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)

//arc099_d.cpp
//Sun Mar  1 10:11:46 2020

#include <iostream>
#include <string>
#include <queue>
#include <map>
#include <unordered_map>
#include <vector>
#include <algorithm>
#include <math.h>
#include <set>
#define INTINF 2147483647
#define LLINF 9223372036854775807
using namespace std;
using ll=long long;
typedef pair<int,int> P;

int main(){
	int k;
	cin >> k;

	ll keta = 1;
	ll base = 0;
	ll add = 1;
	ll num = 1;
	while (k){
		ll temp = num*(base+1)+base;
		cout << temp << endl;
		num++;
		if (num==10){
			keta++;
			base = pow(10,keta-1)-1;
			num = 1;
		}
		k--;
	}

}