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: Runtime Error)

#include<bits/stdc++.h>
using namespace std;
#define ll long long
#define db double
#define p pair<double, int>
template<class T> void chmin(T& x, T y){if(x > y) x = y;}
template<class T> void chmax(T& x, T y){if(x < y) x = y;}

ll K;

int S(ll x){
    int res = 0;
    for(int i = 0; i < 20; i++){
        res += x % 10;
        x /= 10;
    }
    return res;
}

db g(ll x){
    return (db)x / (db)S(x);
}

ll snuke(ll x){
    priority_queue<p, vector<p>, greater<p>> pq;
   ll md = 1;
    while(x % (md / 10) != x){
        ll t = x - (x % md) + md - 1;
        pq.push({g(t), t});
        md *= 10;
    }
    return pq.top().second;
}

int main(){
    cin >> K;
    ll idx = 1;
    for(int i = 0; i < K; i++){
        cout << idx << endl;
        idx = snuke(idx + 1);
    }
    return 0;
}