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 <cstdio>
using namespace std;
int main()
{
	int n;
	cin>>n;
	for(int i=1;i<=n&&i<10;i++)//1-9
		cout<<i<<" ";
	if(n-9>0){//19-99
		n=n-9;
		for(int i=1;i<=n&&i<10;i++)
			cout<<i<<"9 ";
	}
	if(n-9>0){//199-999
		n=n-9;
		for(int i=1;i<=n&&i<10;i++)
			cout<<i<<"99 ";
	}
	if(n-9>0){//1099-
		n=n-9;
		int s=0;
		for(int i=2;s<n;i++)
		{
			for(int j=10;j<=99&&s<n;j++)
			{
				printf("%d",j);
				for(int k=0;k<i;k++)
					printf("9");
				printf(" ");
				s++;
			}
		}
	}
	return 0;
}