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 <vector>
#include <queue>
#include <algorithm>
#include <complex>

#define forin(i, f, t) for(auto i = f; i < t; i++)

using namespace std;
using ll = long long;


double f(ll n) {
    auto cn = n;
    ll sn = 0;
    while (cn > 0) {
        sn += cn % 10;
        cn /= 10;
    }
    return double(n) / sn;
}

int main() {
    ll k;
    cin >> k;
    
    vector<ll> v;
    ll d = 1;
    for (auto i = 0; i < 15; i++) {
        for (auto j = 1; j < 10; j++) {
            v.push_back(d * (j + 1) - 1);
        }
        d *= 10;
    }
    
    vector<double> fv(v.size(), 0);
    for (auto i = 0; i < fv.size(); i++)
        fv[i] = f(v[i]);
    
    for (auto i = 0; i < fv.size(); i++) {
        for (auto j = i + 1; j < fv.size(); j++) {
            if (fv[i] > fv[i + j]) {
                v.erase(v.begin() + i);
                fv.erase(fv.begin() + i);
                i--;
                break;
            }
        }
    }
    
    for (auto i = 0; i < k; i++)
        cout << v[i] << endl;
    
    return 0;
}