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)

/*
ID: richard124
PROB: kimbits
LANG: C++11
*/


#include <iostream>
#include <fstream>
#include <vector>
#include <queue>
#include <map>
#include <set>
#include <string>
#include <chrono>
#include <algorithm>
#include <bitset>

using namespace std;
using namespace std::chrono;

typedef pair<int, int> pii;
#define pb push_back;

long long K;
long long ans = 0;
vector<long long> anss;

double s_n(int x) {
    double sum = 0;
    while (x > 0) {
        double lastdigit = x%10;
        sum += lastdigit;
        x /= 10;
    }
    return sum;
}

bool test(double x) {
    double one = x / s_n(x);
    double two = (x+10.0)/ s_n(x+1);
    if (one < two) {
        return true;
    }
    else {
        return false;
    }
}

int main() {
	high_resolution_clock::time_point t1 = high_resolution_clock::now();
	
	cin >> K;
	if (K <= 9) {
	    for (int i=1; i<=K; i++) {
	        cout << i << '\n';
	    }
	    return 0;
	}
	else {
	    for (int i=1; i<=9; i++) {
	        cout << i << '\n';
	    }
	    K -= 9;
	}
	double curr = 19;
	long long bound = 100;
	while (anss.size() < K) {
	    if (test(curr)) {
	       while (curr < bound) {
	           anss.push_back(curr);
	           curr += 10;
	       }
	    }
	    bound *= 10;
	    
	}
	/*cout << anss[0] << '\n';*/
    for (int i=0; i<K; i++) {
        cout << anss[i] << '\n';
    }
	
	return 0;
}