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 <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef pair<ll, ll> pll;

int main()
{
    cin.tie(0);
    ios::sync_with_stdio(false);
    ll K;
    cin >> K;
    ll current = 2;
    map<ll, ll> base;
    base[9] = 10;
    base[99] = 1e2;
    base[1999] = 1e3;
    base[29999] = 1e4;
    base[399999] = 1e5;
    base[4999999] = 1e6;
    base[59999999] = 1e7;
    base[699999999] = 1e8;
    base[7999999999] = 1e9;
    base[89999999999] = 1e10;
    ll plusNum = 1;
    for(int i = 0; i < K; i++)
    {
        cout << current << "\n";
        if(base[current])
        {
            plusNum = base[current];
        }
        current += plusNum;
    }
    cout.flush();
    return 0;
}