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 <string>
#include <algorithm>
#include <map>
#include <cmath>
#include <iomanip>
#include <vector>
#include <queue>
#include <functional>
#include <random>
#include <ctime>

using namespace std;
#define FOR(i, a, b) for(int i=(a);i<(b);++i)
#define REP(i, n) FOR(i,0,n)
#define ALL(v) (v).begin(),(v).end()
#define fi first
#define se second
typedef long long int ll;
typedef pair<ll, ll> P;

int main() {
    int a;
    cin >> a;
    int count = 0;
    REP(i, 16) {
        REP(j, 9) {
            if (count >= a) return 0;
            ll sunuke = j + 1;
            REP(k, i) {
                sunuke *= 10;
                sunuke += 9;
            }
            cout << sunuke;
            cout << "\r\n";
            count++;
        }
    }

    return 0;
}