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++ (Clang 3.8.0) (judge verdict: Wrong Answer)

#include <iostream>
#include <cmath>

using namespace std;

int main() {
    long long k;
    cin >> k;

    long long num = 0;
    long long top_digit = 1;
    while (k) {
        num += top_digit;
        cout << num << endl;
        if ( num / top_digit == 9) top_digit *= 10;
        k--;
    }

    return 0;
}