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>
#include <vector>
#include <string>
#include <numeric>
#include <iomanip>
#include <deque>

using namespace std;    
typedef long long ll;
#define all(x) (x).begin(),(x).end()
#define rall(x) (x).rbegin(),(x).rend()

double func(ll n){
    ll n_tmp = n;
    double div = 0;
    while(n_tmp > 0){
        div += (n_tmp % 10);
        n_tmp /= 10;
    }
    return (div);
}

int main(){

    ll K;
    cin >> K;

    ll cnt = 0;
    for(ll i = 1; true ; i++){
        if(i < 10){
            cnt ++;
            cout << i << endl;
        }
        else if(i % 10 == 9) {
            cnt ++;
            cout << i << endl;

        }

        if(cnt == K) return 0;
    }
}