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<cstdio>
#include<algorithm>
#include<vector>
#define ll long long
using namespace std;
int n;
vector<ll> vt;
ll ch[16];
ll x;
int main()
{
	ch[0] = 1;
	for (int i = 1; i <= 15; i++)
		ch[i] = ch[i - 1] * 10;
	for (int i = 1; i < 10; i++)
		vt.push_back(i);
	for (int i = 1; i < 10; i++)
		vt.push_back(i * 10 + 9);
	for (int i = 2; i <= 15; i++)
	{
		ll sum =ch[i]+9;
		ll Ssum = 10;
		for (int y = 1; y <= i; y++)
		{
			int update = 0;
			for (int z = 0; z < 9; z++)
			{
				if (sum <= Ssum*ch[y]) {
					update = 1;
					break;
				}
				sum += ch[y];
				Ssum++;
			}
			if (update) {
				while (sum < ch[i + 1]) {
					vt.push_back(sum);
					sum += ch[y];
				}
				break;
			}
		}
	}
	scanf("%lld", &x);
	for (int i = 0; i < x; i++)
		printf("%lld\n", vt[i]);
}