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;

double S(ll a){
    string sa=to_string(a);
    ll res=0;
    for(int i=0;i<sa.size();++i){
        res+=sa[i]-'0';
    }
    return res;
}

int main(){
    ll k;
    cin >> k;
    ll res=0;
    int x=0,cnt=0;
    ll a[18]={9,9,19,28,37,46,55,64,73,82,91,190,289,388,487,586,685,784};
    for(int i=0;i<20;++i){
        for(int j=0;j<a[i];++j){
            if(cnt>=k)return 0;
            res+=pow(10,x);
            ll tmp=res;
            bool ok=1;
            for(int k=0;k<150;k++){
                tmp+=pow(10,x);
                if(res/S(res)>tmp/S(tmp)){
                    ok=0;
                    break;
                }
            }
            if(ok==0)continue;
            cout << res << endl;
            cnt++;
        }
        x++;
    }
}