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 <vector>
#include <iostream>
using namespace std;

int main()
{
    vector<long long> v;

    for(int i = 1; i < 10; i++)
        v.push_back(i);


    for(long long int i = 10, j = 1; i < 1e15; i *= 10, j++) {
        long long m = i + 9, mm = 10, mmm = 1;

        for (long long k = 1, l = 1, b = i; k <= j; k++, l *= 10) {
            b += l * 9;

            if (b * mm < m * (k * 9 + 1)) {
                m = b;
                mm = k * 9 + 1;
                mmm = l * 10;
            }
        }


        while (m < i * 10) {
            v.push_back(m);
            m += mmm;
            if (!(m / mmm % 10))
                m -= mmm, mmm *= 10, m += mmm;
        }
    }




    int K;
    cin >> K;
    for (int i = 0; i < K; i++) {
        cout << v[i] << '\n';


    }


}