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<iostream>
#include<vector>
#include<algorithm>
#include<string>
#include<cmath>
#include<climits>
#include<map>
#include<set>
#include<queue>
#include<stack>
#include<bitset>
#include<iomanip>
using namespace std;

#define rep(i,j,n) for(int i=(j);i<(n);i++)
#define rep2(i,j,n) for(int i=(j);i<=(n);i++)
#define all(i) i.begin(),i.end()
#define rall(i) i.rbegin(),i.rend()
#define INF 1e9

typedef vector<int> vi;
typedef vector<vector<int>> vvi;
typedef vector<string> vs;
typedef vector<vector<string>> vvs;
typedef pair<int, int> pi;
typedef long long i64;
typedef vector<long long int> vll;

int main() {
	int k;
	cin >> k;
	int a = 0;
	i64 ans = 1;
	cout << ans;
	rep2(i, 2, k) {
		ans += pow(10, a);
		cout << " " << ans;
		if (i % 9 == 0) a++;
	}
	cout << endl;
}