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;
typedef pair<int, int> pii;
typedef vector<int> vi;
typedef vector<ll> vl;

#define REP(i,a,b) for(ll i=a;i<b;i++)
#define rep(i,n) REP(i,0,n)

ll N, K;
string s;
ll ans = 0;

ll S(ll n) {
    ll ret = 0;
    while (n) {
        ret += n % 10;
        n /= 10;
    }
    return ret;
}

void solve() {
    cin >> K;
    ll keta = 1;
    ll l = 1;
    REP(i,1,K+1) {
        if (i <= 9) {
            cout << i << endl;
        } else {
            string ans = "";
            ans += to_string(l);
            rep(j,keta) ans += to_string(9);
            if (l == S(stoll(ans))) {
                l = 1;
                keta++;
                ans = "";
                ans += to_string(l);
                rep(j,keta) ans += to_string(9);
            }
            cout << ans << endl;
            l++;
        }
    }
}

int main() {
    cin.tie(0);
   	ios::sync_with_stdio(false);
    solve();
    return 0;
}