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>
#pragma GCC optimize ("Ofast")
using namespace std;
typedef long long ll;
//vector<int> v = ;

ll K;
float mini=1e9;
ll sum(ll a){
    ll r=0;
    while(a) r+=a%10,a/=10;
    return r;
}
int main() {
    cin.tie(NULL);
    ios::sync_with_stdio(false);



    /*

    cout<<"{1,2,3,4,5,6,7,8,9";
    for(ll i=1e6;i>=2;i--){
        float pi = (float)i/(float)sum(i);
        if(pi <= mini){
            cout<<i<<" "<<pi<<endl;
            //cout<<","<<i;
            mini = pi;
        }
    }
    cout<<"}"<<endl;

    */

    cin>>K;
    ll add=1,i=8,val=1;
    while(K){
        cout<<val<<'\n';
        val+=add;
        K--;
        i--;
        if(!i){
            add*=10;
            i = add - 1;
        }
    }

    return 0;
}