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 INF 1<<30
#define LINF 1ll<<60ll
#define pb(a) push_back(a)
#define vi vector<int>
#define vl vector<long long>
#define vvi vector<vi>
#define P pair<int,int>
#define all(vec) (vec.begin()),(vec.end())
#define ll long long
#define sz(x) ((int)(x).size())
#define in(x) int x;cin>>x
#define bit(n) (1<<(n))

#define REP(i, n) for(int i=0, i##_len=(n); i<i##_len; ++i)
#define REPR(i, n) for(int i = n;i >= 0;--i)
#define REP3(i, m, n) for(int i = m, i##_len=(n);i < i##_len;++i)
#define FORVEC(i, v) for(int i = 0;i < sz(v);++i)

template<class T>bool chmax(T &a,const T &b){if(a<b){a=b;return true;}return false;}
template<class T>bool chmin(T &a,const T &b){if(a>b){a=b;return true;}return false;}

#define fil0(i,n) cout<<swet(n)<<setfill('0')<<i<<resetiosflags(ios_base::floatfield)


int main(){
    int k;
    cin>>k;
    /*1-9
    19-99
    199-999
    1999-9999*/
    int cnt=1,keta=0;
    REP(i,k){
        cout<<cnt;
        REP(j,keta){
            cout<<"9";
        }
        cout<<endl;
        cnt++;
        if(cnt==10){
            cnt=1;keta++;
        }
    }
    return 0;
}