) {
    ll cnt = i / 9;
    cout << (i % 9 + 1);
    REP(f, cnt) cout << "9";
    cout << endl;
  }
}