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 FOR(i,a,b) for(int i=(a);i<(b);++i)
#define rep(i,n)   FOR(i,0,n)
#define pb emplace_back
typedef long long ll;
typedef pair<int,int> pint;

vector<ll> v;
int main(){
    int k;
    cin>>k;
    //FOR(i,1,10) v.pb(i);
    ll t=10,tt=100;
    rep(i,16){
        ll q=t;
        FOR(p,0,10){
            
        ll s=q+t*p-1,s2=q+t*(p+1)-1;
        //cout<<s<<" "<<s2<<endl;
        tt=s2;
        double z=0;
        while(s2){
            z+=s2%10;
            s2/=10;
        }
        z=(double)(tt)/z;    
        rep(j,10){
            ll tmp=s-j;
            double A=0;
            while(tmp){
                A+=tmp%10;
                tmp/=10;
            }
            A=(double)(s-j)/A;
            if(A<=z) v.pb(s-j);
            else break;
        }
        }
        t*=10,tt*=10;
    }
    int cnt=0;
    sort(v.begin(),v.end());
    for(auto it:v){
        cout<<it<<endl;
        ++cnt;
        if(cnt==k) break;
    }
    return 0;
}