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;
#define ll long long

ll s(ll x)
{
    ll sum=0;
    while (x)
    {
        sum+=(x%10);
        x/=10;
    }
    return sum;
}

vector<ll>vc;

int main()
{
    for(int i=1; i<10; i++)
        vc.push_back(i);


    string s;
    s = "9";
    int cnt = 15;

    while(cnt--)
    {
        for(int i=1;i<=10;i++)
        {
            stringstream ss;
            ss << i;
            string tmp;
            ss >> tmp;

            string str2 = tmp+s;

            stringstream ss2;
            ll num;
            ss2 << str2;
            ss2 >> num;
            vc.push_back(num);
        }
        s+="9";
    }
    ll k;
    cin >> k;
    for(int i=0;i<k;i++) cout << vc[i] << endl;
    return 0;
}